Thermal Power Plant Simulation and Control (IEE Power and Energy Series)

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Thermal Power Plant Simulation and Control Edited by

Damian Flynn

The Institution of Electrical Engineers

Published by: The Institution of Electrical Engineers, London, United Kingdom © 2003: The Institution of Electrical Engineers This publication is copyright under the Berne Convention 2003 and the Universal Copyright Convention. All rights reserved. Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act, 1988, this publication may be reproduced, stored or transmitted, in any forms or by any means, only with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency. Inquiries concerning reproduction outside those terms should be sent to the publishers at the undermentioned address: The Institution of Electrical Engineers, Michael Faraday House, Six Hills Way, Stevenage, Herts., SG1 2AY, United Kingdom While the authors and the publishers believe that the information and guidance given in this work are correct, all parties must rely upon their own skill and judgment when making use of them. Neither the authors nor the publishers assume any liability to anyone for any loss or damage caused by any error or omission in the work, whether such error or omission is the result of negligence or any other cause. Any and all such liability is disclaimed. The moral rights of the authors to be identified as authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.

British Library Cataloguing in Publication Data

Thermal power plant simulation and control. - (lEE power & energy series ; 43) 1. Electric power-plants - Management 2. Electric power systems - Control 3. Electric power systems - Computer simulation I. Flynn, D. II. Institution of Electrical Engineers 621.311210113

ISBN 0 85296 419 6

Typeset in India by Newgen Imaging Systems Printed in the UK by MPG Books Limited, Bodmin, Cornwall

List of contributors

A. Alessandri Institute for the Studies of Intelligent Systems for Automation National Research Council of Italy Genova, Italy A.E Armor Electric Power Research Institute Palo Alto, California, USA M.D. Brown Atkins Aviation and Defence Systems Bristol, England A. Cipriano Electrical Engineering Department Pontificia Universidad Cat61ica de Chile Santiago, Chile P. Coletta Institute for the Studies of Intelligent Systems for Automation National Research Council of Italy Genova, Italy M. Cregan School of Electrical and Electronic Engineering The Queen's University of Belfast Belfast, Northern Ireland G.Q. Fan Veritas Software Sydney, Australia

x

List of contributors

D. Flynn

School of Electrical and Electronic Engineering The Queen's University of Belfast Belfast, Northern Ireland A. Fricker

Innogy plc Swindon, England R. Garduno-Ramirez

Electrical Research Institute Cuernavaca, Morelos, Mexico G.W. Irwin

School of Electrical and Electronic Engineering The Queen's University of Belfast Belfast, Northern Ireland K.Y. Lee Department of Electrical Engineering Pennsylvania State University Pennsylvania, USA A. Leva Department of Electronic Engineering and Information Sciences Politecnico di Milano Milan, Italy K. Li

School of Mechanical and Manufacturing Engineering The Queen's University of Belfast Belfast, Northern Ireland C. Maffezzoni Department of Electronic Engineering and Information Sciences Politecnico di Milano Milan, Italy T. Moelbak

Elsam A/S Fredericia, Denmark

List of contributors J.H. Mortensen Tech-wise A/S Fredericia, Denmark G. Oluwande Innogy plc Swindon, England T. Parisini Department of Electrical, Electronic and Computer Engineering University of Trieste Trieste, Italy G. Poncia United Technologies Research Center East Hartford, Connecticut, USA G. Prasad School of Computing and Intelligent Systems University of Ulster Londonderry, Northern Ireland N.W. Rees School of Electrical and Telecommunication Engineering The University of New South Wales Sydney, Australia J.A. Ritchie School of Electrical and Electronic Engineering The Queen's University of Belfast Belfast, Northern Ireland D. S~iez Electrical Engineering Department Universidad de Chile Santiago, Chile S. Thompson School of Mechanical and Manufacturing Engineering The Queen's University of Belfast Belfast. Northern Ireland

xi

Preface

During the past decade power generation has undergone several extremely significant changes. These include deregulation of the electricity industry in many parts of the world, with a greater focus on economic and financial concerns instead of purely engineering issues. In conjunction with this, environmental matters are of increasing interest, leading to an assessment of existing greenhouse gas emissions and the exploitation of renewable energy sources. Additionally, combined cycle gas turbines (CCGTs) have emerged as an extremely economic and efficient means of electricity generation. Finally, many power plants have been retro-fitted with modern and sophisticated, plant-wide instrumentation and control equipment. These computerbased distribution control systems (DCSs) are intended to enhance regulation control performance and more importantly provide a means for implementing supervisory control/monitoring schemes. These various considerations have led to significant changes in the philosophy of how power stations are operated, while at the same time affording engineers the opportunity to introduce monitoring and plant-wide control schemes which were previously infeasible. However, a distinction has largely arisen between those working in the power and control oriented research communities, with centres of excellence in scattered locations, and engineers engaged in power plant design, operation, consultancy, etc. The objective of this book is to address this issue, through a number of case studies, which illustrate how various methodologies can be applied to various subsystems of power plant operation, or indeed introduced into the overall control hierarchy. The case studies presented focus on what can feasibly be achieved with an indication of the subsequent benefits of doing so, using results from live plant where possible. The level of the book makes it suitable for engineers working in the power generation industry who wish to gain an appreciation of the advances which have taken place in this field within the research community. It should also provide a very useful overview for new and experienced researchers working in this area. A number of the contributions to this book arise from work carried out at, or in collaboration with, universities and research institutions, while others benefit from the experience of practitioners in the industry. A natural consequence of this is that a mixture of viewpoints is offered, with a contrast between the use of academic and industrial

xiv

Preface

terminology. The mathematical content of the book is sufficient to give an indication of the underlying technologies, and the deficiencies of more traditional techniques, with the reader directed to related work for further detail. The text is split into three main parts covering, respectively, power plant simulation, specific control applications and optimisation/monitoring of plant operations. Chapter I provides a brief introduction to power plant fundamentals, outlining different plant configurations, the control requirements of various loops, and the hardware and instrumentation on which these systems are based. An essential aspect of investigating and developing novel control and monitoring schemes is a detailed simulation of the system in question. Chapter 2 illustrates how a complex power plant model can be constructed using an object-oriented approach. The reader is introduced to the Modelica modelling language, and issues such as testing and validation are discussed. Part 2 (Control) comprises five contributions and forms a major part of the book. A number of diverse applications are considered, and differing control strategies are proposed and implemented. Chapter 3 investigates the highly complex problem of both modelling and controlling pulverised fuel coal mills. Linear quadratic and predictive control techniques are investigated, with a supervisory operator support system introduced. Chapter 4 tackles the problem of excitation control of a synchronous machine. Local model network and adaptive control-based approaches are examined in detail. Chapter 5 then examines steam temperature control of a once-through boiler for both the evaporator and superheaters. Linear quadratic Gaussian, fuzzy logic and predictive control schemes are applied, with the benefits of feedforward action using suitable instrumentation strongly highlighted. Chapter 6 examines the problem of controlling combined cycle plant. An objective function is defined based on operational costs, and alternative hierarchical control configurations are examined. Finally, in this section, Chapter 7 explores the development of a multi-input multi-output (MIMO) predictive controller sitting on top of the plant's conventional control systems to improve the overall plant's capabilities. Part 3 (Monitoring, optimisation and supervision) again comprises five contributions, and demonstrates how the ability of distributed control systems to gather plant-wide, real-time data can be constructively employed in a range of applications. Chapter 8 introduces a sophisticated plant-wide, neurofuzzy control scheme with feedback and feedforward actions to provide improved unit manoeuvrability and an improved distribution of control tasks. Chapter 9 then focuses on the task of modelling NOx emissions from a coal-fired power station. A grey-box modelling approach is proposed, taking advantage of a priori knowledge of NOx formation mechanisms. Chapter 10 introduces model-based approaches for fault detection of a high-pressure heater line. Again grey-box identification, coupled with non-linear state estimation techniques are considered, to aid fault diagnostics. Chapter 11 continues with an examination of how the data stores which distributed control systems now offer can be exploited for both fault identification and process monitoring activities. The part concludes in Chapter 12 with an overview of a number of performance support and monitoring applications that have been successfully applied to real plant, largely based around a real-time expert system.

Preface

xv

The final part of the book highlights some possibilities and issues for the future. Chapter 13 demonstrates how a physical model of a power plant can be integrated into a predictive control strategy to provide enhanced unit control by recognising the true system characteristics. Finally, Chapter 14 discusses some topics of concern including the impact of age and maintenance requirements on existing units in an increasingly competitive environment, and how technology is expanding the capabilities of modern power plant. The editor would like to take this opportunity to thank all the authors for their contributions, and for their assistance in bringing together the final text. The support and guidance from Roland Harwood and Wendy Hiles of the IEE has also been most welcome. The editor also wishes to acknowledge the significant role played in the creation of this work by Brian Hogg and Edwin Swidenbank in establishing the Control of Power Systems research group at The Queen's University of Belfast. Finally, the advice and encouragement offered by Brendan Fox and Nataga Marta6 from Queen's has been greatly appreciated. Damian Flynn April 2003

Contents

List of contributors

ix

Preface

xiii

List of abbreviations

xvii

1 1.1 1.2 1.3 1.4 1.5 1.6

Advances in power plant technology M. Cregan and D. Flynn Power plant historical development Plant configuration and design Control and instrumentation External influences Plant technology developments References

1

2 5 9 13 13

Part 1: Modellingand simulation 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8

Modelling of power plants A. Leva and C Maffezzoni Introduction Model structuring by the object-oriented approach Basic component models Modelling of distributed control systems Application of dynamic decoupling to power plant models Testing and validation of developed models Concluding remarks and open problems References

17 17 18 27 50 52 53 56 57

vi

Contents

Part 2: Control 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8

4 4.1 4.2 4.3 4.4 4.5 4.6 4.7

5 5.1 5.2 5.3 5.4 5.5 5.6 6

6. l 6.2 6.3 6.4 6.5 6.6 6.7

Modelling and control of pulverised fuel coal mills N.W. Rees and G.Q. Fan Introduction Modelling of coal mills Plant tests, results and fitting model parameters Mill control Intelligent control and operator advisory systems Conclusions Acknowledgements References

63 63 64 71 80 92 97 97 97

Generator excitation control using local model networks M.D. Brown, D. Flynn and G. W. Irwin Introduction Local model networks Controller design Micromachine test facility Results Conclusions References

101

Steam temperature control T. Moelbak and J.H. Mortensen Introduction Plant and control description Advanced evaporator control Advanced superheater control Conclusions References

131

Supervisory predictive control of a combined cycle thermal power plant D. Sdez and A. Cipriano Introduction A combined cycle thermal power plant Design of supervisory control strategies for a combined cycle thermal power plant Application to the thermal power plant simulator Discussion and conclusions Acknowledgements References

101 102 108 113 117 124 127

131 133 137 147 159 159

161 161 162 168 171 176 177 177

Contents

7 7.1 7.2 7.3 7.4 7.5 7.6 7.7

Multivariable power plant control G. Poncia Introduction Classical control Of thermal power plants Multivariable control strategies An application: MBPC control of a 320 MW oil-fired plant Conclusions Acknowledgements References

Part 3:

vii 179 179 181 184 189 200 200 201

Monitoring, optimisation and supervision

Extending plant load-following capabilities R. Garduno-Ramirez and If. Y Lee 8.1 Introduction 8.2 Power unit requirements for wide-range operation 8.3 Conventional power unit control 8.4 Feedforward/feedback control strategy 8.5 Knowledge-based feedforward control 8.6 Design of neurofuzzy controllers 8.7 Wide-range load-following 8.8 Summary and conclusions 8.9 Acknowledgements 8.10 References

205

9

Modelling of NOx emissions in coal-fired plant S. Thompson and K. Li Emissions from coal-fired power stations An overview of NOx formation mechanisms NOx emission models for a 500 MW power generation unit Conclusions Acknowledgements References

243

Model-based fault detection in a high-pressure heater line A. Alessandri, P Coletta and T. Parisini Introduction Description of power plant application Grey-box modelling and identification of a power plant A general approach to receding-horizon estimation for non-linear systems Conclusions References

269

8

9.1 9.2 9.3 9.4 9.5 9.6 10 10.1 10.2 10.3 10.4 10.5 10.6

205 207 209 213 221 224 228 238 239 239

243 248 253 263 267 267

269 271 287 295 307 307

viii

Contents

11

Data mining for performance monitoring and optimisation

309

J.A. Ritchie and D. Flynn

11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8

Introduction Outline of data mining applications Identification of process and sensor faults Process monitoring and optimisation Non-linear PLS modelling Discussion and conclusions Acknowledgements References

309 310 311 325 334 338 341 341

12

Advanced plant management systems

345

A. Fricker and G. Oluwande

12.1 12.2 12.3 12.4 12.5 12.6 12.7

Plant management in a deregulated electricity market Supervisory control System integration and HMI issues Performance monitoring Added value applications Conclusions References

345 346 350 351 354 360 361

Part4: The future 13

Physical model-based coordinated power plant control

365

G. Prasad

13.1 Introduction 13.2 A review of physical model-based thermal power plant control approaches 13.3 Control problems of a thermal power plant 13.4 Applying a physical model-based predictive control strategy 13.5 Simulation results 13.6 Discussion and conclusions 13.7 Acknowledgements 13.8 References

365

14

395

Management and integration of power plant operations

366 368 375 381 389 391 391

A.E Armor

14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8 14.9

Index

Introduction Age and reliability of plants Improving asset management The impacts of cycling on power plant performance Improving maintenance approaches Power plant networks: redefining information flow Conclusions References Bibliography

395 396 401 405 407 410 413 414 415 417

List of abbreviations

AF ANN API APMS ARMAX ARX ASME AVA AVR BETTA BMS CARIMA CBR CCGT CCR CEGB CFD COL DCDAS DCS DMA EAF EC EDL EKF EPRI FB FERC FF FFPU FGD GHG

availability factor artificial neural network application program interface advanced plant management system AutoRegressive Moving Average model with eXogenous input AutoRegressive model with eXogenous input American Society of Mechanical Engineers added value application automatic voltage regulator British-wide Electricity Trading and Transmission Arrangements burner management system controlled auto-regressive integrating moving-average case-based reasoning combined cycle gas turbine central control room Central Electricity Generating Board computational fluid dynamics cost of losses distributed control and data acquisition system distributed control system direct memory access equivalent availability factor European Commission electronic dispatch and logging extended Kalman filter Electric Power Research Institute feedback Federal Energy Regulatory Commission feedforward fossil fuel power unit flue gas desulphurisation greenhouse gas

xviii List of abbreviations GMV GPC

generalised minimum variance generalised predictive control HMI human-machine interface HP high-pressure HRSG heat recovery steam generator HSC hierarchical supervisory control IAF integrated application framework ICOAS intelligent control and advisory system IGCC integrated gasification combined cycle ILC integrated load control ILM integrated load management IOAS intelligent operator advisory system IPCC Intergovernmental Panel on Climate Change IPP independent power producer ISA Instrumentation, Systems and Automation Society KBOSS knowledge-based operator support system LMN local model network LP low-pressure LPC lumped parameter components LQ linear quadratic LQG linear quadratic Gaussian LQR linear quadratic regulator LS least squares MBPC model-based predictive controller MCR maximum continuous rating MIMO multi-input multi-output MISO multi-input single-output MLP multilayer perceptron MLR multiple linear regression MVC multivariable steam control NARMAX Non-linear AutoRegressive Moving Average model with eXogenous input NARX Non-linear AutoRegressive model with eXogenous input NDE non-destructive evaluation NETA New Electricity Trading Arrangements NIPALS non-linear iterative partial least squares NPMPC non-linear physical model-based predictive control OIS operational information system OOM object-oriented modelling OSC one-side components PCA principal component analysis pf pulverised fuel PFBC pressurised fluidised bed combustion PLC programmable logic controller

List of abbreviations PLS PRBS PRESS RBF RLS RMS RSME SCADA SEGPC SISO SMS TSC UV VOC

projection to latent structures pseudo-random binary sequence predicted residual sum of squares radial basis function recursive least squares root mean square root squared mean error supervisory control and data acquisition state estimation-based generalised predictive control single-input single-output startup management system two-side components ultraviolet volatile organic compound

xix

Chapter 1

Advances in power plant technology M. Cregan and D. Flynn

I.I

Power plant historical development

Fossil fuelled power plants have been supplying electricity for industrial use since the late 1880s. At first, simple d.c. generators were coupled to coal-fired, reciprocating piston steam engines. Electricity was delivered over relatively short distances, and was primarily used for district lighting. The first central generating station was opened by Thomas Edison in September 1882 at Pearl Street, Lower Manhattan, New York City. Lighting alone, however, could not provide an economical market for successful commercial generation, so new applications for electricity needed to be found. The popularity of urban electric tramways, and the adoption of electric traction on subway systems, coincided with the widespread construction of generating equipment in the late 1880s and 1890s. Initial power plant boiler designs generated steam in a simple water tube boiler, from a coal or coal gas supply. They typically operated at 0.9 MPa (8.6 bar) and 150 °C (300 °F), and would have been connected to a 30 kW generator. Since then the topography of the typical power plant has evolved into a highly complex system. Today, advanced turbine and boiler designs, utilising new metal alloys, can operate at supercritical conditions of 28.5 MPa (285 bar) and 600 °C (1112 °F), generating 1300 MW of electricity (Smith, 1998; DTI, 2000). In a search for reduced operating costs, plant design has moved on from generating units based on the Rankine cycle, which typically achieved thermal efficiencies in the range 30--40 per cent. Now combined cycle gas turbine (CCGT) units utilising the latest heat recovery steam generator (HRSG) plant can achieve efficiencies of 50-60 per cent. The removal of European Community restrictions on burning gas for power generation, coupled with other factors, has resulted in increased deployment of CCGT units. However different current plant may now appear, the underlying principles of generation and distribution had been mastered by the end of the nineteenth century. Since then the evolution of power plant design has been largely incremental, driven mainly by new technology. The past three decades

2

Thermal power plant simulation and control

have witnessed the integration of microprocessor equipment into every aspect of generation and distribution. The next 20 years should see this technology develop further, bringing with it pseudo-intelligent applications which truly harness the rapidly expanding computational power available. New computer-based systems will increase plant automation, improve unit control and permit more flexible plant operation, while at the same time maximising unit efficiency and reducing harmful emissions. New developments in plant design are continually being sought and investigated to improve unit performance. Currently integrated gasification combined cycle (IGCC) and advanced pressurised fluidised bed combustion (PFBC) are emerging technologies that are showing great potential for yielding high efficiency and low emissions. The short-to-medium term targets that have been mapped out by Vision 21 (US Department of Energy) for new plant designs are 60 per cent thermal efficiency for coal/solid fuels and 75 per cent efficiency for natural gas units, combined with zero or very low environmental emissions (DOE, 1999).

1.2

Plant configuration and design

Although there are many variations in power plant configuration and design, at the most basic of levels, a fossil fuel is combusted to raise steam, which then rotates a turbine that drives an alternator, to provide three-phase a.c. electricity at 50/60 Hz. Illustrated in Figure 1.1 is the turbine hall of a modern power station. At the heart

Figure 1.1

Premier Power turbine hall

Advances in power plant technology Boiler

Turbines

3 Fu~

Air

Figure 1.2

~ Feedwater Boiler feed pump

Simplified power plant

of a conventional power plant is the boiler, which operates by following the thermodynamic Rankine steam cycle, a practical implementation of the ideal Carnot cycle. Figure 1.2 provides a simplified illustration of the steam flow path in a fossil fuel power plant.

1.2.1

Subcritical plant

In subcritical boilers steam temperatures and pressures never exceed the 'critical point' of steam which occurs at 373.9 °C (705.1 °F) and 22.1 MPa (220.6 bar). The steam cycle is conveniently analysed by beginning with the feedwater flow from the condenser. The condenser's hotwell maintains a large reservoir from which boiler feed pumps draw their supply. The temperature and pressure of the feedwater is raised by a series of low- and high-pressure feed heaters which draw heat from steam, bled from the turbines, thereby improving unit efficiency. The economiser is the last stage of heating prior to entering the drum. The dual role of the drum is to supply feedwater to the walls of the furnace and to separate the resulting steam from incoming water. The temperature of the superheated steam leaving the drum is constrained only by the metallurgical limits of the pipework. In the turbine, normally consisting of multiple stages, the kinetic energy of the steam is converted to mechanical torque as the steam expands across the turbines. After the initial high-pressure stage the steam returns to the boiler for reheating. On exiting the low-pressure turbine the now saturated steam is condensed back into liquid by the cooling water in the condenser. One of the advantages of operating in the subcritical region is that the differential density of water and steam, before and after the drum, permits 'natural circulation' of the feedwater around the boiler. If the flow becomes unbalanced, as a result of operating at elevated temperatures and pressures, then boiler feed pumps are required to provide the extra driving force. Hence, in unbalanced 'forced circulation' boilers the rating of the boiler feed pumps is significantly increased.

4 1.2.2

Thermal power plant simulation and control Supercritical plant

The world's first supercritical power plant began operating in 1957 and was commercially operated until 1979. This 125 MW installation at the Philo Plant operated at 31 MPa (310 bar) and 621 °C or 1150 °F (Smith, 1998). When operating a boiler in the supercritical region improvements can be made to both unit efficiency and heat-rate, due to the elevated temperatures and pressures. Currently, operating at state-of-the-art steam conditions a 3 per cent improvement in unit efficiency can be achieved, as compared with subcritical plant (Goidich, 2001). Supercritical boilers operate at pressures greater than 22 MPa (220 bar) and are also referred to as 'oncethrough' boilers, since the feedwater circulates only once through the boiler in each steam cycle. When operating at pressures above the critical point of steam there is no clear distinction between the vapour and liquid states, rather a fluid results, whose density can range from vapour-like to liquid-like. Consequently, a drum, normally required to separate the steam from the water, is eliminated, as shown in Figure 1.3. Control in a supercritical boiler is somewhat different from that in a drum boiler. While for a supercritical boiler it is the boiler feed pump that determines the steam flow rate, this requirement is met by the fuel-firing rate for a drum boiler. Consequently, to control superheat steam temperatures a once-through boiler first adjusts the fuel-firing rate, as opposed to using spray water attemperation for a drum boiler (Goidich, 2001). While supercritical plant should be more efficient than conventional drum plant, their development and deployment has been slow. Despite the reduction in operating costs resulting from higher unit efficiency, their increased installation cost can not often be justified over the life of the plant.

To turbine

~ 'Drum' boiler

Figure 1.3

Boiler steam flow paths

[[

P

, To turbine

erfee .7. 'Once-through'boiler

Advances in power plant technology Air

Gas Turbine

5

ill

Alternator

tl Exhaust, gases

Flue

Turbine Alternator

HRSG

II

Steam

•L

Condenser

..........................1~_.~

Cooling water

I

Feed water Boiler feed pump

Figure 1.4 1.2.3

Simplified CCGT plant

Combined cycle gas turbines

Combined cycle gas turbines, as their name suggests, combine existing gas and steam technologies into one unit. They bring together the Rankine cycle from conventional steam plant and the Brayton cycle from gas turbine generators, yielding significant improvements in thermal efficiency over conventional steam plant. In both types of plant it is the inherent energy losses in the plant design that constrain their thermal efficiency. However, in a CCGT plant the thermal efficiency is extended to approximately 50-60 per cent, by piping the exhaust gas from the gas turbine into a heat recovery steam generator, operating on the Rankine cycle. In general, the heat recovered in this process is sufficient to drive a steam turbine with an electrical output of approximately 50 per cent of the gas turbine generator. A simplified multishaft CCGT plant is illustrated in Figure 1.4. Alternatively, for single-shaft systems, the gas turbine and steam turbine are coupled to a single generator, in tandem. For startup, or 'open cycle' operation of the gas turbine alone, the steam turbine can be disconnected using a hydraulic clutch. In terms of overall investment a single-shaft system is typically about 5 per cent lower in cost, with its operating simplicity typically leading to higher reliability. Benefits of multishaft arrangements are shorter shafts, fewer stability problems and more degrees of freedom in the mechanical design.

1.3

Control and instrumentation

Modern power plant is a complex arrangement of pipework and machinery with a myriad of interacting control loops and support systems. However, it is the boiler

6

Thermal power plant simulation and control

control system that is central in determining the overall behaviour of the generating unit. All the main control loops must respond to a central command structure, which sets their individual setpoints and controls the behaviour of the plant. It is the demand for steam that resides at the top of this control hierarchy. From this all other individual loop controllers receive their demand or setpoint signal. Due to its importance, the steam demand signal is often known as the master control signal. The strategic behaviour of the unit is governed by various boiler control configurations, and the behaviour of the master control signal within these arrangements is now discussed. •

•

•

Boiler following mode Boiler following or 'constant pressure' mode utilises the main steam governor as a fast-acting load controller, since opening the governor valves, and releasing the stored energy in the boiler, meets short-term increases in electrical demand. Conversely, closing the governor valves reduces the generated output. These actions alter the main steam pressure, so it is the role of the master pressure controller to suitably adjust the fuel-firing rate. Operating a unit in this mode does, however, contain inefficiencies as throttling of the governor valves reduces the available steam flow, creating energy losses. Turbine following mode A generating unit may alternatively be configured to operate in turbine following mode, whereby the combustion controls of the boiler are set to achieve a fixed output. The position of the main steam governor valve is controlled by the valve outlet pressure, not the input as in boiler following. Consequently, such units can be operated with their governor valves remaining fully open. Turbine following mode is preferred for thermal base load and nuclear plant, since it allows the generating units to operate continuously at their maximum capacity rating. However, such units do not respond to frequency deviations and so cannot assist in a network frequency support role. For nuclear plant, there are also safety benefits in providing continuous steady state operating conditions. Sliding pressure mode Although boiler following mode is commonly used, sliding pressure mode is an 'instructive' development, where the constant steam pressure is replaced by a variable steam pressure mode. The reduced throttlingback action by the governor control valves, at lower outputs, leads to improved unit efficiency. Variable pressure operation also provides faster unit loading, and enables operation of the turbines at lower temperatures and pressures. However, the ability to use the stored energy of the boiler to meet short-term changes in demand is restricted. For safety reasons, fast-responding, electrically operated safety valves are essential for variable pressure operation to protect against sudden, dangerous increases in steam pressure that may occur while the pressure setpoint is low.

1.3.1

Combustion control

Burning a fossil fuel releases energy in the form of heat, which is absorbed by the feedwater through convection and radiation mechanisms. Controlling the volume of heat released when burning large quantities of fossil fuel is a demanding and

Advances in power plant technology

7

potentially dangerous problem, which is very much dependent on the fuel being burned- a coal-fired boiler being significantly different from that of an oil- or gas-fired boiler. The fundamental problem of combustion control is to adjust the fuel and air flow rates to match the energy demand of the steam leaving the boiler. The ideal or 'stoichiometric' ratio for complete combustion of the fuel is impractical and results in incomplete combustion due to unavoidable imperfections in the mixing of fuel and air. Excess air is always necessary in a real plant and can be as high as 10 per cent above the 'stoichiometric' ratio to achieve complete combustion. Without sufficient air flow to the furnace, incomplete combustion results in the formation of black smoke, poisonous carbon monoxide and the danger of unburnt fuel accumulating within the boiler. In contrast, excess air may generate unwanted NOx and SOx emissions and reduce the efficiency of the boiler by carrying useful heat out the chimney, as well as increasing ID/FD fan requirements. The continuous flow of air to the boiler furnace is achieved using forced draft (FD) fans to force air into the furnace and induced draft (ID) fans to extract the combustion gases. The internal draft pressure (furnace pressure) is maintained just below atmospheric pressure to prevent hazardous gases from escaping through observation portholes, soot-blower openings and other orifices in the furnace. The natural ingress of air through these openings is referred to as 'tramp air'. Overseeing the combustion process is the burner management system (BMS) which regulates the extremely hazardous process of firing the fuel. To ensure safety, numerous sensors supply data on current operating conditions. These include a UV flame detector, and furnace pressure, air flow, oxygen, NOx and CO sensors, to name but a few.

1.3.2

Boiler control subsystems

Boiler control systems exist in a hierarchial arrangement. As previously stated, residing at the top is the master control signal, which determines the steam load for the unit. Control systems or loop controllers at lower levels derive their demand or setpoint values from the master controller. A short list of other (boiler) control loops is as follows: •

•

•

Coal pnlveriser control regulates the supply ofpulverised fuel to the boiler from coal mills. The time delay between coal entering the mill and reaching the boiler, along with the startup time of additional mills, is often a limiting factor when the unit is required to respond quickly. D r u m level control is closely linked with feedwater control. The 'swell' and 'shrinkage' effects, resulting from changes in steam demand, are confusing to simple single-element controllers. Typically, a 'three-element' controller is used, which combines drum level, steam flow and feedwater flow signals. Steam temperature control regulates the temperature of the steam exiting the boiler after the superheater and reheater stages. The long time delays associated with these loops make for challenging control.

8

Thermalpower plant simulation and control

In addition to the control systems previously described there are many others that are essential for operation: generator excitation, burner angle, cooling water flow rates, LP/HP feed heating, flue gas recycling, etc.

1.3.3

Plant instrumentation

More than any other aspect of power generation, control and instrumentation equipment has changed unrecognisably in the last hundred years. When power stations were first constructed in the 1880s control was typified by the steam governor, where a simple mechanical flywheel with rotating weights was connected to a hydraulic system through a series of sliding linkages and springs. Since then, pneumatic and then analogue electrical equipment have been introduced for general plant control. However, the radical transformation in control came with the advent of the microprocessor, leading to stand-alone devices being adopted for individual loop control in the 1970s and early 1980s. The microprocessor permitted new and innovative control solutions to be considered, so as processing power advanced, system functionality grew. Today these isolated control systems have evolved into distributed control systems (DCSs), with the capability to control entire power stations. Although distributed control systems are used primarily for loop control their processing power and flexibility has allowed them to handle many other data management applications.

1.3.4

Distributed control systems

Over the course of the last two decades, distributed control systems have become the domain of large industrial processes and power plants. Indeed, it is their ability to handle control on large-scale systems that distinguishes them from their smaller programmable logic controller (PLC) and PC-based counterparts. The dichotomy between high-end PLC systems and DCS installations is, however, uncertain as both have similar functionality and network topologies. The distinguishing features of a DCS can be summarised as: Size - capacity to handle many tens of thousands of signals. Centralised administration - complete control of distributed units from one single node on the network. Data management - ability to handle and store tens of thousands of data points in real time. A simplified generic DCS network is illustrated in Figure 1.5. At its core, the DCS has a dual redundant, bidirectional, high-speed communications network, which facilitates the transfer of vast amounts of data between nodes. Connected to a typical network, four distinct types of device can be identified, each with unique functionality. Arranged in hierarchial order they are: The engineering workstation provides complete control over the DCS. Typical tasks may involve programming the distributed control units and adding/removing spare I/O capacity to the network.

Advances in power plant technology

9

Plant

*~put/output 0ffice~etwork '~

~ Data

~

~[l~l

~

II~l

atwaomr=t ¢:::::q

Distributedcontrolunits

~

"

Operatorworkstation

Figure 1.5

Simplifieddistributed control system

The data managementworkstationis usually assigned the task of managing the process database containing all the process data points or 'tags' on the DCS. Time stamping new data as it arrives on the network may also be performed. The operatorworkstationprovides high-resolution mimics of the plant, allowing the plant operator to control the unit using a human-machine interface (HMI). Distributed control units are responsible for implementing plant control. They are directly connected to plant signals and can usually operate independently of the rest of the DCS. Like most other parts of the DCS, dual or triple redundancy is employed to ensure availability of control equipment at all times.

1.4 Externalinfluences The environment in which power stations operate has undergone a radical shakeup over the last two decades and still remains in a state of flux. No longer can a station be operated in isolation, where unit efficiency and good engineering practice are the main considerations. Managing a station today involves juggling a myriad of conflicting external factors. On one side there may be shareholders anticipating a profitable return on their investment, and on the other, environmental legislation forcing the procurement of emissions reducing plant and equipment. As already suggested the two areas which have had the most significant influence on station management are liberalisation of the energy markets and environmental legislation.

10 1.4.1

Thermalpower plant simulation and control Power system deregulation

During the years between the end of World War II and the 1970s, utility management in the United States and Europe focused on the major task of building new power plant and improving the transmission and distribution grids to meet the demands of rapidly growing economies. The only competition that existed was between individual concerns trying to install the largest generating unit of the day or the most thermally efficient unit. Beyond this, utility managers remained cooperative with their colleagues. The business and technological strategies they employed were all very similar and governed mainly at national level. The level of cooperation extended to national research and development organisations, for example, the Central Electricity Generating Board (CEGB) in the United Kingdom and the Electric Power Research Institute (EPRI) in the United States. These organisations engaged in collaborative research and openly shared their findings, as few secrets existed among their members. The United States was the first to truly witness the 'winds of change' for the regulated utilities. Growing discontent from the general public was fuelled by the continued price increases in electricity, the spiralling costs of large generation plant and widespread fears about nuclear generation. In an attempt to placate the public the United States introduced the Public Utilities Regulatory Policies Act in 1978 to allow unregulated generators to supply the grid. By doing so it was hoped that nonconventional and independent sources of power would appear. These independent power producers (IPPs) were not allowed to sell to end users but it was mandatory for local regulated utilities to purchase their generated output. This measure proved sufficiently successful that by 1993 some 50 per cent of new generating capacity in the United States was being constructed by IPPs. These changes challenged the long-held belief that electrical generation and distribution was a natural monopoly. With this realisation the next step was to open up the market whereby customers could, in theory, benefit from increased competition. In the United Kingdom, the Electricity Act of 1989 legislated for the breaking up of the nationalised CEGB industry into smaller privately owned companies. A 'pool' system was introduced, where generators competed against each other for contracts to generate electricity (Hunt and Shuttleworth, 1997). The new legislation separated the product (generated electricity) from the transportation medium (the transmission grid). In doing so, costs could be unbundled into an 'energy' and a 'delivery' component. These arrangements were replaced in March 2001 by the New Electricity Trading Arrangements (NETA) in an attempt to facilitate greater market freedom for generators and suppliers, particularly in the wholesale market. Plans exist to extend these arrangement to Scotland by creating the British-wide Electricity Trading and Transmission Arrangements (BETTA). The United States has gradually been moving towards increased competition. Here, privatisation is not considered an issue, as the majority of electricity companies are investor-owned utilities that are territory based. In 1992 the Energy Policy Act permitted wholesale customers the choice of supplier, and obligated the relevant utilities to transmit power across their networks. Their restructuring model resembles that which was implemented in the United Kingdom.

Advances in power plant technology

11

In Europe, the European Commission (EC) is similarly endeavouring to liberate the electricity markets of its 15 member states. Amendments to Directive 96/92/EC on March 2001 committed member states to be fully open to competition by January 2005. Unfortunately, loopholes in the legislation allow individual countries to opt out entirely or comply in a piecemeal fashion. As of February 2000, approximately 60 per cent of EU customers have a choice of electricity supplier (Lamoureux, 2001). The two member states who led the way, and have already taken action to deregulate their electricity industries, are Belgium and the United Kingdom.

1.4.2

Environmental factors

From an environmental perspective, burning fossil fuel releases undesirable and harmful emissions into the atmosphere - carbon dioxide (CO2), carbon monoxide (CO), sulphur dioxide (SO2), nitrogen dioxide (NO2), nitric oxide (NO), etc. In addition to the above, particulate emissions may be produced, especially when burning coal and heavy oil. Oxides of sulphur (SOx) are formed when the fossil fuel itself contains sulphur. Coal burning is the single largest man-made source of sulphur dioxide, accounting for almost 50 per cent of annual global emissions, with oil burning accounting for a further 25-30 per cent. The simplest approach to reduce SOx emissions is to burn fuel with a low sulphur content. Hence, the current popularity in burning natural gas and low sulphur oil and coal in conventional power stations. Alternatively, flue gas desulphurisation plant 'scrubbing' is available, but expensive. Oxides of nitrogen (NOx) are formed during high-temperature burning of fossil fuel. Nitric oxide (NO) and nitrogen dioxide (NO2) are formed when nitrogen from either the fuel or air supply, and oxygen from the air, combine. Minimising NOx formation requires correct design of the furnace bumer, and optimised boiler control. However, the higher the combustion efficiency the higher the formation of nitric oxide. Nitrogen dioxide also contributes to the formation of ground-level ozone (O3) when mixed with volatile organic compounds (VOCs) in a sunlight-initiated oxidation process. In addition, both NOx and SOx, when absorbed into the atmosphere, slightly increase the acidity of the precipitation that falls to earth. Hence, the term acid rain. Carbon dioxide and ozone (formed from NO2) are classed among the greenhouse gases (GHGs) that are contributing to global warming. Recent attempts at environmental legislation, in particular the Kyoto Protocol, have focused on reducing emissions by setting stringent targets. The treaty specifies that industrial countries have until 2010 to reduce their GHG emissions by particular percentages below 1990 levels. The European Union committed to cutting its emissions to 92 per cent of its 1990 level, and the United States to 93 per cent. During this time it was assumed that emissions for industrial countries would substantially increase, without any restrictions in place. James Markowsky, on behalf of the American Society of Mechanical Engineers (ASME), at a luncheon briefing on Capitol Hill, Washington, 1999, pointed out that to meet that goal the United States would have to retire most of its coal-burning plant, which then currently generated approximately 56 per cent of the country's

12

Thermal power plant simulation and control 500+ 400 e~ o

~ 300 200 g~ lOO

North Southand Europe Former Africa America Cent. America Soviet Union Figure 1.6

Asia Pacific

Fossil fuel reserves as of 2001

electric power (ASME, 1998). Given today's technology, the only way to generate the power the United States requires and still meet the emissions standard is to burn gas. Unfortunately, burning gas is not a sustainable long-term solution. From Figure 1.6, based on data from the BP Statistical Review Of World Energy (BP, 2001), it can be seen that proven reserves of gas are limited. If the current rate of consumption of gas continues, world reserves will be severely depleted within 40-50 years. The total reserves for coal, however, are substantially larger than those for oil and natural gas combined. This would suggest that future technology may focus on 'clean coal' plant, as viable alternatives to fossil fuel are somewhat limited. IGCC plant typify emerging technology aimed at combating the emissions problem associated with coal. Here, the fuel is gasified and cleaned, before being burnt in a conventional combined cycle plant. Gasification technology has also been combined with fluidised bed designs. In a typical demonstration plant, situated in the city of Lakeland, Florida, a carboniser receives a mixture of limestone, to absorb sulphur compounds, and dried coal. The coal is partially gasified to produce syngas and char/limestone residue. The latter is sent to a pressurised circulating fluidised bed, where it joins a stream of crushed fresh coal which is burned in the boiler furnace (DOE, 2001a,b). Gasification and gas reforming, i.e. the production and separation of gas into carbon monoxide and hydrogen, appear to be the most promising technologies at present (DOE, 1999). The former produces a gas stream that can be burned for electric power, while the latter offers a source of hydrogen for a fuel cell or chemical process. Renewable sources (biomass, wind, hydro, tidal, solar, etc.) have been presented as part of any future solution to energy needs. In November 1997 the European Commission set itself a target of doubling renewable energy supply from 6 to 12 per cent by 2010. Similarly, the United Kingdom, for example, established a target of 10 per cent renewable generation by 2010. Indeed, the UK Cabinet Office Performance and Innovation Unit proposed a target of 20 per cent renewables

Advances in power plant technology

13

by 2020 in March 2002. More recently at the UN World Summit on Sustainable Development, in Johannesburg, September 2002, a pledge was made to increase 'substantially' the use of renewable energy in global energy consumption. Worldwide, the United Nation's Intergovernmental Panel on Climate Change (IPCC) postulated a 'coal intensive' scenario with renewables contributing 65 per cent of the primary energy by 2100 (IPCC, 1996). However, on shorter time-scales, it may remain for nuclear fission (or perhaps someday, fusion) to meet growing energy needs (VGB, 2001). It is also worth noting that electricity consumption is projected to grow by 75 per cent relative to 1999 figures (DOE, 2002) by 2020.

1.5

Plant technology developments

Many power stations view the DCS as a direct replacement for older stand-alone analogue or digital controllers. Hence, the control systems used in the DCS are often simply a copy of what had been used in the past. In most cases loop control is implemented using single-input single-output (SISO) linear structures in the form of PI or PID controllers. For sequence control, the DCS provides an abundance of logical function blocks (AND, OR, XOR, etc), with programming software allowing these to be tied together to create multilevel control programs. However, from the vast amount of real-time data available only a small proportion is typically used, usually to alarm the operator of plant faults and occasionally to drive simple data trending for fault finding or management summary reports. Minimal advantage is taken of the high-speed communication network for plant-wide control schemes or supervisory layers. An enlightened view of distributed control systems, however, reveals that the constraints of former mechanical and analogue solutions are gone. A new vista is opening in power plant control and management, with novel and innovative approaches being given consideration. It is now possible to implement non-linear multiple-input multiple-output (MIMO) model-based control, coordinated plant control (trajectory following and optimisation) or pseudo-intelligence in the form of expert systems, artificial neural networks (ANN), data mining and genetic algorithms for supervisory control. These new technologies are embracing all aspects of power plant operation, from intelligent maintenance, environmental protection, data management systems, intelligent alarm management, fault diagnostics, productivity management, purchasing and accounting. The potential list of applications is virtually endless (DOE, 2001 a; Oluwande, 2001; Lausterer, 2000).

1.6

References

ASME: 'Technology implications for the US of the Kyoto protocol carbon emission goals'. ASME general position paper, ASME, December 1998 BP: 'BP statistical review of world energy' 50th edition, London, June 2001 DOE: 'Vision 21 program plan'. US Department of Energy, Federal Energy Technology Center, April 1999

14

Thermalpower plant simulation and control

DOE: 'Environmental benefits of clean coal technologies'. US Department of Energy,

Topical Report Number 18, April 2001a DOE: 'Software systems in clean coal demonstration projects'. US Department of

Energy, Topical Report Number 17, December 2001b DOE: 'International energy outlook 2002'. Energy Information Administration, US

Department of Energy, March 2002 DTI: 'Innovative supercritical boilers for near-term global markets'. Department of

Trade and Industry, London, United Kingdom, Pub. URN 00/1138, September 2000 GOIDICH, S.: 'Efficient power operational flexibility: The once-through supercritical boiler'. Foster Wheeler Review, Autumn 2001, Foster Wheeler Energy Corporation, pp. 11-14 HUNT, S. and SHUTTLEWORTH, G.: 'Competition and choice in electricity' (John Wiley, Chichester, 1997) IPCC: 'Working group II to the second assessment report, intergovemmental panel on climate change, climate change 1995: impacts, adaptations and mitigation of climate change' (Cambridge University Press, 1996) LAMOUREUX, M.A.: 'Evolution of electric utility restructuring in the UK', 1EEE Power Engineering Review, June 2001, pp. 3-5 LAUSTERER, G.K.: 'Knowledge-based power plant management - the impact of deregulation on it solutions', lEE Control, Proceedings of lEE Control 2000 Conference, Cambridge UK, September 2000, pp. 1-8 OLUWANDE, G.A.: 'Exploitation of advanced control techniques in power generation', Computing and Control Engineering Journal, April 2001, pp. 63-67 SMITH, J.W.: 'Supercritical (once through) boiler technology' (Babcock & Wilcox, Barberton, Ohio, US 1998, BR- 1658) VGB: 'Research for a sustainable energy supply - recommendations of the Scientific Advisory Board of VGB PowerTech e.V.'. July 2001

Part 1

Modelling and simulation

Chapter 2

Modelling of power plants A. Leva and C. Maffezzoni

2.1

Introduction

Modelling power plant processes may be approached from different points of view, depending on the purpose for which the model is intended. Here, we shall restrict the presentation to the case (most interesting for engineering) where the model is built to allow system simulation over a rather wide range of operation (non-linear model) and is based on first principles and design data. This specification naturally leads to a model structuring approach based on the representation of plant components and of their interconnections, with evidence given to variables and parameters corresponding to well-defined measurements or physical entities. Possible experimental data are, generally, not used for system identification but for model validation, which may also include some model tuning. The models here are referred to as dynamic, that is, they are able to predict transient responses, even for large process variations. Since power plant dynamics operate on a range of time scales, it is advisable to focus on the use of a dynamic model over a defined horizon. For simulation models representing an entire power plant or a large subsystem, it is quite common to seek model accuracy over an intermediate time-scale, i.e. in the range of a few tenths up to a few thousands of a second. This will be the implicit assumption in the description of the basic models. Finally, we shall limit the scope of this chapter to power plants based on the firing of a fossil fuel, i.e. conventional thermal and gas turbine plant, possibly equipped with heat recovery boilers. There is a long track record of research and engineering effort in this area, dating back to the pioneering work of Chien et al. (1958), passes through the earlier engineering-oriented works of Caseau et al. (1970), Weber et al. (1976), Modular Modelling System (1983), Lausterer et al. (1984), Maffezzoni et al. (1984), and leads to presently available simulation codes (APROS; ProTRAX; Cori et al., 1989; SIMCON-X, 1994a,b). With reference to the survey papers of Carpanzano et al.

18

Thermal power plant simulation and control

(1999) and Maffezzoni (1992), the objective here is to review the important knowledge (concerning both methods and applications) accumulated along that track and to transfer it to the unifying framework of object-oriented modelling, which appears to be most effective in dealing with real-size engineering problems and in sharing modelling knowledge among diverse users. So, the chapter is organised as follows: first the basic concepts of object-oriented modelling are introduced with reference to the typical structures met in thermal power plant, then a review is presented of basic models for typical power plant components. Subsequently, the task of defining a realistic model of the plant distributed control system (DCS) is investigated; some remarks about the application of dynamic decoupling and methods of model validation are then reported.

2.2 Model structuring by the object-oriented approach 2.2.1

Foreword

Object-oriented modelling (OOM) is a widely accepted technique which has already produced both modelling languages (Mattsson and Andersson, 1992; Maffezzoni and Girelli, 1998; Elmqvist et al., 1999) and software packages (Piela et al., 1991; Elmqvist et al., 1993; gPROMS, 1998). The approach is based on a number of paradigms, among which a fundamental role is certainly played by the following: •

• •

The definition of physical ports (also referred to as terminals) as the standard interface to connect a certain component model, in order to reproduce the structure of the physical system. The definition of models in a non-causal form permitting reuse, abstraction and unconditional connection. The mutual independence of the model interface (the physical ports) and its internal description.

State of the art OOM is well represented by the development of the Modelica project (1999), a recent international effort to define a standard modelling language. At present there are well-assessed methods to treat lumped parameter components (LPC) while, on the contrary, there are no unified solutions to describe distributed parameter components (DPC), which are quite important in power plant modelling. As such, in the remainder of the chapter we shall adopt the Modelica language as the formalism for writing the described models (whose specification manual is available at www.modelica.org) with the minimum extension required to cope with DPC's, for example heat exchangers, according to the approach proposed by Aime and Maffezzoni (2000).

2.2.2

Classification of plant components and of physical ports

From the point of view of model structuring, it is convenient to look at the typical layout of a fossil-fired power plant (Maffezzoni and Kwatny, 1999). In the case of a classical Rankine-cycle unit, the principal subsystems are the steam generator

Modelling of power plants

19

(or boiler), the steam turbine, the condensed water cycle and the electrical subsystem. The structure of the power station's electrical subsystem is not relevant to the principal characteristics of a power unit, so in the following the electrical subsystem will be drastically simplified by considering only the electromechanical balance of the alternator. Modelling power units by aggregating component models is very convenient because it reflects the physical plant layout and enhances reuse of modelling software. Plant components may be classified first by looking at the subsystem they belong to, then considering the nature of the process transformations that they implement. Structuring by modules is, to a certain extent, a matter of choice: defining large modules implies a simpler aggregation structure, while defining small modules implies a larger reuse when the plant structure changes. Here, the 'size' of basic modules is chosen according to the best practice employed in engineering dynamic simulators: this choice is compatible with packages like APROS (www.vtt.fl) and LEGO (Coil et al., 1989), widely used for power plant simulators, and DYMOLA (www.dynasim.se), appropriate for implementing an object-oriented approach to physical system modelling. 2.2.2.1

Boiler components

The boiler is the most complex subsystem, and it can be split into a pair of interacting circuits: the water-steam circuit and the air-gas circuit. There are components which take part in one circuit only (one-side components, OSC) like pumps, valves, headers, etc., while there are components, namely heat exchangers, which take part in both circuits (two-side components, TSC), being devoted to heat transfer from the combustion gas to water and steam. To define the structure of an OSC it is convenient to introduce a physical port through which a component may interact with another, i.e. the thermohydraulic terminal (THT), which is specified through the following Modelica script: type

Pressure

= Real(quantity

=

"Pressure",

type

MassFlowRate

= Real(q~antity

=

"MassFlowRate",

type

Enthalpy

= Real (quantity

=

"Enthalpy",

connector

=

displayUnit

displayUnit

=

"Pa", =

unit

=

"kg/s",

"J/kg",

unit

"Pa"); unit =

=

"kg/s");

"J/kg" ) ;

THT Pressure

flow

displayUnit

p;

MassFlowRate Enthalpy

w;

h;

end THT ;

The Modelica language (like many others) allows type definitions to enhance the clarity of the simulation code. This is illustrated in the previous script by defining Pressure, MassFlowRate and Enthalpy. Throughout this work we shall assume that all the required types are defined in this way, hence we shall refer to types like Quality, AngularVelocity, and so forth. We do not report their definitions because of space limitations and because they can be immediately deduced from those given. Note also that Modelica has an extensive library of predefined types. For instance, the process scheme of Figure 2.1 a suggests the model structure of Figure 2. lb. The connection between the pump THT Out (outlet) and the valve THT In (inlet) means that the pressure and enthalpy at the pump outlet coincide with the pressure

20

Thermal power plant simulation and control

a< Figure 2.1

°ut Simple process scheme and its model structure

Gas

Figure 2.2

Typical heat exchanger configuration

and enthalpy at the valve inlet, respectively, while the mass flow rates at the pump outlet and valve inlet sum to zero. Pressure and enthalpy are effort variables while mass flow rate is a flow variable. The interaction between a couple of neighbouring OSCs can always be modelled by the direct connection of two THTs. The Modelica script stating the aggregation of Figure 2.1 is as follows: c o n n e c t (PUMP. Out, V A L V E . In) ;

where, of course, PUMP and VALVE are instances of suitable elementary models stored in some library. The THT can be used both for OSCs belonging to the steamwater circuit and to the air-gas circuit. Considerably more complex however, is TSC structuring, because in this case we need to model, in a modular way, the variation in heat transfer configurations of boiler tubular heat exchangers. A typical situation is depicted in Figure 2.2, where gas flowing through the boiler back-pass exchanges heat with the principal bank (A) disposed in cross-flow and with an enclosure panel (B) disposed in long-flow. The model of a complex heat exchanging system like that of Figure 2.2 could be structured according to the very general approach proposed by Aime and Maffezzoni (2000), where spatially distributed heat transfer configurations are introduced. More pragmatically, one can exploit two common properties of boiler heat exchangers: •

Gas flows have negligible storage with respect to metal wall and steam-water flows.

Modelling of power plants

Figure 2.3

•

21

Modular structure for heat exchanging system

The gas ducts may be split into a cascade of gas zones, where the gas temperature can be assumed to be almost uniform or linearly varying.

Zone splitting is guided by the structure of the tube bank: typically a gas zone extends to include one row or a few rows of tubes. The model structure corresponding to the situation of Figure 2.2 is sketched in Figure 2.3. The connection between a bank and a gas zone takes place through a distributed heat transfer terminal (dHT), which consists of the bank walls' temperature profile Tw(x, t) and the heat flux profile ~0(x, t) released to the wall. Tw(x, t) and qg(x, t) are functions of time t and of the banks' tube abscissa x. A typical finite-element discretisation of Tw(x, t) and ~0(x, t) replaces such functions with their interpolating approximations obtained from two vectors of nodal temperatures and fluxes. Thus, in simulation code, Tw(x, t) and ~0(x, t) are represented by two vectors of suitable dimensions, denoted in the following by Tw (t) and • (t), respectively. In Figure 2.3, it has been assumed that the transfer of energy from one gas zone to the adjacent one is solely due to mass transfer, as implicitly established by the connection of two THTs. There are, however, high-temperature gas volumes (either in the furnace or in other parts of the back-pass) where radiation heat transfer from one gas zone to those adjacent is not negligible. This requires the introduction of a specific port that extends the THT to permit transfer of heat independent of mass flow. In principle, at a boundary surface between two fluid volumes, we may have transfer of energy by convection (expressed by the group wh), radiation and/or diffusion; mechanical work is already included in the product wh. We may call this physical

22

Thermal power plant simulation and control

Furnace ~ zone i- 1

Zones interaction

Furnace ~ zone

i

I I .T

Zones ~ interaction

Furnace zone i +1

r

Gas wall interaction

I

[aHT] Furnacewall tubes Figure 2.4

Interactions between furnace zones and walls

port the thermo-hydraulic and heat transfer terminal (THHT), which will consist of the following variables: • •

the mass flow-rate w, enthalpy h, pressure p and heat rate Q at the interface between the gas volumes; the radiation temperature Tr (e.g. the flame temperature) of the lumped gas volume.

For instance, a model of the furnace zone, where there are neither burners nor secondary air inputs, can be structured as shown in Figure 2.4, where the heat transfer terminal (HT) consists of the following two variables: • •

Qw, the heat rate to the furnace wall Tr, the radiation temperature of the gas zone.

Terminals dHT, THHT and HT are defined in the Modelica language as follows: dHT Integer vectorSize=l; Temperature tempProfile[vectorSize] flow HeatFlux heatFluxProfile[vectorSize] ; e n d dHT; c o n n e c t o r THHT extends THT; Temperature Tr; f l o w HeatFlow Q; e n d THHT; c o n n e c t o r HT Temperature Tr; flow HeatFlow Qw; e n d HT;

connector parameter

;

Modelling of power plants

23

Note the distinction between He a t F l u x ( W / m 2) and He a t F 1 ow (W). These scripts employ the Modelica e x t e n d s clause, which allows us to define a model or a connector by adding elements to a previously defined one. Such clauses are available in any object-oriented modelling language. It should be noted that the situation of Figure 2.3 is a particular case of that depicted in Figure 2.4: in Figure 2.3 the interaction between two adjacent zones is very simple (there is no heat transfer besides convection) so that zone interaction becomes trivial and is omitted; the gas-wall interaction is summarised by a heat transfer coefficient, directly incorporated in the gas zone. To fully understand the role of the model ZONES INTERACTION, we provide here a possible implementation: WL + WR = 0

(2.1)

PL -- PR = 0

(2.2)

hL -- hR = 0

(2.3)

QL + QR = 0

(2.4)

QL = K(T 4 - T4)

(2.5)

where the subscripts 'L' and 'R' denote variables belonging to the left and fight terminals, respectively, and K is the radiative heat transfer coefficient.

2.2.2.2

Steam turbine components

For the purpose of power plant simulation, turbines are generally modelled as lumped parameters. When accurate modelling is required, it is usual to split a turbine into a number of cascaded sections, a section being in turn composed of a number of cascaded stages. The extension of a section is typically dictated by some physical discontinuity along the steam expansion, such as the presence of steam extraction or a change in the stage design (e.g. when passing from impulse to reaction stages). Interaction between a turbine section and other components at its boundary may simply be modelled by THTs as shown in Figure 2.5, while a mechanical terminal (MT) is needed to represent the power transfer to the shaft. The MT consists of the two variables w (angular speed) and r (torque). The same approach can be used for gas turbines, where the situation is even simpler because there are no present physical discontinuities. The MT is represented in Modelica as follows: connector

MT

AngularSpeed flow Torque end MT ;

2.2.2.3

omega ; tau;

Condensate cycle components

The condensate cycle is composed simple compact components like valves, pumps, headers, etc. and of more complex heat exchangers and/or storage tanks. Model

24

Thermalpower plant simulation and control

Steam

I

extraction

I

Turbine Turbine section IH[~HI section [ H [ ~ I

Turbine section

Turbine section

Header

~-----~--] I

]

_

I

IMTI-

Shaft I

Alternator Figure 2.5

Interactions between turbine sections and boundary components

I

Low pressure I turbine I

C°°ling ~ water discharge piping

_

I THT ' ~ Condenser ~

~

C°°ling water pump _

I

I T.TI I

Extraction pump

i

Figure 2.6

Model structuring example for the condensate cycle

structuring is quite obvious for the former components, whereas non-trivial questions arise for complex heat exchangers such as the condenser, deaerator, and low-pressure and high-pressure heaters. There are two possible approaches: to build the heat exchanger model as the aggregate of simpler objects or to directly define the heat exchanger as an elementary (indivisible) component. Since the internal structure of the condensate heat exchangers is quite complex while the design of such large components is highly repetitive, it is advisable to follow the latter approach. In this case, physical ports between cycle components are still THTs. An example of structuring is given in Figure 2.6.

Modelling of power plants

I

Fuel storage

25

I

I

]~ Fuelvalve

] THT

Valveposition

I

~ Atmosphere

~ 1 Compressor I

I MT I Figure 2.7 2.2.2.4

THT 1 ~ Combust chamberion Shat~

Gasturbine

T~Exhaust header

I

I MT I

Model with an input control terminal

Gas turbine components

Gas turbines have become increasingly important in power generation, because of the outstanding efficiency achievable by combined cycle plants. The essential components are: • • •

the gas turbine the compressor the combustion chamber.

Model structuring is generally simple, as sketched in Figure 2.7, where ICT denotes an input control terminal, that is a control port where a command signal is issued. Internal modelling of basic components is, however, a non-trivial task, especially because it is often very important not only to predict power release of the turboalternator but also concentration of pollutants to the atmosphere. This is discussed in the next section.

2.2.3

Aggregation of submodels

Reuse of models for different case studies is enhanced by modularity, structuring of elementary models as non-causal systems and standardisation of physical ports (or terminals). However, it is common practice to repeat plant or subsystem designs from one power unit to another. For instance, we may store in a library the model of an economiser, which may result from aggregation of a block scheme like that of Figure 2.3. Of course, by aggregating model objects internal physical terminals disappear (they saturate with one another) so that the global model of the economiser (including its enclosure) may look as in Figure 2.8. Reusing an aggregate model implies that the model structure and model equations are not accessible to the user (they cannot be changed when using the aggregate); what are specific to a given instance of the aggregate model are the model

26

Thermal power plant simulation and control Connectionto enclosuretubes

Connectionto enclosuretubes Connectionto gas circuit Connectionto high-pressure condensatecircuit

Figure 2.8

Economiser

~T ~

Connectionto gas circuit

~T HT

Connectionto steam drum

Aggregation of model objects (economiser)

parameters which must be transferred from the internal submodels to the resulting aggregate.

2.2.4

Internal model description

The typical internal structure of a simple (non-aggregate) model using the Modelica language may be as follows:

model SIMPLEMODEL parameter ParamType paramName; ConnectorType connectorName; VariableType variableName; equation end SIMPLEMODEL; When an aggregate model AGGREGATEMODEL is obtained by composing two or more simple models (S IMPLEMODEL1, S I MPLEMODEL2 in the example), it can be defined by a Modelica script of the form:

model A G G R E G A T E M O D E L SIMPLEMODEL SIMPLEMODELI SIMPLEMODEL SIMPLEMODEL2

(paramName=paramValuel); (paramName=paramValue2);

connect(SIMPLEMODELl.connectorName,SIMPLEMODEL2.connectorName); end AGGREGATEMODEL;

It is worth noting that the section equation in the format of the simple model is generally constituted by switching differential-algebraic equations (DAEs), i.e. alternative sets of DAEs that describe the system dynamics under different conditions. (Maffezzoni and Girelli, 1998; Maffezzoni etal., 1999). Moreover, both for the DAEs and the logical conditions, some quantities may be evaluated by referring to functions

Modelling of power plants

27

of one or more variables, including look-up tables. Partial differential equations may be treated by finite element or finite difference approximations written as implicit matrix equations (Quarteroni and Valli, 1997). All these constructs are compatible with the Modelica language (and with several other modelling formats.)

2.3

2.3.1

Basic component models

The evaluation of steam and other fluid physical properties

2.3.1.1 Steam properties The large majority of models considered in this chapter require that various thermodynamic properties are evaluated starting from a couple of state variables. It is quite common that the computation of a global power plant model requires many thousands of steam property evaluations at each time step. So, an efficient and accurate treatment of water-steam properties is crucial for power plant simulation. Moreover, it is generally required that one or more properties be evaluated from at least three different couples of entry variables, typically (p, h), (p, S) and (p, T), where p is the pressure, h enthalpy, S entropy and T temperature. Finally, for dynamic modelling, not only standard thermodynamic quantities, like enthalpy, entropy, pressure and density are needed, but also viscosity, conductivity and thermodynamic partial derivatives (in particular specific heats at constant pressure Cp and constant volume Cv) or line derivatives along the saturation curve.

Water-steam properties can be computed using steam tables, based on (very complex) empirical formulas (Properties of Water and Steam, 1989), from which the required derivatives can be obtained by symbolic manipulation. These formulas, however, cannot be used for modelling in their current form, because entry variables are not those needed, formulas are very complex and, being non-linear, they should be used in a Newton-like algorithm to determine even a single property. Therefore, the sole practical approach is to build a suitable grid in the thermodynamic plane, with a convenient number and disposition of nodes with respect to the saturation curve, so as to allow smooth and accurate approximation over the whole plane. Then, the 'model of the steam-water fluid' is constituted by large look-up tables with the required entry variables, yielding either a single property or a vector of properties, depending on the application. Within the object-oriented modelling environment, the s t e a m - t a b l e s may be treated either as a set of functions or as a simple model to be incorporated by any component model, when required. In this work the first option has been chosen. The steam tables are implemented as a set of functions receiving two parameters. In the case of the full tables these are the (p, h), (p, S) or (p, T) couple; in the saturation tables these are the pressure and a two-valued parameter stating whether the liquid or vapour properties are required. This can be a boolean parameter, although in the examples presented herein its value

28

Thermal power plant simulation and control

is represented by the strings l i q u i d and v a p o u r for better clarity. There is one function for each property and for each input couple. For example, the functions

SteamPHtablesEnt ropy (p, h) SteamPStablesDdensityDpressure (p, S ) SteamSATtablesDensity (p, "vapour" ) SteamSATtablesDenthalpyDpressure (p, "liquid" ) return the steam entropy at pressure p and enthalpy h, the partial derivative of the steam density with respect to pressure at pressure p and entropy S, the saturated vapour density at pressure p and the derivative of the saturated liquid enthalpy with respect to pressure computed along the saturation curve at pressure p, respectively. Several functions like these are used in the equations of the models that will be introduced from now on, and the syntax should be self-explanatory. For simplicity it will be assumed that all these functions are overloaded for vector treatment, so that for example if in the first of the previously mentioned functions the 13 argument is a scalar while h is a vector, the corresponding vector of entropies is returned. This is not difficult to implement in modern programming languages.

Air and flue gas properties Similar to the steam case, it is also necessary to evaluate various properties of air or flue gas including enthalpy, density, specific heat, etc. from the state variables. As is known, the 'state' required to determine any property of a gaseous mixture comprises the gas composition, as well as some thermodynamic variables like the mixture pressure and temperature. Accurate modelling of gas dynamics would require balance equations for the different species involved, accounting also for the chemical kinetics, at least in the equilibrium state. However, when the combustion gas composition undergoes such limited variation so as not to affect the relationships among the relevant thermodynamic properties significantly, and/or the accuracy required for the model is not very high, then one can evaluate the gas properties as if the composition was equal to a constant (nominal) value. In this case, the gas functions depend on two state variables only. The same simplification can be used for the air, provided a suitable 'nominal' composition is employed. As a result, for air and flue gases this work adopts the same solution as for steam: two sets of functions similar to those presented are used, where the function names' prefix is G a s or A i r in lieu of S t e a m and the rest of the syntax is the same. The Gas and A i r functions employ two different nominal compositions, which can be coded in the functions themselves or as a global variable, leaving only a couple of thermodynamic variables as arguments.

2.3.1.2

2.3.2 2.3.2.1

The boiler's water-steam circuit Heat exchanger segment

This describes the dynamics of the fluid flowing into a tube bundle and of the metal wall, interacting with the external fluid (gas). For one-phase flow, the classical way to build such a model is by the equations of mass, energy and momentum for the fluid

Modelling of power plants

29

stream and the energy equation for the metal wall: ai~

Ow + ~x

A Oh

= 0

Oh

(2.6)

P i - ~ - Ai~---Pt+ W~x = witPi

(2.7)

dz Cf wlwl ai ~x -'l-p Aig-~x + -~ooi--~i = O

(2.8)

0Zw

AwpwCw ~

----OgetPe -- O)i~0i

(2.9)

where p, p, h, w are the density, pressure, enthalpy and mass-flow rate of the fluid (depending on the tube abscissa x, 0 < x < L, and on the time t), Tw is the wall (mean) metal temperature, ~oi the heat flux from the metal wall to the fluid, ~Pethe heat flux from the external gas to the wall, Ai the tube (bundle) internal cross-section, o)i the corresponding total perimeter, We the total external perimeter, z the tube height, g the acceleration due to gravity, Cf a frictional coefficient, and Aw, Pw and Cw the metal cross-sectional area, the density and specific heat capacity. Note that, in the momentum equation, the effects of inertia and of kinetic energy variation along x have been neglected, as normal. To complete the model, a suitable correlation for evaluating ~0i is needed. Assuming turbulent flow in the tubes, ~oi is usually expressed as:

qgi = yi(T - Tw)

(2.10)

where T is the fluid temperature at (x, t) and Vi is the heat transfer coefficient for turbulent internal flow (Incropera and Witt, 1985). Since the pressure drop and mass storage in a heat exchanger tube have definitely faster dynamics with respect to thermal energy storage, it is convenient to build the model with the following approximations: •

•

The pressure p(x, t) can be considered 'nearly constant' along x, 0 < x _< L, i.e. p(x, t) ~- p(L, t) :--- po(t), for the sake of the evaluation of p and Op/Ot in equations (2.6)-(2.8). The mass flow-rate w(x, t) can be considered 'nearly constant' along x, 0 _< x <_ L, i.e. w(x, t) ~- to(O, t) := wi(t), in equations (2.7) and (2.8).

Then, integrating equations (2.6) and (2.8) with respect to x, we obtain:

Ai

-~ p "~dx-'l-ai

Ai(Po - Pi) + Aig

~P h dx - - : / / ) i - t o O d t

fOL P-~x dz dx + -~-Cf .--Twwilwil (oi fo L -1 dx = 0 Z A . ~i P

(2.11) (2.12)

where (8p/Oh)p and (Op/Op)h denote the partial derivatives of p with respect to the thermodynamic state variables h and p.

30

Thermal power plant simulation and control Equation (2.1 1) can be written as: O(po(t), h(., t)) dp°(t) - wi(t) - Wo(t) + F(po(t), h(., t), h(., t)) dt

(2.13)

where the functions 69 and F correspond to the second and first integral of (2.11), respectively, while h(., t) and/;t (., t) are the enthalpy profile and its derivative on the whole domain 0 < x < L. Equation (2.12), in turn, can be written as: Po - Pi + g L ~ ( p o , h(., t)) + kwilwilO(po, h(., t)) = 0

(2.14)

where ~p and ~ are suitable functions and k = (LCfogi)/(2A~), Cf obtained from suitable correlations. If any spatial approximation of the enthalpy profile is assumed, for example the finite element approximation N

h(x, t) ~ ha(x, t) := Z

hj(t)otj(x)

j=l

then 69, F, ~ and fi become functions of the nodal enthalpy vector H ( t ) = [hl (t), hz(t) . . . . . hu(t)]' and of its derivative i-/(t). Applying the finite element approximation with a Petrov-Galerkin type method (Morton and Parrot, 1980; Quarteroni and Valli, 1997), to equations (2.7) and (2.9), one obtains a couple of N-vector equations to be used for the computation of the fluid and metal temperature profiles. In the most general case, if weak boundary conditions are imposed (Quarteroni and Valli, 1997), such equations take the form AI-I + w i B H + E H : A dp° V - D T + D T w + MhIN dt K T w : G ( T - Tw) + C ~ e where T and Tw are the fluid and metal nodal temperature vectors, ~e is the nodal external heat flux vector, and the matrices A, B, C, D, E, G, K and vectors V, M depend on dimensional data, on the fluid properties and on the specific finite element method chosen (applied to the interpolating functions otj and on the weighting functions used for computing the residual over the whole domain 0 < x < L). Details are omitted for brevity and can be found in Lunardi (1999), but it is important to note that weak boundary conditions do not constrain the first and last element of H to equal the terminal enthalpies. Moreover, the matrix E and vector M enforce the boundary condition on the side where the fluid enters the heat-exchanger segment (with enthalpy hiN). As such, they have only one non-zero element. The position of this element depends on the sign of the flow rate, but even despite this, the vector equations are affected only by the input and output structure, while the state variables (vector H ) remain the same and cannot undergo change. Assuming a positive direction flow that from the 'i' terminal to the 'o' terminal, and indicating by m and e the non-zero

Modelling of power plants

31

elements of M and E, this means that ifw >0 hlN=hi,

M=[m

0

...

0]', E = d i a g ( e , 0 . . . . . 0), h o = H ( N )

while if w < 0 hlN=ho,

M=[0

m]', E = d i a g ( 0 . . . . . 0, e), ho = H ( 1 ) .

...

Hence, this model can be implemented seamlessly in any language assuming a conditional equation construct like the i f clause in Modelica. It is also worth noting that, with the adopted approach, a heat-exchanger segment uses a coarse approximation for the pressure and flow-rate profiles along the tube (one node for each segment) and a more accurate approximation for the enthalpy/temperature profiles. This really corresponds to the nature of the process dynamics, where hydraulic phenomena in heat exchangers are characterised by a much simpler spatial distribution with respect to thermal phenomena. The external flux vector ~ e is one of the variables included in the dHT (Figure 2.3); a convenient correlation as a function of the external gas properties and, possibly, of the wall temperature is naturally incorporated in the model of the gas zone corresponding to the heat-exchanger segment. A possible Modelica formulation of the model is given by the following script: model H e a t E x c h a n g e r S e g m e n t parameter Length parameter Area parameter Density parameter SpecificHeat parameter HeatXferCoeff parameter FrictionCoeff parameter Integer parameter Length parameter Acceleration

L,omegai,omegae; Ai,Aw; row; cw;

gammai; Cf; N=I; heightProfile[N];

g; (vectorSize=N);

dHT

Wall

THT

Pressure

Inlet,Outlet; pi,po;

MassFlowRate

wi,wo;

Enthalpy

Temperature

hi,ho,H[N],hIN; T [N] ,T w [N] ;

HeatFlux

Phie[N];

SpecificVolume V[N]; Real

k,m,e;

Real

A[N,N] ,B [N,N] ,C[N,N] ,D [N,N], E IN,N] ,G [N,N] ,K[N,N] ,M[N] ;

equation

Expression ofvec~rsand matricesdependingontheFE me~odchosen(Lunardi, 1999). TW

= Wall.tempProfile;

Phie

= Wall.heatFluxProfile;

pi wi hi

= Inlet.p; = Inlet.w; = Inlet.h;

k

= L*Cf*omegai/(2*Ai^3);

po wo ho

= Outlet.p; = -Outlet.w; = Outlet.h;

Thermalpower plant simulation and control

32

FunTheta

(po, H) * d e r (po)

= wi-wo+FunGamma

po-pi+g*L*FunPsi(po,H,heightProfile) A*der if

(H) + w i * B * H + E * H

wi>0

else

hIN=

then

hIN=

ho;

M[I]

= A*der hi; =

=

0;

(po) * V - D * T + D * T w + M * h I N ;

M[I] O;

(po, H, d e r (H)) ; + k*wi*abs(wi)*FunVtilde(po,H)

M[N]

= m; = m

M[N!

=

0

; E[I,I]

; E[I,I] =

0;

= e;

E[N,N]

E[N,N] = e

; h

=

0

; ho

= H[N];

= H[I];

end i f ; K*der(Tw)

= G*(T-Tw)+C*Phie;

end H e a t E x c h a n g e r S e g m e n t

;

Note that the parameters used for the vector expansion (like N in this case) must be assigned a (default) value in the prototype models; this value can then be changed when instantiating the model. For completeness it must be said that some modelling languages (e.g. gPROMS, 1998a,b) provide native support for partial differential equations. In such cases it is possible to define a variable over one or more continuous spatial coordinates (in gPROMS this is termed a d i s t r i b u t ion domain) and write equations in their partial differential form (using constructs like the partial clause in gPROMS). In these languages, the choice of spatial discretisation is made by the user separately from the model. The models presented herein could be implemented in such languages by convenient redefinition of the distributed terminals. In the presented script the heat transfer coefficient )4 has been considered a parameter. Accurate modelling may require that it be considered as a variable, computed from empirical correlations. These can be implemented as functions if required, since the data needed for calling these functions are the fluid properties and some geometrical data, which are available in the model. In the heat-exchanger segment script, the parameter N determines the length of the vectors used for spatial discretisation, while h e i g h t P r o f i 1 e is passed to the F u n P s i function implementing 7t as defined in (2.14) and represents the tube height profile. Moreover, F u n T h e t a , FunGamma and F u n V t i l d e implement 0 , F and as defined in (2.13) and (2.14). In steam generation, it is very important to work with two-phase flow heat transfer, because the evaporator is often the core of the power generation. In the forced convection regime (which is generally applicable to boiler evaporators), two possible models are applicable to power plant simulation: (a) (b)

a flow model where the vapour and liquid phase velocities vv and VLare assumed identical (vv = vL); called a fully homogeneous model; a flow model where the vapour and liquid phase velocities may be different but related by a static factor depending on the fluid conditions; this model is also called a slip model (vL = svv) or drift model (rE = vv - VD), where the slip s or the drift velocity VD are given by suitable correlations (Collier, 1981).

For high-pressure evaporations model (a) is often acceptable: in this case the twophase flow representation takes the same form as system (2.6)-(2.9), with suitable definition of the density and enthalpy of the two-phase mixture. A non-trivial aspect of two-phase flow is the evaluation of heat transfer through the boundary layer (Collier, 1981), because heat transfer is heavily affected by the flow regime. Empirical correlations are available for typical conditions, but the variety of

Modelling of power plants

33

situations is very large. For boiler dynamic modelling, it is often acceptable that the heat transfer coefficient - to be used in equation (2.10) - is so large as to assume, in equation (2.9) that, 0Tw

dTsat dp

Ot

dp dt

where Tsat(p) is the saturation temperature of the fluid depending on the pressure p. This allows the elimination of Tw and of the corresponding equation. Of course, in this case the evaluation of Yi is not necessary. 2.3.2.2

Steam drum

A model of the steam drum is useful for circulation boilers but is also applicable to other components where the vapour and the liquid phase interact within a large volume (for instance, the deaerator). A typical steam drum is equipped with the following fluid inlets and outlets (Figure 2.9): • • • •

feedwater inlet wf (usually subcooled liquid) two-phase mixture inlet Wr (coming from the risers) (nearly) saturated steam outlet Wv slightly subcooled water outlet wd (to downcomer tubes).

The mixture flow Wr coming from the risers, with a steam quality of Xr, separates into a nearly saturated steam flow w vt (with steam quality x~) and a saturated water flow (Wr - w~). As the flow rates coming from the risers and from the feedwater are considerable, interaction between the two phases at the separation surface turns out to have a negligible effect (Leva et al., 1999). With this assumption of perfect phase segregation and the further approximations that the pressure is uniform, that the heat flux to the wall is negligible and that each phase is well stirred, the model equations

wf

Figure 2.9

Steam drum component

Thermal power plant simulation and control

34

can be written as follows: , Xr tOv =tOr-57

(2.15)

Xv

dMv , dt -- wv - Wv dEv

dt

dM~ dt dEl dt

!

l

= wvh v -

(2.16)

(2.17)

wvhv

= (Wr - Wtv) + w¢ - Wd

(2.18)

W'v)hls + wfhf

(2.19)

(Wr

Wdhl

where Mv = Pv Vv is the steam mass (Pv and Vv are the steam density and volume), E v = V v ( p v h v - p ) is the total steam energy (hv is the steam enthalpy and p the pressure in the cavity), h~v = hvs - (1 -XPv) (hvs - his) is the enthalpy of W'v (hvs and his are the saturation vapour and liquid enthalpies), Ml = p l ( V - Vv) is the liquid mass (V is the total volume of the drum and Pi the liquid density), E1 = ( V - V v ) ( p l h l - p ) is the total liquid energy (hi is the liquid enthalpy) and ht is the feedwater enthalpy. Equations (2.15)-(2.19) represent the steam separation (x~ is a parameter), mass conservation in the steam volume, energy conservation in the steam volume, mass conservation in the liquid volume and energy conservation in the liquid volume. The model has four state variables: p, hv, hi, Vv. The parameter X~vcharacterises the separation efficiency and should be given a value in the interval 0.97-1.0 according to the design specification. Experiments (Leva e t a l . , 1999) show that steam wetness may have a non-negligible effect on the superheated steam temperature; unfortunately, it is quite difficult to correlate its value to the drum conditions (e.g. the unit load), so setting x v' at its nominal value is generally an appropriate choice. Of course, Pv, Pl, hvs, his are computed using steam tables with entries p and hv or hi. A possible Modelica script for the drum model is as follows: model S t e a m D r u m parameter parameter

Volume

v;

Quality xvprime;

THT

FeedWaterInlet,SteamOutlet;

THT

RisersInlet,DowncomersOutlet;

Mass MI,Mv; Volume Vl,Vv; MassFlowRate wf,wr,wd,wv,wvprime; Density rol,rov, rols,rovs; Pressure p; Enthalpy hf,hr,hd,hl,hv,hvprime,hls,hvs; Quality

xr;

Energy EI,Ev; equation wf = F e e d W a t e r I n l e t . w ; wr = RisersInlet.w; wd = - D o w n c o m e r s O u t l e t . w ; wv = -SteamOutlet.w; hf = F e e d W a t e r I n l e t . h ; hr = RisersInlet.h; hd = DewncomersOutlet.h ; hv = S t e a m O u t l e t . h ; p

=

FeedWaterInlet.p

; p

p

= DowncomersOutlet.p

; p

xr =

(hr-hls)/(hvs-hls);

= =

RisersInlet.p; SteamOutlet.p;

wvprime

=

wr*xr/xvprime;

Modelling of power plants der(Mv)

= wvprime-wv;

der(Ev)

der(Ml)

=

der(El)

(wr-wvprime)+wf-wd;

Mv

= Vv*rov;

V

= Vv+Vl;

hvprime rov rovs= hvs end

Ev

= Vv*(rov*hv-p);

M1

35

= wvprime*hvprime-wv*hv; =

(wr-wvprlme)*hls+wf*hf-wd*hl;

= Vl*rol;

E1

= Vl*(rol*hl-p);

= hvs-(l-xvprime)*(hvs-hls);

= SteamPHtablesDensity(p,hv); SteamSATtablesDensity(p,"vapour"); = SteamSATtablesEnthalpy(p,.vapour.);

rol

= SteamPHtablesDensity(p,hl);

rols

= SteamSATtablesDensity(p,"liquid");

hls

= SteamSATtablesEnthalpy(p,"liquid");

SteamDrum;

2.3.2.3

Control valve

A control valve (see Figure 2.10) is a 'small-volume' component, for which storage of any quantity can be neglected. Its model will therefore be expressed by algebraic equations, which in fact are: ho = hi

(2.20)

w = f(Pi, Po, hi, y)

(2.21)

where hi and ho are the inlet and outlet enthalpies, Pi and Po the upstream and downstream pressures, w the mass-flow rate and y the valve stroke. The flow equation (2.21) can be written according to a recommended intemational standard, for instance the Instrumentation, Systems and Automation Society (ISA Handbook of Control Valves, 1971), which generally covers all the possible fluid states, flow conditions and valve types. These international standards are conceived to supply formulas applicable for valve sizing, so that their application to the flow equations is affected by the following limits: • •

prediction may be a little conservative in general and even crude in those conditions where the valve should not operate (e.g. cavitation) flow prediction at partial valve opening may not be very accurate.

However, there is no practical alternative to the use of sizing equations, except for those cases where specific experimental data are available. For simulation, the robustness of the valve model at low flow rate is very important because it is often necessary to simulate conditions where the valve enters no-flow conditions. Since the flow equation (2.21), derived from sizing formulas, does not consider this case, it is necessary to modify the equation to extend its applicability down to w --+ 0, though for very small values of w the accuracy is not important. This measure can also be combined with the representation of a typical device which prevents the valve from undergoing reverse flow. The modification of the flow equation

Pi

~

Po

hi

ho w

Figure 2.10

Control valve component

36

Thermal power plant simulation and control

at low w is required to avoid discontinuity of the equation Jacobian when w ~ 0. The Modelica script of the control valve may be as follows, where the parameters are the valve Cvmax and the integer identifier CharTD used for selecting the valve characteristics: model C e n t r o l V a l v e p a r a m e t e r Real Cvmax; parameter Integer CharID; THT Inlet,0utlet; Real y; equation Inlet.h = Outlet.h; I n l e t . w = -Outlet.w; Inlet.w = V a l v e C h a r a c t e r i s t i c ( I n l e t . p , O u t l e t . p , I n l e t . h , y , C v m a x , C h a r I D ) ; end ControlValve;

2.3.2.4

Header

The typical situation is depicted in Figure 2.11. There are n inlet flow rates, which are supposed to mix perfectly, and m outlet flow rates. Simplifying assumptions are that the pressure p is uniform, as is the fluid enthalpy. Energy storage in the metal body may be relevant. The model is built by mass and energy conservation for the finite volume V of the header: dh

do

n

p V - - - V ---5-~ = Z dt dt

wu(hij -- h)

+ v S ( T w - T)

(2.22)

j=l dTw

pwVwcw-dt

--

g (3t0)_~P-~dhq- V (~pp) -~dP= ~ h

(2.23)

y S ( T w - T)

j=l

m Woj

WiJ -- Z

(2.24)

j=l

where the notation is analogous to that of the previous models. Head losses due to inlet and outlet effects may be incorporated in the model of the upstream and/or

wi,

wi2

W

[] [] [] [] ~//////////////~///////////////A

I wol Figure 2.11

Header component

l worn

Modelling of power plants

37

downstream tubes. Equations (2.22)-(2.24) describe the fluid energy, metal body energy and fluid mass conservation, respectively. The Modelica script of the model may be as follows: model H e a d e r parameter

Area

S;

parameter

Volume

V,Vw;

parameter

SpecificHeat

cw;

parameter parameter parameter parameter

Density

row;

HeatXferCoeff

gamma;

Integer n=l; Integer m=l;

THT

Inlets[n],Outlets[m];

MassFlowRate

wi In] ,wo [m] ;

Pressure

p;

Density

ro;

Enthalpy

h, hi [n] ,h i m i n u s h [n] ;

Temperature

T,Tw;

Real

drodh,drodp;

equation for i in l : n loop end for; for i in l : m l o o p end for; ro*V*der(h)-V*der(p) row*Vw*cw*der(Tw) V*drodh*der(h)

wi [i] = I n l e t s [i] .w;

p = I n l e t s [i] .p;

hi[i]

= I n l e t s [i] .h;

himinush[i]

wo[i]

= - O u t l e t s [ i ] .w;

= I n l e t s [i] .h-h;

p = O u t l e t s [ i ] .p;

= sum(ElementwiseProd(wi,himinush))

h = O u t l e t s [ i ] .h;

+ gamma*S*(Tw-T);

= -gamma*S*(Tw-T);

+ V*drodp*der(p)

= sum(wi)-sum(wo);

T = SteamPHtablesTemperature(p,h); ro = SteamPHtablesDensity(p,h); drodh

= SteamPHtablesDdensityDenthalpy(p,h);

drodp

= SteamPHtablesDdensityDpressure(p,h);

end H e a d e r ;

In this script, ElementwiseProd is a function requiring two vectors as input and returning a vector formed by their element by element product, S is the header inner surface and Vw the metal wall volume. 2.3.2.5

Pump

Storage of mass and energy are negligible and the model is expressed by algebraic equations. With reference to the notation of Figure 2.12 the model is formed by the

Pij~, hi Figure 2.12 Pumpcomponent

Po ho

38

Thermal p o w e r plant simulation and control

following equations (Dixon, 1975; Perry and Green, 1985): Po ----Pi + Pp

(2.25)

Pp = f I ( ~ , q)

(2.26)

rH = fii(S-2, q)

(2.27)

where pp is the pump head (Pi and po are the inlet and outlet pressures), £2 is the pump shaft speed, q the volumetric flow rate (q = w / p ) and rH is the resistant hydraulic torque applied by the fluid to the shaft, while f l ( ~ , q) and fix(12, q) are suitable functions derived from the manufacturer's design data. Equations (2.26) and (2.27) are termed the first and second characteristic equations. It is also possible to include the total rotor inertia J in the pump model: dl2 rH = rM -- J - dt

(2.28)

where rM is the active motor torque. Modelling of the pump drive in detail may be complex, because the speed of feedwater pumps is often regulated by an oleodynamic coupling, which is not easy to model. A possible simplification can be made when the pump is subject to feedback speed control, by assuming that the angular speed £2 is nearly equal to its set-point. To complete the model it may be necessary to include an energy balance for the fluid volume; assuming that heat losses through the pump body are negligible, one obtains: w(ho - hi) ---- %'H -(-2 (2.29) which allows the computation of the outlet enthalpy. The model can be given a more efficient formulation by using dimensionless quantities and/or introducing the pump characteristic angular speed. A useful approximation can be obtained for centrifugal pumps by assuming a parabolic characteristic equation and introducing suitable dimensionless numbers (Dixon, 1975). A Modelica script for the model pump may be as follows (a boolean parameter decides whether the rotor inertia must be included or not and an integer parameter is used for selecting the characteristic functions): model P u m p parameter parameter parameter

I n e r t i a J; Boolean IncludeRotInertia; Integer CharFunID; Inlet,Outlet; Shaft; tauH; q; ro;

THT MT Torque VolumetricFlowRate Density equation Outlet.p = Inlet.p+ PumpCharFunI(Shaft.omega,q,CharFunID); q = Inlet.w/ro; ro = S t e a m P H t a b l e s D e n s i t y ( I n l e t . p , I n l e t . h ) ; Inlet.w = -Outlet.w; tauH = PumpCharFunII(Shaft'°mega'q'CharFunID) ;

Modelling of power plants

39

if I n c l u d e R o t I n e r t i a t h e n t a u H = S h a f t . t a u - J * d e r ( S h a f t . o m e g a ) ; else tauH = Shaft.tau; e n d if; Inlet.w*(Outlet.h-Inlet.h) = tauH*Shaft.omega; e n d Pump;

2.3.3 2.3.3.1

The boiler's air-gas circuit Gas zone

The gas zone was introduced in Figure 2.3. Mass and energy storage within the gas volume are generally negligible because of the very low density, so that the model is given by the following set of algebraic equations, where the generic case of n heat transfer surfaces is considered:

O)ejd~ej dx

wg(hgi - hgo) =

(2.30)

j=l

q~ej = Yej(Tg - Twj),

j = 1. . . . . n

~g = ~rg~ + (1 - z)rgo

(2.31)

(2.32)

where tOg is the gas mass flow rate, hg i and hgo are the inlet and outlet gas enthalpies, q~ej(t, x) is the heat flux from the gas to the j-th tube bundle at its abscissa x, O~ej the total perimeter of the j-th tube bundle, I"g is the 'average' gas temperature in the zone, ~. is a weighting parameter, while Tgi and Tgo are the gas inlet and outlet temperatures, Twj (x, t) is the j-th wall temperature and Yej is the heat transfer coefficient between the gas and the j-th tube bundle. Notice that equation (2.30) represents gas energy conservation. Evaluation of Yej is a complex function of the gas properties and the bank geometry; it can be obtained from empirical correlations set up by boiler manufacturers (Incropera and De Witt, 1985; Stultz and Kitro, 1992) and accounts both for convection heat transfer and intertube radiation. The gas pressure is not included in the model as it is generally fair to assume that it is atmospheric pressure; only for certain problems (e.g. furnace pressure control studies) is it necessary to consider pressure dynamics. In that case, since the mass storage is essentially due to the furnace, the gas zone model may simply be completed by a head-loss equation: Pgi -- Pgo =

k w~

(2.33)

Pg where Pgi and Pgo are the inlet and outlet pressures,/Sg is the average gas density and k is a suitable constant (k ~ 0 is often acceptable because head losses are essentially concentrated in gas dampers and fans). The Modelica script for the gas zone model may be as follows: model GasZone parameter parameter parameter parameter

Integer Integer Length GeomData

nTubeBundles= 1 ; tbSizes [nTubeBundles] =ones (nTubeBundles) ; omegae [nTubeBundles] ,L [nTubeBundles] ; g e o m e t r y D a t a [nTubeBundles] ;

40

Thermal p o w e r plant simulation and control

parameter Real lambda; dHT tubeBundles[nTubeBundles] (vectorSize=tbSizes); THT Inlet,Outlet; Temperature Tgtilde; H e a t X f e r C o e f f gammae [nTubeBundles]; HeatFlow IntOfPhieOmegaDx[nTubeBundles]; equation for j in i: n T u b e B u n d l e s loop tubeBundles[j].heatFluxProfile = gammae[j]*(Tgtilde*ones(tbSizes[j])-tubeBundles[j].tempProfile); gammae[j] = G a m m a F u n ( I n l e t . w , T g t i l d e , g e o m e t r y D a t a [ j ] ) ; I n t O f P h i e O m e g a D x [j] = o m e g a e [ j ] * L [ j ] * A v e r a g e ( t u b e B u n d l e s [ j ] . h e a t F l u x P r o f i l e ) ; end for; Inlet.p = Outlet.p; Inlet.w = -Outlet.w; Inlet.w*(Inlet.h-Outlet.h) = sum(IntOfPhieOmegaDx); Tgtilde = l a m b d a * G a s P H T a b l e s T e m p e r a t u r e ( I n l e t . p , I n l e t . h ) + (i l a m b d a ) * G a s P H T a b l e s T e m p e r a t u r e ( O u t l e t . p , O u t l e t . h ) ; end GasZone;

In this script G e o m D a t a is a record type (a feature provided by any language) used for storing geometry data and provided as a parameter to the function GammaFun computing Yej in equation (2.31). Also, A v e r a g e is a function requiring a vector argument and returning its average. 2.3.3.2 Furnace zone A generic furnace zone, introduced in Figure 2.4, may be depicted as in Figure 2.13. Assuming a uniform gas temperature in the zone, a grey gas approximation, infinitely fast combustion kinetics and a diffusion heat radiation mode (Fryling, 1966; Hottel and Sarofim, 1967; Glassman, 1977), the following equations model the furnace zone:

dMg dt

-- toi -- tOo + tOf q- Wa q- Wr

(2.34)

dEg dt

-- toihi - woho + tofhf + Qc + toaha + wrhr - Oi - Qo - Qw

(2.35)

where Qc is the heat rate due to the combustion reaction, Qi is the radiation heat rate to the upstream zone, Qo is the radiation heat rate to the downstream zone and Qw is the total heat rate released to the wall, while hi, ho, ha and hr are the enthalpies of wo (gas flowout, upwards) ~- . . . . . . . . . . . . . . . . . . . . . . .

wf (fuel flow),',,

.w.~k,,N~! a / ~

Wa(air fl°w): ,

~radiatio

,,

Wr(recirculatinggas fl°w):l,, : S

/ /+~ .............

Wall or ~ walls

~

l Gas] c_onv_ectlon_I_

Losses .,...~/2 wi (gas flow in, frombottom) Figure 2.13

Furnace zone component

Modelling of power plants

41

the corresponding flows. Equations (2.34) and (2.35) represent the mass and energy balances, respectively. If an ideal reaction is assumed, Qc can be simply computed by the following equation:

Qc = min

( Wa) tOf/-/f, -~-s nf

where Hf is the fuel calorific value and )~s the stoichiometric ratio. To interface the model with the i n t e r a c t i o n s modules (see Figure 2.4), it is necessary to estimate the flame radiation temperature Tg. There are various empirical correlations to use for relating Tg to the inlet and outlet enthalpies, hi and ho, and possibly to the heat release Qc. The matter is quite complex and strongly based on manufacturers' data. However, if the zone is rather narrow, one may simply assume Tg = (/] + To)/2,/] and To being the inlet and outlet temperatures. Neglecting gas composition variations as discussed in section 2.3.1.2, the Modelica script implementation may be as follows: model F u r n a c e Z o n e parameter Real parameter ChalorificValue parameter Volume THT

lambdas; Hf; V;

FuelInlet,AirInlet,RecGasInlet;

THHT

GasFromBottom,GasUpwards;

HT

Wall;

Mass

Mg;

MassFlowRate

wi,wo,wf,wa,wr;

Enthalpy

hi,ho,hf,ha,hr;

Energy

Eg;

Pressure

p;

Temperature

Tg;

HeatFlow

Qc,Qi,Qo,Qw;

equation wi

= GasFromBottom.w

wa

= AirInlet.w;

hi

= GasFromBottom.h

ha

= AirInlet.h;

p p Tg

; wo

wr

; ho

hr

= FuelInlet.p;

p

= GasUpwards.h;

= AirInlet.p; p

wf

=

FuelInlet.w

;

hf

= FuelInlet.h

;

p

= RecGasInlet.p;

= GasUpwards.p;

Tr;

Tg

der(Mg)

= wi-wo+wf+wa+wr;

der(Eg)

=

Mg

-GasUpwards.w;

= RecGasInlet.h;

= GasFromBottom.p; = GasFromBottom.

=

= RecGasInlet.w;

= GasUpwards.Tr;

Tg

= Wall.Tr;

wi*hi-wo*ho+wf*hf+Qc+wa*ha+wr*hr-Qi-Qo-Qw;

= V*GasPTtablesDensity(p,Tg);

Eg

= Mg*GasPTtablesEnthalpy(p,Tg)-p*V;

Tg

=

Qc

=

Qi

= GasUpwards.Q;

Qw

= Wall.Qw;

(GasPHtablesTemperature(p,hi)+GasPHtablesTemperature(p,ho))/2; min(wf*Hf,wa/lambdas*Hf); Qo

= GasFromBottom.

Q;

end F u r n a c e Z o n e ;

If one cannot neglect the composition variations, it is necessary to extend the affected terminals (in the case of the F u r n a c e Z o n e model, the THHTs and the THTs) to

42

Thermal power plant simulation and control

recognize fluid composition, typically expressed as a vector of mass or molar fractions. Of course, models will then have to include the appropriate balance equations for the relevant species. The Modelica script is complemented by the following two additional models. 2.3.3.3

Zones interaction

Model equations are given by the system (2.1)-(2.5); the coefficient K in equation (2.5) can be computed according to empirical correlations (Hottel and Sarofim, 1967). The Modelica script (treating K as a parameter for simplicity) may be as follows: model

ZonesInteraction

parameter Real K; THHT Left, Right ; equation Left.w+Right.w = 0; L e f t . p - R i g h t . p = 0; Left.h-Right.h = 0; L e f t . Q + R i g h t . Q = 0; Left.Q = K*(Left.Tr^4-Right.Tr^4) ; end ZonesInteraction;

2.3.3.4

Gas-wall interaction

The following model equation accounts for radiation and convection heat transfer from gas to wall: Qw = K w ( T 2 - 7"4w)+ ycSw(Tg - Tw)

(2.36)

where Sw is the contact wall surface, while the radiation coefficient Kw and the convection coefficient Yc are given by empirical correlations (Stultz and Kitro, 1992) relating them to the zone geometry and gas properties. In equation (2.36) Tw denotes the average wall temperature: this approximation is not critical because the wall temperature is generally quite uniform and, however, much lower than Tg. The Modelica script may be as follows: model G a s W a l l I n t e r a c t i o n parameter Real Kw; parameter Surface Sw; parameter Integer N=I; parameter H e a t X f e r C o e f f gammac; HT Gas; dHT Wall (vectorSize=N); Temperature Tg,Twtilde; equation Twtilde = A v e r a g e ( W a l l . t e m p P r o f i l e ) ; Tg = Gas.Tr; Gas.Qw = Kw*(Tg^4-Twtilde^4)+gammac*Sw*(Tg-Twtilde); for i in I:N loop Wall.heatFluxProfile[i] = Gas.Qw/Sw/(N-l); end for; end GasWallInteraction;

Modelling of power plants 2.3.3.5

43

Fan

The model is conceptually similar to that of a pump: we use an algebraic model consisting of the first and second characteristic equations. In general, however, fans are operated at rated speed, while the flow is regulated by inlet vanes. So, using the same symbols of Figure 2.12, the model equations are: Po = Pi nt- Pp

(2.37)

pp = fl(~QN, q, O)

(2.38)

rH = f[[(~2N, q, 0)

(2.39)

where S2N is the nominal angular speed and 0 the orientation angle of the inlet vanes. To extend the model (2.37)-(2.39) to variable speed conditions (e.g. startup), one has to keep in mind that q, pp and rH are proportional to I2, ~ 2 and Y22, respectively. Rotor inertia and enthalpy increases can be taken into account by equations (2.28) and (2.29), or suitable approximations. The theory of similarity is generally not applicable: the characteristic equations are then derived from manufacturers' data. 2.3.3.6

Miscellanea

To complete the component library for the air-gas circuit we need to model at least the following elements: • • • • •

adiabatic gas duct (by mass, energy and momentum balances) adiabatic gas plenum (by mass and energy balance only) control damper (by a flow equation similar to a control valve) air preheater coal pulverisers.

For the sake of brevity, details of the above models are omitted here. It is only worth noting that: • •

for air and flue gas, ideal or real-gas state equations are applicable with suitable formulas or tables for the computation of gas properties; control dampers are strongly non-linear elements for which the flow characteristics need to be estimated by experimental and/or design data.

Air preheaters may be of different types; widely employed is the rotating Ljungstrrm preheater, which is a complex item of equipment characterised by considerable energy storage. Coal pulverisers are described in detail by Ferretti and Maffezzoni (1991) and Cao and Rees (1995).

2.3.4

Steam turbine

Depending on the required accuracy (especially with reference to the interaction between the turbine and the feedwater heaters through steam extraction), the turbine can be presented as a compact or more detailed representation. A reasonable trade-off,

44

Thermal power plant simulation and control

compatible with the object-oriented approach, is to structure the model according to the scheme of Figure 2.5, which, applies to all turbine sections but the control stage. Excluding the latter, a generic turbine section is constituted as a cascade of similar stages (generally reaction stages) without any extraction in between.

2.3.4.1

(Generic) turbine section

Mass and energy storage in the steam volume are negligible, so that the model consists of the following algebraic equations.

2.3.4.2

Flow equation

In this case the Stodola law (Cooke, 1985) proved to be quite accurate: W = kT~/1

-- rs2

(2.40)

where w is the mass flow rate, Pi and Pi are the upstream pressure and density, rs = Po/Pi, with Po the downstream pressure and kT is a constant (which can be derived from design and/or experimental data).

2.3.4.3

Energy equation hi - ho = (hi - hlso)r/

(2.41)

where hi and ho are the inlet and outlet enthalpies, hlso is the enthalpy that would be at the outlet if the expansion were iso-entropic and r/is the section efficiency. Of course, hlso is a function of hi, Pi, and Po. The evaluation of the section efficiency r/ might be quite complex (Salisbury, 1950), but for turbine operation at rated speed and at reasonably high load ( > 2 0 per cent) one may assume 0 -~ const.

2.3.4.4

Power output Pm = to(hi - ho)

(2.42)

where Pm is the total mechanical power transferred from the steam to the wheel. We may note that the mechanical terminal (MT) of Figure 2.5 consists of two variables, the angular speed $2 and the torque rm; of course, the computation of rm is simply given by: rm = Pm/S-2 (2.43) and the angular speed S2 is a state variable of the 'shaft' model. The possible inconsistency of formula (2.43) as ,f2 ~ 0 is naturally avoided bearing in mind that ~ ~ 0 as .f2 --+ O.

2.3.4.5

Control stage

The control stage is usually an impulse stage equipped with a set of independently operated control valves, which allow the steam flow to be admitted in full-arc or partial-arc mode. Partial arc admission is applied to ensure good thermodynamic

Modelling of power plants

45

Impulse chamber

From the boiler

To the downstream stages Valve m

Figure 2.14

Nozzle

Turbine control stage component

efficiency at partial load. To develop a model of the control stage, reference must be made to its structure, schematically shown in Figure 2.14, where it is indicated that there are m parallel lines, each one equipped with a control valve, corresponding to the m sectors into which the control stage is partitioned. At the outlet of the control stage, the steam flows coming from the different paths mix to form the total flow feeding the downstream turbine stages. A detailed model can be built by assembling elementary modules according to the scheme of Figure 2.15. Among the model objects of Figure 2.15, we must only specify that the 'nozzle and wheel sector' is, in fact, the model of an impulse turbine stage for which we may apply the modelling approach expressed by equations (2.40)-(2.43), with possible refinements for the flow equation (2.40) and for the computation of the thermodynamic efficiency r/, as nozzle conditions are more variable in the control stage with respect to the downstream stages. The model of Figure 2.15 may be replaced by a global approximate model (Maffezzoni and Kwatny, 1999), which is based on particular steam turbine design parameters. The approximate model is determined under the restriction that the control valves are moved according to a fixed opening program, activated by a master control signal; under this condition it can be proved that it is subject to quite limited errors.

2.3.5

Condensate and feedwater cycle

The principal components in the considered subsystem are the following: (a) (b) (c)

deaerator condenser feedwater heaters.

46

Thermal power plant simulation and control D

-

-

Control valve

wheel sector L_

m

_

~ ICT' ~ ~ N°zzle&~ Control wheel valve sector --

Header

Header

L_

I---

~ Control ICTI ~ ~ Nozzle& ~ wheel valve sector U +-q [___ Figure 2.15

I

Model structuring for turbine control stage

They are complex heat exchangers, whose models might also he obtained by assembling smaller model objects, for instance, the condenser is a typical tube and shell heat exchanger where condensation takes place; the tube bundle could be modelled by a heat exchanger segment interfaced to a two-phase cavity through a condensing thin layer. The interaction structure would be quite complex (especially for feedwater heaters), so that it is advisable to conceive simple models of the components (a)-(c), exploiting the standardisation of the mechanical design. To this end, it is generally required to build two types of model for feedwater heaters, to meet the two possible designs: vertical or horizontal shell heaters. The model equations are, as usual, derived from mass and energy balances applied to suitable control volumes: the detailed formulation is rather tedious and is beyond the scope of this work.

2.3.6

Gas turbine

Apart from auxiliary equipment, there are three principal components of gas turbines: the compressor, the combustion chamber and the turbine (Coen et al., 1987). 2.3.6.1

Compressor

Thanks to the very limited mass of air in the compressor volume, the model consists of two characteristic algebraic equations describing the global machine performance

Modelling of power plants

47

(Coen et al., 1987). To this aim, it is useful to introduce the following three dimensionless quantities: •

• •

the pressure ratio rp := Po/Pi between the outlet and inlet pressure; the flow number nf :-- to/pi~QD3, where w is the mass flow rate, Pi the inlet gas density, I2 the rotor angular speed and D the mean wheel diameter; the blade Mach number Mb := ~ D/~/y R Ti, where F is the ratio between the gas specific heat at constant pressure and constant volume, R the ideal gas constant and Ti the inlet gas temperature.

Then, the two characteristic equations may be written as r p - - g l (nf, Mb)

(2.44)

= g 2 (nf, Mb)

(2.45)

where r/is the compressor global efficiency, defined as hlso q-- - ho

--

--

hi

(2.46)

hi

where hi and ho are the inlet and outlet enthalpies, while hIso is the enthalpy that there would be at the outlet with an isoentropic compressor (of course hiso depends on pi, po and hi). The major problem is that, for unit simulation the functions gl and g2 are required to cover quite extended off-design conditions. They can be built as suitable interpolations of manufacturers' data, possibly validated and extended by experimental data. Simple approximations with low-order polynomials generally work only in a quite restricted operation domain. The net mechanical power transferred to the air is Pm = w(ho hi). If air composition variations due to air humidity are neglected, the Modelica script of the compressor model is as follows: -

model

Compressor parameter integer CharFunID; parameter length D; MT Shaft; THT Inlet,Outlet; Real rp,eta,nf,Mb,gammaR; Enthalpy hiS©; equation gammaR = AirPHtablesCp(Inlet.p,Inlet.h)/AirPHtablesCv(Inlet.p,Inlet.h) *(AirPHtablesCp(Inlet.p,Inlet.h)-AirPHtablesCv(Inlet.p, Inlet.h)); Mb = Shaft.omega*D*sqrt(gammaR*AirPHtablesTemperature{Inlet.p, Inlet.h)); rp = O u t l e t . p / I n l e t . p ; rp = C o m p r e s s o r C h a r F u n G l { n f , M b , C h a r F u n I D ) ; eta = C o m p r e s s o r C h a r F u n G 2 { n f , M b , C h a r F u n I D ) ; eta = { h I S O - I n l e t . h ) / ( O u t l e t . h - [ n l e t . h ) ; I n l e t . w = -Outlet.w; nf = I n l e t . w / ( A i r P H t a b l e s D e n s i t y ( I n l e t . p , I n l e t . h ) * S h a f t . o m e g a * D ^ 3 ) ; hISO = AirPStablesEnthalpy(Outlet.p,AirPHtablesEntropy(Inlet.p, Inlet.h)); end C o m p r e s s o r ;

48

Thermal p o w e r plant simulation and control

2.3.6.2

Combustion chamber

Though rather small, the combustion chamber has a certain storage volume, so that mass and energy storage should be considered. The scope of the model is generally twofold: (1) (2)

to predict the chamber outlet gas enthalpy; to predict the production of pollutant emissions (mainly NOx and CO).

While meeting scope (1) is quite easy by global mass and energy balance, modelling NOx and CO production is deeply affected by reaction kinetics and by the actual temperature field in the combustion chamber volume. For this reason, low-order, first-principles modelling does not guarantee reasonable accuracy for task (2). When both scopes (1) and (2) are relevant, a possible solution is to organise the model into two parts: a 'thermo-mechanical' part, based on global mass, momentum and energy balances, and a 'chemical' part based on non-linear interpolations (e.g. neural networks) of more detailed design or experimental data. Here, only the first part will be considered, formed by the following equations:

dt dEg dt

= tOa q- VJf -- tog

(2.47)

-- waha -Jr-wf (hf q- nf) - toghg - Q1

(2.48)

Pa - Pg = kwza

(2.49)

Pa where Wa is the total inlet air flow rate, wf is the fuel flow rate, wg the outlet combustion gas flow rate, Mg the mass of the gas stored in the combustion chamber, Eg the corresponding energy, ha the inlet air enthalpy, hf and Hf the enthalpy and the calorific value of the fuel, hg the outlet gas enthalpy, Q1 the heat losses, Pa the pressure before the air nozzles, pg the pressure in the chamber volume, Pa the density of the inlet air and k a suitable constant. Equations (2.47)-(2.49) represent the mass and energy balances and the pressure losses, respectively. In the model, it is assumed that the pressure drop is across the air nozzles and that the mass Mg and energy Eg can be evaluated from the outlet gas enthalpy: M g = VcPg

Eg = V c ( p g h g - pg) w h e r e pg is the gas density corresponding to h g , p g . It is worth noting that, since gas turbine combustion chambers are operated with a large excess of air, combustion is always complete and most of the chamber volume is close to the exit temperature. Of course, to complete the model, suitable functions or tables are required to

Modelling of power plants

49

compu~ gas prope~ies (e.g. ~mperature and density from enthalpy and pressu~); this makes the model quite complex. The Modelica script of the model can be as follows: model C o m b u s t i o n C h a m b e r parameter R e a l k; parameter CalorificValue parameter E n t h a l p y hf; parameter Volume Vc;

Hf;

THT

FuelInlet,AirInlet,GasOutlet;

Mass

Mg;

MassFlowRate

wa,wf,wg;

Enthalpy

ha,hg; pa,pg;

Pressure Energy

Eg;

HeatFlow

QI;

equation wa ha

= AirInlet.w = AirInlet.h

; wf ; hf

pa = A i r I n l e t . p

; pg

= FuelInlet.w;

wg

= -GasOutlet.w;

= FuelInlet.h; = FuelInlet.p;

hg

= GasOutlet.h;

pg

= GasOutlet.p;

der(Mg)

= wa+wf-wg;

der(Eg)

= wa*ha+wf*(hf+Hf)-wg*hg-Ql;

pa-pg

= k*wa^2/AirPHTablesDensity(pa,ha);

Mg Eg

= Vc*GasPHTablesDensity(pg,hg); = Mg*hg-Vc*pg;

Q1

= FunQloss(wa,wg);

end C o m b u s t i o n C h a m b e r ;

In this script, F u n Q l o s s is a function devoted to computing the heat losses. 2.3.6.3

Turbine

The model of the turbine is built using the same line of reasoning as that of the compressor. There is, however, a significant simplification because the first characteristic equation (2.44) can be implemented by the simple Stodola law (Cooke, 1985):

W= kT~l

p--~°)2

-- \Pal (

(2.50)

where only the constant kT is derived from design data.

2.3.7

Special problems in modelling combustion processes

Combustion of fossil fuel is a complex chemical process which involves many components either contained in the reactants or produced by the reaction itself (like CO, CO2, NOx, H20). For the case of power plant simulation, reaction kinetics can be considered so fast that all the reactions are at their equilibrium. Moreover, combustion modelling is aimed at two different scopes: (1) (2)

predicting heat release in combustion chambers; predicting pollutant concentration at the chamber outlet.

50

Thermal power plant simulation and control

For scope (1), the reactions involved are the oxidation of hydrogen and carbon, for which 'very high' equilibrium constants can be assumed, with further simplification of the model. What is generally needed is the computation of combustion gas composition and the evaluation of gas properties (see section 2.3.1.2). A crucial issue is the evaluation of radiation in a large furnace, in particular the computation of flame/gas emissivity which is due to the superposition of the non-luminous gas emissivity (due to CO2 and H20) and of the luminous soot emissivity (formed in the combustion flame), as discussed by Hottel and Sarofim (1967), Siegel and Howell (1972) and Perry and Green (1985). Since radiation depends on T 4, the correct evaluation of radiation temperature is very important: experimental validation showed (Caruso et al., 1979) that if a large furnace is modelled by 10-20 layers, gas temperatures can be predicted quite well at least at sufficiently high load. On the contrary, simple lumped parameter balances do not give reliable results for scope (2) above, because NOx production is very sensitive to local flame temperature. Empirical models combined with the first-principle models used for purpose (1) yield good results (Ferretti and Piroddi, 2001), though they need experimental tuning (e.g. neural network training).

2.4

Modelling of distributed control systems

A power plant DCS is a very complex system involving many thousands of signals and specified by hundreds of I/O diagrams collected in a CAD database. The system specification is generally expressed by functional block diagrams, based on some international standard such as IEC 1131 (1993), DIN 40719-6 (1992), DIN IEC 3B/256/CD (1999), ANSI/ISA 5.1, ANSI/ISA 88.01-1995 and many others, (www.normung.din.de and www.isa.org). The block diagrams, which concern both logic control functions and modulating control, can actually be considered as a control software specification. Because of the essential role of automation in modern power plant, the correct simulation of the DCS is necessary to assess power plant performances during the design phase. There are two possible approaches to DCS modelling: (1)

(2)

reproduce the control specification with a one-to-one correspondence of blocks (at least for the functional areas under investigation), thus using a control block library tailored to the appropriate international standard; describing the control strategy assuming a functional equivalence, i.e. replace any (complex) functional group consisting of cascaded control blocks by a global control function implementing the same control concept while ignoring equipment and instrumentation details.

In the second case, control functions may be simulated by a simpler library consisting of generic blocks (lead-lag, PID, etc.) ignoring most auxiliary signals devoted to logics, interlocks, protection and so on. Then, even the digital nature of the real control system may be not relevant, so that even the control components are treated

Modelling of power plants

51

as continuous-time dynamic systems. Such generic control components are generally available in the libraries of power plant simulation packages (www.vtt.fi; Coil et al., 1989). The approach based on functional equivalence requires the analyst to develop a subjective translation of the original control scheme into a compact functional equivalent, while respecting the process control concept. It is widely applied to check control strategies in the early stages of the design process, but the validity of the model is not ensured; implementation problems are not critical, especially because it is often not necessary to simulate events (including those related to the sampling process). Detailed modelling of control software specifications or designs is, however, very important when actual DCS verification is needed. Then, two major problems need to be tackled: (a) (b)

consider system complexity with adequate support for analysis; recognize systems that combine continuous process simulation with events, i.e. hybrid systems.

Detailed DCS modelling is typically approached in two steps: (1) (2)

build a control library consistent with the selected industrial standard; assemble block diagrams using constructs provided by the modelling language for model aggregation, possibly in the same way as CAD tools for control do.

Implementing the two-step procedure for real-size systems requires that the modelling language is equipped with control-oriented libraries and paradigms, in particular to deal with discrete-time, event-driven and logical blocks. Experience of Matlab/Simulink ® for detailed modelling and testing of a power plant DCS is reported by Carpanzano et al. (2001) and shows that this environment can be effectively customised to be consistent with a DIN standard (1992). Synchronous events that are scheduled at the simulation start are correctly processed, activating zero-time switching of discrete and logical variables while stopping continuous-time integration. Problems may arise, however, with unscheduled events. A full treatment of hybrid modelling is supported in Modelica (www.dynasim.se; www.modelica.org); however, the extension of the modelling power and generalisation to any relation-triggered event implies further effort in the model specification. As an example, the Modelica script of a sequence step, described using the functional block diagram (FBD) formalism (IEC1131-3, 1993) in Figure 2.16a, is reported in Figure 2.16b. It is worth stressing that most power plant simulation environments do not support hybrid systems modelling; in these cases the interaction between the continuous time and event driven parts (including sampled signal control systems) is to a certain extent left to the user. As an example, we may mention the solution implemented by Guagliardi et al. (2000), where a client-server architecture is provided. The continuous process simulator modelled by the specialised power plant simulation code LEGO runs with a fixed integration step and acts as a server for a Matlab/Simulink ® application where the DCS is modelled.

52

Thermal power plant simulation and control logicalSignal Info; e n d Logicalsignal; block LogicController input LogicalSignal If, I2, I3; Output LogicalSignal 01, 02; equation Ol. Info = not II.Info a n d I2.Info; 02.Info = 01. Info or I3.Info; end LogicController; connector

boolean

0!

02

13

a

b

Figure 2.16

2.5

Simple controller specified in FBD and implemented in Modelica

Application of dynamic decoupling to power plant models

In general, dynamic decoupling is applicable to dynamic system simulation when the system consists of sections characterised by different dynamics, i.e. typically a 'slow' and 'fast' subsystem. We may recognise such a situation in power plant models. For instance, in the one-phase subnet of the steam-water circuit there are state variables, such as pressures and flow rates, that are characterised by fast dynamics, and state variables, such as temperatures, that are characterised by slow dynamics. Moreover, flue gas dynamics are very fast, because the gas inertia is very small. It is known that when the system is stiff, stabilisation of the integration process may be obtained by using implicit integration methods (Brenan et al., 1989), which ensure numerical stability even for rather large integration steps. This approach may make the numerical solution quite involved because, at every integration step, a largescale non-linear system (by a Newton-like method) must be solved. However, if the number of 'fast' state variables is small with respect to the total, a more efficient solution may be obtained by decoupling the integration of the two subsystems, using an implicit method (e.g. backward Euler) for the fast part and an explicit method (e.g. forward Euler) for the slow part, according to the recursive scheme of Figure 2.17. This expedient has been applied in power plant simulators (Busi et al., 1985; Bartolini et al., 1998) and is also supported in Dymola (www.dynasim.se), where the system splitting is under the user's control. The dynamic decoupling stemming from different-scale dynamics can effectively be introduced in power plant modelling with the concept of 'weak interaction' in recognition of typical situations found in thermo-hydraulic networks: •

.

When part of a pressure net is linked to another one through a weak branch (i.e. a branch with little discharge capacity), then the two parts can be solved in two steps at any integration instant. When a pressure net contains a node with a large capacity having one inlet branch (i.e. a node characterised by a slowly varying pressure), then the net can be split into two subnets by 'freezing' the node pressure when solving that part of the net containing the inlet branch.

Modelling of power plants

53

k=k+ 1

I o' e st y.am cs I 1 o' es ow yoamic J I Figure 2.17

Recursive scheme for dynamic decoupling

In fact, the application of dynamic decoupling can be extended with the introduction of the concept of 'weak variable', which has a 'weak' dynamic participation in a certain equation, either because it is slowly varying or because it has a minor effect (Casella and Maffezzoni, 1998). In power plant modelling, dynamic decoupiing is relevant to a number of typical physical situations and can be systematically applied to split the system integration into a considerable number of small tasks, e.g. the solution of feedwater system hydraulics, flue gas hydraulics, and so on. These principles have been systematically implemented in the development of ProcSim (Bartolini et al., 1998), a process simulation environment oriented to thermohydraulic networks. Experience (Leva et al., 1999) showed that the application of these decoupling criteria requires particular care when dealing with two-phase flows (e.g. in the simulation of the circulation loop) where mass, momentum and energy balances are more tightly coupled.

2.6

Testing and validation of developed models

We consider the case where a model is developed by aggregating component representations based on first principles. A typical situation is that the model is structured into components by looking at the design flow diagrams, and each component model (CM) is either taken from a library or built by analysing the component design data. Very often it is necessary to customise, to a certain extent, a library CM on the basis of some specific feature of the case at hand. Then, we have to tackle the following problems related to 'model certification': • • •

testing intrinsic correctness of model, i.e. model correctness versus physical principles; model validation versus design data, generally only available for steady-state conditions; model validation by experimental tests, which may concern both steady-state and transient conditions.

In all the above situations, testing and validation may involve either a component, subsystem or the whole system.

54

2.6.1

Thermalpower plant simulation and control Testing intrinsic model correctness

When a powerful object-oriented modelling environment is employed, the creation of new component models or the modification of existing ones (by the mechanisms of inheritance, override and polymorphism) is quite easy. It is then very important to establish procedures ensuring that the new models respect the fundamental principles of mass, momentum and energy conservation. This can be done at the component level (aggregate models inherit this property from submodels) by equipping each CM with a switchable monitoring function devoted to automatic checks. As an example, a Modelica script may consist of two sections: one corresponding to the standard model and always active, the other computing the mass and energy of all the species and phases that are present (e.g. those of liquid and vapour in a drum) and active only when some global logic variable or parameter is set true. Note that often it is not advisable to take masses and energies as state variables, so devoting a subsidiary model section to their computation reduces the simulation effort. Once the model is equipped with this section, the correctness testing can be done at any time and in any relevant condition, for instance when the component model is part of a larger model where certain significant transient conditions may be simulated. Testing can be done during simulation, if the environment permits access to its variables in that phase, or after simulation, performing the necessary computations on the logged variables.

2.6.2

Model validation versus design data

Power plant simulation is frequently used during the late phases of plant design or during plant construction. In these cases, the sole source of information for modelling consists of design data, which may be split in two parts: (a) (b)

dimensional parameters (geometrical and physical data); steady-state design code computations, required to performance.

evaluate

plant

Moreover, the plant manufacturer has important additional knowledge about component behaviour, typically expressed by empirical or semi-empirical correlations (e.g. heat transfer correlations). For power plants, non-linearities are very important and many complex phenomena (particularly combustion and heat transfer in the furnace and through the convection banks) can be captured even in the steady-state. Thus, steady-state validation is quite significant; since design data are generally detailed and extensive (they cover plant operation in different conditions) and incorporate the best knowledge about the plant before commissioning, validation versus design data is a basic step toward model 'certification'. Thanks to their detail, design data allow validation component by component, that is the identification of the actual source of modelling errors. Cases of extensive validation by design data are reported by Castoro and Oldnati (1995) and Maffezzoni and Aime (2000). It should also be noted that using design data for validation means that component models are usually built with 'tuning knobs' expressing uncertainties about model parameters: those knobs are actually set to minimise the discrepancies between

Modelling of power plants

55

model outputs and design data. As an example, the parameterisation of the flow characteristics and efficiency curves for a gas turbine may be found in Maffezzoni and Aime (2000).

2.6.3

Model validation versus experiments

Unlike design data, experiments generally supply an incomplete set of data. The major source of experimental data is the supervision system, which is designed to record and store data in forms suitable for steady-state performance evaluation. Such data are generally sufficient for an extensive validation of the plant model in the steadystate, even though the available measurements do not allow independent validation of each component model (for instance temperatures of combustion gases are not measured in the different plant sections because of technological problems and for cost reasons). Moreover, experience shows that reconciliation of measurement data is often required when using standard instrumentation. So, it is necessary to combine information coming from design data with information coming from measurements. Unfortunately, there is no systematic method to integrate all the available information: it is difficult to properly weigh experimental measurements with respect to design computations because experiments cover the whole field of operation irregularly and measurements are incomplete. However, steady-state validation (with the inherent parameter tuning) must always precede dynamic validation, where possible. As an example, it is worth mentioning the assessment of heat balances concerning the convection part of a fossil fired boiler: • •

Design data and manufacturer's correlations lead to the formulation of gas zone models incorporating heat transfer coefficients. steady-state experimental data allow thermal balances across the different convection banks to be computed; based on these, correction (fouling) factors of the involved coefficients can be tuned.

Examples of this procedure are reported by Maffezzoni et al. (1984) and Castoro and Oldrati (1995). Once steady-state model assessment has been done, dynamic validation may consider selected plant responses for which ad hoc experiments are then performed, since process measurements are sampled at a slow rate for routine supervision purposes. So, dynamic validation of power plant models is sporadically available, normally as part of special research programmes, and concern limited parts of the plant (a few relevant variables). Two different examples are worth mentioning: the first relating to a commercial unit (Astr/3m and Bell, 1993) subject to small pseudo-random excitation and the second to a laboratory boiler to which extensive step response tests have been applied (Leva et al., 1999). It is clear that step responses are much more significant for validation because the plant dynamics are sufficiently excited, but they are very costly in commercial plant. Validation programmes are also reported also for a once-through boiler (Cori et al., 1974) and a drum boiler (Coil and Busi, 1977). One of the major problems is that open-loop tests are very critical to obtain because a boiler is not

56

Thermal power plant simulation and control

asymptotically stable and tends to move away from its equilibrium point. On the other hand, closed-loop tests do not highlight the process dynamics, being strongly dependent on control actions. In addition, dynamic measurements are rather scarce so that isolation of components for validation is impossible. So, the strong interactions among the different sections of the plant make it difficult to identify the source of plant-model discrepancies. For all these reasons, the results of dynamic model validation are quite limited for thermal power plant and also for available test databases for independent model validation. From the reported experience it may be inferred that pressure, level and load dynamics are well reproduced by large-scale modular models, while more problems have been found in the validation of steam temperature dynamics. Areas substantially lacking in validation of boiler dynamics modelling are the behaviour of furnaces at low loads (Kwatny and Bauerle, 1986) and the behaviour of drum level at very low loads, with special emphasis on its stability (Kwatny and Berg, 1993).

2.7

Concluding remarks and open problems

Modelling by component for power plants has been greatly enhanced by objectoriented techniques based on non-causal model formulation and model connection through physical ports. Though many existing simulation codes treating power plant (Carpanzano etal., 1999) adopt a model structured approach oriented to components, the underlying modelling language suffers from the following drawbacks: • •

component models are neither inspectable nor assignable in descriptive form; hybrid systems modelling is not supported in a general and rigorous form.

Emerging standards in object-oriented modelling (such as Modelica, which has been assumed herein) overcome the above drawbacks, though application libraries are not yet available for power plants. For that reason, we have outlined here the basic principles by which a component library can be developed, and aggregation to form subsystems can be used. Control systems are also considered with the aim of facing real-size control engineering problems based on two key issues: adherence to widely accepted standards (e.g. IEC 1131 and 1499) and proper consideration of the hybrid nature of the control-process combination (which is essential when control system functionality has to be tested). Further investigation and development is required on the following aspects: •

•

•

full integration between lumped-parameter and distributed parameter modelling, particularly with reference to the complex heat exchangers employed both in conventional and heat recovery boilers; modelling of pollutant production (NOx, CO, etc.) in furnaces and combustion chambers, for which simple zero-dimensional models based on first principles fail; improvements in symbolic and numerical techniques to efficiently deal with hybrid systems and to exploit dynamic decoupling in the simulation of large-scale power plant models.

Modelling of power plants

57

For aspects peculiar to an engineering environment (crucial to enable modelling and simulation for engineering practice), we may observe that modelling and simulation environments are generally not equipped to efficiently manage large amounts of data, as is necessary when developing a power plant project in any phase of its life cycle. A preliminary effort has been made with the prototype environment MOSES (Maffezzoni and Girelli, 1998), which combines object-oriented modelling and database management, but the state of the art is far from satisfactory. Finally, much attention has been given here to object-oriented modelling languages (e.g. Modelica) and to software tools supporting them. However, to the authors' knowledge, as such languages are quite recent, there is a substantial lack of model libraries for power plant applications. This could be the scope for international cooperation to eliminate this dearth by developing libraries in a non-proprietary language to be shared by interested contributors.

2.8

References

AIME, M. L., and MAFFEZZONI, C.: 'Modelling and simulation of combined lumped and distributed systems by an object-oriented approach', Mathematics and Computers in Simulation, 2000, 53, (4-6), pp. 345-351 APROS home page, www.vtt.fi. /~STROM, K. J., and BELL, R. D.: 'A nonlinear model for steam generation process'. Preprint 12th IFAC World Congress, 3, pp. 395-398, Sydney, 1993 BARTOLINI, A., LEVA, A., and MAFFEZZONI, C.: 'A process simulation environment based on visual programming and dynamic decoupling', Simulation, 1998, 71, (3), pp. 183-193 BRENAN, K. E., CAMPBELL, S. L., and PETZOLD, L. R.: 'Numerical solution of initial-value problems in differential algebraic Equations' (North-Holland, Amsterdam 1989) BUSI, T., COLOMBO, P., and DE MARCO, A.: 'An efficient modelling technique for power plant training simulators: the FAST method'. Proceedings of 1 lth IMACS World Congress, Oslo 1985 CAO, S. G., and REES, N. W.: 'Fuzzy logic control of vertical spindle mills'. IFAC Symposium on Control of Power Plants and Power Systems; Cancan 1995 pp. 49-55 CARPANZANO, E., FERRARINI L., and MAFFEZZONI, C.: 'Simulation environments for industrial process control'. Proceedings ESS '99, Erlangen-Nuremberg, 1999, pp. 443-450 CARPANZANO, E., FERRARINI L., and MAFFEZZONI, C.: 'Modular testing of logic control functions with Matlab'. Proceedings 13th European Simulation Symposium, Marseille 2001 CARUSO, F., DE MARCO A., and QUATELA, S.: 'One-dimensional mathematical model of a furnace'. Technical report ENEL 372053-14, 1979 (in Italian) CASEAU, P. P., GODIN, P., and MALHOUITRE, G.: 'Numerical simulation of a steam generator'. Journ~es de I'AIM, Likge, 1970 (in French)

58

Thermalpower plant simulation and control

CASELLA, E, and MAFFEZZONI, C.: 'Exploiting weak interactions in objectoriented modelling', EUROSIM- Simulation News Europe, 1998 22, pp. 8-10 CASTORO, M., and OLDRATI, S.: 'Heat recovery boiler simulator based on decoupling criteria'. Laurea thesis, Dipartimento di Elettronica e Informazione, Politecnico di Milano, 1995 (in Italian) CHIEN, K. L., ERGIN, E. I. LING, C., and LEE, A.: 'Dynamic analysis of a boiler'. Trans. ASME, 1958 80, pp. 1809-1819 COEN, H., ROGERS, G. E C., and SARAVANAMUTTOO, H. I. H.: 'Gas turbine theory, (Longman, Harlow, 1987, 3rd edn.) COLLIER, J. G., 'Convective boiling and condensation' (McGraw-Hill, New York, 1981, 2nd edn.) COOKE, D. H., 'On prediction of off-design multistage turbine pressures by Stodola's ellipse',. Journal of Engineering for Gas Turbines and Power, 1985, 107 pp. 596-606 CORI, R., and BUSI, T. 'Parameter identification of a drum boiler power plant'. Proceedings 3rd Power Plant Dynamics, Control and Testing Symposium, Knoxville, 1977 CORI, R., DE MARCO, A., GARBOSSA, G., LABANTI, E, and SKULL, G.: 'Validation and application of a digital-computer mathematical model, for the simulation of the static and dynamic behaviour of a steam generator'. Proceedings LXXV Annual Meeting of the Italian Electrotechnical and Electronic Association, 1974 (in Italian) CORI, R., SPELTA,S., GUAGLIARDI, G. A., PRETOLANI, E, MALTAGLIATI,P., and PERSICO, F.: 'The LEGOCAD system: a computer aided power plant modelling environment. Proceedings AEI National Symposium, Lecce, 1989 DIN 40719-6, 'Diagrams, charts, tables; rules for function charts'. DIN, 1992 DIN IEC 3B/256/CD, 2nd Edition: 'Specification language GRAFCET for sequential function charts', DIN, 1999 DIN standards home page, www.normung.din.de DIXON, S. L., 'Fluid Mechanics, thermodynamics of turbomachinery' (Pergamon Press, Oxford, 1975) DYMOLA home page, www.dynasim.se ELMQVIST, H., CELLIER, E E., and OTI'ER, M.: 'Object-oriented modelling of hybrid systems'. Proceedings of the ESS Symposium, Delft, 1993 ELMQVIST, H., MATTSSON, S., and Oq"I'ER,M.: 'Modelica- a language for physical system modelling, visualization and interaction'. Proceedings IEEE Syrup. CACSD, Hawaii, 1999, pp. 630-639 FERRETTI, G., and MAFFEZZONI, C.: 'Monitoring and diagnosis of a pulverization process'. Proceedings IFAC/IMACS Symposium on Fault Detection, Supervision and Safety for Technical Processes, Baden-Baden, 1991 FERRETTI, G., and PIRODDI, L. 'Estimation of NOx emissions in thermal power plants using neural networks', ASME Journal of Engineering for Gas Turbines and Power, 2001, 123, (2), pp. 465-471

Modelling of power plants

59

FRYLING, G. R.: 'Combustion engineering - a reference book on fuel burning and steam generation' (Combustion Engineering Inc., New York, 1966) GLASSMAN, I., 'Combustion' (Academic Press, New York, 1977) 'gPROMS: advanced user guide'. Technical report, Process Systems Enterprise, 1998a) 'gPROMS: introductory user guide'. Technical report, Process Systems Enterprise, 1998b GUAGLIARDI, G. A., MIGLIAVACCA, G., and SPELTA, S.: 'Simulink has a new partner: LegoPC'. Info@teoresi bulletin, June 2000 (in Italian) HOTTEL, H. C., and SAROFIM, A. F.: 'Radiative transfer' (McGraw-Hill, New York, 1967) 'IEC1131-3 programmable controllers: programming languages'. IEC TC65/SC65B, 1993 INCROPERA, E P., and DE WITT, D. P.: 'Fundamentals of heat and mass transfer' (John Wiley, Chichester, 1985, 2nd edn.) ISA: 'ISA handbook of control valves' (ISA, 1971, 2nd edn.) ISA home page, www.isa.org 'ISA standard ANSI/ISA-88.01-1995', (ISA, 1995) KWATNY, H. G., and BAUERLE, J.: 'Simulation analysis of the stability of coal fired furnaces at low load'. Proceedings 2nd IFAC Workshop Modelling and Control of Electric Power Plants, Philadelphia, 1986 KWATNY, H. G., and BERG, J.: 'Drum level regulation at all loads: a study of system dynamics and conventional control structures'. Preprint 12th IFAC World Congress, Sydney, 1993 LAUSTERER, G. K., FRANKE, J., and EITELBERG, E.: 'Modular modelling applied to a Benson boiler'. Proceedings first IFAC Workshop on Modelling and Control of Electric Power Plants, Pergamon, 1984 LEVA, A., MAFFEZZONI, C., and BENELLI, G.: 'Validation of drum boiler models through complete dynamic tests', Control Engineering Practice, 1999, 7, (1), pp. 11-26 LUNARDI, L. A.: 'The finite element method in the dynamic simulation of heat exchangers'. Master thesis, Dipartimento di Elettronica e Informazione, Politecnico di Milano, 1999 (in Italian) MAFFEZZONI, C.: 'Issues in modelling and simulation of power plants'. IFAC Symposium on Control of Power Plants and Power Systems (invited paper), Munich, 1992 pp. 15-23 MAFFEZZONI, C., and AIME, M. L.: 'Compact dynamic modelling of gas turbine including N Ox emissions'. IFAC Symposium on Power Plants and Power Systems Control 2000, pp. 182-187, Brussels, 2000 MAFFEZZONI, C., and GIRELLI, R.: 'MOSES: Modular modelling of physical systems in an object-oriented database', Mathematical Modelling of Systems, 1998, 4, (2), pp. 121-147 MAFFEZZONI, C., and KWATNY, H. G.: 'Control of electric power generating plants', in LEVINE, W. S. (Ed.): Control systems applications, (CRC Press, New York, 1999)

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MAFFEZZONI, C., MAGNANI, G., and MARCOCCI, L.: 'Computer-aided modelling of large power plants'. Proceedings first IFAC Workshop 'Modelling and Control of Electric Power Plants, Pergamon, 1984 MAFFEZZONI, C., FERRARINI, L., and CARPANZANO, E.: 'Object-oriented models for advanced automation engineering'. Control Engineering Practice, 1999, 7, (8), pp. 957-968 MATTSSON, S., and ANDERSSON, M.: 'OMOLA - an object-oriented modelling language'. In JAMSHIDI, M., and HERGET, C. (Eds.): 'Recent advances in computer aided control systems engineering' (Elsevier, Amsterdam, 1992) 'Modelica: a unified object-oriented language for physical systems modelling language secification, v. 1.2'. Technical report, Modelica Design Group, 1999 'Modular modelling system (MMS): a code for the dynamic simulation of fossil and nuclear power plants, overview and general theory. Technical report CS/NP-2989, EPRI, 1983 MORTON, K. W., and PARROT, A. K.: 'Generalized galerkin methods for first-order hyperbolic equations'. Journal of Computational Physics, 1980, 36, pp. 249-270 PERRY, R. H., and GREEN, D.: 'Perry's chemical engineers' handbook' (McGrawHill, New York, 1985) PIELA, P. C., EPPERLY, T. G. WESTERBERG, K. M., and WESTERBERG, A. W. 'ASCEND, an object-oriented computer environment for modelling and analysis: the modelling language', Computers and Chemical Engineering, 1991, 15, pp. 53-72 'Properties of water and steam in SI Units, 4th enlarged printing'. (Springer-Verlag, Berlin, 1989) ProTRAX home page, www.traxcorp.com QUARTERONI, A., and VALLI, A.: 'Numerical approximation of partial differential equations' (Springer-Verlag, Berlin, 1997, 2nd edn.) SALISBURY, J. K.: 'Steam turbines and their cycles' (John Wiley, New York, 1950) SIEGEL, R., and HOWELL, J. R.: 'Thermal radiation heat transfer' (McGraw-Hill, New York, 1972) 'SIMCON-X engineering station: model development'. Technical report ABB SIMCON, 1994a 'SIMCON-X Profile'. Technical report ABB SIMCON, 1994b STULTZ, S. C., and KITRO, J. B. (Eds.): 'Steam: its generation and use' (Babcock & Wilcox, Barberton, 1992, 40th edn.) WEBER, D. S., KONOPACKI, W. A., and MASSIMO, E M. 'Modelling and simulation of hanford K-Area boiler-turbine-generator system'. Technical report ERDA 76-151, 1976

Part 2

Control

Chapter 3

Modelling and control of pulverised fuel coal mills N.W. Rees and G.Q. Fan

3.1

Introduction

There can be no doubt that the ideas of modelling and control have generally been found quite acceptable within the electric power generation industry. With the introduction of modem distributed control systems (DCSs), it is now possible to implement many of the ideas resulting from modelling and control studies, although control engineers generally feel much more could be done than is currently the case (Rees and Lu, 2002). The control vendors and the applied control literature now regularly describe 'modem' control systems for the industry. Particular attention has been paid to steam temperature control (Mann and Lausterer, 1992; Nakamura and Uchida, 1989), load pressure control (Maffezzoni, 1996; Waddington and Maples, 1987) and water level control (Kwatny and Maffezzoni, 1996; Peer and Leung, 1993). An area of power plant control that has received much less attention from modelling and control specialists is the coal mills. This is in spite of the fact that it is now accepted that coal mills and their poor dynamic response are major factors in the slow load take-up rate and they are also a regular cause of plant shut-down (Maffezzoni, 1986). The reasons for this lack of interest are uncertain but relate very much to the idea that modelling mills is very difficult, if not impossible, and that mills are subject to all sorts of disturbances such as wear, choking and unknown coal properties, beyond the wit of the engineer to model. Against this, however, there is plenty of evidence that properly modelled and controlled mills can respond much better than at present; indeed it has been suggested that performance equal to that of oil-fired plant is possible (Rees, 1997). In the rest of this chapter we take a closer look at the modelling and control of coal mills and give some ideas from our own experience, and from that of others, where the future automation of this important area may be going.

64

Thermal power plant simulation and control

3.2

Modelling of coal mills

The problem of the transient performance of coal mills has been recognised for some time. Early work by Profos (1959) on pressure and combustion control, introduced models of coal mills relating input demand to firing rate by transfer functions, consisting of a first-order lag and a pure transport delay. Typical values of these parameters for different types of mills were given. Numerous studies based on these models using step response or frequency response testing have been carried out both for single-input single-output (SISO) systems and multivariable control (Bollinger and Snowden, 1983; Hougen, 1980; Neal et al., 1980). Slightly more complicated models based on overall mass balancing (O'Kelly, 1997; Rees and Mee, 1973) or heat balance analysis (Dolezal and Varcop, 1970) have also been developed. Whilst these models have been beneficial it is now recognised that some aspects of particle size distribution as well as the complicated internal structure of the mill must be considered (Corti et al., 1986; Robinson, 1985). We will discuss this matter soon but first we need to look a bit more closely at the mills themselves.

3.2.1

Vertical spindle mills

There are many types of coal mills in use, with one of the most popular types being the pressurised vertical spindle bowl mill as shown in Figure 3.1. This mill is very popular because it is economical; however, it has very low coal storage so that good control is very important. In operation, raw coal enters the mill down a chute dropping on to a constant speed of rotation table or bowl. The coal then moves under centrifugal force outwards and under three passive rollers where grinding and crushing take place. The coal output then moves towards the throat of the mill where it mixes with high-speed hot primary air. The heavier coal particles are immediately returned back to the bowl for further grinding whilst the lighter particles are entrained in the air flow and carried into the separator section. The separator contains a large amount of coal particles in suspension by the powerful air flow. In addition some of the heavier particles entrained in the primary air-coal mix lose their velocity and fall back onto the mill table as shown, for further grinding, whilst particles that are travelling fast enough enter the classifier zone. These particles are given a swirl behaviour by vanes or deflector plates. The lighter particles are drawn out of the resulting vortex as classified pf fuel for the burners, whilst the heavier particles hit the side of the classifier cone and drop back onto the mill table for further processing. As in the separator the classifier contains a significant mass of suspended coal. These masses of coal, together with the mass of coal on the mill table and the three recirculating loads, primary, secondary and tertiary, play a major role in the dynamic behaviour of the mill. As shown in Figure 3.1 the main inputs to the mill are the raw coal and the primary air while the output is the pf flow. The size distribution of the pf flow particles or 'finers' is usually required to be less than 75 microns and cannot be measured. It is determined largely by the intemal mill behaviour and the classifier settings which

Modelling and control of pulverised fuel coal mills Raw coal

from feeder 06~O

Deflector plates Tertiary recirculating load Secondary recirculating load Primary recirculating load Flash drying zone

Mill throat

Figure 3.1

Physical structure of a vertical spindle mill

65

66

Thermal power plant simulation and control

are usually not varied during mill operation. The size distribution of the raw coal input is measured infrequently using mechanical sieves and the particles are mainly in the range 75 microns to 70 mm. Air flow can be measured accurately although the measurement is often noisy. There is no doubt that mill control would be much improved if particle size measurements were available, but no satisfactory measuring equipment has yet been developed. Other important variables around the mill are mill temperature, which is easily measured and controlled by hot air and cold air dampers; mill motor current, which gives some indication of mill load; and the differential pressure between the top part of the mill and the under bowl. This AP measurement is very useful in helping to understand mill recirculating load. 3.2.2

Modelling vertical spindle mills - mass balance models

A useful physical model of the mill can be developed using internal mass balances. A block diagram schematic of the mill is shown in Figure 3.2. rhrc and rhpf represent the raw coal flow entering the mill and the pulverised fuel flow leaving, rhpre, rhsr e and rhtre are the recirculating loads and rhpff, rhsff and thtff represent the entrained coal flow picked up at the throat, separator and classifier by the primary airflow rhpa. rhff = kfrhrc is the amount of fine coal in the raw feed that is blown straight out of the mill. Mpr is the mass of coal on the table, rhg the flow of coal to the grinding table, and rhgc the output of the grinding mills. Figures 3.1 and 3.2 show the key mill structure and the variables necessary to write the mass balances.

~pf fT.., mtre

mtff ClassifierMtfl.,~ ~ Phsff

~r~_~

ii

Figure 3.2

ow,

] [

I

m~r~

Roll

Schematic of a vertical spindle mill

i Separator I

I

M~,

I

Modelling and control of pulverised fuel coal mills

67

A detailed transient model of the mill based on Figure 3.2 has been developed by Robinson (1985). This model considers coal in 15 particle sizes with detailed physically based models developed for each box. In the bowl modelling, for example, the flow of raw coal from the chute to the grinding zone has been modelled in terms of centrifugal effects and the difference in height of the raw coal as it flows across the coal bed. Likewise, treatment of the grinding zone includes an analysis based on known communition theory and established breaking rate functions and breakage distribution functions. The entrainment of coal from the table into the separator and classifier is examined using Lagrangian particle calculations and empirically determined classification functions. As a consequence of all this detail the model consists of 76 ordinary differential equations and is more of a knowledge-based model (Maffezzoni, 1996) than a control model. It is an excellent reference model and highly recommended reading but too complicated for most control studies. A more control-oriented model has been developed by Fan (1994) and Fan and Rees (1994). This model uses the same physical structure as shown in Figure 3.2 but the processes in each box are simplified. Eleven particle sizes are assumed in the raw coal but the grinding model is much simplified over the size mass balance model (Prasher, 1981). The following mass balances can be written by inspection: rhg -- 1 - w0 (1 - kf)rhrc q-- thre

(3.1)

1 -wl

rare = ff/pre -[- rhsre q- rhtre

(3.2)

/hpf = ff/tff - thtre -[- thff

(3.3)

where w0 and Wl represent the moisture in the raw coal and in the coal on the bowl. The recirculating loads in equation (3.2) can be adequately determined from drhpre rpre dt t'sre

drnsre dt

rhpre q- kprerhpff

(3.4)

- -rhsr e -4- ksrerhsff

(3.5)

d/htre "t'tre- -dt

rhtre q- ktrerhtff

(3.6)

where kpre, ksre and ktre are the appropriate steady-state gains and the time constants rpre, rsre and rtre are due to aeroresistance and inertia to the flow with the finer particles having longer time delays. The suspended mass of coal in the separator Msr and the classifier Mtr can be calculated from

dMsr

= (1 - kpre)rnpff - rhsff dt dMtr = (1 -- ksre)rhsff - rhtff. dt

(3.7) (3.8)

68

Thermal power plant simulation and control

To complete the model we need to determine the mass of coal Mpr on the table and the entrainment flows rhpff, rhsff and rhtff. The coal mass balance on the table can be written as dMpr -- thg -- rhpff. (3.9) dt However from the entrainment point of view it is the ground coal conditions at the rim (throat) that matter so that we really need to know the flow output of the grinding rolls rhgc. This can be determined in a complex way using the size mass balance concept (Prasher, 1981), but a simpler model is used here based on the idea of 'similarity' (Fan, 1994; Prasher, 1981), which results in the rolls being described by 1 drhgc R

dt

-- rhg - rhgc

(3.10)

where R is the size reduction rate of the raw coal particles and rhgc is defined as the flow of ground coal such that 80 per cent of the particles will pass through a 75 micron sieve. In this study R has been determined by measuring the weight of coal in each of 11 sieve sizes and feeding this information into a Matlab program for calculation (Fan, 1994). To determine the entrainment rate of the coal by the air at the throat, in the separator and in the classifier we need to find a relationship between the air mass flow rate at the point of interest and the pick-up rate of the coal particles. The particles are picked up by the drag force and will be entrained as long as this force is greater than the gravitational force. Kunii and Levenspiel (1969) show that the entrained particles travel at the same velocity as the carrier air and from this it is straightforward to show (Fan, 1994) that rhpff = kpr Mprrhpa

(3.11)

where kpr is a shaping factor that depends on the area of the particle flow path, the area of the primary air flow path, the density of the air and the volume of the mill occupied by the fine coal particles near the classifier. Assuming that the mass of primary air passes quickly through the mill then the secondary and tertiary final flows can be expressed by similar formulas: rhsff = ksrMsrrhpa

(3.12)

rhtff = ktrMtrrhpa

(3.13)

where all the shaping constants have the same structure as kpf but with their own local parameter values. Since a small amount of 'finer' coal enters the mill in the raw coal and gets blown straight out again as pf coal it is appropriate to add this flow to equation (3.13) so that rhpf : kpf(Mtr + Mff)rnpa -- rhtre.

(3.14)

Modelling and control of pulverised fuel coal mills

:D

69

,Q Mill pf flow (kg/s)

Sum6 Gain9

I

Small portion fine coal (%)

~ Transfer Fen3

Coal near classifier (kg)

Coal returned due to classification (%)

Gain7

Co;~]. u 2 e d due ~ ' to air velocity (%) Transfer Fen2 Mill level (kg) Coal returned due to mill rim (%)

dmd Raw coal Saturation Transport (kg/s)

Sum

aulrll

Grinding zo~e~Vtable ......... (kg) Raw coal (l~g/s)

Primar air (kg/s)

Figure 3.3

Verticalspindle mill- Matlab/Simulink ® simulation

A complete Simulink simulation model of the mill based on the above mass balance is shown in Figure 3.3. It is interesting to compare the above model with the more empirical model developed by O'Kelly (1997). This model uses three particle sizes that are carried through all the calculations. The grinding model is similar to equation (3.10) except that of the two particle sizes in the ground coal the production of one is seen as proportional to the mass of raw coal on the table while the production of the other is proportional to the mass of the larger size ground coal on the table. An interesting non-linear model is described for the entrainment of coal of the larger ground size at the bowl rim. This is expressed as

rhpff = kpr(mprmgc) n' thpa

(3.15)

where nl is an experimentally fitted constant and Mgc is the mass of ground coal on the table. A non-linear function such as this allows saturation to be modelled as might occur for example in mill choking.

3.2.3

Modelling vertical spindle mills - temperature, pressure and energy issues

Whilst the mass balance model describes the pf flow quite well, it is essential for any control studies that thermodynamic and hydrodynamic effects are also considered. The mill temperature Tm measured at the mill outlet is a critical variable from a safety viewpoint, and must be controlled within narrow bands. Likewise mill differential pressure A P measured between the mill under-bowl and the separator is a critical variable since it is an indirect measure of mill recirculating load - too high a A p

70

Thermal power plant simulation and control

indicates possible mill overload and will trip the plant. Mill wear can also be related to A P. Another useful measurement and model relates to the energy E needed to drive the mill and its coal load. The simulation equations for Tm, A P and E are outlined below. 3.2.3.1

Mill t e m p e r a t u r e - Tm

A simple and useful model of mill temperature can be obtained from a global input/output energy balance. It is assumed that the mill temperature is measured in the mill pf outlet duct and that this lumped parameter Tm is the same as the mill body, coal and air mass temperature in the mill. The mill energy balance then results in

dTm

MmCn---~- = qin -- qout = 0pai + qrei + C)moi-- qpao - qpfo -- Ümoo

(3.16)

where the 0 terms represent the input and output heat in the primary air, raw coal and the moisture, and Mm and Cn are the mass of metal in the mill and its specific heat. By standard techniques these quantities can be written as: C)pai = Clthpa(Tpa - Tin) C)rci = (1 - to0)thrc(Ta - Tin)C2 C)moi -----to0rhrc(Ta - Tin)C3 qpao = C1 thairTm 0pro = C2rhpfTm qmoo = C3tolrhrcTm + Co(wo - tol)rhrc where Tpa and Ta are the primary air and ambient air temperature, rhair is the air flow outlet of the mill and the coefficients Ci are the appropriate specific heats. Equation (3.16) with the above substitutions represents the temperature equation used in the simulations. It may be possible to improve the temperature model by including heat generated during grinding so that the temperature of the coal bed differs from the measured pf outlet temperature. This would require a higher-order dynamic model and much more information on coal mass and surface parameters. Early results, however, suggest that significant improvements are possible using this approach. 3.2.3.2

Mill differential pressure - A P

As the primary air flows through the mill, picking up coal from the table, a differential pressure A P is developed between the under-bowl pressure and the pressure in the separator. This pressure loss is caused by frictional losses, changes in the air flow path area due to the suspended coal, and energy lost by the air in picking up the coal. The problem is complex because there is a mixture of single-phase air flow below the bowl and two-phase coal/air flow in the separator.

Modelling and control o f pulverised fuel coal mills

71

A global model for A P can be developed from an energy balance between the air input and the mill measuring point. Details are given in Fan (1994) with the resulting equation for A P being kree-Tds

- •2

A P = kpedh + kpadth~a + (1 + Tms) 2dmrc + krldMtr

(3.17)

where dh is the distance between the mill entry and the measuring point. The parameters kpe, kpa, kre and krl are complex functions of mill air flow. Consequently, the global model is represented by a set of constant-coefficient lumped-parameter models. These parameters can be determined off-line and stored in a look-up table relating their values to operating conditions or they can be determined adaptively on-line. This will be discussed in subsequent sections.

3.2.3.3 Energy model Large coal mills consume significant amounts of power amounting to about 500 kW at full load. In addition by observing the mill power requirements for coal pulverising, useful information about mill wear, coal hardness and other operational issues can be resolved. If Eu is the energy required by a unit mass of coal particles to be ground from size Zl to size z2 and W is the energy required to drive an empty mill, then the energy E required by a mill charged with coal mass m is E = m E u + W.

(3.18)

Assuming Eu is given by Bond's law (Kunii and Levenspiel, 1969) then E = mkB(Z21/2 -- z l I/2)

(3.19)

where kB is a constant depending on the coal. Since z2 is determined by the mill classification settings which are fixed, and the raw coal distribution is more or less constant, the mill power consumption E is mainly a function of the amount of coal mass m on the mill grinding table. It should be noted that the mass of the mill M is constant. A similar relationship for the consumed energy is given by Corti et al. (1986).

3.3

Plant tests, results and fitting model parameters

Models of physical plant are of course only as good as how well they fit the data. Unfortunately there is little coal mill data available so that most of the few models available in the literature are qualitatively evaluated or checked against a number of simple step responses. Some frequency response testing has been performed (Neal et al., 1980), and it has been suggested by Corti et al. (1986) that data collection was being carried out by ENEL in Italy.

72

Thermal power plant simulation and control

In this section we describe some model data fitting carried out using the model from section 3.2 when fitted to data collected from power stations in New South Wales, Australia. Unfortunately, the data are not available for general use. It was developed in a collaborative project between the University of New South Wales and Pacific Power International in a project designed to develop and test modern control concepts as applied to coal mills. In passing, it is worth mentioning the fact that the data was collected from experiments carried out on two plants, one a 500 MW plant and the other a 660 MW plant. Data logging includes the mills (six of them) and appropriate pressures, temperatures and flows from all around the boiler turbine plant. The experiments were specially designed by the modellers, plant technical staff and operators so that model parameter estimation was possible without excessively disturbing the plant or placing too much demand on the operators. This means that step and ramp changes are made and during the experiments normal plant controls are maintained except around the mills. Three different mill control configurations were used. In the first experiment, plant power demand was ramped up and down with the normal mill mass/mass control in place so that fuel and primary air varied. In the other two experiments mill controls were removed, power demand was set constant, and a step change was applied to fuel flow with constant primary air setpoint, or air flow with constant fuel set-point. Extensive experiments were carried out for five different power demands between 60 and 90 per cent MCR. Following each step the plant was allowed to settle before the next step occurred. The tests were also carried out for new mill rollers and worn mills. In addition special tests were carried out, for example, on an empty mill to determine the no-load relationship between mill A P and primary air. No particular parameter identification method was used to fit the model parameters. Rather steady-state data, transient data, data from the special tests and design data were used in a heuristic way. Since the experiments were carefully designed it was possible to fit many of the parameters to the data by simple least squares. Once the first set of parameters was determined the simulation model was run in parallel with the mill and the resulting error signal was then used to further refine parameters. It was quickly found that a large number of parameters were constant throughout plant operation, but a small set of parameters varied with load and other factors such as wear. To cope with these variations a distributed model parameter set was determined as discussed later. Although this approach might appear somewhat ad hoc it is a very effective engineering approach and an excellent way of building up knowledge and understanding of the plant for modeller and plant engineer alike. The fitted model test results against the data are shown in Figure 3.4 where the mill power and mill A p outputs are shown. In this test the mill PA flow was constant and the feeder speed step changed after 90 and 430 samples. The parameters used in the model were determined for 70 per cent load as the feeder speed indicates. It can be seen that the model responses are quite satisfactory. In Figure 3.5 a similar test is carried out but at 80 per cent load. However, the model has the same 70 per cent load parameters as the previous simulation. Deterioration in the results is obvious both for

Modelling and control of pulverised fuel coal mills

73

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Step changes in feeder speed at 70per cent load (fixed parameter model): solid line -field test data; dotted line - model output. Sample time = 3 s

steady-state values and for the transient response. A similar test at 50 per cent load showed even worse transient performance. Figure 3.6 shows the results of a more complicated test. In the first 600 samples the feeder speed was constant and the air varied. After 800 samples both feeder speed

74

Thermal power plant simulation and control 85

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a n d air vary t h r o u g h r a t h e r large c h a n g e s . It can b e seen t h a t the data fit for a fixed m o d e l for this test is n o t very g o o d a n d especially after 800 s a m p l e s w h e r e the error increases. In this data the mill is ' c h o k i n g ' d u e to the h i g h coal flow a n d low air flow. S u c h a n e v e n t is n o t u n u s u a l and c o u l d c a u s e the mill to b e shut down. T h i s

Modelling and control of pulverised fuel coal mills 90

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p h e n o m e n o n , however, is largely missed by our fixed parameter model. It might be noted that in these figures we have not chosen to show the p f flow from the mill. This is because it cannot be measured and so cannot be c o m p a r e d with the model. We will discuss this in section 3.4.

76

Thermal power plant simulation and control 7 5 - -

T

r

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........................ i

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T h e mill m o d e l l i n g p r o b l e m s j u s t d e s c r i b e d are d u e to the n o n - l i n e a r i t i e s in the p l a n t so t h a t one set o f p a r a m e t e r values w i t h the s i m p l e m o d e l c a n n o t g l o b a l l y fit the data. T h i s difficulty can b e o v e r c o m e by u s i n g a d i s t r i b u t e d p a r a m e t e r set m o d e l w h e r e different p a r a m e t e r s are u s e d for different o p e r a t i n g c o n d i t i o n s as m e a s u r e d

Modelling and control of pulverised fuel coal mills

77

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Figure 3.8

800

Step changes in feeder speed at 80 per cent load (distributed parameter model): solid line - test data; dotted line - model output. Sample time = 3 s

by mill feeder speed and PA flow. By dividing the operating space up into regions and then forming a database of parameter sets for each region a more satisfactory model can be produced. The results of the same experiments shown in Figures 3.43.6 are shown with the distributed models in Figures 3.7-3.9 and are obviously much

78

Thermal power plant simulation and control 90

i

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1500

Step changes in both airflow and feeder speed (distributed parameter model): solid line - test data; dotted line - model output. Sample time = 3 s

improved. The results of Figure 3.9 are particularly interesting since they show the 'choking' behaviour well. Figure 3.10 shows the distributed results for a 'worn mill' over a range of loads and these are also good. The modelling results shown in this section are very encouraging. It should be remembered, however, that to obtain this behaviour requires a lot of plant

Modelling and control o f pulverised fuel coal mills

79

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Operation with a worn mill (distributed parameter model): solid line - test data; dotted line - model output. Sample time = 3 s

testing a n d data collection, w h i c h m u s t be d o n e for g o o d a n d w o m mills, for all loads a n d for c h a n g e s in o t h e r factors such as coal calorific value a n d m o i s ture, a n d thus requires a large database. In section 3.5 a n alternative a p p r o a c h will b e discussed.

80

Thermal power plant simulation and control

3.4

Mill control

3.4.1

General issues

To understand mill control and all its issues, it is helpful to fit mill control into the broader base of unit control. The unit load controller essentially maintains the balance between thermal power in the boiler, and mechanical-electrical power developed by the turbine generator. Fundamental to this balance is the steam pressure at the inlet to the throttle valves (TVs) or turbine governor valves. There are many ways in which this can be done, but increasingly coordinated or integrated controls are used as shown in Figure 3.11. In this figure the controlled outputs are steam pressure and MW load, and the controlled variables are fuel flow and TV position. The figure also shows an oxygen controller, since fuel gas composition is strongly linked with furnace behaviour. In operation the unit demand sets the set-point for pressure and power output, either locally (LC) or remotely (RC) from the load dispatch centre, and the control systems do the rest. With most plants now controlled by distributed control systems, it is fairly straightforward to set controller parameter values for stable operation over an acceptable load range. Variations of the controller structure are also possible, e.g. the use of derivative control in the feedforward signals. There are a number of key issues that must be discussed in relationship to Figure 3.11. The two most important issues are the use of pulverised fuel pf feedback in the fuel control loop and the contents of the milling group box. In practice, it is

1

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]

Heat~Bcle-~r .... Isu',~ I

Steampressure output

L._

~A1 ~

] nator ]M~

Unit fuel, air and MW controllers and power plant

output

Modelling and control of pulverised fuel coal mills

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Unit fuel control with air/fuel mass/mass submill control

not possible to measure the pf feedback and in addition the milling block is not just one mill but many mills - up to eight for example for a 500 MW unit. This means that depending on load, mills must be switched in and out of service. In addition, since pf flow cannot be measured, it is usual to replace this measurement by the feeder speed measurement of fuel flow. In steady-state operation this is a satisfactory thing to do, but transiently there are significant differences resulting in challenging environmental problems during load change that significantly reduce maximum load change rates. Figure 3.12 shows a more detailed description of the unit fuel control part of Figure 3.11. Note that the fuel demand is for the entire mill group and this has to be split into the fuel demand for each of the individual mills. The above two issues of fuel flow measurement and multiple mill use are key issues in overall mill control. In addition, there are major mill problems due to the uncertainty in mill input, especially calorific value and wetness. Mill performance is also influenced by mechanical issues like mill wear, mill choking and mill fire. These operator diagnostic issues are of great importance and must be considered in the development of any useful mill control system. In the rest of the chapter we will first consider the control of a single mill in an attempt to improve how an individual mill is actually controlled. The final part of the chapter will then discuss overall mill control and the development of an intelligent operator advisory system.

3.4.2

Control studies on a single mill

As we have seen it is very important that the milling group and hence the individual mills provide the correct amount of fuel, as set by the unit demand. For safe and efficient mill and furnace operation primary and secondary air flow must also be correct. Primary air flow and temperature are significant influences in mill control as we shall now see. Secondary air flow is important in the furnace but does not affect the mill. Its control is usually fairly simple and is done by measuring the air pressure

82

Thermalpower plant simulation and control

in the hot air duct to the burners and controlling this by simple feedback to a desired set-point. The basic idea behind the control of primary air and fuel to the mill, the submill control system, is fairly straightforward and is based on the so-called 'load line' of the mill. This load line is predetermined for a mill and shows the relationship between the air mass flow and the coal mass flow required for the mill to operate in the safe air-fuel range of 1.5-2.5. Note that it is a purely static relationship and most mills are only operated at 40-100 per cent MCR. The minimum air flow is set by the need to establish a satisfactory recirculating load in the mill. The air temperature is set by the requirements of having the coal sufficiently dry in the mill whilst at the same time not having the mill temperature too high and thus risking mill explosion. There are a number of ways of controlling the mill to meet all these requirements with the most usual being so-called mass/mass mill control. The mass/mass mill controller can be operated in either air follow mode or coal follow mode with the basic idea being shown in Figure 3.13 for the air follow mode, which is usually used since it allows fuel to move first. In this mode the overall fuel demand is compared with the fuel being produced as measured by the feeder speed, a PI fuel controller then regulates the feeder speed as required. The box RB is the rnnback controller whose purpose will be described later. In the PA controller the feeder speed and the computed air flow are compared with the load line in the function generator (FG) and an error signal generated to drive the

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Modelling and control of pulverised fuel coal mills

83

hot air damper thus modulating air flow. Simultaneously the temperature control loop adjusts the cold air input so that the mill outlet temperature remains at its set-point. The mill AP measures the resistance of the mill to the primary air flow and is thus indirectly measuring the amount of coal in the recirculating load in the operating mill. Should this value rise too high then the runback controller (RB) reduces the coal feeder speed to a minimum value securing safe operation of the mill, since a high A P indicates dangerous mill operation (ICAL, 1989). The mill mass/mass controller is simple and reliable and extensively used. Its transient operation is, however, poor since it does not continuously use information about the internal coal storage in the mill, the recirculating load, which is an important factor in dynamic mill control. The performance of the mass/mass controller can be improved using a method based on the Hardgrove grindability index (ICAL, 1989). This method is shown in Figure 3.14 where the main difference can be seen to be the use of feeder speed as a control variable working on a pressure measurement ratio, as shown, instead of the fuel demand error, which is then used to control hot primary air flow. The pressure ratio is defined as A P divided by A Pair. This pressure ratio is compared to a predetermined constant KRLD, the recirculating load derivative, and if they are equal no change in feeder speed from its normal mass/mass value is used. Any difference, however, will cause a change in feeder speed with an increase in pressure ratio indicating too high a recirculating load and vice versa.

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84

Thermal power plant simulation and control

Based on this idea the feeder speed can either be increased or decreased to take into account the transient effects of the recirculating load. It has been suggested (Fan, 1994; ICAL, 1989) that, provided all the functions required to set up the Hardgrove control loops are known, excellent performance is possible from this control system - indeed it has even been suggested that pulverised fuel mills might, when appropriately tuned, have performance almost matching oil-fired systems. The sensitivity of the controller performance to its parameter values and the cost of setting the system up properly are, however, reasons given by the industry for the low take-up rate of the system. The results of Figure 3.15 show that for a mill operating alone under mass/mass control or Hardgrove control the performance of the Hardgrove controller is significantly faster. The reasons for this can be seen from Figure 3.15c where the Hardgrove controller has an overshoot in coal on the grinding table following a demand change. Here the airflow measurement A Pair changes instantaneously, modifying the pressure ratio, rapidly resulting in an overshoot in feeder response. The extra coal contains a percentage of fines that are immediately transported to the pf flow. The mass/mass controller by contrast does not produce this extra coal. In section 3.4.3 the performance of the mass/mass controller and the Hardgrove controller, when integrated into the coordinated control of the overall plant, is discussed. In both the above control systems, no account is made for the dynamics of the primary air response and the coal response. In practice, attempts are made using lag-lead filter networks. The difference in the speed of response causes significant pollution problems during transients, because of the out-of-balance fuel-air ratio. Improved pulveriser control is usually achieved by lagging the PA flow to the load demand change whilst having the feeder speed respond immediately and including a lead feedforward signal from the PA flow measurement (Peet and Leung, 1993). Unfortunately, the lag and lead settings are strongly affected by the operating conditions of the mill, such as load, wear and moisture. It should be noted in passing, however, that the basic problem with the mass/mass control remains, namely, the output of the mills in the form o f p f flow or energy is not measured.

3.4.3

Mill control using p f flow

Many attempts have been made to develop suitable instruments for on-line measurement of pf flow (Maffezzoni, 1986) most of which have not been satisfactory. More success has been achieved by inferential methods, usually based on Kalman filtering using mill models, and a number of these are working on-line (Waddington and Maples, 1987). All on-line experiments or simulation studies seem to show significant improvement in the mill control provided that good estimates of the pf flow can be determined. This of course is not surprising since the pf flow is now controlled directly by feedback. The essence of the idea is to set up a linear dynamic model of the boiler turbine and mills such that the pf flow and other important states of the mill are observable from available measurements. The model can be obtained either by linearising a dynamic model of the system (Fan, 1994), if one is available, or on a more ad hoc basis (Clarke et al., 1989). Parameters of the model can then be fitted to

Modelling and control of pulverised fuel coal mills

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plant data with process and measurement noise parameters being particularly important. Standard Kalman filter (KF) programs can then be run to determine the filter gains. The whole process is non-trivial, requiring skilful setting up and plant testing if robust estimates are to be available. Properly set up, however, the KF filter feedback system produces a time leading fuel estimation signal that can provide significant

86

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improvement. The process is well described by Clarke et al. (1989) and Fan (1994), where particular emphasis is placed on obtaining good low-order models. Kalman filter estimators have been operating successfully in a number of power stations in the UK since the 1980s (Clarke et al., 1989; Waddington, 1994; Waddington and Maples, 1987). To get some idea of the performance of the pf estimated controller the system of Figure 3.16 was simulated in Matlab/Simulink ® (Fan, 1994). It should be noted that the simulation contains the boiler turbine systems and the pressure and power output controllers, as well as the mill and its controllers. The results shown in Figure 3.17 show the performance of the mass/mass controller under feeder speed feedback and pf feedback for a step increase in power demand at 10 samples. From Figure 3.17a and b the throttle valve pressure and generator output responses are faster using feedback of the estimated pf due to the observed faster change in pf flow (Figure 3.17d). The responses show some oscillation but this is not serious. Even better performance of the pf feedback is shown in Figure 3.18 where a 20 per cent disturbance in the fuel input energy has occurred at 50 samples. The figure indicates that the pf controller keeps much tighter control of the generated power output and this is very significant since the stability to such unknown disturbances is very important. In Figure 3.19 simulation results are shown of the mass/mass controller with estimated pf feedback compared with the system under Hardgrove control. Figure 3.19a shows that the power output response of the Hardgrove controller is almost twice as fast. To achieve this response, however, costly, fast actuators are needed on the

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control feeder and precise knowledge is required about the mill, such as the relationship between mill pressure and mass flow. These relationships are usually difficult to obtain and must be determined regularly for each mill, and even slight modelling errors dramatically affect performance. By contrast a properly tuned mass/mass controller

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with pf feedback performs acceptably well, is easy to set up, very robust, and does not require high-performance actuators. Hardgrove control is therefore not very often used in industry whilst mass/mass controllers with pf feedback are becoming more popular (Waddington and Maples, 1987). The tuning of the mill control systems shown in Figures 3.11 and 3.12 has been carried out using simulation, plant knowledge and control experience. Most of the controllers are PI or PID controllers, which are part of a complex multivariable system that includes pressure control, electrical power and throttle valve control as well as local submill controllers. The procedure used is to tune the inner loops first, then the subsystem loops and finally add in feedforward compensation. The method has proved quite quick and satisfactory. The controller settings also vary with the mode of control, e.g. boiler or turbine following, so this must also be considered. The control system developed in this section is outlined in Figure 3.20. It is similar to the scheme of Maffezzoni (1986), which includes a special instrument for measuring pf flow as against the use of a soft sensor here. Note also the inclusion of limits in the control valves/dampers that are a function of mill level. 3.4.4

Advanced multivariable and predictive control

The control described in section 3.4.3 is essentially SISO control with ad hoc procedures used in the design. Mills, besides being highly non-linear, are also multivariable. In this section we examine the use of multivariable control using linear quadratic (LQ) and predictive control techniques. Rees and Mee (1973) describe a very simple study of mill control using LQ techniques. The resulting control scheme decoupled the two major control loops and added dynamic LQ designed compensators. Major studies using LQ control were

Modelling and control of pulverised fuel coal mills

91

carried out in the UK in the 1980s resulting in a number of power stations adopting LQ methods on-line (Clarke et al., 1989; Waddington, 1994; Waddington and Maples, 1987). Significant improvements in mill control were shown. In more recent times there has been some attempt made to control mills using predictive control with quite interesting results (O' Kelly, 1997; Palizban et al., 1995; Rees, 1997). In the simulation study described by O'Kelly the model used is similar to the model of section 3.2. Hard non-linearities are placed on both state and control variables with tests driving the plant over the whole non-linear operating region. A fairly simple receding horizon predictive controller forms the basis of the control and is implemented in Simulink on a 486 platform. Figure 3.21 shows the response of the mill during start-up. In developing the responses it is assumed that the mill model used by the controller acceptable. The simulation assumes that mill wanning starts at t = 0 and at 20 minutes the feeder is started at its minimum speed. At 30 mins mill loading commences at around 10 per cent rated flow per minute until the mill reaches its operating condition. After 90 mins the results show the mill responding to fast ramp changes. The results of Figure 3.21 show that the predictive controller has excellent setpoint tracking control even though the plant has strong interactions and non-linearity, and the controls and their rate of change are bounded. In the start-up test shown, the performance of the controls is superior to the current control. Robustness studies have shown that the controller is not sensitive to quite large modelling errors and will respond well provided that the linear model response is regularly updated and the general direction of the model response is correct. The controller does not require excessive computing performance and is capable of being implemented on most modem DCSs. Advanced techniques of mill control using fuzzy logic and neural network concepts have also been tried in simulation with promising results (Cai et al., 1997; Cao and Rees, 1995).

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92

Thermal power plant simulation and control

3.5

Intelligent control and operator advisory systems

In the work that has been described so far, it has been shown that it is possible to develop non-linear dynamic models of a vertical spindle mill and to use these models to better understand the mill and design improved control systems. This is especially true for normal operation of the mill where the model is a satisfactory global predictor of plant behaviour. Mills, however, are also subject to regular non-normal changes caused by such factors as roller wear, coal grindability and calorific value changes, moisture content, mill blockage and the like, and these major events which are not modelled currently require experienced operator intervention or mill shut-down. It might therefore be expected that any successful advanced mill control system would be able to handle all these conditions. This can only be done, however, by combining mill controllers with some type of knowledge-based system to take into account the critical events that have just been described. To the authors' knowledge, no such system exists for coal mills, although some expert systems have been used for power plant control (Majanne et al., 1991). In this section, we try to show what could be done by listing some work from our own experience, mainly simulation studies, but carried out in collaboration with the local power industry. The motivation for doing such work is quite strong, since it can be estimated that substantial savings can be made from such factors as fewer mill fires, fewer mill runbacks, automatic operation of the mill over a wider range, optimal mill operation, and rapid diagnoses of mill faults. An intelligent control and advisory system (ICOAS) adds considerable expertise to the existing control system. It can be developed either as part of the existing DCS or as a stand-alone system. Its two major features are the intelligent operator advisory system and its associated alarms (IOAS), and the hierarchical supervisory control (HSC). The IOAS performs quick and early diagnostics of plant faults and possible causes and it also gives reasoning behind the alarms and recommended operator actions. A 'history' feature allows this information to be stored for future use and operator training. The HSC integrates the existing controls with plant operational knowledge and operation. It can also supply limits to controlled process variables to ensure mill stability under all operating conditions. An important feature of ICOAS is its use as a 'soft sensor', using either the process model or a Kalman filter. These estimates can then be used to improve the IOAS and to create useful indices for features such as mill wear, the effect of excessive moisture and other operational issues not included in the dynamic models. Included with the ICOAS is an additional advanced graphical user interface (GUI), which displays all the additional information developed above in a form compatible with existing plant graphics.

3.5.1

Knowledge-based operator support system

The ICOAS system just described can be extremely complex and there are many problems in modelling, expert control and the like, to be overcome. A prototype ICOAS

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has been developed by the University of New South Wales in a collaborative project with the utility Pacific Power International (PPI). The system known as KnowledgeBased Operator Support System (KBOSS) has been installed in stand-alone mode in a small Bailey Infi90 DCS (Fan and Rees, 1997). It has been tested, for a limited number of plant faults, including mill wear, mill choking and mill optimisation on a Matlab/Simulink ® boiler, turbine and mill simulation and also partially tested on a 500 MW power plant. The essential features of KBOSS are shown in Figure 3.22. The scope of KBOSS essentially covers the IOAS part of the ICOAS system. The KBOSS rule base has been developed to recognise 15 faults or operational conditions covered by approximately 50 rules. The rule sets have been developed to provide a range of examples or scenarios including plant faults (feeder blockage, worn mills), operational problems (mill choking, mill moisture) and supervisory control (auto mill load sharing). Rule development has been achieved by surveying the operational literature, talking with plant experts, carrying out mill tests and reading training and maintenance literature. Direct experience of faults has also been included. To extend the work to cover all major faults, a more formal knowledge-base development process is needed, as described by AI-Dabbagh et al. (1993) and Parker (2003). The system described

94

Thermal power plant simulation and control

in Figure 3.22 has been developed using a reference model combined with a fuzzy logic/pure rule base inference mechanism. For normal process behaviour the model matches the plant behaviour and no advice needs to be presented to the operator. However, when there is a system mismatch, the knowledge base is searched and appropriate advice given to the operator for action. The searching mechanism used in the knowledge base is multilayered with a branch tree structure. This means that the complete knowledge base need not be searched for all situations, thus increasing search efficiency and reducing the computational burden. A key feature of the KBOSS system is the existence of a good reference model. In section 3.3 it has been shown that this requires a large database and this entails extensive plant experimentation. Furthermore, each time the worn mill rolls are replaced (approximately 6,000-10,000 hrs) a completely new model of the mill must be established. To avoid this problem, KBOSS uses a special adaptive control system that continuously computes local dynamic models. Snapshots of these models are then stored in the database as the reference models. These snapshots will only need to be changed when future plant behaviour indicates significant differences between the database reference model and the latest dynamic model. A point of significant interest is that the adaptive model can be used very effectively by any advanced model-based controller such as those described in section 3.4.4. The above system seems to work quite well in its limited task for both simulation and plant studies as the two examples in the next section indicate. 3.5.1.1

Mill runback and KBOSS control

The mill runback controller described in section 3.4 is essentially a switch which detects high mill load defined by a specified value of high mill A P (4.5 kPa). Whilst it is certainly the case that the mill should be shut down to minimum load if the high A P is due to mill overload, high A P can be caused by other factors which do not require such action. Since shutting down to minimum load is an operational loss and under certain circumstances can result in mill instability, there is a considerable incentive to be sure that runback is absolutely necessary. In Figure 3.23, the high mill A P has been caused not by load, but by high moisture content in the raw coal and reduced mill grindability. This can be determined by KBOSS using not just a mill A P measurement but also mill power, mill level and other soft sensed mill conditions, together with a set of rules. Once this possibility has been recognised, the operating condition can be alleviated without running the plant down. Figure 3.23 shows that when using the runback controller, the plant is run back to base load when 4.5 kPa is reached. However using KBOSS stops A P rising above 4.5 kPa so that the mill can continue running.

3.5.1.2 Optimal grinding control Mills consume large amounts of power so it makes sense to try to optimise the coal grinding process. Experiments show that there is a best depth for the most efficient coal grinding and that this depth can be related to mill power and the soft sensed mill

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Modelling and control of pulverised fuel coal mills

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level through a set of knowledge-based rules. The results of Figure 3.24 show that an expert system can hold the mill power in a tight optimum range (350-400 kW) as shown in Figure 3.24a. Note that in Figure 3.24d the mill control keeps A P just below its critical value.

3.6

Conclusions

In this chapter we have looked at some problems associated with the control of vertical spindle coal mills. It is now well recognised that all the various types of coal mills associated with power plant have difficult control problems and often restrict plant take-up of load or cause plant shut-down. The chapter shows that, contrary to conventional wisdom, it is possible to develop fairly simple models of coal mills which can be used to obtain better performance. The chapter develops a vertical spindle mill model to better understand mill control. This can be done by estimating pf flow from the mill and by evaluating the internal mill recirculating loads. This information can also be used as part of an intelligent control system to improve operator performance and the analysis of mill alarms. The results given in the chapter are largely the outcome of simulation studies. Limited studies have however been carried out on a 500 MW plant in a collaborative project with PPI. These studies also show promising results indicating that mill control is a fruitful area for research and development.

3.7

Acknowledgements

The authors wish to acknowledge the support given to this project by the former Australian Electrical Research Board and by Pacific Power International. The latter support was made possible by Mr Don Parker of PPI whose knowledge and enthusiasm were a great help. Dr Michael Cheng must also be thanked for his work on the simulation and site tests towards the end of the project.

3.8

References

AL-DABBAGH, M., CHEN, D., MOORTHY, S., and ACHORN, E.: 'The development of an intelligent alarm processor - an alternative approach'. Proceedings of the Australian Universities Power Engineering Conference, Wollongong, Australia, 1993, pp. 361-367 BOLLINGER, K. E., and SNOWDEN, H. R.: 'The experimental determination of coal mills', IEEE Transactions on Power Apparatus and Systems, 1983, 102, (6), pp. 1473-1477 CAI, J., LI, Z., and WANG, P.: 'Fuzzy control of a ball mill for the pulverizing system of a thermal power plant'. Proceedings of the IFAC/CIGRE Symposium on ControlofPowerSystems and Power Plants, Beijing, China, 1997, pp. 214-218

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CAO, S. G., and REES, N. W.: 'Fuzzy logic control of vertical spindle mills'. Proceedings of the IFAC Symposium on Control of Power Plants and Power Systems, Cancun, Mexico, 1995, pp. 49-55 CLARKE, R., WADDINGTON, J., and WALLACE, J. N.: 'The application of Kalman filters to load/pressure control of coal fired boilers', lEE Colloquium, 1989, Digest No. 1989/27 pp. 2/1-2/6 CORTI, L., DEMARCO, A., RADICE, A., and ZIZZO, A.: 'Control and modelling of coal mills'. Proceedings of the IFAC Symposium on Power Plants, Pittsburgh, 1986, pp. 92-97 DOLEZAL, R., and VARCOP, L.: 'Process dynamics' (Barking Elsevier, New York, 1970) FAN, G. Q.: 'Modeling and control of vertical spindle mills in power plant'. ME thesis, University of New South Wales, 1994 FAN, G. Q., and REES, N. W.: 'Modelling of vertical spindle mills in power plant'. Proceedings of the Electrical Engineering Congress, Sydney, 1994, 1, pp. 235-240 FAN, G. Q., and REES, N. W.: 'An intelligent expert system (KBOSS) for power plant coal mill supervision and control', Control Engineering Practice, 1997, 4, (1), pp. 101-108 HOUGEN, J. O.: 'Control strategies for pulverised coal fired systems'. ISA Transactions, 1980, 19, (1), pp. 29-35 ICAL: 'General principles of coal milling' (ICAL Publication, Windsor, Connecticut, 1989) KUNII, D., and LEVENSPIEL, O.: 'Fluidisation Engineering' (Krieger, Huntington, New York, 1969) KWATNY, K. G., and MAFFEZZONI, C.: 'Control of electric power', in LEVINE, W.S. (Ed.): 'The Control Handbook' (CRC Press, New York, 1996, pp. 1453-1482) MAFFEZZONI, C.: 'Concepts, practice and trends in fossil fired power plant control'. Proceedings of the IFAC Symposium on Power Plants and Power Systems, Beijing, China, 1986, pp. 1-9 MAFFEZZONI, C.: 'Boiler-turbine dynamics in power plant control'. Proceedings of the IFAC 13th Tri-annual World Congress, San Francisco, 1996, vol. O, pp. 1-13 MAJANNE, Y., RVORONEN, T., KURKI, M., and ALASIVRU, P.: 'Hierarchical online diagnostics system for power plants'. Proceedings of the IFAC Symposium on Fault Detection, Supervision and Safety for Technical Process, Baden-Baden, Germany, 1991 MANN, J., and LAUSTERER, G. K.: 'Temperature control using state feedback in fossil power plant'. Proceedings of the IFAC Symposium on Control of Power Plant and Power Systems, Berlin, Germany, 1992, pp. 37-42 NAKAMURA, H., and UCHIDA, M.: 'Optimal regulation for thermal power plant', IEEE Control Systems Magazine, 1989, 9, (1), pp. 33-38

Modelling and control of pulverised fuel coal mills

99

NEAL, R W., WADDINGTON, J., and WILSON, R. G.: 'Determination of mill and boiler characteristics and their effect on steam pressure control', Chemical Engineering Science, 1980, 35, pp. 2107-2114 O'KELLY, E A.: 'Synthesis of advanced mill control'. Proceedings of the IFAC/CIGRE Symposium on Control of Power Systems and Power Plants, Beijing, China, 1997, pp. 208-213 PALIZBAN, H. A., O'KELLY, E A., and REES, N. W.: 'Practical optimal predictive control of power plant coal mills'. Proceedings of the IFAC Symposium on Control of Power Plants and Power Systems, Cancun, Mexico, 1995, pp. 177-183 PARKER, D.: 'Prototype design of operator knowledge base support system for pf mills'. ME thesis, University of New South Wales, 2003 PEET, W. J., and LEUNG, T. K. E: 'Dynamic simulation application in modem power plant control and design'. Proceedings of the IEE 2nd APSCOM Conference, Hong Kong, 1993, 1, pp. 121-129 PRASHER, C. L.: 'Crushing and grinding process handbook' (John Wiley, New York, 1981) PROFOS, E: 'Dynamics of superheater control', Combustion, 1959, 31, (4), pp. 34-43 REES, N. W.: 'Advanced power plant control for large load changes and disturbances'. Proceedings of the IFAC/CIGRE Symposium on Control of Power Systems and Power Plants, Beijing, China, 1997, pp. 641-649 REES, N. W., and LU, C. X.: 'Some thoughts on the advanced control of electric power plants', Transactions Institute of Measurement and Control, 2002, 24, (2), pp. 209-228 REES, N. W., and MEE, D. H.: 'Simulation and control studies of coal fired boiler systems'. Proceedings of the IFAC Symposium on Automatic Control of Mining, Mineral and Metal Processing, Sydney, Australia, 1973, pp. 150-155 ROBINSON, G. E: 'A model of the transient operation of a coal pulveriser', Journal of the Institute of Energy, 1985, 51, pp. 51-63 WADDINGTON, J.: 'Kalman filter applications for coal fired generating unit control'. IEE Control'94 Conference, 1994, no. 389, pp. 379-384 WADDINGTON, J., and MAPLES, G. C.: 'The control of large coal and oil fired generating units', lEE Power Engineering Journal, 1987, 1, (1), pp. 25-36

Chapter 4

Generator excitation control using local model networks M.D. Brown, D. Flynn and G. W. Irwin

4.1

Introduction

The increasing complexity of electric power systems, coupled with the demands of economic and operational requirements, drives the need for continuing improvements in power plant performance and control. Accurate plant modelling and subsequent controller design is paramount to attaining the required performance and to seeking future improvements in design and operating procedures. Conventional fixed parameter control technology is unable to provide the most effective plant and system control over the full non-linear power plant operating range (Kanniah et al., 1984). Moreover, the tuning and integration of the large number of control loops typically found in a power station can prove to be a costly and time-consuming business. Research studies have suggested a number of strategies, such as adaptive control, that attempt to improve overall control of turbo-generator systems, extending their operational stability margins (Wu and Hogg, 1991). The main difficulty, however, with adaptive control strategies lies in the robustness of the parameter estimation stage. So, if a self-tuning controller is to be a practical prospect, it must incorporate a reliable jacketing scheme. One solution to these problems is to obtain an accurate non-linear model of the plant, and use this in an appropriate control scheme. However, these methods tend to be very complex and, as such, have had limited success in industry (Unbehauen, 1996). Recently, neural networks have generated considerable interest as an alternative nonlinear modelling tool (Hunt et al., 1992). Utilising the ability of the neural network to approximate arbitrarily non-linear vector functions and combining this with dynamic elements such as integrators, filters or delays, yields a powerful, yet relatively easily applied modelling technique. In power systems, neural networks have been applied to load forecasting, alarm processing and system diagnostics. However, the application

102

Thermal power plant simulation and control

of neural networks for modelling and control does have some fundamental limitations. Firstly, the non-transparent, black-box approach makes it difficult to incorporate a priori system information, and secondly, neural network modelling fails to exploit the significant theoretical results available in the conventional modelling and control domain, making it very difficult to analyse their behaviour and to prove stability. An alternative approach that facilitates the use of conventional control techniques within a non-linear context is the local model network (LMN). This chapter investigates the use of LM control for generator excitation control, and compares its performance with both a conventional fixed gain controller and a more sophisticated model-based self-tuning regulator, when used to control a laboratory-based microalternator system. The chapter begins with a description of the LM technique and explains how the technique is used to both model the generator system and to form a transparent and simple non-linear controller. The micromachine test facility is then described and all three controllers are compared against a series of typical disturbance rejection and set-point-following scenarios.

4.2

Local model networks

Local model networks are a recent development in the neural network field (MurraySmith and Johansen, 1997). The architecture can be considered as a generalisation of a radial basis function neural network and is similar in form to a Takagi-Sugeno fuzzy inference system, Figure 4.1. The output, ~, of the LMN is given by:

M = F(~k, ¢p) = Z fi(¢)Pi(CP). i=1 The M individual local models fi (~) are functions of the measurement vector ~, and are multiplied by a basis or interpolation function Pi (¢P). ¢Pis a function of the current

~--

controller

Inputs

controller Model/ controller

Interpolation~)-----------~[ controller Model/ regions Figure 4.1

Local model network structure

Output

Generator excitation control using local model networks

103

operating region vector, and can be generated from a subset of the measurement data available, rather than using the full model input vector, ~t. The basis functions Pi (~0) are commonly chosen to be normalised Gaussian functions: exp (-II~0 - cill2/2a 2)

Pi(~O) =

cill2/2~ 2)

EM_I exp (--lifo -

where ci and ai represent the centre and width of each multidimensional Gaussian function. The interpolation function can be viewed as a model validity function, such that Pi (~0) --~ 1 in regions of ~0 where the local f / 0 are such that F(,) is a good approximation to ~, while Pi (~0) ~ 0 when the local f / 0 are such that F(,) is not a good approximation to ~. In order to take advantage of established linear techniques at the control design stage it is customary to use linear local models such as ARX (AutoRegressive model with eXogenous input), ARMAX (AutoRegressive Moving Average model with eXogenous input), state space, etc. Hence, if the local models are of the linear ARX form, and y(k) and u(k) are the plant input and output at time k,then the LM network represents the non-linear ARX model ~(k + 1) = otly(k) + ct2y(k - 1) + ..- + Ctn~+ly(k - nc~) + ~ou(k) + ~lu(k - 1) + . . . + f l n u ( k - n~) where n,, n~ > 0, and if aij and bij are the parameters of the local linear ARX models, then the parameters ~j and flj are dependent on the operating point, ~o(k), such that M

aJ = Z i=l

M

PJ (¢p(k)) aij,

flJ = E

PJ (~o(k)) bij.

i=l

It is worth noting that in comparison with, for example, adaptive control schemes, where the equivalent f f j and fljare time varying to represent non-linearities in plant behaviour, here they depend on the operating point (Brown et al., 1997). 4.2.1

Plant modelling

A major advantage that the local model network structure offers, over other nonlinear modelling techniques, is that a priori knowledge of the process can be utilised in model structure selection, e.g. the number and initial position of the interpolation functions, the form of the local models, and the operating point vector. For the present application of an automatic voltage regulator (AVR), a linear single-input single-output (SISO) ARX model of the generator-exciter system (Wu and Hogg, 1988) can be formed as: a ( z - l ) y ( k ) = B ( z - l ) u ( k - kd) + ~(k)

(4.1)

where the system output, y(k), is represented by the terminal voltage, VT, of the synchronous machine, and the system input, u(k), by the exciter voltage, VR. kd is

104

Thermal power plant simulation and control

the time delay in an integer number of samples, ~(k) is a zero mean white noise sequence disturbing the system, at sample time k, and z -1 is the backward shift operator. Here the polynomials A ( z - 1) and B ( z - 1) are deft ned as: A(z -1) -- 1 + a l z -1 + a 2 z -2 + . . . +anaz -ha B(z - l ) = bo + b l z -1 + b2z -2 q- "" • q- bnb z-nb

where na and nb are the orders of the respective polynomials. Previous work by the authors and others, based on both simulation and practical studies, has suggested that second-order ARX models are sufficient to capture the main dynamics of the AVR loop, and hence suitable selections are na = 2, n b = 1 (Brown and Irwin, 1999). The operating point of an alternator, synchronised to an infinite busbar system, is normally defined in terms of its real power output, Pr, and reactive power output, QT. For the local model network it is, therefore, convenient and intuitive to select the operating point ~o(k), as the vector [Pr(k) QT(k)]. Each local linear model can then be identified for small perturbations about different values of PT and QT. In an attempt to determine M, the number of local models required to adequately cover the operating space for the application, response time and gain characteristics were examined, Figures 4.2 and 4.3. These were obtained by performing open-loop step tests in simulation across a wide range of operating points. The response time is determined as the time to reach approximately 63 per cent of the final, steady-state

vt/vr res ~onsetime

•

.

.

.

.

...

4020-

~

10-

~

5

~

2 0.8 0.5 Reactive power (p u )

Figure 4.2

0

02

~e~\~°

Synchronous machine response time characteristic

Generator excitation control using local model networks

105

vt/vr gain

4000

-

000 2000

•~

i

-

""'

".......

i.......

. .....................

1000-

°

....

i

i

......... .......

io.

200 0.5 Reactive power(p.u.)

Figure 4.3

8

0

02

~e~\9

Synchronous machine gain characteristic

value, while the gain equates the variation in terminal voltage to that of the exciter input. It is clear that the turbo-generator system is highly non-linear, particularly when operating at leading power factors where QT < 0. It is also interesting to remember that a synchronous machine is open-loop unstable when PT is high and QT sufficiently negative. By inspection, seven local models were considered sufficient to provide an accurate representation, with the majority of these models being centred in the leading power factor region where the variation in non-linearity is changing most rapidly. In order to create a more parsimonious representation, a hybrid optimisation strategy was implemented, whereby a least squares cost function was minimised using non-linear optimisation for the centres and widths (ci and o-i ) of the interpolation functions, followed by linear optimisation of the local linear models (aij and bij) (Brown et al., 1997). The cost function was formed as the predictive errors of the LMN against an extended training data set. However, if Figure 4.2 is re-examined it indicates that the minimum plant response time is around 1.6 s which would suggest a steady-state sampling interval of approximately 300 ms, while an AVR requires a sample period of 10-20 ms to enable boost/buck excitation transient response post fault. This requirement potentially conflicts with the actual response time of the turbogenerator itself and could lead to ill-conditioning of the linear optimisation due to oversampling effects. Consequently, training of the LMN was performed using training data sampled at 300 ms, in order to establish the interpolation region parameters, given that the operating point changes comparatively slowly. Subsequently, with the interpolation region parameters fixed, the local linear models were identified using a linear optimisation method with a sampling period of 20 ms. Such an arrangement

106 Thermal power plant simulation and control Interpolation on model 1

0.5 0.4 0.3 0.2 0.1 0 0.6

Reactive power

4).2

0

Interpolation on model 2

0.5 0.4 , . '

....~

.

.

0.3

...i . . . . . . . ':

. ,

0.2

...i ....... i

i .....

i .....

o.1

...i ....... ! "

i

'

07 0.6

: 0.4

b Reactive power

Figure 4.4

1 0 ~ . ~ _ ~ ~ 4).2 0

0.4 Real power

LMN interpolation regions

reduces the amount of training data required, and it, furthermore, speeds up the optimisation process. The training data itself was obtained on a laboratory micromachine by superimposing a pseudo-random binary sequence (PRB S) on the exciter input with a 20 ms sample period, while driving the plant across different regions of the operating space. This type of perturbation is permissible on real plant, and would be largely undetectable

Generator excitation control using local model networks

107

Interpolation on model 3

0.5

i....... :

0.30.4

~ ~ ' . . !

'

0.2 ...... ~

"1

C

....... :.

:

,:. <.

0.4 d Figure 4.4

Reactivepower

1 ~).2 0

0.2

Real power

LMN interpolation regions (Continued)

as the operating point of the machine changes during scheduled load-following or two-shifting operations. The data was then decimated to create the LMN model with a sample period of 300 ms. The result of the optimisation process was that the original figure of seven local models was reduced to five. The normalised interpolation regions for the models are shown in Figure 4.4.

108

Thermal power plant simulation and control Interpolation on model 5

0.4 0.3 0.2

....

.

0.1 0 0.6 "1

P

Figure 4.4

4.3

~l 2

0

Real p o w e r

LMN interpolation regions (Continued)

Controller design

Having developed a non-linear model of the turbo-generator system it now remains to design controllers for each of the individual local models. For comparison between the individual schemes, self-tuning and fixed gain controllers are also described. The fixed gain controller is intended to be representative of existing commercial implementations, while prototype self-tuning schemes have performed acceptably in power stations (Malik et al., 1992), with commercial power system control manufacturers beginning to apply such strategies to their own automatic voltage regulators.

4.3.1

Local model network control

The local model network has been formed from second-order linear models, which makes it relatively straightforward to design appropriate linear controllers for each model. Since these local controllers are interpolated to form a composite control output, in the same manner as the local models, the designer can shape the response of each controller to ensure uniform control performance across the entire operating range. In this way, conventional linear control theory can be exploited within a nonlinear control framework. The transparency of the LM structure permits any suitable linear design method, e.g. PID, generalised predictive control or pole placement, to be used. However, examination of the individual linear models reveals that some of them are both unstable and non-minimum phase; this is not surprising given that individual models were deliberately placed in the leading power factor region. Consequently, for this study

Generator excitation control using local model networks

109

the generalised minimum variance (GMV) algorithm (Wellstead and Zarrop, 1991) has been selected. Form the plant pseudo-output y (k) as y(k + kd) = S ( z - 1 ) y ( k + kd) + W ( z - l ) u ( k ) - R ( z - l ) r ( k ) where r(k) is the set-point, kd the time delay in an integer number of samples, y(k) the system output and u(k) the system input at sample time k, and R(z -1) = ro + rlz -1 + r2z -2 -1- ... -k- rnr z-nr S(Z -1) = 1 + slz - l + s2z -2 + "'" + SnsZ-ns W ( Z - 1 ) = / / 3 0 -~-//)lZ - 1 --[- w2Z - 2 -~- . . . -~- WnwZ-nw"

G(z -1) is introduced as

S(z -1) ----A(z -1) -I- z-kdG(z -1) where G(z -1) = go + glz -l + g2z -2 + . . . + gngZ -ng. Since, in this case na 2 and if it is assumed that kd = 1 and nw = 0, it follows that G(z -1) = go + glz -1 = (sl - al) + (s2 - a2)z -1 ~--

whereupon, the GMV controller equation is defined as (B(z -1) + wo) u(k) = - G ( z - l ) y ( k )

÷ R(z-t)r(k).

(4.2)

For a regulator application r(k) = 0, and since nb = 1, the controller equation reduces to 1

u(k) -- - [-(go + g l z - 1 ) y ( k ) - b l z - l u ( k ) ] • bo + wo

Controller design is completed by selecting the polynomial S(z -1) = 1 + SlZ - l ÷ S2z -2, and the scalar term wo. A convenient approach for choosing S(z - l ) is to assume that it is a discrete, stable, second-order filter. Hence, using the discrete equivalent pole positions to an ideal continuous second-order filter, ~<1:

si = - 2

~ > 1:

Sl------exp(-~oJnTs)[exp(-wnTs ~ 2 ~ - 1 ) + e x p ( w n T s

× exp (-~ognTs)× cos (o)nTs 1 ~ - ' ~~- 2) ~2~-~-1)]

s2 = exp (-2~wnTs) where ~ is the damping ratio, Wn the natural frequency, and Ts the sampling period.

110 Thermal power plant simulation and control The weighting factor, w0, where w0 > 0, permits detuning of the control signals and becomes necessary when dealing with non-minimum phase systems. The selection of w0 trades closeness of desired output reference following against control effort. Since there are five local models, suitable S(z -l) and W(z -1) polynomials can be selected for each of the five controllers, tailored to the particular operating region. These five controllers are operated in parallel and all receive the same input from the plant. The output of each controller is then multiplied by the respective interpolation function, and the resulting weighted signals are summed to form the full control signal, which is then subsequently applied to the plant.

4.3.1.1 Power system stabilisation For practical implementation, the plant output y(k) can be gainfully modified as follows

y(k)=VT(k)+~.w(k)

-1 <,k<0

(4.3)

where VT(k) is the terminal voltage, ~o(k) the rotor shaft speed, while ~ is a factor that determines how much weight is placed on the speed signal. Under some circumstances, the voltage regulator can introduce negative damping into a power system, with almost all the negative damping for a regulated machine originating in the AVR. The inclusion of an auxiliary signal w(k) in y(k) introduces a power system stabilisation (PSS) function to enhance system damping (Kanniah et al., 1984), by introducing a damping torque through regulating the field flux linkage, in phase with variations in shaft speed (Bayne et al., 1975). For large steam turbine generators, turbine shafts cannot be regarded as infinitely stiff, and speed detectors have to be restricted to points along the turbine shaft corresponding to nodes of oscillation. Any vibrations can lead to operational difficulties of power system stabilisers. Consequently, the auxiliary signal may be conveniently derived from electrical output power, although the potential for excessive terminal voltage excursions during mechanical power changes, etc. requires the stabilising signal to be limited. For the micromachine arrangement, excessive vibrations are not considered an issue and speed is adopted as an auxiliary signal.

4.3.2

Self-tuning control

Self-tuning control relies on the principle of separating estimation of unknown process parameters from the controller design (Isermann and Lachmann, 1985). Hence, the scheme can be thought of as consisting of two loops - an outer loop incorporating the process and feedback regulator, and an inner loop containing a recursive parameter estimator and design calculation.

Generator excitation control using local model networks

111

An important aspect of adaptive control is the need for an estimated model of the plant. The SISO ARX model of equation (4.1) is again appropriate: A ( z - 1 ) y ( k ) = B ( z - 1 ) u ( k - kd) + ~(k)

and recursive least squares (RLS) identification can then be employed to identify the parameters of the A(z -1) and B(z -1) polynomials on-line (Wellstead and Zarrop, 1991). As before the plant input u(k) is the exciter voltage and the plant output y(k) is formed, as equation (4.3), as y(k) = V T ( k ) + L o g ( k )

- 1 < X < O.

The parameters of the plant model are allowed to adapt with time, and in this way the non-linearities of the system can effectively be captured. This arrangement contrasts with the LM architecture where the local model parameters are fixed, and the relative contribution of the individual models is determined based on the current operating point. If it is, subsequently, assumed that the estimated parameters represent the true parameters then a selection of methods becomes available to design the self-tuning controller itself. For convenience, and ease of comparison, the identified model is used to design a generalised minimum variance controller, equation (4.2), as (B(z -1) + wo)u(k) = - G ( z - 1 ) y ( k ) + R ( z - 1 ) r ( k ) and the polynomial S(z -1) and the scalar term w0 can again be suitably selected by the user. The task here is slightly more challenging than before since two fixed polynomials are required for the entire operating region, rather than individual polynomials for each local controller.

4.3.2.1 Supervision schemes The non-linear nature of power systems implies that the model of equation (4.1) is only valid for a small region about a given operating point. So, given that a power system is frequently subjected to various disturbances such as transformer tap-changing, line switching and occasional major disturbances such as short-circuits or lightning surges, a self-tuning controller must incorporate a reliable and robust supervision scheme if it is to work safely in practice (Astrom and Wittenmark, 1989). A number of methods have been developed in the literature to ensure satisfactory operation of self-tuning controllers. These usually take the form of protection algorithms for the parameter estimator, and are commonly referred to as jacketing software. Four such methods are now briefly outlined. For the process of identification it is essential that the dynamics of the process are persistently exciting to eliminate ambiguity in the relationship between plant input and output signals. However, under normal circumstances, the excitation present on a system is not sufficiently rich in frequency, and artificial input signals must be introduced. A PRBS is often selected, simulating a white noise process. To ensure

112 Thermal power plant simulation and control that the estimator inputs are persistently exciting the energy (variance) of the control signal can be monitored. It is important that the parameter estimator should be able to track slowly varying process conditions, while at the same time not discarding important information too rapidly. This leads to a scheme involving a variable forgetting factor (Isermann and Lachmann, 1985). However, for a generator system there may be long periods at constant operating conditions, which may cause the estimator to discard old information, and uncertainties in the parameters will rise, leading eventually to estimator wind-up. This problem can be counteracted by monitoring the Kalman gain vector of the estimator, so that should this measure exceed a preset level then the forgetting factor is reset (Brown et al., 1995). Transient disturbances on a power system may give rise to abrupt changes in the estimated parameters, which are not due to a change in the process dynamics. Individual moving boundaries are therefore introduced to protect each of the parameters against such disturbances (Wu and Hogg, 1988). The permissible positive and negative deviations for each parameter are determined as a weighted fraction, r/, of the mean value of the estimated parameter. By adjusting r/and the time period over which the mean is calculated the adaptability of the parameters can therefore be controlled. Finally, perhaps the most important feature of the supervision scheme is deciding when the estimator should be used. During a transient condition, the synchronous machine outputs may vary to an excessive degree, leading to ill-conditioning of the estimator and a model that does not represent the process behaviour. Since the purpose of the control scheme is to regulate the terminal voltage, the deviation of this signal from its set-point has been selected as an estimator deactivation indicator. Consequently, if the terminal voltage deviation exceeds a preset limit the estimator will be switched off, and will only be switched on again once the terminal voltage returns to its preset level, remaining there for a fixed time. This ensures that the estimator will remain deactivated during severe oscillations and generator hunting.

4.3.3

Fixed gain automatic voltage regulator

For industrial applications, an automatic voltage regulator is traditionally implemented as a proportional filter with a transfer function of the form

K

(1 + Tls) (1 + T3s) (1 q- Z2s) (1 -k- T4s)"

The controller is typically tuned from open-circuit step response tests, and as the controller does not incorporate integral action, a steady-state control error may be anticipated. Being intended for industrial use, the software will also contain provision to restrict the AVR output under field forcing conditions to avoid overheating the rotor, VAr limiting under leading power factor operation, overflux protection during generator synchronisation, etc.

Generator excitation control using local model networks

113

Terminal voltage, VT

VTref

5/

I

F

Exciter voltage, VR

-k

G(I + Tls )

Speed deviation, A~o

( | + T2s )

Figure 4.5

Fixed gain AVR implementation

Experience shows that the above arrangement is not able to match the steady-state regulation or transient damping capabilities of the previously outlined schemes (Flynn et al., 1996). Consequently, an alternative fixed gain control scheme is proposed consisting of an AVR coupled with a PSS, Figure 4.5. The controller parameters were obtained using eigenvalue analysis with a linearised tenth-order state variable turbo-generator model (Ahson and Hogg, 1979). Fault studies and long-term operation tests, through simulation and on a microaltemator, have proved the acceptable performance of this controller over a wide range of operating conditions and environments. It should be noted though that the derivation of the fixed gain controller gains is based on an analytical model of the generator system. While this is readily available for a laboratory machine, such models are difficult to obtain in practice, and consequently the selection of individual gains is not a trivial exercise.

4.4

Micromachine test facility

The local model network controller was initially developed and tested using a simulation of a single-machine infinite-busbar system, driven by a boiler/turbine system, with associated step-up transformer and double transmission line (Hogg, 1981). However, a simulation environment has difficulty in representing effects such as non-ideal transducer characteristics leading to limited resolution and noise, computational delays, variations in busbar voltage and frequency, saturation, hysteresis, and other non-linearities present on a real machine. A laboratory micromachine provides a practical test-bed for both measurement and control algorithms under an industrial environment. A full-scale generator will have up to six or more rotating masses, while a micromachine system typically constitutes a two-rotating mass system. It is unrealistic, therefore, to expect results comparable to a full-scale power station. However, it does provide a means of verifying simulations as well as permitting control systems to be tested under real-time conditions.

114

Thermalpower plant simulation and control Field voltage ]_ amplifier ]- Field excitation

d.c.

~ , , . , , , ~

motor Generator Turbine simulation 9 Valve demand

Figure 4.6 4.4.1

Transmission line system

Micromachine system

Micromachine system

The micromachine system, Figure 4.6, consists of a specially designed synchronous generator, with an associated turbine simulator, tied to the busbar through a transformer and artificial transmission lines (Flynn etal., 1997). The synchronous machine is a 3 kVA, 220 V, 50 Hz, four-pole microalternator, whose parameters have been selected to match those of a full-size machine. The alternator is driven by a separately excited d.c. motor, whose armature current is controlled by the analogue turbine simulation. A three-stage turbine with reheater and a fast electrohydraulic governor is emulated, with each turbine stage, reheater and governor being simulated by a single time constant. The weighted sum of signals from each stage is proportional to the turbine mechanical power. The alternator is directly connected to a delta-star transformer which has an onload tap-changing device on the secondary terminals, with tapping ratios from 65 to 116 per cent available in seven steps. This transformer is connected through a transmission line simulation to the laboratory busbar. The transmission system is simulated by lumped-parameter n-networks, representing a typical double line transmission system. Provision is made for the application of short-circuits at the secondary terminals of the transmission transformer or half-way through the line. It is also possible to switch out one of the transmission lines.

4.4.2

Hardware platform

The performance of any control system depends almost entirely on the quality of information received. In an electrically noisy power station environment, reliable and accurate measurements of generator terminal quantities are difficult to achieve. Harmonic interference and unbalanced generator operation inevitably lead to distortion and ripple, while any subsequent filtering may further degrade the information content, especially during transient conditions. Therefore, improved control can only truly be achieved if enhancements in measurement strategies are introduced. 4.4.2.1

Fourier measurement

algorithm

Signals from a synchronous machine are contaminated by harmonics and noise. If a three-phase system is perfectly balanced, the harmonic content in the signals will

Generator excitation control using local model networks

115

cancel out, permitting existing RMS techniques to be applied. However, physical systems are rarely perfectly balanced, so that any unsymmetrical behaviour will invalidate the measurements obtained. Consequently, during transients the RMS measurement may cause violent fluctuations in the controller signal due to the highly oscillatory nature of the estimated feedback signals, and that often means that more advanced control algorithms work no better than their simpler counterparts. An advanced algorithm based on a finite Fourier series has instead been adopted. The Fourier algorithm effectively acts as a band-pass filter, centred around the main power frequency of 50 Hz. High-frequency noise, d.c. offsets, and low frequencies are completely rejected. The harmonic content will also have no effect on the final calculation of the terminal quantities. During even severe transients the Fourier algorithm supplies continuous feedback signals, permitting smooth control. The applied Fourier analysis algorithm is based on an N sample point, moving window approximation to the general Fourier series for a periodic waveform (Brown et al., 1995). As a compromise between accuracy and computational burden, N is selected to be 12. Any periodic waveform, F(t), can be expressed by its Fourier series as Oo

ao

F(t) = -~ + ~_~(an Cos(nt) + bn sin(nt)). n=l Through approximating the series as a0

F(t) = -~- + al cos t ÷ • .. + a6 cos 6t + bl sin t + b2 sin 2t + • • • + b5 sin 5t

(4.4) an expression for F(t) with 12 unknown coefficients is obtained. So, applying equation (4.4) for the sampled point U0, a0

Uo = F(to) =-~ +al cost0 + azcos2t0 + . . . + a6cos6t0 + bl sin to + be sin 2t0 + • .. + b5 sin 5t0. Repeating for the remaining sample points, a system of 12 equations in the 12 unknown coefficients [a0 . . . . . bs] is created. The fundamental components, al and bl, are then obtained as an algebraic sum of past samples as follows,

al = l [ ( U o - U6) q- 4 ( U I

- U5 - U7 =[- UII) Jr" I(U2 - U4 - U8 -1= UIO)] (4.5)

bl = l [ ( u 3 - U9) -[- 4 ( U 2 q- U4 - U8 - UlO) Jr- 1(UI "4- U5 - U7 - U11)].

116 Thermalpowerplant simulationand control The time series filter equations (4.5) and (4.6) are executed at every sample interval to provide a moving average of the fundamental components of the periodic waveform, assuming 12 samples per a.c. cycle. If al and bl are the fundamental components of a phase voltage, and Cl and dl of the equivalent phase current then the electrical terminal quantities of voltage (VT), current (IT), real (PT) and reactive power (QT) can be calculated as

VT=

IT=

?

+2 b 2

1 PT =~(alCl + bldl)

+d2 2

QT=~(aldl-blCl).

An average value can be taken for each quantity by repeating this process across all three phases. Equivalent expressions may be formed in terms of the fundamental components of the line voltages, since the neutral point of a synchronous machine is generally inaccessible: ~/3(alCl

VT:V/~+b26

IT=

?+4 2

+bldl)+(aldl - blCl)

-

4~/3 ~/3(aldl

-blCl)-(alCl + b l d l )

Q~ -

4,v/~

4.4.2.2 Measurement of machine speed and rotor angle Measurement of machine speed and rotor angle is achieved here by attaching an aluminium disc, with four slots cut at approximately 90 ° intervals, Figure 4.7, to the non-drive end of the alternator rotor by a flexible coupling. The disc rotates through Lamps&

_ L _ _ _

\ \" ~ ~.

/

_

,M. c,ock ~

. ., Mlcrocontroller

Slotteddisc

I l

Machine speed

Figure4.7 Speedand rotorangle measurement

Rotor angle

Squared phase voltage q

Generator excitation control using local model networks

117

a fixed head that contains an optical transducer consisting of three lamps, and associated light detectors and circuitry. Each time a slot passes through the fixed head a pulse is generated, triggering the reading of a l MHz counter. A moving average of the last four counts is calculated, corresponding to a complete revolution of the disc, every l0 ms (for a four-pole machine), as a measure of the machine speed. The machine rotor angle is determined in a similar manner to that for speed. A line voltage signal is squared and similarly triggers a further read of the 1 MHz counter. The angle measured is that between the terminal voltage and the generated EME rather than the true transmission angle between the infinite busbar and the generated EMF of the machine. In a power station, the infinite busbar voltage is difficult to measure and so the terminal voltage of the machine would be used instead. This policy has been adopted for measurement of the rotor angle on the micromachine, although the mains signal is available in the laboratory environment.

4.4.2.3

VME hardware system

The measurement and control algorithms have been implemented on a standard VMEbus based system. This structurally open-ended environment is already being used by power system control manufacturers (White et al., 1994), and is well established in many industries. Indeed, the control system has been integrated with and tested on existing industrial implementations (Flynn et al., 1996). The three-phase voltages and currents are sampled using installed instrumentation on the micromachine. The waveforms from the voltage and current transformers are directed through signal conditioning circuits and anti-aliasing low-pass filters, before reaching an analogue I/O board. An Intel 8751 programmable microcontroller generates an interrupt signal at 12 times the system frequency, which triggers the master Motorola 68020 board to read in samples of the filtered electrical waveforms from the analogue I/O board, and to record measurements of machine speed and rotor angle. On completion of a read sequence, the raw values are passed to shared direct memory access (DMA) memory for retrieval by an IMS BO11 T800 transputer. The Fourier measurement algorithm is then performed on the transputer, to produce the four electrical terminal quantities. They are then transmitted along with speed and rotor angle, through a hardware link, to a program running on a TMB04 transputer board. The multitasking parallel implementation of the measurement and control algorithms is facilitated by the use of transputers. The VME transputer can be linked to an external network containing any number of processors. This creates a system with vastly increased computing power, and potentially provides the control systems designer with the opportunity to implement virtually any advanced control strategy.

4.5

Results

Having outlined the development of a local model network controller, the algorithm was subsequently implemented on the VME system using a single transputer module, for testing on the micromachine system. Previously, comprehensive tests

118 Thermal power plant simulation and control were conducted in simulation to ensure both the short-term transient and long-term dynamic stability of the turbo-generator system, following both severe and minor disturbances. During these tests, comparison is made with self-tuning (STR) and fixed gain controller (FGC) schemes. It should be noted that the self-tuning controller is tuned at each operating point, by applying a PRBS input as part of the on-line estimation process, prior to commencing each test. The performance of the controllers is illustrated under the following test conditions: •

• •

Three-phase-earth short circuit, duration 180 ms, after 2 s, at the sending end of the transmission line system, at an operating point of P'r = 0.8 pu and QT = 0.2 pu. Voltage set-point change of A VTref --0.05 pu after 4 s, and subsequent set-point recovery after 9 s, at an operating point of Pr = 0.6 pu and QT = 0.2 pu. Transformer tap change from position 5 to 6 after 4 s, and from position 6 to 5 after 9 s, at an operating point of PT = 0.5 and QT = 0.1 pu. -'-

Figures 4.8 and 4.9 illustrate the terminal voltage and rotor angle responses for the three controllers following the three-phase short-circuit at the sending end of the transmission line. While at first sight the main purpose of an automatic voltage regulator should be to minimise deviations of the terminal voltage, its main role is actually to maintain machine rotor angle, and, therefore, to assist in preserving steady-state stability (Hirayama et al., 1993). Paradoxically, reducing the rotor angle oscillations is more important than minimising voltage deviations after a fault condition. From the responses, it is clear that the LMN and self-tuning controllers provide significantly better damping than the fixed gain controller (despite the explicit inclusion of a PSS), with large improvements in the second rotor angle swing and subsequent oscillations. For all controllers the terminal voltage rapidly recovers, following the clearing of the short-circuit. Figure 4.10 shows the FGC, STR and composite LMN controller inputs. The responses are somewhat similar in shape, although the STR is significantly more vigorous - this is partly due to the injection of a PRBS, during the first few seconds, to aid estimation model convergence. Figure 4.11 shows the output of the LMN local controllers, which are subsequently multiplied by the weightings of Figure 4.12, and then combined to form the composite response of Figure 4.10. Prior to the fault, the contribution from controllers 1 and 2 is insignificant, which can be understood by examining the interpolation functions of Figure 4.4a and b. It can be seen in Figure 4.11 that the controller responses vary significantly, confirming the fact that they have been tuned for different nominal operating points. During the fault, the operating point changes rapidly causing highly non-linear behaviour, and the relative contributions of the individual controllers changes significantly, with individual local controllers being phased in and out at various stages of the event. By contrast, the protection software for the self-tuning controller will ensure that the estimator is deactivated during the voltage transients, which effectively freezes the identified model parameters.

Generator excitation control using local model networks 1.3 1.2 1.1

o 0.9 >

~ 0.8 0.7 0.6 0.5

0

i

i

i

i

i

i

1

2

3

4

5

6

Time (s)

Figure 4.8

Three-phase short-circuit- terminal voltage

85 8O 75 70 65 60 •

.

.

.

.

.

.

.

.

.

.

55 50 45 0

i

i

L

i

i

h

1

2

3

4

5

6

Time (s)

Figure 4.9

Three-phase short-circuit - rotor angle

7

119

120

Thermal power plant simulation and control 5:

,~.

O >

i

2

0

-2 -3 -4 0

1

2

3

4

5

6

7

Time (s)

2 1

o

0 -1 -2 -3 -4 -5

b

Figure 4.10

[

I

I

I

I

I

1

2

3

4

5

6

Time (s)

Three-phase short-circuit- controller outputs

Figures 4.13 and 4.14 illustrate the terminal voltage and rotor angle responses following successive voltage set-point changes. Here, the LMN responses are well damped with a short settling time. The steady-state voltage regulation for all the controllers is acceptable, although the STR response is now more clearly overdamped and, as seen from Figure 4.15, the controller remains vigorous in operation. Figure 4.16

Generator excitation control using local model networks

2

0 o

-2 -3 -4 -5

i

t

I

i

i

t

l

2

3

4

5

6

c

Time (s)

Figure 4.10

Three-phase short-circuit - controller outputs (Continued)

L

I

i

[-- lmn controller outputs

2 &

1

~-o

0

a<

-2 -3 -4 -5

0

L

i

1

2

11 I

i

J

i

3

4

5

6

Time (s)

Figure 4. I 1

Three-phase short-circuit - L M N local controller outputs

121

122

Thermal power plant simulation and control 0,7

i

i

,

[-- lmn controller weights [ 0,6 0.5 ¢3

0.4

e~

._= 0.3 0.2 ol

2 0~

,

7~

0

1

2

gN

3

i

i

i

4

5

6

7

Time (s)

Figure 4.12

Three-phase short-circuit - LMN interpolation weightings

1.15 1.14

1.13 "~ 1.12

g 1.11 o

> 1.1 .3 ~ 1.09 El .08 1.07 i

5

10 Time (s)

Figure 4.13

Voltage set-point changes - terminal voltage

15

Generator excitation control using local model networks

123

54 52 50 48 46 *6 44 ..'.

42 ~ 40 38

I

0

5

10

15

Time (s) Figure 4.14

Voltage set-point changes - rotor angle

displays the relative contributions of the five local controllers. It is interesting to note that the contribution from controllers 2 and 4 is increased at the higher operating point, i.e. the rotor angle is increased, while that from controllers 3 and 5 is decreased. Finally, the tap change between positions 5 and 6 corresponds to an 8 per cent variation in the output of the delta-star transformer. Figures 4.17 and 4.18 illustrate the voltage and rotor angle responses, with the LMN and STR controllers again providing excellent damping with a very fast transient response. The LMN controller proves slightly better at minimising the rotor swings, with the STR response marginally over-damped. The presence of a PRBS during the first 3-4 seconds can again be seen on the STR responses. Figure 4.19 shows the relative weightings of the LMN local controllers. In a similar manner to the voltage set-point test, the majority of the control signal is formed from models 2, 3 and 5 at the original operating point, while during the transient phase the contribution from controller 2 is significantly reduced, leaving controllers 3 and 5 to each provide approximately 40 per cent of the excitation signal. As a final point, it can be seen that controller 1 does not play a significant role either in steady-state or during transients for any of the test scenarios presented. By examining Figure 4.4a it can be seen that the associated model is centred at an operating point of approximately PT = 0.1 pu and QT = 0.1 pu. This model is required to ensure that the LMN controller is capable of maintaining performance over the entire operating region, however, it is unlikely in practice that the generator will be required to operate at such low output levels.

124

Thermal power plant simulation and control

2

.6

l

~o e~ o

0

u~

2 -3 -4 -5

i

i

5

10

15

Time (s)

a

5

~.

Q >

I--Imnl

2

0

-2 -3 -4

-5

i

10

5 b

Figure 4.15

4.6

15

Time (s)

Voltage set-point changes - controller outputs

Conclusions

Industrial AVR implementations are typically based on proportional filters, and offer relatively crude performance with a steady-state control error and poor regulatory capabilities. Even the fixed gain scheme presented here would provide much improved performance, but requires the availability of an analytical model of the synchronous

Generator excitation control using local model networks

~.

2

eo Q

~,.~

0

.a,~,~,,~,....~.a~,_~, ,~

.~ -| -2 -3 -4 -5 0

5'

Figure 4.15

10'

15

Time (s)

C

Voltage set-point changes - controller outputs (Continued)

0.4

m

3 0.35

5

0.3

I -- lmn controller weights [ 0.25 e~o

0.2

..~

0.15 0.1 0.05 /~.

0 0

Figure 4.16

,,/N~ f

5

Time (s)

10

Voltage set-point changes - L M N interpolation weightings

15

125

126

Thermal power plant simulation and control 1.15

1.1

1.05 0

.=.

1

E0.95

0.9 0

2

4

i

i

i

6

8

10

12

14

Time (s)

Figure 4.17

Transformer tap changing - terminal voltage

55

50

45

40 o

35

30

25

0

i

i

2

4

6

8

Time (s)

Figure 4.18

Transformer tap changing - rotor angle

10

12

14

Generator excitation control using local model networks 0.45 - -

r

_

r

1

I-

lmn controller

127

weights I

0.4 0.35 1~

0.3 taO

0.25

3 ~

.=.

2

0.2 0.15 0.1 0.05 0

Figure 4.19

0

~

2

4

6 8 Time (s)

10

12

14

Transformer tap changing - LMN interpolation weightings

machine to determine the control gains. Consequently, a local model network controller has been developed for the excitation loop of a synchronous machine. Using information from plant tests and previous simulation studies, estimates were obtained for the non-linear interpolation regions and the structure of the local linear models. Subsequently, a hybrid optimisation algorithm was applied to provide a parsimonious representation to capture the non-linear dynamics of the system. Generalised minimum variance controllers were then designed for each of the local models. Using a laboratory micromachine setup, the performance of the LMN controller was compared with a GMV self-tuning controller and a fixed gain arrangement comprising an AVR and PSS. A range of tests was performed and the LMN controller provided excellent disturbance rejection and set-point-following capabilities. The performance of the self-tuning controller was comparable with the LMN scheme, but requires significant protection software to safeguard the on-line model estimation. By contrast, the interpolation regions and GMV parameters for the LMN controller were selected off-line, leading to a much more robust implementation, while maintaining performance over the entire operating regime. The LMN approach to improved excitation control is therefore seen as a low-risk option compared with self-tuning control and more complex non-linear techniques such as neural networks.

4.7

References

AHSON, S. I. and HOGG, B. W.: 'Application of multivariable frequency methods to control of turbogenerators', Int. J. Control, 1979, 30, (4), pp. 533-548

128 Thermal power plant simulation and control ASTROM, K. J. and WITTENMARK, B.: 'Adaptive control' (Addison-Wesley, 1989) BAYNE, J. P., KUNDUR, P. and WATSON, W.: 'Static exciter control to improve transient stability', IEEE Trans. Power Apparatus and Systems, 1975, 94, pp. 1141-1146 BROWN, M. D. and IRWIN, G. W.: 'Non-linear identification and control of turbogenerators using local model networks'. 1999 American Control Conference, San Diego, 1999, pp. 4213-4217 BROWN, M. D., LIGHTBODY, G. and IRWIN, G. W.: 'Non-linear internal model control using local model networks', lEE Proceedings Part. D, 1997, 144, (6), pp. 505-514 BROWN, M. D., SWIDENBANK, E. and HOGG, B. W.: 'Transputer implementation of adaptive control for a turbogenerator system', Int. Journal of Electric Power & Energy Systems, 1995, 17, (1), pp. 21-38 FLYNN, D., HOGG, B. W., SWIDENBANK, E. and ZACHARIAH, K. J.: 'A self-tuning automatic voltage regulator designed for an industrial environment', IEEE Transactions on Energy Conversion, 1996, 11, (2), pp. 429-434 FLYNN, D., MCLOONE, S., BROWN, M. D., SWIDENBANK, E., IRWIN, G. W. and HOGG, B. W.: 'Neural control of turbogenerator systems', Automatica, 1997, 33, (11), pp. 1961-1973 HIRAYAMA, H., TONE, Y., TAKAGI, K., MURAKAMI, H., SHIBATA, M., NAGAMURA, H. and TAKAGI, Y.: 'Digital AVR application to power plants', IEEE Transactions on Energy Conversion, 1993, 8, (4), pp. 602-609 HOGG, B. W.: 'Representation and control of turbogenerators in electric power systems', in NICHOLSON, H. (Ed.): 'Modelling of dynamic systems' (P. Peregrinus, London and New York, 1981) pp. 112-149 HUNT, K. J., SBARBARO, D., ZBILOWSKI, R. and GAWTHROP, P. J.: 'Neural networks for control systems - a survey', Automatica, 1992, 28, (6), pp. 108-112 ISERMANN, R. and LACHMANN, K. H.: 'Parameter adaptive control with configuration aids and supervision functions', Automatica, 1985, 21, (6), pp 625-638 KANNIAH, J., MALIK, O. P. and HOPE, G. S.: 'Excitation control of synchronous generators using adaptive regulators', IEEE Trans. Power Apparatus and Systems, 1984, 103, (5), pp. 897-910 MALIK, O. P., MAO, C. X., PRAKASH, K., HOPE, G. and HANCOCK, G.: 'Tests with a microcomputer based adaptive synchronous machine stabilizer on a 400 MW thermal unit', IEEE Transactions on Energy Conversion, 1992, 8, (1), pp. 6-12 MURRAY-SMITH, R. and JOHANSEN, T. A.: 'Multiple model approaches to modelling and control' (Taylor and Francis, London, 1997) UNBEHAUEN, H.: 'Modelling of nonlinear systems'. EURACO Workshop on 'Control of nonlinear systems: theory and applications', Portugal, 1996, pp. 201-218 WELLSTEAD, P. E. and ZARROP, M. B.: 'Self-tuning systems - control and signal processing' (John Wiley, 1991)

Generator excitation control using local model networks

129

WHITE, B. J., ZACHARIAH, K. J. and HINGSTON, R. S.: 'Commissioning of a power system stabilizer using a dynamic signal analyzer'. IEE Control '94, Coventry, 1994, pp. 356-361 WU, Q. H. and HOGG, B. W.: 'Robust self-tuning regulator for a synchronous generator', IEE Proceedings Part. D, 1988, 135, (6), pp 463--473 WU, Q. H. and HOGG, B. W.: 'Laboratory evaluation of adaptive controllers for synchronous generators', Automatica, 1991, 27, (5), pp. 845-852 ZACHARIAH K. J., FINCH, J. W. and FARSI, M.: 'Application of digital selftuning techniques for turbine generator AVRs'. Proc UPEC, Aberdeen, 1990, pp. 623-626

Chapter 5

Steam temperature control T. Moelbak and J.H. Mortensen

5.1

Introduction

A power production system is a very complex structure - in a technical sense as well as in a business sense. In a control sense it can be regarded as a multilevel distributed system - see Figure 5.1. At all levels optimisation is very important and top-level performance is dependent on the performance of all the underlying levels. The steam temperature control of a power plant is part of the process control level and strongly interacts with the plant control level as well as the servo system level.

es

rvo systems

Figure 5.1

Control levels in a power production system

132 Thermal power plant simulation and control The control of steam temperatures in power plants is one of the most widely discussed control problems in power plants. The reasons for the extensive attention to this problem are mainly found in issues such as:

•

•

•

•

Plant lifetime: The steam temperature control has a significant influence on the variation of the steam temperatures and accordingly on the thermal stress of the plant. A significant reduction in the low cycle fatigue of superheaters, headers and turbine can of course be advantageous. If the variation in the steam temperatures is large, e.g. -4-10°C during steadystate operation due to a poorly performing control loop, lifetime improvements can be obtained to some degree by introducing better control performance. For small temperature variations, e.g. ±2 °C during steady-state operation, the costs incurred will most probably exceed the profits as regards increased lifetime. Efficiency: If the steady-state variations can be reduced significantly, the outlet set-point can be increased and the turbine efficiency will increase accordingly. If the fluctuations during normal operation are already small, the potential for increasing the set-point is of course modest. An important point when determining the upper set-point limit is the temperature distribution across the superheater pipes to the outlet header. The steam temperature control has no influence on this distribution. A rule of thumb says that increasing the live steam temperature by 10 °C will increase the efficiency of a 400 MWe unit by approximately 0.25 per cent, leading to large fuel cost savings. Load-following eapahility: Improved steam temperature control improves the boiler stability, which can improve the load-following capability of the plant significantly. Improving the boiler stability in general can, of course, lead to improved load-following capability, but it is crucial in so-called special situations such as load changes, start/stop of coal mills, soot blowing, fault situations, etc. Since the power market is becoming increasingly liberalised, the load-following capability is increasingly becoming an important commercial parameter in the competition. Availability: The improved overall stability and the resulting reduced probability of forced plant outage is an indirect advantage of improving the steam temperature control. Nevertheless, it is an important advantage - e.g. a forced outage of a coalfired base-load unit will imply additional fuel costs for restart, lack of power sales, increased wear of the plant and reduced availability. The costs of a forced outage will be dependent on plant size, time of occurrence, duration, but will most often be of major economic significance.

This chapter will focus on steam temperature control based on the experiences of Elsam-owned power plant in Denmark with emphasis on once-through boilers. After introducing the processes in question and outlining conventional control strategies, the focus will be on advanced control strategies. Due to the fundamental

Steam temperature control

133

differences in behaviour the discussions will be separated into evaporator control and superheater control.

5.2 5.2.1

Plant and control description Plant description

A characteristic feature of the once-through boiler is that the pumps force the feedwater/steam through the boiler tubing, which in principle is arranged a continuous pipe. In contrast to a drum boiler there is no large internal water reservoir. The nomenclature used throughout this chapter is shown in Figure 5.2. The boiler process includes several steam superheating processes - most often boilers include superheaters in a number of levels often divided into parallel lines thus giving typically 4-8 high pressure superheaters and 2-4 intermediate pressure superheaters. Each of these processes serves as an energy transferring system-energy being transferred from the flue gas to the steam. Each superheater is equipped with an attemperator device (water injection at the inlet) for control of the steam outlet temperature. A superheater process with its typical instrumentation is shown in Figure 5.3.

Once-through boiler

ser

m

Is

%11 Feedwater

Figure 5.2

Outline of steam power plant. Eco: economiser; Eva: evaporator; Sh: high-pressure superheater; Ish: intermediate pressure superheater; Att: attemperator

Thermal power plant simulation and control

134

rhi

Steam outlet Steam

Ill

Energy transfer from flue gas

Figure 5.3

5.2.2

Superheater process with typical instrumentation: To: outlet steam temperature (°C); Ti: inlet steam temperature (°C); X: valve position (%); mi: water injection flow (kg/s)

Control characteristics

The interactions between the inputs and outputs of the once-through boiler can be set up in a matrix equation:

y(s) = G(s)u(s)

psh3(s) rshl(S)l Zsh2(s)l=lg Tsh3(s) / ]qsh2(s)l

i /,mfwS,,

I-g~(s) g~*2(~) g~(s)g~(s)g+(s) 1 ~,hfue,(S)1 (s) /g41(s) Lgs+(s)

g (s> O g;2(s) g33 (s) g4z(s) gs-2(s)

g43(s) g53(s)

o 0 g~(s) g54(s)

(5.1)

/,ha,, (s)/ . /rhatt2(s)/

g ~ ( s ) l Lrhatt3(s).J

The sign of the response is shown as a superscript on the individual transfer functions. The control problem can be characterised as being: • • • •

multivariable the dynamics are of high order (lumped system) the dynamics (time constants and gains) are load dependent it is exposed to major stochastic disturbances from flue gases

5.2.3

Conventional control

5.2.3.1 Evaporator control The control of the steam temperature in the low part of the boiler is tightly connected to the control of the live steam pressure, utilising the main boiler inputs, feedwater flow and fuel flow. The reason why the control of these two variables is so very tightly

Steam temperature control

135

Load demand(La)

Temp. ~,

I ~ Kp(Ld) Ti(Ld) Enthalpy

Pressure Kp(td) ~'i(Ld)

~Fe FF edwater ~,demand

Figure 5.4

L

FF Fuel ~, demand

Control diagram for Benson boiler: fl (x), f2(x): set-point generation from load demand; F FI (s), F F2(s): feedforward transfer functions; Cl(S), C2(s): decoupling network; PI(D): feedback controllers with proportional gain and integral time scheduling from load demand

connected can be found in equation (5.1), where it is clear that we are dealing with a fully connected 2 × 2 system from mfw and mfuel to Tsnl and Psh3. The conventional control of feedwater and fuel flow is normally divided into a feedforward control (FF) and a feedback control (FB). Figure 5.4 shows an example of a control diagram structured according to the above.

5.2.3.2

Feedforward control

The purpose of the feedforward control structure from the load demand to the feedwater and fuel demand is to feed the correct amount of feedwater and fuel to the boiler. From a static point of view the required input is known for each parameter to operate the boiler at a certain load point. This is given through the gain = 1 part of the feedforward structure. The other part of the feedforward is a filter which ensures that the feedwater and the fuel are fed to the boiler in a dynamically optimal way thus

136

Thermal power plant simulation and control

ensuring that no control fault arise - neither for the temperature nor for the live steam pressure during load changes. Because of the presence of large time constants in the boiler due to the large metal masses and delays in the firing system there is a limitation to how hard the feedback loops can be tuned. This implies that if it is required to operate the plant at large load gradients or it is desired to stress the plant as little as possible the presence and correct tuning of the feedforward part is very important.

5.2.3.3 Feedback control The purpose of the feedback control is to reject disturbances (the feedforward blocks act as a good 'reference follower' as described above) which mostly originate from the furnace during normal operation (mainly due to changes in fuel flow and quality). The feedback control consists of a temperature and a pressure control loop. The Tshl temperature is controlled by a cascaded control loop. The enthalpy at the evaporator outlet is PI controlled in the inner loop, while the Tshl temperature is PI controlled in the outer loop, as illustrated in Figure 5.4. The reason for controlling the entbalpy at the evaporator outlet instead of the steam temperature is that in this way non-linearities originating from the steam characteristics are automatically incorporated. The proportional and integral part of the PI controllers must be scheduled according to the actual load point since the gain and time constant of the boiler are highly dependent on the load point (because of the change in steam flow). The live steam pressure is controlled by a single PID-based control loop. For this loop the parameters of the PID controller must also be dependent on the actual load point following the same arguments as above. Since the boiler process is fully connected (the feedwater flow and the fuel flow affect both the steam temperature and the live steam pressure) it is important to introduce a decoupling network between the two feedback loops. Consequently, the two feedback loops can be tuned independently and with as high a bandwidth as possible since no oscillatory modes will arise between the two feedback loops. Isermann (1989) presents three different representations of a decoupling network.

5.2.3.4 Superheater control As can be seen from equation (5.1) the superheaters form part of a multivariable system. Nevertheless, the superheater control problem is conventionally considered as a SISO control problem. A simple example of an existing scheme for steam temperature control is shown in Figure 5.5. This is a cascade control based on fixed PID controllers in which the controlled variable is the outlet temperature. The inner loop is required to reject temperature disturbances originating upstream. The inner loop is, of course, much faster that the outer loop. Due to the load dependent dynamic and gain variations, a strategy based on fixed controllers, like that shown in Figure 5.5, can only be well tuned in one operating point.

Steam temperature control

ro

+

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Pl-based control strategy at Skaerbaekvaerket, Unit 2

Performance can be improved relatively easily by introducing load-dependent gain scheduling in the inner control loop. In special cases where the superheater operation is close to the wet steam range, gain scheduling in the outer loop might also be beneficial. Furthermore, introduction of feedforward disturbance compensation may also improve performance, e.g. using fuel flow as an indicator of combustion disturbances. Further details on conventional superheater control can be found in Klefenz (1986).

5.3

Advanced evaporator control

Adopting the control structure described in section 5.2.3 and assuming model-based tuning has been performed, it is possible to obtain good performance, for the loadfollowing operation as well as for disturbance rejection during steady-state operation. To estimate the boiler dynamics for the purpose of performing model-based tuning, an open-loop test must be performed or estimation performed in closed loop. Both tasks might be difficult. Furthermore, for plant equipped with non-programmable control systems the implementation of the conventional way is quite tedious. To overcome these difficulties, an alternative concept has been developed. The objective was to improve the load-following capability of existing power plant units. During fast load changes, the major problem is to keep certain critical variables (e.g. steam temperature and steam pressure) within predefined limits, as excessive

138

Thermal power plant simulation and control

Load demand ""~1

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Figure 5.6

Scheduled LQG controler

Boiler

Scheduled LQG controller with feedforward action from load demand signal as a complement to an existing boiler control system

deviations will seriously affect the lifetime of the components or cause a trip. One way of improving the load-following capability of power plants is to improve the control of these critical variables. In order to increase the robustness and facilitate commissioning and switching between automatic and manual modes, the control system has been designed as a complement to the existing boiler control system. Figure 5.6 shows how an optimising LQG controller is connected to the boiler process and the existing control system. It can be seen from the figure that the optimising LQG controller calculates an additive control signal, Uad~t, from the control error, e, and from the load demand, which is added to the control signal from the existing control system. The process to be controlled thus comprises the boiler as well as the existing boiler control system. The additive control signal, Uaad, can be weighted between 0 and 1, which facilitates commissioning and switching between automatic and manual operating modes. In stationary operation when the control error is 0 and the load demand is constant, the additive control signal is 0, because no integral action is included in the optimising controller (this is normally present in the existing boiler control system). When a control error arises, or when a load change is imposed on the boiler, the optimising controller will be active.

5.3.1

L Q G controller

The problem of finding the control law for a linear state space system, when the states are directly measurable, can be solved by minimising a performance index formulated as a weighted quadratic function of the states and the control signal. Minimising this function results in an optimal linear controller known as the linear quadratic regulator

Steam temperature control

139

(LQR). When stochastic perturbations are considered, the linear quadratic Gaussian (LQG) regulator is obtained. In this case the states must also be estimated. The state space model of the system to be controlled is:

x(k + 1) = Ax(k) + Bu(k) + w(k) y(k) = Cx(k) + v(k)

(5.2)

wherex is the state vector, u the input vector andy the output vector. The process noise w(k) and the measurement noise v(k) are assumed to be sequences of independent random variables with zero mean value and covariance: E[w(k)] -- 0, E[v(k)] = 0,

E[w(k)wT(k)] = Rw, E[v(k)vT(k)] = Rv,

(5.3)

E[w(k)vT(k)] = O. According to the separation theorem (Isermann, 1989) the design of the LQG controller can be divided into two parts, one concerned with an optimal control problem and another concerned with an optimal filtering problem. These two issues will be described below. Optimal control: The performance index is defined as:

I =E

xT(k)Qlx(k) + uT(k)Q2u(k

(5.4)

Lk=0

where Q1, positive definite, and Q2, positive semidefinite, are weighting matrices used for tuning the controller. The linear state feedback controller is given by:

u(~) = -Lx(k)

(5.5)

which minimises the performance index. This is calculated by (Isermann, 1989): L = (Q2 + BTSB) -1BTSA

(5.6)

where S is given as the stationary solution to the discrete Riccati matrix equation:

S = QI +ATSA -ATSB(Q2 + BTSB) -1BTSA.

(5.7)

Optimal filtering: A Kalman filter is introduced: ~(k + 1) = AJ~(k) + B u ( k ) + K ( y ( k ) - CYc(k))

#(k) = C~(k). where .~ is the estimated state and K the Kalman gain.

(5.8)

140

Thermal power plant simulation and control The Kalman gain K can be calculated as (Srderstrrm, 1994): K = A P C T ( c P C T + Rv) -1

(5.9)

where P is the stationary solution to the discrete Riccati matrix equation: P = Rw + APA T - A P C T (CPC T + R v ) - 1CPA T"

(5.10)

According to the separation theorem, the state estimate .~ can be used in the control law given in equation (5.5). Another approach is to identify a model in the directly parameterised innovations form, where the Kalman gain is estimated together with the model parameters: .~(k + 1) = A~(k) + Bu(k) + Ke(k)

(5.11)

y(k) = CYc(k) + e(k). It can be shown that equations (5.2) and (5.11) are statistically equivalent descriptions (Van Overschee and Moor, 1996). Since there is often no available knowledge about the covariances in equation (5.3), this method is a good alternative.

5.3.2

L Q G controller with f e e d f o r w a r d action

A state space model of the system to be controlled including a measurable disturbance d(k), is obtained: x(k + 1) = Ax(k) + Bu(k) + Bdd(k) + w(k)

(5.12)

y(k) = Cx(k) + v(k). Feedforward and feedback control based on the LQG theory can then be introduced, as will be explained. In the concept derived, the feedforward feedback parts are tuned individually, which is preferable. The feedforward controller is given as: uff(k) = -Lff.~ff(k)

(5.13)

with the open-loop state estimator: kff(k + 1) = AJ:ff (k) + Buff(k) + Bdd(k).

(5.14)

The feedforward controller matrix, Lff, is calculated as described in the previous section.

Steam temperature control

141

The feedback controller is given as (5.15)

Ufb(k ) = - L ~ f b ( k )

with the closed-loop state estimator: .~fb(k + 1) = aYcfb(k) + Bu(k) + K(y(k) - ~fb(k))

(5.16)

~fb(k) = C~fb(k).

The feedback controller matrix, Lfb, is also calculated as described in the previous section. The structure of the LQG controller with feedforward action is shown in Figure 5.7. g(k)

~,k

+l)r-----~ ~ff(k)

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LQG feedforward and feedback controller

142

5.3.3

Thermalpower plant simulation and control Scheduling an LQG controller

If it is known how the dynamics of a process change with the operating conditions, it is possible to adjust the controller parameters accordingly, known as gain scheduling. A measurable process variable, descriptive of the operating condition and used to adjust the controller parameters, is known as a scheduling variable u and in this context is assumed to be a scalar. A set J = {oq . . . . . am}, containing m values of the scheduling variable is chosen and arranged according to: o~i > 0t'j for i > j. For each value of a in the set J a linear model (A, B, Bo, C, K) is given and for each model the state feedback matrices Lff and Lfb are calculated from equations (5.5) and (5.6). The LQG controller (A, B, C, K, L) can be scheduled between the frozen operating points using linear interpolation: X(a) = X ( a l ) +

X(at+l) -X(at)

(u-at)

(5.17)

~1+1 --~1

wherel=l ..... m-l. A disadvantage of this method is that security is not provided for placement of the closed-loop poles when interloping between the frozen operating points. An alternative and more preferable method is to perform the scheduling directly on the calculated control signals: U(Ol) = U(Oll) d- U(~I+I) -- U(Oq)(0/ -- Otl) ~1+1 - - ~ l

(5.18)

where l = 1. . . . . m - 1. An alternative to the described scheduling policy would be to designate each controller to a specific operating range. To obtain a bumpless change from one controller to another, one needs to perform some automatic adjustment of the inactive controllers. By applying the described scheduling policy this problem is automatically overcome.

5.3.4

Case study

The plant used for test purposes is the Skaerbaekvaerket unit 2 (SKV2), a 265 MW coal-fired unit equipped with a Benson boiler. At SKV2 oscillations in Tshlb and partly Teva and Psh3 (Figure 5.4) are considered as the limiting factor in the load-following capability for the boiler and hence the unit as a whole. Improvement of the control of these variables and especially of Tshlb during load changes, is therefore expected to improve the load-following capability of the unit. The maximum allowable deviations in the outlet pressure (Psh3) are about 7 bar, about 25 °C in the steam temperature after superheater lb (Tshlb) with a maximum gradient in the evaporator temperature of 8 °C/min. Hence during load changes, the design goal is to decrease the deviations primarily in Tshlb,err, but also in Psh3 keeping ATeva < 8 °C/min.

Steam temperature control

143

In the optimising control system, the following control inputs are used: • •

additive control signal to fuel flow, if/fuel,add additive control signal to feedwater flow, rhfw,add.

The following controlled output variables are used: • • •

control error on outlet steam pressure, Psh3,err control error on steam temperature after superheater lb, Tshlb,err evaporator temperature, Teva.

Feedforward control and parameter scheduling are introduced using the boiler load demand PB. Eleventh-order linear state space models of the following form are the basis for the controller design:

x(k + 1) = Ax(k) + Bu(k) + Bad(k) + Ke(k)

(5.19)

y(k) = Cx(k) + e(k) for the operating points JsKv2 = {115 MW, 130 MW, 187 MW, 240 MW} = {43%, 49%, 71%, 91%}. The load range to be covered was chosen so that the normal operating range is covered. The number of load points (four) was chosen to be the minimum possible while allowing for the non-linear dynamic behaviour of the combined boiler and existing control system. The distribution was not chosen to be equally spaced because of dedicated load intervals for start/stop of coal mills. The models were estimated from SKV2 data (PRBS excitation of controllable inputs (u : Uadd) and ramps in boiler load demand (d = PB)) using the N4SID, subspace system-identification method (Van Overschee and Moor, 1994; MathWorks, 1995). 5.3.4.1

Feedforward control

Feedforward controllers of the form (5.13) are designed for each operating point in JSKV2, with the open-loop observer as given by equation (5.14). The sensitivity function from the load disturbance PB to the outputs Psh3,err and Tshlb,err is shown in Figure 5.8 at the 187 MW operating point. Theoretically, this plot reveals that the impact of the load change on Psh3,err and Tshlb,err is significantly reduced (~ 10 dB). Figure 5.9 shows the responses to a load change from 200 to 180 MW at a gradient of 4 MW/min. for cases with and without the LQ feedforward controller active. Figure 5.10 shows the corresponding additive control signals. The offset in TsH,err is caused by the existence of a deadband in the existing control system. The test results show that an almost perfect dynamic compensation of the load disturbance has been obtained with the feedforward controller, since there are practically no deviations in either Psh3 or in Tshlb. The action of the LQ feedforward controller can be interpreted as follows: the decrease in the steam temperature (note that the control error is defined as the reference value minus the measured value) is compensated for by increasing the fuel rate and decreasing the feedwater rate, both resulting in an

144

Thermalpower plant simulation and control Sensitivity from PB to Psh3,err, (187 MW) 20 lOm

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Steam temperature control

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Load change from 200 to 180 MW at 4 MW/min

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increased steam temperature. These two actions have a mutually opposite impact on the steam pressure, which ultimately results in a reduced steam-pressure deviation. Similar improvements have been obtained for all operating points in JsKv2. $.3.4.2

Feedback control

The purpose of the feedback part of the LQG controller with coordinated feedforward action is defined as a general improvement in the stability of the boiler, and specifically to reduce the impact of starting/stopping coal mills on the controlled variables since this event typically occurs during load changes. Start/stop of coal mills introduces significant transient disturbances in the furnace, in the form of a redistribution of the coal and combustion air flow to the furnace, which affect the steam temperatures and the steam pressure. It is intended, by designing the LQG controller given by equations (5.15) and (5.16), to reject disturbances entering the furnace. In practice this is done by tuning the controller with good fuel disturbance rejection properties. In order to test the controller performance a test case is examined in which a 5 per cent fuel ( ~ 1.5 kg/s) disturbance is introduced. A coal mill start/stop has not been used for comparison purposes since the stochastic content in this disturbance is too high. In Figure 5.11 the responses for the outputs Psh3,err and Tshlb,err are shown with and without the LQG feedback controller. Figure 5.12 shows the generated control signals together with the imposed fuel disturbance. It can be seen that the deviations in both outputs are reduced significantly.

146

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Steam temperature control 5.3.5

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Cost~benefit a s s e s s m e n t

The resulting control system consists of the LQ feedforward compensator and the LQG feedback controller as shown in Figure 5.7. In order to adjust to load-dependent non-linearities the feedforward and the feedback control signals are scheduled according to the policy shown in equation (5.18). Similar results to those shown in Figures 5.9 and 5.10 have been obtained with the scheduled LQG feedforward and feedback controller. The field test results reveal that the maximum allowable load gradient can be increased from 4 to 8 MW/min. Furthermore, the test results indicate that it is possible to perform smaller (40-50 MW) load changes without coal mill start/stop at a gradient of 10-12 MW/min.

5.4

Advanced superheater control

As previously mentioned, the development within steam temperature control has until now - almost exclusively focused on feedback control, so it is relevant to survey the predominant methods. Below, an evaluation on a general level will be attempted, starting with practical applications at Elsam power plants. The common characteristics of the power plant involved in the field tests are: • •

coal-fired once-through boiler most dominant disturbances: start/stop of coal mills, soot blowing and load changes.

The objective of the steam temperature control is to maintain specified temperatures after the superheater, independent of disturbances. The outlet temperature is most often controlled by injection of water before the heating surface, as shown in Figure 5.3. All controllers discussed in this section were tuned according to identical criteria. 5.4.1

G e n e r a l i s e d p r e d i c t i v e control

Each strategy was compared to an adaptive control scheme based on the generalised predictive control (GPC) concept, which minimises the performance function:

PcPc = E

+ j ) - w ( t + j)]2 + )~ ~--~[Au(t + j - 1)l 2 j=l

(5.20)

where A u ( t + j - 1) = 0 for j > N,. Here N1 and N2 are the minimum and maximum cost horizons, N, is the control horizon and )~ is the control weight. Further details regarding GPC control theory can be found in Clarke et al. (1987). Adaptivity was obtained by on-line identification of the model parameters using the recursive least squares (RLS) identification method. As shown in Figure 5.13, the GPC controller was introduced in the outer control loop, with the load-dependent

148

Thermal power plant simulation and control

T~

~ T°'ref mst~ msteam,]00B~ °/°

mh.1J

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dynamics it was scheduled as a function of the load (steam flow). As this is an adaptive strategy, a supervisory function is a necessity. The main objectives of the supervisor function are to ensure anti-wind-up in the identification algorithm, an online check of model validity and explicit utilisation of a priori process knowledge. The minimum/maximum selectors in Figure 5.13 were included to limit the scheduling signals. A comparison between the two strategies can be carried out simultaneously, as the second superheater of the boiler is divided into two parallel lines to which the old and the new control strategies were applied. Figure 5.14 shows an example of a field test during which the boiler was exposed to soot blowing and a load gradient - the improvement in temperature regulation is obvious. The improvements are, of course, a result of faster and larger control actions on the control device (water flow), which can be introduced without causing instability because the model-based controller explicitly utilises process knowledge. Figure 5.15 shows another field test result in which the boiler was exposed to a coal mill start after 40 minutes. Again the improvements are evident, with the GPC controller reducing the variation in outlet steam temperature, and effectively rejecting the disturbance by 60 minutes. Further details can be found in Moelbak (1991). The results confirm

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that control of the superheater temperatures can be improved using some kind of model-based control method rather than fixed parameter PID controllers.

5.4.2

PTx control

At the 380 MWe Esbjergvaerket, Unit 3 two model-based control strategies were compared: • •

A strategy based on GPC and the main principles such as the strategy shown in Figure 5.13. A so-called 'simple' model-based strategy as shown in Figure 5.16.

The 'simple' model-based strategy is actually a cascade control with a PI controller in the inner loop and a P controller in the outer loop. To compensate for the high-order and load-dependent dynamics of the superheater a PTx-model of the superheater is used: PTx (s) --

1

(5.21)

thsteam Ts

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Steam temperature control

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the range 3-6. It is sufficient to perform one step response for establishing the PTx model - the scheduling function will adapt the model to cover the total operating range. Due to load-dependent variations in the differential pressure it may be necessary to introduce gain scheduling of the PI controller. Sliding pressure operation and steam temperatures near the saturation conditions may necessitate gain scheduling of the P controller as well. This type of strategy has been widely used by Siemens and others. Figure 5.17 shows that both model-based controllers produce very tight control during soot blowing - the maximum deviation is approximately 2 °C for both controllers. The water injection flows behave in much the same way. In Figure 5.18 the boiler was exposed to one of the most significant disturbances the stopping of a coal mill. In this case the maximum deviation was approximately 8 °C for both controllers. During this sequence, the full control range of both control valves was used. Comparing the two model-based strategies it can be concluded from the field tests that the differences in performance are only marginal, most probably a result of slightly different closed-loop bandwidths which again are a result of minor differences in the tuning of the controllers.

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5.4.3

Fuzzy control

In a simulation study on the utilisation of fuzzy control within the Danish power industry (Moelbak and Hammer, 1996) among other issues, the applicability of fuzzy control for the regulation of superheater temperatures was investigated• The simulations were based on a fuzzy PI controller complemented by a set of 'breaking rules' to handle the high-order dynamics. The rule set is shown in Figure 5.19. In the fuzzy controller, triangles were used as membership functions on the inputs and singletons were used as membership functions on the output. A performance comparison between a conventional PI-based strategy, Figure 5.5, a model-based strategy, Figure 5.16, and a fuzzy-based strategy, is illustrated in Figure 5.20 where the boiler was exposed to disturbance from the flue gas. In this case the controllers were tuned to maximise the disturbance rejection capability without exhibiting oscillatory behaviour.

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NM

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PM

PM

PL

PL

ZE

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(u(t)-u(t- L) = PL) THEN

(Au - PL)

IF (u(t) u(t-L)=PM) THEN (Au=PM) IF (u(t)-u(t L)=ZE) THEN (Au=ZE) IF IF

Figure 5.19

(u(t)- u(t (u(t)-u(t

L) = NM) THEN (Au = NM) L)=NL) THEN (Au=NL)

Fuzzy rule set for superheater PI control: e, &e: control error and change of error; Au: change of control signal; L: load-dependent deadtime

As regards performance (overshoot) the model-based controller is the best, while the P! controller is the worst. Faster and larger control actions can be allowed in the case of the model-based controller as it uses an explicit and accurate process model while the fuzzy controller uses a less accurate and implicit process model (rules). As regards commissioning and tuning the fuzzy controller is significantly more resource demanding compared with the P! controller and the model-based controller. This conclusion is related to the indirect type of process modelling in a fuzzy controller which implies a very time-consuming trial and error type of commissioning.

5.4.4

Dynamic measurement of flue gas temperatures

As already mentioned, the predominant disturbances to the superheater process come from the flue gas. Most of these disturbances are initiated by the processing and combustion of fuel (coal). One possibility for improving steam temperature control further could be to measure the disturbances even before they are reflected in the outlet steam temperature. Such measurements will of course be suitable for feedforward control. The coal flow would be a good measure for the disturbances, but it cannot be measured on a continuous basis. Alternatively, the temperature of the flue gas in the vicinity of the heating surface could be suitable. These considerations have resulted

154

Thermal power plant simulation and control

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0

Figure 5.20

5

10

15 Time (rain.)

20

25

30

Simulation results comparing a fuzzy, P I and model based controllers. At time = 5 min. the superheater was exposed to a disturbance from the flue gas

in a project mainly dedicated to developing an efficient feedforward function based on dynamic measurement of the flue gas temperatures. Until recently, it was the general understanding that reliable dynamic measurement of flue gas temperatures was not possible. Conventional methods, such as thermocouples, suction pyrometry and radiation pyrometry, all involve significant disadvantages/limitations concerning the practical handling and the information quality. Two types of equipment have been investigated with respect to utilisation in boiler control: acoustic pyrometry, exploiting the fact that sound velocity varies as a function of the media temperature - in this case the temperature of the flue gas; radiation pyrometry (new type), exploiting that fact that gases emit electromagnetic radiation in a narrow band of wavelengths - in this case radiation emitted by the CO2 in the flue gas. From field tests of both types it has been found that the equipment based on radiation pyrometry was preferable for feedforward control of superheater temperatures. This decision was based partly on correlation analysis between flue gas temperatures and

Steam temperature control

155

ToZ ,2 ro,~f

~."

mst~ rhsteam'10~B A/B I

Adaptive

::i'::! adiati!n pyrometer

r~

+

l

F"

LL __Min value Max value

Figure 5.21

The control strategy used infield tests in Esbjergvaerket, Unit 3.

steam temperatures and partly on a cost/benefit evaluation. Further details can be found in Moelbak and Jensen (1994).

5.4.5

Feedforward control using radiation pyrometry

The implemented control strategy comprises a feedforward function based on radiation pyrometry and a feedback function based on a model-based controller - see Figure 5.21. The feedforward function consists of two main features: (i)

(ii)

An adaptive filter, which has to filter out the noisy part of the signal. The adaptive feature is necessary because the noise band is dependent on the state of operation, e.g. burner setting - see Figure 5.22. A derivative function with a conventional low-pass filter for which the gain and the time constants have to be tuned.

The idea is that the feedforward action should be inactive most of the time and only intervene when significant disturbances occur. The most frequent and significant disturbance at Esbjergvaerket Unit 3 is the start and stop of coal mills. Figure 5.23 shows a sequence caused by the start of a coal mill. Using the previous approach, feedforward action is only applied to one of the superheater parallel lines. The field test sequence in Figure 5.23 illustrates very well that introducing the feedforward

156 Thermal power plant simulation and control ~1100 L)

~ 1050 1000 c~

950 0

100

Figure 5.22

300

i

400 500 Time(min.)

i

600

i

700

800

i

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Measurement of theflue gas temperature using radiation pyrometry

570 ~-~568 ~ 566 564 . . . . ~ 562 560 I

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Figure5.23

0.5

1

1.5

3.5

4

4.5

Field test results comparing control strategies with and without feedforward. The disturbance is initiated by the start of a coal mill

function halves the temperature overshoot. The significant improvements are due to earlier detection of the disturbance and an accordingly earlier control action, which is clearly indicated by the development of the water flows, shown in Figure 5.23.

Steam temperature control ~" 580

I

575

I

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With feedforward

~ !

~

157

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2

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..............................................................

e~

-5 -10

0

Figure 5.24

1

2

4

5 Time (min.)

10

Field results comparing control strategies with and without feedforward. The disturbance is initiated by a fault situation (fire in separator)

In Figure 5.24 a fault situation occurred - a fire was detected in the separator of one of the coal mills and as a result the coal was forced out. Again significant improvements were obtained for the superheater line on which the feedforward was implemented. The flue gas temperature and the resulting feedforward signal are also shown in the figure.

5.4.6

Cost~benefit assessment

The experiences with different types of feedback controllers are summarised in Table 5.1.

158 Thermalpower plant simulation and control Controllertype

Control performance

Resource demand

PI

Low

Low

Fuzzy

Medium

High

Adaptivemodelbased

High

High

'Simple' modelbased

High

Medium

Table5.1 Comparisonof different types offeedback control methodsfor superheater control The experience acquired indicates that a model-based controller should be used for feedback control of the superheater temperatures, and that the load-dependent dynamics should be handled directly by a scheduling function. When choosing a type of model-based controller the implementation and commissioning effort should be considered. The field test results shown and experience from other plants indicate that an efficiency limit has been reached as regards pure feedback control relying on modelbased methods. This limit is actually set by the superheater itself and is determined by the metal mass of the superheater pipes. As a consequence, it is suggested that future work put less emphasis on the development of feedback control strategies for this process. More likely, improvements in steam temperature control should be sought in other areas: •

•

Steam temperature control makes up only a small part of the boiler process and the control system. The boiler process, on the whole, is a highly multivariable system and further improvements in overall performance, including steam temperature regulation, should be sought using multivariable methods. This issue will not be discussed further here - work on this issue can be found in Nakamura et al. (1989) and in Mortensen et al. (1997). New measurement techniques are continually being developed and becoming commercially available. These new techniques pave the way for the development of control schemes offering performance improvements.

Assuming an effective feedback controller is already present, e.g. a model-based controller, the introduction of a feedforward function based on radiation pyrometry will only have little influence on the lifetime and efficiency of the plant, as previously discussed. However, as the feedforward function is only active when major disturbances occur, the improvements regarding the load-following capability and availability will justify the investment. A future perspective is to introduce a similar strategy to the feedwater control loop, which is even more significant to the stability and availability of the plant.

Steam temperature control

5.5

159

Conclusions

In this chapter conventional and advanced steam temperature controls have been discussed. It is obviously very important to keep objectives and perspectives in mind when improved solutions are targeted and conclusions are drawn. The choice of advanced methods in the discussed applications have, to some extent, been determined by historical issues like the theoretical developments at the time and personal preferences. Nevertheless, it can be concluded that it is important to choose some kind of model-based method. As the thermal processes are quite well known in mathematical terms, modelling of the processes should be direct this conclusion favours methods like LQG, GPC and PTx, as opposed to fuzzy-based methods, which are based on indirect modelling. Furthermore, it was decided to use a complementary strategy for evaporator control while it was decided to substitute the existing strategy in the case of superheater control. This difference in strategy should be seen as a consequence of the difference in process and control complexity. Evaporator control is more complex than superheater control in terms of the number of required inputs and outputs and control structure, interlocks, etc. The state-of-the-art is that advanced control methods have been widely applied in the power industry to steam temperature control. In general, much effort has been put into the theoretical development of improved feedback control methods, only some of which have been applied and of which most are based on linear methods. The practical experience presented indicates that model-based methods are capable of coming close to the upper performance limit for feedback control for the processes in mind. Experiments with new measurement techniques and advanced filtering methods for disturbance detection have shown significant improvements in critical situations. The deregulation of the power industry and the increased utilisation of renewable energy sources are some of the reasons why further improvements are still in demand, particularly in relation to disturbance rejection and improved dynamic stability during abnormal situations. Future developments and applications should focus on new ways of acquiring information regarding disturbances and abnormalities. One way could be to develop new measurement techniques and new methods for signal utilisation, e.g. combining several measurements into high-level information (sensor fusion methods). Another way could be to focus on the development and application of more accurate (nonlinear) models and hence adapt or develop control methods based on the new model structures.

5.6

References

CLARKE, D. W., MOHTADI, C. and TUFFS, E S.: 'Generalized predictive control Part I. The basic algorithm. Part II. Extensions and interpretations', Automatica, 23, (2), pp. 137-160, 1987

160 Thermalpower plant simulation and control ISERMANN, R.: 'Digital control systems, volumes 1 and 2' (Springer Verlag, Berlin, 1989) KLEFENZ, G.: 'Automatic control of steam power plants' (Wissenschaftsverlag, 1986) The MathWorks Inc.: 'System identification toolbox user's guide' (1995) MOELBAK, T.: 'Robust adaptive control of superheater temperature in a power station', VGB Kraftwerkstechnik 6, 1991, 71, (6), pp. 558-561 MOELBAK, T. and HAMMER, L.: 'Utilization of fuzzy control in power plants Part 2: simulation study'. ELSAMPROJEKT A/S, report EP96/694, 1996 (in Danish) MOELBAK, T. and JENSEN, S. B.: 'Model-based steam temperature control in PFUSC plants - Part 1: analysis of methods for dynamic measurement of flue gas temperatures. ELSAMPROJEKT A/S, report EP94/582, 1994 (in Danish) MORTENSEN, J. H., MOELBAK, T. and PEDERSEN, T. S.: 'Optimization of boiler control for improvement of load following capabilities using neural networks'. Proceedings of IFAC/CIGRE Symposium on Control of Power Systems and Power Plants, Beijing, China, 1997 pp. 169-174 NAKAMURA, H., TOYOTA, Y., KUSHIHASHI, M. I. and UCHIDA, M.: 'Optimal control of thermal power plants', Journal of Dynamic Systems, Measurement and Control, 1989, 111, (3), pp. 511-520 SIEMENS: Lettechnische Konzepte: Regelung der Hochdruck-Dampftemperatur, E66 ProzeBtechnik Energieerzeugung SODERSTROM, T.: 'Discrete-time stochastic systems, estimation and control' (Prentice Hall, New York, 1994) OVERSCHEE, E V. and MOOR, B. D.: 'Subspace identification for linear systems' (Kluwer, Dordrecht, 1996)

Chapter 6

Supervisory predictive control of a combined cycle thermal power plant D. S6ez and A. Cipriano

6.1

Introduction

During the last few years the ever-growing demand for electric power has given rise to increasing interest in combined cycle thermal power generation plants because of their high efficiencies and relatively low investment costs. Though well-known regulatory control strategies, usually PI and PID controllers (Ordys et al., 1994), have been developed for these plants, it is extremely important to determine the improvement that more advanced control strategies, like fuzzy, neural or predictive optimal control, can provide in order to reduce the operational costs further. In many industrial processes cost optimisation and the inclusion of operational constraints are necessary. Many approaches examine the steady-state costs to provide optimal static set-points. However, this methodology does not recognize transient behaviour (Becerra et al., 1999). There are some papers that deal with dynamic models. For example, de Prada and Valentin (1996) propose a predictive control strategy based on the optimisation of an economic index, applied to a chemical reactor. Katebi and Johnson (1997) describe a decentralised control strategy, based on the optimisation of a particular objective function, such as a generalised predictive control (GPC) cost index. In this work, a state space representation was used. The control strategy, possessing only a regulatory objective, is applied to a thermal power plant simulator. Bemporad et al. (1997) and Angeli and Mosca (1999) propose a reference governor at the supervisory level. Adopting a state space representation, the objective function was formed by the minimisation of the reference trajectory error. The main goal was to satisfy certain constraints. The algorithms were developed using a state space representation. A different approach for a reference governor with the same

162

Thermal power plant simulation and control

objective was proposed by Gilbert and Kolmanovsky (1999). In this case, the reference governor was defined by a non-linear pre-filter. In this work, a supervisory objective function is considered in order to minimise both the economic index and a regulatory criterion for a combined cycle thermal power plant. This problem can be solved using two alternatives. First, a centralised control strategy directly gives the control actions, without using the regulatory level. The second one, the decentralised control strategy, provides the set-points for the PI controllers using on the same objective function. A combined cycle thermal power plant is first described, covering the simulator and the regulatory level controls. Then, the design of both the centralised and decentralised supervisory control strategies are introduced. Next, the proposed supervisory controllers are assessed using a thermal power plant simulator and are compared with a more traditional control strategy where the set-points remain constant, obtained from a static optimisation. Finally, the conclusions are summarised.

6.2 6.2.1

A combined cycle thermal power plant Process description

Combined cycle power plants have high efficiencies and they require comparatively low investment costs relative to other technologies. These plants use a gas turbine and a steam turbine to generate electricity (Ordys et al., 1994). As shown in Figure 6.1,

Boiler

fQ) Steam turbine

Air

Fuel

"1

0

I I

'l Exhaustgas

Fuel

Air- - ~

0

t

-@

Gasturbine Figure 6.1

A combined cycle power plant

Supervisory predictive control of a combined cycle thermal power plant

163

both turbines are combined into one single cycle in which energy is transferred from the gas turbine to the steam turbine. The exhaust gases from the gas turbine and additional firing are used to provide the necessary heat for the steam production in the boiler. This steam is fed to the steam turbine. Combined cycle (CC) operation offers practical advantages for both the hightemperature and the low-temperature part of the combustion process. The gas turbine cycle has good performance in the high-temperature region, and the steam turbine cycle has good performance in the low-temperature region. Therefore, the combination of the gas and steam turbines are joined by the steam boiler, the waste heat boiler and the high-pressure steam generator within one facility (Kehlhofer, 1997).

6.2.2

Thermal power plant models

There are many proposals in the literature concerning modelling of the main components of a combined cycle power plant (boiler, steam turbine and gas turbine). Those models have different complexity levels, depending on the application. 6.2.2.1

Boiler

For the boiler, there are very complex physical models, like those presented by Cori and Busi (1977) and McDonald and Kwatny (1970), consisting of more than 10 differential equations and over 100 non-linear algebraic equations. Also, there are specific models to measure the thermal plant efficiency or to control one variable in particular. In this case, many of the dynamic equations and variables are not included in the modelling process (,~str6m and Bell, 1988; De Mello, 1991). On the other hand, there are intermediate models (Nicholson, 1964; Rhine and Tucker, 1991; De Jager et al., 1995) that characterise with enough detail the dynamics of the most relevant variables of the boiler. Recently, .~strtJm and Bell (2000) presented a non-linear boiler model that balances accuracy against simplicity of its modelling. The model describes the complicated dynamics of the boiler over a wide operating range. 6.2.2.2

Steam turbine Ray (1980) describes a model of the steam turbine that is based on the fundamental thermal balances. In this case, equations that can be applied individually to each stage of the impulse and reaction of the turbine are developed. This model has been utilised in the design of multivariable controllers. On the other hand, there are very simple models for the steam turbine, mainly linear models, that have been introduced for transient stability studies of the electric network (IEEE Committee, 1991). Ordys et al. (1994) present a model that includes the more important nonlinearities associated with the turbine, like the behaviour of equivalent nozzles for the high-pressure, intermediate-pressure and low-pressure stages.

164

Thermal power plant simulation and control

6.2.2.3

Gas turbine

Cohen et al. (1987) and Shobeiri (1987) present very detailed distributed parameter models of the gas turbine. The gas flow dynamics are described for each section of the turbine. Hung (1991) and Biss et al. (1994) present much simpler models, using steadystate equations derived experimentally. Rowen (1983) describes an intermediate model for the gas turbine that permits design of a supervisory control strategy. This model includes the main dynamic of the gas turbine for a wide range of operating conditions. In this work the models proposed by Ordys et al. (1994) are used, because they are a modelling solution that incorporates the main process variables and the nonlinear behaviour, including only 34 differential equations and about 100 algebraic equations.

6.2.3

A Simulink-based simulator

A computer-based physical simulator was developed for a 45 MW combined cycle thermal power plant, consisting of a boiler, a steam turbine (Ps = 1 1 MW) and a gas turbine (Pg = 34 MW).

4.6 ~ 4.4 Superheated steam pressure 4.2 0

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100

150

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300

350

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i

i

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i

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400

5 ,~E 4.5

Drum water level ]

40

5J0

0.104

400 |

Furnace gas pressure ~ 0.102 0.100 0

i

i

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100

i

150

I

I

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i

200

250

300

350

r

,

i

718

400

Superheated steam temperature 717.8 717.6 0

Figure 6.2

i

50

I

i

i

i

I

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100

150

200 Time (s)

250

300

350

400

Step change in drum water level set-point (controlled variables)

Supervisory predictive control of a combined cycle thermal power plant 14.5

.

.

.

.

165

. Gas turbine fuel flow

z~ 14 0

5~0

L 100

, 150

i

J

i

J

200

250

300

350

400

100 50 I 0

0

~

Feedwater flow

5'0

~ 100

L 150

L 200

~ 250

~ 300

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, 150

, 200

~ 250

~ 300

k 350

400

64.1 64.05 Furnace air flow 64 0 0.5

~

, 350

400

i

o Attemperator water flow -0.5 0

i

i

i

i

i

i

i

50

100

150

200

250

300

350

400

Time (s)

Figure 6.3

Step change in drum water level set-point (manipulated variables)

The models and their parameters were adapted from Ordys et al. (1994). There are algebraic loops in the gas turbine and steam turbine models, which are solved numerically using a non-linear equation at each step of the simulation. The simulator was programmed in the Matlab®/Simulink ® environment under the Windows 2000 system. As Ordys et al. (1994) propose, the integration step for the simulations is 0.1 s, applying the fifth-order Runge-Kutta integration method.

6.2.4

Regulatory control strategies

The regulatory controllers for the combined cycle power plant are established for each subsystem, i.e. the boiler, the gas turbine and the steam turbine. The tuning of PI controllers was obtained from the work of Ordys et al. (1994). Next, a qualitative analysis of the models is presented considering different tests and analysing the similarities between the simulation responses and real plant behaviour. First, the boiler response with the control strategy based on PI controllers is tested. In this case, the controlled variables are the superheated steam pressure (Ps), the drum water level (L), the furnace gas pressure (PG) and the superheated steam temperature (Ts). The manipulated variables are fuel flow (wf), feedwater flow (We) or valve position (Xl), air flow to the furnace (WA) and attemperator water flow (Watt) or valve position (x2), respectively.

166

Thermalpower plant simulation and control 11.5 ll.0

Steam turbine power

10.5 10.0 9.5

5'o

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200

250

300

11 HP turbine steam flow

10 9 8

0

Figure 6.4

i

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150 Time (s)

200

250

300

Step change in steam turbine power reference

1150 ~

/

1100 1050 Io

1000 34.0

5

GT exhaust gas temperature

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100

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5

300

91

9o8l_

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90.6 t 0

Figure 6.5

5

0

i

100

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150 Time (s)

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200

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300

Stepchange in gas turbine exhaust gas temperature reference (controlled variables)

Supervisory predictive control of a combined cycle thermal power plant

167

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; 5

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Figure6.6

i

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'

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100

150 Time (s)

2 0

250

300

Step change in gas turbine exhaust gas temperature reference (manipulated variables)

As an example, Figures 6.2 and 6.3 present the boiler responses to a 10 per cent step in the drum water level set-point. The simulation shows that the PI controllers respond appropriately, providing good performance with a settling time less than 100 s, as would be anticipated for real plant. Also, the responses for superheater steam pressure (Ps), and steam temperature (Ts) and furnace gas pressure (Pc) are non-minimum phase, as described in Ordys et al. (1994). For the control strategy for the steam turbine, the manipulated variable is the flow of steam to the high-pressure turbine (Win) that controls the steam turbine power output (Ps). In Figure 6.4 the step response of a closed-loop steam turbine system subject to a 10 per cent decrease in the power reference is presented. The results show acceptable behaviour of the controlled variable, comparable with real plant, and with a settling time less than 50s and a maximum overshoot is about 2.5 per cent. Finally, for the gas turbine, the controlled variables are exhaust gas temperature (TTout), the power output of the gas turbine (Pg) and the NOx concentration in the exhaust gases (gcNox). The manipulated variables are the air flow to the compressor (Wa), the fuel flow (Fa) and the flow of the steam injected into the combustion chamber (Wis).

Figures 6.5 and 5.6 show the responses of the closed-loop gas turbine system to a 10 per cent step change in the exhaust gas temperature reference. The settling time is

168 Thermal power plant simulation and control less than 30 s. The gas turbine power exhibits slightly non-minimum phase behaviour due to an existing controller saturator.

6.3

Design of supervisory control strategies for a combined cycle thermal power plant

In this work, the proposed objective function considers both an economic and a regulatory level objective, that is, the minimisation of the operational costs (Jcf) and the minimisation of both the set-point trajectory error together with the control action effort (Jcr). Hence, the total objective function to be optimised at the supervisory level is:

J = Jcf + JCr.

(6.1)

Also, considering the fuel flow to the gas turbine Fd, the fuel flow to the boiler wf and the feedwater flow We as the main process costs, the economic objective function (Jcf) is given by:

N Jcf = Z C F F d ( t W i i=1

N 1 ) + E Cfwf(tWi i=1

-

N 1)+ Z C e w e ( t W i i=1

-

1)+CF

(6.2)

where CF and Cf are the fuel unit costs, Ce the feedwater supply unit cost and CF fixed costs given by the cost of operational technical personnel, etc. N is the prediction horizon. The regulatory level objective (JCr) is given by:

JCr = CrPg j=l

)

(/3g(t + j ) _ p;)2 + ZFd E AFg(t + i - - 1) i=1 (/3s(t + j ) - P2) 2 + )-wfZ

+ Crps

j=l

+ CrL

(/,(t + j) -- L*) 2 + Zwe Z j=l

AW2(t q'- i -- 1)

i=1 Aw2e(t + i --

1)

(6.3)

i=1

where/;g(t + j) is the j-step-ahead prediction for the gas turbine power,/3s(t + j ) is the j-step-ahead prediction for the superheated steam pressure and L(t + j) is the j-step-ahead prediction for the drum level. Also, CrPg, Crps and CrL are the cost factors of the regulatory levels and ZFd, ~.wf and Zwe are the control weightings. The external set-point trajectories for the gas turbine power, P~, the superheated steam pressure, p*, and the drum level, L*, respectively, are constant and previously fixed. As the currency unit, a fictional $$ was chosen to evaluate costs. Table 6.1 shows the parameters of the objective function for the CC power plant. The cost values CF, Cf and Ce were chosen to represent economic criteria for real

Supervisory predictive control of a combined cycle thermal power plant Table 6.1

169

Objective function parameters

Parameter

Value

CF Cf Ce

100$$/kg 100$$/kg 1$$/kg

P~

34MW

p* L* CrPg Crps

4.5251MPa 4.1425m I$$/MW2s 10-9$$/MPa2s

CrL

106 $$/M 2 s

~-Fd

1022MW2s2/kg2

)~wf )~we N

1011MPa2 s2/kg2 I m2s2/kg 2 100

plant, with the weightings for the fuel costs significantly higher than the feedwater cost. The external set-point trajectories Pg, p* and L* were selected using operational criteria, while the cost factor values of the regulatory level CrPg, Crps and CrL were chosen by trade-off criteria. ~-Fd, ~-wf and )~we were selected by regulatory criteria that encourage stable behaviour at the regulatory level, and N was chosen near the maximum settling time. Next, two solution algorithms are proposed in order to solve the optimisation problem of equation (6.1).

6.3.1

Centralised control strategy

The centralised control strategy introduces a supervisory level which directly determines the optimal control actions of the process, with the corresponding PI controllers replaced by a supervisory level. As Figure 6.7 shows, the economic optimiser provides the optimum control actions for the gas turbine and the boiler. The optimisation variables proposed here are the fuel flow to the gas turbine, Fd, the fuel flow to the boiler, wf, and the feedwater flow, We. Hence, in this case, the PI controllers for the power output of the gas turbine, for superheated steam pressure and for the drum level are eliminated. The set-points for the exhaust gas temperature (T~out), the NOx concentration in the exhaust gases (grNox), the exhaust gas pressure (p~), the superheated steam temperature (Tsr ) and the steam turbine power (Pr), respectively, are maintained constant, as the corresponding manipulated variables do not affect the economic optimiser.

170 Thermal power plant simulation and control

Pg* Ps* L*

Supervisorylevel: Economicoptimiser

~T~out~gcrNox

rI 1

PG

PI Controllers

FZd,

Pl ~_ Controllers

We ,welwA~Wa,t,

~Wa ~Wis Gas turbine

PI Controllers

~__

Boiler

Win Steam turbine

I

Figure 6. 7

Centralised control strategy for the combined cycle thermal power plant

Pg* Ps* L*

Supervisorylevel: Economicoptimiser

TT°ut Pg

,Wa ~ ~ *~i Gas Turbine

Figure 6.8

6.3.2

m

~esr

gcNox

PI ~ Controllers

4 .~-----------

PI ! Controllers

~wf~We~WA~

Controllers

~ Win

Boiler

Steam turbine

L

I

Decentralised control strategy for the combined cycle thermal power plant

Decentralised control strategy

In the proposed decentralised control strategy based on the supervisory level, all the PI controllers remain untouched. Thus, the supervisory optimiser gives the optimal set-points at the regulatory level (S~ez et al., 2002). The economic optimiser shown in Figure 6.8 will provide the optimum set-points for the regulatory level.

Supervisory predictive control of a combined cycle thermal power plant

171

The optimisation variables proposed here are the set-points of the power of the gas turbine, P~, the superheated steam pressure, pr, and the drum water level, L r, as they directly depend on the main process inputs: the fuel flow to the gas turbine, Fd, the fuel flow to the boiler, wf, and the feedwater flow, We, which are included in the proposed objective function. As for the centralised control strategy, the set-points T~out, grcNOx, Pg' r Tr and Psr will be constant as they do not impact on the economic optimiser.

6.4 6.4.1

Application to the thermal power plant simulator Centralised control strategy

In order to design the centralised control strategy, linear models of the boiler process and gas turbine process are necessary.

6.4.1.1 Boiler process models The dynamics of the main variables of the boiler process are identified around their operating points using controlled auto-regressive integrating moving-average (CARIMA) models. These models are appropriate for many industrial process in which disturbances are non-stationary (Clarke et al., 1987). The parameters of the CARIMA models were obtained using a least squares approach from the Matlab Identification toolbox. Identification of the superheated steam pressure, Ps, loop dynamics was achieved by superimposing an excitation signal on the fuel flow, wf. The resulting C A R I M A model using a one second sampling time is formed as the following expression:

e(t) A(z-1)ps(t) :- B ( z - l ) w f ( t ) + - A

(6.4)

where

A(z - 1 ) = 1 - 0 . 9 7 4 z

-1,

B(z - 1 ) = 2 7 1 3 z - 1 + 3 5 3 6 z -5

and while A --:--1 - z -1 , e(t) is zero-mean white noise and z -1 is the backward shift operator. Similarly, a C A R I M A model for the drum level, L, was obtained using feedwater flow as an excitation signal, so that:

e(t) A(z-1)L(t) -----B(z-1)We(t) q- - A

(6.5)

where

A(z -1) = 1 - 0.228z -1 - 0.772z -2, B(z -1) = (0.754z -1 + 0.570z -2 + 0.014z -3 + 0.007z -4 + 0.002z -5) × 10 -3.

172

Thermal power plant simulation and control

6.4.1.2

Gas turbine process model

The dynamics of the gas turbine process are similarly identified around its nominal operating points using CARIMA models. The resulting CARIMA model for the gas turbine power, Pg, with respect to the fuel flow, Fd, is obtained as:

e(t) A(z-1)pg(t) = B(z-1)Fd(t) + --£-

(6.6)

with

B(z -1) = 1.244 x 107z -7.

A(z -1) = 1 - 0.717z - j , 6.4.1.3

Supervisory controller

The centralised control strategy minimises the economic objective function defined in equation (6.1), giving the optimal control actions. The process models (6.4)-(6.6) are considered as constraints. The optimum control actions are calculated, using the Matlab Optimisation toolbox, by numerically solving the defined quadratic objective function.

6.4.2

Decentralised control strategy

In the decentralised control strategy, the optimiser provides the optimum set-points for the PI controllers. Thus, models of the PI for the fuel flow and the feedwater flow are necessary. As previously outlined, the parameters of the PI controller were obtained from the work of Ordys et al. (1994). 6.4.2.1

PI controller models

A discrete model for the boiler fuel flow control loop is:

ac(z-1)wf(t) = Bcr(z-l)p~(t) -~- Bcy(Z-1)ps(t)

(6.7)

where Ac(z -1) = 1 - z - l ,

Bcr(Z -1) = 1.55 × 10 -5 - 1.45 × 10-5Z -1,

Bcy(Z-1) = -1.55 × 10 -5 + 1.45 × 10-5z - l ,

Kp ---- 1.5 × 10 -5 ,

Ki = 10 -6.

Similarly, a model for the feedwater flow control loop is obtained as:

Ac(z-l)we(t) = Bcr(Z-1)Lr(t) + Bcy(Z-1)L(t)

(6.8)

where Ac(z - 1 ) = l - z Bcy(Z-1)

=

-1,

Bcr(Z - 1 ) = 1 8 1 - 1 6 4 z -1,

--181 + 164Z-1,

Kp = 10,

K i ----

1.

Finally, a model for the gas turbine fuel flow control loop follows as:

Ac(z-l)Fd(t) = Bcr(z-l)pg(t) + Bcy(z-l)pg(t)

(6.9)

Supervisory predictive control of a combined cycle thermal power plant

173

where Ac(z -1) = 1 - z - l , Bcy(Z- l ) ----2.95 × 10 -9, 6.4.2.2

Bcr(Z-1) = 2.95 x 10 -9,

Kp = 1.48 × 10 -9,

Ki = 2.95 × 10 -9.

Supervisory controller

The decentralised control strategy minimises the objective function defined in equation (6.1), giving the optimum set-points for the PI controllers. The process models (6.4)-(6.6) and the PI controller models (6.7)-(6.9) are introduced as constraints. As previously, the optimum control actions are calculated by numerically solving the quadratic programming optimisation problem, using the Optimisation toolbox of Matlab.

6.4.3

Comparative analysis

We assume that the superheated steam flow (Ws) changes, corresponding to changes in power output produced by the steam turbine, and, for the purpose of this simulation, this is treated as a disturbance. As shown in Figure 6.9, the steam flow varies between 12.6 and 10.8 kg/s over a period of 800 s. The proposed supervisory centralised and decentralised control strategies are compared with a control strategy in which the set-points remain constant, calculated by optimisation of the proposed objective function considering a static model of the boiler process. Then, using the static model for the superheated steam pressure given by equation (6.4) and the static minimisation of the objective function given by equation (6.1), the optimum set-point for the superheated steam pressure is:

p~(t) = p~

Cf 2CrpsKps

t > 0

(6.10)

where Kps = 0.322 Mpa s/kg is the static gain between the superheated steampressure and the fuel flow. Similarly, using the static model for the drum level, given by equation (6.5) and the static minimisation of the objective function, given by equation (6.1), the optimum 13 / ~. [ ~o 12

Superheatedsteamflow

~11

I 10

Figure 6.9

0

'

100

200

~

300

400 Time (s)

•

500

|

600

Disturbance sequence for superheated steam flow

700

800

174

Thermal power plant simulation and control 14 Boiler fuel flow J 13 12.5

0

4.4o

..

~ 200

100

L_

~ 300

~ 400

500

4.25

-

i

0

100

)

~

"

-

700

800

i,,,_

L___

¢~ 4.35 ~ 4.30

600

Superheated steam pressure i

i

i

i

400

500

600

700

i

200

30

i

i

i

~

1

i

200

300

400 Time (s)

500

600

700

800

4.40

~

4.35

~4.30 Superheated steam pressure (reference) 4.25

i

0

Figure 6.10

100

800

Closed-loop response for superheated steam pressure with constant setpoint (thick line), centralised control (dotted line) and decentralised control (solid line)

static set-point for the drum water level is: Lr(t) = L*

Ce

t _> 0

(6.11)

2CrLKL ' where KL ---- 0.345 m s/kg is the static gain between the drum water level and represents feedwater flow. Figure 6.10 shows the closed-loop response for superheated steam pressure (Ps) with constant set-point, with the centralised decentralised control strategy. Figure 6.11 presents the drum level response applying the same control strategies. The fuel flow to the boiler decreases when using the proposed optimal control strategies, while the feedwater flow remains similar to the original control strategy. This follows from the much higher value for the fuel cost coefficient (Cf), relative to the feedwater supply cost coefficient (Ce) in equation (6.2). The centralised and decentralised controllers give similar improvements in performance. This is because the decentralised control strategy is intended to eliminate the action of the low-level PI controller and the algorithm implicitly replaces the PI controller with the predictive control action given by the regulatory objective function (equation 6.3) (S~iez et al., 2002). Also, the centralised control strategy directly provides the control action based on the same regulatory objective function.

Supervisory predictive control of a combined cycle thermal power plant

175

14

10 8

Feedwater flow 0

I

I

100

200

4.16~4.14

.

300

.

I

I

I

L

400

500

600

700

.

. Drum level

4.12 0

100

._ 4"16 t ~'~4.14 ~

200

; 30

400

, 500

/"-'""-~

/----'"~

I

I

I

200

300

4.12

; 60

, 700

800

/~'~ Drum level (reference)

0

Figure 6.11

800

100

400 Time (s)

I

I

I

500

600

700

800

Closed-loop response for drum level with constant set-point (thick line), centralised control (dotted line) and decentralised control (solid line)

Table6.2

Comparison of the economic and regulatory objective functions

Control strategy

Supervisory level

Constant set-points Centralised Decentralised

Savings %

Jce [$$]

Jcr [$$]

J

135,520 133,100 133,120

33,799 13,603 13,280

169,310 146,700 146,400

[$$]

1.79 1.77

In Table 6.2, the mean values of the objective functions (6.2) and (6.3) are evaluated according to the results presented in Figures 6.10 and 6. ! 1. Also, the savings for the fuel costs regarding the control strategy with constant set-point are defined by:

Savings =

ffCf with supervisory level "] 100 - 100 Jcf with constant set-points/ per cent.

(6.12)

176

Thermal power plant simulation and control

The savings obtained with the centralised and decentralised control strategies are approximately 1.78 per cent. Therefore, as the operational costs of a thermal power plant are very high and each percentile point in savings represents a significant amount of money, the implementation of those control strategies is recommended.

6.5

Discussion and conclusions

Of all the physical models available in the technical literature, the Ordys et al. (1994) model has been selected for this study, because it represents quite accurately the nonlinearities of the process. Based on this model, a non-linear dynamic simulator has been developed for the evaluation of supervisory and regulatory control strategies. The simulation tests using the regulatory control strategy show similar behaviour to real power plant. In this study, the objective of the supervisory optimal control is to minimise the operational costs, which mainly depend on the fuel flow and feedwater flow. The supervisory control strategy has also to maintain the superheated steam pressure, drum level and gas turbine power variables close to their set-point values. Therefore, an objective function has been defined, which combines an economic (operational cost) and a regulatory component. For the implementation of the optimal control strategy, two alternatives are considered. In the first strategy, called a centralised controller, the optimisation algorithm directly gives the final manipulated variables, that is to say, the fuel flow to the gas turbine, boiler and the feedwater flow. Alternatively in the decentralised control strategy, the optimisation algorithm calculates the optimum set-points for the gas turbine power output, the superheated steam pressure, and the drum water level for the regulatory level. Then, using these optimum set-points, the PI controller gives the control actions, that is to say, the fuel flow to the gas turbine, the fuel flow to the boiler and the feedwater flow. The results show that both strategies present very similar behaviour to changes in superheated steam flow. The first component of the objective function, that is the plant operational costs, are reduced by 1.79 per cent when using the centralised controller, compared with a regulatory control strategy with constants set-points, obtained from static optimisation of the same objective function. The same component, in the case of the decentralised control strategy, is reduced by 1.77 per cent, also compared with the same regulatory control strategy. The minimum difference between both strategies can be explained because the decentralised controller is intended to eliminate the PI control action, generating the manipulated variable based on the defined objective function. The supervisory controllers also reduce considerably the second component of the objective function that minimises the differences between the controlled variables and their set-points, and minimises the control energy, also improving the regulatory level with PI controllers. The results of this exploratory study show that supervisory control offers interesting perspectives in order to reduce the operational costs of a combined cycle thermal

Supervisory predictive control of a combined cycle thermal power plant

177

power plant. The decentralised strategy maintains the existing regulatory level, which is better known by plant operators. This also offers a number of advantages: (a) it allows safer operation in the case of a failure; (b) it reduces the natural opposition of the operators to the incorporation of more sophisticated advanced automatic controllers which, in some cases, may limit manual intervertion; and (c) it improves the supervisory controller without modifying the regulatory level, which implies low implementation cost in comparison with the centralised control strategy.

6.6

Acknowledgements

The authors wish to thank FONDECYT for the support given to project 4000026 'Stability for optimal supervisory control systems with a fixed regulatory level', 2980029, 'Design of predictive control strategies based on non-linear models and its application to the control of thermal power plants', 1990101 'Non-linear predictive control with fuzzy constraints and fuzzy objective functions' and 1020741, 'Failure diagnosis and detection for non-linear and time-variant dynamic systems'. Doris S~iez also wishes to thank the Facultad de Ciencias ffsicas y Matem~iticas, Universidad de Chile, for their support.

6.7

References

ANGELI, D., and MOSCA, E.: 'Command governors for constrained non-linear systems', IEEE Transactions on Automatic Control, 1999, 44, (4), pp. 816-820 /kSTROM, K., and BELL, R.: 'Simple drum boiler models'. Proceedings of the IFAC Power Systems Modeling and Control Applications, Brussels, Belgium, 1988, pp. 123-127 ,~STROM, K., and BELL, R.: 'Drum-boiler dynamics', Automatica, 2000, 36, pp. 363-378 BECERRA, V., ABU-EL-ZEET, Z., and ROBERTS, P.: 'Integrating predictive control and economic optimisation', Computing and Control Engineering Journal, 1999, 10, (5), pp. 198-208 BEMPORAD, A., CASAVOLA, A., and MOSCA, E.: 'Non-linear control of constrained linear systems via predictive reference management', IEEE Transactions on Automatic Control, 1997, 42, (3), pp. 340-349 BISS, D., SCHAUTT, M., and WALZ, M.: 'Robust control of a 1.5 MW free turbine with complex load: non-linear closed loop simulations', IEE Control'94, 21-24 March, 1994, pp. 1176-1181 CLARKE, D., MOHTADI, C., and TUFFS, P.: 'Generalised predictive control,' Automatica, 1987, 23, (2), pp. 137-160 COHEN, H., ROGERS, G., and SARAVANAMUTI'OO, H.: 'Gas turbine theory', (Longman, Harlow, 1989, 3rd edn.) CORI, R., and BUSI, T.: 'Parameter identification of a drum boiler power plant'. Proceedings of the 3rd Power Plants Dynamics, Control and Testing Symposium, September 7-9, 1977, Knoxville, Tennessee, pp. 26-1:26-19

178 Thermal power plant simulation and control DE JAGER, B., ANNEVELD, H., and DE BLOK, E: 'Modeling, simulation and control of multi-fuel once-through boilers'. Proceedings of the IFAC Conference on Control of Power Plants and Power Systems, December 6-8, 1995, Canctin, MOxico, pp. 77-82 DE MELLO, E: 'Boiler models for system dynamic performance studies', IEEE Transactions on Power Systems, 1991, 6,(1 ), pp. 66-74 DE PRADA, C., and VALENTIN, A.: 'Setpoint optimization in multivariable constrained predictive control'. Proceedings of the 13th World Congress of IFAC International Federation of Automatic Control, San Francisco, June 30-July 5, 1996, pp. 351-356 GILBERT, E., and KOLMANOVSKY,I.: 'Fast reference governors for systems with state and control constraints and disturbance inputs'. Int. J. Robust Non-linear Control, 1999, 9, (15), pp. 1117-1141 HUNG, W.W.: 'Dynamic simulation of a gas-turbine generating unit', Proceedings of the IEEPart C, 1991, 138, (4), pp. 342-350 IEEE COMMITTEE: 'Dynamic models for fossil fueled steam units in power system studies', IEEE Transactions on Power Systems, 1991, 6, (2), pp. 753-761 KATEBI, M., and JOHNSON, M.: 'Predictive control design for large-scale systems'. Automatica, 1997, 33, (3), pp. 421-425 KEHLHOFER, R.: 'Combined cycle gas and steam turbine power plants' (PennWell Publishing Company, Oklahoma, 1997) MCDONALD, J., and KWATNY, H. 'A mathematical model for reheat boilerturbine-generator systems', Proceedings of the IEEE PES Winter Power Meeting, January 25-30, 1970, New York, pp. 1-19 NICHOLSON, H.: 'Dynamic optimisation of a boiler', Proceedings of the lEE, 1964, 111, (8), pp. 1479-1499 ORDYS, A., PIKE, A., JOHNSON, M., KATEBI, R., and GRIMBLE, M.: 'Modeling and simulation of power generation plants' (Springer-Verlag, London, 1994) RAY, A.:'Dynamic modelling of power plant turbines for controller design', Applied Mathematical Modeling, 1980, 4, (2), pp. 109-112 RHINE, J., and TUCKER, R.: 'Modeling of gas-fired furnaces and boilers' (McGraw-Hill, London 1991) ROWEN, W.: 'Simplified mathematical representations of heavy-duty gas turbines', ASME Journal of Engineering for Power, 1983, 105, (4), pp. 865-871 SAEZ, D., CIPRIANO, A., and ORDYS, A.: 'Optimisation of industrial processes at supervisory level: application to control of thermal power plant' (Springer-Verlag, London, 2002) SCHOBEIRI, T.: 'Digital computer simulation of the dynamic operating behaviour of gas turbines', Brown Boveri Review, 1987, 74, (3), pp. 161-173

Chapter 7

Multivariable power plant control G. Poncia

7.1

Introduction

The introduction of new control concepts and technologies in thermal power plant is very difficult. The push for innovation must overthrow several cultural obstacles and well-assessed procedures that designers and operators are not keen to modify. Usually, the control system of a thermal power plant is based on a number of regulation loops and feedforward compensators that contribute to maintain the main thermodynamical variables within reasonable values. With a few variations, this structure has been adopted in all Rankine cycle-based plants. Its success is motivated by the fact that it is highly reliable and allows the operator to intervene manually on single components in emergency situations. Moreover, the control system dynamic performance is in general satisfactory under normal plant operation. The main drawback of these systems, based on separate single-input, singleoutput (SISO) loops, is that they do not account for the interactions of the different thermal properties in the plant. More precisely, a given control variable used to regulate the respective controlled property in a loop influences the dynamic behaviour of all the others. The mutual influence of the regulation loops is often minimised by enabling frequency decoupling strategies (DoleZal and Varcop, 1970; Klefenz, 1971) that are penalising in terms of performance. Performance degradation can be so significant that, in emergency situations, the thermodynamical variables could oscillate significantly, producing thermal stresses of the plant components and affecting their lifetime. A typical case where the dynamic evolution of the thermal variables is unsatisfactory takes place when a portion of the grid, including the plant, remains isolated due to failures of the distribution system. In this case, the power request to the plant suddenly drops and the thermal variables start to oscillate. Sharp changes of the power demand are more likely to occur in plants operating in a deregulated market, where a significant number of units are not available for the central

180

Thermal power plant simulation and control

dispatch centre. Moreover, the introduction of distributed generation and microgrid systems requires plants with enhanced load-following capability (Oluwande, 2001). In the occurrence of sudden load changes, emergency procedures or safety features are introduced in the control system, avoiding potentially dangerous behaviour. When such procedures are activated, the fulfillment of the load requirements and the minimisation of the operational costs are no longer the primary control objectives. In processes where the dynamics of the state variables are strongly interacting, multivariable techniques are known to improve the dynamic performance significantly. Indeed, these techniques consider the system as a whole, and generate a single controller that allows optimal response. Therefore, the migration from a multi-SISO control system to a new concept based on multivariable techniques in a thermal power plant appears to be a good solution to improve plant operation. A multivariable, multiple-input, multiple-output (MIMO) control system would reduce the occurrence of potentially dangerous events and the intervention of the emergency procedures. The power reliability as well as the plant efficiency would therefore be increased. Still, multivariable controllers are far from being widely employed, because of the reluctance of the power plant industry to accept changes that would revolutionise well-assessed procedures. The transition to a new system would lead to various problems: •

• •

Controls centralisation. A multivariable controller would work on a centralised control unit. A failure of the control algorithm would induce a failure of the entire plant. SISO controllers are preferred because a regulation loop can be disconnected in case of emergency, with the remainder still operating. Design. The design process would include a thorough testing programme on the plant, which may require the temporary shutdown of the commercial operation. Training. The presence of a new control structure would make necessary the training of plant personnel. A multivariable controller may also induce dynamic phenomena that the supervisory personnel, used to traditional systems, may not expect.

Therefore, the conventional multi-SISO solution cannot be completely abandoned. Its presence in the control structure keeps alive a well-assessed technology, whose reliability is not in question. In this way, any new multivariable system could be disconnected anytime, without compromising the plant safety. An appealing solution would therefore be a multivariable control structure that corrects the existing classical regulation system. In this way, both performance improvements and plant operability would be guaranteed. The latest developments in the field of power plant multivariable design try to follow this principle. Industry and academic institutions have proposed a variety of solutions, based on different structures and control techniques, that consider SISO loops as part of the whole control structure. In the following sections, the most recent approaches to the design of multivariable controllers for thermal power plant will be presented and discussed. First (section 7.2), a description of a typical fossil fuel power plant and its main control requirements will

Multivariable power plant control

181

be provided. The structure of the classical control, based on frequency decoupling, will also be introduced. A variety of multivariable control configurations and techniques will be discussed, referring to the most recent research studies in the field, and to the latest developments in the industrial realm (section 7.3). The emphasis will be put on multivariable techniques based on predictive control theory. The success of predictive approaches is mostly related to the fact that they can include constraints and measurable disturbances in their formulation. The relevance of methodological aspects will be emphasised. The design process must be based on a rigorous approach, including the choice of architecture, modelling and identification of the plant, and the choice of the control framework. Finally, the design of a multivariable controller for a once-through boiler will be described in section 7.4. The MIMO system acts in parallel with the traditional one, correcting its actions. A state space model predictive control technique has been adopted, dealing effectively with the presence of measurable disturbances such as the power request. The suggested system significantly improves plant performance in extreme situations, where sudden changes of the power load occur.

7.2

Classical control of thermal power plants

Thermal power plants represent the majority of electricity generation units worldwide. They are characterised by a multitude of possible configurations, according to the adopted thermodynamic cycle, the fuel and the fluid that undergoes the thermodynamic transformations. Plants with a water-steam Rankine cycle, operating on gas, oil or pulverised coal, have been traditionally preferred for their simple and reliable operation. Notwithstanding that the newest generation units are built on the basis of modern designs such as the combined cycle, the vast majority of plant in operation worldwide are still based on the water-steam cycle. Their typical structure is sketched in Figure 7.1. Here, the economiser is denoted by ECO; SH1 and SH2 are the superheaters and RH is the reheater between the high and low pressure sections. Attemperators are used for the control of the steam temperature. In this class of power plant, the control system is required to guarantee the correct operation of the whole process. The power load must be adjusted to the instantaneous requests of the grid, with the highest possible thermodynamic efficiency. Plant durability and safety must also be guaranteed (Moelbak and Mortensen, 2003). In general, such requirements are fulfilled by controlling relevant thermal variables in the plant, namely: • • •

The electric load, Pe. The evaporation pressure, Pt, to keep the thermal energy stored in the evaporator within acceptable margins. The temperatures at the outlet of SH2 (TsH2) and RH (TRH), the hottest zones of the plant.

182

Thermalpower plant simulation and control Intercept valve . 9 Furnice

~ Feeding valv

q

Combustion chamber

~

Feed pump Hopper.

Turbines

To chimney

- -

Feed pump

Water/steam main path

............. Combustion gases path

Figure 7.1

Schemeof the plant

The mass of water in the evaporator. While in drum boilers the water level (yw) can be regulated, in once-through boilers a direct measure of the water content is not possible. For this reason, the control of some related variable is carried out. To meet the energy demand of the grid, both in steady-state and transient conditions, the turbine power output must be promptly controlled. This task is achieved by acting on the governor valve at the turbine inlet, or modifying the heat released to the generator. In both cases, such changes affect the pressure at the turbine inlet and in the boiler. In order to preserve the amount of thermal energy stored in the plant, it is preferred to restore the pressure level to a defined value in the fastest possible way. A control concept that fulfils this requirement is known as boiler following mode (Hagedorn and Klefenz). Here, the load is controlled with a fast loop acting on the turbine governor valve. Moreover, the resulting pressure changes are minimised by the modulation of the fuel-air system in the combustion chamber. Turbine following mode is an alternative method that secures plant safety. Here, the pressure is restored with an action on the governor valve, through a fast-acting loop. The load demand is met by acting on the fuel-air system. In some cases, it is preferred to keep the pressure proportional to the load, using a sliding pressure mode. Here the pressure set-point is allowed to slide within a range of admissible values, resulting in smoother turbine operation and simpler plant startup. In a large class of plant, the coordination between boiler and turbine following modes is implemented. This configuration allows the fast tracking of the power requests and the prevention of potentially dangerous situations. During normal operation, the control system is in boiler-following mode. Moreover, the feedforward action of the power load on the fuel system anticipates any load variation and reduces pressure fluctuations. When critical conditions occur, the turbine-following mode

Multivariable power plant control

Powerload controller I

Setpoint

wt °

\

Steammass flow required

Power Pe load -~

Pt° Setpoint ~ ~

~

183

g

Pressure controller

/

g

/. Pt° - Pt

Fuel/air required

Evaporation Pt pressure Figure 7.2

The coordinated control boiler/turbine

is selected. The control scheme is represented in Figure 7.2. A non-linear deadband element, g, limits the steam mass flow when the pressure exceeds a security threshold. Steam temperatures are controlled to avoid excessive heating of the metal pipes, and eliminate poor performance when temperatures are too low. The dynamics of the boiler and SH1, SH2 and RH are strongly interacting, because of the way hot gases are distributed in the combustion chamber. Consequently, the problem of controlling their temperatures is intrinsically multivariable. A solution by means of SISO techniques is carried out by introducing decoupling methods based on feedback loops with different bandwidths and feedforward compensation (Moelbak and Mortensen, 2003). Briefly, the temperature at the SH2 outlet is often controlled by acting on the attemperator placed downstream of SHI. This control is characterised by significant delays because of the propagation time of steam in the exchanger, and the inertia of the metal masses. The regulation of the temperature at the RH downstream is performed by the attemperator only in emergency situations. The narrow bandwidth control of TRH is based on the modification of the heat distribution in the furnace by means of burner position, the distribution of the hot exhaust gases or their recirculation. In power plants with a drum boiler, at constant pressure, the water contained in the steam generator can be represented by the water level. Its control is provided by acting on the mass flow of feeding water Ww. The water content of once-through boilers is instead determined by the nature of the evaporation process and is strongly coupled with the pressure dynamics. The

184 Thermal power plant simulation and control

pe°

Wt°

Set-point ~'-P~ower Pe load Pt°

CVp

Steammass flow required

Ww° itWatermassflow

~_(~

Set-point

required

EvaporationPt pressure

~o ~ Set-point

C¢

Evaporation temperatureor enthalpy Figure 7.3

~ ~,_#

Wco, Wao Fuel and air mass flow required

Decoupling of the pressure and load controls with the regulation of water content

control of the water content is achieved by indirectly regulating the enthalpy or the temperature (denoted by, say, ~) in the proximity of the evaporator outlet. The adopted control solution (Figure 7.3) is then based on frequency decoupling. To minimise interactions, the pressure is controlled by acting simultaneously on the fuel-air and the water feed systems. The control signal is provided by the control system C ~ which provides the regulation of power load and boiler pressure. A second, slow loop that comprises the regulator C~ introduces a correction of the fuel-air mass flow to adjust ~. In most systems, ~ is the temperature difference across the attemperator, while in others it is simply the temperature at the superheater output. In any case, the process interactions limit the speed of the control action.

7.3

Multivariable control strategies

Generally, multi-SISO control systems based on frequency decoupling are characterised by satisfactory performance when load variations are smooth and small. This condition is satisfied in normal operation, where the load demand profile does not change suddenly, and when startup and shutdown are safety-compliant procedures. As highlighted in section 7.1, plant interactions are no longer compensated by the control system when sudden and significant changes of the power demand are observed. Significant oscillation of the thermal variables occur, with an impact on the thermal stress of metal parts. In order to avoid the overshoot of temperatures and pressures, and to improve the load-following characteristics of the control system, variations in the schemes

Multivariable power plant control

185

presented in section 7.2 have been suggested and adopted on existing plant. The efforts of the industrial community have been directed in part to the development of intelligent load-tracking systems that limit the effect of coupling. Klefenz and Krieger (1992) suggested a control system that introduces a delay change to the load set-point, allowing optimised use of the energy stored in the boiler. Clearly, coupling sets a trade-off between load-tracking needs and the reduction of thermal stresses. With the same intent, Lausterer and Kallina (1994) introduced a model-based estimator of the load margin, which modifies the control system set-points in order to achieve smoother evolution of the thermal variables. The design of innovative control solutions has recently been promoted by several industries that build thermal power plants. Modem configurations like those developed by Toshiba or Siemens have improved supervisory systems based on the most recent advances in the field of distributed control systems and communication protocols. Information on the introduction of multivariable solutions dealing with coupling is scarce due to intellectual property issues. ABB Simcon is among the companies that expressly cite the advantages of MIMO controls applied to thermal plant. In particular, the adopted solution is based on the STAR® multivariable predictive control system by ,9. At Hitachi (see Takita et al., 1999) predictive control and dynamic advanced parallel systems are applied to improve operability. Many alternative control configurations and methods, based on modem techniques, have also been suggested by researchers in academic institutions. For instance, 7-{oo techniques are used by Zhao et al. (1999) in a coal-fired power plant. Other studies have been devoted to the adoption of solutions based on fuzzy logic (Ben Abdennour and Lee, 1996), hybrid supervision systems (Garcia et al., 1995), genetic algorithms (Dimeo and Lee, 1994) and CAD/CAE environments (Bolis et al., 1995). Optimal and robust control techniques (LQG, ~ / / z ) have been adopted by Hangstrup (1998) and Mortensen et al. (1998). A description of these solutions is also provided by Moelbak and Mortensen (2003). The control structure adopted in these works is of extreme interest, since it addresses the presence of a built-in classical regulation system. 7.3.1

M o d e l b a s e d predictive control

Particular attention has been devoted to the study of designs that include model based predictive control (MBPC) algorithms. Since the appearance of the first contribution on MBPC in 1976 (Richalet et al.), the area of model predictive control has been enriched by many valuable techniques (see Qin and Badgwell, 1996, 1998, for an updated outline of MBPC approaches). There are a number of reasons to adopt MBPC in the power plant context: •

•

the inclusion of several constraints such as limits on the operability of actuators, admissible ranges on the thermodynamic variables imposed to guarantee safe operation; the possibility of dealing easily with the compensation of measurable disturbances such as the power needs of the grid;

Thermal power plant simulation and control

186 •

the fact that MBPC has a tradition of success in the realm of thermochemical processes.

Different techniques have been adopted in recent years. Prasad et al. (1999) base their multivariable model predictive controller on estimation of states and plant parameters on-line with an extended Kalman filter. In this way, the algorithm adapts to the nonlinear behaviour of the plant. A different proposed solution (Prasad et al., 1998) exploited an artificial neural network. Oluwande and Boucher (1999) illustrate the implementation of MBPC for pressure and temperature control on a coal-fired power plant. Here, the existing PID-based regulation system is upgraded with a multivariable algorithm that modifies the PID's set-points, leading to improved control trends.

7.3.2

The design process

The introduction of a multivariable control system for a power plant requires a MIMO structure added to the existing multi-SISO regulations. To achieve this objective, three activities can be identified: • • •

the definition of the control architecture, i.e. the interactions of the MIMO controller with the conventional system; the synthesis and identification of a model of the plant and existing control system, as part of the optimising control algorithm; the selection of the control framework and its application.

7.3.2.1

The control architecture

The implementation of a MIMO control over an existing multi-SISO control configuration can be carried out by considering that the new, multivariable system is required to modify the dynamic behaviour of an enlarged plant that unites the plant components and the various feedback loops of the classic regulation system. The controlled variables of the enlarged plant are a subset of the outputs of the power generation unit. For instance, the boiler pressure and the turbine inlet temperature can be considered as controlled variables of the enlarged plant. All other outputs that are regulated by a classical controller but not by multivariable controllers (e.g. the power load and the temperature at RH) are not outputs of the enlarged plant. Two different possible configurations can be defined, depending on which control variables are chosen. The first possibility is to act on the set-points of the classical control, whereas an alternative is to inject a correction signal, added to the control input variables of the plant. The schemes of the two architectures, named from now on controlled reference value (CRV) and control action correction (CAC), are sketched in Figure 7.4. In the figure, y is the controlled output vector and y° the corresponding reference value. The control variables are denoted as u, while Um is the control variable of the multivariable controller. Both configurations have been successfully implemented in the past.

Multivariable power plant control

r En-large-d-plant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

~ Multivariable control

Classical

I

control

I

t•

,,

u I nrowerptant [

1 _ _

i

IIiI

Y

I ' , L1 I

i.............................................

Multivariable control

,

187

Ig m

En]arge-d-plant. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . yO

_

[ Classical I . t . - I _ 1 ~I ~

~ , [ rower ' plant

! i

y.

b Figure 7.4

MIMO control architectures a b

controlled reference value; control action correction

A configuration similar to CRV has been adopted by Ordys and Grimble (1996) to optimise the control of a combined cycle turbine power plant. A non-linear simulation model was used for the design and test of the final control scheme, based on a multivariable state space linear quadratic Gaussian (LQG) predictive controller. Also, Oluwande and Boucher (1999) use a CRV structure to synthesise a MPC controller for a coal power plant. Structures based on the CAC architecture have also been adopted. Nakamura and Akaike (1981) introduced a variant of CAC, recognising the benefits of combining a conventional control system with an optimising multivariable strategy. Their approach was put into operation on a Japanese power plant in 1978, and a remarkable reduction of thermal stresses was experienced. After more than ten years of operation (Nakamura and Uchida, 1989), the optimising controller was still in operation without any readjustment of its control parameters. This was possible despite the modifications of the power plant dynamics due to ageing and subsequent maintenance operations. The approach was later implemented at several other Japanese power plants owned by the Kyushu Electric Power Company. Hangstrup (1998) and Mortensen et al. (1998) have designed a CAC-based multivariable control system for the control of steam pressure and temperature of a 85 MW

188

Thermal power plant simulation and control

coal-fired power plant boiler (see also Moelbak and Mortensen, 2003). The results obtained show a significant improvement of the control system performance. CAC is also the structure of the control system, based on MBPC, designed by Poncia and Bittanti (2001). The details will be discussed in section 7.4. 7.3.2.2

Identification of a model for control

A reduced order model of the plant is usually included in optimal control algorithms. Such models are linear for most implementations. The choice of a specific control algorithm imposes the model structure that needs to be implemented. Physical-based models derived from thermodynamic governing equations allow the designer to better understand the plant dynamics. Indeed, their structure and parameterisation can be related to the geometric and physical characteristics of the plant. Physical-based models describe the process non-linearities, providing accurate simulation of the plant behaviour over a wide range of operating conditions. The availability of a plant simulator extremely simplifies the work of the control designer, since expensive and time-consuming testing in the field can be avoided. The design cycle time is reduced significantly, since alternative configurations can be tested rapidly and with no impact on the plant. Also, the simulator can be used to extract the reduced order model needed for the implementation of the control algorithm. Usually, this can be achieved by linearising the non-linear equations to obtain a set of state space linear relations. This procedure is indeed complicated for a multivariable system with a high number of state variables, especially when the system is characterised by implicit relations. This process can be carried out automatically by resorting to specific modelling tools, e.g. Dymola and gPROMS, around a specified equilibrium point. Symbolic manipulation or numerical methods are usually applied. The linearisation of model equations has been adopted, for instance, by Prasad et al. (1999) for the implementation of a multivariable control system that replaces the pre-existing controllers. When the control architecture includes SISO feedback control loops, linearisation is more difficult. It is preferable, in these cases, to apply methods based on the blackbox identification of a multivariable model from available data sets generated from the simulator. The black-box identification procedure has several advantages, when the CRV or CAC architectures are adopted: • • •

the speed of execution, once the data set has been extracted from the simulator; the availability of several well-assessed identification tools; the training data set can be obtained directly from the enlarged plant, via a set of experiments that can be carried out without shutting down the plant.

Models identified by prediction error methods (PEM) are based on external representations such as Auto Regressive with eXogenous input (ARX) or Auto Regressive, Moving Average with eXogenous input (ARMAX). In the multivariable case, such

Multivariable power plant control

189

models contain a very large number of parameters. Consequently, their estimation and the selection of the model complexity are affected by an excessive computational load and numerical errors. In order to deal with high-order MIMO systems, a representation based on a state space model is often preferable, since the information on the dynamics is contained in a limited number of parameters. An effective way of estimating state space models from data is provided by subspace model identification (SMI) methods (Viberg, 1995; Lovera, 1998). Generally, SMI methods lead to reliable models with reduced computational effort when the number of states, inputs and outputs is high. The appropriate order of the system can be visually or automatically extracted from data. The identification procedure must consider the following steps:

•

• • • •

Experiment design: The system (the simulator or the enlarged plant) is excited around a steady operating condition for a given interval of time. The input must excite the plant in order to reveal the plant dynamics. Data preprocessing: All data need to be depolarised and normalised, in order to assure the effectiveness of the identification. Choice of complexity: The model complexity is chosen based on defined criteria. In SMI methods this step is part of the identification algorithm. Identification: The parameters are estimated from data. Validation: The model performance is confirmed by carrying out a comparison with unseen sets of data.

7.3.2.3

Control framework

The choice of an appropriate control technique is necessarily influenced by the nature of the problem, its objectives and constraints. The possibility of comparing several different techniques by means of simulation greatly simplifies the decision process. The designer might look for a solution that is more focused on optimal performance rather than robustness, and choose algorithms that include the compensation for measurable disturbances and the presence of constraints. This is particularly important in power plants, since actuators can saturate, and precise requirements in terms of the allowable range of the thermodynamic variables is also imposed. Finally, the need for real-time operation and smooth transition from MIMO to multi-SISO control cannot be neglected.

7.4

An application: MBPC control of a 320 M W oil-fired plant

The design methodology discussed in section 7.3.2 was used for the development of the multivariable control system of a conventional power plant with a once-through boiler (Poncia and Bittanti, 2001). As observed in section 7.2, this class of plant shows strong coupling between the pressure dynamics, the water content in the boiler and the temperature at the turbine inlet.

190 Thermal power plant simulation and control Power Pe loadset-point AWl~ P~ Set-po~ Set'p°intl [

Figure 7.5

~ ~

Multivariable controller AWw#

Fuel feed 1 adjustment # Plant with classical regulation adjustment Water feed I l

Temperature

at SH 2 outlet

T~H2 {EvaporPttion pressure

The multivariable control system structure

The type of plant considered is oil-fuelled, and generates 320 MW at maximum load. The Italian plants of Castel S. Giovanni and Rossano Calabro, owned by ENEL S.p.A., belong to this category. A complete simulator of the plant dynamics was built on the basis of a nonlinear model, derived from first principles equations (Bottinelli and Facchetti, 1996). The simulator was validated with data from the Castel S. Giovanni plant. A classical control system was added to build a model of the enlarged plant. It includes a coordinated control structure, feedforward actions that anticipate load changes, control of the temperature at SH1 by means of an attemperator plus a slow control via modulation of the fuel feeding system. The temperature of RH is regulated by changing the mass flow of the recirculating gases in the furnace. The proposed multivariable structure (Figure 7.5) is based on the CAC architecture. The main control variables of the plant, namely the requests for fuel and water flow rates, are the result of two contributions. One is the control signal decided by the classical control law, which is obtained by comparing the actual pressure with their reference values p~ and temperature T'°SH2"Additional contributions, imposed by the multivariable controller (wf# and W#w)are added. All other variables are regulated by means of the pre-existing SISO loops. Also, Pe, the electric power demand, is measured and used for compensation purposes. The MPC algorithm described by Ricker (1990) was adopted here. Its state space formulation needs only a small number of parameters of the associated linear plant model, and takes advantage of SMI identification techniques. Also, the unconstrained case was chosen since, in the considered plant, the classical regulation was good enough to avoid the saturation of the control variables. Moreover, the safety boundaries imposed on the thermal variables were never reached.

Multivariable power plant control 7.4.1

191

Model identification via subspace methods

A linear low-complexity model of the plant was designed by adopting a SMI method, in the neighbourhood of a preset operating condition. Specifically, the innovation model identification problem (Verhaegen, 1994; Lovera, 1998) was used. In the identification procedure, the pressure Pt and the temperature TSH2 constitute the output vector, whereas the corrections of water w w # and fuel w~ mass flows, and the load request Pe°, are input variables. The identification was carried out by setting: •

•

steady-state condition of interest. Specifically, the power load Pe was set to 290MW, the pressure Pt to 170MPa, and the temperatures TSH2 and TRH both to 813 K. Since all the SISO classical controls have integral action, the regulated variables are equal to their respective set-point at steady-state (in the absence of unsteady disturbances). The input/output vectors, namely: A

u(k) = [gw#w gw~ 3Pc]',

y(k)

~-

[~Pt

STsH2]t,

where 8 ( ) are the normalised fluctuations of the variables. The data set to be used for identification purposes. All inputs are pseudo random binary sequences (PRBSs) with range of variability q- 1 per cent of the nominal value. All data were depolarised and normalised. An additional data series (step identification data), consisting of the system step response, was also used for identification. In this way, one could identify the convergence of the controlled variables to their reference values at steady-state. On the basis of the simulated sequences, the identification of the reduced order model was performed by resorting to SMI techniques. A distinctive feature of this system is that all gains are zero, due to the presence of the integral action of classical controllers. Therefore, the original identification problem is reformulated by defining a new output vector, denoted by y* (k), such that

y*(k) =

z y(k), Z--1

where z is the time shift operator. The system with input u(k) and the new output y* (k), represented by the matrices A*, B* and C*, is identified instead of the enlarged plant. The matrices A, B and C of the original model can be reconstructed from A*, B* and C*: * A = [ aC*

001

B:

[B*]

C=[C*

-I].

The identification algorithm also provides an estimation of the optimal system order, by performing a singular value analysis (Verhaegen, 1994). In this specific case, the value n = 10 was found. Finally, the algorithm provides the estimated matrices .4, and C of A, B, and C.

192

Thermalpower plant simulation and control Evaporatorpressure, variation i

i

i

i

i

~

p

i

i

I

I

I

I

I

I

I

I

I

i

i

r

i

i

I

I

I

I

0.01

,y

o

~).Ol

SH2outlet temperature, variation i

i

t

I

0.01 o -0.01 I

2000

4000

I

6000

I

8000

10,000

Time (s) -

Figure 7.6

-

Simulator

Identified linear model

Performance of the identified reduced order model: PRBS identification data

The model was finally validated on the basis of a third sequence (PRBS validation data), not used for identification, generated by exciting the process with a new PRBS sequence. Simulations carried out with the identified system show very good performance for the identification and validation data sets (see Figures 7.6-7.8). Remark. The choice of the operating condition influences the identification of the linear model, since the power plant dynamics are intrinsically non-linear. Usually, the control set-points of temperatures and pressures are seldom changed during plant operation. Consequently, for the identification of a linear model around different set-point configurations is not required for control purposes. On the other hand, a linear model cannot correctly represent the plant within a wide range of admissible loads. Linearisation errors are therefore introduced when the load differs significantly from the chosen reference value, with an impact on the control system performance. Such errors can be reduced with a sound choice of the reference set used for identification. When needed, performance can be further improved by adopting gain-scheduling solutions that incorporate models linearised at different operating conditions. In the present case, the plant was linearised assuming that the plant operates at full load (320 MW) most of the time, and that the controller can compensate for a

Multivariable power plant control

193

Evaporator pressure, variation 0.005

o

I

-0.005

I

I

I

I

SH2 outlet temperature, variation 0.004

o

~).004 L

0

t

4000

8000

I

12,000

t

16,000

I

20,000

24,000

Time(s) --

Simulator

Identified linear model

Figure 7. 7 Performance of the identified reduced order model." step identification data Evaporator pressure, variation

0.01

~

o ~0.01 I

t

I

I

t

SH2 outlet temperature, varialion 0.01

o

~).01 0

200

4000

6000

8000

10,000

12,000

Time (s) -

Figure 7.8

-

Simulator

Identified linear model

Performance of the identified reduced order model: PRBS validation data

Thermal power plant simulation and control

194

sudden drop of 20 per cent. For this reason, the identification has been carried out at the intermediate condition of 90 per cent load (about 290 MW).

7.4.2

Implementation and evaluation of the controller

As discussed, the unconstrained case of the algorithm presented by Ricker (1990) was chosen. Its state space formulation allowed the use of the model identified in section 7.4.1. The control algorithm is based on a state space model of the enlarged plant with structure

x(k + 1) = Ax(k) + Bmum(k) + Bvv(k) + Bww(k) + Bzz(k) y(~) = Cx(k) where urn is the vector of control variables, v represents the set of measured disturbances, and w and z the unmeasured disturbances. The optimal controller is the solution of an optimisation problem, where the cost function n

J = Z [ r ( k ÷ i) - ~(k + ilk)]'#y(k)[r(k + i) - ~(k ÷ ilk)] i=1 c

+Z

Aum(k + ilk)'lx,(k)Aum(k + ilk)

(7.1)

i=1

is minimised. In (7.1), r(k) is the reference value and ~(k + i Ik) is the predictor based on the observations y(k) and v(k), i time steps ahead. This cost function is a weighted sum of the error between the reference and predicted value of the output upton steps ahead starting from k + 1 (the so-called prediction horizon) and the control effort upto c steps ahead (the control horizon), expressed in terms of the control increment Aum. In the absence of constraints, a state space model for the controller can be found. Its output Yc(k) = um(k) is a function of the state prediction, the measured signals y(k) and v(k), and the reference value r(k), all contained in the state xc(k) and input uc(k) vectors (Ricker, 1990). The matrices of the controller, Ac, Bc, Cc and Dc depend on the model matrices A, B and C, and on the horizons n and c and the w e i g h t s l/,y and #u. The tuning of the controller can be completed by choosing the prediction horizons n and c and the weights #y and/L u in (7.1). The following parameterisation, based on a rough evaluation of the closed-loop performance, was adopted: prediction horizon n = 15; output weight # y : diag[0.5 1.5];

control horizon c ----2; input weight /t u = diag[0.5 0.3].

This choice was made on the basis of the following observations: •

The increment of the prediction horizon n usually allows better performance, since a greater prediction of the future error is possible.

Multivariable power plant control 195 •

•

The weight on the temperature control error must be high. This is due to the fact that the classical regulation of temperature is slow and largely responsible for the overall performance. c and #u influence the strength of the control action. In order to achieve good performance, #u should not be too high, to avoid the excessive penalisation of the control action. Moreover, it has been seen that high values of c induce undesired oscillations of the control variables.

R e m a r k . When the control problem is formulated without constraints on the control variables, the selection of #u must be carried out conservatively, by choosing values high enough to avoid the saturation of the actuators. On the other hand, saturation does not occur when control constraints are included, so t h a t / t u can have a lower magnitude. The main drawback of this option is that the resulting control algorithm is much slower, since an optimisation problem needs to be solved at every control step. Conversely, in the unconstrained case the controller solution is computed off-line, leading to faster on-line operation.

320

electric load

178

300

2

174

280

~ 170

260

166 SH2 outlet temperature

820

evaporatorpressure

RH outlet temperature

830

810 a: 810

790 802

0

4000

8000 Time (s) --

Figure 7.9

12,000 classical - -

0

4000

8000 Time (s)

12,000

MBPC

Comparisonbetween MBPC and classical control responding to sudden changes of the power load: simulation of the controlled variables

196

Thermal power plant simulation and control Attemperator valve at SH]

Turbine valve

0.8

0.5

0.6 4000

8000

12,000

4000

Time (s)

8000

12,000

Time (s)

Pump (rpm)

Fuel flow rate (kg/s)

18

3400

16

3200

3000 0

4000

8000

12,000

14

0

4000

Time (s)

8000

12,000

Time (s)

Air flow rate (kg/s)

Recirculation gas flow rate (kg/s)

280: 80

60 250 40

220 4000

8000

12,000

4000

Time (s) --

Figure 7.10

8000

12,000

Time (s) Classical - -

MBPC

Comparison between MBPC and classical control responding to sudden changes of the power load: simulation of the variables used to control the plant performance

The control system was evaluated by simulating a sudden step change of the load request. This test replicates the critical situation that occurs when an unexpected change of Pe takes place (e.g. in the isolated grid case). A set of three large step changes were imposed on Pe, starting from the reference condition: •

starting from Pe = 290 MW, a positive step of 25 MW is imposed;

Multivariable power plant control Evaporator pressure

Electric load

/

320

~" 310

300

197

170

168.8

168.6

290

168.4 RH outlet temperature

SH 2 outlet temperature 815 817

814 815 813

813 0

4000 Time (s)

8000 - -

Classical

4000 Time (s) ~

8000

MBPC

Figure 7.11 Classical and MBPC control performance: a ramp change of Pe

• •

then, after settling to the steady-state condition, a change o f - 5 0 MW is simulated; finally, a +25 MW step is generated.

Step changes occur at every 4000 s. The simulation results (Figure 7.9) show that the multivariable controller performs much better than the classical one, in rejecting the disturbance Pe. The convergence of the pressure and the two temperatures TSH2 and TRH to their respective references is faster. In this case, the steady-state condition is reached in a shorter interval of time for Pe and TSH2, and the overshoot observed for the classical controller is significantly reduced. The sudden and ample change of Pt introduces unwanted behaviourin the enlarged plant, such as the initial overshoot of the pressure and the occurrence of sizeable oscillation of the temperatures (particularly Tsnt ). The MIMO controller eliminates the first case and greatly reduces the second. The evaluation of the control signals indicates a negligible change in the magnitude of the input signals, passing from the classical to the multivariable solution (Figure 7.10). In other words, the correction signals introduced by the optimising algorithm are indeed small. One significant accomplishment achieved with the new controller is the possible use of theattemperator at the SHI downstream only to manage emergencies. Indeed,

198

Thermal power plant simulation and control PressurePt

IncreasingN -0.2 Temperature TSH2 0.04

0 0

Increasing N

",7 2000 Time (s)

",7

~ 4000

Figure 7.12 Controller tuning: change of the prediction horizon N = 2 . . . . . 15

in Figure 7.10 it is shown that this attemperator can be kept closed when the MIMO controller is active. This particular aspect could be beneficial, since efficiency losses and the risk of having water droplets in the turbine are avoided. To further evaluate the behaviour of the new control system, a further set of simulations is shown in Figure 7.11. Here, a ramp change of the load request (from 290 to 300 MW at a velocity of 10 kW/s) was imposed, simulating a slow transition from one regime to a new one. Again, the multivariable control provides a performance improvement. Finally, the evaluation of the sensitivity of the control performance to changes in the MBPC's parameterisation provides guidelines for controller tuning. Trends have been observed for changes in the prediction horizon n, the control weight /*u and the component of the error weight /£y related to TSH2, denoted as #yT (Figures 7.12-7.14). The simulations refer to the normalised values of the controlled variables when a step change of the disturbance Pe is imposed on the identified model. This analysis confirms the assumptions originally made. Short prediction horizons n cause significant oscillation of the responses to step variations of Pe, and high/*u leads to a degradation of performance due to the penalisation of the control action. To conclude, it can be observed that a stronger weighting of the error on TSH2 leads to significantly improved behaviour, with negligible changes in the controlled pressure dynamics.

Multivariable power plant control Pressure Pt

-0.2 I

h

i

Temperature

TSFI2

0.1

I

i

0

4000

2000 Time (s)

Figure 7.13

Controller tuning." change of the control weight/Zu

= 0.1 . . . . .

5.0

Pressure Pt

asilg.yonTs~2

-0.2 I

I

i

Temperature TSH2 0.1

Increasing/~y o n

i

0

TSH2

I

2000

4000

Time (s)

Figure 7.14 Controllertuning: change of the error weight/Zy r

= 0.1 . . . . .

1.0

199

200

Thermal power plant simulation and control

7.5

Conclusions

The application of multivariable techniques to the control of fossil fuel power plants has been discussed in this chapter. Solutions that replace the classical multi-SISO configuration have not found application in the industrial realm, mainly because of the diffidence towards systems that revolutionise well-assessed technologies and design procedures. For this reason, attention is mainly devoted to structures where the classical regulation is kept in operation, and a multivariable solution corrects it, in order to improve the trajectories of the thermodynamic variables. The design process is achieved in a sequence of steps, which involve: •

•

•

• •

The choice of the control architecture, alternatively controlled reference value or control action correction. Both architectures consist of a multivariable controller that corrects the action of a traditional regulation system. The development of a non-linear model of the power plant, used for simulation and verification purposes. The model is validated against experimental data from the real plant. The synthesis of the reduced order models that will be incorporated in the control algorithm. The models can be identified from simulation or experimental data in a fast and reliable way by applying state space identification techniques. Model based predictive control strategies have been demonstrated to be effective and reliable for the control of many chemical and thermal processes. The controller synthesis and verification over the operating range of the plant, according to the design specifications.

The benefits of the introduction of a control action correction multivariable controller based on state space MBPC have been illustrated by presenting an application to a simulated 320 MW oil-fired plant. It can be observed that: • • •

•

7.6

The application of the multivariable solution allows a reduction of thermal stresses and pressure oscillations when extreme conditions are encountered. Amplitudes of the control variables are also reduced, thus diminishing the stress and effort of the actuators. Moreover, the results suggest the possibility of eliminating the temperature control by attemperation, a solution that generates efficiency losses and increases the possibility of damage in the turbine. The improved control system is conceived in such a way that when the multivariable controller is disconnected, the traditional regulation devices guarantee safe operation of the plant.

Acknowledgements

The author is gratefully indebted to Professor Antonio de Marco for being a guide and mentor during his time at the Politecnico di Milano. Also, many thanks to Professor Sergio Bittanti for his constant support and advice.

Multivariable power plant control

7.7

201

References

BEN ABDENNOUR, A., and LEE, K.: 'An autonomous control system for boilerturbine units', IEEE Transactions on Energy Conversion, 1996, 11, (2), pp. 401-6 BOLLS, V., MAFFEZZONI, C., and FERRARINI, L.: 'Synthesis of an overall boiler-turbine control system by a single-loop autotuning technique', Control Engineering Practice, 1995, 3, (6), pp. 761-71 BOTTINELLI, M., and FACCHETTI, M.: ' Simulazione di un generatore di vapore ad attraversamento forzato e identificazione di un modello ridotto per il controllo (Simulation of a once-through steam generator and identification of a reduced order model for the control)'. Master's thesis, Politecnico di Milano (in Italian), 1996 DIMEO, R. M., and LEE, K. Y.: 'Genetics-based control of a MIMO boiler-turbine plant'. Proceedings of the 33rd IEEE Conference on Decision and Control, Karlsruhe, Germany, 1994. DOLEZAL, R., and VARCOP, L.: 'Process dynamics, automatic control of steam generation plant' (Elsevier, Amsterdam, 1970) DOT PRODUCTS INC.: 'STAR(R) adaptive multivariable controller', Website *http://www.dot-products.com/star.html, 2000 GARCIA, H., RAY, A., and EDWARDS, R.: 'A reconfigurable hybrid system and its application to power-plant control', IEEE Transactions on Control Systems Technology, 1995, 3, (2), pp. 157-70 HAGEDORN, E, and KLEFENZ, G.: 'H&B Power Station Control. Part I: Unit Load Control. Part II: Combustion Control'. Monograph 3587EN, Hartmann & Braun - Schoppe & Faeser HANGSTRUP, M.: ' Strategies for industrial multivariable control with application to power plant control'. PhD thesis, Aalborg University, Department of Control Engineering, 1998 KLEFENZ, G.: 'Automatic control of steam power plants' (Bibliographisches Institut, Mannheim, 1971) KLEFENZ, G., and KRIEGER, J.: 'New concept for co-ordinated power-plant control', Transactions of the Institute of Measurement and Control 1992, 14, (2), pp. 71-8 LAUSTERER, G. K., and KALLINA, G.: 'Advanced unit control within stress limits'. Proceedings of the ASME Joint International Power Generation Conference, Phoenix, AZ, 1994 LOVERA, M.: 'Subspace identification methods: theory and applications'. PhD thesis, Politecnico di Milano, Milano, Italy, 1998 MOELBAK, T., and MORTENSEN, J. H.: 'Steam temperature control', in FLYNN, D. (Ed.): Thermal power plant simulation and control' (IEE, London, 2003) MORTENSEN, J., MOELBAK, T., ANDERSEN, P., and PEDERSEN, T.: 'Optimization of boiler control to improve the load-following capability of power-plant units', Control Engineering Practice, 1998, 6, (12), pp. l 531-40

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NAKAMURA, H., and AKAIKE, H.: 'Statistical identification for optimal control of supercritical thermal power plants', Automatica, 1981, 17, (1), pp. 143-55 NAKAMURA, H., and UCHIDA, M.: 'Optimal regulation for thermal power plants', IEEE Control Systems Magazine, 1989, 9, (1), pp. 33-8 OLUWANDE, G.: 'Exploitation of advanced control techniques in power generation', Computing and Control Engineering Journal, 2001, 12, (2), pp. 63-7 OLUWANDE, G., and BOUCHER, A. R.: 'Implementation of a mutivariable model-based predictive controller for superheater steam temeprature and pressure control on a large coal-fired power plant'. Proceedings of the European Control Conference ECC'99, Karlsruhe, Germany, 1999 ORDYS, A. W., and GRIMBLE, M.: 'A multivariable dynamic performance predictive control with application to power generation plants', Proceedings of the IFAC World Congress, San Francisco, 1996 PONCIA, G. and BITTANTI, S.: 'Multivariable model predictive control of a thermal power plant with built-in classical regulation', International Journal of Control, 2001, 74, (11), pp. 1118-30 PRASAD, G., IRWIN, G., SWIDENBANK, E., and HOGG, B.: 'Plant-wide physical model-based control for a thermal power plant'. Proceedings of the 38th IEEE Conference on Decision and Control, 1999, 5, pp. 4631-6 PRASAD, G., SWIDENBANK, E., and HOGG, B.: 'A neural net model-based multivariable long-range predictive control strategy applied in thermal power plant control', IEEE Transactions on Energy Conversion, 1998, 13, (2), pp. 176-82 QIN, S., and BADGWELL, T.: 'An overview of industrial model predictive control technology'. AIChE Symposium Series 316, number 93, CACHE and AIChE Chemical Process Control-V, Tahoe, CA, USA, 1996, pp. 232-56 QIN, S., and BADGWELL, T.: 'An overview of nonlinear model predictive control applications, Proceedings of the Nonlinear MPC Workshop, 'Ascona, Switzerland, 1998 RICHALET, J., RAULT, A., TESTUD, J. L., and PAPON, J.: 'Algorithmic control of industrial processes'. Proceedings of the 4th IFAC Symposium on Identification and System Parameter Estimation, 1976, pp. 1119-67 RICKER, N. L.: 'Model predictive control with state estimation', Industrial Engineering Chemical Results, 1990, 29, pp. 374-82 TAKITA, A., TAKAHASHI, S., FUKAI, M., and TAKEI, T.: 'Recent technical developments in thermal power station supervisory and control systems', Hitachi Review, 1999, 48, (5), pp. 267-72 VERHAEGEN, M.: 'Identifcation of the deterministic part of MIMO state space models given in innovations form from input-output data', Automatica, 1994, 30, (1), pp. 61-74 VIBERG, M.: 'Subspace-based methods for the identification of linear time-invariant systems', Automatica, 1995, 31, (12), pp. 1835-51 ZHAO, H., LI, W., TAFT, C., and BENTSMAN, J.: 'Robust controller design for simultaneous control of throttle pressure and megawatt output in a power plant unit, International Journal of Robust and Nonlinear Control, 1999, 9, (7), pp. 425-46

Part 3

Monitoring, optimisation and supervision

Chapter 8

Extending plant load-following capabilities R. Garduno-Ramirez and K.Y Lee

8.1

Introduction

The current operating environment of a fossil fuel power unit (FFPU) is characterised by many needs and requirements. First, a FFPU must support the main objective of the power system, which is to meet the load demand for electric power at all times, at constant voltage and at constant frequency (Elgerd, 1971). In addition, competition among utilities and other market driven forces has increased the usage of FFPUs in load-following duties (Armor, 1985). Moreover, stringent requirements on conservation and life extension of major equipment, and regulations on reduced environmental impact, have to be fulfilled (Divakaruni and Touchton, 1991). This context may be synthesised as an essential requirement for a FFPU to achieve optimal and robust wide-range load-following operation under multiple operation objectives, such as minimisation of load tracking error, minimisation of fuel consumption and heat rate, maximisation of duty life, minimisation of pollutant emissions, etc. (Garduno-Ramirez and Lee, 2001a). Effective participation of a FFPU in load-following duties requires the ability to undertake large variations in the power being generated in the form of daily, weekly, and seasonal cycles, as well as random fluctuations about those patterns. The major courses of action that have been undertaken to facilitate wide-range load-following operation with improved performance include upgrading the physical components of the power unit and the control system (Miller and Sterud, 1989). Since wide-range operation imposes strong physical demands on the unit equipment, which inherently lead to conflicting operational and control situations, the load-following capability of a FFPU may also be improved by enhancing the control system strategy. Currently, most FFPU control systems consist of multiloop configurations based on conventional PID controllers. Such an approach has proved its value during normal operation maintained at base load, where plant characteristics become almost constant, nearly linear and weakly coupled. Nevertheless, under load-following conditions the traditional control

206

Thermal power plant simulation and control

schemes, designed and tuned for regulation and disturbance rejection, but not setpoint tracking, may decrease the global performance of the power unit because its non-linear process dynamics vary with the point of operation. This situation makes the traditional control structures less acceptable for wide-range load-following operation. A control approach that has found its way into practical application to achieve wide-range operation at power plants is a combination of feedforward and feedback (FF/FB) controls. In Uram (1977) the feedforward power reference is modified by the output of a PI controller that is driven by the difference between the power reference and the power feedback. The combined action of both controllers yields fast response and steady-state accuracy, with the feedback control action providing the necessary adjustments for the control valve non-linearities, or for changes in steam pressure resulting from the boiler transient conditions. In addition, several simulationbased studies have explored FF/FB schemes using different approaches. Weng and Ray (1997) report a wide-range robust controller for a steam power plant. The FF control is generated via non-linear programming to provide optimised performance. The FB law is synthesised by the H~-based structured singular value approach to achieve the desired stability and performance robustness. Zhao et al. (1997) present a FF/FB scheme for a nuclear steam generator. The FF control provides a predictive command input, based on the required performance and a simplified steam generator model. The FB control path shows a PI-based multiloop configuration with cross-coupling gains, which are tuned optimally by a genetic algorithm technique. In general, the main idea of a FF/FB scheme is to complement the feedback controllers with feedforward control actions to compensate in a predictive way for known large and frequent disturbances, and long time constants and time delays. That is, feedforward control actions are issued before the deviations occur in the measured variables, so that better response to load and set-point changes can be achieved. In this chapter, the load-following capability of a fossil fuel power unit is enhanced by augmenting the existing control system with a multivariable feedforward control strategy. With the aim of having a better distribution of the control tasks, the proposed open-loop reference feedforward control is used to improve the manoeuvrability of the power unit, while the existing closed-loop feedback control is now only used to compensate for uncertainties and unknown disturbances around the commanded unit load demand trajectory. The feedforward controller is designed as a process knowledge-based controller that approximates the static behaviour of the power unit through its whole operation range. The required process knowledge is extracted from a set of input--output data patterns directly measured at the power unit during normal operation. The feedforward controller is implemented as a set of multiple-input-single-output fuzzy systems whose inference rules are determined through a supervised neural learning procedure (Garduno-Ramirez and Lee, 2000). Section 8.2 provides descriptions of the overall operation and the qualitative dynamics of a FFPU as a way to establish the most general operational requirements to be satisfied by the control system. Section 8.3 shows through simulation experiments how typical control systems based on conventional PI controllers fall short in providing satisfactory wide-range load-following operation. Section 8.4 justifies the need for a hybrid feedforward and feedback control scheme and introduces the corresponding

Extending plant load-followingcapabilities 207 control system configuration for the FFPU. Section 8.5 presents a detailed specification of the feedforward controller as a knowledge-based system to be implemented as a set of fuzzy systems. Then, section 8.6 describes the design of the proposed fuzzy systems using a neurofuzzy paradigm, which allows automating the design process for the multivariable knowledge-based feedforward control. Section 8.7 presents a specific realisation of the neurofuzzy systems and their application for wide-range load-following operation. Finally, section 8.8 summarises this work and concludes that the results demonstrate the practical feasibility of the proposed feedforward control approach to achieve effective wide-range load-following operation.

8.2 Power unit requirements for wide-range operation A power system is intended to supply the electric power demanded by the consumers in a reliable form with high quality characteristics. The total system load is not under direct control and follows daily, weekly, and seasonal cylical patterns; in addition, connection and disconnection of individual loads cause random fluctuations about these patterns. Since there are no practical means to store large quantities of electric energy, it should be produced as needed by the consumers. Consequently, the power system never really operates in steady-state; it is always trying to match power generation with the load in what is known as the load-frequency problem. Thus, FFPUs participating in load-frequency control are always subject to changing load demands and load disturbances as part of their normal operation regime (Dunlop and Ewart, 1975). From the power system perspective the overall input-output behaviour of a FFPU has noteworthy relevance. On one hand, long-term frequency stability analysis, which assumes that all electromechanical oscillations have died out and that the system is operating at constant frequency, perhaps different from the nominal value, could be in a time frame of several to tens of minutes. On the other hand, the main boiler dynamics are relatively slow: steam pressure and temperature oscillations, and the effect of fuel flow variations on the generated power are in the order of minutes. Therefore, the dynamics of FFPUs are considered a major factor in frequency stability analysis (Kundur, 1994). Accordingly, any FFPU participating in load-frequency control duties should be equipped with control systems that take into account the long-term overall input-output dynamic behaviour of the unit. The electric power in a drum-type FFPU is the resultant of a series of energy conversion processes within the unit. All those energy conversion processes are rather complex and show very complex relationships among them. However, the essential overall dynamics may be described in terms of the major inputs (fuel flow, air flow, steam flow into the turbine, feedwater flow, and spray flows into the superheater and reheater) and outputs (electric power, steam throttle pressure, drum water level, superheater outlet temperature, and reheater outlet temperature) (Maffezzoni, 1997). Electric power and steam pressure are tightly coupled and are affected heavily by the fuel/air flow and the steam flow. Feedwater flow slightly affects power and pressure, but greatly impacts on the drum level, which in turn is considerably affected by the fuel and steam flows. Similarly, the spray flows have a minor effect on power and

208

Thermal power plant simulation and control

pressure, but greatly affect the heat exchanger outlet temperatures, which are heavily influenced by the fuel flow. In summary, fuel and steam flow may be used to drive the unit to the desired values of power and pressure. This will disturb the drum water level and heat exchanger outlet temperatures, which may then be manipulated with the feedwater and spray flows. The interaction between fuel, steam, and feedwater flows as inputs, and power, pressure and water level as outputs, suggests these as the primary variables to consider to achieve wide-range operation. Spray flows and temperatures can be used for further improvement. Consequently, this chapter concentrates on the former situation. Furthermore, the open-loop behaviour determines the input-output pairing to form the feedback control loops. Figure 8.1 shows the simulation response to a step change in the steam valve with the fuel and feedwater valves kept constant. Power increases and then decays back close to its original value, while pressure decreases to a new value and the level keeps decreasing. Similarly, Figure 8.2 shows the response to a step in the fuel valve, with the steam and feedwater valves at a fixed position. Both throttle pressure and power increase to a new fixed higher value, while the drum level continually decreases. From these tests, it can be seen that for short-term purposes, a fast response to load variations may be attained using the throttle valve to control power output and the fuel valve to regulate the steam pressure. Conversely, for long-term purposes, fuel flow should be used to control power output, and the throttle valve to maintain the steam pressure. In both cases, the drum level has to be regulated to balance plant operation. Power output i

80 Throttle pressure 102~

~

98 ~

I

Drum level ~ 1 0 0 0 ~

~-100

Figure 8.1

I

0

500

1000 Time (s)

1500

Open-loop response to a step in steam valve position

2000

Extending plant load-following capabilities 209

Power output i

g 80

Throttle pressure , 1 0 2 ~ 100 a~ 98 Drum level

200,

-20

Figure 8.2

8.3 8.3.1

I

o

500

1000 Time (s)

1500

2000

Open-loopresponse to a step in fuel valve position

Conventional power unit control Conventional coordinated control

In fossil fuel power units, the coordinated control (CC) scheme constitutes the uppermost layer of the control system. The CC is responsible for driving the boiler-turbine-generator set as a single entity, hannonising the slow response of the boiler with the faster response of the turbine-generator, to achieve fast and stable unit response during load tracking manoeuvres and load disturbances. To attain a fast response, the turbo-generator is allowed to draw upon the energy stored in the boiler. To achieve stability, the boiler control adjusts the fuel firing rate according to the required load, while keeping the turbine from exceeding the energy provided by the boiler. Typically, the CC governs the dominant behaviour of the power unit through the power and steam pressure control loops. Given a unit load demand, Euld, the CC provides set-points to both control loops. Ordinarily, the set-point for the power control loop, Ed, is equal to the unit load demand, and the set-point for the pressure control loop, Pd, is obtained from the unit load demand through a non-linear power-pressure mapping, which is said to implement the operating policy of the unit. Depending on how the controlled and manipulated variables are paired, there are two possible CC modes: coordinated boiler-following mode and coordinated turbinefollowing mode (Landis and Wulfsohn, 1988). In coordinated boiler-following mode (Figure 8.3), the load controller generates the demand to the steam throttle valve, u2, from the unit load demand, Euld, and the measured generated power, E, while the pressure controller generates the demand to the fuel/air valves, u 1, from the measured

210

Thermal power plant simulation and control

Euld

Pressure "]_ mapping ) Pd Pressure controller

1

u 2 ~

Combustion controller ) Steam r ' ~ I /1

Load controller

%+

E

--1/ © Figure 8.3

Coordinated boiler-following control scheme

throttle pressure, P, and the pressure set-point, Pd- In coordinated turbine-following mode (Figure 8.4), the load controller generates the demand for the fuel/air valves, u l, from the unit load demand, Euld, and the measured generated power, E, while the demand to the throttle valve, u2, is calculated from the measured throttle steam pressure, P, and the pressure set-point, Pd. Based on the unit step responses shown in the previous section, the boiler-following CC should be preferred for fast transient response, while the turbine-following CC should be chosen to achieve long-term process optimisation objectives. As for most control systems in the process industries, the CC scheme in a FFPU consists of a decentralised multiloop configuration of single-input-singleoutput feedback control loops evaluating conventional PI or PID algorithms. Despite its simple structure, decentralised PID control has a long record of satisfactory performance; its effectiveness to regulate a process under random load disturbances around a fixed operating point is proven daily all over the world. The main reason for this is the relatively simple structure of the control system, which is easy to understand and to implement, and its reliability in the case of actuator or sensor failure, which could make it relatively easy to manually stabilise a system when only one loop is directly affected. In addition, the number of tuning parameters is relatively small, and increases only linearly with the number of control variables (i.e. 3n tuning parameters for a control system with n control loops).

Extending plant load-following capabilities 211 Pressure mapping

Pd

Euld

1 q I

Load controller

Pressure controller Combustion controller

u2

P Steam

E

B Fuel Air

L

Figure 8.4

(3

i

Coordinatedturbine-following control scheme

Normally, the controller parameters are tuned at some predefined operating point (i.e. base load) assuming nearly constant load conditions, and are left fixed thereafter. This approach works well for process regulation about the operating point used for tuning. However, current requirements demanding wide-range operation of FFPUs challenge this approach. The performance of the power unit may decrease due to the non-linear and interactive dynamics of the process that change with operating conditions. Consequently, strong physical demands that are detrimental to the unit duty life may be imposed on the plant equipment. In the subsections that follow the drawbacks of a typical CC, considered as a PID-based multiloop control system, are shown through simulation experiments. The results obtained are later used as reference for comparison and to evaluate the performance of the CC augmented with the knowledge-based feedforward control, which thus provides a feasible solution to the optimal wide-range requirements of FFPUs (Garduno-Ramirez and Lee, 2001 b).

8.3.2

Control loop interaction and tuning

The main difficulty for decentralised control of multivariable processes is that of control loop interaction due to the coupling dynamics between the process inputs and outputs, as illustrated in section 8.2, through the open-loop control valve step responses. The effects of control loop interaction for the same FFPU were observed through the closed-loop response to step changes in the set-points, i.e. power, steam

212

Thermal power plant simulation and control

pressure, or level set-point. All tests were carried out starting from an operating point at half-load, defined by E = 80 MW, P = 100kg/cm 2, and L = 0mm. The controllers were tuned to achieve an almost critically damped response in all loops. Results show that the strongest and most significant interaction is from the pressure control loop to the power output, which normally requires the tightest control for either tracking or regulation. Second in importance is the interaction between the power loop and the pressure output, which may adversely affect the physical condition of the plant equipment. Next are the interactions between the power and pressure control loops to the level output, for which tight regulation is not usually required provided that the magnitude of the oscillations about the zero level is kept within safe limits. Finally, the interactions between the level control loop to the power and pressure outputs are both relatively small and are usually a minor concern. Certainly, satisfactory step responses are an indicator of good control performance. Most control systems of all kinds are usually assessed using this approach. Unfortunately, for the case of non-linear multiple-input multiple-output (MIMO) systems, subject to wide-range reference-tracking operation requirements the above is not sufficient to guarantee good performance. In the case of FFPUs there are several practical considerations that prevent the utilisation of step responses; ramp responses are preferred. Strictly speaking, ramp responses provide the same amount of information about the system. Step responses will, however, be used in the rest of this chapter to exhibit the behaviour of the system solely in simulation experiments, under the understanding that these tests are not recommended to be carried out in practice. Now, the ramp response of the FFPU is investigated for a low ramp-up loading manoeuvre using the same controller parameters as in the step-response test, which previously provided excellent step responses. The power output is required to increase from 80MW (half load) to 90MW in 150 s, that is a 6.25 per cent power set-point change at a rate of 2.5 per cent per minute, which would normally be considered a straight forward test. Accordingly, the pressure set-point is obtained from the unit load demand through the mapping: 150 - 65 Pd -- - - E u l d 1 8 0 - 10

+ 65MW

(8.1)

which implements a typical sliding-pressure operating policy, which is a fairly common practice in CC schemes (Ben-Abdennour and Lee, 1996). As can be seen from the graphs in Figure 8.5, the power set-point tracking is adequate, with an excellent low control activity. Pressure set-point tracking is poor, particularly at the end of the ramp with a large overshoot and settling time, but its control activity is excellent. The oscillations in the water level are fine and the control activity is again acceptable. These results demonstrate that controller tuning based on step responses does not imply good load-tracking performance, which is a major concern for wide-range operation. The inverse situation is also interesting. Controllers tuned to achieve excellent ramp response, Figure 8.6, do not necessarily provide a good step response, or even a stable response. This fact is shown by Figures 8.7-8.9 for the previously described

Extending plant load-following capabilities Power response

213

Fuel valve demand

92 90 0.8~

88

86

0.6~

84

0.4~

82

0.2~

80

0[ 50

100

150

200

250

300

Time (s)

0

50

150

200

250

300

250

300

Time(s)

Pressure response

Steam valve demand

107

1

106 ~-. 105

0.8

104 ~ 103 ~" 102 ~-~ 101 100 99

100

b

0.6 ~' 0.4 0.2

0

50

100

150

200

250

300

Time (s)

0

50

100

d

150

200

Time (s)

Level response

Feedwater valve demand

20 1

10

0.8

E

0.6

o

..__..-/ 0.4

-10

0.2 0

-20 0

50

100

150 Time (s)

200

250

300

0 f

50

100

150

200

250

300

Time (s)

Figure 8.5 Ramp load tracking with step-tuned controller parameters step response tests, but with the controller parameters retuned to improve the ramp response.

8.4

Feedforward/feedback control strategy

As will be shown shortly, the load-following capabilities of a FFPU may be enhanced by augmenting the existing control system with a multivariable feedforward control

214 Thermalpower plant simulation and control Fuel valvedemand

Power response

92

j

90 88 86 84 82 80

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0.8 0.6

O.

100

150 200 Time (s)

250

300

0

50

160

b

Pressure response 107 106 105 104 ~ 103 102 ~7 101 100 ! 99

150 260 Time (s)

250

300

250

300

Steam valve demand 1

0.8 0.6 0.4 0.2 0 50

100

150 200 Time(s)

250

300

0

50

100

d

150 200 Time (s)

Feedwater valvedemand

Level response 20 1

10

0.8 0.6 0.4

-10 -20

0.2 0 0

Figure 8.6

50

100

150 200 Time(s)

250

300

0 f

50

100

150 200 Time(s)

250

300

Ramp load tracking with ramp-tuned controller parameters

strategy. With the aim of obtaining a better distribution of the control tasks, the feedforward control is mainly used to improve the manoeuvrability of the power unit along any arbitrary load demand profile, while the existing closed-loop feedback control is now mainly used to compensate for uncertainties and unknown disturbances. In general, a feedforward control action takes advantage of the available information about external events affecting the FFPU operation before the action of the feedback control takes place. In this way, both changes in the reference signals and measurable

Extending plant load-following capabilities Power response

215

Fuel valve demand

81.5 1

81

0.8

80.5

~- 0.4

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o.

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Time (s)

Pressure response

Steam valve demand

101 1

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d

Level response

150 200 250 300 Time (s)

Feedwater valve demand

20 1

10

0.81

E

E

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~, 0.6

k

0.4 -10

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Figure 8. 7

100 150 200 250 300 Time (s)

50 f

100

150 200 250 300 Time (s)

Response to step in power set-point with ramp-tuned parameters

disturbances can be effectively compensated by feedforward actions. Nevertheless, since the major interest of this chapter is on load-following e n h a n c e m e n t through wide-range unit load d e m a n d tracking, only open-loop reference feedforward control actions will be considered. The compensation of control loop interaction as measurable disturbances is out of the scope of the work reported here, but can be found in Garduno-Ramirez and Lee (2002).

216

,j

Thermal power plant simulation and control Power response

300 200 ~" 100

~

o

Fuel valve demand

0.8. ~

0.6

~

0.4.

~-100 0.2-200 0.

-300 0

50

100

150 200 Time (s)

250

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50 l;O 1;0 2;0 2;0 300

b

Time (s)

Pressure response

Steam valve demand

ll0 1

i

105

0.8 ~- 0.6

lOO

"-~ 0.4 ~

95

0.2

90 0

50

100

150 200 Time (s)

250

5'0 l;O l;O 2;0 250 300

300

Time (s) Feedwater valve demand

Level response 1000 1

500

0.8

o

~, 0.6 e~

-500

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Figure 8.8 8.4.1

50

100

150 200 Time (s)

250

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300 f

100

150 200 Time (s)

250

300

Response to step in pressure set-point with ramp-tuned parameters

Motivation for feedforward/feedback control

The initial idea for the proposed FF/FB scheme comes from the two degrees of freedom single-input-single-output linear control system shown in Figure 8.10, where the output to set-point transfer function is given by:

Y (s) = [I + Gp(s)Gfb(S)] -1 [Vp(s)Gff(s) + Gp(s)Gfb(S)] Yd(s).

(8.2)

Perfect reference tracking, Y(s) = Yd(s), may be achieved if Gff(s) = [Gp(s)] -1, that is, if the transfer function in the feedforward control path is equal to the inverse process transfer function. Hence, in the absence of uncertainty and disturbances,

Extending plant load-following capabilities 217 Power response

Fuel valve demand

81 1

80.5

0.8 ~,

0.6

80 0.4

~2

79.5

0.2

79 50

100

150 200 Time (s)

250

300

0

50

Pressure response

100

150 200 Time (s)

250

300

250

300

Steam valve demand

101 l

100.5

0.8 ~,

100

0.6

e~

~, 0.4 ~

99.5

0.2

99 50

100

150 200 Time (s)

250

300

0

50

100

150 200 Time (s)

Feedwater valve demand

Level response 8 1

6 E

0.8

4

~&

2

i

0.6 0.4 ! 0.2

0 -2 0

50

e

Figure 8.9

100

150 200 Time (s)

250

50 f

100

150 200 Time (s)

250

Response to step in level set-point with ramp-tuned parameters

t Gff(s) rd(s)

300

+,~

Gfo(s)

[ Ue(s) Urd~) + Gp(s)

Figure8.10 Referencefeedforward/feedbackcontrolconfiguration

--~

300

218

Thermal power plant simulation and control

perfect tracking may be attained without the feedback control path, Gfb(S). Perhaps the greatest disadvantage of this approach for real implementation is its dependence on the accuracy of the process model. A FFPU is a large complex system for which Gp(s), if known, is only valid around a single operating point, and its inverse cannot be guaranteed to exist, nor to be causal should it exist. Hence, the ideal FF/FB strategy with Gff(s) = [Gp(s)] -1 is inadequate to attain wide-range operation. Nevertheless, the requirements on the FF control Gff(s) can be lessened to only approximate the plant inverse dynamics, and let the FB control path compensate for uncertainty when tracking any unit load demand profile. However, there is still a need for a plant model valid throughout the plant operation space, which is a particularly difficult issue for FFPUs (Ghezelayagh and Lee, 1999). To overcome this problem FF control is introduced as a knowledge-based system that solves the inverse kinematics model of the FFPU as determined by steady-state input-output data. The key advantage of this approach is that the inverse steady-state model always exists, since it is based on inputoutput measurements. The measured data represents the actual plant characteristics, and statistical data may be used to increase the accuracy of the approximation. In addition, the design of the FF control may be automated using machine-learning techniques. In general, feedforward and feedback control complement each other. Feedforward actions are meant to perform fast corrections due to changes in the reference value and known disturbances, while feedback provides corrective actions on a slower time-scale to compensate for inaccuracies in the process model, measurement errors, and unmeasured disturbances. Nevertheless, in any application the drawbacks and advantages of both feedforward and feedback must be taken into account. Limitations of feedback include: • • •

Corrective actions are not issued until after a deviation in the measured variable is detected. Feedback cannot compensate for known disturbances in a predictive way. Feedback may not be satisfactory in systems with long time constants or long time delays.

Difficulties with feedforward include: • • •

Compensation of load disturbances requires on-line measurements, which are not always feasible. A model of the process is required and the quality of the feedforward action depends on the accuracy obtained. The inverse model often contains pure derivatives that cannot be realised in practice in a feedforward controller.

Advantages of feedback include: •

Regardless of the source and type of disturbance, corrective action occurs as soon as the plant output deviates from the set-point.

Extending plant load-following capabilities 219 •

A model of the process does not need to be perfectly known; compensation can be made for model inaccuracies and dynamics not modelled.

Advantages of feedforward include: • •

A fast corrective action can be made in a predictive way if the disturbance can be measured. Approximations to ideal pure derivatives often provide effective control.

Applied in a control system for a power plant, feedforward may help to: • • • • •

Deal with time delays mainly encountered in temperature control loops. Achieve wide-range process optimisation along optimal static operating points. Avoid plant trips and shutdowns due to faulty measurements that will disable a feedback control loop. Replace faulty sensors on-line without stopping the plant or switching to manual operation, since the process can be sustained by the feedforward control action. Facilitate manual to automatic mode transfers since the feedback controllers should be initialised while the feedforward action controls the process.

8.4.2

Feedforward/feedback control scheme

As mentioned before, the purpose of the feedforward controller is to facilitate widerange set-point driven operation, that is to improve manoeuvrability for load-following tasks. For the reasons stated in the previous section, the feedforward controller is proposed as an open-loop non-linear MIMO compensator in the form of a nonlinear multivariable mapping that implements the inverse static model of the FFPU, with set-points, Yd, as inputs, and the feedforward control signals, uff, as outputs (Figure 8.11). The design of the feedforward controller is obtained off-line by fitting a set of input-output data patterns measured directly at the plant. In this way, the feedforward controller is built on knowledge about the actual operation of the FFPU. To achieve an open design, a structure is proposed for the feedforward controller which can be easily and systematically expanded or contracted, as required by the scope of the control actions that need to be coordinated to achieve wide-range operation. To do so, a multivariable feedforward controller is proposed which consists of several independent multiple-input single-output (MISO) mapping subsystems, one for each feedforward control signal being generated. Thus, each subsystem implements a non-linear MISO mapping, valid across the whole operating range of the FFPU, supplied with the set-point signals of all the control loops considered for coordination to provide a single feedforward control signal. For the case study in this chapter, the feedforward controller consists of three MISO subsystems, which provide the feedforward control signals for the fuel, ulff, steam, u2ff, and feedwater, u3ff, control valves, in terms of the power, Ed, pressure, Pd, and drum level, Ld, setpoints (Figure 8.12). Note that compared to a typical coordinated control system, the inclusion of the drum water level control loop enables unit internal balance required

220 Thermalpower plant simulation and control _ ..................................

,,

Feedforward .~..................................................... ................... controller i designer ~--, /

/

,. .................................

.:

i

YO

I Multivariable inversestatic v l FFPUmodel

+u

U

_I rl

Fossil-fuel powerunit

Y

fb

I

Feedback control

Figure 8.11 Feedforwardcontroller design

Poweroutput (Ed)

Wide-range MISO \ mapping J

Wide-range MISO mapping

Pressure

(uiff) Fuelvalve

(u2ff) Steamvalve

# Wide-range ~] MISO

Drum level Figure 8.12

(Ld)

\, mapping )

(u3ff) Feedwatervalve

Feedforward controller MISO submodules

for wide-range operation, in accordance with the process behaviour explained in section 8.2. The main steam temperature control loop could also be embraced, but its use is preferred for overall process optimisation purposes rather than for extending the load-following capabilities of a FFPU.

Extending plant load-following capabilities

8.5 8.5.1

221

Knowledge-based feedforward control Neurofuzzy paradigm

Each MISO subsystem of the feedforward controller is a knowledge-based fuzzy system that is designed as an artificial neural network through a neural learning procedure, thus being equivalently called a neurofuzzy system to reflect its dual nature. The neurofuzzy paradigm is intended to synthesise the advantages of both fuzzy systems and neural networks in a complementary way that overcomes their disadvantages, facilitating subsequent application. First, a neural network is used to represent the parallel-processing nature of a fuzzy system. Then, the components of the fuzzy system are determined using a neural-network learning algorithm. The resulting neurofuzzy system may approximate a usually unknown function that is partially defined by a set of input-output data. The knowledge rules of the neurofuzzy system represent the relationships within the given data in a high-level abstract way. The learning procedure is a data-driven process that operates on local information, causing only local modifications in the underlying fuzzy system. In addition, the learning procedure takes into account the properties of the associated fuzzy system, constraining the possible modifications to the system parameters. Since the neurofuzzy structure is always a fuzzy system at each stage of the learning process, the learning procedure can be initialised by specifying the components of a fuzzy system that are to be enhanced based on the provided data. There are currently several methods available to synthesise a neurofuzzy system, including GARIC (Berenji and Khedkar, 1992), NEFCON (Nauck and Kruse, 1994), FuNe (Halgamuge and Glesner, 1994), ANFIS (Jang, 1993), and Neurofuzzy (Ghezelayagh and Lee, 1999). In this work, the neurofuzzy MISO subsystems for the feedforward controller are fuzzy systems of the Takagi-Sugeno-Kang (TSK) type (Takagi and Sugeno, 1985), which are individually synthesised, in a systematic and automated way, through the general-purpose adaptive neuro-fuzzy inference system (ANFIS) technique (Jang, 1993) using steady-state input-output process data. 8.5.2

TSK-type f u z z y systems

In essence, a fuzzy system establishes an input-output non-linear mapping, determined by a series of procedural statements and an inference mechanism that mimics the human knowledge processing capabilities during reasoning. Regarding the format of the procedural knowledge rules, the fuzzy systems may be classified into two types: Mamdani fuzzy systems and Takagi-Sugeno-Kang (TSK) fuzzy systems (Wang, 1997). In Mamdani fuzzy systems, the knowledge rules are of the form: IF xl is X~ and ... and Xn is X~,

THEN u r is U r

(8.3)

where the xi, for i = 1, 2 . . . . . n, are the system inputs, and X r are fuzzy sets, u r is the rule output, U r is an output fuzzy set, and r = 1, 2 . . . . . R, is the rule number index. In Mamdani type systems both the antecedent and the consequent of the knowledge rules are fuzzy propositions.

222

Thermal power plant simulation and control

In TSK fuzzy systems, the antecedent of the knowledge rules is a fuzzy proposition, and the consequent is a crisp relation. For first-order systems, the rule output is calculated as a linear function of the inputs: THEN u ~ = c~ + crlxl + ' " + crxn

IF Xl is X~ and ... and x, is Xr,

(8.4)

where crare constants. Given input values xl, • • •, Xn, the total output, u, of the TSK fuzzy system is a weighted average of the individual rule outputs: U

Zr wrur _

-

-

Zr

(8.5)

1Or

where each weight w r, called the degree of fulfilment of the r-th rule, is calculated as the product of the input membership values: n

11)r = H # x r (Xi).

(8.6)

i=1

In general, the TSK fuzzy systems are a combination of fuzzy and non-fuzzy models that integrate qualitative knowledge representations with precise quantitative data expressions. The major advantage of TSK fuzzy systems is their ability to act as universal approximators. They allow the representation of complex non-linear mappings through simple linear relations. The knowledge rules establish an approximation of a non-linear input-output mapping, X 1 X X 2 x • "" × X n ~ R, by a piecewise linear function. The rule antecedents define a decomposition of the input space into a set of overlapping partitions, and implement a switching function that selects, given the actual input values, the appropriate linear functions needed for the approximation. Then, the approximated output value is obtained by interpolating the combination of two or more relations in the rule consequents, as defined by the inference mechanism of the TSK system. The ANFIS method allows the design of TSK-type fuzzy systems. Given arbitrary initial knowledge rules, the ANFIS method adjusts the membership functions, LX{, and the coefficients, c~, in the consequents of all the rules. To do so, the TSK fuzzy system must be represented as a feedforward neural network, with its components refined through a neural learning procedure to fit the input-output behaviour of the fuzzy system.

8.5.3

Fuzzy feedforward controller

So far, the feedforward controller consists of three MISO neurofuzzy systems: FISU I, FISU2, and FISU3, which provide respectively the feedforward control signals for the fuel, ulff, steam, u2ff, and feedwater, u3ff, control valves, in terms of the power, Ed, pressure, Pd, and level, Ld, set-points, as shown in Figure 8.12. The feedforward controller design problem may be stated as: given a set of steady-state input-output patterns, [Ul u2 u3, E P L], determine the MISO neurofuzzy systems FISU1, FISU2,

Extending plant load-following capabilities 223 and FISU3. More specifically, the problem consists of finding out the values of the parameters of the membership functions in the rule antecedents and the coefficients in the rule consequents of the three TSK-type fuzzy systems. Note that FISU1, FISU2, and FISU3 should reproduce the sets of patterns: [E P L, ul], [E P L, u2], and [E P L, u3] as [Ea PaLd, Ulff], [Ed Pd Ld, U 2 f f ] , and [Ed Pd La, u3ff], respectively, once embedded in the feedforward control path. The feedforward controller design problem is solved independently for each fuzzy system using the necessary data from the complete set of steady-state input--output patterns, [ul u2 u3, E P L]. All three fuzzy systems in the feedforward controller are of the TSK-type and have similar structures, so without loss of generality and to simplify the presentation, hereafter all explanations refer to FISU1, the fuzzy system that generates u lff. The knowledge rules of the fuzzy system have the form: IF: Ed is LErd and Pd is LP[j and Ld is LLrd THEN: u~ff = c6 + CrEEd+ Crppd + C[Ld

(8.7)

where r = 1,2 . . . . . R is the rule number, LE o, r LP~, r and LL~ are the linguistic terms of the input signals Ed, Pd, and Ld, respectively, in the r-th rule, u~ff is the contribution of the r-th rule to the total output of the fuzzy system, and c6, c~, c~,, and c~ are the consequent coefficients. For a given input pattern [Ed Pd Ld], the output of the fuzzy system is given by (8.5) as: Z r =Rl //3r Ulff r Ulff -R E r = l tOr

(8.8)

where 1/dr, for r = 1, 2 . . . . . R, are the rule fulfilment degrees or weights. For each rule, its fulfilment degree is calculated from (8.6) as the product of the input membership values as:

w r = IZLE~(Ed) × lZLPS(Pd) × lZLLrd(Ld)

(8.9)

where #LE~,('),/*LPS ('), and IZLL~(') are the membership functions corresponding to the linguistic terms LE~, LPS, and LLrd, respectively, in the r-th rule. In addition, note that (8.8) can be written as:

Ulff =

U r

~ r=l

-r

lff =

r=l wr

r

-r

//) Ulff = r----I

Ulff

(8.10)

r=l

where tbr, for r = 1, 2 . . . . . R, are the so-called (normalised) relative rule fulfilment weights: ( wr ) /~r ~_ ~ (8.11) Z r = l //)r

224

Thermal power plant simulation and control

and fi~ff, for r = consequents:

1, 2 . . . . . R, can be equivalently called the normalised rule -r ~//3-r Ulff. r Ulff

8.6 8.6.1

(8.12)

Design of neurofuzzy controllers Neural representation of fuzzy controller

Each fuzzy system in the feedforward controller is designed using the ANFIS technique. To this aim, the fuzzy system is represented as a three-input, one-output, five-layer feedforward neural network, as shown in Figure 8.13 where, without lose of generality, each input signal spans its whole operating range with three overlapping fuzzy regions, i.e. fuzzy sets with bell-shaped membership functions and linguistic terms: low, medium, and high. Therefore, for this case a complete knowledge base will have 3 × 3 × 3 = 27 rules of the form given in (8.7). Also, the neural network will have three distribution units in layer L0, nine neurons in L1, 27 neurons in L2, L3, and L4, and one neuron in Ls. With these dimensions, the number of

EaPd La

!ifl

Lo Figure 8.13

LI

L2

L3

L4

Neural network structure of feedforward fuzzy controller

Ls[

Extending plant load-following capabilities

225

parameters to determine is calculated as follows: 27 rules × 4 consequent parameters per rule ---- 108 consequent parameters, and 3 inputs x 3 membership functions per input x 3 parameters per membership function = 27 membership function parameters. Then, the total number of parameters to be determined is 108 + 27 = 135 per fuzzy system. This number clearly illustrates the difficulty of tuning a fuzzy system following a trial and error approach, which simply gets worse as the number of input linguistic terms increases. Fortunately, this process can be fully automated using the neurofuzzy paradigm and a low-dimensional fuzzy system will do the job perfectly, as will be shown shortly. The distribution units in layer L0 route the crisp input signals of the fuzzy system to the neurons in layer L1. Each neuron in layer L1 fuzzifies the incoming input signal using a bell-shaped membership function. In this layer, the neuron's input and output processing functions are of the form:

1Yi =lgi (x)

=

1

1 + ((x - ci)/ai) 2bi

(8.13)

where i = 1,2 . . . . . 9 is the neuron number, ai, bi, and ci are the parameters of the bell-shaped output function that define the membership function of a fuzzy set or linguistic term and lyi is the output that corresponds to the degree of membership of the input to the fuzzy set defined in the i-th neuron in L 1. Neurons in layer L2 calculate the rule fulfilment weight for each rule (8.9). Neurons in layer L3 calculate the relative rule fulfilment weight for each rule (8.11). Neurons in layer L4 calculate the normalised output for each rule from (8.12) and (8.7). The unique neuron in layer L5 calculates the total system output in (8.10).

8.6.2

Neurofuzzy controller design

Given a set of M steady-state input-output patterns {[u I 1 u21,1/31, E1 P1 L l ] . . . . . [ulg u2M UaM, EM PM LM]}, and an initial MISO TSK fuzzy system defined as in (8.7)-(8.12) and specified by arbitrary sets of parameters {[al bl Cl] . . . . . [a9 b9 c9]} and [ [c~ c 1 c 1 c 1 ] . . . . . [c27 c 27 c 27 c 27] ] corresponding to the membership functions and the consequent coefficients, respectively; the design process adjusts the parameters of FISU1 so that it reproduces the set of patterns {[El Pl L1, Ull] . . . . . [EM PM LM, ul~t]} corresponding to the inverse static model generating u lff. The learning process is achieved iteratively, with two phases per iteration. First, the input patterns are propagated keeping the antecedent parameters constant, and then the optimal consequent parameters are estimated using a least squares (LS) estimation procedure. Secondly, the input patterns are propagated again with the antecedent parameters modified by back-propagation.

226

Thermal power plant simulation and control

As briefly outlined, the consequent parameters are to be estimated using a least squares procedure• Each input-output pattern is related by:

27 Ulffm = Z ~Or(C~ -}-CrEEm -}-crppm +CrLLm)

(8.14)

r=l where m = 1, 2 . . . . . M is the input--output pattern index. Using a vector representation and considering all M input-output training patterns:

-4 4 Ulffl] i_UlffM..l

F /~1 tblE1 /hip1 ~ILI ~1 ColEM ffjlpM (olLM

...

/b27 tb27E1 tb27p1 tb27L1

4

...

tb27 Co27EM Co27pM Co27LM

c~z

_

c 2~ L

(8.15) which adopting appropriate definitions can be written as: u = xc

(8.16)

where U is M x 1, X is M x (4)(27) = M x 108, and C is 108 x 1. In general the problem of calculating the coefficients in C is overdetermined, that is M > 108. A least squares solution for C can be computed recursively using:

T -- Xl+lCi) Ci+l = Ci -~ tlli+lXi+l(Ui+l

d2i+1 = tl/i --

tllixi+lXl+ 1tll i

1 + xiT+lOttiXi+l

(8.17) (8.18)

where xi is the i-th row vector of matrix X and u i is the i-th element of vector U, for i = 0, 1,2 . . . . . M - 1 , and • is called the covariance matrix. The initial conditions are Co = 0 and ~0 = Y I, where y is a large positive number. At the end of iterations, C = CM may have been calculated using all available information in the M input-output patterns. The adjustments in the membership function parameters are determined by backpropagation. Let z be any of the a, b or c parameters of any membership function #, and Eio be the usual error measure given by the sum of the squared difference

Extending plant load-following capabilities 227 between the target output, uTff, and the actual output, u lff: (8.19)

Eio = 1 (U~ff -- U l f f ) 2

Then, the change in parameter z, Az, for a single rule after a pattern has been propagated is given by: 0Eio Az = - ~ (8.20)

Oz

where tr is an arbitrary learning rate factor. Successive application of the chain rule to (8.20) through the layers of the neural network yields:

OEio OUlff Ow r 0113r O~ OUlff O~ r qoVdr qo~ qoz

AZ : -or

, r = ~r(uTf f -

ulujulf

l b r ( 1 -- t ° r ) tOr 0 # f

wr

o r = --Ulff(Ulff _ Ulff)tbr(1

Iz

Iz OZ

_ ~r).~

(8.21)

OZ

where the final term, Olz/Oz, depends on the specific parameter of the membership function being considered:

OIZ -

-

0a 0#

Iz(X)2 ( ( X - c ) 2 ) = _

a

-~-~---b.(X)

Olz ac

-

-

b (8.22)

a 2

( ( X a c)2 )

2blz(X)2 ( ( X - c ) 2 ) ~77 a

b-1

(8.23)

b

(8.24)

where X = E, P or L depends on the membership function being considered. Thus, the parameter changes for a single rule, after a pattern has been propagated, can be calculated as: z * f -- Ulff ) tO r (1 -- tO r ) AO = -O" - U lrf f ~Ulf

/_t

o

r

#2 ( ( X - ¢ ) 2 )

_a_

b

i ,

Ab = - - - U l f f [Ulff - U l f f ) to r (1 -- to r ) b u Z ( x ) /z Ac = - - u l f f tUlff -- ulff) t? r (1 - t~ ~) 2 b # z ( x ) /z X-~c

(8.25)

a

(8.26)

(X - c) 2 a

Thermalpower plant simulation and control

228

8.6.3

Learning procedure

As previously mentioned the learning process is carried out iteratively, consisting of the following steps: (1)

(2)

(3)

(4)

Propagate all patterns from the training set and determine the consequent parameters using the least squares method in (8.17) and (8.18). During this step, the antecedent parameters remain fixed. Propagate all patterns again and update the antecedent parameters by backpropagation using (8.25)-(8.27). During this step, the consequent parameters remain fixed. If the error is reduced in four consecutive steps then increase the learning rate by 10 per cent. If the direction of error change is unpredictable, then decrease the learning rate by 10 per cent. Stop if the error is small enough, otherwise repeat from step 1.

For practical application, the learning process is incorporated in a three-stage design process. First, a set of input-output data, to be used as training data, needs to be generated or obtained from the process. Another optional data set can be used as test data after training to evaluate the performance of the learning process. Second, initial structures for the fuzzy system need to be created. For each input, the range of operation, number of membership functions, as well as their shape, must be defined. Finally, the learning process is carried out using the training data set to adjust the membership functions, and to determine the consequent parameters, with the resultant fuzzy system verified using the test data set.

8.7 Wide-range load-following In this section, neurofuzzy controllers are implemented and applied to enhance the load-following capabilities of the FFPU, subject to a given power-pressure operating policy. First, the input-output process information to be used to design the knowledgebased feedforward controllers is presented. The information corresponds to a typical sliding-pressure operating policy. Next, the effect of the number of membership functions and the number of training epochs on the approximation accuracy of the feedforward controller to the inverse static model of the FFPU is illustrated. Finally, the resultant MISO neurofuzzy controllers are presented.

8.7.1

Realisation of wide-range neurofuzzy controllers

The present application requires the realisation of a neurofnzzy feedforward controller under a sliding-pressure operating policy. Recalling that since the control objective is to approximate the inverse static behaviour of the FFPU, the control signals will be considered as outputs and the power, pressure and drum water level deviation will provide the inputs. Figure 8.14 shows the data for the pressure, P, and the control

Extending plant load-following capabilities 229 250 ~E 200 150 100 E

50

!

210

4'0

60

8'0

i

i

i

i

100 120 Power (MW) i

i

1'~0

140

180

i

i

i

~' & 0.8 0.6 .~ 0.4 0.2

200

/d 1 o

o

U2 U3

I

20

I

40

I

60

I

80

I

I

1O0 120 Power (MW)

I

140

I

160

I

180

200

Figure 8.14 Input-output steady-state datafor the sliding-pressure operatingpolicy signals ut, u2, and u3, for the sliding-pressure operating policy with power, E, as an independent variable. Note that the drum water level deviation L is not shown since, at steady-state, it is always zero.

8. 7.2 Effect of number of membership functions and training epochs Once the data required to design the neurofuzzy controllers are available, two major decisions have to be made in order to obtain controllers with satisfactory performance. First, the number of linguistic terms (or equivalently, the number of membership functions) to be used to fuzzify the input signals has to be decided. The number of linguistic terms per input not only determines the size of the knowledge base, that is, the number of knowledge rules, but will also affect the number of parameters to be calculated, and the number of input-output data patterns required for the learning process. Second, it must be decided how to stop the learning process. The stopping condition may be set in terms of reaching a predefined approximation accuracy, or in terms of the execution of a predefined number of training iterations (epochs). Whatever is decided, the issue of major interest is the impact on the accuracy of the resulting fuzzy system and its ability to provide an inverse steady-state model of the power unit. In what follows the effect of both the number of linguistic terms and the number of learning iterations on the approximation accuracy is shown. Note that since all three neurofuzzy controllers exhibit similar characteristics, only the results for FISU 1 are provided.

230

Thermalpower plant simulation and control

...........j- ''/s'/ 20

40

60

70

80

90

80 100 Power (MW)

100

110

120

120

140

130

160

140

180

150

Pressure (kg/cm 2)

Figure 8.15 FISU1membershipfunctions, sliding-pressure operation

First, typical membership functions for the sliding-pressure operating policy using three membership functions are plotted in Figure 8.15. Note that the same number of linguistic terms is used for all inputs of the neurofuzzy controller. Also, only the membership functions for the power and pressure inputs are provided since the membership functions of the drum water level deviation are singletons at L = 0. The importance of the number of training epochs is illustrated for three, five, and seven input membership functions. For each case, the root squared mean error (RSME) of the output approximation is plotted for training during 20 epochs in Figure 8.16. By inspection of these results, it can be seen that very good approximations of the inverse steady-state model of the plant can be obtained with a low-dimensional system (three membership functions) and a small number of training epochs (10 epochs). This is because the non-linear steady-state behaviour of the plant is benign, that is, the non-linearities are quite smooth and continuous. Ideally, it will always be preferred to use a low-dimensional system requiring a small number of training iterations if the obtained approximation accuracy is acceptable.

8.7.3

Neurofuzzy feedforward controllers

Following the same procedure for FISU 1, fuzzy representations were also created for FISU2 and FISU3. In each case three membership functions and I0 training epochs were considered appropriate. Table 8.1 summarises the approximation performance

Extending plant load-following capabilities 231 o 3rnf o o 5mf ~ - ~ 7rnf

2.5 2 X

1.5 1

0.5 i

C2

I

J

I

h

2

4

6

8

I

10 Epochs

l~

13

~

I

I

I

12

14

16

18

O

20

Figure 8.16 RSME for sliding-pressure operation

Table 8.1 Approximation accuracy of neurofuzzy controllers (RSME × 106) Output

RSME ×106

ulff u2ff u3ff

8.5579 265.2692 24.6003

of each fuzzy system in generating the corresponding steady-state feedforward control signals throughout the FFPU operating range. The resultant power and pressure membership functions for FISU2 and FISU3 are very similar to the membership functions for FISU1 presented in Figure 8.15, while the membership functions for the drum water level deviation input are singletons at L = 0. Then, Figures 8.17-8.19 show the fuzzy inference surfaces over the power-pressure plane for FISU1, FISU2 and FISU3, respectively, where Ed and Pd are the power output and pressure demand set-points. Note that each fuzzy system is graphically represented by a fuzzy inference surface, which is a more intuitive representation than the corresponding knowledge base. A graphical representation has the advantage that the contours change very little with an increasing number of membership functions.

232

Thermal power plant simulation and control

0.8

0.6 0.4. 0.2 14q

Pressure demand (Pd)

Figure 8.17

(Ed) Power demand

FISU1 fuzzy inference surface, fuel valve control

0.8 ~

0.6 0.4 14~

Pressure demand (Pd)

Figure 8.18

8. 7.4

(Ed) Power demand

FISU2 fuzzy inference surface, steam valve control

Wide-range load-following simulation results

Incorporation of the three MISO neurofuzzy controllers described in the previous section within the existing decentralised feedback control system of a FFPU creates a multivariable two-degrees-of-freedom control scheme (Figure 8.20). As presented in section 8.4, the main purpose of the resultant hybrid feedforward-feedback control scheme is to provide a better distribution of the control actions to enhance the load-following capabilities of a FFPU. It was suggested that the feedforward control components provide the main contribution to the control signals and thus support the wide-range set-point tracking duties of the FFPU. Meanwhile, the feedback control

Extending plant load-following capabilities 233

0.8 0.6 0.4

0.2 14~

Pressure demand(Pd)

Figure 8.19

(Ed) Powerdemand

FISU3 fuzzy inference surface, feedwater control value

Ed

Pa Ld

~' ~

U2ff ¢ U3ff

+~(

u3

£

)~-

Figure 8.20

Hybrid feedforward/feedback control scheme

components, which used to carry all the control weight, will now provide a smaller contribution to the control signals, which is necessary to compensate for uncertainties and disturbances in the vicinity of the commanded set-point trajectories. Demonstration of the benefits of the proposed feedforward-feedback control scheme is carried out through simulation experiments. First, it is shown that solely with the introduction of the feedforward control, the response of the FFPU may improve significantly. Figure 8.21 shows the ramp response of the FFPU with the addition of the feedforward control, keeping the feedback settings. Performance is

234

Thermal power plant simulation and control Fuel valve demand

Power response

92

1

9O

0.8

84

0.6 f ff 0.4

82

0.2

86

~

0

8O 50

100

150 200 Time(s)

250

300

0

50

100

b

Pressure response

150 200 Time (s)

250

300

250

300

Steam valve demand 1

106

0.8 ~

104

0.6 ~' 0.4

~ 102

0.2 100

0 50

100

150 200 Time (s)

250

300

0

50

100

d

150 200 Time (s)

Feedwater valve demand

Level deviationresponse 20 1

10 0

0.8 0.6 ...............................~ 7

.............

0.4

-b

020

-10 -2O 0 e

50

100

150 200 Time (s)

250

300

0 f

50

100

150 200 Time (s)

250

300

Figure 8.21 Ramp response with feedforward/feedback control

better than that shown in Figure 8.5 in section 8.3.2, where power is required to ramp from 80 to 90 M W at 4 MW/min under a sliding-pressure operating policy. Tracking performance of the power and pressure set-points is as good as previously obtained with the ramp-tuned parameters in Figure 8.6, but without the disadvantage of possibly becoming unstable for steps in the pressure set-point (Figure 8.8). The improved performance of the above extends through the entire FFPU operating region, even under more demanding operating requirements. Figure 8.22

Extending plant load-following capabilities Power response

235

Fuel valve demand 1

150

0.8 0.6

100

e~

0.4

0.2i

50

0 0

500

1000 1500 2000 2500 Time (s)

500

Pressure response

1000 1500 2000 2500 Time (s)

Steam valve demand

140 0.8

120

0.6

100

0.4

80

0.2 0

60 0

500

c

1000 1500 2000 2500 Time (s)

500 d

Level deviationresponse

1000 1500 2000 2500 Time (s)

Feedwater valve demand

20 1

"

0

0.8

•

.........................................

-ff 0.6

.~ -10

0.4

-20

0.2

313 0 e

Figure 8.22

0 500

1000 1500 2000 2500 Time (s)

0 f

500

1000 1500 2000 2500 Time (s)

Wide-rangecyclic response with feedforward/feedback control

shows the response of the FFPU, using the hybrid feedforward-feedback control scheme, for wide-range cyclic operation under a sliding-pressure operating policy. The power output is required to ramp from half-load (80 MW) to base load (160 MW) at 8 M W / m i n (5 per cent base load/min, the maximum allowed by American standards), then from base load to 20 M W at the same rate, and finally back to half-load. Again, the tracking performance of the power and pressure set-points is very good throughout, while the oscillations in the drum water level deviation are within very small bounds. The control activity of all control signals is excellent.

236

Thermalpower plant simulation and control

These results demonstrate the feasibility of the proposed control scheme to enhance the load-following capability of a FFPU in a practical and cost-effective way. Certainly, the improved manoeuvrability of the FFPU is mainly due to the feedforward control action, with a collaboration of the feedback control to compensate for the inaccuracies in the inverse static model implemented by the feedforward control. Figure 8.23 shows the contributions of both the feedforward (u lff, u2ff and u3ff) and

Feedforward and feedback components of fuel valve demand 1

0.8 0.6 5"

0.4 0.2 0 -0.2

500

1000 1500 2000 2500 Time (s)

Feedforward and feedback components of steam valve demand 1

0.8 & 0.6 0.4 0.2 0 -0.2

500

1000 1500 2000 2500 Time (s)

Feedforward and feedback components of feedwater valvedemand 1

,-ff 0.8 & 0.6 0.4 0.2

o -0.2

500

1000 1500 2000 2500 Time (s)

Figure 8.23 Feedforward andfeedback contributions to control signalsfor set-point tracking

Extending plant load-following capabilities Table 8.2

237

Control effort of feedforward and feedback controls

Control signal

Puff

Pulb

Pufb/ Puff

Fuel valve 779.9 11.662 1.50 x 10-2 Steam valve 1263.2 0.0416 3.29 x 10-5 Feedwater valve 695.1 16.307 2.35 x 10 - 2

the feedback (u lfb, U2fb and U3fb) controls to form the final control signals to the fuel, steam and feedwater valves (u l, u2 and u3). To have a better appreciation of this situation, the control effort of both feedforward and feedback controls is quantified by an approximate measure of the control signal power during the cyclic test of the previous paragraph:

Puiff -~ Z (uiff(k))2 k

(8.28)

Puifb = Z (Uifb(k))2 k

(8.29)

where i = 1,2, 3, and k is the sampling number during all the simulation tests. Results are given in Table 8.2, where the ratio of the feedback to the feedforward control effort is also provided. Clearly, in all cases the feedforward contribution is larger than the feedback contribution, that is, the feedforward control actions carry out the set-point tracking duties across the FFPU operating range. The new role played by the feedback controls is to compensate for the inaccuracies in the inverse model implemented by the MIMO feedforward controller, as well as for the effects of external disturbances. Figure 8.24 shows the response of the hybrid feedforward/feedback control scheme when an external disturbance affects the pressure control loop. A variation in pressure with the form of a pulse of 0.5 kg/cm 2 magnitude and 5 s duration is imposed on the pressure measurement. The power and level responses are affected due to the process interactive dynamics. Regarding the control system, only the feedback controls try to compensate for the disturbance, with the pressure feedback control being the most aggressive. These and the previous results demonstrate that the proposed feedforward/feedback control scheme provides a very convenient distribution of the control tasks for setpoint tracking and disturbance rejection, which in turn enhances the load-following capabilities of the FFPU.

238

Thermal power plant simulation and control Feedforward and feedback components of fuel valve demand

Power response 92 1

90

f

88 86 84 82 80

50

0.8 0.6 0.4 0.2

100

150 200 Time (s)

250

~).2

300

0

50

100

b

150 200 Time (s)

250

300

Feedforward and feedback components of steam valve demand

Pressure response 106

E

__.............._,'....................................... \

0

1

0.8 104

,~ 0.6 o.4

102

0.2

I

i

o

100 50

100

150 200 Time (s)

250

~0.2

300

|

i 0

5'0

100

200

300

Time (s) Feedforward and feedback components of feedwater valve demand

Level deviation response 20 1

0.8

I0

0.6 0

0.4-0.2

-10

0

.....

•

......... ....

-20 0 e

.,, t ............... ,3

/" ..........................

~).2 50

100

150 200 Time (s)

250

300

50 f

100

150 200 Time (s)

250

300

Figure 8.24 Feedforwardand feedback contributions to control signals for disturbance rejection

8.8

Summary and conclusions

This c h a p t e r p r e s e n t e d the d e s i g n o f a k n o w l e d g e - b a s e d f e e d f o r w a r d controller that e x t e n d s the existing f e e d b a c k control s y s t e m o f a fossil fuel p o w e r unit to e n h a n c e its l o a d - f o l l o w i n g capabilities. T h e resulting f e e d f o r w a r d / f e e d b a c k control

Extending plant load-following capabilities

239

scheme allows a better distribution of the control tasks. The reference feedforward control improves the manoeuvrability of the power unit throughout the range of operation, while the existing feedback control compensates for uncertainties and unknown disturbances around the commanded trajectories. The feasibility of the proposed knowledge-based feedforward controller to effectively enhance the loadfollowing capabilities of a fossil fuel power unit was demonstrated through simulation experiments. The MIMO feedforward controller was designed as a set of MISO fuzzy inference systems that approximate the inverse steady-state behaviour of the power unit across the entire operating range. The fuzzy inference systems are implemented as TSK fuzzy systems, which may be represented by a feedforward neural network. Tuning of the fuzzy systems is carried out through a supervised neural learning procedure based on a set of input-output data patterns that can be directly measured at the power plant. This approach makes it feasible to apply the feedforward controller in an actual plant. Furthermore, the proposed design procedure can be fully automated for on-site design, and any of the TSK fuzzy systems can be easily programmed into the FFPU control system software as a function that evaluates the fuzzy system output formula (8.8). These features make the proposed feedforward/feedback control approach an economically competitive option to enhance the load-following capabilities of any computer-controlled power plant.

8.9

Acknowledgements

This work was supported in part by NSF under grants INT-9605028 and ECS9705105, The Pennsylvania State University, the Electrical Research Institute (liE-Mexico), and the National Council for Science and Technology (Conacyt Mexico). Thanks to Mr Rafael Chfivez and Dr Salvador Gonz~ilez for promoting innovative research and development at liE.

8.10

References

AHMED, M.: 'Modernizing fossil power plant controls'. Proceedings of the 1992 ISA Conference, USA, 1992, pp. 459-466 ARMOR, A. F.: Cycling of fossil plants: the key issue for the next 10 years. Proceedings of the 1985 Fossil Plant Cycling Conference, EPRI CS-4723, 1985 BEN-ABDENNOUR, A., and LEE, K. Y.: 'A decentralized controller design for a power plant using robust local controllers and functional mapping', IEEE Transactions on Energy Conversion, 1996, 11, (2), pp. 394-400 BERENJI, H. R., and KHEDKAR, P.: 'Learning and tuning fuzzy logic controllers through reinforcements', IEEE Transactions on Neural Networks, 1992, 3, pp. 724-740 DIVAKARUNI, S. M., and TOUCHTON G.: 'Fossil power plant automation: issues and future trends'. Proceedings of the ISA/EPRI Joint Controls and Automation Conference, USA, 1991, pp. 1-28

240

Thermal power plant simulation and control

DUNLOP, R. D., and EWART, D. N.: 'System requirements for dynamic performance and response of generating units', IEEE Transactions on Power Apparatus and Systems, 1975, 94, (3), pp. 838-849 ELGERD, O. I.: 'Electric energy systems theory: an introduction' (Mc-Graw-Hill, New York, 1971,2nd. edn.). GARDUNO-RAMIREZ, R., and LEE, K. Y.: 'Wide-range operation of a power unit via feedforward fuzzy control', IEEE Transactions on Energy Conversion, 2000, 15, (4), pp. 421-426 GARDUNO-RAMIREZ, R., and LEE, K. Y.: 'Multiobjective optimal power plant operation through coordinate control with pressure set-point scheduling', IEEE Transactions on Energy Conversion, 2001a, 16, (2), pp. 115-122 GARDUNO-RAMIREZ, R., and LEE, K. Y.: 'Intelligent hybrid coordinated-control of fossil fuel power units'. Proceedings of the International Conference on Intelligent System Applications to Power Systems, Budapest, June 2001b, pp. 177-182 GARDUNO-RAMIREZ, R., and LEE, K. Y.: 'Power plant coordinated-control with wide-range control-loop interaction compensation'. Proceedings of the 15th IFAC World Congress, Barcelona, Spain, July 21-26, 2002 GHEZELAYAGH, H., and LEE, K. Y.: 'Neuro-fuzzy identifier of a boiler system', Engineering Intelligent Systems, 1999, 7, (4), pp. 227-231 HALGAMUGE, S. K., and GLESNER, M.: 'Neural networks in designing fuzzy systems for real world applications', Fuzzy Sets and Systems, 1994, 65, pp. 1-12 JANG, J. S. R.: 'ANFIS: adaptive-network-based fuzzy inference system', IEEE Transactions on Systems, Man, and Cybernetics, 1993, 23, (3), pp. 665-685 LANDIS, R., and WULFSOHN, E.: 'The control philosophy for a unit control system for co-ordinated operation of a boiler and turbine', Elektron., 1988, (February), pp. 19-23 KUNDUR, P.: 'Power system stability and control' (Mc-Graw-Hill, New York, 1994) MAFFEZZONI, C.: 'Boiler-turbine dynamics in power plant control', Control Engineering Practice, 1997, 5, (3), pp. 301-312 MILLER, H. L., and STERUD, C. G.: 'Replacement pressure control and superheater bypass valves permit 93% cyclic load cutback at PG&E's 750-MW units at Moss Landing'. Proceedings of the American Power Conference, Chicago, 1989, pp. 217-221 NAUCK, D., and KRUSE, R.: 'NEFCON-1: an X-window based simulator for neural fuzzy controllers'. Proceedings of the IEEE International Conference on Neural Networks, Orlando, 1994, pp. 1638-1643 TAKAGI, T., and SUGENO, M.: 'Fuzzy identification of systems and its applications to modeling and control', IEEE Transactions on Systems, Man, and Cybernetics, 1985, 15, (1), pp. 116-132 URAM, R.: 'Computer control in a combined cycle power plant. Part III: The digital steam turbine system'. Proceedings IEEE PES Winter Meeting, New York, USA, 1977, paper A77-079-7, pp. 1-11 WANG, L. X.: 'A course in fuzzy systems and control' (Prentice Hall, Englewood Cliffs, 1997)

Extending plant load-following capabilities 241 WENG, C. K., and RAY, A.: 'Robust wide-range control of steam-electric power plants', IEEE Transactions on Control Systems Technology, 1997, 5, (1), pp. 74-88 ZHAO, Y., EDWARDS, R. M., and LEE, K. Y.: 'Hybrid feedforward and feedback controller design for nuclear steam generators over wide range operation using a genetic algorithm', IEEE Transactions on Energy Conversion, 1997, 12, (1), pp. 100-105

Chapter 9

Modelling of NOx emissions in coal-fired plant S. Thompson and K. Li

9.1

Emissions from coal-fired power stations

Around 55 billion tons of coal are produced annually throughout the world, and combustion of pulverised coal in large power station boilers accounts for over 50 per cent of total world coal consumption (ETSU, 1997). This makes power stations one of the main contributors to global emissions. Current legislation, such as the UK Environment Protection Act (1992) and the US Clean Air Act Amendment (1990), requires that power plants make significant reductions in pollutant emissions, especially in NOx emissions. These restrictions will undoubtedly become more stringent. For existing plant, the technology holding the most promise for future reductions in power plant NOx emissions is the introduction of more sophisticated operation and control systems. The analogy is that between two drivers driving the same car, with one driver who 'thinks ahead' and the other who 'just wants to get there as quickly as possible'. Over the same route and similar road conditions both drivers are likely to take about the same length of time to complete the journey. However, the driver who 'thinks ahead' and uses the accelerator (gas) and brake pedals sparingly, will achieve lower emissions, better fuel economy and extends the car's useful life. From an emission and economic viewpoint to provide power station operators with models that allow them to 'look ahead' and adjust the various controls accordingly produces a win-win situation. The purpose of this chapter is to examine and compare various methods of modelling NOx emissions in order to develop operational and control aids.

9.1.1

Emission reduction methods in pulverised fuel plant

During the coal combustion process, various pollutants are produced, such as oxides of carbon (COx), oxides of sulphur (SOx), oxides of nitrogen (NOx) and particulates. S02 and NOx can cause acid rain and C02 is the most important greenhouse gas held responsible for climate changes.

244

Thermal power plant simulation and control

Approximately 99 per cent of fly-ash (particulates entering the flue) can be removed by fitting electrostatic precipitators and over 90 per cent of SO2 with the installation of a flue gas desulphurisation plant. Such systems are extensively used throughout the world. The best way to reduce CO2 emissions is to improve power generation efficiency. However, no practical methods exist for reducing NOx to such a degree, leading to increased research into this area (Copado et al., 2001; ETSU, 1997; Holmes and Mayes, 1994). During the combustion process in a coal-fired power plant, nitrogen from the coal and air is converted into nitric oxide (NO) and nitrogen dioxide (NO2); together these oxides of nitrogen are commonly referred to as NOx. The methods for reducing NOx emissions in coal-fired power plants can be classified as either primary (or combustion modification) based technologies (Copado et al., 2001; ETSU, 1997; Holmes and Mayes, 1994), which achieve reduction of NOx formation by limiting the flame temperature or the availability of oxygen in the flame; or secondary (or flue gas treatment) technologies. NOx reduction by adding a reagent such as ammonia or urea into the flue gas is classified as a secondary technique. Installation of low-NOx burners and implementation of advanced boiler operation and control systems for NOx emission reduction would normally be classified as combustion modification technologies. In general, new pf power generation plants are installed with low-NOx burners, rather than employing secondary techniques which are relatively expensive. Although low-NOx burners are usually sufficient to achieve the required target under current legislation, it is often at the expense of other important operational parameters such as incomplete combustion, steam temperature and boiler performance. This is one of the reasons why advanced operational and control systems in coal-fired boilers (usually pulverised fuel or pf boilers) is so important.

9.1.2

Operational parameters in p f boilers

In pulverised fuel boilers, the parameters that determine the combustion operations include the following: • • • •

primary air to coal ratio secondary air distribution for tangentially fired boilers, burner tilt position mill firing patterns.

However any change in boiler parameters cannot be made freely. Of particular importance is safety and efficient operation of the various burners. For example, loss of an individual flame can lead to unburned fuel in the boiler and cause accumulation of a potentially explosive fuel/air mixture. Irregular mill firing patterns can cause instability in the flame ignition plane and affect the process combustion efficiency. Therefore, the introduction of sophisticated operation and control systems would first need a compressible set of system models to capture the boiler dynamics under varying operation conditions (Copado et al., 2001; ETSU, 1997; Holmes and Mayes, 1994).

Modelling of NOx emissions in coal-fired plant 245 9.1.3

Emission reduction using operation and control methods

Generally speaking, NOx emission reduction using operation and control methods consists of two stages. The first stage is some form of plant modelling in order to capture the plant dynamics. Such models attempt to capture the relationship between the plant's operational inputs and the NOx output. In the second stage constrained optimisation is performed in order to deduce the optimal operation inputs for minimising the NOx output without decreasing the combustion efficiency. These values are then presented to the operator (open-loop mode) as the operational references or used to automatically adjust the system inputs (closed-loop mode). The requirements for system models in plant operation and control are that they should be simple enough to compute the optimal solutions (subject to given requirements and constraints), yet complex enough to accurately capture (under varying operation conditions) the relationship between operational inputs and NOx output.

9.1.4

NOx emission models for operation and control

NOx formation in coal-fired power plants is a complex process involving various thermodynamic and fluid-dynamic processes within the combustion chamber and complex NOx formation chemistry (De Soete, 1975; Ferretti and Piroddi, 2001; Gormley, 2001; Lockwood and Romo-Millares, 1992; Nimmo et al., 1995; Visona and Stanmore, 1996). For an existing plant, many factors influence the overall NOx emission level. These include: • •

•

Fuel-related factors such as coal type, coal particle size, coal blending, etc. Process conditions such as flame ignition characteristics, air to fuel ratios in the devolatilisation and combustion zones, residence time and temperature-time history of furnace gas, changes in heat transfer rates, etc. Changes in operational inputs, etc.

Unfortunately, in most coal-fired power plants, available on-line information for NOx emission modelling is limited. This is reflected in the types of model available for predicting NOx emission, which may be broadly classified as shown in Figure 9.1. Computational fluid dynamics (CFD) models (Lockwood and Romo-Millares, 1992; Visona and Stanmore, 1996) look in detail at the process behaviour (thermodynamics, fluid dynamics and NOx generation chemistry). Since the theoretical basis for CFD models is transparent (based on physical and chemical properties) such modelling methods may be classified as white-box methods. The resulting threedimensional finite element type models can produce accurate models of the overall

White-boxmethods • CFD model

Figure 9.1

Classification of NOx emission models

246

Thermal p o w e r plant simulation and control

combustion process and are widely accepted. However, such models are not easily developed and there is an insatiable demand for more computing power and finer meshes. Results of CFD modelling are often given the general form: [NOx] = f ( P , T, r, y . . . . )

(9.1)

where P is the pressure, T is the temperature, r is the residence time, and y is the fuel-air ratio. The other variables are undefined but might include the effects of evaporation and mixing, etc. Different boiler types might however use different variables. So, for another boiler, y may become the fraction of primary air in the combustion zone, Tmight be the 'stoichiometric' temperature, or the 'reaction' or flame temperature. In CFD modelling the correlations between NOx level with operating conditions are often acquired using a finite element approach that looks in detail at the process behaviour (thermodynamics, fluid dynamics and NOx generation chemistry). CFD modelling is now well established as a design tool for burner and furnace design. It has been widely applied in the power generation industry to help combustion engineers reduce emissions, increase efficiency, and select fuels. The documentation claims that given well-characterised operating conditions, CFD models are able to predict NO emissions within 10 per cent. CFD methods have been successfully applied to various types of boilers. Commercial software packages, such as CFX-4, 5 and 6 of AEAT technology (Stopford, 2002; Stopford and Benim, 1994), as well as FLUENT of Fluent Inc., etc. (Fluent, 1996), are available. In general, white-box CFD models are not suitable for real-time operation. There are some one- and two-dimensional approaches available (Ferretti and Piroddi, 2001) that are claimed to produce real-time models suitable for use in operation training and for control testing/design. However, there is the inevitable loss of detail (both internal detail and input/output relationships) and a requirement for experimental data in order to identify unknown parameters. For these reasons it is arguable that these one- and two-dimensional models should be categorised as grey-box methods. Also, for NOx control purposes the loss of input/output information can be critical. Black-box models are built based on experimental data sets or field operation data sets, and require no a priori knowledge (such as the fluid dynamics, thermal dynamics or chemical reactions) of the NOx formation and destruction process. They are widely used in industry (Henson and Seborg, 1996; Irwin et al., 1995; Sabharwal et al., 1999). Black-box models may include static, dynamic and recurrent artificial neural network models (Copado et al., 2001; ETSU, 1997; Ikonen et al., 1996; Li and Thompson, 2000) and identification models such as ARX (AutoRegressive model with eXogenenous input) and NARX (non-linear ARX) (Li and Thompson, 2001a). Artificial neural networks (ANNs) are also called artificial neural systems, neurocomputers, parallel-distributed processors or connectionist models, etc. The motivation behind their development is originally to mimic, at least partially, the cognitive information processing of human brains using the structure and functions of the human central nervous system. A neural network is composed of a large number of simple processing units, called artificial neurons or nodes, which are interconnected

Modelling of NOx emissions in coal-fired plant 247 by links called connections. These nodes are linked together to perform parallel distributed processing in order to solve a desired computational task. A typical artificial neural network consists of a set of input nodes that are connected to a set of output nodes through a set of hidden nodes, thus forming a multilayered network. Depending on the type of nodes (activation functions) and the type of links, there exist a variety of neural networks, such as Hopfield networks, Kohonen networks, multilayer neural networks, radial basis function networks, B-spline networks, etc. As a universal approximator, neural networks have been widely used in engineering system modelling to map the relations between system variables, and various neural network models have been developed to model the NOx emissions. Among various neural network models, static neural networks map the relations between current NOx output with current inputs, and are widely implemented in industry. Static neural networks are used to optimise the plant operational conditions, however they cannot capture the dynamics of the system embedded in the data samples. Alternatively, dynamic neural network models consider past changes in the input data, i.e. neural network models are trained to capture the relation between current NOx output with past operation input samples. Finally recurrent neural networks use both past inputs and outputs to predict current NOx outputs, and have been widely used for process control. Identification models such as ARX and NARX are time-domain regression models with linear or non-linear terms. The linear and non-linear terms in identification models are functions of past system input variables and output variables. Identification models are widely used in process control. In general black-box models are simple enough for real-time operation and control. On the down side, such models have to be regularly updated as operation conditions change. That is, black-box models cannot in general be used to predict outside the range of the training data, and such models are said to have poor generalisation performance. A model with good generalisation performance requires less retraining. It is argued that for complex engineering systems all available information should be used rather than solely relying on physical modelling or some data-dependent identification approach. The reasons for such a 'pragmatic' approach are that: •

•

For physical modelling, the underlying physical and chemical laws of an engineering system (which are generally formulated as a set of partial differential equations (PDEs) and ordinary differential equations (ODEs)) can sometimes be too complex to build a simplified system model; or the underlying mechanism of the system is unknown or such knowledge is incomplete. Also, the system under study may exhibit properties that change in an unpredictable manner, etc. Data-dependent identification models may not be able to nest the 'true' system structure, therefore their prediction capacity cannot be guaranteed. In addition, for operational plants, safety and quality considerations often indicate that the duration of field experiments and the intensity of test-signal perturbation must be kept to a minimum. Consequently, such methods may fail to produce physically consistent models from data that is finite and noise corrupted.

248

Thermal power plant simulation and control

The pragmatic approach to system modelling uses both a priori and a posteriori information and is referred to as grey-box modelling. In grey-box approaches, physical modelling and system identification form two interacting paths. Depending on bow much and, in what form, a priori information is used, various grey-box modelling methods can be categorised. In general, grey-box methods, unlike white- or black-box methods, can provide a balanced framework that utilises both a priori knowledge regarding the NOx formation and destruction mechanism as well as a posteriori knowledge derived from the analysis of experimental/field operation data. Grey-box models are essentially a trade-off between model complexity and model prediction performance (Bohlin, 1991; Li and Thompson, 2001 b; Li et al., 2002; Pearson and Pottman, 2000; Tulleken, 1993). Ideally, any comparison of modelling methods for emission control should include representative models from each category. However, as indicated, a three-dimensional CFD model is not suitable for plant operation and control purposes. Therefore, in this chapter, six NOx models will be produced for the same thermal coal-fired power generation plant. These will include five black-box models (static neural network model, dynamic neural network model, recurrent neural network model, ARX model and NARX model), and one grey-box model. For model comparison purposes, the generalisation performance of the resultant models over unseen data is examined.

9.2

An overview of NOx formation mechanisms

The formation and destruction of NOx is inherently linked with the reactions of the other products of coal combustion. In particular, models for the combustion of volatiles and char are required to predict the oxygen available for the NOx reaction. For these reasons any NOx model should not be developed in isolation. In the current study the main NOx reactions are included (where appropriate) but the other gaseous products of combustion are not. This does not invalidate the work but will introduce the same unmodelled dynamics into all the models.

9.2.1

Coal combustion process

In the coal combustion process, many important reactions occur between the initial heating of the coal particle and the formation of fly-ash. This section attempts an overview of this process based on the work of Gormley (2001 ) and Zhu et al. (1999) and their indexed references. As the particle heats up, the volatile components of the coal will evaporate and diffuse into the gas stream, leaving a carbon-rich char particle. Once ignition temperature is reached, both volatiles and char will undergo combustion. The complex hydrocarbon volatiles will experience thermal cracking into simpler compounds or soot before oxidation, while the heterogeneous oxidation of char will eventually result in an ash residue.

Modelling of NOx emissions in coal-fired plant 249 9.2.1.1

Devolatilisation

When a raw coal particle is subjected to high temperature, it will release a gaseous volatile compound. This is a multistage process, and is know as devolatilisation. The simplest and most commonly used devolatilisation models are empirical and use global reactions, where the rate equations are of the Arrhenius type: Reaction rate coefficient = A e x p ( - E / R T )

(9.2)

where R is the gas constant, E is the activation energy, Tis the temperature, and A is some constant. 9.2.1.2

Volatile combustion

The coal devolatilisation process can produce several hundred gaseous compounds. Volatiles generally are composed of tars, hydrocarbon liquids, hydrocarbon gases, H2, H20, CO and CO2. Most of the compounds will continue to react in the vicinity of the char particles to produce successively lighter gases as the more complex molecules decompose, eventually forming CO2 and H20, provided that sufficient oxygen is available. However, if volatile combustion occurs at substoichiometric conditions, the heavier products (tars) may react to form soot. The combustion of volatiles is highly exothermic, accounting for up to 50 per cent of the total energy released during combustion, despite forming less that half of the total coal mass. The volatile hydrocarbon combustion process is complex, and global reaction kinetics can be used to simplify the modelling. Such a global reaction rate kv is expressed as: kv= A exp(~T)[Fuelff[Oxidant] ~

(9.3)

where R is the gas constant, E is the activation energy, T is the temperature, and A is a constant; ot and ~ are coefficients. A wide variety of hydrocarbons may be considered as fuel, but according to (9.3), a single fuel type is required. To achieve this, the carbon to hydrogen ratio of the volatiles is determined and the overall hydrocarbon volatiles can be considered to be composed of 'pseudo-molecules' of CnHm. Hence the simplest overall reaction for the oxidation of hydrocarbon fuel is formulated as: (R1)

Fuel + O2 ~ CO2 d- H20;

and for the generalised single step hydrocarbon CnHm the reaction can be expressed as:

C "m

m

with the generic single reaction rate expressed in (9.2). 9.2.1.3

Char combustion

Char is the residual mass after full devolatilisation of coal, and it is mainly composed of carbon and mineral matter with traces of hydrogen, sulphur and oxygen. The

250

Thermal power plant simulation and control

physical structure, or morphology, of char particles will vary depending on the speed of devolatilisation, ash content and structure of the raw coal. Char oxidation is a heterogeneous (solid/gas phase) reaction, where the gaseous oxygen diffuses into the particle, and is absorbed and reacts on the char surface. The reaction is much slower than the volatile combustion, and depends on various factors. Oxygen may react at the char surface or diffuse through the pores before reacting with the particles. Oxidation produces both carbon monoxide and carbon dioxide. CO may also be formed by the reduction of CO2 by the surface carbon of the char. However, given sufficiently fuel-lean combustion conditions, all carbon and CO will be oxidised to CO2. The variations in coals and their chars make the accurate modelling of all the combustion reactions of any individual coal extremely difficult. Therefore, a global modelling approach is widely used. The reaction of oxygen with the char surface ks is related to both external char surface area and the partial pressure of oxygen. The rate coefficient takes the form of a first-order Arrhenius equation, as formulated in (9.1); and the overall char combustion can be formulated as: ( 1 ) Rchar = q)s~pApPo2 1/ks + 1/kdiff

(9.4)

where ~0s is the stoichiometric factor with 1 for CO2 and 2 for CO, Ap is the particle surface area, ~p is the particle area factor to account for irregularity and internal surface burning, Po2 is the oxygen partial pressure at the char surface, and kdiff is the reaction rate of char particles with oxygen diffusing through the pores. 9.2.2

Overview of NOx formation process

Although NOx refers to all oxides of nitrogen, during fossil fuel combustion, the major part of NOx emission has been found to be NO. According to De Soete (! 975), there are three main sources of NO in combustion, namely thermal NO, prompt NO and fuel NO. Thermal NO results from the reaction of atmospheric nitrogen and oxygen at high temperature, prompt NO is formed by the reaction of nitrogen with hydrogen-derived radicals in the fuel-rich zone of combustion, whilst fuel NO results when nitrogen compounds present in the fuel are released and react with oxygen. In coal-fired power plant, fuel NO is the major contribution to NOx emission, with some of the fuel NO being released from the devolitisation of the fuel and some from the oxidation of the char. The simplified NOx formation process associated with the combustion process of coal is briefly described in Figure 9.2. As indicated in Figure 9.2, thermal, prompt and fuel NOx are formed during different combustion processes and in different combustion zones. Based on the work of De Soete (1975); Lockwood and Romo-Millares (1992); Nimmo et al. (1995); Visona and Stanmore (1996) and Williams et al. (1994) and their indexed references, these three NOx mechanisms may be summarised as follows. 9.2.2.1

Thermal NO formation

Thermal NO formation can be modelled by the 'extended Zeldovich' mechanism (De Soete, 1975). High-temperature combustion causes atmospheric oxygen and

Modelling of NOx emissions in coal-fired plant 251 Fuel NO x ....................... .....~ N? Fuel NO x / ...-.

Char

Ash N2

Prompt

NOx Thermal NOx

Devolatilisation

~- Volatilecombustion

~

Char combustion

Figure 9.2 Simplified NOx formation processes nitrogen to react forming nitrogen oxide. The principal reactions are: (R3)

N2 + O .k~ ~- NO + N k_ I

(R4)

N -4- 02 ~

NO + O

k_ 2 k3

(R5)

N + OH ¢ = ~ NO + H

(for a fuel-rich mixture).

k_ 3

The reaction rate coefficients (kl, k - l , k2, k-2, k3, k-3) for the forward reactions and the corresponding backward reactions are generally expressed in the Arrhenius form:

kior-i =otexp(E/RT)

or

kior_i =otT~ exp(E/RT)

(9.5)

where i = 1, 2, 3, R is the gas constant, T is the temperature, E is the activation energy, and ct,/~ are constants. Hence, the rate of thermal NO formation can be expressed as: d[NO]T - -

dt

1 - [NO]2/k[O2][N2] - - 2k~ [ N 2 ] [ O 2 ]

1 + k - i [NO]/(k2[O] q- k3[OH])

(9.6)

where k = (kl/k-1)(kz/k-2) is the equilibrium constant for the reaction between N2 and Oz. The value for [O] and [OH] may be obtained from the predicted concentration of major species using the partial equilibrium assumption. For example, the

252

Thermal power plant simulation and control

concentration of the oxygen atom is obtained from the partial equilibrium of oxygen dissociation: (R6)

½Oz ¢~ O.

The above analysis shows that the thermal NOx formation rate is highly dependent on the temperature, linearly dependent on oxygen atom availability and is associated with a long residence time.

9.2.2.2

Prompt NO formation

Prompt NO is formed by the reactions of N2 with fuel-derived radicals such as CH and CH2 in regions near the flame zone of a hydrocarbon fuel. Although its overall contribution can be small relative to the formation of total NO (less than 5 per cent), the concentration of prompt NO in fuel-rich zones can be significant. Additionally, in fuel-rich conditions of some low NOx burners, the proportion of prompt NO in the total NO formation may be greater. A global kinetic mechanism can be used to predict the prompt NO emission (Visona and Stanmore, 1996): d[NO]p _ f T ×A p r [ O 2 ] ~ [N2][Fuel]¢~ exp(Ea/RT) dt

(9.7)

where f is a correction factor applicable for all aliphatic alkane hydrocarbon fuels. For an air to fuel ratio of 0.75-1.56, f -- 4.57 + C1 n -- C269 + C3 (92 - C4 O3, where Cl-C4 are constants with values of 0.0819, 23.2, 32 and 12, respectively, n is the number of carbon atoms per molecule for the different hydrocarbon fuel types, and tO is the equivalence ratio. T Y represents the non-Arrhenius behaviour of the equation at conditions where the maximum flame temperature is exceptionally high or low. Apt is the pre-exponential factor having the value of 6.4 × 106(RT/P) c~+l where P represents the pressure, c~ and 13 are reaction order constants for oxygen and fuel, respectively, and vary between 0 and 1, depending on the rate of consumption of fuel and oxidiser, and the activation energy Ea = 303 kJ/mol.

9.2.2.3

Fuel NO formation

Fuel NO is the main source of NOx emissions in fossil fuel combustion, and constitutes 70-90 per cent of the total NO (Lockwood and Romo-Millares, 1992; Nimmo et al., 1995; Visona and Stanmore, 1996). Fuel NO is formed from the homogeneous oxidisation of nitrogen constitutes released during devolitisation or from the heterogeneous oxidisation of nitrogen compounds in the char after devolitisation. It is believed that the main gas species containing nitrogen produced during coal evolution are HCN and NH3. Once the fuel nitrogen is converted to HCN it rapidly decays to form various NH compounds (NHi), which react to form NO and N2. Recognising the importance of HCN as a precursor to the subsequent nitrogen compound intermediates, De Soete (1975) correlated the rate of NO formation and decay with a pair of

Modelling of NOx emissions in coal-fired plant

253

competitive parallel reactions, each first order in HCN, which represent the pool of nitrogen-containing species: d[NO]f ----101°pXcNX~2 e x p ( - 3 3 , 7 0 0 / T ) kg/m 3 s dt HCN---~NO d[N2]dt NO~N2 =3 ×

IOI2pXcNX~o

e x p ( - 3 0 , 0 0 0 / T ) kg/m 3 s

(9.8)

where X is the mole fraction of the chemical species, and b is the order of reaction for molecular oxygen which is a function of oxygen concentration. The two reaction rates are included in the transport equations for HCN and NO and form the basis for the fuel NO post-processor, which allows the calculation of NO formation for a pulverised coal flame. 9.2.2.4

NO2 formation

Formation and destruction of NO2 is believed to occur via the reaction of NO with 02, O, OH and HO2 in the flame. Chemical equilibrium considerations indicate that for temperatures greater than 1500 K the ratio of NO2 : NO is close to zero in the flame. However, significant NO2 concentrations have been measured in turbulent-diffusion flames near the combustion zone. There are no valid formulae for the production of NO2 from NO. However, the reaction rate will generally resemble that of (9.2).

9.3

NOx emission models for a 500 MW power generation unit

Various models have been developed to model NOx emissions in a 500 MW power generation unit. These models are grouped together for comparison purposes.

9.3.1

Plant description

The 500 MWe power generation unit studied is installed with a low NOx concentric firing system (LNCFS). The burners are provided with over-fire air, and a proportion of the air in the combustion chamber is offset from the walls. The coal delivery system for each unit comprises four subsystems: coal feeder, coal mill, separator and pf pipework to supply fuel to the burners. There are five coal mills in the coal delivery system. The furnace of this boiler is separated into two sides, namely the A and B sides, by a wall. Each side has four burners per level and there are five levels of burners with each level linked to one of the five mills. The fuel flow (feeder speed) to each of the mills can be measured. Each mill feeds eight burners on a level (four on the A side and four on the B side). Damper settings on each side of the boiler tend to be ganged together. For this unit the following variables are identified to be related with NOx formation and emission, and are used as model inputs: 1.

Speed of the conveyor belt feeding the coal for each of the five mills (rpm): vl (t), vz(t), v3(t), v4(t), v5(t).

Thermal power plant simulation and control

254 2. 3.

02 in A and B sides of the furnace that are measured at the economiser (percentage in wet): O~j (t), 022 (t). Burner tilt position, A and B side of the furnace (degree, relative to horizontal): 01 (t), 02(t).

Other factors affect NOx emission. For example, the coal type strongly affects the overall NOx emission, and power plants normally use different coal sources. However during the period of study, the coal type did not change and is therefore not reflected in the models. Also the number of burners in use depends on the electrical load; in addition, different operators may use different burner combinations, possibly leading to unexpected excursions of overall NOx levels. Finally the temperature of the air, which preheats the pf coal, will also have an impact on overall NOx emission levels. All these factors will be treated as model noise/disturbances. This gives nine independent input variables: Ul(t) = Vl(t),

uz(t) = vz(t),

u3(t) = v3(t),

u4(t) = v4(t),

us(t) = vs(t),

u6(t) = O21 (t),

uv(t) = O22(t),

u8(t) = 01(t),

u9(t) = 02(t)

(9.9)

In addition to the above nine inputs, another two dependent input variables are introduced: U l 0 ( t ) = ~J~--~5-1uj(t), which indicates the overall coal feed, and ull (t) = Y~=6 uj (t) which indicates the overall oxygen level. Data covering three weeks' field operation is available, with NOx emission and the various inputs sampled every minute. The sample data is segmented into four data sets, among which one set (training period with 7000 samples) is used for training; all the other data sets (termed test period 1, 2 and 3) are used for validation, and therefore not used for training in any form. Tables 9.1 and 9.2 show the variation in the data over the four time periods. Table 9.1 shows variations in the validation data relative to the training data. That is in each period the range of data used is calculated (maximum value minus minimum value) and divided by the range calculated for the training period. For example, in test period 3 the range of measured NOx values is approximately one and a half times greater than that used in training. Obviously the training period does not cover all the operating conditions found in the validation data. In particular, the difference between the ranges of NOx values in the training period and test period 3 is more significant and therefore test period 3 data has been used later in the article to compare graphically the errors produced by each of the modelling techniques.

9.3.2

Neural network models

Although it has been proved that neural networks may approximate a wide range of non-linear systems to arbitrary closeness given a sufficient number of nodes and a single hidden layer, a neural network with a fixed number of hidden nodes does not necessarily nest the true structure of the real system and, since the samples used for training are limited, the training data is unlikely to cover all operational conditions. Therefore, it is possible that an ANN model will produce biased solutions for

Modelling of NOx emissions in coal-fired plant Table 9.1

NOx v 1(t) v2(t) v3(t) v4(t) v5(t) 02] (t)

022 (t) 01 (t) 02(t)

NOx Vl(t) vz(t) v3(t) v4(t) v5(t) O21 (t) O22 (t) 01(t) 02(t)

Variations in data ranges

Training period

Test period 1 Test period 2

Test period 3

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

1.2552 0.9516 0.5140 0.4410 0.5756 0.9093 0.9527 1.0000 0.2000 0.7419

1.4816 0.9887 1.0595 0.9955 1.2578 0.9175 1.1745 1.1457 1.0000 1.0000

Table 9.2

255

1.1069 0.9576 0.9826 0.9727 0.5463 0.9282 0.8218 0.9213 0.7667 0.9329

Variation in data averages

Training period

Test period 1 Test period 2

Test period 3

0 0 0 0 0 0 0 0 0 0

-0.0639 0.2513 0.0096 0.0430 -0.0249 -0.3848 0.0175 0.0727 -0.1989 -0.2076

0.0099 -0.0063 0.2167 0.0810 -0.0310 -0.0682 -0.0169 -0.0372 -0.2304 -0.3095

0.0018 0.1357 0.0248 0.0058 -0.0749 -0.7020 0.0395 0.1092 -0.1691 -0.1701

unseen data. To combat this problem two general approaches are available. One is to achieve better generalisation performance through network configuration, and the other focuses on the training process. In this chapter we choose the methods used by Li and Thompson (2000) to generate the model structure. This method also provides good generalisation performance. As indicated earlier, there are three types of multilayer perceptron (MLP) models that can be constructed, i.e. a static neural network, which maps the relation between current NOx output with current inputs; a feedforward dynamic neural network model which introduces dynamics by considering the past changes in the input data, i.e. neural network models are trained to capture the relation between current NOx output with two, or more, operation input samples; and, finally, a recurrent neural network that uses both past inputs and outputs to predict current NOx outputs.

256

Thermal power plant simulation and control Table 9.3

Prediction performance of three A N N models

Model type

Number of hidden nodes Performance (MP)

Static ANN Dynamic forward ANN Recurrent ANN

30 30 20

23.8% 12.7% 14.4%

Models based on the above three networks have been developed for the 500 MWe power generation unit. All these network models were trained using the same technique by Li and Thompson (2000) and the Levenberg-Marquardt (LM) method found in the Matlab ® Neural Network Toolbox is used as a basic training algorithm. The training data set consists of 7,000 samples taken from the plant operation data file. The number of hidden nodes in the static and dynamic neural network model is 30, whereas the recurrent neural network model uses 20 hidden nodes. Table 9.3 lists the prediction performance of various ANN models. In this table, the performance averaged over all the unseen data is defined as

n P = / y~N1e2

(9.10)

where N is the number of samples, ei (i = l, 2 . . . . . N) is the modelling prediction (MP) error, and yi (i = 1, 2 . . . . . N ) is the NOx emission. In order to ensure that the various comparisons are fair, those models requiring past output data only use predicted data after the first few samples. That is Tables 9.3 and 9.4 (page 263) indicate the long-term prediction performance of the models on unseen data. Note, if the measured output data had been used the performance measures for all models except the static neural network model, which uses no past output values as inputs, would be much improved. 9.3.3

Linear ARX model

Development of a linear ARX (AutoRegressive model with eXogenous input) model is a two-stage process: namely, model structure selection and parameter identification (Ljung, 1987; Soderstrom and Stoica, 1989). Model structure selection decides which terms are to be included in the model. Consider an ARX model that includes all possible terms:

P Oi~oi(t) + 8 ( t )

y(t) = Z i=1 ~pi(t) =

uj(t-k), y(t - k),

(9.11) k=l,2 ..... nj,j=l,2 k = 1, 2 . . . . . ny

. . . . . 11; or

Modelling of NOx emissions in coal-fired plant

257

where p is the total number of possible terms, uj (j = 1,2 . . . . . 11) are defined in (9.9), y(t) is the NOx emission, nj = 4, j = 1, 2 . . . . . 11, ny = 4, and e(t) is a white noise series. Obviously not all of the 48 terms in (9.11) are required since linear dependency among the terms exists. Also some terms will have little to contribute to model accuracy. If N samples are used for identification, equation (9.11) becomes: Y =q~O+S

(9.12)

where yT = [y(1), y(2) . . . . . y(N)], ~I~T = [~01, ¢P2. . . . . ~Op]T, i=1,2

~0i : [¢Pi(l), ¢pi (2) . . . . . ~0i(N)] T,

. . . . . p,

S T = [e(1), E(2) . . . . . e(N)]. The loss function is defined: E ( O ) = , wT -,--

(9.13)

Suppose that all regressors in (9.12) are normalised, i.e. ¢pTcpi=I (i = 1, 2 . . . . . p), and also y T y = 1. Then, by minimising (9.13), the minimal loss function can be computed recursively (Li and Thompson, 2001a): Eq+l(Oq+l) -- E q ( ~ q ) =

K

g q + l = Kq -KO = I N x N ,

(yTKqcPq+I)2 T ~Oq+l KqCPq+l

.... T KT qWq+l~q+l q T ~Oq+l KqCPq+l

(9.14)

EO = 1

where ~ q is the estimated parameter vector with q terms in the model.

Furthermore, let ~ i ) = Kq~oi, i = (q + 1), (q + 2) . . . . . p. Since K q K q = Kq then (9.14) may be rewritten as: Eq+l(~q+l) = Eq(~q) -

(yT~(qq+l))2 (~(q+l).~T~(q+l) ,.~.q j ~.q

(qaT~(q+l) ~ ~.(i) = ~ i ) _ "ri q 1 ~(q+l), ~*q+l ( ~ , ~ + 1) q ~o~q j o,q ~(oi)=¢pi, E o = I ,

i=1,2

(9.15) i = (q + 2) . . . . . p

. . . . . p.

According to (9.15), if a new term, e.g. ¢Pq+l, is added into the regression model, its contribution to the loss function will depend solely on the value

Thermal power plant simulation and control

258

of (Y T ~q(q+l) ) 2 / ( ~ q(q+l) ) T ~q(q-I-l) , where ~ q + l ) is the previously reformulated regressor as indicated in (9.15). There are various criteria to compare and select appropriate model structure, such as the F-test, Akaike's information criterion (AIC), and the final prediction error (FPE) criterion (Ljung, 1987; Soderstrom and Stoica, 1989). In this chapter, the following simple criterion is used:

FPEq = Eq((gq) [I + ~ ]

(9.16)

where Eq (~q) is the minimal loss function with q terms, ~ is some positive integer normally chosen to be 2, and N is the number of samples. The model selection process in this chapter will be performed in a stepwise forward way, i.e. at each step only the term satisfying Max (yT~(qi))2

~Pi (~.(i) ~ q ~T j ~.~.(i) ~q '

i c {unselected terms}

will be selected. This process continues until FPEq starts to increase (instead of decreasing). The final linear ARX model for NOx emission takes the following form: y ( t ) ( l + alz -1 q- a2z -2 q- a3z -3 -q- a4z -4)

= bo q- blz-lu3(t) + (b2z -1 -k- b3z -2 + b4z-4)u5(t) + b5z-4u6(t) + b6z-3u8(t) q- (b7z -1 + b8z-4)u9(t) + (b9z -2 + bloz-4)UlO(t) + e(t) (9.17) where z -1 is the time lag, ai (i = 1, 2, 3,4) and bi (i = 0, 1. . . . . 11) are model parameters.

9.3.4

NARX model

NARX (Nonlinear AutoRegressive model with eXogeneous input) / NARMAX (Nonlinear AutoRegressive Moving Average model with eXogeneous input) models have been widely used in non-linear dynamic system modelling (Chen and Billings, 1989; Harber and Unbehauen, 1990; Henson and Seborg, 1996). In NOx emission NARX models, only first and second-order terms are considered and the non-linear ARX model takes the form: P

y(t) = Z Oi~oi(t) + E(t) i=l

uj(t - k), ~Oi(t) = I ( u j ( t -- k)) 2,

[y(t - k ) ,

k=l,2

. . . . . nj, j = l , 2

. . . . . 11; or

k=l,2

. . . . . nj, j = l , 2

. . . . . ll; or

k:

1,2 . . . . . ny

(9.18)

Modelling of NOx emissions in coal-fired plant

259

where uj (j = 1, 2 . . . . . 11) are defined in (9.9), y is the NOx emission, nj = 4, j = 1, 2 . . . . . 11, ny = 4 , and therefore the total number of candidate terms p in (9.18) is 92. Again, using the previous argument, not all of the 92 terms will be included in the NARX model and a model selection procedure is required. The model structure selection procedure is identical to that used with the linear ARX model. Using the same data set for identification the final NARX model takes the form y(t)(1 + alz -1 + a2z -2 + a3z -3 -k- a4z -4) = bo + (blz -1 + b2z-3)Ul (t) + (b3z -2 + b4z-4)u2(t)

nc b5z-lu3(t) + b6z-3u4(t) -q- (b7z -1 + b8z-2)u5(t) + b9z-4u6(t) + bloz-3u8(t) -k-bllz-lu9(t) -t-bl2z-4ulo(t) + bl3z-4(Ul(t)) 2 q- bl4z-l(u2(t)) 2 q- bl5z-3(u3(t)) 2 q- bl6z-l(u5(t)) 2 + bl7z-n(u6(t)) 2 + bl8z -1 (UlO(t)) 2 + E(t)

(9.19)

where z -1 is the time lag, and ai (i = 1, 2, 3, 4) and bi (i = 0, 1. . . . . 18) are model parameters.

9.3.5

Grey-box modelling

In the grey-box approach, physical modelling and system identification form two interacting paths. There are many shades of grey depending on the mix. Fundamental grey-box modelling (Li and Thompson, 2001 a, b) assumes that the underlying mechanisms of the system to be modelled are either too complex or only partially known. For this reason the model structure of the fundamental grey-box model considered here is that of a Hammerstein model having the following form: P

y(t) = y ~ Oiq)i (t) + ~(t)

(9.20)

i=0

where ¢o(t) = 1

~oi(t) = ~oi(y(t -- ky), uj(t - d - kuj)),

i = 1. . . . . p

and y and uj (j = 1,2 . . . . . m) are the output and inputs, 0 is the parameter, E(t) is a white noise series, q)i (t) denotes fundamental elements (FEs) and their derived terms, and ky and kuj are input and output time delays. One of the essential concepts in fundamental grey-box modelling is that of the fundamental element. For engineering systems where a priori fundamental knowledge exists it is possible to extract basic information in the form of simple expressions. For example, reaction rates will be of the form exp(x; c) or oscillatory behaviour might

260

Thermal power plant simulation and control

take the form sin(x; c), etc., for which x is a vector of variables and c is a vector of parameters. These simple functions acquired from the fundamental a priori system knowledge are associated with system behaviour. Such FEs may appear in the system model in a variety of forms, and can also undergo change (mutation). For example in the function sin(x; c), the value of the parameters in vector c can be different in different situations, while sin(x; c) may also undergo mutation and become cos(x; c). Once the FEs are collected, a system model which reflects the dynamics of the system may be produced by appropriately combining these FEs. At this model construction stage experimental or on-line operational data are required. Therefore, the proposed modelling technique involves a search for the fundamental elements of the system, and then constructing the system model using appropriate combinations of these FEs, hence the name fundamental grey-box modelling. The framework of such a grey-box modelling method is illustrated in Figure 9.3. The underlying motivation can also be formulated as follows. Suppose a non-linear unknown function f ( x ) has the following form: (9.21)

f ( x ) -~ f(g01(Cl; X) . . . . . qgm(Cm; x))

where x is the variable vector, and ~01(Cl; x) . . . . . ~Om(Cm;x) are fundamental elements that are mutually linearly independent, and ci (i = 1, 2 . . . . . m) are parameters in those FEs. That is f ( x ) may be approximated by functions that are related to f ( x )

, i t

..........

Identifyingfundamental elements module

i

- -

PDEs+ODEs

~_~ Fundamental elements

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.

ro ess l| .... l"

Physical modelling (a priori)

................

(a posterior) -System identification

,]

r --....

i ....

: :

iiiiiiiiiiiiiiiii St

i . . . . . . . . . . . . . . ~-] Data i Experiment ~ collection ~ !'1 design ] i'1 and ] i" ,, . . i ] analysis ] I 'L. . . . . . . ~_. . . . . . . J

iYi

]I' • * estimationParameter,,h---z II T

~"

!

r

Structure iIll; determination ct ~ " ' I : u ', e --~ Validation or

n

' If possible

falsification I I I

Competition modelling module

Figure 9.3

Fundamental grey-box modelling framework

I

Modelling of NOx emissions in coal-fired plant 261 as follows:

f(x) = f(g01(Cl; x) . . . . . f (x) IX=X0+ ~

qgm(Cm;

X))

bi (qgi (ci; x o -1- f i x ) - ~oi (ci; x o ) )

(9.22)

i=1

where b i = f'(x)/qg~(ci;X)lx=xo, and ~r indicates a small number. One issue in (9.22) is how to identify the fundamental elements and their particular form.

The following remarks on selecting FEs are made.

Remarks: 1.

2.

3.

FEs are the simplest form of expressions. If a priori information regarding an engineering system exists (based for example on first principle laws and chemical reactions), these can be used to produce FEs. It is possible that some of these FEs will be strongly correlated with each other. Therefore to determine which FEs should be used to construct the model requires a posteriori information (typically obtained through an identification method which includes model structure selection and parameter identification). Some of the FE functions may be of the same type, and only the parameters in the functions differ. In this case, the derived model partially resembles a neural network where the activation functions in the hidden layers are all of the same type and only the weights and bias are different. However, it should be pointed out that the FEs are derived from a priori information regarding the system mechanism. Parameters in the FEs, if unknown a priori, may have to be determined from experimental data.

9.3.5.1 Fundamental grey-box modelling procedures Step 1. Establish the fundamental mechanisms of the system. Typically these will consist of a set of PDEs and ODEs.

Step 2. From these equations select a set of fundamental elements in which each element describes a basic relationship between system variables. Step 3 (optional). Construct a set of derived terms that are the production of two or more FEs. Derived terms are used to reflect couplings among system variables and should be based on the mechanism governing the system behaviour.

Step 4. Those FEs and their derived terms constitute a term pool. Use plant data together with the term pool to establish a suitable linear-in-parameter model (generalised polynomial model) through model structure selection and parameter identification.

Step 5. Validate the model.

262

Thermal power plant simulation and control

Two technical problems stand out: 1. 2.

How to identify the unknown parameters in the FEs and their derived terms. How to select the model structure. (The term pool can be very large. Therefore there is a combination problem, and the correlation between terms can be strong.)

Two general approaches can be used to resolve the above problems: 1. 2.

Perform two distinct but sequential processes. First identify the parameters in the FEs and the derived terms and then select the model structure. Perform an integrated process in order to identify the model structure and the parameters in the FEs and derived terms.

With respect to the first approach, various analytical methods might be applied. The second approach lends itself to the use of genetic algorithms (Peng et al., 2001). In this chapter, the first approach is used to construct the fundamental grey-box model. That is, the parameters in the FEs and their derived terms are first identified, and then the model structure selection procedure (identical to that used with the linear ARX and NARX models) is used to construct the model. For each iteration in the step-wise forward model construction process, only the term in the term pool that contributes most to decreasing the cost function is selected. In deriving the grey-box model for the NOx emissions, FEs are selected based on the NOx formation mechanism as described in equations (9.6)-(9.8). In general the coal feeds are associated with the total energy released in the furnace, and hence the average temperature in the furnace. Coal feeds are also associated with the concentration of fuel nitrogen in fuel NOx formation. The oxygen concentrations are associated with the thermal and temporal NOx formation. The burner tilt positions affect the shape of the fireball in the furnace, and are therefore associated with the temporal and thermal NOx formation. Therefore, the following FEs are formulated:

Fi = ( u i ( t ) ) ci,

i = 1, 2 . . . . . 11

Fi = e (ci/(uj(t)+bj)),

i = 12, 14 . . . . . 17, j = 1,2, 3, 4, 5, 10,

(9.23)

where c i (i = 1, 2 . . . . . 17) and bj (j = 1, 2, 3, 4, 5, 10) are coefficients. Besides the 17 fundamental elements, the following 121 derived terms can be constructed:

Di =(Fj)Cp(Fk) cq,

j 6 { 1 , 2 . . . . . 11}, k 6 { 1 , 2 . . . . . 17}, j ( = k .

(9.24)

Modelling of NOx emissions in coal-fired plant Table 9.4

263

Prediction performance of three analytical models

Model type Linear ARX model NARX model Grey-box model

Number of terms*

Performance (MP)

15 22 14

17.1 11.3 10.2

* The numberof termsexcludesthe DC term and noise term. Using the same 7,000 samples in the training period for model identification, the grey-box model takes the following form:

y(t) + aly(t - 1) + a 2 y ( t - 2) + a3y(t - 3) + a4y(t - 4) = bo + blz -1F2(t)Flo(t) + bzz -1F2(t)Fl3(t) + b3z -1Fll (t)Flv(t) + b4z-4F2(t)Fl7(t) + bsz-3F4(t)Flo(t)e(t) + b6z-lF3(t)F9(t) q- b7z-l F3(t)F14(t) + bsz-a F4(t)Flo(t) + b9z-3Fg(t)Flv(t) + bloz-3F7(t) + e(t).

(9.25)

Table 9.4 shows the prediction performance of various linear and non-linear NOx emission models. Figure 9.4 shows the prediction performance of the grey-box model for the training period, while Figures 9.5-9.7 cover three distinct periods of unseen data. As with all the models, after the first few sample points only input information (and predicted NOx values if required) is used. Note that in these figures 1440 samples is equivalent to one day of operational data. Because the data points are close together the prediction values appear as a thick smooth line whereas the actual values appear more erratic. Figure 9.8 shows the prediction errors for all six models when applied to the unseen data of test period 3. Although this figure suggests that the static ANN is better than, say, the ARX model this would only be true for this time period. Also, if the ARX approach used measured output data (rather than past predictions) to produce the prediction at the next sample then even over this time period the ARX model would appear better than the static ANN.

9.4

Conclusions

In this chapter, NOx emission modelling for plant operation and control has been studied. The NOx formation mechanism has been identified, and various model types have been introduced. In particular six types of model have been produced to estimate the NOx emission of a 500MWe power generation unit. Tables 9.3 and 9.4 show the

264

Thermal power plant simulation and control Model prediction and NO x emission 15o

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Grey-boxmodel performance (test period 1)

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Modelling of NOx emissions in coal-fired plant Model prediction and NO~ emission

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Grey-boxmodel performance (test period 3)

4000

5000

265

266

Thermal power plant simulation and control Static ANN Dynamic forward ANN Recurrent ANN

ARX

NARX

Figure 9.8

Prediction errors for different model structures (test period 3)

overall performance of the six models when predicting NOx emissions over different periods of time and different operation conditions. From these results it can be seen that: • •

• • •

A static neural network gives the worst overall performance, though widely used in industry. Introducing input dynamics (dynamic feedforward ANN model) gives improved overall prediction performance. However, the best recurrent neural network does not necessarily produce a better overall performance than a dynamic feedforward ANN model. A linear ARX model is better than a static neural network model in general. A non-linear ARX model is better than a dynamic ANN model in general. A fundamental grey-box model has the best overall prediction performance.

It is unlikely that in plant operation and control only one type of model will be required, and each type of model has its particular advantages and disadvantages. Neural network and identification models are easier and quicker to build, but lack physical meaning, their generalisation performances are not as good as grey-box models, and more frequent retraining is required. In comparison, grey-box models take a little longer to build, but they do have some physical meaning that can be interpreted by the operators, and in general have better generalisation performance. Therefore the frequency of retraining is reduced. Once these models have been obtained on-line or off-line, they will then be used either in an advisory system to support the human operator on such aspects as task analysis, condition monitoring,

Modelling of NOx emissions in coal-fired plant 267 fault detection and isolation, and operation optimisation, or in boiler advanced control systems.

9.5

Acknowledgements

Acknowledgement is made to the British Coal Utilisation Research Association (BCURA) and the UK Department of Trade and Industry for a grant in aid of this research, but the views expressed are those of the authors, and not necessarily those of BCURA or the Department of Trade and Industry.

9.6

References

BOHLIN, T.: 'Interactive system identification: prospects and pitfalls' (Springer: Berlin, 1991) CHEN, S., and BILLINGS, S. A.: 'Representations of nonlinear systems: the NARMAX model', International Journal of Control, 1989, 49, (3), pp. 10131032 COPADO, A., et al.: 'Boiler efficiency and NOx optimisation through advanced monitoring and control of local combustion conditions'. Sixth International Conference on Technologies and Combustion for a Clean Environment, Porto, Portugal, 9-12 July, 2001, 1, pp. 903-908 DE SOETE, G. G.: 'Overall reaction rates of NO and N2 formation from fuel nitrogen'. 15th Symposium (International) on Combustion, Tokyo, Japan, 1975, The Combustion Institute, pp. 1093-1102 ETSU COAL R&D PROGRAMME: 'Technology status report: NOx control for pulverised coal-fired power plant'. ETSU, Harwell, 1997 FERRETTI, G., and PIRODDI, L.: 'Estimation of NOx emissions in thermal power plants using neural networks', ASME Journal of Engineering for Gas Turbines and Power, 2001, 123, pp. 465-471 FLUENT INC.: 'Fluent user's manual, release 4.4, vols. 1-4' (Lebanon, NH, Fluent Inc., 1996) GORMLEY, C.: 'Modelling coal fired power station NOx emissions'. PhD thesis, The Queen's University of Belfast, 2001 HARBER, R., and UNBEHAUEN, H.: 'Structure identification of nonlinear dynamic systems - a survey on input-output approaches', Automatica, 1990, 26, pp. 651-667 HENSON, M. A., and SEBORG, D. E.: 'Nonlinear process control' (Prentice-Hall, Upper Saddle River, 1996) HOLMES, K., and MAYES, L. W.: 'Progress report on the development of a generic NOx control intelligent system (GNOCIS)'. Coal R & D Program, Project Profile 103, ETSU, 1994 IKONEN, E., NAJIM, K., and KORTELA, U.: 'Modelling of NOx emissions based on a fuzzy logic neural network'. IFAC 13th World Congress, San Francisco, 1996, pp. 61-66

268

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IRWIN, G. W., WARWICK, K., and HUNT K. J.: 'Neural network applications in control' (The Institution of Electrical Engineers, Short Run Press, Exeter, 1995) LI, K., and THOMPSON, S.: 'Developing a NOx emission model for a coal-fired power generation plant using artificial neural networks'. UKACC International Conference on Control, Cambridge, 4-7 Sept., 2000 LI, K., and THOMPSON, S.: 'NOx emission models for operation and control of power generation boilers'. 6th International Conference on Technologies and Combustion for A Clean Environment, Oporto, Portugal, 9-12 July, 2001a, 2, pp. 889-895 LI, K., and THOMPSON, S.: 'Fundamental grey-box modelling'. Proceedings of the European Control Conference, 3-7 Sept. 2001 b, Oporto, Portugal, pp. 3648-3653 LI, K., and THOMPSON, S., DUAN, G. R., and PENG, J.: 'A case study of fundamental grey-box modelling'. 15th IFAC World Congress on Automatic Control, Barcelona, July 2002 LJUNG, L.: 'System identification: theory for the user' (Prentice Hall, Englewood Cliffs, 1987) LOCKWOOD, E C., and ROMO-MILLARES, C. A.: 'Mathematical modelling of fuel-NO emissions from PF burners', Journal of the Institute of Energy, 1992, 65, pp. 144-152 NIMMO, W., RICHARDSON, J., and HAMPARTSOUMIAN, E.: 'The effect of fuel-nitrogen functionality on the formation of NO, HCN and NH3 in practical liquid-fuel flames', Journal of the Institute of Energy, 1995, 68, pp. 170-177 PEARSON R. K., and POTTMANN, M.: 'Gray-box identification of block-oriented nonlinear models', Journal of Process Control, 2000, 4, (10), pp. 301-315 PENG, J., LI, K., and THOMPSON, S.: 'GA based software for power generation plant NOx emission modelling'. 6th International Conference on Technologies and Combustion for A Clean Environment, Oporto, Portugal, 2001,2, pp. 881-887 SABHARWAL, A., SVRCEK, W. Y., and SEBORG, D. E.: 'Hybrid neural net, physical modeling applied to a xylene splitter'. Preprints of 14th IFAC World congress, N: 517-523, 1999, Beijing SODERSTROM, T., and STOICA, P.: 'System identification' (Prentice Hall, London, 1989) STOPFORD, P. J.: 'Recent applications of CFD modelling in the power generation and combustion industries', Applied Mathematical Modelling, 2002, 26, pp. 351-374 STOPFORD, P. J., and BENIM, A. C.: AEA Technology Report AEAIntec-1788, 1994 TULLEKEN, H. J. A. E: 'Grey-box modelling and identification using physical knowledge and Bayesian techniques', Automatica, 1993, 29, pp. 285-308 VISONA, S. P., and STANMORE, B. R.: '3-D modelling of NOx formation in a 275 MW utility boiler'. Journal of Institute of Energy, 1996, 69, pp. 68-79 WILLIAMS, A., POURKASHANIAN, M., BYSH, P., and NORMAN, J., 'Modelling of coal combustion in low-NOx p.f. flames'. Fuel, 1994, 73, (7), pp. 1006-1018 ZHU, Q., JONES, J. M., WILLIAMS, A., and THOMAS, K. M.: 'The predictions of coal/char combustion rate using an artificial neural network approach', Fuel, 1999, 78, pp. 1755-1762

Chapter 10

Model-based fault detection in a high-pressure heater line A. Alessanclri, P Coletta and T. Parisini

I0.I

Introduction

Increasing attention to safety and the need for reduction of energy production costs motivate the research into methodologies that enable one to provide long-term monitoring and early detection of faults and abnormal process behaviour in power plants. This chapter focuses on analytical redundancy techniques that can be conveniently employed to detect failures in the heater line of a 320 MW power plant, regarded as a testbed. The main topics are modelling, identification, and design of estimators that may be used to diagnose faults in the plant. Grey-box modelling allows one to account for different levels of knowledge regarding a plant. In the literature, many works on grey-box identification techniques are available that deal with linear models (Tulleken, 1993; Gawthrop et al., 1993) and hence are unsuitable for modelling real complex physical processes. A few investigations have focused on non-linear systems and proposed multiple-hypotheses statistical identification techniques (Bohlin, 1994 a, b; Bohlin and Graebe, 1995). Such methods evaluate models of differing structure and complexity from a statistical point of view so as to select one that is acceptable in terms of a given criterion. In any case, the on-line adaptation of the model remains in general rather difficult. As will be explained later on, our approach is substantially different from the aforementioned and may be split into two phases. In the first phase, a model is built that is as consistent as possible with the physical reality of the various components of the process under examination; this allows one to take into account different levels of component knowledge. In the second phase, the model is tuned so as to compensate for the unavoidable inaccuracies that depend on the hypotheses and assumptions introduced in the first phase. Modelling errors are due to both uncertain parameters and unknown subsystems of the plant. Neural networks may be used

270

Thermal power plant simulation and control

to model those parts of the system that are completely unknown. Thus, the problem is reduced to the identification of both uncertain parameters and the weights of the neural networks (Alessandri and Parisini, 1997). This identification turns out to be quite difficult for systems with a large number of state variables. In this context, it is preferable to apply an identification procedure that does not rely on computation of gradients and higher-order derivatives. Among the possible alternatives, a method based on stochastic approximation has been chosen (Spall, 1992; Spall and Criston, 1994). Once a dynamic model of the plant has been designed and tuned, it is possible to predict on-line the system behaviour by feeding such a model with the current input signals. This procedure has been followed, for instance, by Parisini (1997). In this way, it could be possible to monitor internal state variables that are important for the purpose of fault diagnosis. However, the on-line simulation and tuning of such a complex dynamic model may not be feasible in some power plant automation systems. Therefore, to estimate the above state variables, a non-linear state estimation scheme could be more appropriate. Estimation for non-linear systems is difficult and most commonly used techniques are difficult to apply (see, for an introduction, Jazwinski, 1970; Gelb, 1974; Anderson and Moore, 1979). Further complications arise when the underlying physical process is described by numerous state variables, as appears in many fields of engineering and applied sciences. In addition, standard stochastic models do not usually match real world settings, for which the statistics of the random disturbances are often unknown. Thus, a method is required which introduces low on-line computation effort but, at the same time, does not rely on disturbance statistics. Finally, it is preferable for the method to be easily tunable. A possible solution is the neural approach presented by Alessandri et al. (1997). Process and measurement noise statistics are not required for this method as estimation is obtained by minimising a cost function (in general, non-quadratic) defined on a sliding window composed of a finite number of time stages, according to a generalised least squares approach. The problem is solved by constraining the estimation functions to take on given structures in which a certain number of parameters have to be optimised. Among various possible solutions, multilayer feedforward neural networks have been chosen for their approximating properties. It is worth mentioning the popular extended Kalman filter (EKF) (see, among others, Jazwinski, 1970; Gelb, 1974; Anderson and Moore, 1979), which is well known and the most widely employed in industrial applications for state estimation. This estimator, however, is quite demanding in terms of computation requirements with many state variables and performs poorly in the considered case, due to the presence of numerous, strong non-linearities, as will be clarified later by means of simulation results. This chapter provides a summary of the experiences gained in modelling, identification, and estimation for power plant fault diagnostics. The contents include the results of previous work (Alessandri and Parisini, 1997; Parisini, 1997;

Model-based fault detection in a high-pressure heater line 271 Alessandri et al., 2002). A complete overview of the power plant is given in section 10.2: in section 10.2.1 the high-pressure heater line is described, followed by a description of a single heater, and section 10.2.3 is devoted to the modelling of the main faults and malfunctions. In section 10.3, grey-box modelling and identification are considered and an optimisation method based on stochastic approximation is described. Section 10.4 then provides a general description of the above-mentioned neural estimation method outlining successive steps regarding the structure of the optimal estimator, its approximation, and design. Finally, the simulation results are reported in section 10.4.3. Concluding remarks are included in section 10.5.

10.2 Description of power plant application In this section, the considered 320 MW power plant is described. The power plant is located at Piombino, Italy and, in particular, one of the two electronically controlled feedwater high-pressure heater lines is considered (see Figure 10.1). These lines are devoted to the regeneration process, i.e. a technique that improves the plant efficiency. More specifically, the thermodynamic cycle implies that the energy produced by the boiler to transform the water from the liquid phase into the aeriform phase is not completely used in the turbine. This occurs not only because of the intrinsic losses in the turbine, in the boiler, and in the pump, but mainly because it is necessary to condense the steam coming from the turbine at the same temperature and at the same pressure values as those at the beginning of the process. In the standard thermodynamic cycle the heat exchanged with the cold source, Qc, to condense the steam is lost; the regeneration process consists in using a part of the heat to increase the temperature of the water that flows into the boiler. Thus, the required heat input, QH, in the boiler is reduced.

10.2.1

Description of the high-pressure heater line

The high-pressure heater line is depicted in Figure 10.2. The feedwater provided by the feed pump flows through the four heaters, and goes into the boiler. After leaving the turbine, the superheated steam exchanges heat with the feedwater and then condenses. In addition to the heater line, Figure 10.2 presents some components of the control system which are used to regulate the condensate levels inside the heaters. Figure 10.3 illustrates the control components in each heater, numbered as follows: (1) steam tap valve; (2) no-return valve; (3) heater steam valve; (4) drain valve; (5) condenser high-drain valve; (6) feedwater inlet-outlet valve; (7) bypass feedwater valve; (8) incondensable component valve; (9) safety valve; (10) drain valve. Finally, the available sensors are shown in Figure 10.2 (see Parisini, 1997 for details).

272

Thermal power plant simulation and control

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Assuming a model of the heater and associated controllers, actuators and sensors, a set of state equations can be derived for each heater. Clearly, the model is very complex and strongly non-linear. For instance, it makes use of steam tables, which relate the pressures, temperatures, enthalpies and specific volumes in the superheating, saturation, and subcooling states. Obviously, the state of each heater is influenced by the upstream heater via the variables defining the pressure in the cavity, the specific enthalpies, the pressures, and the flow rate of the feedwater. Each heater in turn influences the state of the previous upstream heater via the flow rate of the output drain, the specific enthalpies of the output drain flow, and the positions of the feedforward draining valve. Some variables of the global model are assumed to be proportional to the unit load of the power plant. The most important are the enthalpy, the pressure, and the flow of the feedwater going into the first heater. Other variables assumed to be proportional to the unit load include the steam pressure and enthalpy in the various turbine stages and the pressure in the drain expansion tank. In the next section, we shall describe the model of a single heater in more detail. The final model can then be built on the basis of the four single heaters that make up the high-pressure line (see Figure 10.2), of the

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274

Thermal power plant simulation and control

sensors, of the actuators and of the controller elements. Clearly, the main modelling effort concerns the heaters, as the other parts are very simple to represent.

10.2.2

The model o f a single heater

Each heater (see Figure 10.4) consists of a vertical-axis cylindrical cavity, divided into halves by a vertical septum, including a N-shaped tube-bundle where the feedwater flows. Three different areas are considered in the cavity: A: desuperheating area, where the superheated steam cools down until it reaches the saturated steam condition through heat exchange with the feedwater flowing in the tube-bundle; B: condensing area, where the saturated steam condenses (vapour-liquid transition); C: subcooling area, where the condensed steam and the drain coming from the downstream heaters undergo a process of heat exchange with the feedwater. Under normal conditions, a drain valve conveys the resulting liquid to the upstream heater, whereas, under special operating conditions, the condensed steam can bypass the heaters, as can be seen in the alternative paths shown in Figure 10.2. However,

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Model-based fault detection in a high-pressure heater line

275

in the first heater, the condensed steam flows to the condenser, so it is possible to complete the thermal cycle. The equations describing each heater have been derived from the mass, energy and momentum conservation laws. In particular, we have analysed: (i) the behaviour of the fluid inside the cavity by using the equations for the conservation of the mass of drain water, for the conservation of the mass of water and steam, and for the conservation of the energy of subcooled water; and (ii) the behaviour of the fluid in the tube-bundle by heat exchange in the desuperheating, drainage and condensation areas, and loss of pressure in the tube-bundles due to metal friction. Regarding the fluid inside the cavity, we have made the following assumptions: -negligible heat exchange between the cavity and the external environment;

-negligible exchanges of energy and mass, due to surface phenomena at the interface between the condensing and subcooling areas; -the heat-exchange surface between the cavity fluid and the tube-bundle is fixed in the desuperheating area, with the heat exchange magnitude dependent on the condensing and subcooling areas; -uniform pressure distribution inside the cavity; - uniform enthalpy distribution inside each area (A, B, and C); -negligible density variations inside the subcooling area. Moreover, the following assumptions about the feedwater have been made: -feedwater is in the liquid state and in a subcooling condition;

-constant fluid pressure in the tube-bundle; the pressure is equal to the input pressure in the heater; -uniform physical properties of the tube-bundle metal; -negligible longitudinal heat conduction in both the pipe metal and the fluid. From the above assumptions, a set of non-linear equations can be derived to define the thermodynamic behaviour in each heater (Barabino et al., 1993). In the following, we will refer to the state variables xl : liquid level in the heater (mm); x2: pressure in the cavity of the heater (atm); x3: specific enthalpy of the output drain (kJ/kg); x4: specific enthalpy of the output feedwater (kJ/kg); xs: specific enthalpy of feedwater in the condensing area (kJ/kg); x6: specific enthalpy of feedwater in the subcooling area (kJ/kg). The input variables are:

Pprev" pressure in the previous heater (atm); Pdet: pressure in the drain expansion tank (atm); L: load required by the electric network (MW); Sp: percentage of steam spillover from the turbine;

276

Thermal power plant simulation and control htur: specific enthalpy of the steam from the turbine (kJ/kg); Wfw: feedwater flow (m3/s); hfw: specific enthalpy of the input feedwater (kJ/kg); Widr: drain water flow (m3/s); hidr: specific enthalpy of the drain water flow (kJ/kg).

Moreover, the remaining quantities, including constant parameters and functions of the state variables, are briefly introduced as follows: Wcon(X1, x2, x4, x5, Wfw): condensate steam flow; Wodr(X2, Xll, Pprev, edet): output drain flow;

Wev(Xl, x2, x3): evaporated water flow; Podr(X3): density of the output drain;

Psst(X2): density of the saturated steam; Wtur(X2, L, Sp): steam flow from the turbine; mw(xl, x3): mass of liquid in the heater; hsw (x2): specific enthalpy of the saturated water; hsst (x2): specific enthalpy of the saturated steam; Q A (Wtur, h tur, h sst): heat exchange in the desuperheating area; QB(xl, x2, x4, xs, Wfw): heat exchange in the condensing area; Qf(xl, x2, x3, x4, x11, Wfw): heat exchange in the subcooling area; LB (xl): height of the condensing area; m me(X5): mass of water and equivalent metal per unit; 69l (x3): temperature of the output drain; 692(x4): temperature of the output feedwater. A more detailed description of the functions of the state variables as well as the values of the constants Ah (cavity area not including the pipes), Vh (cavity volume not including the pipes), LA (height of the desuperheating area), Ol (off-set), time constants of the actuators and sensors, and the gains of the regulators can be found in (Gugliemi et al., 1995; Parisini, 1997). The models of the heaters have an identical structure and differ only in constants such as geometric coefficients (tank height, inside tank diameter, pipe length, inside and outside pipe diameters, desuperheating area), thermal coefficients (pipe-metal specific heat, pipe-metal thermal conductivity, steam thermal exchange coefficient, water thermal exchange coefficient), number of tubes in the tube-bundle, etc. In the following, we outline the model derivation highlighting the physical principles and the main assumptions that have been introduced. Derivation of the dynamic equation for x l. the mass in the draining area is

The equation for the conservation of

dmw = Widr -[- Wcon -- Wodr -- Wev dt

(10.1)

where mw = PodrAhXl. This equation follows from the assumption of uniform density of the water (equal to the output drain) and neglecting variation over time.

Model-based fault detection in a high-pressure heater line 277 Derivation of the dynamic equation for X2. Since mass conservation applies to the mass of water, mw and steam, ms, in the cavity: d(mw + ms) -- Wtur -1- Widr -- Wodr. dt

(10.2)

Again, neglecting the output-drain density variation over time, we have alms dt

-

dxl Wtur + Widr -- Wodr -- P o d r A h dt

As the steam volume can be obtained from the total volume by subtracting the volume of the drain water, and assuming that the steam density equals the saturated steam density, we have ms = (Vh -- AhXl )Psst. Differentiating with respect to the time, and after algebraic manipulation, we obtain dpSStdt -- Vh --1AhXl [ Wtur -'F Widr -- Wodr -- Ah(Podr -- Psst)-'~'-J dxl ]

Using the fact that dpsst

dpsst dx2

dt

dx2 dt

the dynamic equation for x2 may be obtained.

Derivation of the dynamic equation for X3. Now conservation of energy is applied to the subcooled fluid, so obtaining .

dx2

mw dx3 d--T = Widr(hidr -- hodr) + Wcon(hsw - x3) - Wev(hsst - x3) + Vw--~-

Qc

(10.3) from which the dynamics of x3 follow by setting hidr equal to the specific enthalpy of the saturated water at the pressure x2, when the input drain is saturated. The cavity volume Vw = AhXl.

Derivation of the dynamic equation for x4. This equation models the heat exchange in the desuperheating area. Conservation of energy is applied to heat exchange in the desuperheating area: dmf = Wfw(X5 - x4) q- Q~ (10.4) dt where mf and Q~ denote the mass of feedwater and the heat exchange of feedwater in the desuperheating area, respectively. Then, following standard thermodynamic arguments for the heat exchange in the metal of the tube-bundle and denoting Ome, Vme, Pme, Cme as temperature, volume, density, and specific heat of the metal, respectively, we have QtA = QA + VmePmeCmedome d~--

and

dmf dx4 dome dt = m m e Z A - ~ - + VmePmeCme d~T-

278

Thermalpower plant simulation and control

Now, the dynamic equation for x4 can be obtained, assuming that, in the desuperheating area, the temperature of the feedwater coincides with that of the metal. Note that, by definition, we can assume the pressure of the desuperheated steam and the transformation from superheated into saturated steam to be punctiform, so we can write QA = Wtur(htur - hsst), where hsst is the bleeding enthalpy.

Derivation of the dynamic equationfor xs.

Analogous to the derivation for x4, heat exchange in the draining area can be modelled, although that for QB is somewhat more complex. More specifically, we can write QB ---- ~ ' G d ( 6 9d -- od)(eedx' -- 1)

(lO.5)

where Pe is the external circumference of the tubes, [~)d and 6) d are the temperatures in the drainage area and the metal in this area, respectively, and ~9d is a suitable constant dependent on geometrical and thermal quantities related to the tubes, like thermal resistance and conductance, specific heat, and so on.

Derivation of the dynamic equation for x 6. As for xs, heat exchange in the condensing area is modelled, leading to the derivation of a similar relation to QB for Qc. Summing up, from (10.1)-(10.5) we can write the equations that describe the nonlinear dynamics of a single heater: dxl

Widr + Wcon - Wodr - Wev

dt

,OodrA h

dx2 dt

(10.6)

Wtur q- Widr -- Wodr -- (Podr -- Psst)Ah(dxl/dt) (Vh -- AhXl)(dPsst/dx2)

dx3

1

dt

mw

(10.7)

Widr(hidr -- X3) + Wcon(hsw - x3)

dx2

-Wev(hsst - x3) + AhXl--~- -- Qc dx4

Wfw(X5 - x4) -~- QA

dt

LAmme

dx5

Wfw(X6 - x5) -~- QB

dt

LBmme

dx6 dt

Wfw(hfw - x 6 ) + Qc Xlmme

]

(lO.8)

(10.9)

(10.10)

(10.11)

Model-based fault detection in a high-pressure heater line 279 10.2.3

Fault and malfunction modelling

In the following, the main malfunctions that may occur in a line of high-pressure heaters are described and examples of the related dynamics are given. According to technicians expert in power plants, the considered faults are the most frequent ones; moreover, they are of notable interest, as they involve significant operational effects. For example, in order to ascertain a leak in the tube-bundle (see the discussion below), at present, it is necessary to remove the line from the thermal cycle. For such a check, the condensates are completely drained and the pressure in the line is raised, that is, the water coming from the feed pump is made to circulate in the tube-bundle, after checking that no water is contained in any part of the feed-heater cavity. This complex procedure points out the importance of diagnostics that allow the on-line detection of such malfunctions, while the plant follows the cycle of electric-power generation. In the following paragraphs, the three kinds of faults under concern are discussed from a physical viewpoint and, in the case of a plant malfunction, we also describe in some detail the 'physical' modelling of the fault (in the other cases, such a modelling phase is straightforward), in the context of the general model previously developed. This allows us to stress once again the importance of developing an accurate model of the complex system and minimising simplifying hypotheses.

10.2.3.1

Tube bursting inside a high-pressure feed heater

This malfunction causes the feedwater to flow into the external jacket. In the following, we assume that the feedwater reaches the draining area. The most visible effects of this fault concerns the levels and pressures inside the feed heaters. For example, if the burst of a tube occurs in heater 3, an immediate increase in the level in this component follows. This increase will soon be compensated for by the regulation system through a positive variation in the opening of the drainage valve in heater 2 and a possible opening of the valve in the drainage expansion tank, if the level moves too far from the set-point value. Moreover, the system will decrease the rate of flow of the water in heater 4 before the water reaches the boiler. The decrease will activate the system that controls the level of the drum: this system will request a higher rate of flow from the feed pumps located at the rear of the line of high-pressure heaters. As long as the control system does not succeed in compensating for the variation in the rate of flow, the reduction in flow through feed heater 4 will decrease the capability of the feedwater to cool the steam bled from the turbine. Therefore, a smaller amount of steam will condense, with two main consequences: (1) it will cause the internal pressure to rise, thus reducing the steam bled from the turbine (the pressure and the amount of steam are regulated through the fall in pressure between the turbine stage and the heater); (2) a regulator loop will close the drainage valves in heater 3 (these valves keep the level at the set-point value). Therefore, the malfunction has no consequences that can be interpreted immediately: in the feed heater where the burst tube occurred and in the upstream ones, the levels tend to rise, whereas in the downstream heaters, the levels tend to fall; the opposite occurs for pressure. Moreover, such behaviour may involve measure variations that are comparable with those recorded during normal functioning, and that may be caused, for example, by

280

Thermal power plant simulation and control

a variation in the load on the turbine. This makes the task of a diagnostic instrument particularly difficult. It is worth noting that the detection of a malfunction is not associated with a decrease in the rate of flow of the feedwater, as such a decrease is rapidly compensated for by the control system of the drum. In order to model the system behaviour when the burst of a tube occurs inside a feed beater, it is necessary to act directly on the equations that describe the dynamics of the system. In particular, we can immediately notice that the flow of the feedwater is not constant along the tube-bundle. If we denote Wfw~nand Wfwout as the input and output flows of the heater where the leaking tube occurred, we can write Wfwin m_ Wfwout + Wleak

where Wleak denotes the flow of the fluid coming out of the tube-bundle. As the tube bursts inside the heater, the flow Wleak can be calculated by considering the fall in water pressure while passing from the bundle into the cavity, as follows: Wleak m_ Y V ~ f w -- x2

(10.12)

where Pfw is the pressure of the feedwater at the input of the tube-bundle (this pressure

is assumed to be approximately equal to the pressure at the fault point) and x2 is the pressure inside the heater. For a given fall in pressure, the multiplicative factor g defines the ratio of fluid coming out of the tube bundle versus the percentage of fluid flowing in the tube-bundle before reaching the fault point. Under the assumption that the burst of the tube occurred in the condensation area so that all the fluid coming out of the tube bundle flows in the drainage area, we can describe the liquid level dynamics inside the heater as dxl

Widr + Wcon -- Wodr -- Wev

WlWak

dt

PodrAh

PodrAh

where WleWakis the flow of the water from the tube-bundle. If we assume that the fluid,

once it has left the tube-bundle, becomes saturated, the flow WleWakcan be calculated as follows: Wl~ak ~---(1 - Xleak)Wleak

and hence Xleak --

hleak -- hsw hsst - hsw

where hleak coincides with x6, i.e. the enthalpy of the feedwater in the subcooled area. Taking into account the term describing the fluid coming out of the tube-bundle, from the mass conservation equation we can describe the dynamics of the pressure inside

Model-based fault detection in a high-pressure heater line 281 the heater as dx2 dt

Wleak = Wtur + Widr -- Wodr -- (Podr -- Psst)Ah(dXl/dt) + (Vh -- AhXl)(dpsst/dx2) (Vh -- AhXl)(dpsst/dx2)

The enthalpy of the water coming out of the heater includes the contribution from the water exiting the tube bundle and flowing into the drainage area dx3 dt

-

-

1 F /Widr(hidr -- x3) + Wcon(hsw - x3) - Wev(hsst - x3)

mw

I

dx2 +AhXl ~

w w 7 Q c + Wleak • (hleak -- X3)

J

where /hleak hlea k w = {[hsw

if Xleak ~ 0 if Xleak > O.

Finally, we can derive the equations for the enthalpies of the feedwater in the drainage area and in the condensation area, taking into account that the flow in the tube-bundle is no longer Wfw, but is Wfw - Wleak, SO that dx4

(Wfw - Wleak)(X5 -- X4) + QA

dt

LAmme

dx5

(Wfw - Wleak)(X6 -- x5) + QB

dt

LBmme

The above modifications were inserted in the plant model and some simulations of the considered plant malfunction have been performed. More specifically, consider again equation (10.12): y = 0 implies the absence of leaks, so an increase in y, under the same operating conditions, means an increase in the leakage flow. In particular, three different leak speeds were simulated: y = 0.01, y = 0.03, 2 / = 0.05, as indicated in Figure 10.5. For example in Figure 10.5c, consistent with the above discussion, after an initial transient due to the initialisation of the simulation, note that a feedwater leak in the tube-bundle of heater 3 causes a fast increase in condensate level. The draining valve linking heater 2 then opens, with an increase in the condensate level of heater 2 and, in turn, in heater 1. At the same time, the feedwater flow toward heater 4 decreases due to the leak, until the pump system is able to restore the feedwater flow. Thus the cooling capabilities of heater 4 are reduced, the pressure in heater 4 rises and the steam spillover falls, as does the condensate level. To sum up, a feedwater leak in the tube-bundle of a heater causes a decrease in the levels of the downstream heaters and an increase in the faulty heater and those upstream. It is worth noting that a similar malfunction due to a leakage with Y = 0.05 results in a quite different behaviour in heaters 1 and 3, respectively. This difference arises from the position of the two heaters in the high-pressure line, as the effect of a fault in heater 1 propagates much less than the corresponding leak in heater 3.

282

Thermal power plant simulation and control -66

--

Heater 1

---

Heater2

-

- 66.5 -67 -67.5

....

Heater 3

.....

Heater 4

g -68 2 -68.5 "~

-69

O

c..) -69.5 -70 -70.5 -71 0

20

40

60

8L0 Time (s)

100

120

140

160

~9 -

Heater 1

---

Heater2

....

Heater 3

.....

Heater 4

-

~59.2

E

-69.4

E

I I

-69.6

t.-

~9.8

-70

-70.2 b

Figure 10.5

I

i

i

i

i

i

i

i

20

40

60

80 Time (s)

100

120

140

160

Condensate levels o f heaters 1, 2, 3 and 4 due to a plant malfunction is (a) heater 1 with y = 0.05, (b) heater 2 with y = 0.01, (c) heater 3 with y = 0.04 and (d) heater 4 with y = 0.03

Model-based fault detection in a high-pressure heater line

283

-66 I1.

-66.5

1 -67 ,'~ ~67.5 .~

--

Heater 1

---

Heater2

....

Heater 3

.....

Heater 4

\

-68

I' r

-68.5

\" \.

-69 o

i

--

i~

i

-69.5

~ ' - ~ . . .

-70 -70.5 -71 0

20

40

60

80

100

120

140

160

Time (s)

-67 Heater 1 -67.5 -68 E

g

---

Heater2

....

Heater 3

.....

Heater 4

-68.5

"/! ~

-69

IJ ~

• i,'~

""-..

=o -69.5

I'/L/-'-~:

-70

.....

V

-70.5 -71 0

Figure I0.5

_--_

20

40

60

80 Time (s)

100'

i

I

120

140

160

Condensate levels of heaters 1, 2, 3 and 4 due to a plant malfunction in (a) heater 1 with )/ = 0.05, (b) heater 2 with y = 0.01, (c) heater 3 with y = 0.05, and (d) heater 4 with y = 0.03 (continued)

284

Thermal power plant simulation and control

10.2.3.2

Fault or m a l f u n c t i o n o f a valve

This type of malfunction may affect one of the valves that regulates the drainage flow between two heaters, or between a heater and the recovery cavity, i.e. the drainage expansion tank, the condenser, or the degasser. Like the previous malfunction, the malfunction of a valve affects the levels and pressures inside the heaters, and involves other quantities, too. A typical valve malfunction is a position block or jamming, which occurs when the actuator no longer responds to the control signals sent by the regulator. The position of the actuator may be locked in three different ways: in the same position as when the fault happens, completely open, and completely closed. Figure 10.6b shows the effect of a position block on the drainage valve of heater 2 (i.e. D2 in Figure 10.2). In practice, this means that, from the instant at which the fault occurred, the role of the drainage outflow will remain constant and equal to the rate just before the position block (the pressure in the cavity, in the drainage expansion tank and in heater 2 being the same). If, at that instant, the level was below the set-point value, the actuator position will be such as to make the level rise. But this rise will continue even after the level has risen above the set-point value. As a consequence, one will notice a ramp with a positive slope in the measure of the level in heater 2 (see Figure 10.6b). The regulator feedforward action will open the drainage valve in heater 3, thus decreasing the level inside this heater. Moreover, as soon as the level falls below the set-point value, the feedback regulator will control the valve in such a way as to bring the level back to the value desired. Note that, if the actuator is blocked after the transients have occurred, as in Figure 10.6a and b, the actuator position will be very close to the steady-state one, as, under such conditions, the actuators oscillate with little overshoot as compared with the largest variations. As a consequence, the effects of the block will show themselves slowly and, over a non-negligible time interval, simulated system behaviour will not differ from before. Let us now describe the simulations of such faults in heaters 3 and 4. Figure 10.6c shows what happens when the valve D3 breaks in open position. In this case, a loss of liquid occurs and the condensate level of heater 3 falls instead of rising like in the other simulation runs of Figure 10.6. Figure 10.6d shows how the condensate levels of the heaters vary when a locked position of D4 is simulated. Consistent with the above general discussion, observe that when the draining fault from heater 4 towards heater 3 occurs, the level of heater 4 increases after temporarily falling beneath the set-point value. Then, due to the feedforward action of the regulator, the level of heater 3 decreases until it becomes lower than its set-point value, giving rise to the action of the regulator, which stabilises around the desired value.

10.2.3.3

Malfunction of a sensor

A sensor malfunction may affect the level sensors as well as the temperature, pressure or flow sensors. In particular, the malfunction of a level sensor is very significant, in that the control of each heater is based just on the level measure. In order to better understand the problem above, let us assume that the level in heater 3 is - 7 0 mm versus the nominal height of 4.095 m for the subcooling area. The controller will utilise a relative level measure, i.e. the level measured with the reference to the nominal value, specified for each heater on the basis of optimal performance

Model-based fault detection in a high-pressure heater line 285 -67 --67.5 •

Heater 1 -

-

-

-

Heater2 Heater 3

-68

•~ - 6 8 . 5 O

69

-69.5

-70

-70.5

20

40

60

a

80 Time (s)

100

120

140

160

-64 -

Heater 1

-

--.

-65

•

-

-

....

Heater2 Heater 3 Heater 4

pSSSJsjs

-66

-67

./

68

~

-69

-70

0 b

Figure 10.6

I

I

l

20

40

60

I

80

100

120

I

140

160

Time (s)

Condensate levels of heaters 1, 2, 3 and 4 due to a locked position of actuators: (a) El, (b) D2, (c) D3 and (d) D4

considerations. This measurement is subtracted from the value - 7 0 mm and given as reference error to the PI controller. If y is the relative level measure of the sensor, yd the level desired, and e the input error to the PI block, we can write e = y _ y d . Therefore, if the relative error was - 6 5 mm, the PI regulator will see a positive input error equal to + 5 mm, and will tend to open the valve, thus decreasing the level in the heater. However, if the sensor had introduced (due to a malfunction) a measure affected by an

286

Thermal power plant simulation and control

. . . . .

~" - 1 0 0 I --

Heater Heater Heater Heater

-

• -....

\

1 2 3 4

-150 I

i

-200 0

20

10

40

C

i0

i

i

i

8 Time (s)

100

120

140

t

160

20 °o. • o

0 .....

-20

Heater 1 Heater 2

E E

Heater 3 Heater 4

-40

-60

-80

,,,\ \

-100

-120 / 0 d

Figure 10.6

20'

4 'o

]..-~

/ f-

\

/

6b

80 ' Time (s)

_

100 '

1~ 0

140 '

160 '

Condensate levels of heaters 1, 2, 3 and 4 due to a locked position of actuators: (a) El, (b) D2, (c) D3 and (d) D4 (continued)

Model-based fault detection in a high-pressure heater line 287 offset, for example, of - 10 mm versus the actual relative level, the PI regulator would have received the input difference e = ~ - yd = --75 -- (--70) = --5 mm, where is the relative measure affected by the offset. Accordingly, the regulator would have closed the valve, thus increasing the level in the heater up to a relative position of - 7 0 mm; in this situation, ~ = - 7 0 mm and e = 0. In practice, what happened is equivalent to the operation of changing the set-point by + 1 0 mm. If e is the offset introduced by the malfunction we have e = (y + e)

-

yd

=

y

_

(yd

_

~,)

Therefore, the system evolves as if the relative value desired were not equal to yd but to (yd _ e). As to the simulation of sensor faults, additive errors on the measures provided by the level sensors were simulated: the errors were set at 30 mm, - 3 0 mm, 60 mm, - 6 0 mm, 90 mm, and - 9 0 mm. It is worth noting again that this type of fault is entirely equivalent to a variation (of equal magnitude but opposite in sign) in the level set-point. Thus a sensor malfunction stresses the action of the regulators, until steady-state conditions are reached, as depicted in Figure 10.7.

Remark 1. The simulation results suggest that it is possible to detect the occurrence of plant faults by properly processing the measured signals. Moreover, the plant technicians can predict typical system behaviour for the various kinds of faults. The model described in this section can be used to generate the outputs of the measurable variables and to compare them with the outputs of the plant affected by the fault. Warning signals, can then be generated after comparison with threshold levels. The behaviour of the condensate levels and other measurable state variables, such as the pressure of each heater, appear strongly correlated with the kind of fault acting on the system. Then it is easy enough to fix thresholds and design a decision logic for fault recognition. The complexity of the decision logic depends on the number of faults to be detected and on the experience in plant operation. Of course, both threshold signals and the decision logic need proper adjustments to reduce false alarms. Clearly, it is important to construct the model as accurately as possible, which will be the subject of the next section.

10.3

Grey-box modelling and identification of a power plant

In this section, we will consider the problem of refining the non-linear model of a plant like that presented in section 10.2. This task will be accomplished by means of an identification method based on stochastic approximation. We will refer to a discretetime representation of the above-described model, which can be easily obtained by applying standard techniques for numerical discretisation of continuous-time systems. Moreover, for the sake of clarity, the presentation of the identification method will be initially non-specific and only later on will it be specialised to the considered power plant.

288

Thermal power plant simulation and control -60

t

-65

-70 E

g

t~

I ,t

-75

~

I

-80

Heater 1

I ~

-

-

-

-

....

-85

H e a t e r

2

Heater 3 Heater 4

--

o

-90

-95

-100

I

0

20

40

60

i

i

L

i

J

80 Time (s)

100

120

140

160

0 Heater 1 - - - Heater 2 -

I -20

• \ -

--

....

~"

/

o

4o

i),

-80

t.-

\

/

/ I

-140

-

0

Figure 10. 7

~ "

."'"---Z

, " ~

-120

Heater 3 Heater 4

20

40

~

,

,

,

,

60

80 Time (s)

100

120

140

160

Condensate levels of heaters 1, 2, 3 and 4 due to (a) an additive fault of - 2 0 mm on the level sensor of heater 2; (b) an additive fault of +60 mm on the level sensor of heater 3

Model-based fault detection in a high-pressure heater line 10.3.1

289

A general approach to grey-box identification o f a plant

Consider a discrete global model of a plant whose dynamics can be described by the following equations: Xt+l

:

f ( x t , Ut)

E : I yt = h ( x t )

(10.13)

where xt represents the state vector, ut represents the input vector, and Yt represents the vector of measurable variables. Unfortunately, when large complex plants are considered, the above model generally includes a significant number of simplifying hypotheses regarding the mathematical structures of individual blocks and the values of particular parameters. In many cases, the large variations in the plant over time may give rise to non-negligible errors in some model subsystems. Therefore, despite the intrinsic complexity of the plant, it would be useful to employ techniques that make it possible to reduce modelling errors. Such techniques would allow the development of a more accurate model that might be simulated in parallel with the plant, with obvious advantages for supervision tasks. More specifically, consistent with the grey-box approach, we consider two main types of uncertainty affecting the model: (i) uncertainties in the mathematical structure and (ii) uncertainties in parameter values. The uncertainties in the mathematical structure can be represented by using a set of unknown functions y J ( f c J ) , j = 1. . . . . M, where M represents the number of subsystems characterised by a partially/totally unknown structure, and $:J is the part of the state vector corresponding to the j-th section. As far as (ii) is concerned, the vector # contains all the unknown mathematical and physical parameters. Thus, we obtain the following approximate model to be identified: : /~t+l = f(Yct, ut, O)

(10.14)

[ ~, = h(~,, O) where f and/~ implicitly depend on yJ(YcJ), j = 1. . . . . M, Xt A_~COI(.~]. . . . . .~M). NOW, in order to identify the model (10.14), for a given initial state and a given time instant t, we define the following cost function t

j t ( y l . . . . . yM, #) :

y~

IlYi -- Yi II2

(10.15)

i=t-N

where N is the size of the time window and P is a given positive definite matrix. The identification problem can be stated as the following parametric-functional optimisation problem.

290

Thermal power plant simulation and control

Problem 1. At time t, find the optimal functions y 1°, . . . . y M° and the optimal parameter set 0 °, such that the cost (10.15) is minimised for every possible set of measures Yt-N, . . . , Yt. Clearly, the general assumptions under which Problem 1 has been stated prevent us from solving it in an analytical way. Actually, Problem 1 entails the solution of non-linear functional optimisation problems. Our approach consists of assigning the unknown functions defined in Problem 1 for which a certain number of parameters have to be determined in order to minimise cost. In particular, the functions ), j (~J) are approximated by parametrised functions of the form ~J (.~J, wj), j = 1. . . . . M, where ~J is the input/output mapping of a multilayer feedforward neural network and w j is a vector of parameters to be selected. Among various possible approaches, we have chosen non-linear approximators based on feedforward neural networks, as these approximators are computationally easy to handle, and, above all, exhibit powerful approximating capabilities (Barron, 1993). A Now, the vector w = col(w j, j = 1. . . . . M) represents the weight vectors of all the neural networks approximating the unknown functional parts of the model. As a result, if 13 ~ col(w, 0) is the total parameter vector, we require the following approximate parametric model to be identified: [-~t+l 7 f ( x t , ut,/3) f~ : 1~, = h(~,,/3~.

(10.16)

Accordingly, the cost function takes on the form

Jt(~):

Z

IlYi--YiII2P

(lO.17)

i=t-N

Hence, we have the following

Problem 2. At time t, find the optimal value of the parameter/3°, such that the cost function (10.17) is minimised for every possible set of measures Y t - u . . . . . Yt"

Problem 1 has been reduced to the parametric optimisation Problem 2, and, in the next section, we present an algorithm to solve it in an approximate way. 10.3.2

A solution method via the simultaneous perturbation stochastic approximation algorithm

The data samples provided by the available sensors and of the other accessible signals of the plant may be used for the on-line estimation of the vector/3. This can be done by applying a descent algorithm. However, for the aforesaid reasons, the exact

Model-based fault detection in a high-pressure heater line 291

Figure 10.8

Scheme of the tuning algorithm

gradient of the expected cost cannot be computed, and hence a stochastic approximation approach has to be followed. We chose the smoothed simultaneous perturbation stochastic approximation (Spall and Cristion, 1994). In the following, the most significant features of this algorithm will be summarised for the reader's convenience (see Figure 10.8). The algorithm can be written as

flk=flk-l--akGk,

k=0,1 ....

(10.18)

where Gk is a smoothed approximation to gk (ilk) ix V# k E (Jk+N) of the form

Gg = pkGk-I + (1

-

Pk)gk(flk-1),

GO = 0

(10.19)

where gk is the so-called simultaneous perturbation approximation to gk (see Spall, 1992, for the original definition of the unsmoothed simultaneous perturbation technique). More specifically, the l-th component of gk(/~k-1) is given by gkl(flk-1)

--

?(+)

^(-)

~k+N

-- Jk+N

2ck Akl ^(-)

(10.20)

^(+)

where Jk+N and Jk+N are two observations corresponding to the parameter perturbations [Jk -- CkAkotk and ~1k + ck AkOtk, respectively. Akt are suitable random variables and {Ck} is a sequence of positive scalars that satisfy some regularity conditions (Spall, 1992; Spall and Cristion, 1994). The use of the smoothed SPSA algorithm, instead of standard finite difference stochastic approximation (FDSA) techniques, is motivated by the fact that only two perturbations are needed, instead of the 2p perturbations necessary for the computation of the approximation to g~ (p = dim(fl)). Analogous stochastic convergence properties are however maintained. The fundamental computational advantage is of basic importance, given the large number of parameters to be estimated, which represents a common characteristic of neural network training.

292

Thermal power plant simulation and control

10.3.3

Grey-box modelling and identification of the high-pressure heater line

The complex model described in section 10.2 includes a large number of simplifying hypotheses about both the mathematical structures of some blocks and the values of different parameters. In many cases, the large variations plant behaviour over time may give rise to non-negligible errors in some model subsystems that cannot be accessed by the available sensors. Therefore, it would be very useful to employ the technique presented in section 10.3.2 in order to reduce the aforesaid uncertainty during the plant operation. In this respect, consider the global scheme in Figure 10.9. Such a scheme includes sections that are specific for the plant model considered, but that do not affect the generality of the proposed methodology, as previously stressed. Hence two main types of uncertainty affecting the developed model are considered:

1. Uncertainties in the mathematical structure. For example, the quantities related to

2.

the other parts of the power plant have been assumed to be proportional to unit load. This assumption may turn out to be very simplistic. Other approximations about the mathematical structure are inherent in the use of steam tables and in the various transformation functions. In Figure 10.9, we refer to completely unknown and approximately known structures. The former are effectively black-box models, while the latter are made of known and unknown subblocks. This classification framework is very useful in the application considered here and may also have general applicability. Uncertainties in parameter values. For example, we have used thermodynamic constants and geometrical parameters that are not known with precision and that

d* .

yr I

l

xl

•

Matrix

ym I

X1

X x SS

Block with known structure and known parameters

I ~

~,~1

Block with uncertain paramete~

Figure 10.9 Scheme of the global grey-box model

Block with approximately known structure

Unknown block

Model-based fault detection in a high-pressure heater line 293 may vary during the plant operation (e.g. pipe diameters, thermal capacities of the various metals used, etc.). Furthermore, the model includes several non-linearities placed in the different blocks depicted in Figure 10.9, which make it necessary to use the tuning algorithm presented in sections 10.3.1 and 10.3.2. The list of the above non-linearities for each block include as follows:

Input block: load saturation; Sensors block: water level saturation; Regulator block: anti-wind-up action and control saturation; Actuators block: rate limiters and saturation; Elaboration block: square-root functions in the output feedwater sections; Transformation block: steam tables and square-root functions in the output feedwater sections. By replacing all the parts affected by uncertain functioning with neural networks, A one obtains a model like (10.16), where x = col(x/, x A, x s) represents the state A vector (dim(x) = 71), y = col(y m, yr) represents the vector of the measurable variables (dim(y) = 34), w is the total vector of the synaptic weights of all the neural networks, and 0 is the vector of the unknown mathematical and physical parameters. Gugliemi et al. (1995) list the parameters (i.e. the components of the vector 0), together with their approximate values based on the expertise of plant technicians. As clearly stated in section 10.3.1, two distinct types of quantities have been identified, which have to be estimated on the basis of the measures provided by the available sensors of the plant: (i) parameters of the model parts whose mathematical structures are assumed to be accurate enough, and (ii) synaptic weights of the neural networks that describe the model parts whose mathematical structures are very approximate. The simulator on which the global model (including the neural networks) has been implemented can be connected to the FIP (Fieldbus Internet Protocol) automation system of the power plant (Alessandri and Parisini, 1997). This allows the on-line tuning of the model parameters. However, inaccessible model parts can be estimated to a reasonable accuracy by the proposed tuning method only via simulation. Therefore, we have developed an emulator of the physical model validated against the real plant. Such a simulated model has then been regarded as a real system, thus allowing one to measure even the inaccessible internal model pans. In parallel, we have developed an analogous model whose parameters had yet to be tuned. We aimed to ascertain if the proposed methodology makes it possible to tune the model parameters and if the internal parts are estimated correctly. More specifically, the actuators, the steam tables and enthalpy-temperature conversion have been modelled by means of neural networks. In addition, the heights in the desuperheating areas have been estimated as unknown parameters. For the actuators, we used neural networks with two input units, four hidden units and one

294

Thermal power plant simulation and control

output unit; for the steam table, we used neural networks with 10 input units, 20 hidden units and 10 output units; for the table of the enthalpy-temperature conversion, we used neural networks with eight input units, 15 hidden units and four output units. As to the cost function (10.17), we chose experimentally N ----- 1 and P = 0.1 x I , where I is the identity matrix. For the parameters of the smoothed SPSA algorithm, we chose ak = 0.O04/k 0"602, ck = 0 . 6 / k 0"101, and Pk = 0.5/k°'6°3; the scalars Otk were suitably chosen according to the magnitude of the a priori estimated values of the corresponding parameters. We assumed the perturbations Aki to be Bernoulli -4-0.5 distributed, so guaranteeing the fulfilment of the main regularity assumptions made by Spall and Cristion (1994). The effectiveness of the method can be seen in Figures 10.10 and 10.11. Figure 10.10 gives the behaviour of four estimated parameters, i.e. the height in the desuperheating areas for the four heaters. As can be seen, for all four heaters, satisfactory convergence of the parameters to their true constant values were obtained after only 250 iteration steps. Figure 10.11 shows the norm of the error in the state variables between the 'real' simulated plant and the model approximation. Moreover, Figure 10.12 shows a comparison between the actual behaviour of the

Heater 2

Heater 1

2.5

j

2.5

f

f

2 1.5

2 ~'~ 1.5

1

1

50

100 150 Iterationstep

200

Heater 3

3.5

# 50

2.9

2.5

2.8

2

2.7

I

.

Figure 10.10

50

100 150 Iterationstep

200

200

Heater 4

3

3

0

100 150 Iterationstep

0

50

.

.

i

.

100 150 Iterationstep

Estimation of the heights of the desuperheating areas

200

Model-based fault detection in a high-pressure heater line f

i

i

i

295

i

5.5

e@

x__

4.5 0

Figure 10.11

100

200

300

400

500 600 Iteration step

700

80

9 0

1000

Behaviour of the estimation error during the learning procedure

water level in the condensing area and the estimated value in heater 1, after 1,000 iteration steps. As a concluding remark, it is important to emphasise that an accurate non-linear model like the one developed so far could be very helpful to monitor on-line state variables that are significant in terms of fault diagnosis. However, the on-line simulation and tuning of such a complex dynamic model may not be feasible in some power plant automation systems. Therefore, a technique which can provide such estimates would be very useful. In this respect, in the next section, a moving-horizon estimation algorithm will be presented.

10.4

A general approach to receding-horizon estimation for non-linear systems

This section presents an approach to estimation that is well suited to the plant described in section 10.2. Specifically, here we focus on the problem of estimating the state variables for a single heater (Alessandri et al., 2002).

10.4.1

Problem statement

We refer to the state estimation methodology presented by Alessandri et al. (1997). Let us consider the discrete-time system

Xt+l : f ( x t , Ut, ~t),

t = 0, 1 . . . .

(10.21)

296

Thermal power plant simulation and control

-lO -20

E E

-30 -40

e~

-50

\

o

-60 -70 -80

i

0

i

10

15 Time (s)

i

i

20

25

30

786 785 784

783 ~

782

~

781 780 779 778 0

b

Figure 10.12

' 5

i

i

i

i

10

15 Time (s)

20

25

30

Comparison between the predicted (dashed line) and true (continuous line) behaviour of the condensate level in heater 1 (a), specific enthalpy of output feedwater in heater 1 (b), temperature of output feedwater in heater 2 (c), and spillover temperature in heater 4 (d)

Model-based fault detection in a high-pressure heater line 297 200

I

I

2~0

25 '

180 160 140

I/11//////"/ I

o~120 i 100

J

~ 8o 60 40 20 0

0

/! / / I 5

1'0

15 ' Time (s)

30

450 400 350

//

3OO

77/

o

250 ~200 150 100 50

o d Figure 10.12

I

I

I

I

L

i

5

10

15 Time (s)

20

25

30

Comparison between the predicted (dashed line) and true (continuous line) behaviour of the condensate level in heater 1 (a), specific enthalpy of output feedwater in heater 1 (b), temperature of output feedwater in heater 2 (c), and spillover temperature in heater 4 (d) (continued)

298

Thermal p o w e r plant simulation and control

where xt E X C 1~ n is the state vector (the initial state x0 6 X0 C 1Rn is unknown), t/t E U C ]1~m is the control vector, and ~t 6 ~ C ~q the random noise vector. The state vector is observed through the noisy measurement equation Yt = h ( x t , / / t ) ,

t = 0, 1 . . . .

(10.22)

where Yt E Y C II~p is the observation vector and 1/t 6 H C ~[~r is the random measurement noise vector. The random vectors x0, ~t, and I/t are defined on suitable probability spaces. We assume the statistics of these random noises to be unknown. Consequently, our approach has to be statistical, and this leads us to take the classical least squares approach. Moreover, the model estimates are based on recent data, or, equivalently, the estimator has a finite memory. To this end, we introduce the following general estimation cost, which can be regarded as a non-quadratic generalisation of the classical least squares loss function t

¢P[IIYi-h(.ffit, it)H]

s,= x i=t-N t

t

E v.,[Xit--f(Jgi-l,t,lli-l,~i--l,t)}

+Z i=t-N

i=t-N+l

t-I

+

E

~ r l ( ~it ) ,

t=N,N+I

(10.23)

....

i=t-N

where N > 1 is the number of measurements made within a 'sliding window' [t - N, t], and :tit, ~it, and 11it are the estimates of xi, $,i, and ~i determined at the instant t, respectively, on the basis of the measures Y t - N , " " , Yt, of the controls Ut-N . . . . . Ut-1, and of the 'prediction' i ' t - U = Xt-N,t-1. X(Z), ~O(Z), qgl(Z), ~P(Z), and ~Pl(z) are increasing functions for z _> 0, with X(0) = ~p(0) = ~0i(0) = ~(0) = ~Pl (0) = 0. The functions X, ~o, ~ , ~01, and ~1 have to be regarded as penalty functions by which we express our beliefs in the prediction -~t-N, in the observation model, in the state equation model, and in the magnitudes of the measurement and process noise, respectively. All these functions are assumed to be sufficiently smooth (class C 3) enabling application of the proposed method (Alessandri et al., 1997). Let us define the information vector

I N A col(.~t_U, Y t - N . . . . . A

^o

Yt, Ut-N .....

t = N, N + 1 . . . .

Ut-1), o

(10.24)

where 2~_ N = X t _ N , t _ 1 denotes the prediction o f x t _ N. Of course, :78 = X0,N-i : -~0 denotes an a priori prediction. The estimation procedure performs as follows. At the time instant t, the state esti^o N mates Xit are computed on the basis of I t . Note that, up to this time instant, N + 1 state estimates have been computed, but only YCt_N+I, t is retained for the next estimates. When the measures Yt+l and ut become available, we can refer to the new information vector I N 1 = col (.i';_N+l, Y t - u + ' . . . . . Y t + I ' U t - N + I . . . . . Ut) and generate the new estimates 3gi°,t+l . The same mechanism is used at the successive stages.

Model-based fault detection in a high-pressure heater line

X0- [--'7"1Xl

x~(~

Yl

~N-l

299

T XN

?IN~

YN

|

A XO~~/A ~ '

I

tll

Figure 10.13

"~ICN~_~ ~N

Structure of the neural estimator

A possible way to determine the optimal estimates consists in solving on-line, at any temporal stage, a non-linear programming problem of which (for the specific information vector I N acquired at time t) -tit, ~it, and ~it constitute the optimal solution. Clearly, this approach entails a heavy on-line computational load, which may turn out to be unacceptable, as pointed out by Alessandri et al. (2002), where a different approach is proposed. Instead of the optimal vectors J i t , ~ i°t, and qit, we want to determine the optimal functions ait (.), bit (.), and cit (.), which determine the values ° f xit, ~it, and ~it, respectively. Such functions have to be derived off-line and stored in the estimator's memory so as to generate the optimal estimates almost instantly. The estimators characterised by this computation property will be called 'estimation functions' throughout the chapter. Alessandri et al. (2002), simplified structures of these estimation functions. More specifically, we have to solve the following. P r o b l e m 3.

At any stage t = N, N + 1 . . . . . find the optimal estimation functions

^o Xt-N,t

^o = a to- N , t ~t i Nt. J'~ ~ °it = b Oi tt~: '.toi t , Y i. +t l , u ti - 1 ) , i = t - N , " ' ' ' t - l, andllit = c°t(x°t, Yi), i = t -- N . . . . . t, that minimise cost (10.23) under constraints (10.21). The minimisations are linked sequentially by the optimal predictions -o

^o

^o

Xt_ N = f(Xt_N_l,t_

t=N+I,N+2

1, U t - N - I ,

~t-N-l,t-1),

. . . . ; x- oo = f ¢ O C XO.

Of course, the other optimal state estimation functions within the window [t - N, t] ^o

^o

^o

are simply given by X i + l , t = f ( x i t , lgi, ~ i t ) , i ---- t - N . . . . . t - I. For this reason, we have not addressed these functions in Problem 3. The resulting estimation scheme for the neural estimator at t ---- N is depicted in Figure 10.13, where the vectors ui are omitted for the sake of simplicity. 10.4.2

A m e t h o d to f i n d approximate solutions

Deriving analytically the solution for Problem 3 is, in general, an almost impossible task. Instead we shall resort to an approximation technique that consists in assigning

300

Thermal p o w e r plant simulation and control

u~-l),

o N o ^o t and given structures to the estimation functions at_N,t(It ), bit(xit, Yi+I, ci°t ('¢ci°t, Yi)" In such structures, a certain number of parameters must be determined in order to minimise the estimation cost. More specifically, we constrain the estimation functions to take on fixed structures of the form

it_N,

t :

~it

=

(10.25)

~ l ( l N , lOta N , t )

[~(iit,

Y it+ l '

Uit - I '

~iit : c ( i i t , Yi, wCt),

w/bt),

i = t-- X,.

""'

i = t - N ..... t

t-

1

(10.26) (10.27)

where Wt_u, a t, Wbit, i = t - - N . . . . . t - - l, and wCt, i = t - N . . . . . t, are the vectors of the parameters to be optimised. In the approximate estimation functions, the information vector I ~ replaces I ~ (see (10.24)). Actually, in such functions the predictions 2 t - U in general differ from the optimal ones i t _ N ; then we have iN A col(i,_N, ~ t-1 = Y t - N ' Ut-N)" If we now substitute (10.21), (10.25), (10.26) and (10.27) into (10.23), the cost

_ t-I function takes on the form Jt(wt, i t - N , Y t - N ' U t - N ),,' where wt =A col(lOt_N,t, c ). As to the optimisation of the approximate llOtb- N , t ' " ' ' ' 10bt - l , t ' llOtc- N , t . . . . . lIJ tt estimation functions, we may distinguish between two situations: (1) optimisation at stage N, and (2) optimisation at stages t = N + 1, N ÷ 2 . . . . . In the former situation, since we have assumed the statistics of the primitive random variables to be unknown, it may be reasonable to regard them as random variables uniformly distributed on the compact sets from which they take their values. Then it is possible to compute the expected value of the cost JN(WN, :20, y~V, uN-1) and to minimise this expected cost with respect to YON (of course, if the statistics are known, one can take a correct average). In the same way, since we have to eliminate the dependence of the optimal value of WN on the control vector u N - l , we may also interpret u~v - l as random variables uniformly distributed on U N and compute the average of JN with respect to them. To sum up, at stage N, a parameter vector WN has been computed (somewhat arbitrarily), and the (provisional) estimators of the form (10.25), (10.26) and (10.27) have turned out to be available, hence the estimation process may begin. Then we can go on and consider stages t = N + 1, N ÷ 2 . . . . where the estimation functions can be improved on the basis of the data (i.e. measures and controls) that become available. Consequently, OFI and ONT procedures can be defined (Figure 10.14).

Off-line initialisation (OFI) procedure. Find the vector W°N that minimises the expected cost E -

N

N-1

Ju(Wu, io, y~,

UOV-1).

x o , y o ,u o

Clearly, due to the introduction of the fixed-structure estimation functions (10.25), (10.26) and (10.27), Problem 3 has been approximated, at stage N, to an unconstrained non-linear programming problem that can be solved by some descent algorithm. We

Model-based fault detection in a high-pressure heater line 301 Patterns y N(0), u N- ~(0)

o

N

t y~(|), ff NO-I(1)

0

~

N

t

Pattern Y t - N , Ut N

0

N

t

01

N N+ 1 t-N ONT procedure

OFI procedure

Figure 10.14

t~

The OFI and ONT procedures

focus our attention here on gradient algorithms mainly for their simplicity (as we shall see, this will enable us to introduce the concept of 'stochastic approximation' in a straightforward way). For our problem, the gradient algorithm can be written as follows l O N ( k + l ) : iON(k)--OtVWN

E

JN[ION(k),xo, yI~,uN-1],

k : 0 , 1. . . .

N N-I X o , y o ,U o

(10.28)

where ot is a positive constant step-size and k denotes the iteration step of the descent procedure. However, due to the general statement of the problem, we are unable to express

E -

N

JN[ION(k),xo, y N , u N-' ] N-I

xo,Yo ,u o

in explicit form. This leads us to compute the 'realisation' VwN JN[WN(k), x0(k), y ~ (k), u~v (k)] instead of the gradient expression appearing in (10.28). Then, in lieu of (10.28), we consider the updating algorithm

ION(k+1) ~- ION(k)--ot(k)VwuJN[iON(k), J:0(k), yU(k), u U - l ( k ) ] ,

k = 0, 1 . . . . (10.29) where the sequence {xo(k), yU(k), u~v - I (k), k = 0, 1. . . . } is generated randomly on the basis of the above-mentioned uniform probability density functions. R e m a r k 2. The probabilistic algorithm (10.29) belongs to the class of 'stochastic approximation' algorithms. Sufficient conditions for the convergence of these algorithms can be found, for example, in Polyak and Tsypkin (1973) and Benveniste et al. (1990). Some of these conditions are related to the decreasing behaviour required for the step-size or(k) (in the example given in section 10.4.3, we take (k) = Cl/(C2 + k), cl, c2 > 0, which satisfies such conditions). The other conditions

302

Thermal power plant simulation and control

are related to the shape of the cost surface. In general, such conditions are 'local' and may be unneccessary in the present situation, as our cost surfaces will always be multimodal, since we shall choose feedforward neural networks for the structures of the estimation functions (10.25), (10.26) and (10.27). However, this is not too severe a drawback for algorithm (10.29), as it is easy to show that the use of multilayer networks leads to a multimodality of the cost surface that consists of the presence of a large number of global minima. As to local minima (Finnof, 1994), a large amount of experimental results shows that they are seldom encountered. There is also an interesting theoretical result reported by Finnof (1994), where it is claimed that algorithm (10.29) is persistently perturbed by a Gaussian diffusion that makes it unlikely that the algorithm will get stuck in local minima having small and shallow basins of attraction. The updating algorithm (10.29) gives rise to a tuning procedure when the on-line estimation process begins, that is, when the sliding window is moved to stages N ÷ 1, N ÷ 2 . . . . (see Figure 10.14). The tuning procedure differs from the initialisation t-1 one in the fact that the training vectors Y tt - N and Ut_ N a r e not generated randomly; instead, they are generated by the stochastic and control environment at each stage.

On-line tuning (ONT) procedure. For any t > N, update the weight vector by one step o f the algorithm lot+l

= 10t -- o l t V w t J t ( l o t , f C t - N ,

t-1 Y t - N , Ut--N)'

t =

N, N + 1. . . .

(10.30)

^

where £Ct-u = f ( ~ C t - N - l , t - 1 , U t - N - I , ~ t - N - 1 t - l ) , t =

N + 1, N + 2 . . . . ;

Yco ~ Xo.

Due to the very general framework within which Problem 3 has been stated, we are not able to give convergence results for the ONT procedure. It is well known that on-line gradient-based techniques are extensively used for parameter identification. For neural network weights to be tuned, convergence results are available, which have been established for the updating algorithms presented by Srinivasan et al. (1994). Among various possible non-linear approximators, we have chosen multilayer feedforward neural networks thanks to their very interesting approximation properties. A discussion on this issue is beyond the scope of the present chapter; the reader is referred to Alessandri et al. (1997) and to the bibliography therein. Back-propagation may be used to train the neural networks, i.e. to find the values for initialisations of the gradients of the cost function in the OFI and ONT procedures (Alessandri et al., 1997 for details). R e m a r k 3. It is worth noting that the approximate method proposed for the solution of Problem 4 is aligned with the requirement (stated in Remark 2) of performing off-line as many computations as possible so as to minimise the on-line computational load. The OFI procedure is implemented before the estimation process begins,

Model-based fault detection in a high-pressure heater line 303 whereas the ONT procedure requires an on-line computation that consists only in the execution of a single step of the algorithm (10.30). Note also that a neural estimator optimised by the OFI procedure does not seem advisable. Indeed, for practical reasons, the width of the sliding window has to remain rather small. Training of the neural networks will then be inadequate if the dynamic characteristics of the system 'slow' compared with the width of the window.

10.4.3

Simulation results on state estimation in the power plant fourth heater

A discrete state equation of the fourth heater, described in section 10.2, was developed by a first-order Euler approximation with a sampling time At = 0.01 s. The desired level in the simulation was set at 4,026 mm. The initial state vector x0 was randomly generated according to a Gaussian distribution with mean value co1(4026, 79.9, 1087.7, 1293.6, 1242, 1084.9, - 7 0 , 291.2, 249.1, 1386.3, 69.3) corresponding to the steady-state value of the state xt and covariance Y~x = diag (1.0, 4.0, 20.0, 20.0, 20.0, 20.0, 1.0, 1.0, 10.0, 4.0, 1.0). The process noise fit (i denotes the component and t is the temporal stage) were given by zero-mean random variables that were added to the steady-state input variables, i.e. _Pprev,t = /3prey + f i t , Pdet,t ~- /3det q- f2t, L t = L -~- f3t, Sp,t = Sp -}- fat, htur,t = htur q- f5t, Widr,t = 0

(since we deal with one of the last heaters, i.e. heaters 4 or 8 in Figure 10.1), Wfw,t = ~/fw -+-f6t, and hfw,t = f/fw-'l-f7t, where/Sprev,t = 38.97 atm,/3de t = 8.0 a t m , L = 320MW, Sp = 100 per cent, fttur = 3367.9kJ/kg, ff'fw = 146.0m3/s, and hfw = 1074.6 kJ/kg. The three measurement devices assumed linear, i.e.

Yit = Xit + T]it,

i = 7, 8, 9; t = 0, 1. . . .

where 7, 8, and 9 are the state vector elements corresponding to the sensors. The process and measurement noise were mutually independent Gaussian white sequences with/it ~ A/'(0, Z~) and I/t ~ .Af(0, Z~), where Z~ = diag(0.0, 0.0, 0.0, 2.0 x 10 -9, 6.0 × 10 -8, 3.0 × 10 -8, 0.0) and Eo = diag(1.5, 5.0, 5.0). The stochastic variables were chosen Gaussian for a fair comparison with the EKF (Gelb, 1974; Anderson and Moore, 1979): the structure of Z~ and Eo ensure that/~t and 1/t effectively belong to suitable compact sets. The cost function (10.23) was taken to be quadratic, i.e., t

t

t-1

i=t-N

i=t-N

i=t--N

^ i2

where N = 18, Yt = col(Y7t, Yst, Y9t), Px = diag(l.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0), Py ----diag(1.0, 1.0, 1.0), P~ ----diag(10.0, 10.0, 10.0), and P~ = diag(0.0, 0.0, 0.0, 10.0, 10.0, 10.0, 0.0). It is worth noting that the weight matrices Py, P0, and P~ were selected as distinct from X~-! and Z~-1. We had to respect the fact that the statistics of the noise were unknown. However, as we shall see, this does not degrade the behaviour of the neural estimator, as compared with the

304

Thermal power plant simulation and control

EKF. All the approximate estimation functions were implemented by feedforward neural networks, each containing one hidden layer of five units. To evaluate the performances of the neural estimator and to make comparisons with the EKF, RMS estimation errors (averaged over 1000 trials) were considered. For the OFI procedure, we took cl = 10 -7 and c2 = 100 (algorithm (10.29) was run for approximately one million steps); for the ONT procedure, we assumed ot = 10 -9. In Figure 10.15, the RMS estimation errors for the first six state variables generated by the neural estimator and by the EKF are plotted. From the diagrams of the RMS errors, it is important to note the divergent behaviour of the EKF; instead, this does not happen for the neural estimator. Due to the complexity of the system under consideration, it is not easy to provide a theoretical explanation for this divergent behaviour. However, from a heuristic point of view, such poor performance is likely to be ascribed to the large number of strong non-linearities present in the model. Such non-linearities affect some state equation relationships and in functions like Wcon(x l, x2, x4, xs), Wodr (x2, x 11), etc. The fact that the proposed neural estimation

15

:~ 50t

/

5

0 _~.--~'~_--__7. . . . . . . ,. . . . . . . 0 10 20 Time (s)

0

30

0

. . . . . . . .

10

20 Time (s)

30

10

20 Time (s)

30

100 ~7 5o

~ 50

005 j:0 0

o

. . . . . . . . . . . . . . . . .

0

10

20

30

20

30

Time (s)

0

0 0

10

Time (s)

Figure 10.15

0

--10

20 Time (s)

30

RMS estimation errors for selected state variables (continuous line for the EKE dashed line for the neural estimator)

Model-based fault detection in a high-pressure heater line 4100

i

305

_

4090 4080

True value Neural estimate EKF estimate

.....

........ 4070 4060 ~" 4050 ~- 4040 4030 4020 4010 4000 0

i

i

t

5

10

15

a

i

20

i

25

30

T i m e (s)

85 84 .....

........

83

True value Neural estimate EKF estimate

82 -"

2

80 79 78 77

-z

~.

76 75 b

Figure 10.16

1

15

20

25

30

T i m e (s)

Behaviour of (a ) liquid level, X l , and ( b ) cavity pressure, x 2, of heater 4

method does not involve any linearisation procedure seems to be the main reason for the better performance of the neural estimator as compared with the EKE Finally, in Figures 10.16 and 10.17, the estimates of most important state variables provided by the neural estimator and by the EKF are compared with the actual values, during the transient from a given initial state vector x0 to the steady-state, under

306

Thermal power plant simulation and control 1100

1095

1090~~

~,~ 1085

1080 - ..... ........

1075

1070 0

5

1()

1'5

True value Neural estimate EKF estimate

20

2'5

30

Time (s) 1100

1095

1090

1085

4t

1080 ..... ........

1075

1070

Figure 10.17

0

5

10

~ 15 Time (s)

True value Neural estimate EKF estimate

, 20

, 25

30

Behaviour of(a) output drain specific enthalphy, x3, and (b)feedwater in subcooling area specific enthalpy, x6, of heater 4

the action o f r a n d o m l y c h o s e n stochastic processes. A s can be seen, the d i v e r g e n t b e h a v i o u r o f the E K F is c o n f i r m e d , w h e r e a s the neural e s t i m a t e s are v e r y c l o s e to their true values.

Model-based fault detection in a high-pressure heater line

10.5

307

Conclusions

In this chapter, we have presented a complete overview of various methodologies, starting with the construction of models of a power plant in normal and faulty conditions and continuing with its tuning by means of on-line grey-box identification. Modelling provides the basis for designing estimators that give estimates of the state variables of the system for the purpose of fault diagnostics. Both grey-box identification and estimation were based on the combined use of neural network and stochastic approximation. The solutions of the problems have been obtained by reducing the original functional optimisation problem to a non-linear programming one. This reduction was made possible by the use of feedforward neural networks, which, as is well known, exhibit excellent approximation properties. The low computational demand and good performance obtained with respect to the EKF suggest that the proposed estimator is well suited to being used in real power plant applications concerning process monitoring and fault detection over the long term. It is worth recalling that a lot of work has to be devoted to the construction of a model, its identification, and to the learning required for the design of the neural estimator. This effort provides a flexible, powerful, and accurate tool to supervise and predict how the plant performs on-line and to prevent dangerous and undesirable situations.

10.6

References

ALESSANDRI, A., and PARISINI, T.: 'Nonlinear modelling of complex large plants using neural networks and stochastic approximation', IEEE Trans. on Systems, Man, and Cybernetics Part A: Systems and Humans, 1997, 27, pp. 750-757 ALESSANDRI, A., PARISINI, T., and ZOPPOLI, R.: 'Sliding-window neural state estimation in a power plant heater line', Int. J. of Adaptive Control and Signal Processing 2002, 15, pp. 815-836 ALESSANDRI, A., PARISINI, T., and ZOPPOLI, R.: 'Neural approximations for nonlinear finite-memory state estimation', Int. J. of Control, 1997, 67, (2), pp. 275-302 ANDERSON, B. D. O., and MOORE, J. B.: 'Optimal Filtering' (Prentice Hall, New York, 1979) BARRON, A. R.: 'Universal approximation bounds for superpositions of a sigmoidal function', IEEE Transactions on Information Theory, 1993, 39, pp. 930-945 BOHLIN, T.: 'A case study of grey box identification', Automatica, 1994a, 30, 307-318 BOHLIN, T.: 'Derivation of a 'designer's guide' for interactive 'grey box' identification of nonlinear stochastic objects', Int. J. Control, 1994b 59, pp. 1505-1524

308 Thermal power plant simulation and control BOHLIN, T., and GRAEBE, S. E: 'Issues in nonlinear stochastic grey box identification', Int. J. Adaptive Control and Signal Processing, 1995, 9, pp. 465-490 BENVENISTE, A., MI~TIVIER, M., and PRIOURET, P.: 'Adaptive algorithms and stochastic approximation' (Springer-Verlag, Heidelberg, 1990) BARABINO, M., DE MURO, G., LAUDATO, D., and MAINI, M.: 'Simulatore integrato: controllo su bus di campo', Automazione e Strumentazione (in Italian), 1993, 41, (10), pp. 85-91 FINNOF, W.: 'Diffusion approximations for the constant learning rate backpropagation algorithm and resistance to local minima', Neural Computation, 1994, 6, pp. 285-295 GELB, A.: 'Applied optimal estimation' (MIT Press, Cambridge, Mass., 1974) GUGLIEMI, G., PARISINI, T., and ROSSI, G.: 'Fault diagnosis and neural networks: a power plant application', Control Engineering Practice, 1995, 3, (5), pp. 97-109 GAWTHROP, P. J., JEZEK, J., JONES, R. W., and SROKA, I.: 'Grey-box model identification', Control Theory and Advanced Technology, 1993, 9, pp. 139-157 JAZWINSKI, A. H.: 'Stochastic processes and filtering theory' (Academic Press, New York, 1970) PARISINI, T.: 'Physically accurate nonlinear models for model-based fault detection: the case of a power plant', IFAC Journal of Process Control, 1997, 7, 97-109, 1997 POLYAK, B. T., and TSYPKIN, Ya. Z.: 'Pseudogradient adaptation and training algorithms', Automation and Remote Control, 1973, 12, pp. 377-397 SPALL, J. C.: 'Multivariate stochastic approximation using a simultaneous perturbation gradient approximation', IEEE Transactions on Automatic Control, 1992, 37, pp. 332-341 SPALL, J. C., and CRISTION, J. A.: 'Nonlinear adaptive control using neural networks: estimation with a smoothed form of simultaneous perturbation gradient approximation', Statistica Sinica, 1994, 4, pp. 1-27 SRINIVASAN, B., PRASAD, U. R., and RAO, N. J.: 'Backpropagation through adjoints for the identification of nonlinear dynamic systems using recurrent neural models', IEEE Trans. Neural Networks, 1994, 5, pp. 213-228 TULLEKEN, H. J. A. E: 'Grey-box modelling and identification using physical knowledge and Bayesian techniques', Automatica, 1993, 29, pp. 285-308

Chapter 11

Data mining for performance monitoring and optimisation J.A. Ritchie and D. Flynn

11.1

Introduction

It is estimated that across the world data storage doubles every 18 months (Milne et al., 1997). Sources range from retail (Song et al., 2001 ), to the telecommunications industry (Hatonen et at., 1996), to industrial processes (Kresta et al., 1991). Although conceivably containing valuable information, this data is largely archived, with its full potential never realised. Data mining is the non-trivial process of identifying valid, novel, potentially useful, and ultimately understandable patterns in data. Applications within diverse areas such as marketing, finance and industrial processes have been considered, with varying degrees of success. However, despite being a widely applied technique, it is said that three-quarters of all companies who attempt data mining projects fail to produce worthwhile results (Matthews, 1997). Unfortunately, this only proves that the potential of data mining, with regard to the available data, is often greater than the reality. The most successful applications are probably in the fields of scientific research and industrial processes, e.g. chemometrics and chemical engineering (MacGregor et al., 1994; Dunia et al., 1996; Chen and Liao, 2002), industrial process control (Milne et at., 1997; Sebzalli et al., 2000) and to a lesser degree power engineering, where data mining has been used, for example, for fault analysis in transmission networks (Wehenkel, 1996; Rayudu et al., 1997). The emphasis in these applications has been the provision of on-line support systems for operators, in the form of fault detection and diagnosis, and high-level analysis of system operation and performance for engineers. Here, the users tend to have well-defined goals and a well-developed knowledge of both the application and the nature of the stored data. For less scientific environments, such as retail product targeting or the rise and fall of share prices, where 'rules of thumb' are typically applied, the aims of the data mining

310

Thermal power plant simulation and control

exercise are often not clearly defined while expectations are overstated (Weiss and Indurkhya, 1998). Data mining is a generic term for a wide range of techniques which include intuitive, easily understood methods such as data visualisation to complex mathematical techniques based around neural networks and fuzzy logic (Wang, 1999; Olaru and Wehenkel, 1999). Data mining is itself part of an even larger domain known as knowledge discovery in data (KDD), which encompasses the gathering, selection and preparation of data for subsequent mining applications. The collation of resources is perhaps the greatest barrier to successful knowledge discovery, due to the large amount of historical records potentially required. Large stores of data have a number of inherent problems such as missing and corrupted values, and related information being stored in a number of different locations, and using different media ranging from paper to magnetic tape to CD-ROM. To obtain the best results from any data mining project it is clearly important to investigate data that provides an accurate representation of the problem. It should be noted that a large amount of data does not always equate to a large amount of information, leading to a lot of company databases being regarded as data rich, but information poor. These difficulties can be resolved using feature selection methods such as clustering and principal component analysis, or the application of process knowledge. However, acquiring 'good' data for mining is one of the most timeconsuming parts of the process. It is estimated that up to 80 per cent of the duration of a data mining project may be occupied by data preparation (Mannila, 1996). However, time spent in this phase will be reflected in the subsequent results. Within this chapter, it is proposed to outline a range of techniques, some of which have been successfully applied to fault monitoring in chemometrics and chemical process control, and to the detection, isolation and reconstruction of faulty sensors within a power station environment. Section 11.2 presents background information concerning the power station to be analysed. Section 11.3 then discusses the difficulties posed by faulty sensors and identifies possible solutions. Principal component analysis (PCA) is then applied. The monitoring of unit efficiency and emissions levels, as measures of plant performance, is then discussed along with possible analytical approaches in section 11.4. Projection to latent structures (PLS) is demonstrated as a viable solution. The PLS approach is then extended in section 11.5 by incorporating a neural network for the inner mapping to enable modelling of plant behaviour over non-linear conditions.

11.2

Outline of data mining applications

Ballylumford power station is the largest of four power stations in Northern Ireland and is located on the Antrim coast, near Lame. Originally owned by Northern Ireland Electricity (NIE), it is now operated by Premier Power plc, a subsidiary of British Gas plc, as a result of privatisation of the local industry in 1992. The power station houses six generating units, 3 x 120 MW and 3 x 200 MW, which were originally

Data mining for performance monitoring and optimisation 311 designed to operate using heavy residual fuel oil (HFO). However, after a conversion programme between July 1994 and July 1996 they now fire on either gas or oil. Data concerning operation of Ballylumford power station are available from a number of sources. These include a wide range of variables recorded from the distributed control system (DCS) for both oil and gas operation on all units. The DCS is restricted to recording values for the boiler, although variables concerning the turbines, condenser, electrical equipment, etc. may be accessed using equipment such as programmable logic controllers scattered around the plant. Further parameters are recorded manually and irregularly by plant operators. Maintenance records and operator logs are also available for consultation. In total, approximately 2,500 sensors record information such as temperatures, pressures and flow rates throughout the plant on a second by second basis. The frequency of measurement and the distribution of sensors throughout the plant provide a great deal of redundancy within the data. This can be exploited for sensor fault detection and signal replacement among other problems. Despite continuously growing computer storage capabilities, the enormity of the data generated means that it is not realistic to store these data on such a regular basis, unless specifically requested for test purposes. Hence, data are regularly stored at five minute intervals, which still generates a significant amount of data which is largely not examined, excepting the investigation of occasional faults. It is suggested that within these records there is potential information regarding factors affecting plant operation. However, it is often obscured by the sheer volume of data presented on a day to day basis, making it difficult to analyse using manual methods. This information may help to improve the operation of the plant by identifying variables influencing efficiency and plant performance, while enabling a comparison of different operator shifts and/or comparative performance across the station's three 120MW units and three 200MW units. It may also be possible to identify warning signals leading to component/system failures, which would help minimise unit down-time. The data stored from the process, combined with the aims for process monitoring and analysis, lend themselves to the application of data mining techniques, capable of providing detailed and interpretable solutions.

11.3

Identification of process and sensor faults

A relatively common experience with any monitoring system is that of faulty sensors. Problems include 'stuck at' signals, a loss of sensor precision, drifting, biases or offsets, etc. Against this background, the process operators and engineers must also distinguish between genuine faults, where the unusual measurements actually reflect plant behaviour, short-term disturbances affecting the process, and/or variations in plant performance arising from changes in operating conditions, product quality, etc. Within a power station environment the above difficulties are clearly evident. Fortunately, however, many of the sensor measurements are highly correlated due to a number of parallel paths for the 'steam' and 'gas' circuits, a closed loop for the steam/water circuit, etc. The advent of distributed control systems also

312 Thermalpower plant simulation and control implies that signals are recorded on a regular basis, providing a large historical database for the plant. In 1994 an explosion at the Texaco refinery, Milford Haven, resulted in plant damage which cost £48 million to repair, in addition to a severe loss of production and injury to 26 people (Bransby, 1998). Although the triggering event was an electrical storm which took place between 7.49am and 8.30am, the explosion did not take place until 1.23 pm. It was later discovered that if the operators had known that the debutaniser outlet valve, which was indicated as being open, was actually stuck closed, then the incident could have been averted. Similarly, during the Three Mile Island incident in 1979 an indication was given that the reactor coolant system electromatic relief valve had closed, when in fact it never did so (Rubinstein and Mason, 1979). Both of these incidents highlight that it is important not merely to indicate on operator displays any demanded actions, e.g. open valve, close switch, but also to ensure that these actions have the anticipated effect, and to clarify if data measurements are intemally consistent. So, when a particular sensor becomes faulty it is desirable to first detect that there is a problem, then identify the failing signal, and finally to either disable the sensor or reconstruct/substitute the readings, if possible. Should the signal be used for feedback/feedforward control applications, this requirement becomes especially important. In the case of a process or actuator fault a slightly different strategy is required. Once the fault has been recognised, and perhaps identified and diagnosed by the operators, a decision is then required. The plant control systems may well be able to ameliorate the effects of the fault, thus permitting process operation to continue. The degradation in performance or drop in product quality should be considered, however, along with longer term implications for plant life and/or required maintenance. Alternatively, entire subsystems, or the process itself, may be required to be taken off-line for further investigation and servicing.

11.3.1

Process analysis techniques

With industrial processes, and the associated control and supervisory layers, becoming ever more sophisticated the possibility of a human operator detecting and coping with operational problems in real-time becomes ever more difficult. The benefits of distributed control systems are clear in terms of improvements in productivity, and plant manoeuvrability. However, a significant side-effect has been increased accessibility to a range of plant-wide signals, arising not only from physical measurements but also from control loops, and other automatic features forming part of the DCS itself. Computer-based solutions do, however, have the opportunity of accessing and analysing vast, continuous streams of data, potentially full of correlated and collinear data. The task remains to identify normal operating regions and relationships within the historical data, and to subsequently apply the collated rules, reference cases, etc. to detect problems with new, on-line data and suggest appropriate courses of action. Perhaps the simplest method of detecting faults and other anomalous behaviour is univariate statistical monitoring, whereby the user defines upper and lower bounds for each signal. Any variable that crosses either threshold is deemed to be faulty,

Data mining for performance monitoring and optimisation

313

and an alarm is triggered. The problems with this approach are many. For example, a sensor may present a faulty value which is actually within the specified range for the sensor, e.g. a 'stuck at' fault. Furthermore, no recognition is taken of the plant's operating status. It is fairly straightforward to list different plant operating modes, e.g. startup, shut-down, steady-state, lifting load. It is also possible to identify the status of individual plant items, e.g. normal operation, startup transients, out of service, under test. As an illustration of the difficulties that can arise, an operator of a nuclear reactor would wish to be informed if, during normal operating conditions, a control rod became fully inserted into the reactor. However, following a plant trip be would instead prefer to be warned if any control rod was not fully inserted. Expressed succinctly, the above problems arise because all variables are treated independently of each other and the validity of one sensor in relation to all other variables is not considered. This inevitably leads to the introduction of multivariate techniques. Should the process to be monitored be well defined and comprise a limited number of variables then model-based approaches may be successfully applied. Alessandri et al. (2003) apply a model-based approach to fault detection of power plant HP feed heaters. A mathematical model, physical or empirical, enables faults to be identified, based on the assumption that the faults are known and have been incorporated into the model. However, inclusion of each fault can be time-consuming and require the designer to have a comprehensive knowledge of the application (Yoon and MacGregor, 2000). Data mining techniques offer a convenient alternative. These tend to be 'data driven' rather than 'knowledge driven' and therefore require much less refinement for particular processes. Potential solutions, falling into this broad category, include case-based reasoning (CBR), cluster analysis or principal component analysis (PCA), amongst others. Case-based reasoning involves the collation of exemplars of past problems, and the solutions identified by the user from historical data and past experience (Luger and Stubblefield, 1998). The focus is on the indexing and retrieval of relevant precedents. In contrast to other data mining techniques, a large number of historical data patterns is typically not required. CBR is particularly useful when the data has complex internal structures, and can also enable an expert system to learn from its experience. However, difficulties can be encountered due to a lack of deep knowledge of the domain, thus restricting diagnostic and explanation facilities. Storage and computation facilities may also be demanding for large case bases. As a consequence, the technique is generally more suited to fault diagnosis rather than plant monitoring. Alternatively, clustering aims to discover structure hidden within data. Given a number of data patterns, each of which is described by a set of attributes, objects are grouped which share a number of similar properties (Olaru and Wehenkel, 1999). This may be achieved by calculating a similarity or distance measure. Once a structure has been formed, the most important attributes for the application can be identified and outlying values removed. Sebzalli and Wang (2001) applied this approach to identification of operational strategies for minimising the impact of product changeover in a chemical refinery process. Principal components were initially determined to analyse the process, before fuzzy c-means clustering was applied to distinguish distinct operating regions within the process.

314

Thermal power plant simulation and control

The approach adopted here is that of principal component analysis (PCA) which aims to reduce the dimensionality of a set of interrelated variables, while retaining as much of their variance as possible. This is achieved by identifying new, latent variables, known as principal components, which are linearly independent. An ordered, reduced set of principal components may then be selected which capture the essential correlations and the majority of the observed variability. The degree of reduction achieved depends on the correlation of the original data set - the greater the correlation the fewer principal components required. PCA readily lends itself to process monitoring as the developed models are intended to characterise normal operation. Modelling of individual faults is not required, although detected deviations in plant behaviour can be investigated in depth if required. PCA has been used in a wide range of applications including chemical process control for the monitoring of batches from an industrial polymerisation reactor (MacGregor and Kourti, 1995) and sensor fault detection in a boiler process (Dunia et al., 1996). 11.3.2

Principal c o m p o n e n t analysis

Given a data matrix X (m × n), consisting of m samples of n variables, a set of n principal components can be obtained, such that X = t i p T + t2p T + t3p T + . . . q - t n p T where Pi (n x 1) is the loading, and describes the relative importance of individual variables for principal component i, while ti (m x I) is known as the score vector for that particular principal component and determined as ti = X p i • Since typically only the first A principal components are required to explain the majority of the variance in the data, PCA models may be formed by retaining only those components, thereby creating a reduced order model

X=TP

A T+E=ZtipT+E i=1

where T and P represent the score and loading matrices for the retained principal components and E represents the unexplained variance in the model. For a linear system E accounts mainly for process noise. Principal component analysis is scale dependent, and, therefore, data should generally be normalised prior to processing. A number of methods are available for selecting the required number of principal components, A, to generate the most parsimonious model. For example, Johnston (1998) suggests that the principal components selected should explain at least 93 per cent of the variance. Alternatively, the quality of the model (Lewin, 1995) can also be conveniently calculated as

Quality, QA

Y~A_ 1Li ~'i

-- Y~i=I

Data mining for performance monitoring and optimisation 315 for the first A components based upon the eigenvalues, ~-i, of the data covariance matrix. For applications, as demonstrated here, involving monitoring and reconstruction it is advisable to develop more sophisticated selection methods using techniques based on cross-validation or the unreconstructed variance of the data. Applying the cross-validation method of Wold (1978) requires the training data to be split into a user defined number of groups. The first group is removed, and a PCA model is then trained using the remaining data. The performance of the model is determined, subsequently, by calculating the sum of squared prediction errors, for one component, on the removed first group. The first group is then restored, the second group deleted, and the above process repeated until all groups have been removed once. The summation of the above errors, divided by the size of the removed groups or the number of degrees of freedom, gives rise to PRESS, the prediction residual sum of squares, for one component. Should the number of components be too high then PRESS will increase due to modelling of noise. So, by repeating this process for an increasing number of components, a minimum value can be observed in the calculated statistic. Examination of the model's unreconstructed variance can also assist in determining the required number of principal components (Dunia and Qin, 1998). If a degree of correlation is assumed, a sensor can be estimated using the remaining sensor measurements, with the accuracy dependent on the number of principal components employed. The reconstructed signal is, however, unlikely to be a perfect match due to variations arising from unmodelled non-linearities, noise, etc. This leads to a reconstruction error. Clearly, an insufficient number of principal components may lead to an inability to distinguish normal residuals from sensor failure, and as outlined later in section 11.3.2.3, sensor reconstruction and substitution will be ineffective.

11.3.2.1

Multiblock PCA

It is not uncommon for a system to have several hundred, if not thousands, of process sensors. For reasons of convenience and practicality, rather than developing a single model, perhaps requiring a significant number of components to sufficiently model plant behaviour, a number of small models could be developed to model related sensors (Lewin, 1995). Alternatively, multiblock methods can be introduced (Nomikos and MacGregor, 1994). Within many processes, a number of distinct, perhaps physically distinct, linking subsystems can be defined. It is, therefore, suggested that individual PCA models are developed reflecting these natural boundaries. In a thermal power station, subsections such as the condenser, boiler and turbine stages can be readily identified - it can be informative and constructive to include some linking 'flow' variables from the inputs and outputs of neighbouring sections. There are a number of guidelines available regarding the division of a process for multiblock methods (MacGregor et al., 1994), but no solid rules are available as process and engineering knowledge are a significant factor. The advantages of multiblock methods become abundantly apparent when fault identification is considered. Should a sensor fail, or a plant fault develop, then only

316

Thermal power plant simulation and control

the model associated with that particular section of the plant will be affected, at least at first, making fault diagnosis that much more straightforward.

11.3.2.2 Quality control methods Once a model for normal operating conditions has been developed, it may be used to determine whether recorded plant measurements are consistent with historical values and neighbouring sensors, by reconstruction from the selected number of principal components. A comparison can then be made between the reconstructed value for each variable and the actual measurement. Performed manually this can be a time-consuming task. Two, more efficient, methods that can quickly help to identify differences between the actual and reconstructed value of a variable are the squared prediction error (SPE) and Hotelling's T 2 test. The SPE value, also known as the distance to the model, is obtained by calculating an estimate of each variable, .~i, from the model and then comparing it with the actual value, xi. The squared sum of errors for all variables for each data sample, x, is calculated as

SPEx

= ~ (xi - .~i)2. i=1

The SPE should remain low for normal operating conditions, attributable to measurement noise and the degree of variation not accounted for by the principal components retained in the model. Conversely, a high value of SPE will indicate that the model is not valid for the current observation and that a new event may be occurring. However, this new event is not necessarily a fault and may merely be something not accounted for in the training data. To distinguish between normal and high values of SPE, a confidence limit, known as the Q statistic 32, is available (Jackson and Mudholkar, 1979) which can be determined as

(co o ~ = O1 ~ ~1

\ +1+

l/ho

02ho (ho - 1 ) |

)

0 i is the sum of the unused eigenvalues to the i-th power, h0 is a combination of these

terms, and ca the confidence limit for the 1 - ot percentile of a Gaussian distribution, as outlined below:

t/

h0= I

20103 302

and

Oi =

y~ j=A+I

i. i = 1,2,3. )~j,

Data mining for performance monitoring and optimisation

317

The T 2 statistic (Hotelling et al., 1947), designed as a multivariate counterpart to the Student's t statistic, is a measure of the variation within normal operating conditions. If £ is the vector of mean values of x, and S is the covariance matrix of the model, then T 2 -----(x - ~)T S-1 (x - x ) . T 2 is a measure of how far the predicted value is from the multivariate mean and is thus only capable of detecting if the variation in the new data can be explained by the variation in the training data. Hence, if a new event occurs, which has not been included in the training of the normal operating conditions model, the T 2 value will move away from the multivariate mean of the data. As with SPE, an upper control limit, T2, can be calculated, which relates the degrees of freedom in the model to the F distribution,

#

--

n(m2-1) F~ ( n , m m (m - n)

-

n)

where a is the selected confidence level. It should be noted that a rise in the T 2 value does not always indicate a fault. Instead, it may be highlighting that the process is moving to a different, in control, operating point not included in the training data. This information can be useful as SPE may well not highlight what is essentially extrapolation of the training model. Consequently, it is insufficient to rely on either SPE or T 2 in isolation, but rather both values should be monitored. Additionally, both indicators are affected by noise on the system and deviation of the measurements from a normal distribution. This can result in nuisance values for both T 2 and SPE. However, false alarms can be largely eliminated by simple filtering, and adjustment of the associated threshold (Qin et al., 1997). Care must, however, be taken with both SPE and T 2, as they are unlikely to differentiate between a failing sensor and a fault on the plant. The plotting of t scores can be combined with the previous methods to distinguish between the two conditions. Scores for normal operating conditions should fall within a limited, known range. So when a process fault occurs, the individual points on the t score plots may be observed drifting away from the normal grouping into a separate cluster. The relative position of these 'fault' clusters can assist in latter diagnosis (Kourti and MacGregor, 1995). 11.3.2.3

Fault identification and reconstruction

Having confirmed that there is a sensor fault, and not a process condition, the next step is to identify which sensor is failing, and, if possible, to substitute a replacement value. Since determination of SPE involves comparing the predicted value with the available measurement for each sensor, fault reconstruction could be conveniently achieved by an iterative technique, whereby the faulty signal is replaced by the predicted value, and SPE recalculated, until the SPE and/or T 2 figures are satisfactory, with the replacement value converged. The main problem with this approach is that the faulty variable is itself included in the data used for reconstruction, while the iterative nature of the technique is inherently inefficient.

318

Thermal power plant simulation and control

Alternatively, identification and reconstruction can be achieved by assuming each sensor has failed and estimating a value for that signal from the remaining values. If the signal is faulty, a significant reduction in SPE before and after reconstruction would be expected. However, in certain situations the reduction in SPE can affect all inputs, making the faulty sensor unidentifiable. This situation arises due to a lack of redundancy, or degrees of freedom, among the measurements. The above difficulties can be overcome by calculating a sensor validity index (SVI) (Dunia et al., 1996). If zi, the adjusted value, represents the predicted value of xi, without incorporating xi itself, i.e. it is assumed that xi has a missing value, and Zi is the predicted value of xi, but with xi replaced by zi then r/i, the sensor validity index for variable i, can be expressed as

172 =

(Zi - -

ZT=, (xj

i)2 2

The sensor validity index is determined for each variable, with a value between 0 and 1 regardless of the number of samples, variables, etc. A sensor validity index close to unity is indicative of a normal, in-control signal, while a value approaching zero signifies a fault. It is assumed that a single sensor has failed, and the remaining signals are used for reconstruction, although the model is equally capable of identifying faults occurring sequentially. As described earlier, system transients and measurement noise can lead to oscillations in 17i, and the possibility of false triggering. Consequently, each signal is filtered and compared with a user-defined threshold.

11.3.3

P C A tests a n d results

The above methods are now applied to Unit 6 at Ballylumford power station. Individual faults will be detected using the SPE and T 2 indicators, and further clarified using the sensor validity index. A failing sensor can be identified when the index falls beneath a threshold. The reconstructed, or adjusted, value then substitutes for the failing sensor. The t scores are also examined to confirm, alternatively, that the fault is actually with the plant, and corrective maintenance or other actions should then be scheduled. For convenience, a number of tests are now applied to a simulation of a 200 MW, gas/oil-fired unit (Lu and Hogg, 1995). The non-linear boiler-turbine model has been developed using object-oriented principles, with individual models formed for subsystems consisting of the combustion chamber, superheaters, economiser, etc. by applying the laws of conservation of mass, energy and momentum. The model consists of 14 non-linear differential equations and more than 100 algebraic equations. A large number of wide-ranging tests were subsequently performed on the actual plant to validate the model's performance. Two PCA models were developed for normal operating conditions around generation outputs of 100 and 150 MW. The principal components derived for the 150 MW model, similar to those obtained for the 100 MW model, can be seen in Table 11.1

Data mining for performance monitoring and optimisation 319 Table 11.1 Principal components for 150 MW model Principal component

Eigenvalue

Percentage variance explained

Cumulative percentage variance explained

PRESS

1 2 3 4 5

0.5460 0.0938 0.0211 0.0005 0.0003

82.48 14.17 3.19 0.08 0.05

82.48 96.65 99.84 99.91 99.96

0.0619 0.0069 0.0061 0.0049 0.0051

along with their percentage contribution to the variance and cumulative variance explained. Subsequently, the PRESS statistic was determined for each model order, resulting in two principal components being considered sufficient for both operating points. Given that the model was to be applied to on-line sensor reconstruction it was essential that the predictive performance was examined and that the model was not overfitted to the training data. The simulation was then used to create three types of fault to enable an assessment of the models' monitoring and predictive capabilities. First, a bias of 0.1 per cent was introduced into the reheater outlet pressure signal after approximately 5 hours of operation while generating at approximately 150 MW, as can be viewed in Figure 11.1. The corresponding SPE and T 2 plots for the same time period are shown in Figures I 1.2a and 2b respectively. Based on a 95 per cent confidence limit for both tests it can be seen that both tests promptly detect the fault after 30 and l0 minutes. Having detected that there is a problem, Figure 11.2c shows the variation in the sensor validity index for each variable over the period in question, with a defined threshold of 0.75. The reheater outlet pressure signal can now be readily identified as being in error, with the associated index for this signal falling to a value in the range 0.3-0.6. This identifies it as being inconsistent with the rest of the signals and therefore most likely to contain a fault. It is also of note that when the reheater pressure signal fails, the associated indices for the remaining sensors rise towards unity, accentuating identification of the biased sensor. As the fault is with the sensor, not the process, the biased sensor is replaced by the adjusted measurement, as shown in Figure 11.1. Although this signal is not directly utilised for control purposes, it forms an input to an on-line, advisory efficiency monitoring system on the plant, and thus invalid measurements may unduly influence operator actions. A positive drift is now introduced into the main steam pressure signal, which is regulated within the plant by a PI controller operating on the fuel flow. The plant is operated at an approximate load of 100 MW. Since the faulty signal is being fed back for control there is, paradoxically, minimal impact on the measured value, as can be seen in Figure 11.3. Instead, the controller, observing that the pressure signal is

320

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drifting upwards, decreases the fuel flow, and associated air flow, to the boiler, so that the faulty sensor now indicates the correct value. In actuality, the main steam pressure is being progressively reduced, with knock-on effects for many of the sensors around the plant. Figures 11.4a and 4b again depict the SPE and T 2 measures, with the fault being detected after 50 and 30 minutes, respectively. The associated confidence limits were recalculated for operation at the lower operating point. Figure 11.4c illustrates the validity index for each sensor, and a problem with the main steam pressure sensor is quickly confirmed. Unlike Figure 11.2c, the effects of this fault are more significant across the plant, and it is now more challenging, although still straightforward, to identify the failing sensor. However, as time progresses with the increasing sensor drift not corrected, the variation in other sensors becomes more noteworthy. The actual activity of the steam pressure can be reconstructed by the model and Figure 11.3 confirms that the pressure falls as a result of the fault. For the final test, the efficiency of the HP turbine was reduced by 2 per cent after approximately 6 hours, while generating 150 MW. Normalised values for all the process signals are plotted in Figure 11.5, illustrating the relatively severe nature of the disturbance introduced. The SPE plot of Figure 11.6a then shows that the control limit is exceeded 5 minutes after the fault is introduced. Examination of the t scores for the first two principal components, Figure 11.6b, reveals that there are now two operating regions. From comparison with the training data, region A, in the top left of the graph, corresponds to the normal operating region, while the presence of region B,

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in the bottom fight region of the graph, indicates that there is a physical problem with the plant. Reconstruction of the signal is therefore inappropriate. Further examination of Figure 11.5 reveals that the HP turbine outlet temperature and the reheater inlet and outlet temperatures are unusually high for the problem period indicating the most appropriate area for further investigation.

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Process monitoring and optimisation

As outlined in section 11.2, Ballylumford power station operates on two types of fuel, namely heavy residual fuel oil and gas. Although initially designed for oil operation alone, the plant is now predominantly operated with gas for economic and

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environmental reasons. However, the gas supply is under an interruptible contract. It is further recognised that problems may occur at the gas pressure reducing station or further upstream. Both factors may require the plant to be operated using oil on occasion. Consequently, operators regularly practice switching between gas and oil supplies. Not surprisingly, using two different fuels requires subtle changes in control strategies by the operators. Considering that the experience and knowledge of senior operators, something which is not readily or easily passed on to others, plays a large part in the control of a power plant it would not be surprising that a lack of familiarity with operating the plant on oil can lead to optimal levels for unit efficiency and emissions levels not being as easily achieved, as compared with gas operation. Superficially, unit efficiency depends on the power output of a generating unit with increased efficiencies being achieved close to maximum continuous rating. In practice, though, it is a multidimensional problem with factors such as calorific value of the fuel, configuration of burners, daily cyclic variations of the local sea (cooling water) temperature due to tide movements, cleanliness of heat exchanger tubes, etc. contributing to the end result. Issues such as clogging of the condensers with shells, twigs, etc. are common to both types of operation. However, the implications of soot are clearly much more significant for oil operation. Attemperator spraying is also operated differently for the two fuels: for gas operation, the flame ball is higher up and further back in the furnace, resulting in a differing heat distribution and more reheater spraying, in particular. Environmental regulations require emissions levels to be monitored and maintained under acceptable limits, subject to financial penalties if exceeded. In a power plant the emissions from HFO operation are of particular interest. Conventional methods for emissions monitoring employ analytical sensors, which are expensive, and off-line analysis, which may be slow and infrequent. Due to the associated expense and high level of maintenance associated with these methods (Mandel, 1996) it is often deemed desirable to develop on-line monitoring systems which project values for the emissions from other process variables. Qin et al. (1997) apply this method to an industrial boiler with the aim of modelling NOx emissions. A lack of good historical data, due to infrequent sampling, potentially makes this task more challenging.

11.4.1

Monitoring and analysis techniques

With power generation becoming an increasingly competitive marketplace it is important that individual units endeavour to operate at their maximum possible efficiency while meeting contractual load obligations and monitoring emissions levels. Load cycling operation of generation plant is increasingly common, leading to a wide range of operating conditions and exposure to plant non-linearities and interactions between control loops. From available records it is possible to investigate periods of operation identified by the operators as being representative of plant performance, particularly following unit overhaul and cleaning operations. Potentially, this information can then be used to develop a 'best case' model for monitoring purposes. Solutions using linear analytical techniques such as clustering (see discussion for PCA), association

Data mining for performance monitoring and optimisation 327 rules, regression, dependency modelling or projection to latent structures (PLS) may be proposed. Association rules is a summarisation technique describing the nature and frequency of relationships between data entities. For example, Sebzalli and Wang (2001) first use PCA to analyse a refinery fluid catalytic cracking process, and then fuzzify these results to create a set of association rules describing different operating conditions for three products. Given a relational database, all associations of the form if {set of values} then {set of values} are mined using methods such as decision trees, decision rules, etc. What should result is a concise, readily understood rule base. However, while each individual rule may be evident in itself, it can be difficult to visualise the system as a whole. The application of association rules is also somewhat limited in that it assumes that all the data is categorical, and hence numerical data needs to be grouped or fuzzified into categories before use. Alternatively, statistical regression methods enable a linear model, based on past process outputs and appropriate, user selected, inputs, to be fitted to the data set. Model selection, however, requires the user to have a sufficient understanding of the underlying process, although correlation-based techniques, for example, can assist in determining model structure from available data. Similarly, multiple linear regression (MLR) attempts to establish a linear relationship between a block of independent data and a block of dependent data, by forming a least squares solution (Draper and Smith, 1998). One common and limiting problem which arises with MLR is that of collinearity within the data.

11.4.2

Projection to latent structures

Projection to latent structures, also known as partial least squares (PLS), is a robust, multivariate linear regression technique more suitable for the analysis and modelling of noisy and highly correlated data than MLR (Otto and Wegscheider, 1985). A model is developed which attempts to explain the variation in the process that is most predictive of the product quality variables. PLS makes use of techniques previously applied in PCA to reduce the dimensionality of data and create latent variables representing a system. This procedure is then enhanced, through linear regression, to provide a relationship between the process variables and the product quality variables. PLS has been successfully applied in a range of chemometrics, chemical engineering and process control applications such as calibration in chemical analysis (Geladi and Kowalski, 1986b), and performance monitoring and fault detection of both a fluidised bed reactor and extractive distillation column (Kresta et al., 1991). PLS requires two blocks of data, an X block (m × n) representing m samples of n independent process variables measured frequently, and a Y block (m × r), representing m samples of r dependent product quality measurements, which may be measured irregularly or not as frequently as the X block. PLS then aims to provide an estimate of Y using the X data. Linear representations could be obtained for the X and Y blocks separately, as demonstrated using principal component analysis. If T

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and U represent the score matrices for the X and Y blocks, respectively and P and Q are the associated loadings, then, for the required number of principal components, X=TpT

+E

Y =UQTq-F with the residual matrices E and F sufficiently small. The above outer relations can be linked by a linear relationship, B, between the score matrices of the X and Y block, namely T and U: U:BT where B is a diagonal matrix. The resulting model, however, is not optimal, since the principal components for each block are calculated separately. Consequently, variation of the X block may be discarded when it appears insignificant towards the reconstruction of X, but may well be highly predictive of the output variables Y. More constructively, applying the non-linear iterative partial least squares (NIPALS) algorithm, the t and u vector scores for each component can be interchanged, so that slightly rotated principal components are obtained, such that X= TpT+E Y:~IQT

+F

where t] is the estimate of the score U, based on T. The NIPALS algorithm determines the principal components in sequence, so after each iteration the data blocks are reduced as follows, Ei+l

:

Ei -

tip T

Fi+l = F i - ( b i t i ) q T

: Eo = X " Fo= Y

where Ei and Fi are the residuals after the i-th iteration (component). However, in order to obtain orthogonal X block scores it is necessary to introduce a weighting matrix, W, as outlined by Geladi and Kowalski (1986a). Having obtained the PLS model it then remains to determine the required number of principal components. Methods similar to those employed for PCA can also be applied here. However, in this instance the emphasis is on selecting sufficient principal components to explain the majority of variance that is most predictive of the Y variables, rather than the X variables. Consequently, although it is possible to consider multiple variables in the Y block the resulting PLS model achieved will be a compromise between the requirements of the different quality variables. A simpler, and indeed more informative approach, is to develop distinct PLS models for each Y variable.

Data mining for performance monitoring and optimisation 329 Again, in a similar manner to that discussed for PCA, multiblock PLS methods are also available. The same benefits carry forward in terms of simpler fault detection and more interpretable models for large systems (MacGregor et al., 1994).

11.4.3

PLS tests and results

PLS models were created using plant data gathered over the period of two weeks for a phase 1,120 MW unit which was being operated for that period on oil. Although the unit went through several load cycles during this period, the model was specifically trained for operation in the range 100-120 MW as the majority of the unit's current, and expected future, operation was within this range. For the purposes of further analysis, two quality variables were selected, namely unit thermal efficiency and SOx emissions. Distinct models were created for each Y variable, and their associated quality measures are summarised in Tables 11.2 and 11.3. Examination of the PRESS statistic for the normalised quality variables suggests that three principal components are required in both cases. For the efficiency model

Table 11.2 PLS efficiency model Number of components

Percentage X variance unexplained

Percentage Y variance unexplained

PRESS

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34.48 22.12 17.24 12.56 8.78 6.65

26.19 14.03 7.86 6.61 5.20 3.95

0.2548 0.1323 0.0651 0.0931 0.0882 0.0973

Table 11.3 PLS SOx emissions model Number of components

Percentage X variance unexplained

Percentage ¥ variance unexplained

PRESS

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38.21 26.64 17.33 14.24 10.57 8.44

32.64 11.66 9.13 6.85 5.57 4.89

0.2196 0.1113 0.0832 0.0899 0.0946 0.0876

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this is sufficient to explain 92 per cent of the variance in Y, while still explaining 87 per cent of the variance in the X block. Similarly, for the SOx model, three principal components were capable of explaining 91 per cent of the Y variance, and 83 per cent of the X variance. It should be noted that the above models are intended for oil operation alone. Although a hybrid model could be formed for both fuels, if the same logic as above is followed, then it would be clearly more informative to create distinct models for both gas and oil operation. Having developed two PLS models it now remains to investigate their monitoring capabilities on the plant. In passing it is noted that the models could be used for fault reconstruction as described for PCA, but this shall not be demonstrated here. It is of some interest to examine how each variable contributes to the percentage X unexplained variance for the first component of each model. This is a measure of how individual variables affect the quality variable Y. Figures 11.7a and 7b, therefore, show the percentage explained variance of the X data block, for both efficiency and SOx models. There are many similarities between the bar charts with, for example, unit output (1), primary steam flow (2), economiser feed inlet temperature (7), etc. being significant for both models. It is, however, of greater interest to highlight differences between the two charts. Therefore, boiler flue gas oxygen (18) is significant for SOx, while variables such as final outlet steam temperature A (8) and B (9), HP turbine exhaust temperature (29), etc. are much more significant for the efficiency model. These results highlight the most important variables to be monitored/adjusted when attempting to achieve different goals of operation. Figure 11.8 illustrates the performance of the SOx model using data from the same two-week period, but previously unseen by the model. The PLS target is seen to closely follow the actual emissions monitored on the plant. Having now successively trained a model, significant deviation between the model and plant outputs would be considered indicative of a problem within the plant requiring further investigation. Figure 11.9 shows the actual efficiency deviation during a subsequent period when the plant was again running on oil. Superimposed on the graph is the PLS estimate of the plant's efficiency, and it can be seen that there is a clear distinction between the two characteristics. If the scores of the efficiency model for the first two components are now examined, Figure l l.10a, region A represents the training data while region B represents this later period. In particular, the graph reveals that the tl score has significantly increased for the new period. Examination of how the tl score is formed from the measured variables should reveal which section(s) of the plant is unduly impacting on overall operation. Figure 11.10b plots the deviation from normal operation of the contribution to the tl score for each PLS variable. The contributions from condenser cooling water outlet temperatures A (22) and B (23), and condensate temperature (24) are unusually high for this period. From examination of the operator logs for this unit it is known that on the following day the unit was switched off for a number of days, during which maintenance of the condensers was carried out in the form of removing debris from the pipework. The unit was then switched on again towards the end of the same month. The thermal efficiency for this period, along with the model's estimated efficiency, can

Data mining for performance monitoring and optimisation

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be viewed in Figure 11.11. A higher efficiency is now being achieved which is comparable with the PLS model, except for the time period of approximately 4 - 6 hours. During this time plant output was reduced to around 80 MW, an operating point for which the model was not previously trained. Experience shows that attempting to train the PLS model over a wider operating range would result in a generally poor

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fit being achieved over the entire regime, for an acceptable number of components. Instead, as can be seen, the model operates well over the intended range. It should also be noted that the PLS model was trained using a two-week period of data alone, so that the full significance of cooling water (sea) temperature variability, amongst other

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factors, will not have been experienced. More wide-ranging training data would be required. To cope with the apparent non-linearities revealed above, an array of linear models could be developed for the entire operating range, or as outlined in the next section a neural PLS structure could be created.

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Non-linear PLS modelling

Projection to latent structures (PLS) has already been shown to be a powerful regression technique for problems where the data is noisy and highly correlated, and can also be of benefit where there are only a limited number of observations for the quality measurements. It has been shown in the previous sections, however, that while linear models, both PCA and PLS, operate well over a limited range, all processes are inherently non-linear, with power generation being no exception. When applying linear PLS to a non-linear problem the minor latent variables cannot always be discarded, since they may not only describe noise or negligible variance/covariance structures in the data, but may actually contain significant information about the nonlinearities. The resulting PLS model may then require too many components to be practicable for the purpose it was intended, i.e. monitoring or analysing the system of interest. Recognition of the non-linearities can be achieved using intuitive methods, for example, which apply non-linear transformations to the original variables or create an array of linear models spanning the whole operating range. More advanced methods have also been proposed including non-linear extensions to PCA (Li et al., 2000; Ku et al., 1995), introducing modifications to the relationship between the X and Y blocks in PLS (Baffi et al., 1999a; Holcomb and Morari, 1992) or applying neural network, fuzzy logic, etc. methods to represent the non-linearities directly (Tan and Mavrovouniotis, 1995).

Data mining for performance monitoring and optimisation 335 Transformation of the original variables using non-linear functions can be introduced prior to a linear regression technique such as PCA or PLS. This is a relatively simple approach that does not require the NIPALS algorithm in PLS to be modified. Instead, the input matrix is extended by including non-linear combinations of the original variables e.g. x~, sin(x2 + x3), etc. Process knowledge and experience is, however, required to intelligently select suitable non-linear transformations that will sufficiently reflect the underlying non-linear relationships within the plant. The main problem with this approach is the assumption that the original set of variables are themselves independent (Wold et al., 1989). This is rarely true in practice, which can make the resulting outputs from the data mining exercise difficult to interpret. An alternative and more structured approach is to modify the NIPALS algorithm in PLS by introducing a non-linear function which relates the output scores u to the input scores t, without modifying the input and output variables. Initial approaches used a second-order polynomial to 'curve fit' the relationship between the latent variables (Wold et al., 1989), although neural network approaches are generally seen to be more capable of providing an accurate representation of the relationship for each component. However, while the dimensions of the model will be reduced (one or two components are normally sufficient), the dependency between latent variables is not as transparent as in linear methods (Sebzalli and Wang, 2001). Since the purpose of the neural network is merely to capture the non-linearity between t and u, then a variety of neural structures can be arbitrarily applied. In this case a radial basis function (RBF) network has been selected over other approaches. Multilayer perceptron (MLP) networks are popular for many applications, but training is a non-linear optimisation problem, requiring conjugate gradient and Hessian-based methods to avoid difficulties arising from local minima, etc. Similarly, spline networks can require arbitrary selection of spline parameters, and may require a relatively high number of splines to model the relationship. By contrast, a standard RBF network consists of a single-layer feedforward architecture, with the neurons in the hidden layer generating a set of basis functions which are then combined by a linear output neuron. Each basis function is centred at some point in the input space and its output is a function of the distance of the inputs to the centre. Selecting a Gaussian function as the basis function means that each neuron can be viewed as approximating a small region of the model surface neighbouring its centre. Using techniques such as k means clustering, etc. and/or a priori experience, the number and positioning of basis function centres and widths can be carefully chosen. The remaining weights then appear as linear terms, and can be conveniently determined using least squares techniques, or singular value decomposition (SVD) approaches if the data are ill-conditioned. Although Wold et al. (1989) originally proposed replacing the diagonal B matrix to describe the inner relationship with a neural network their method did not update the weighting matrix W. Such an approach is acceptable if the inner mapping is only slightly non-linear. For generality, the error-based updating approach of Baffi

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Thermal power plant simulation and control

et al. (1999b) is applied. It is assumed that the model between the latent variables is continuous and differentiable with respect to W, whereupon the non-linear mapping can be approximated by a Taylor series expansion. The NIPALS algorithm is subsequently modified to perform updating of the weights at each iteration of the algorithm. 11.5.1

R B F - P L S tests and results

RBF-PLS models were subsequently trained using both efficiency and SOx emissions as quality Y variables, using data from the same period of HFO operation. In this case, however, the operating range was extended to encompass 30-120 MW. Selection of centres and training of the RBF networks was performed using the Matlab neural network toolbox. The efficiency model required seven neurons for the first component, and three neurons for subsequent components. This resulted in a model where the first component explained 45 per cent of the variance on the X data, and 99 per cent of the variance in the Y data, as shown in Table 11.4. The relatively high unexplained X variance for the RBF model, even after four components, is not of concern, as the primary purpose of the PLS model is to explain the variability of the Y variables. Both RBF models were subsequently tested on previously unseen data to ensure that overparameterisation of the model had not occurred. This is a common problem using neural networks as they have the ability to provide such an accurate representation of the system, that even the system noise is incorporated, leading to poor generalisation capabilities (Doherty et al., 1997). Figure 11.12a-d illustrates the scores scatter plots for the first four components. Particularly, for the first, dominant component the RBF network provides a smooth and good approximation to the underlying non-linearities. Finally, Figure l l.13a illustrates the predictive performance of the RBF-PLS model, using one component, for a further time period. For comparison a linear model was trained and tested using the same data as the neural PLS model. Figure 11.13b shows that the predictive

Table 11.4 Number of components

1 2 3 4 5

RBF-PLS efficiency model RBF

Linear

Percentage X variance unexplained

PercentageY variance unexplained

PercentageX variance unexplained

PercentageY variance unexplained

55.43 53.96 51.84 45.10 --

0.99 0.64 0.62 0.48 --

45.40 36.50 19.30 15.20 11.89

21.90 13.l 0 12.40 9.78 7.71

Data mining for performance monitoring and optimisation

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performance, for a five component model, is significantly inferior to the RBF version. Even though Table 11.4 indicates that five parameters explain 92 per cent of the variance in Y, the system non-linearity has been captured in the lower components, leading to deficiencies in the capabilities of the linear model.

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Discussion and conclusions

The availability of vast amounts of data from various application domains has been noted, while the minimal use to which it is often put is also observed. Instead, it is possible to exploit this historical information, in many cases for commercial

Data mining for performance monitoring and optimisation 339

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advantage, using data mining techniques. Difficulties often associated with historical data are the quality and ease of accessibility, exacerbated by the quantities stored over lengthy periods of time. Once data has been gathered it is essential to highlight incomplete and faulty records, leaving 'cleaned up' data which are representative of the process to be modelled. A range of pre-processing techniques is available, and

340

Thermal power plant simulation and control

includes feature selection methods to reduce the dimensions of the data and clustering to identify, and subsequently remove, outliers. Before initiating a data mining exercise a clear outline of project objectives should be drawn up. As well as influencing the nature of the data selected for the study, an informed selection of data mining techniques can then be performed. There are many techniques available ranging from transparent methods such as association rules to more advanced, 'black box' techniques based around neural networks. Each approach has different characteristics which must be considered in relation to the project aims. Consideration must also be given as to whether the results are required to be qualitative/quantitative in nature and whether linguistic/numerical descriptions are appropriate. The application considered here was that of process monitoring at Ballylumford power station. Since the objective of mining techniques is to take advantage of existing data, gathered from monitoring equipment already in use throughout the plant, hardware and instrumentation costs incurred should be minimal. A range of potential tasks was identified and the suitability of various data mining techniques was assessed. Faults arising both with the plant and with instrumentation were first investigated. After consideration of a number of possible solutions, principal component analysis (PCA) was selected. A model of the plant under normal operating conditions was created, which focuses on identifying unusual deviations. The need for representing specific faults, as required in model-based approaches, is thus removed. PCA models were created for limited operating ranges and their ability to detect, and ultimately correct, sensor problems, with a minimal number of principal components, were discussed. Model performance was acceptable for the investigated scenarios, although it is recognised that PCA, a linear technique, was being applied to a nonlinear process. With sufficient principal components it should be possible to model the non-linear plant behaviour, but the advantages of PCA are then largely lost. Nonlinear extensions to PCA making use of 'principal curves' and/or neural networks have been proposed, but care needs to he taken that the transparency offered by PCA is not lost. Monitoring of plant operating performance, and in particular measures such as thermal efficiency, NOx and SOx emissions, can be greatly assisted through the availability of extensive historical records. Establishing reference plant behaviour is not always straightforward and deviation from target can arise from a myriad of causes. Again, a number of data mining techniques were considered, and PLS was selected as being the most appropriate. Similar techniques to that investigated above could have been applied but PCA attempts to explain all the observed variability in available data, rather than focusing on particular quality/performance measures. Likewise, PLS could be successfully employed for fault identification and sensor reconstruction. Distinct models were developed to model both unit efficiency and SOx emissions. Subsequently, by running these models in parallel with the actual plant, operators could monitor how close to optimum the plant was performing. Furthermore, by tracking t score plots, and observing how individual plant signals contribute to the PLS scores it was demonstrated that the nature of any discrepancies in plant performance can be pinpointed to particular items of plant. Through access

Data mining for performance monitoring and optimisation

341

to historical data, and cross-referencing to maintenance actions, it then becomes possible to identify particular faults, or disturbances, by the relative position on t score plots. As with PCA, the PLS models were trained over a limited operating range, corresponding to the normal loading range for the unit. In order to capture the unit's global non-linear behaviour, neural strategies were proposed. Consequently, the inner mapping between the t and u scores was replaced by a RBF network 'curve fit' for each component, which, while improving model performance did not compromise model interpretability. Comparison with a linear PLS approach illustrated a clear advantage in predictive capabilities for the RBF strategy.

11.7

Acknowledgements

The authors wish to acknowledge Premier Power plc for permitting access to their plant, and to the assistance provided by the unit operators and engineering staff at Ballylumford power station. The support of Michael Cregan, The Queen's University of Belfast, during this project is also greatly appreciated.

11.8

References

ALESSANDRI, A., COLETFA, D., and PARISINI, T.: 'Model-based fault detection in a high pressure heater line' in FLYNN, D. (Ed.): 'Thermal power plant simulation and control' (lEE Publishing, London, 2003) BAFFI, G., MARTIN, E. B., and MORRIS, A. J.: 'Non-linear projection to latent structures revisited: the quadratic PLS algorithm', Computers and Chemical Engineering, 1999a, 23, (3), pp. 395-411 BAFFI, G., MARTIN, E. B., and MORRIS, A. J.: 'Non-linear projection to latent structures revisited (the neural network PLS algorithm)', Computers and Chemical Engineering, 1999b, 23, (9), pp. 1293-1307 BRANSBY, M. L.: 'Explosive lessons', lEE Computing and Control Engineering Journal, 1998, 9, April, pp. 57-60 CHEN, J., and LIAO, C.: 'Dynamic process fault monitoring based on neural network and PCA', Journal of Process Control, 2002, 12, pp. 277-289 DOHERTY, S. K., GOMM, J. B., and WILLIAMS, D.: 'Experiment design considerations for non-linear system identification using neural networks', Computers and Chemical Engineering, 1997, 21, (3), pp. 327-346 DRAPER, N. R., and SMITH, H.: 'Applied regression analysis' (John Wiley New York, 1998, 3rd edn.) DUNIA, R., QIN, S., EDGAR, T. F., and MCAVOY, T. J.: 'Identification of faulty sensors using principal component analysis', AIChE Journal, 1996, 42, (10), pp. 2797-2812 DUNIA, R., and QIN, S.: 'Subspace approach to multidimensional fault identification and reconstruction', AIChE Journal, 1998, 44, (8), pp. 1813-1831

342 Thermal power plant simulation and control GELADI, E, and KOWALSKI, B. R.: 'Partial least squares regression: a tutorial', Analytica Chimica Acta, 1986a, 185, pp. 1-18 GELADI, E, and KOWALSKI, B. R.: 'An example of 2 block predictive partial least squares regression with simulated data', Analytica Chimica Acta, 1986b, 185, pp. 19-32 HATONEN, K., KLEMETTINEN, M., MANNILA, H., RONKAINEN, E, and TOIVONEN, H.: 'Knowledge discovery from telecommunication network alarm databases'. 12th IEEE International Conference on Data Engineering, New Orleans, USA, 1996, pp. 115-122 HOLCOMB, T. R., and MORARI, M.: 'PLS/neural networks', Computers and Chemical Engineering, 1992, 16, (4), pp. 393-411 HOTELLING, H., EISENHART, C., HASTAY, M., and WALLIS, W.: 'Multivariate quality control' (McGraw-Hill, New York, 1947) JACKSON, J. E., and MUDHOLKAR, G. S.: 'Control procedures for residuals associated with principal component analysis', Technometrics, 1979, 21, (3), pp. 341-349 JOHNSTON, D. E.: 'Applied multivariate methods for data analysts' (Duxbury Press, London, 1998) KOURTI, T., and MACGREGOR, J. E: 'Process analysis, monitoring and diagnosis, using multivariate projection methods', Chemometrics and Intelligent Laboratory Systems, 1995, 28, pp. 3-21 KRESTA, J. V., MACGREGOR, J. E, and MARLIN, T. E.: 'Multivariate statistical monitoring of process operating performance', Canadian Journal of Chemical Engineering, 1991, February, 69, pp. 35-47 KU, W., STORER, R. H., and GEORGAKIS, C.: 'Disturbance detection and isolation by dynamic principal component analysis', Chemometrics and Intelligent Laboratory Systems, 1995, 30, pp. 179-196 LEWIN, D. R.: 'Predictive maintenance using PCA', Control Engineering Practice, 1995, 3, (3), pp. 415--421 LI, W., YUE, H. H., VALLE-CERVANTES, S., and QIN, S. J.: 'Recursive PCA for adaptive process monitoring', Journal of Process Control, 2000, 10, pp. 471-486 LU, S., and HOGG, B. W.: 'Integrated environment for power plant performance analysis and control design', IFAC Control of Power Plants and Power Systems, Cancun, Mexico, 1995, pp. 37-42 LUGER, G. E, and STUBBLEFIELD, W. A.: 'Artificial intelligence, structures and strategies for complex problem solving' (Addison-Wesley, Reading, 1998, 3rd edn.) MACGREGOR, J. E, JAECKLE, C., KIPARISSEDES, C., and KOUTOUDI, M.: 'Process monitoring and diagnosis by multiblock PLS methods', AIChE Journal, 1994, 40, (5), pp. 826-838 MACGREGOR, J. E, and KOURTI, T.: 'Statistical process control of multivariate processes', Control Engineering Practice, 1995, 3, (3), pp. 403-414 MANDEL, S.: 'Continuous emission monitoring systems: an overview', Control Engineering, 1996, 43, (April), pp. 47-48

Data mining for performance monitoring and optimisation 343 MANNILA, H.: 'Data mining: machine learning, statistics and databases'. 8th IEEE International Conference on Scientific and Statistical Database Management, Stockholm, Sweden, 1996, pp. 2-8 MATTHEWS, R.: 'Data miners only strike fool's gold', New Scientist, 1997, 8 March, p. 8 MILNE, R., DRUMMOND, M., and RENOUX, E: 'Predicting paper making defects on-line using data mining, Studies in Informatics and Control, 1997, 6, (4), pp. 329-337 NOMIKOS, E, and MACGREGOR, J. E: 'Monitoring batch processes using multiway principal component analysis', AIChE Journal, 1994, 40, (8), pp. 1361-1375 OLARU, C., and WEHENKEL, L.: 'Data mining', IEEE Computer Applications in Power, 1999, July, 12, pp. 19-25 OTTO, M., and WEGSCHEIDER, W.: 'Spectrophotometric multicomponent analysis applied to trace metal determinations', Analytical Chemistry, 1985, 57, (1), pp. 63-69 QIN, S., YUE, H., and DUNIA, R.: 'Self-validating inferential sensors with application to air emission monitoring', Industrial Engineering Chemical Research, 1997, 36, pp. 1675-1685 RAYUDU, R. K., SAMARASINGHE, S., KULASIRI, D., and YPSILANTIS, J.: 'Model-based learning for fault diagnosis in power transmission networks', Engineering Intelligent Systems, 1997, 5, (2), pp. 63-73 RUBINSTEIN, E., and MASON, J. E: 'An analysis of Three Mile Island', IEEE Spectrum, 1979, 16, (11), November, pp. 32-45 SEBZALLI, Y. M., LI, R. E, CHEN, E Z., and WANG, X. Z.: 'Knowledge discovery from process operational data for assessment and monitoring of operator's performance', Computers and Chemical Engineering, 2000, 24, (2), pp. 409-414 SEBZALLI, Y. M., and WANG, X. Z.: 'Knowledge discovery from process operational data using PCA and fuzzy clustering', Engineering Applications of Artificial Intelligence, 2001, 14, (5), pp. 607-616 SONG, H. S., KIM, J. K., and KIM, S. H.: 'Mining the change of customer behaviour in an internet shopping mall', Expert Systems with Applications, 2001, 21, pp. 157-168 TAN, S., and MAVROVOUNIOTIS, L.: 'Reducing data dimensionality through optimizing neural network inputs', AIChE Journal, 1995, 41, (6), pp. 1471-1480 WANG, X. Z.: 'Data mining and knowledge discovery for process monitoring and control' (Springer-Verlag, London, 1999) WEHENKEL, L.: 'Contingency severity assessment for voltage security using nonparametric regression techniques', IEEE Transactions on Power Systems, 1996, 11, (1), pp. 101-111 WEISS, S. M., and INDURKHYA, N.: 'Predictive data mining, a practical guide' (Morgan Kaufmann, San Francisco, 1998) WOLD, S.: 'Cross-validatory estimation of the number of components in factor and principal components models', Technometrics, 1978, 20, (4), pp. 397-405

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WOLD, S., KETrANEH-WOLD, N., and SKAGERBERG, B.: 'Nonlinear PLS modelling', Chemometrics and Intelligent Laboratory Systems, 1989, 7, pp. 53-65 YOON, S., and MACGREGOR, J.F.: 'Relationships between statistical and causal model based approaches to fault detection and isolation', IFAC Control of Chemical Processes, Pisa, Italy, 2000, pp. 81-86

Chapter 12

Advanced plant management systems A. Fricker and G. Oluwande

12.1

Plant management in a deregulated electricity market

The privatisation and deregulation of the UK electricity industry has profoundly changed the way power plants need to be controlled and managed. Initially after privatisation a Pool system was introduced in which generation companies competed on price and availability to supply the Pool. However, in 2001 New Electricity Trading Arrangements (NETA) were introduced which rely on contracts being struck between generators and consumers and a complicated balancing market is used to ensure supply meets demand at all times. Under NETA the delivery of power, energy and other ancillary services is subject to complex contractual obligations and monitoring procedures. The effect of NETA on power generators is that there is now an even greater emphasis on plant availability and flexibility, in addition to the continuing requirement to minimise costs. Local and global environmental concerns are resulting in increased regulation and the tightening of emission limits requires improved combustion control. All these factors have resulted in a major shift in what is expected from power station operations staff. In particular, the role of the operator has moved from an equipment controller to a plant manager who has to balance competing demands to achieve optimal performance. To be able to continue to achieve better performance, improve the technical controllability and flexibility of the plant and meet the commercial requirements imposed, such as environmental constraints and contractual obligations, it has become necessary for utilities to put in place advanced plant management systems. The rest of this chapter will describe the various measures that can be taken to improve power plant management in a competitive market, drawing on the authors' experience of how their company responded to these challenges. The applications described have been built on commercially available software packages unless otherwise stated.

Thermalpower plant simulation and control

346

12.2

Supervisory control

An important element in the architecture of an advanced plant management system is the requirement for a supervisory control layer above the primary control system of the plant, which typically is a distributed control system (DCS). The main purpose of this supervisory layer is to provide optimisation of the operation of the plant via its control system, and also to provide the bridge between the commercial or business drivers and the plant's operation. By this it is meant that if the main business driver is efficiency for example, then the supervisory control layer determines the best operational means for the control system to achieve this through the manipulation of the set-points for the individual modulating controllers on the plant. Usually there tends to be more than one commercial driver for the plant; in addition to maximisation of production efficiency there might be the requirements for operational flexibility, minimisation of plant damage, delivery of contracted output (be it electrical power or ancillary services) and keeping within environmental emission limits for NOx, SOx, etc. Given the multiplicity of the business/commercial drivers for plant management, one of the requirements for the supervisory control layer would be the arbitration between the various drivers and the derivation of optimal set-points for the controllers which tend to be a compromise that tries to balance between these drivers. As an example, a means of reducing NOx emissions is by increasing the air flow through the boiler, but this will probably be at the expense of efficiency and may restrict the plant output if the increased air flow were to lead to constraints on the boiler fans. In this situation, what will be required in order to arrive at an optimised (compromise) solution will be to know the cost of the output, cost of penalty for failing to meet output, and the cost of complying with emissions requirements, with the solution based on the determination of set-points that minimise the cost of operation. Two example supervisory controllers that have been developed and are in use on power plants are: • •

integrated load control (ILC) multivariable steam control (MVC).

12.2.1

Integrated load control

Load control is a key component in a station's process control system. It provides automatic control of generator-set output and coordinates the required response of the boiler and turbine control loops. It is an essential element if the plant is to achieve generation demands accurately and consistently. Integrated load control (ILC) is a new load control system specifically developed to meet the requirements of UK generators. It provides a system that integrates and coordinates the plant controls with key business systems, i.e. • •

optimising ancillary services frequency response payments by ensuring a generator can match performance to contract requirements; improving marginal plant generating opportunities by offering a high-quality frequency response capability;

Advanced plant management systems 347 Load MV & DV 600 60{

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achieving a consistent high-quality service in meeting grid operator requirements that will help avoid disputes or penalties and will enhance company reputation.

ILC provides a generator with a strategic load control system to consistently meet current requirements and also allowing it to adapt efficiently to new requirements as grid system rules and operating practice continue to mature. The edge ILC provides is in its coordinated turbine and boiler control structures which enable load, energy and plant constraints to be controlled by both governor and fuel. It has also been integrated with Integrated Load Management (ILM)/Electronic Despatch and Logging (EDL) (see section 12.4) to allow automatic transfer (with veto) of instructions and contract parameters. The plots below show typical results in terms of load changing and frequency regulation using ILC. Figure 12.1 shows a load change from 550 MW to 420 MW where the measured value (MV) follows the desired value (DV) almost exactly. The lower plot of Figure 12.2 shows the measured system frequency and the target value of 50 Hz. To compensate for the error between the target value and the measured system frequency, requires the desired load to 'mirror' the measured frequency. The upper plot shows the effect of this frequency error on both the desired load and the measured load output (note these two values are indistinguishable in the plot).

12.2.2

Multivariable steam control

Traditionally, the superheater outlet steam temperature and the boiler master pressure have always had independent PID controllers on them, the superheater (S/H) steam temperature control being regulated using attemperators or spray valves, and pressure control regulated by firing (a mode of operation commonly referred to as boilerfollowing-turbine). Given that most large coal-fired power generating units were

348

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originally run as base-load plants, this concept was very effective as the plant had stable firing and consequently stable operation. The introduction of competition at all levels in the UK electricity market has meant that most fossil-fired plants, especially the larger coal-fired generating units, have had to operate more flexibly over a range of load conditions, in order to remain competitive. With flexible generation, there is a greater requirement for firing changes which perturb the whole plant, and can cause swings in both temperature and pressure. Large temperature excursions are known to be a major contributor to plant life reduction through increased stress and creep life damage on boilers. The performance of conventional (PID) controllers in minimising the impact of these excursions is limited, especially for plants that are required to operate flexibly over their full load range. To minimise swings in temperature which can cause plant damage due to creep and thermal fatigue, coordinated control of both steam temperature and pressure is required (Rossiter et al., 1991; Vasudeva, 1991; Perez et al., 1994; Oluwande and Boucher, 1999). This is because firing, though used to control pressure, also has considerable influence on temperature. In our organisation, a multivariable model-based predictive controller (MBPC) has been developed and implemented at key coal-fired stations. At the supervisory level there is a cost function used to

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determine the controller actions required from both the firing and the attemperation, this is based on minimising the impact of firing changes on the steam temperatures whilst still achieving tight master pressure control. The calculated required controller actions are then sent to the lower-level firing and attemperation control loops for implementation. Significant performance improvements have been achieved through the application of this multivariable model-based predictive control (MBPC) technology. Figure 12.3 shows the results for a generating unit where a multivariable steam temperature and pressure controller has been installed. The introduction of multivariable control of steam temperature and pressure control was the consequence of the need to have improved coordinated control of these parameters as firing which is used to regulate steam pressure also has a strong influence on the steam temperature which is regulated by attemperators. The plot shows the generating unit being put through a series of load changes and the performance of the four S/H steam temperature controllers and the master pressure are depicted under multivariable MBPC. The performance of the controllers under MBPC was significantly better than under single-input, single-output (SISO) temperature and pressure controllers (Oluwande and Boucher, 1999), with the effect of the large load changes on the parameters being significantly reduced under multivariable control.

350

Thermalpower plant simulation and control

12.3

System integration and HMI issues

To facilitate the development of the plant management system, it is essential that all of the different control and operating systems on the plant are integrated, since we wish to avoid many 'islands of automation' on the plant. In our experience the two ways of bringing about integration is through having an integrated human-machine interface (HMI) and the integration of the flow of data and information across the various plant systems through the establishment of a real-time database.

12.3.1

Avoidance of islands of automation

Although most power plant control engineers appreciate the need for an integrated operating and control system, they tend not to be involved in the design and development of the control systems for power stations. The project developers and project managers are more concerned with building a station as economically as possible and this tends to encourage the selection of the least cost option in terms of equipment supplied. This then results in the provision from different suppliers of plant subsystems with their individual control systems, i.e. the steam turbine will come with its own controllers and visual display units (VDUs), the water treatment plant the same, and the boiler or heat recovery steam generator (HRSG) with its own control system. One then ends up in the control room with various VDUs which are subsystem based, sometimes with different alarm systems and limited data flow between the various subsystems. In our view, the long-term limitations and suboptimal operation of such control systems far outweigh the short-term cost gains in going for such islands of automation. We recommend that to ensure the opportunity for plant management systems and the benefits that these will bring, system and plant developers need to follow these principles: •

•

To eliminate, as far as possible, the need for multiple control rooms, and to try to ensure that the central control room (CCR) is where most if not all of the plant control is operated. Ideally the CCR should be equipped such that it provides a single, integrated control facility for all of the plant (note that plant here refers to a steam train unit consisting of boiler and steam turbine for PF-fired plants, or gas turbines, heat recovery steam generators and steam turbines for a combined cycle plant). The VDUs must have access to all plant areas and should not be segregated by plant areas. Though different suppliers might provide different plant components, the plant owner/developer needs to ensure as much as possible that there is only one plantwide integrated distributed control and data acquisition system (DCDAS), for data and information flow around the plant. The different systems should be integrated with the DCDAS such that to the operator in the CCR they are indistinguishable from systems implemented within the DCDAS.

Whilst these principles are easier to follow for new plants, they are more difficult to achieve on existing plants except through refurbishments. In our own organisation the

Advanced plant management systems 351 route we took in refurbishing our existing coal-fired plants based on these principles resulted in the development of the Advanced Plant Management System (APMS). This is described in the following section.

12.3.2

Advanced Plant Management System

APMS has enabled us to provide our plant operators with an integrated HMI from which they can control the plant and have access to all plant data through a real-time database. The development of APMS was based on a supervisory control and data acquisition (SCADA) package RTAP with an open systems approach permitting integration of third-party packages. It also included the integration of new and legacy control systems and implementation of added value applications (AVAs), all interfaced to a uniform operator soft desk. At the heart of APMS lies a real-time database interfaced to all the plant data acquisition and control modules and relevant subsystems. Typically, the database comprises 20,000 data points and resides on dual-redundant servers. The control room operator has plant-wide communication and control via the APMS soft desk facility, replacing the traditional hardwired control desk (which was sometimes supplemented with VDUs connected to specific software systems). The purpose of the new soft desk (Lichnowski and Dicken, 2001) is to provide a single integrated user interface for all the plant and commercial data needed for operational decision-making as well as carrying out control actions. An additional advantage of separating the top-level database and HMI from the lower-level control systems is that it enables future changes to the plant and control systems to be carried out with the minimum of disruption. As an example, the units at one coal-fired station were converted so that they could burn gas in addition to coal. The gas burner management system required a completely new control system and, without APMS, this would normally have required a separate HMI with its own set of VDUs. With APMS, the existing schematics and control panels were modified to include gas firing, allowing all the firing to be managed by the operator within one integrated user interface. The real-time database is interfaced to an operational information system (data archiving system), enabling users to inspect and analyse real plant data. The strength of a plant-wide real-time database can be further exploited through the development of added value applications that implement new advanced technologies targeted at delivering commercial optimisation. Figure 12.4 shows a typical APMS control desk.

12.4

Performance monitoring

In section 12.2 we stated that the supervisory controllers help provide the bridge between the commercial/business drivers and the primary controllers; whilst this is true, the direction of information is 'downwards' into the plant. It is also desirable

352

Thermal power plant simulation and control

Figure 12.4

APMS control desk

to have information flowing 'upwards' from the plant to the rest of the organisation and for use in monitoring of the plant performance and the achievement of business goals for example. In our organisation this has led to the development of systems for monitoring: • • •

plant monitoring using OIS - operational information system commercial monitoring using E D L - Electronic Despatch and Logging, and ILM Integrated Load Management systems alarm analysis tool.

12.4.1

Operational information system

The long-term performance of the plant is monitored using the operational information system (OIS) which is based on the PI (Plant Information) commercial software package. OIS is a set of business and operational applications that have been built on the tools available within PI to create standard menu layouts, displays and reports for all the Innogy sites. The applications use the PI functions to return data in a format that the user wants. These can be in the form of trends or graphics, reports or spreadsheets. At the core of OIS is the PI archive which stores the data fed from the control system. OIS pulls together data from many sources within the company and

Advanced plant management systems 353 is able to distribute information through tools to the different end-users, i.e. boiler or turbine specialists, etc. including those at remote locations such as the corporate head offices.

12.4.2

Electronic Despatch and Logging

In the control room the Electronic Despatch and Logging (EDL) system provides the vital direct link between the grid operator and the production process. Instructions to despatch the plant are sent electronically via the company's IT infrastructure directly to a display on the control room desk. The arrival of new instructions generates an audible signal and the message is automatically checked for accuracy and consistency with the previously declared parameters. The operator accepts or rejects the instruction. The information is logged for future comparison and analysis and sent to the Integrated Load Management system for input to the process control system. The integration of these activities ensures an unambiguous record of the despatch instruction and provides accuracy for the plant control strategy.

12.4.3

Integrated Load Management

Compliance with despatch instructions through the timely and accurate delivery of energy and power is an essential task for both the control room operator and process control system. Achieving it requires a concise interpretation of the instruction and an understanding of the compliance monitoring criteria. To assist the operator an Integrated Load Management (ILM) system has been developed to display the target and to monitor the performance of the plant in accordance with the rules. The system acquires the current despatch instruction from the EDL and at any given moment calculates exactly what a generating unit should be producing and profiles the load into the future. It also acquires real-time data from the plant itself (via the metering system), and graphically displays any discrepancies. NETA requires accurate delivery of the contracted energy over each half-hour period. ILM monitors this situation and provides information for both the operator and the control system on the generation required to achieve the targets.

12.4.4

Alarm Analysis Tool

The Alarm Analysis Tool (aAt) has been designed to perform analysis on alarm logs produced by APMS and other process control systems. The aAt allows users to analyse the performance of their alarm system highlighting problem alarms or times of high alarm activity. Part of what the tool does is to do a frequency analysis on alarms logged and results in the production of a table and graph displaying the total number of times each individual alarm occurs. The information derived is useful for the identification of maintenance issues, i.e. problem alarms could be due to either a plant problem or an incorrect set-up of the alarm definition, whilst regular occurrence of high alarm activity could be identifying an opportunity for improved control or need for more automation.

354

Thermal power plant simulation and control

12.5 12.5.1

Added value applications AVA technologies

Shortly after privatisation a research project was started to determine the type of assistance plant operators would need in a competitive market and whether there were opportunities for exploiting new software technologies. As a result of this work, real-time expert system technology and artificial neural networks (ANNs) were both demonstrated to provide potential opportunities. The real-time expert system product chosen to develop applications was Gensym's G2. This product provides a complete real-time programming environment including object orientation, rule base, integrated graphical interface and interfaces to a wide range of control, SCADA and database products. G2 has been used to develop most of the applications described in this section. Although artificial neural networks appeared to offer the opportunity for modelling complicated non-linear systems such as the combustion process, so far no applications have been deployed using this technology. It was hoped to be able to use an ANN model to predict combustion efficiency and emission levels from a set of input plant measurements and control settings. Such a model could then be used to optimise the control settings to minimise some cost function (e.g. efficiency losses) within a set of constraints (e.g. emission limits). To date we have not been able to produce a model of the combustion process that has been accurate over a long enough period. However, there are many reports of ANNs being successfully used for combustion modelling, particularly in NOx reduction software systems. It would therefore appear that, under certain conditions at least, the modelling has been successful. There are many examples of new applications being installed that are unsuccessful since, for various reasons, operators do not use them. In the authors' experience the most common cause of unsuccessful applications is not technical inadequacies but 'soft' issues of human interaction. To be successful, applications must supply appropriate information to operational staff at the right time and in the right format. It is therefore essential to involve operational staff at all stages of application development.

12.5.2

Integrated application framework

The objective for a suite of added value applications (AVAs) is to provide applications to assist the operator in the full range of his/her responsibilities. These include providing flexible operation, avoiding plant damage, improving efficiency, meeting contracts and staying within environmental limits. In general, these requirements cannot be considered in isolation. For instance, a change in the control settings intended to improve efficiency might have a detrimental effect on plant damage and/or emissions. Another potential problem with several AVAs running concurrently is how to provide an integrated user interface. This problem is particularly difficult if the applications produce unsolicited information and advice to the operator. In most control and SCADA systems (including APMS) the user interface provides no mechanism for displaying unsolicited information or requests apart from the alarm list (which would be inappropriate in many cases).

Advanced plant management systems 355 In Innogy, these problems have been overcome by the development of an integrated application framework (IAF), to produce a single integrated system where applications can co-exist and work together as a single entity, rather than just as a collection of individual modules. IAF uses G2 to provide the underlying programming environment for integrating AVAs. IAF consists of a set of standard objects, tools, templates and guidelines to enable a suite of applications to run in a coordinated manner. Thus if, for instance, an application has some advice to be brought to the operator's attention, the application does not display this directly on the screen since it may obscure some other important information. Instead, the application creates a suitable type of communication object, configures it (e.g. the text, priority, period to display, etc.) and despatches it to the IAF communications handler. IAF will then control how the message is displayed and provide links back to the originating application, if required. IAF 'schedulers' can be used to schedule calculations on real-time data obtained from the common repository. These calculations can be implemented either as G2 procedures or as external C / C + + programs called via a bridge (or a combination of both). The results of these calculations should then be interpreted within G2 before being written back to the repository and/or presented to the operator (either through the IAF user interface or through the control system user interface). Actions such as activating and deactivating applications can be done either manually (through the user interface) or programmatically through the application program interface (API). This means that one application can control another (e.g. activate and deactivate it, block its advice, etc.). The extent to which G2 is used as the application development environment will vary according to the requirements of the application. At one extreme, the whole application could be developed in G2 whilst, at the other extreme, G2 could simply supply the data, schedule the execution and return the results of an application developed in C + ÷ . The IAF can run on the main APMS servers but it is preferable for it to run on a separate AVA server. By using a separate server a large suite of applications can be run without overloading the APMS servers and the security of the APMS servers is improved (i.e. rogue AVAs cannot cause APMS to crash).

12.5.3

Plant object module

Applications that operate within IAF normally obtain real-time data from a single G2 module. This module contains the interfaces to all external systems and also all the plant objects that use external data to derive information such as plant states and validated values. A hierarchy of generic plant classes has been developed that determine the operational states of individual components, subsystems and systems. Each object has one or more attributes that obtain real-time data via an appropriate interface. The operational state of the plant object is then inferred from these data. The plant states can take symbolic values such as starting-up, in-service, etc. in the case of, say, a coal mill, or values such as open, closed, partially open, etc. in the case of a valve.

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Whenever possible more than one data value is used for inferring the plant state in order to improve reliability. If necessary, site-specific subclasses can be developed that contain extra attributes and formulas for determining the states of certain specific plant items at that site. This module also processes raw data to produce other types of validated data and derived values that are required for input to applications. Having determined the plant states and other validated data, it is these values that are subsequently used in other applications. The plant object module also provides the repository for public data generated by other applications. This enables information to be exchanged between applications and also provides a standard method for writing data back into external systems (e.g. control set-points).

12.5.4

Startup Management System

This G2 application assists the operator to bring the plant from a shut-down condition up to synchronising the electrical generator to the National Grid. Depending on the temperature of the boiler, the startup times vary from under an hour to several hours. However, the unit should always synchronise within a 4-5 minute window of the instructed time. Starting up a power plant requires a sequence of operations to be performed to bring auxiliary plant into service and to warm the boiler along a profile that matches thermal constraints of construction materials. Optimising the process requires a careful balance between minimising the startup energy costs and limiting plant damage. Traditionally, the startup of a coal-fired unit has been performed manually using the built-up expertise of well-skilled operators. However, analysis of the startup methodology revealed significant variances in the techniques employed and the times allowed. The Startup Management System (SMS) has therefore been developed to achieve reliable startups at minimum total costs. The overall objectives of SMS are to: • • • •

standardise on best operational procedures for startup provide a specific startup plan and schedule for the current plant conditions monitor the plant in real time to provide information on the progress compared with the plan and advise on the next activities to be carried out provide procedure-specific alarms, information and advice to reduce the likelihood of uneconomic plant damage, delays or deviations from the plan to occur

•

automate specific sets of tasks to achieve greater consistency, reduced operator workload and reduced plant damage.

SMS contains information about the activities within a particular type of startup (e.g. hot-start) and their dependencies. This information is displayed graphically to the user via an 'activity network'. The system monitors real-time plant data from the process control system to determine the plant state and the time various activities will require. By combining the information about the startup procedure, the plant state and the time required for each activity, a schedule of activities and the total time required to synchronise the unit is calculated for the prevailing plant conditions.

Advanced plant management systems

Figure 12.5

357

Startup Management System - operator's screen

During the startup, SMS displays to the operator the relevant part of the startup plan and indicates the recommended next activity, Figure 12.5. Each activity contains a set of rules for determining the state of the activity and, where appropriate, functions for estimating the time until completion. The rate of progress through the startup is compared to the plan and indicated to the operator. The system monitors activities to ensure that they are only carried out when the correct conditions are met, and provides warnings if they are not. Monitors can be incorporated into the system to check that key plant parameters stay within prescribed limits during specific periods of the startup. The final stage in developing SMS for a particular station is to start automating some of the tasks. This automation can simply take the form of automatically starting control sequences at the correct time. However, there are facilities in SMS for developing sophisticated 'plant managers' that replicate the type of decision-making and actions that would otherwise have to be made by operators. Thus if an activity involved starting one of several similar plant items, the relevant plant manager would need to determine which item to start, when to start it and, ideally, have a recovery strategy for if the plant were to fail. The plant manager would control the plant by initiating control sequences and/or providing set-points for lower-level controllers. At most sites a 'drainage manager' has been implemented to control the boiler drain valves to achieve 'progressive drainage' during startup. The drainage manager

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waits until the steam temperature in a boiler section matches the temperatures of the outlet headers before admitting steam into the headers by opening drain valves. The timing of the valve opening and their subsequent closing and/or modulation is critical to achieving smooth increases in temperature and pressure and to minimise thermal stresses. The drainage manager can also automatically adjust target conditions and ramp rates within certain limits to attempt to achieve synchronisation on time while limiting plant damage. A substantial amount of intelligence often needs to be built into the drainage manager to cope with the wide range of circumstances that may arise. One example of the type of problem that can arise is the situation where one boiler section still contains condensate and is therefore at saturation temperature while a down-stream section has boiled off its condensate and its tube temperatures are increasing rapidly because there is no steam flow. Under these circumstances the rules for managing the drain valves need to ensure that no water is admitted into hot headers. However, it may be better to allow the drainage to move on to the next boiler section before the ideal temperature match is achieved in order to protect down-stream tubes from over heating. The drainage manager could also advise the operator if a change in firing could improve the situation. In practice, the application of the Startup Management System has considerably reduced the variability of the startup process, giving the operators greater predictability and consistency in achieving synchronisation times. The operator still has important strategic decisions to make and has to manage unplanned incidents. However, he/she is now much better supported in terms of understanding the options and implications.

12.5.5

Cost of Losses

The Cost of Losses (COL) application calculates the efficiency of all the major systems within a power plant at regular intervals and compares them with target values. Differences between the actual and target values (i.e. the heat losses) are expressed as costs per hour. COL is available as a G2 application within the integrated application framework for use by operators. It is also available as an OIS application that can be accessed by any authorised staff. In the G2 version the information is displayed to the operator in tabular and graphical form and the areas where the largest losses are occurring is highlighted, Figure 12.6a and b. If losses exceed certain thresholds, COL can initiate alarms in APMS. The Cost of Losses application is a general-purpose application that needs to be configured for a particular plant. However, it can be used as the starting point for other more specific performance monitoring systems. For example, in one power station, the costs associated specifically with combustion losses due to non-optimal firing conditions are evaluated and displayed to the operator. It is important that all boiler losses are calculated and displayed, since it is the total boiler losses that need to be minimised and not just one component at the expense of another.

Advanced plant management systems 359

Figure 12.6 Costof losses 12.5.6

Particulate emission monitoring system

The level of particulate emissions from power plant must be continuously monitored and controlled to stay within specified limits. In the UK, the Environmental Agency specifies the way in which the emission measurements must be processed to provide hourly, daily and monthly averages and how the information must be reported. The rules governing how the data is processed are quite complicated, as are the rules regarding the allowable number of exceedances. In order to ensure compliance with particulate limits, two emissions monitoring applications have been developed: (1) an on-line system for operational use and (2) an off-line system for retrospective data analysis and producing reports for the Environmental Agency.

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The on-line system has been developed in G2 and provides real-time information on the particulate emissions processed in the form specified by the Environmental Agency. It provides information on the performance during the current hour, day and month, together with the number of exceedances that have occurred over the previous 12 month period, compared with the allowances. This information is essential for operational decision-making and should mean there are no surprises at the end of the reporting periods. The off-line system downloads data from the OIS data archive into a spreadsheet where it is processed by Visual Basic (VBA) macros and the resulting data is stored in a database. The information can be displayed graphically and reports can be generated suitable for submission to the Environmental Agency.

12.5. 7

Chemical Diagnostic Expert System

The Chemical Diagnostic Expert System (ChemEx) provides on-line monitoring of chemical conditions in water/steam circuits and presents operational advice. The system identifies actual or developing problems, diagnoses possible causes and provides recommended actions. The system is designed to avoid unnecessary corrosion damage on the internal surfaces of the boiler, feed system and steam turbine. The system includes the water/steam circuit of drum-type boilers and generator stator water circuit. The initial system is applicable to on-load operation but will be expanded later to cover all operational modes (e.g. startup, off-load, etc.). The core of the system has been made as generic as possible. However, for each site, a site-specific module needs to be produced that contains configuration information needed to specify (1) the plant components present, (2) the input measurements available, (3) the allowable plant limits and (4) plant-specific advice for dealing with detected problems. The rules used for problem identification and diagnosis have been created in G2 using graphical function blocks that can deal with either discrete or 'fuzzy' logic. Input measurements are first converted into belief values for specific symptoms. These belief values are then used as evidence to indicate if specific problems are present or not. If the belief value for a problem exceeds a certain threshold, it is treated as true and triggers an evaluation to determine the most likely underlying cause(s) and recommended actions and alerts the operator. In addition, all relevant information is available in graphical form so that the operator can see how the problem has developed and can monitor the effects of any remedial actions carried out.

12.6

Conclusions

This chapter has described how the move into a competitive electricity generation market has changed the way power plant has to be operated and the need for operational support systems to assist the operator. Plant management systems provide a supervisory layer above the control system where all the relevant plant, contractual and commercial information resides in order to optimise plant operation.

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This optimisation often involves finding the best compromise between various (sometimes conflicting) requirements. In some cases the optimisation can be performed within a supervisory control system, employing techniques such as model-based predictive control. In many other cases it is currently still the operator that has to make the final decisions, but with the help of suitable support systems. These support systems may simply present the operator with all the relevant information from a variety of sources in a suitable (usually graphical) form. Other applications go further by analysing this information using 'intelligent' technologies such as expert systems to provide recommended actions or even to directly provide set-points for the control system. In order to achieve the full benefits of an advanced plant management system, some of the underpinning requirements are: • •

• •

openness in the underlying process control system real-time database containing all relevant plant, contractual and commercial information integrated human-machine interface a framework for running a suite of applications in a coordinated manner.

12.7

References

LICHNOWSKI, A., and DICKEN, C.: 'Power generation: the advanced control desk', in NOYES, J. and BRANSBY, M. (Eds.): 'People in control: human factors in control room design' (lEE Control Engineering Series 60, 2001) pp. 259-272 OLUWANDE, G., and BOUCHER, R.: 'Implementation of a multi-variable modelbased predictive controller for superheater steam temperature and pressure control on a large coal-fired power plant'. ECC '99, Karlsruhe, Germany, 1999 PEREZ, L., PEREZ, E, CEREZO, J., CATEDIANO, J., and SANCHEZ, J.M.: 'Adaptive predictive control in a thermal power station'. 3rd IEEE Conference on Control Applications, Glasgow, UK, pp. 747-752, 1994 ROSSITER, J.A., KOUVARITAKIS, B., and DUNNETT, R.M.: 'Application of generalised predictive control to a boiler turbine unit for electricity generation', Proceedings lEE Part D, 138, (1), pp. 59-67, 1991 VASUDEVA, K.S.: 'Power plant operation and maintenance cost reduction through control system improvements', Power Engineering Journal, 5, (2), pp. 73-84, 1991

Part 4

The future

Chapter 13

Physical model-based coordinated power plant control G. Prasad

13.1

Introduction

In today's privatised power industry, a thermal power plant capable of making faster adjustments in power output in response to the system demand has significant competitive advantages. Such a plant may often be required to operate in a load-cycling or two-shifting manner resulting in non-linear changes in plant variables. A thermal power plant is a highly coupled large-scale multivariable dynamic system. It is normally controlled by multiloop PI/PID controllers. The control performance of these loops is adversely affected by inter-loop interactions. In addition, normal working of a power plant is severely affected by the occurrence of a range of system disturbances. Some common disturbances are changes in active burner configuration, heat-exchanger tube fouling, and variations in condenser vacuum. Being a highly coupled system, the disturbances in one part of the plant can have a significant effect on the rest of the plant as well. In order to minimise the influence of both plant-wide interactions and disturbances so as to ensure a higher rate of load change without violating thermal constraints, a coordinated control strategy is required. This control strategy should coordinate the activities of various subsystems of a thermal power plant to achieve optimal performance during large load changes and system disturbances by minimising the adverse effects of plant-wide interactions. Such a control strategy can very effectively be implemented by making effective use of the tremendous potential for synergy of a physical model with model-based predictive control (MBPC) techniques (Maciejowski, 2002). This is because a global first-principles (or physical) model can provide an accurate prediction of system behaviour in non-linear operating regions and facilitate inferential estimation of important unmeasured plant variables, such

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Thermal power plant simulation and control

as metal temperature, that are critical to the life of the plant components. Such critical variables, along with inputs and outputs, can explicitly be constrained to vary in the most profitable range by on-line constrained optimisation under an MBPC strategy. A physical model also facilitates on-line estimation of the main plant parameters that are affected during system disturbances. This helps to reject the effect of disturbances extremely quickly (Prasad et al., 2000). Additionally with a global physical model, it is possible to account for dynamic interactions more favourably using a predictive control strategy. Building a physical plant representation is, however, a very time-consuming and expensive task. Nevertheless commonly available industrial power plant simulators can be employed for relatively fast development of a reduced-order generic model, which sufficiently describes the dominant dynamic and static characteristics of a power plant. Recognising the aforementioned potential for gaining substantial advantage by the use of physical models, several proposals for physical model-based coordinated control of thermal power plant have been made in the literature. These are briefly discussed in the next section. Using the example of the 200 MW oil-fired Ballylumford thermal power plant, an analysis of the dynamics of boiler-turbine operation is presented in section 13.3. A model simulating the dominant static and dynamic characteristics of the plant has been used for the purpose of analysis. Section 13.3 gives brief details of this plant simulation. Section 13.3 also includes discussion of the main system disturbances and constraints that have a significant influence on the economics of power plant control. A formulation of a non-linear physical model-based predictive control (NPMPC) approach for application to power plant simulation is described in section 13.4. Section 13.5 discusses the effectiveness of the physical model-based predictive control approach in disturbance rejection, accounting for plant-wide interactions, constraint handling and set-point following. This is based on the simulation results obtained by running the plant simulation under severe but realistic operating conditions. The concluding discussion is finally presented in section 13.6.

13.2

A review of physical model-based thermal power plant control approaches

Using optimal control theory, there have been several attempts to apply physical model-based control to a power boiler. Model-based plant control was first proposed more than forty years ago in the paper by Chien et al. (1958). Other notable early works are those of Nicholson (1964, 1966, 1967) and Anderson (1969). As the plant models used in these early studies could not provide an adequate characterisation of a typical power boiler, the results obtained with a coordinated control scheme using optimal control theory were not very encouraging. McDonald and Kwanti (1973) later proposed applying an optimal controller combined with a complete state estimator (incorporating the estimation of exogenous disturbances to allow steady-state optimal regulation) to a drum boiler power plant. It is based on a detailed non-linear plant

Physical model-based coordinated power plant control

367

model. It makes use of optimal regulator theory recognising the limitation of an imperfect model and produces integral type action which guarantees zero steady-state errors. Cori and Maffezzoni (1984) combined linear quadratic Gaussian (LQG) design with conventional control expedients to provide a practical optimal regulator and evaluated it on a real plant by a direct digital control system. This was an experimental application of optimal control to a drum boiler power plant. They used a physically based mathematical model, some parameters of which had been estimated by field tests. Model reduction was applied to get a simplified control structure. The regulator included feedforward and integral control, and had a number of practical advantages and improved robustness against plant parameter variation. It assumes a hierarchical control structure in which the multivariable optimal regulator acts as a set-point controller at a higher level with 4.8 s sampling period, while the lower-level local feedback loops, with 2.4 s sampling period, maintain their traditional decoupled structure. Kallappa et al. (1997) have proposed a life-extending control strategy for fossil fuel power plants. Its objective is to achieve a trade-off between structural durability and dynamic performance. The paper focuses on structural durability of the main steam header under load-following to illustrate how the life extending control of fossil fuel power plants can be achieved via feedforwardffeedback. The feedforward control policy is synthesised via non-linear off-line optimisation of a multi-objective cost function of dynamic performance and service life, under the constraints of actuator saturation, operational limitations, and allowable structural damage, including thermomechanical fatigue and plastic deformation. The feedforward sequence is based on a 1 s sampling time. A linear robust feedback control law that is superimposed on the feedforward sequence is synthesised, based on induced L2-norm techniques. The feedback sequence is based on 0.1 s sampling time. When implemented in a plant simulation, this control policy is shown to be capable of ramping up the plant power at a rate of 10 per cent of the full load per minute, while maintaining the plant performance and satisfying the damage constraints. In recent years several researchers have proposed model predictive control strategies based on a physical plant model (Katebi and Johnson, 1997; Ordys and Kock, 1999; Prasad et al., 2000; Prasad et al., 2002) for improved control of a thermal power plant. Based on a linear physical plant model, Katebi and Johnson (1997) propose the application of a decentralised predictive control scheme based on a state space implementation of generalised predictive control (GPC) (Ordys and Clarke, 1993) in a combined-cycle power plant. They make use of a two-level decentralised Kalman filter to locally estimate the states of each of the subprocesses of a power plant. A two-level optimisation strategy then decomposes the global GPC problem into manageable subproblems. The GPC solution for each low-level subprocess is independently found, before updating the high-level optimal coordinator. They report improved performance from this two-level optimising control strategy, mainly on the grounds that it optimally accounts for adverse effects of system-wide interactions. In another related notable work, Ordys and Kock (1999) present a comparison of control performance obtained with a linear state space model-based GPC and dynamic

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performance predictive controller (DPC) applied in a gas turbine power plant simulation. They report relatively improved performance of their DPC algorithm in dealing with cross-couplings, specially in tightly constrained cases. Adopting a different predictive control approach, Prasad et al. (2000, 2002) present a non-linear physical model-based predictive control (NPMPC) strategy for effective handling of plant-wide interactions and system disturbances. To account for the effect of sustained system disturbances, the NPMPC strategy models a selected set of plant parameters as stochastic variables. This stochastic disturbance model in combination with the physical plant model is used by the NPMPC algorithm for prediction purposes. Successive linearisation and extended Kalman filtering (EKF) are used to obtain a linear state space model as a basis for a constrained long-range predictive controller design. Adopting the approach taken by Prasad et al. (2000, 2002), this chapter discusses the effectiveness of a physical model-based coordinated control strategy by evaluating its control performance under severe operating conditions involving large load changes and commonly occurring significantly large system disturbances. The chapter also discusses how constraint handling of MPC helps in preventing thermal constraint violation while ensuring the highest possible rate of load change.

13.3 13.3.1

Control problems of a thermal power plant Simulation of a 200 M W thermal power plant

A simplified schematic diagram of the 200 MW Ballylumford power plant is shown in Figure 13.1. Here, the main steam pressure is maintained at 164 bar by manipulating the fuel flow valve (FFV) and accordingly the air flow damper (AFD) to maintain an optimal air-fuel ratio. The plant uses three-stage superheaters: a convection-type primary superheater (PH), a secondary superheater (SH), and a radiant-type platen superheater (PL) for superheating the saturated steam of the drum (DR) to 540 °C. The

PL

TGv

I

I

'

FGR

Figure 13.1

Simplified schematic of Ballylumford power plant

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superheated main steam flow to the HP turbine is controlled by a turbine governor valve (TGV). There is also a reheater (RH) for reheating the exhaust steam from the HP turbine back to 540 °C. The reheat steam enters the IP/LP turbine through an intercept valve (ICV). The main steam temperature is controlled by inter-stage attemperators: a first-stage attemperator (AT1) in the in-coming steam to the PL and a second-stage attemperator (AT2) in the in-coming steam to the SH. There is also an attemperator (ATr) for reheat steam temperature control, but this is used sparingly. Control of reheater temperature is normally achieved by manipulating the flue gas recirculation (FGR) damper, through which flue gases from the economiser exit are injected into the furnace hopper. A simulation of the above plant has been created in Matlab/Simulink ® using a physical model (Lu et al., 1995; Prasad, 1997), describing mainly the boilerturbine dynamics of the Ballylumford power plant for the top 60 per cent of the load range. The model consists of 14 first-order non-linear differential equations and more than 100 algebraic equations. It has 14 states, nine inputs, and 16 outputs (Tables 13.1 and 13.2). Multiloop PID controllers, similar to those in the actual power plant, are also implemented to control all the important plant outputs. Normalised random sequences are added to the outputs to simulate measurement

Table 13.1

Simulation inputs and outputs

Input (u)

Output (y)

Feedwater flow (kg/s) First stage attemperator spray flow (kg/s) Second stage attemperator spray flow (kg/s) Reheater attemperator spray flow (kg/s)

Drum water level (mm) Drum steam pressure (MPa) Main steam flow (kg/s) Primary superheater outlet steam temperature (°C) Platen superheater inlet steam temperature (°C) Platen superheater outlet steam temperature (°C) Secondary superheater inlet steam temperature (°C) Secondary superheater outlet steam temperature (°C) Main steam valve pressure (MPa) Governing stage outlet steam temperature (°C) Total heat flow in steam cycle (MW) HP turbine power output (MW) Reheater inlet steam temperature (°C) Reheater outlet steam temperature (°C) IP turbine inlet steam pressure (MPa) IP/LP turbine output (MW)

Fuel flow (kg/s) Air flow (kg/s) Flue gas recirculation flow (kg/s) Goveming valve area (unity) Intercepting valve area (unity)

370

Thermalpower plant simulation and control Table 13.2 Simulation state variables State variables (x p) Outlet enthalpy of economiser (kJ/kg) Mean temperature of economiser metal wall (°C) Outlet pressure of drum (MPa) Volume of saturated water in evaporation system (m3) Mean temperature of riser metal wall (°C) Outlet enthalpy of primary superheater (kJ/kg) Mean temperature of primary superheater metal wall (°C) Outlet enthalpy of platen superheater (kJ/kg) Mean temperature of platen superheater metal wall (°C) Outlet enthalpy of secondary superheater (kJ/kg) Mean temperature of secondary superheater metal wall (°C) Outlet enthalpy of reheater (kJ/kg) Mean temperature of reheater metal wall (°C) Inlet pressure of high-pressure turbine (MPa)

noise. The following general assumptions and considerations are made in the model formulation: •

• •

•

The effect of feedheater dynamics is omitted, as it makes an insignificant contribution to overall system dynamics. The effect of condenser dynamics is also excluded. The air and gas dynamics are neglected as the time constants involved are much smaller in comparison to other process lags. The compressibility of steam in the boiler subsystems is ignored because velocities in those subsystems are very small in comparison to sonic velocity. It is however considered for link pipes between the high-pressure turbine and intermediatepressure turbine, as the large volume of steam gives the low-pressure turbine a considerable lag. The effects of all of the working media (water and steam) and metal walls are separately considered, as it avoids using inaccurate effective metal coefficients and improves the model accuracy.

13.3.2

Analysis of boiler-turbine operation

The heat transfer in a power plant boiler takes place through radiation and convection modes. Evaporation in the water-wall tubes is mainly due to heat radiation from the translucent flame surface in the furnace. It is this process which has a major influence on the steam pressure and the water level in the drum. The superheating of steam in the platen superheater, secondary superheater and reheater tubes takes place due to either, or both, of the radiation and the convection heat transfer from the flue gases

Physical model-based coordinated power plant control 371 coming from the furnace. This depends upon the relative position and exposure of the particular heat exchanger tubes. The position and the area of the flame surface depends upon the active burner sequence. It also depends on the air-fuel ratio, as excess air pushes the flame surface further upward in the furnace and it also reduces the average flame temperature. Heat transfer through radiation is proportional to the fourth power of the absolute temperature of the flame surface. The convection heat transfer to the superheater and reheater tubes from the flue gases is proportional to temperature and flow rate of flue gases coming out of the boiler fumace. So the final steam temperature coming out of these heat exchanger tubes will depend on the temperature and flow rate of the flue gases and the incoming temperature and flow rate of steam passing through the tubes themselves. Attemperator sprays, which influence the incoming steam temperature, are normally used to control the final superheated steam temperature, before it enters the HP turbine. Flue gas recirculation (FGR) is mainly used for controlling the temperature of steam coming out of the reheater. FGR is a process in which flue gases from a point after the economiser in the rear pass of the boiler are taken out and reinjected into the base of the furnace. This reduces the average temperature of the flame surface, resulting in less heat transfer through radiation. This causes the flue gases to maintain a greater quantity of combustion heat. As a result, the rate of convection heat transfer to the superheater tubes and reheater tubes is altered. This results in changes in the final superheat and reheat steam temperatures. The FGR also influences the radiation process, but although quite small it certainly has some effect on steam pressure and water level in the boiler drum. There are two main modes of plant operation: constant steam pressure and variable steam pressure. In constant steam pressure operation, the governor valve opening responds to changes in power demand by varying steam flow to the turbine for the desired shaft power. In variable pressure operation, it is the combination of both the changes in steam pressure as well as governor valve opening. In any case, there is a strong interaction between the three variables, i.e. governor valve opening, main steam pressure and steam flow. As mentioned earlier, steam flow also has a strong influence on steam temperature dynamics. So, for example, as steam pressure and steam flow change, the drum water level is affected leading to compensatory adjustments in feedwater flow. Based on this brief analysis, it is clear that steam production in the boiler is a highly interactive and multivariable process.

13.3.3

Economics of plant operation

For higher thermodynamic steam cycle efficiency, the plant should operate with maximum possible main steam temperature, as well as main steam pressure and reheat steam temperature (Rogers and Mayhew, 1992). However, metallurgical constraints on the boiler and turbine components limit the maximum temperature and pressure of the steam. Within the allowed metallurgical limits, stresses caused due to the rate of change in both temperature, pressure and temperature differences within particular components

372

Thermal power plant simulation and control

further constrain plant dynamics. Violation of these constraints severely impairs the life of the plant components and sometimes even leads to emergency situations. The actuators driving important control variables such as recirculating gas dampers, servomotors of turbine valves, etc. strongly influence dynamic performance, due to severe non-linearities and intrinsic rate limits. As a result, they impose very important constraints on plant control. The temperature of the steam delivered to the turbine is maintained within close limits of rated main steam temperature at the stop valve outlet. The final temperature is controlled by spraying water into the steam by attemperators. Excessive attemperation, however, causes overheating of the superheater tubes preceding the attemperators, since steam generated by evaporation of spray water does not pass through these tubes. The spray water also causes loss of exergetic efficiency of the superheated steam due to heat transfer through a very high temperature difference. As in the above case, the temperature of reheat steam supplied to the IP turbine is also maintained close to the rated value. This is accomplished first by manipulating the FGR, and if the reheat temperature is still rising beyond the recommended limit, it is then controlled by spraying water through the attemperator. The use of spray water causes loss of steam cycle efficiency, as part of the steam never passes through the HP turbine. It also causes loss of exergetic efficiency of the reheat steam. Thus for economical operation it is not only important to maintain the rated main steam temperature and reheat temperature within extremely close limits, but also that spray water should be minimised. In the constant-pressure mode of operation, the pressure upstream of the turbine valves is held constant over the entire load range, to achieve the highest rate of load change. Load control is achieved by modulating the turbine valves. In the variablepressure mode of operation, the boiler pressure is allowed to vary as a linear function of load, to achieve the optimum temperature conditions in the turbine. Reduced thermal stress within the turbine results from a reduced temperature drop in the first stage wheel in this mode. This is shown in Figure 13.2, obtained as a steady-state result from the plant simulation run. The main steam pressure was linearly varied from 87.2 to 164 bar over the load range 80 to 200 MW. Now, consider the boiler dynamics in the case of a sudden load change. Assume that the load demand ramps up, in the variable-pressure mode of plant operation. The governor valves open quickly to provide the initial load response by taking advantage of boiler-stored energy. The fuel flow increases very rapidly at the beginning of the load change to supply the desired increase in steam flow and also to build up the boiler pressure. Initially the boiler is overtired by a considerable amount in order to make up for the rather slow response of the drum pressure. As the drum pressure starts to increase, the amount of overfiring is decreased. Then as the drum pressure starts to reach its desired value, the turbine valves return to their initial positions. During the time the boiler is being overtired, there is a very fast rise in steam temperatures initially. In order to demonstrate the control complexity of the large load change in variable-pressure mode, the generated power was ramped up at 2.5 per cent of full load per minute in the plant simulation while the plant was controlled using multiloop

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overfiring, as the boiler drum pressure is not significantly affected, with much less attemperation spray water flow to control the steam temperatures. Figure 13.3 shows that the same PI controller gives relatively good performance in regulating the main steam temperature and reheat steam temperature during the ramping up of load in constant-pressure mode. However, this mode of operation results in greater change in the first-stage steam temperature as well as a higher temperature difference between the reheat steam and main steam, resulting in higher thermal stress in the turbine. As a result, the rated main steam and reheat steam temperature cannot be maintained at loads below a typical value of 60 per cent MCR (Dieck Assad et al., 1987), in constant steam pressure mode. It should be noted that although attaining constrained optimal control performance is extremely difficult it may be possible, by better tuning of the multiloop PI controllers, to improve upon the control performance shown. The main objective, however, here is to show the relative difference in control performances between the two operating modes using PI controllers with the same control parameters.

13.3.4

Plant disturbances

Plant dynamics change significantly during major system disturbances. Occurrence of these disturbances thus results in greater plant-model mismatch. Speed of disturbance

Physical model-based coordinated power plant control 375 rejection is one of the most important properties determining the capability of a control technique. However, taking full advantage of the knowledge within the complete physical plant model, it is possible to identify the main plant model parameters affected by commonly occurring major system disturbances. The fundamental sources of major system disturbances (or changes in system response) in a thermal power plant are: • • • • •

heat transfer disturbances in the furnace heat exchanger tube fouling/blockages deterioration in efficiencies of turbine cylinders changes in condenser characteristics due to cooling water temperature variation, air leakage and tube fouling problems in feedheaters due to tube blocking/fouling.

These disturbances alter the system parameters used in plant modelling. In a lumped parameter model, the main parameters affected due to the above disturbances are: • • • • • •

radiation heat transfer coefficient between the evaporator (water-wall) tube metal and the flame surface convection heat transfer coefficients between heat exchanger tube metal and flue gases convection heat transfer coefficients between steam/water and heat exchanger tube metal efficiencies of the HP, IP and LP cylinders condenser vacuum quantity of bled steam and efficiency of heat transfer.

The system disturbances can thus be very effectively modelled as stochastic variations in a subset of the model parameters mentioned above.

13.4

Applying a physical model-based predictive control strategy

A non-linear physical model-based predictive controller (NPMPC) applied in a hierarchical structure to a thermal power plant simulation and developed under the Matlab/Simulink ® environment is shown in Figure 13.4. The drum level and power output are controlled through a two-level control structure. The set-points for the drum level PI controller and the power output PI controller are manipulated by the higher-level NPMPC. The main steam temperature and pressure and the reheat steam temperature are controlled directly by NPMPC. A velocity-type discrete PI implementation is adopted, similar to the lower-level controllers normally employed in a thermal power plant in a multiloop control structure. Here the drum-level PI controller helps stabilise the unstable drum-level dynamics and the power output PI controller facilitates manipulation of the governor valve at a much higher speed independent of the higher-level NPMPC controller for faster rejection of high-frequency

376 Thermalpower plant simulation and control

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Figure 13.4 Hierarchical control strategy disturbances due to imbalances in demand and supply of electric power (Prasad et al.,

2002). 13.4.1

Main control objectives

As discussed in the previous section, a thermal power plant is required to supply electric power with optimum efficiency. The best trade-off between steam-cycle efficiency and plant life (Prasad et al., 2000; Prasad, 1997) results in prescribing certain fixed values along with a recommended range of variation to the main steam pressure and temperature and to the reheat steam temperature. The steam separator should work at a specified value of water level in the drum. An optimum air-fuel ratio is maintained to ensure better combustion quality and to minimise environmental impact. Assuming a fixed air-fuel ratio, the main objectives of the plant-wide coordinated control

Physical model-based coordinated power plant control 377 problem are therefore to optimally control the following output variables. yl (t) ~ drum level y2(t) ~ main steam pressure

y(t) =

y3(t) ~ main steam temperature y4(t) ~ power output

Y5(t ) ~ reheat steam temperature As shown in Figure 13.4, the above outputs will be controlled by the higher-level NPMPC controller by manipulating the following input variables: ul (t) ~ drum level set-point u2(t) ~ first stage spray flow u3(t) =A second stage spray flow u(t) =

u4(t) =`5 RH spray flow

us(t) =`5 fuel flow

u6(t) ~ flue gas recirculation flow u7(t) ='5 power set-point For reasons of thermal efficiency, the reheat spray flow u4 (t) should not be used until the reheat steam temperature starts rising beyond the recommended maximum limit, i.e. 540 + 5.5 °C and the flue gas recirculation control alone is unable to regulate. The controller would also be required to account for frequently occurring disturbances that may have a significant effect on the plant dynamics and the closed-loop plant response as discussed in the previous section.

13.4.2

Algorithmic details

The algorithmic formulation of the control strategy can be summarised by the block diagram shown in Figure 13.5. It consists of a non-linear physical model-based extended Kalman filter (EKF) for reconstruction of the process states, x p, and the unmeasured disturbance states, x d, required for estimating the unmeasured disturbance inputs, u a. These reconstructed or estimated states are then used by the higher-level NPMPC controller to compute set-points for lower-level controllers. A set of directly manipulated input variables is also computed by the NPMPC controller. The disturbance states x d are associated with a set of model parameters (Table 13.3) which are assumed to have stochastic variation to account for commonly occurring system disturbances. The non-linear physical model used in the NPMPC is obtained by combining a physical plant model with an appropriate disturbance model as discussed next. Assume that a plant model is expressed by the following non-linear state space equations: JfP = f ( x p, U, U f, Ud) and y = g ( x p, U, U f, Ud) (13.1)

378

Thermal power plant simulation and control Set-points(Yr)

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Figure 13.5

Non-linear physical model-based control (NPMBC) algorithm

Table 13.3

Selected model parameters

Symbol

Model parameter (x d)

kwww O/ww

Radiation heat transfer coefficient for water-wall Convection heat transfer coefficient between water-wall tubes and saturated water Convection heat transfer coefficient between secondary superheater tubes and steam Convection heat transfer coefficient between reheater tubes and steam Convection heat transfer coefficient between flue gases and platen superheater tubes Convection heat transfer coefficient between flue gases and secondary superheater tubes Convection heat transfer coefficient between flue gases and reheater tubes Condenser vacuum

Otsh Otrh Otwpl t~wsh ~wrh Pcond

where xP, u, u f u d denote vectors of process states, manipulated inputs, the known feedforward inputs, and the unmeasured disturbance inputs, respectively. For discrete controller design, u, u f and u d can be assumed to be constants between sampling instants. A discrete version of the model equations (13.1) can hence be expressed as:

X p = Fts (Xk_l,Uk_l,Uk_l, P f ud_l)

and

Yk

g(x pk, uk, u fk, u dk)

(13.1a)

Physical model-based coordinated power plant control 379 where Ft,(XP_l , uk-1, u~_ l, ud_l) denotes the terminal state vector obtained by integrating the ordinary differential equation (ODE) in equation (13.1 a) for one sample interval ts with the initial condition of Xk_ p 1 and constant inputs of u = uk-1, Uf f and U d -d Uk_ 1 -- Uk_ 1. The unmeasured system disturbances can be taken into account by assuming an integrating zero-mean white noise type variation in a few selected model parameters affected by major system disturbances. However, it is important to ensure that the selected model parameters provide additional degrees of freedom in estimating the controlled outputs in steady-state. Based on these considerations, a set of eight model parameters listed in Table 13.3 was selected. The unmeasured disturbances u d can thus be represented by: xd

d 1 ~ Wk_ d l and u d ----xd Xk_

(13.2)

where w d is a zero-mean Gaussian white noise sequence with a covariance of Qo. Taking into account the possibility of additive process and measurement noise, a discrete version of the model equation (13.1 ) can then be expressed as follows:

[Xp] Lx

fts( k-l,l~k-l,Uf-l,xd d Xk1 f xk) d + vk Yk = g( xp, uA, u A, J=

1)

][I0] +

P

d

w

_l+

(13.3)

w _l (13.4)

where vA and w p are vectors of zero-mean Gaussian white noise sequences with covariances of R v and QP, respectively. Using an EKF the optimal estimates of the process states, xP, and disturbance states, x d, are obtained. A set of linear discrete state space equations is then created using standard iinearisation (Taylor and Antoniotti, 1992) and discretisation techniques. A detailed mathematical formulation of the EKF estimator, and linearisation and discretisation processes is given by Prasad et al. (2000). To the linear system equations, a state space representation of a pair of velocity-type discrete PI controllers is then added in series to account for the lower-level controllers. After further algebraic manipulation (Prasad et al., 2000), the following linear equations for the combined system are obtained:

Xk+i+llk : Axk+ilk q- BAUk+i "q-Bfui+i d- r0k/ Yk+ilk

f

f

Cxk+ilk + DAUk+i + D Uk+i q- tPOkI

(13.5)

where x is a composite state vector and F0k and ~ k are linearisation constants or offsets for states and outputs respectively. From equation (13.5), m-step ahead prediction of outputs can be derived as: m

m

Yk+mlk : C(A)mXkIfk + ~ c(a)m-J BAuk+j-1 + Z c(a)m-J Bfu[+J -1 j=l

j=l

m

+ y ~ C(A)m-JFok + DAUk+m + Dfui+m + 990k. j=l

(13.6)

380

Thermal power plant simulation and control

Assuming unity dead-time and k as the present time interval, the controller performance index is formed as

MinJk = [ ~ (Yk+jlk -- Yrk+j) TAYj(Yk+jtk -- Yrk+j) [j=l + E((AUk+j-I)TAjAUk+j-I) j=l

}

(13.7)

subject to:

Umin < Uk+j-I < Umax, for j = 1 to M

(13.7a)

for j = 1 to N

(13.7b)

Xmin < Xk+jlk < Xmax, for j = 1 to N

(13.7c)

AUmin ~< AUk+j-I ~ AUmax, for j = 1 to M

(13.7d)

AXmin < AXk+jlk < AXmax, for j = 1 to N

(13.7e)

Ymin < Yk+jlk < Ymax,

where N, M, AjY and Aju are the finite output prediction horizon, the number of projected control moves or control horizon, the weighting matrix for prioritising controller action among multiple outputs, and the weighting matrix to penalise incremental changes in controls, respectively. Using equation (13.6), p-predicted outputs can be written in standard GPC format (Ordys and Clarke, 1993) as

Y = Yf + G A U

(13.8)

whereY . [Yk+llk Yk+21k Yk+NIk ]T' Yf [Yf+llg Yk+21k f f T, . . . . "'" Yk+NIk] AU = [AUk AUk+I .'. AUk+M_I] T. Also, G is the step response matrix and Yf+ilt~ is the/-step-ahead predicted output vector keeping u fixed at uk-1. After substituting (I 3.8) into (13.7), the unconstrained solution of the optimisation problem is A U = (GT AYG + A u ) - I G T AY(Yr -- Yf) (13.9) where Yr is a vector of set-point trajectories defined as Yr = [Yrk+l Yrk+2 "'" Yrk+N]" The constrained solution is obtained by solving on-line the constrained optimisation problem (13.7a-13.7e) using a quadratic programming (qp) routine available in Matlab.

13.4.3

Relationship with original state space GPC

Based on the original input-output or transfer function form, the unmeasured disturbances are assumed to act only at the outputs in the state space GPC derivation

Physical model-based coordinated power plant control

381

(Ordys and Clarke, 1993). The non-linear model representation in equations (13.2) and (13.3-13.4) will therefore change to: Xp :

Fts(XP_I,Uk-I,U[_I

P 1 ) -b lOk_

(13.10)

X k : X k _ 1 nt- llOk_ 1

(13.11)

Yk = g( xp, uk, u [) + x d + vk.

(13.12)

d

d

d

This means that the disturbance states, x d, do not correspond to plant parameter states having stochastic variation. Additionally they do not provide corrections to process states, xP. State space GPC can also be implemented using the state estimates obtained from EKF and the model in equations (13.10-13.12), as in the NPMPC above. This form is described as state estimation-based GPC (SEGPC) in later simulation results.

13.5

Simulation results

In order to evaluate the effectiveness of the hierarchical NPMPC control strategy, the plant simulation was run under a set of severe but realistic operating conditions. The following parameters were used as a default set in all the tests. N=20,

M=

10,

Ay=I,

Au=0.1I.

The sampling periods were 10 s for NPMPC and 1 s for PI controllers. The 10 s sampling period for NPMPC was selected based on the fastest dominant dynamics of the plant (Prasad et al., 2000). A detailed discussion about the selection of parameters for the predictive controller and EKF estimator can be found in Prasad et al. (2000, 2002). For comparison purposes, test results were also obtained with a conventional but comparable state estimation-based generalised predictive control (SEGPC) method designed under similar conditions. No comparison is made with multiloop PI controllers, as control performance is far too poor under severe operating conditions, as already demonstrated for the typical case of a large load transition in section 13.3. Test results are discussed and analysed in the following subsections. 13.5.1

F u r n a c e disturbances u n d e r varying c o n d e n s e r v a c u u m

In order to verify the low-frequency disturbance rejection capability of the hierarchical control structure, two commonly occurring system disturbances were applied simultaneously. The turbine side was disturbed by applying random step changes in the condenser vacuum. The heat transfer process in the furnace was disturbed on the boiler side. Along with disturbance injection, as per worst-case performance testing practice in Ballylumford power plant, a 4-40 MW step change in the load-demand set-point was also applied. The mechanical power obtained from the LP turbine is directly affected by changes in the turbine back-pressure or condenser vacuum. In fact, it is one of the most

382

Thermal power plant simulation and control

important plant parameters determining the efficiency of a thermal power unit. The condenser vacuum changes as a result of air leakage, variations in cooling water temperature, and the formation of scale inside the heat exchanger tubes. In order to simulate a situation of varying condenser vacuum, random step changes in the condenser vacuum were made in the range 25-70 mbar. As seen in Figure 13.6a, there is an immediate change in the power output in response to a change in the condenser vacuum. Being a highly coupled system, the rest of the plant outputs also experience significant fluctuations. In a multiple burner furnace, such as a power plant boiler, the position of the flame surface, and thus the radiation heat transfer, is dependent on the configuration of the set of active burners, which are quite often adjusted by plant operators for various operational reasons. In order to simulate furnace disturbances, 4-10 per cent random step changes in the radiation heat transfer coefficient were applied as shown in Figure 13.6c. As seen in Figures 13.6a-d, the step changes have quite a significant impact on all the controlled variables. Another important feature of this control problem is that there are seven manipulated variables and only five controlled variables, thus providing two extra degrees of freedom. Therefore, the particular constraint placed on the reheat spray flow can easily be satisfied by on-line optimisation, while ensuring that the reheat steam temperature is controlled optimally. The main steam temperature is normally controlled by spray water flows in two stages. Such a provision facilitates control of the main steam temperature, even if the spray flow is partially or fully blocked in one of the stages due to some mechanical problems such as tube leakage or valve failure. In order to verify these possibilities, both the NPMPC-based and SEGPC-based control strategies were applied with active amplitude and rate constraints on the manipulated variables. The first stage spray flow was intentionally blocked by setting its maximum amplitude to zero. Similarly, to avoid unnecessary use of reheat spray flow, its maximum amplitude was forced to stay at zero until the flue gas recirculation was fully cut off and reheat steam temperature starts rising beyond 545.5 °C. Based on plant data, typical values of the input rate constraints were: Aumax = [9.0 0.0 0.5 0.0 0.5 3.0 10.0] T and AUmin : -AUmax. As is evident from the results in Figures 13.6a-f, the NPMPC-based hierarchical controller rejects the disturbances very quickly. Disturbance rejection by SEGPC is, comparatively, very slow. Higher deviations from the set-points are observed in all the controlled variables with the SEGPC-based strategy. One obvious reason for the better performance of the NPMPC strategy is the deliberate consideration of the radiation heat transfer coefficient and condenser vacuum as stochastic disturbances, which facilitates their on-line estimation. The estimated condenser vacuum is compared with its true value in Figure 13.6a. A comparison between the estimated radiation heat transfer coefficient and its true value is shown in Figure 13.6c, which demonstrates excellent tracking performance. The estimation of the condenser vacuum is however not as good as that of the radiation heat transfer coefficient. This is because the value returned by the estimator has been adjusted to recognize other plant model mismatches.

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386

Thermal power plant simulation and control

As seen in Figure 13.6d, the on-line optimisation has obtained excellent main steam temperature control even when the first stage spray flow was completely blocked. Furthermore, reheat spray flow was completely avoided, as seen in Figure 13.6e.

13.5.2

Variable-pressure operation

Assuming a linear rise or fall in the main steam pressure with load, a trapezoidal load demand signal was applied to test the performance of the controller under variablepressure operation. As shown in Figure 13.7a, the load demand set-point was varied between 200 and 120MW at a rate of 10MW/min (i.e. 5 per cent MCR/min) and proportionally the main steam pressure set-point was varied between 164 and 112.8 bar (i.e. 0.64 bar/min). As discussed in subsection 13.3.3, the variable-pressure operation involves large changes in drum pressure or saturated steam pressure, leading to significant overfiring or underfiring in the furnace. The resulting large variation in the main steam and reheat steam temperatures and limits the maximum allowed rate of load change. It thus becomes a challenging control problem to achieve a larger rate of load change while ensuring that the thermal stresses in the heat exchanger tubes are within allowed limits. The metal temperatures of the heat exchanger tubes depend upon the temperatures of the superheat or reheat steam inside the tubes. However, increased thermal stresses are caused by a higher rate of change in the tube metal temperatures. It is therefore more appropriate to apply rate constraints directly to the metal temperature of a heat exchanger rather than to the steam temperature, if possible. Two sets of results are shown in Figures 13.7a-e for the constrained and unconstrained cases. A typical value of 0.6 °C/min was applied as a rate constraint on the secondary superheater tube metal temperature, defined as a state variable in Table 13.2. In order to observe the effect of state constraints exclusively, the input constraints were relaxed slightly in comparison to the test of the previous subsection. The first stage spray was not blocked in the current test. As seen in Figure 13.7b, during both the constrained and unconstrained cases, set-point following is so sharp that it is difficult to differentiate between the actual main steam pressure and the set-point. However, during the constrained case, the rate of change in main steam temperature is slowed down. This is shown in Figure 13.7d. The rate of rise in generated power output is also reduced, as seen in Figure 13.7a. Although this has resulted in larger set-point deviations, it has however reduced the rate of rise of metal temperatures of the superheater tubes, as shown in Figure 13.7c. This clearly shows the effectiveness and strong advantages of the rate constraints applied to the heat exchanger metal tube temperatures. It is to be noted that the control performance is significantly different during the periods of negative and positive load transitions because of substantially different initial operating conditions. It is also to be noted that with both constrained and unconstrained approaches, the control performance is far better than that obtained with a multiloop PI controller under variable-pressure operation mode at a much lower rate of rise in the load (2.5 per cent MCR/min), as shown in section 13.3.

Physical model-based coordinated power plant control 387 200/

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388 Thermal power plant simulation and control 538

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reheat steam temperature control during variable-pressure operation

Discussion and conclusions

In order to ensure competitiveness in the deregulated power market, a thermal power unit should operate with maximum possible thermodynamic efficiency and have the ability to make changes in the generated power at the fastest possible rate. It is however difficult to ensure this with multiloop PI/PID controllers. The ability to make a faster rate of change in generated power is limited by thermal constraints on the boiler-turbine components. Also, plant operation is adversely affected by multiloop interactions and commonly occurring system disturbances. Making full and effective use of the information about system dynamics present in a physical power plant model, suggests a non-linear physical model-based predictive control (NPMPC) strategy can be designed that can optimally account for plant-wide interactions and system disturbances and facilitate the running of the plant at the best possible efficiency without violating thermal constraints. Formulation of such an approach for application to a 200 MW oil-fired thermal power plant has been discussed. The NPMPC strategy is applied in a two-level hierarchical control structure. Since the lower-level controllers can act independently of the speed of response of higherlevel controllers, there are sufficient degrees of freedom for handling both fast and slow acting disturbances. The lower-level PI loops have also been used to stabilise the unstable plant dynamics arising due to the presence of a natural integrator in the form of drum level. The combination of a stochastic disturbance model along with a

390

Thermal power plant simulation and control

non-linear plant model and models of local controllers was used by the higher-level NPMPC controller for prediction purposes. The NPMPC algorithm applies successive linearisation and an EKF for state reconstruction to obtain a linear state space model of the plant. The linear model and a quadratic programming routine were then used to design a long-range predictive controller. For verifying the effectiveness of disturbance rejection capabilities, random changes in radiation heat flow were introduced in the boiler, while the condenser vacuum fluctuated in a random fashion on the turbine side. This was done when the load-demand set-point was going through step changes of -4-40MW (20 per cent MCR) following a square-wave pattern. During such severe operating conditions, much superior control performance was obtained with the proposed control strategy in comparison to the SEGPC-based hierarchical control strategy designed under similar conditions. In addition to evaluating the disturbance rejection properties, the simulation tests conducted under multiple disturbances demonstrated the feasibility of implementing such a control strategy on a real plant even when plant model parameters are not accurately known or are time varying. Also these tests clearly demonstrated the excellent performance of the control structure in eliminating the adverse effect of plant-wide interactions through set-point manoeuvring of the local controllers. Successful steam temperature regulation during variable-pressure operation is a very difficult task for any control strategy due to the complex pressure and temperature dynamics in a natural circulation boiler. With the unconstrained NPMPC strategy, no significant overshoot or undershoot was observed in both the main and reheat steam temperatures even during variable-pressure operation mode. Furthermore both the power output and main steam pressure followed the scheduled ramp changes in their set-points with very high precision. Use of a physical state space plant model facilitated application of constraints on state variables in addition to input and output variables. Metal temperatures of heat exchanger tubes were modelled as state variables in the plant simulation. This made it possible to demonstrate through simulation tests that constraints needed to be applied on the metal temperatures rather than the steam temperature. The rate constraint on the superheater tube metal temperature clearly demonstrated the strong advantage of the control strategy in facilitating higher rates of load change in the variable-pressure mode of operation. As it is now very common for thermal power plants to operate as peak-load plants in a cycling or two-shifting manner, these units quite often undergo large set-point changes involving large load transitions. Several types of disturbances invariably accompany such load transitions and degrade the plant performance quite considerably. Some of the most common disturbances are changes in active burner configuration, taking in and out of service of cooling water pumps to maintain the condenser vacuum, and switching on/off coal mills in the case of coal-fired power plant. As shown in the simulation results, making effective use of the detailed information regarding the plant condition, readily available through the physical plant model, enables control performance to be significantly improved during such severe conditions. This would provide an opportunity to push the set-points for steam temperatures and pressure much closer to their physical constraints (Prasad et al., 1999;

Physical model-based coordinated power plant control 391 Moelbak and Mortensen, 2003) resulting in a significant gain in thermal efficiency without adversely affecting the life of the plant. The availability of a differential, algebraic physical model is essential for the implementation of the proposed NPMPC strategy. However, should such a model not be available an appropriate low-order model could be developed using parameters obtained from plant design data and a minimal set of experiments. The complete model could then be fine tuned during a suitably designed validation process. Additionally, the NPMPC strategy requires a significantly large computational effort, as it involves successive linearisation, discretisation, state reconstruction and on-line quadratic optimisation during each control sample. It would therefore require an appropriately fast computing system for its field implementation in a thermal power plant. Fortunately, there has been a spectacular rise in the operating speed of modern computers, while their prices have steadily dropped. For instance, it has been estimated that during the last ten years the increase in processing power, together with the improvements in optimisation algorithms, could in principle allow the speed of solution of convex optimisation problems - which are central to predictive control to have increased by a factor of 106 (Maciejowski, 2002; Roos et al., 1997). It is thus a very realistic proposition to implement such a computationally intensive predictive control strategy in a power plant. It can therefore be concluded that the time is ripe for developing and implementing a physical model-based coordinated control strategy that makes a real difference to the operational performance of today's thermal power plants. In particular, the tremendous potential for synergy between a physical model and the predictive control approach holds great promise for further research to find new and more effective ways of making use of the wealth of information about plant conditions present in a physical model in the development of a coordinated control system for thermal power plant.

13.7

Acknowledgements

A substantial part of the work presented in this chapter was carried out while the author was working in the School of Electrical and Electronic Engineering at The Queen's University of Belfast under the UK Engineering and Physical Sciences Research Council (EPSRC) grant No. GR/L24021. The author is grateful to EPSRC for supporting the research work. He also acknowledges the help obtained from the grant holders Prof. B.W. Hogg, Prof. G.W. Irwin and Dr. E. Swidenbank while working at the University.

13.8

References

ANDERSON, J.H.: 'Dynamic control of a power boiler', Proceedings oflEE, 1969, 116, pp. 1257-1268 CHIEN, K.L., ERGIN, E.I., LING, C., and LEE, A.: 'Dynamic analysis of a boiler', Transactions ASME, 1958, 80, pp. 1809-1819

392 Thermalpower plant simulation and control CORI, R., and MAFFEZZONI, C.: 'Practical optimal control of a drum boiler power plant', Automatica, 1984, 20, (2), pp. 163-173 DIECK ASSAD, G., MASAD, G,Y., and FLAKE, R.H.: 'Optimal set-point scheduling in a boiler turbine system', IEEE Transactions on Energy Conversion, 1987, EC-2, (3), pp. 388-395 KALLAPPA, P., HOLMES, M.S., and RAY, A.: 'Life extending control of fossil fuel power plants', Automatica, 1997, 33, (6), pp. 1101-1118 KATEBI, M.R., and JOHNSON, M.A.: 'Predictive control design for large-scale systems', Automatica, 1997, 33, (3), pp. 421-425 LANSING, E.G.: 'Variable pressure peaking boiler, operation, testing and control', Journal of Engineering for Power, 97, (3), July 1975, pp. 435-440 LU, S., SWIDENBANK, E., and HOGG, B.W.: 'An object-oriented power plant adaptive control system design tool', IEEE Transactions on Energy Conversion, 1995, 10, (3), September, pp. 600-605 MACIEJOWSKI, J.M.: 'Predictive control with constraints' (Pearson Education, Harlow, 2002) MCDONALD, J.E, and KWANTI, H.G.: 'Design and analysis of boiler-turbinegenerator control using optimal linear regulator theory', IEEE Transactions on Automatic Control, 1973, AC-18, (3), 202-209 MOELBAK, T., and MORTENSEN, J.H.: 'Steam temperature control', in Flynn, D. (Ed.): 'Thermal power plant simulation and control' (IEE, London, 2003) NICHOLSON, H.: 'Dynamic optimisation of a boiler', Proceedings oflEE, 1964, 111, pp. 1478-1499 NICHOLSON, H.: 'Dynamic optimisation of a boiler-turboalternator model', Proceedings of lEE, 1966, 113, pp. 385-399 NICHOLSON, H.: 'Integrated control of a nonlinear boiler model', Proceedings of lEE, 1967, 114, pp. 1569-1576 ORDYS, A.W., and CLARKE, D.W.: 'A state-space description for GPC controllers', International Journal of Systems Science, 1993, 24, (9), pp. 1727-1744 ORDYS, A.W., and KOCK, E: 'Constrained predictive control for multivariable systems with application to power systems', International Journal of Robust Nonlinear Control, 1999, 9, pp. 781-797 PRASAD, G.: 'Performance monitoring and control for economical fossil power plant operation'. PhD thesis, The Queen's University of Belfast, 1997 PRASAD, G., SWIDENBANK, E., and HOGG, B.W.: 'A novel performance monitoring strategy for economical thermal power plant operation', IEEE Transactions on Energy Conversion, 1999, 14, (3), pp. 802-809 PRASAD, G., IRWIN G.W., SWIDENBANK, E., and HOGG, B.W.: 'Plant-wide predictive control for a thermal power plant based on a physical plant model', lEE Proceedings on Control Theory and Applications, 2000, 147, (5), pp. 523-537 PRASAD, G., IRWIN G.W., SWIDENBANK, E., and HOGG, B.W.: 'A hierarchical physical model-based approach to predictive control of a thermal power plant for efficient plant-wide disturbance rejection', Transactions of the Institute of Measurement and Control, 2002, 24 (7), pp. 107-128

Physical model-based coordinated power plant control 393 ROGERS, M., and MAYHEW, Y.: 'Engineering thermodynamics work and heat transfer' (Longman, Harlow, 1992) ROOS, C., TERLAKY, T., and VIAL, J.E: 'Theory and algorithms for linear optimisation - an interior point approach' (Wiley, Chichester, 1997) TAYLOR, J.H., and ANTONIOTTI, A.J.: 'Linearization algorithms and heuristics for CACE'. Proceedings CACSD'92, Napa, California, March 17-19, 1992, pp. 156-164

Chapter 14

Management and integration of power plant operations A.E Armor

14.1

Introduction

As we begin a new century, the electricity generating business is transitioning from a cost-plus, monopoly environment with an obligation to serve, to a competitive environment for the sale of its product. Ownership of generation assets is being decoupled from the ownership of transmission and distribution assets. Focus has switched from achieving maximum performance of all generating plants to obtaining the maximum possible return on plant investments. In this new business environment, the electricity produced from any individual plant may be sold to Independent System Operators (ISOs), power brokers, marketers, direct wholesale customers, distribution companies, retail companies and others. These sales may be a result of a daily auction to obtain the lowest-priced electricity or the result of short-term or long-term contracts with an intermediate party or the ultimate end-user (Armor and Wolk, 2000). Spot prices can change daily as electricity demand and availability fluctuate. Figure 14.1 shows a typical summer spike for the month of August 1999. At such times the availability of fast-start peaking power is an opportunity to generate profits over a period of a few hours or a few days. Conversely, it is an inopportune time for units to be out of service, whether the outage is planned or unplanned. Generating companies seek to maximise on-line generation at such times. In order to maintain a competitive edge in such a market, asset managers will be trying to identify the best markets to serve and the most profitable operating modes for each plant. Plant operators need to meet the demands of its identified market and to improve the performance of the plant to allow it to compete for more profitable sales. Emphasis will be placed on minimising the number and duration of forced and planned outages. In contrast to a regulated monopoly situation in which another company-owned plant is most likely to pick up the load when a unit goes down in a competitive market, that load could now be supplied by a competitor. The result is a

396

Thermal power plant simulation and control Dow Jones Index: weighted average price for firm on-peak electricity, August 1999, PJM market 250 200 .,.

150

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Figure 14.1

Electricity price spike

loss of total rather than incremental revenue. It may, for example, be more important in the competitive environment to maximise availability only during peak demand periods (Metcalfe et al., 1997). The availability of peaking capacity at times of high spot market costs for electricity is of increasing importance in taking advantage of a volatile market and has led to a demand for units suitable for cycling and fast startups.

14.2

Age and reliability of plants

During the late 1970s and early 1980s, a seeming inevitability surfaced. A severe reduction in new power plant construction below historic levels occurred, caused by scaled-back nuclear plant programmes and as interest rates and environmental control costs soared, by fewer new fossil plants. The electric power industry in the US appeared unable to replace old fossil-fired units fast enough to avoid power shortages. Estimates suggested a high probability of power curtailments for the year 2000, approaching 100 per cent in parts of the southern United States. This concern led utilities to seek ways to extend the operating lifetimes of fossil units beyond the generally accepted 30-40 year design life and an early utility conference was held. Though the premise of looming power shortages was flawed, the resultant surge of interest in life assessment technologies and diagnostic monitoring of equipment was exactly fight for a rapidly changing industry. Retirement of generating capacity at US stations is expected to be roughly 200 units or 12,000 MW, through 2010 according to the US Energy Information Administration, largely for economic not technical reasons.

14.2.1

Economic life is the issue

The issue now is one of economic life optimisation and of prudent investment in fossil plant assets. In a technologically advanced society, solutions arise to fill needs. So it was with the power industry in the 1980s. First demand-side management emerged, then niche opportunities for new generation were filled by the growing

Management and integration of power plant operations 397 independent power industry. Concurrently, the combustion turbine reemerged as a low-cost, short-schedule supply option and the major turbine vendors rapidly shifted their development focus from the Rankine to the Brayton cycle, leading to today's overwhelming reliance on gas for new generating units. As for the 400-plus GW of installed fossil-steam generation in the US, the vast majority of these units will continue to operate for many years, though less economic units will have lower capacity factors. The focus has now shifted to the selection of the correct plant investment strategy for these older plants. This strategy can range from increased maintenance to full repowering of the unit. With unit profitability as the issue, fossil plants have become business assets to be carefully invested in for maximum return. And as with all business decisions, questions of risk became important. More precisely, owners seek to understand the consequences of operating aging turbine generators and boilers under new operating scenarios such as cycling duty. The good news is that the latest life estimation technology can ensure safe, reliable operation for older plants, relying on systematic approaches to component inspections and analyses, and deeper understanding of the behaviour of power plant materials under operating pressures, temperatures and load cycles.

14.2.2

The environmental challenge

Of all the hurdles facing owners of generating plants, perhaps none is greater than preparing units for meeting environmental limits at minimum cost. Both SO2 and NOx have been decreasing overall nationally since the mid-1980s, despite increasing electricity production, and the trend is likely to continue. In fact SO2 emissions are down nearly 40 per cent and NOx has decreased 20 per cent since 1980, while electricity use increased 35 per cent over the same period. In the US about 150 SO2 scrubbers have been installed on more than 70,000 MW, valuable additions that will permit plants to operate in compliance for many more years. Typically a 450 MW coalfired plant will emit 75 tons of SO2 per day without a scrubber and perhaps 8 tons per day with a 90 per cent flue gas desulphurisation (FGD) system in place, a difference that can be measured in terms of the market for SO2 credits, currently over $100/ton. And for NOx, where most current control activities are focused, the same plant might emit 10-35 tons per day. NOx control options range from burner optimisation to the use of selective catalytic reduction. As for carbon dioxide, the above plant emits about 9,000 tons/day at a plant efficiency of 38 per cent, which translates to 2,450 tons of carbon. Such emissions are certainly of concern when potential future carbon taxes are factored in. A combined cycle gas plant, for comparison, emits about half of this amount due to the higher plant efficiency and lower carbon content of natural gas. There seems little doubt that carbon-lean fuels such as natural gas will continue to substitute for those high in carbon, as Figure 14.2 suggests, but in the meantime the bulk of US generation will come from the installed fossil-steam capacity (largely coal-fired). The maintenance and upgrade of these units remains the number one concern of the US generation business. Carbon intensity here is expressed in terms of carbon per ton of oil equivalent.

398

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NERC GADS 1995-1999fossil steam plant availability data; all unit sizes, all fuels, 1534 units, average size 300 MW

Year

Average unit age, years

Equivalent availability factor, per cent I

Availability factor, per cent 2

Scheduled outage factor, per cent 3

Forced outage factor, per cent 4

1995 1996 1997 1998 1999

30.77 31.33 32.27 33.26 34.20

83.64 84.24 84.77 84.18 84.43

85.94 86.64 87.10 86.61 85.77

10.14 9.79 9.03 9.41 10.37

3.92 3.56 3.87 3.99 3.88

Key: 1 Equivalent availability factor = (available hours - derated available hours) x 100 %/period hours 2 Availability factor = available hours x 100 %/period hours 3 Scheduled outage factor = scheduled outage hours x 100 %/period hours 4 Forced outage factor = forced outage hours x 100 %/period hours

14.2.3

The current reliability of fossil power plants

The North American Electric Reliability Council (NERC) 1999 Generation Availability Data System (GADS) Report covers the period 1995-1999 (NERC, 2000). As indicated in Table 14.1, the age of the average fossil steam plant during this period was about 32 years. The rate of increase averaged almost one year per year, indicating the installation of very little new capacity. The equivalent availability factor (EAF), a measure of how the plant is utilised over the year, averaged about 84 per cent with

Management and integration of power plant operations Table 14.2

399

Plant system availability ranking; NERC GADS 1995-1999 fossil steam plant data; all unit sizes, all fuels, average size ~300 MW

Plant system and other causes of losses

Forced outages average hours/unit-year

Forced deratings average equivalent hours/unit-year

Forced and scheduled outages and deratings average equivalent hours/unit-year

Boiler Steam turbine Balance of plant Generator Pollution control External impacts Regulatory, safety, and environmental issues Personnel errors Performance shutdowns

158.44 42.73 41.37 39.28 3.94 8.11 4.14

38.89 7.88 34.23 1.70 6.00 7.42 10.01

633.20 244.04 153.79 83.95 34.20 27.11 22.28

4.80 0.01

0.23 0.37

5.40 1.90

the availability factor (AF) about 2.5 points higher. It is interesting that the scheduled outage factor (SOF) of 9-10 per cent is about 2.5 times the forced outage factor (FOF) of about 3.9 per cent. Over the last ten years availability has been generally increasing in spite of ageing units and more demanding duty. Plant thermal efficiency however has suffered due to worsening coals, additional environmental control equipment and the natural effects of aging. But this will change, as opportunities to improve fuel utilisation, such as repowering, will be seized by power producers seeking a competitive edge. The availability statistics for specific plant major equipment and for nonequipment issues are listed in Table 14.2 in rank order. By far the largest contributor to loss in availability is the boiler. It is followed in importance by the steam turbine, balance of plant and generator. The other systems and issues listed in Table 14.2 have a significantly smaller impact.

14.2.4

Subsystem outages

The availability impacts of 25 plant subsystems and components are listed in Table 14.3 in rank order. By far the most significant are the availability losses for boiler and turbine overhaul, which occur on average every 2.5 and 5 years respectively. These typically require outages of about one month to complete. For example, turbine disassembly for maintenance requires a planned maintenance schedule that includes careful inspection of rotors, casings, blades, bearings and valves, including dimensional measurements and more detailed non-destructive evaluation (NDE) data, Figure 14.3. Lay-down space is useful but often limited in older stations.

400

Thermal power plant simulation and control

Table 14.3

Subsystem~component availability rankings ; NERC GADS 1995-1999fossil steam plant data; all unit sizes, all fuels, 1534 units, average size 300 MW

Subsystem/component

Average unavailable MWh per unit-year

Average MWh per outage

Number of outages per unit-year

1. Boiler overhaul 2. Major turbine overhaul 3. Boiler inspections 4. Furnace wall leaks 5. Boiler, miscellaneous 6. First reheater leaks 7. Second superheater leaks 8. Feedwater pump 9. First superheater leaks 10. Generator rotor windings 11. Turbine inspection 12. Economiser leaks 13. Opacity - fossil steam units 14. Main transformer 15. Air heater (regenerative) 16. Electrostatic precipitator problems 17. Turbine control valves 18. Other boiler tube leaks 19. Burners 20. High-pressure heater tube leaks 21. Other miscellaneous steam turbine problems 22. Major generator overhaul 23. Pulveriser mills 24. Stator windings, bushings and terminals 25. Boiler water condition

52,555 30,407 21,719 18,617 8,877 6,651 5,177 4,055 4,024 3,810 3,644 3,625 3,535 3,108 3,079 2,951 2,948 2,844 2,577 2,536 2,414 2,407 2,323 2,294 2,181

155,556 175,962 95,502 14,961 13,811 17,950 17,101 63,329 11,977 206,903 98,456 10,430 1,191 16,599 11,118 3,761 9,683 14,913 10,628 5,142 7,246 156,156 1,415 83,717 1,415

0.34 0.17 0.23 1.24 0.64 0.37 0.30 0.64 0.34 0.02 0.04 0.35 2.97 0.19 0.28 0.80 0.30 0.19 0.24 0.49 0.33 0.02 1.99 0.03 1.54

These three tables (14.1, 14.2, and 14.3) suggest that major opportunities exist to improve the availabilities of many plants through reductions in the frequency and duration of scheduled downtime. Additional opportunities exist in the area of extending the operational life of components and reducing the frequency of replacement. Even a one per cent improvement in availability, resulting in 3-4 days each year of additional power generation, for a large unit could yield more than $1 million annual profit for the owner and many units have scope for much greater improvement than this.

Management and integration of power plant operations 401

Figure 14.3 Steam turbine disassembly

14.3

Improving asset management

Asset management is essentially the practice of using resources to create maximum corporate value, which is the essence of a business manager's job. Each business manager must make decisions on how to use company resources. These decisions should be guided by the goals of the business and of the key stakeholders. In this burgeoning competitive market for electricity, generating companies are reviewing the value of their fossil plants, seeking opportunities and making decisions to improve corporate value. Such decisions must be made in a business climate where revenues, fuel costs, environmental needs, competitive challenges and equipment life are not entirely predictable, and indeed could be changing on time scales ranging from hours to weeks or months. Reasoned judgments need to be made about the retention or purchase of power plants, strategic realignment of the fleet, and tactical deployment of capital and O&M resources. The gas-fired Moss Landing plant, Figure 14.4, is one of several power stations that have changed hands in the fast-moving California market. An important plant for Northern California, the new owners have made strategic decisions regarding capital and O&M investments to increase profitability. Pervasive in this environment is the drive to improve plant asset value, so that the generating units provide a steady and reliable cash flow for the owner. The legacy of high fixed costs will almost certainly not be a stumbling block to plant profitability. A typical fossil plant is now 30 years old and cost perhaps $400/kW to build in the mid- 1960s. Fixed charges on this plant may be about 0.45 c/kWh, compared with a production (O&M) expense of perhaps 2.40 c/kWh. It may though take significant efforts to make these plants competitive, requiring upgrade/repowering investment, renegotiated fuel contracts, a streamlined operating staff and a guaranteed market for the electricity.

402

Thermal power plant simulation and control

Figure 14.4 Moss Landing power plant The fact of the matter is that some of the more than 2,000 fossil-fired units in the United States are better equipped than others to make it in a deregulated free market. The 290 GW of coal-fired plants, for example, have much higher capacity factors 65 per cent on average in 1998 - than the 140 GW of oil/gas-fired plants that operate on average at 30 per cent capacity factor. This implies more usage of coal-fired units and thus more profits to the owner. The main reason for this is the base cost of generation. Currently, according to Federal Energy Regulatory Commission (FERC) data, the I0 lowest-production-cost fossil plants in the United States are all coal-fired. In a competitive group of plants in one region of the United States, Figure 14.5, the MWh production cost (includes fuel and O&M cost) of the plant is a key parameter in any assessment of 'worth' and one that is continually monitored by the generation operator. Though this data is a snapshot of one month in 1999, these plants compete at the margin and the ability to realise a profit, and to achieve a high capacity factor, is often based on incremental price advantages in the spot market (Resource Data International Inc. (RDI) data from FERC submissions).

14.3.1

Marks of excellence for fossil power plants

In assessing what it takes to be successful in today's generation business, it is useful to look at some marks of excellence for fossil power plants. Availability is certainly one of these. Quite surprisingly, at a time when fossil plants now average 30 years in age, the average equivalent availability factor of US fossil plants is at a 10-year high of over 84 per cent, as previously indicated in Table 14.1. And since roughly 77 per cent

Management and integration of power plant operations 403 The lowest productioncost coal-firedplants in one US geographicalregion, including capacityfactors and fuel costs. FERC data for the month of April, 1999 100 9080o .~ ~ 70 ¢7,~ 60 ~ 50 ~, "~ 40 oo o o=

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Figure 14.5 Competitiveplant data of the industry's entire fossil fleet was built before the year 1975, these older units are increasingly burdened with newly installed pollution control equipment and have baseload heat rates often 20-30 per cent higher than plants of more modem vintage. In looking at availability, it is hard to ignore the impact of the most pervasive of all fossil plant problems - boiler tube failures. In the last five years, the equivalent availability related to boiler tube failures has levelled out at about 2.8 per cent, after significant reductions had been obtained in the previous five years. The earlier improvements were the result of increased knowledge of tube failure mechanisms and increased management attention to tube failure reduction programmes. Even so, the industry as a whole still suffers losses of more than $1.5 billion a year from boiler tube failures, and the resultant unit unavailability on average is 3 per cent. There are more than 30 failure mechanisms, but the prime causes remain the same: corrosion fatigue, fly-ash erosion, hydrogen damage and overheating. For example, the wellknown 'fishmouth' high-temperature creep blowout usually stems from progressively accumulating intemal deposits and loss of wall thickness, leading to high wall temperatures and stresses, Figure 14.6. However, ways to detect, monitor, repair, and ultimately avoid the problem are definitively known and could be followed by all generation companies (Dooley and McNaughton, 1996). A second mark of excellence is plant operating cost. Of the top 20 units in this category, most are coal-fired, mine-mouth plants in the upper Midwest, although, in the southwestern US, gas-fired plants have the lowest non-fuel O&M costs, less than 0.20 c/kWh, a figure that few, if any, coal-fired plants are likely to match. Third, plant capacity factor is another indicator of success - a measure of how valuable a plant is compared to other competing plants in the regional market. Increased utilisation of plants minimises wear and tear due to cycling and improves heat rate. Capacity factor is an important parameter to maximise if a generating company is to earn a return on its investment and stay profitable.

404

Thermal power plant simulation and control

Figure 14.6 14.3.2

Typicalboiler tube failure

The impact of fuel selection and fuel cost

In the regulated environment, cost of fuel was often a pass-through charge to the customer, so that there was little incentive from a profit standpoint to reduce those costs. In response to the current competitive environment, new methodologies permit generating companies to focus on the profitable operation of each plant, particularly heat rate/fuel cost effects (Corio et al., 1996). The impact of the new competitive environment on fuel cost issues has resulted in the following conclusions: • • • •

•

Fuel cost recovery and customer retention are no longer guaranteed. There should be a short-term tactical plan for fuels, as well as a long-term strategy. Poorly sited plants or plants inadequately designed for low-cost fuels, will likely be non-competitive. Trade-offs will constantly take place between fuel costs and O&M costs. Low fuel cost in itself may not be enough - having the lowest regional fuel cost may be the only winning strategy.

14.3.3

The fuel options

The US electric power industry burns about $30 billion worth of fossil fuels each year, accounting for 70-80 per cent of the operating costs of fossil-fired plants. As a result, opportunities are constantly being sought to modify or change fuels at marginally economic plants. New fuels or fuel mixes in use are: •

• •

A mix of eastern high-sulphurcoal with low-sulphur, low-cost western coals, often from Powder River Basin (PRB) deposits in Montana and Wyoming. Compared with eastern bituminous coals, PRB coals have lower heating value, sulphur and ash, but higher moisture content and finer size. A mix of 10-20 per cent gas with coal in a boiler designed for coal firing. Orimulsion, a bitumen-in-water emulsion produced only from the Orinoco Basin in Venezuela. This fuel is relatively high in sulphur and vanadium. Power plants

Management and integration of power plant operations 405

•

that use this fuel will need to add scrubbers. The fuel purchase contract guarantees that have been offered are aimed at making Orimulsion cost competitive with oil and coal. Petroleum coke, a byproduct of refining, whose cost is currently low but whose sulphur content is high.

A key conclusion is that it is vital for a power plant to optimise fuel choices. In the future, it is likely that there will be increasing volatility in spot prices and downward pressure on fuel prices as competition heats up. It may become necessary for a plant to make fundamental fuel switches to remain competitive in the battle to keep costs down and retain customers.

14.4

The impacts of cycling on power plant performance

The increasingly competitive market for electricity means many units must now follow very short-term market variations in addition to local load variation. Such cycling operation is divided into three types - load following, low load operation down to 15 per cent of maximum continuous rating (MCR), and on/off (two-shift) operation. Long-term cycling problems include excessive wear and tear, equipment repair and replacement and decreased unit reliability/availability. The short-term issues are higher heat rates and higher O&M expenses. The negative impacts of cycling on the plant though must be measured against the potential increases in revenue that can result from cycling operation, Table 14.4 (EPRI, 1993). The cost of a single stop/start cycle could range between $15,000 and $500,000 and is a function of unit type, size, fuel, pressure and design features (Lefton et al., 1997). Cycling changes that may be needed are specific to the plant involved. A survey of 48 utilities that converted 215 units to cycling duty indicated that a wide variety of changes was implemented or planned to avoid potential problems. For fossil-fired boilers, dealing with the stresses imposed on the system from changes in temperature levels and the rate at which temperatures change was identified as the greatest challenge, Figure 14.7. Changes in instrumentation, operating procedures, and corrosion protection are also required to assure high availability and performance. For turbines, the major issue for cycling service is increased stress on turbine components resulting from rapid changes in temperatures, Figure 14.8. Added attention must also be paid to corrosion issues, water induction and the threat of increased solid particle

Table 14.4 Impact of unit cycling operation Increased revenue achieved from:

Increased costs may include:

Reduced startup time Rapid load change rate More starts and stops

Increased maintenance Reduced plant life Reduced reliability

406

Thermal power plant simulation and control

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Management and integration of power plant operations 407

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More frequent startups and shut-downs and the temperature changes that result, clearly stress components more than baseload operation and modifications to equipment and operating procedures may be necessary.

14.5

I m p r o v i n g m a i n t e n a n c e approaches

Better maintenance practices have become an essential part of the strategy for competitiveness. Such approaches as maintenance process management, best-in-class benchmarking, streamlined reliability-centred maintenance (SRCM) and root-cause failure analysis are often keys to invigorating a plant's maintenance staff. A useful model that describes the complete maintenance process is shown in Figure 14.10 (Armor and Wolk, 2000). It has five elements that have been found helpful as a 'check-off' list, ensuring that the selected approach is complete for the plant in question. The degree to which each subelement is addressed greatly depends on how the plant is to be deployed. For example, approaches to predictive maintenance can be extensive (for a key plant), or non-existent for a seldom used asset. The elements are: Maintenance management: business goals, maintenance indicators, plant reliability and performance management, organisation and work culture, and training and people skills. Maintenance bases: the rationale for why maintenance tasks are performed. This includes streamlined reliability-centred maintenance analysis, a living program for updating the bases, a predictive maintenance process, root-cause

408 Thermal power plant simulation and control

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Figure 14.10

Maintenance model

analysis, and proactive maintenance (PAM, equipment design changes that avoid maintenance work). Work identification: preventive maintenance (PM, time-based tasks), predictive maintenance (PDM, condition-based tasks), proactive maintenance (PAM, design changes), corrective maintenance (CM, fixing failed equipment) work order generation, and the computerised maintenance management system (CMMS). •

Work control: planning (estimating resource requirements), scheduling (when to do maintenance), materials management, outage management and CMMS.

•

Work execution:

the actualwork execution, post maintenance testing, close out.

Management and integration of power plant operations 409 One element of SRCM is a reasoned procedure for scheduling predictive maintenance. Work at EPRI's Monitoring and Diagnostic Center has shown that one utility achieved savings of more than $2 million a year through deployment of such on-line devices as turbine blade and bearing monitors, boiler tube and feedwater heater leak detectors, and condenser fouling monitors. New enthusiasm is being kindled by the opportunity to detect damage using the latest sensor technology. For example, infrared thermography offers rapid payback by uncovering electrical connection degradation, boiler casing and ductwork leaks, and steam trap anomalies. A useful first step in assessing plant maintenance is to judge how the current plant approach ranks with the best-in-class. A 'spider-diagram' of the type shown in Figure 14.11 provides some guidance as to where to put the effort, allowing judgements to be made as to how the current process stacks up. The radii of the 'web'

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410 Thermal power plant simulation and control relate to particular measures of performance, with distance measured against a 'best practices' scale. One element, however, all successful programmes appear to have in common is a work culture where the plant staff are all pulling together to make process excellence an imperative.

14.6

Power plant networks: redefining information flow

Networks are the key to managing the flood of data from monitoring and diagnostics applications, processing it into information, and presenting it in appropriate formats through all levels of the utility (Armor and Weiss, 1997). Recently, diagnostic and performance monitoring technologies have been integrated into networks for improved operations in major plant demonstration projects.

Performance monitoring workstation at Morgantown Nineteen advanced monitoring devices together with other process instruments on the 650MW Mirant, Morgantown Unit 2, are analysed by the performance monitoring workstation (PWM) to determine plant heat rate on-line. A data highway is used to interconnect sensor data, display consoles, and a single large performance computer as shown in Figure 14.12. The workstation contains sophisticated software including thermalhydraulic models used to compare measured and optimal performance, determine component degradation, and examine operational changes on plant performance (EPRI, 1989).

Monitoring and diagnostic network at Eddystone Demonstration and integration of diagnostic monitors and the development of predictive maintenance practices is the focus of this work at Exelon's Eddystone station (EPRI, 1991a). Twenty-four on-line and periodic diagnostic technologies comprising over 2,300 monitoring points are integrated through a computer-data highway network at Eddystone. Data is drawn directly onto the highway, over gateways from the distributed control system, and

Analoguecontrol/ , processdata :------, Dispatch Engineer display console

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Management and integration of power plant operations 411 Field data

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A step toward integration: The E1 Segundo demonstration

Integrated diagnostic and performance monitoring, on-line advisory systems and advanced controls are combined at the NRG E1 Segundo Power Plant in California, Units 3 and 4, Figure 14.14. The control and diagnostic retrofit is a step towards fully integrating monitoring technologies with distributed digital control systems. The goal here is to create a single display window on all plant operations and on the current state of major equipment conditions. This project is unique in that it has required an industry control system supplier to integrate distinct diagnostic monitoring systems from various vendors and expert systems with the control system (EPRI, 1990). Total savings for this project have been estimated at $67 million (EPRI, 1991b). The savings relate to operational costs associated with reduced failures and improved plant productivity, over a 10 year period of operation.

The next step in integration: the Roxboro demonstration Recent work at Carolina Power and Light's Roxboro plant, consisting of four 500 MW units, has demonstrated the application of state-of-the-art automation technologies to improve heat rate and unit maneuverability throughout the load range, and to reduce forced outages and O&M costs. This was achieved through full utilisation of the power of a distributed control system, and integration of monitoring, diagnostics, on-line testing, expert systems, and information management functions into a plant-wide automation system

412 Thermal power plant simulation and control

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based on EPRI's Utility Communications Architecture. The plant-wide information system, Figure 14.15, is linked remotely, such that the four units can be optimally dispatched based on heat rate, equipment condition, and emissions considerations.

14.6.1

A cultural change for operators

When fossil plants are equipped with a digital control system (DCS), the primary DCS operator interface then becomes the CRT and keyboard. These CRTs provide

Management and integration of power plant operations 413 the operator with an extensive amount of information. Display application tools and techniques are being developed that expand the view into the process and enable the operator to rapidly comprehend a large volume of data in order to make responsive decisions. However, with a large number of operating displays and an ever growing quantity of data, there is a strong need for enhanced plant information management technologies to avoid information overload. Concurrently there is a change in the role of the control room operator. As DCS advanced control strategies and automated expert systems are implemented in generating stations, the DCS is now performing many of the routine information logging, control actions, and startup activities that were traditionally performed by the operator. As a result, there is now an opportunity to place emphasis on process management and continuous training improvements, and tools are being developed to aid the operator with process management, problem resolution, performance evaluation, and emissions management.

14.7

Conclusions

Today's electric generating company business climate is unlike any previously seen by the long-term regulated industry. A plant manager must focus his/her efforts on two imperatives: (1) 'survival' and (2) 'profit'. It is probably fair to say that these terms have not been the dominant driving forces of electric utilities in the years preceding deregulation, competition and mergers. Businesses exist to create added value from all assets - tangible assets as well as information and personnel expertise. The electric power industry is no exception, and its tangible assets: power plants, land, transmission systems, etc., are capital investments to be utilised and managed to the maximum benefit to stockholders and consumers. Yet the traditional utility business strategy has focused largely on minimising costs and revenue requirements and on meeting the 'obligation to serve', so it has been easy to overlook the intrinsic value of such assets as generating plants and how investment in these assets might be optimised from an overall company viewpoint. Now generating companies are taking a fresh look at power plants, their value to the company, and ways to prudently invest in these capital assets so as to improve bottom-line profitability. The assets at risk are older generating units, increasingly burdened with emission control equipment. They have base-load heat rates typically 20-30 per cent higher than plants of more modern vintage and often far from being base loaded, imposing an additional heat rate penalty. Such old units, though, are unlikely to be faced with large stranded capital investments. The real issue is operating cost. A small improvement in O&M can make the difference between a stranded cost and a viable, money-making generating unit. In fact, generating companies carefully follow key parameters for a given generating unit, such as the precise cost of generating each kWh, the revenues to be made by the unit at current and projected capacity factors, the additional revenues to be gained by incremental investments of either capital or O&M, and the unit's contribution to corporate profits on the basis of energy, capacity, and other value measures.

414

Thermal power plant simulation and control

Finally, as power plant controls and information networks become more complex, additional training of operators and engineers will be necessary. One concern that has often been expressed is that automation is a bar to understanding, the implication being that as we move to more computer-controlled operation of power plants, the human in charge is less cognisant of the physical principles behind plant operation. This is an undesirable situation that could lead to poor decisions in emergency situations. So training, via simulators, expert systems or intelligent tutors, will be an essential growth activity for most forward-looking companies. The successful companies of the future will be those that embrace techniques at the cutting edge of the present 'information age'.

14.8 14.8.1

References Asset management

ARMOR, A.E, and WEISS, J.M.: 'Advanced control for power plant profitability', Annual Reviews in Control, 1997, 21, pp. 171-182 ARMOR, A.E, and WOLK, R.H.: 'Productivity improvement handbook for fossil steam power plants: second edition'. EPRI TR-114910, June 2000 CORIO, M.R., BELLUCCI, J.W., and BOYD, G.A.: 'Applying the competitive market business equation to power generation economics and markets'. Proceedings: 1996 Heat Rate Improvement Conference, EPRI Report TR-106529, May 1996, pp. 5-13 DOOLEY, R.B., and McNAUGHTON, W.: 'Boiler tube failures: theory and practice'. EPRI Report TR-105261, 1996 EPRI: 'MARK I performance monitoring products, GS/EL-5658'. Palo Alto, California; Electric Power Research Institute, September 1989 EPRI: 'Preliminary guidelines for integrated controls and monitoring for fossil fuel plants, GS-6868'. Palo Alto, California, Electric Power Research Institute, June 1990 EPRI: 'Plant monitoring network brings savings through predictive maintenance'. EPRI Innovator IN- 100124, December 1991 a EPRI: 'SCE integrates controls and diagnostics to improve operation of E1 Segundo Units 3 and 4'. EPRI Innovator IN-100145, December 1991b EPRI: Cycling of fossil fueled power plants. EPRI Report CS-7219, September 1993. LEFTON, S.A., et al.: 'Using fossil power plants in cycling mode: real costs and management responses', in ARMOR, A.E, BLANCO, M.A., and BROSKE, D.R. (Eds.): 'Proceedings: managing fossil generating assets in the emerging competitive marketplace, 1996'. EPRI report TR-107844, March 1997 METCALFE, E., REES, C., McINTYRE, P., DELAIN, L., and LANDY, D.: 'Scheduling outages to maximize corporate and customer value', in ARMOR, A.F., BLANCO, M.A., and BROSKE, D.R. (Eds.): 'Proceedings: managing fossil generating assets in the emerging competitive marketplace: 1996'. EPRI report TR-1078444, March 1997

Management and integration of power plant operations

415

North American Electric Reliability Council (NERC): '1995-1999 generation availability data system (GADS)'. Report, July 2000

14.9 Bibliography 14.9.1

Asset management

ARMOR, A.E, BLANCO, M.A., and BROSKE, D.R.: 'Proceedings: managing fossil generating assets in the emerging competitive marketplace conference 1996'. EPRI report TR-107844, March 1997 BOND, T.H., and MITCHELL, J.S.: 'Beyond reliability to profitability'. Proceedings of the 1996 EPRI Fossil plant maintenance conference, EPRI report TR- 106753, July 1996, pp. 5-1-5-12 BOZGO, R.H., and MAGUIRE, B.A.: 'Fossil plant self assessment'. 'Proceedings of the 1996 EPRI Fossil plant maintenance conference, EPRI report TR-106753, July 1996, pp. 3-1-3-9 EPRI: 'Positioning for competition: the changing role of utility fuels'. EPRI report TR- 104550 FOGARTY, J., MILLER, R., and DONG, C.: 'Benchmarking: the foundation for performance improvement'. Proceedings of the 1996 EPRI Fossil plant maintenance conference, EPRI report TR-106753, July 1996, pp. 2-I-2-13 14.9.2

Maintenance

ABBOT, ED., WOYSHNER, W.S., and COLSER, R.J.: 'Pilot application of streamlined reliability centered maintenance at TU Electric's fossil power plants'. EPRI report TR-106503, February 1997, pp. 18-1-18-18 ARMOR, A.E, and WOLK, R.H.: 'Productivity improvement handbook for fossil steam power plants'. EPRI report TR-114910, June 2000, 2nd edn. EPRI: 'Automated predictive maintenance implementation'. Proceedings of the EPRI Fossil plant maintenance conference. 1996, EPRI report TR- 106753, July 1996 EPRI: 'NDE guidelines for fossil power plants'. EPRI report TR- 108450, September 1997 EPRI: 'Streamlined reliability-centered maintenance at PG&E's Moss Landing plant'. EPRI report TR- 105582, September 1995 14.9.3

Productivity improvement tools

ARMOR, A.E, MUELLER, H.A., and TOUCHTON, G.L.: 'Managing plant assets for profitability'. American Power Conference, Chicago, IL, April 29-May 1, 1991 EPRI: 'Condition assessment guidelines for fossil fuel power plant components'. EPRI report GS-6727, March 1990 EPRI: 'Database integration services, volumes 1 and 2'. EPRI report TR-101706, December 1992

416 Thermal power plant simulation and control EPRI: 'Fossil plant instrumentation and monitoring'. EPRI Heat rate improvement conference 1991, EPRI report TR- 100901, July 1992 EPRI: 'HEATRT heat rate improvement advisor'. EPRI report RP2923-13, August 1995 EPRI: 'High reliability condenser application study'. EPRI report TR-102922, November 1993 EPRI: 'Life cycle cost management, workbooks and software'. EPRI report AP105443, January 1996 EPRI: 'Life optimization for fossil fuel power plants'. EPRI report GS-7064, November 1990 EPRI: 'Managing life cycle costs'. EPRI Report TR-102308, 1993 EPRI: 'MARK 1 performance monitoring products'. EPRI report GS/EL-5648, September 1989 EPRI: 'Plant monitoring workstation'. EPRI Report AP-101840, December 1992 EPRI: 'Power plant modification evaluations using the EPRI PMOS model'. EPRI report TR-101715, July 1993 EPRI: 'Reference manual for on-line monitoring of water chemistry and corrosion'. EPRI report TR-104928, March 1995 EPRI: 'Roxboro automation project interim report'. EPRI report TR-102083, May 1994 EPRI: 'The DYNAMICS model for measuring dynamic operating benefits'. EPRI report GS-6401, June 1989 EPRI: 'Utility experience with the EPRI plant monitoring workstation'. Proceedings of the EPRI Heat rate Improvement conference, 1992, EPRI Report TR-102098, March 1993

Index

acid rain 11,243 actuator dynamic performance 372 saturation 293, 367 adaptive control 94, 101 alternator excitation control 110-11, 117-27 steam temperature control 147-9 supervision of 111-12, 148 s e e a l s o parameter estimation adaptive neurofuzzy inference system 221-2, 224 advisory system: s e e operator advisory system air preheater, modelling of 43 air-fuel ratio 244-6, 252, 371 excess air 7, 48 stoichiometric 7, 249 alarm system 92, 287, 353 integration of 350 alternator 2, 114 adaptive control 110-11, 117-27 automatic voltage regulator 112-13 availability of 399-400 excitation control 102 hybrid simulation 113-14 load cycling problems 406-7 local model network control 108-10, 117-27 modelling of 19 power system stabiliser 110 s e e a l s o life ancillary services 345,347 ARMAX model 103, 188 ARX model 188, 246-7 altemator excitation control 103-4, 110-11 NOx emissions modelling 256-8

asset management 401-5 association rules 326-7 attemperator 133, 181-3, 326, 347 deactivation of 195-6 thermal efficiency 195, 371-2 s e e a l s o flue gas recycling; steam temperature / pressure automatic voltage regulator 103, 105 operational protection 112 rotor angle stability 118 availability, power plant 345, 396, 402-3 factors affecting 399-400 steam temperature control 132 availability factor 399

back propagation, algorithm 226, 302 base-load plant 6, 348, 403,407 BETTA, UK electricity market 10 black-box modelling 188, 245-6, 292 adaptation, on-line 269 model scheduling 333 structure selection 189, 256-8, 289 validation of 189, 254 s e e a l s o grey-box modelling; neural network model; physical-based modelling; principal component analysis; projection to latent structures; state-space model boiler availability of 399--400 load cycling problems 397, 405-6 maintenance overhaul 399 stability of 132 tube failure, mechanisms 403 s e e also component model; drum boiler; life; once-through boiler

418

Index

boiler following control 6, 347-8 boiler stored energy 6, 182, 185 load-frequency control 207-9 Brayton cycle 5, 397 bumpless switching, controllers 142 burner management system 7 multiple fuels 351 burners CFD design 246 configuration of 254, 326 coruer-firing 244, 262 low-NOx burners 244, 252

capacity factor 397, 402 load cycling 403 carbon taxes 397 CARIMA model 171-2 Carnot cycle 3 cascade control 136, 149 case-based reasoning 313 cavitation, valve 35 chemical control, water 360 Clean Air Act (US) 243 climate change, intergovernmental panel (UN) 13 s e e a l s o renewable energy clustering analysis 310, 313 k means 335 CO, emissions 7, 11,243 modelling of 49-50, 249-50 C02, emissions 11,243 carbon tax 397 greenhouse gas 11 modelling of 49-50, 249-50 reduction of 244 co-ordinated plant control: s e e supervisory plant control coal calorific value 81, 92 carbon intensity 397-8 fuel combustion 248-50 hardness 71 world reserves of 11 coal mill boiler stability 132, 155-7 choking 63, 69, 74, 93 classifier zone 64, 68 coal hardness 71 control and advisory system 92-7 emissions, during transients 84 explosion of 82 mill table 64, 69

mill wear 70-1, 92-3 model validation 71-9 modelling of 43, 64-71 separator 64, 68 startup/shutdown 91,132, 155-6 vertical spindle mill 64-6 s e e a l s o pulverised fuel coal mill control 80-1 dynamic response 7, 63 Hardgrove grindability index 83-4, 86-90 load line 82 mass/mass 82-4, 86--90 multiple mills 81 multivariable, LQ / predictive 90-1 optimal grinding 94-7 pf flow measurement 64, 81, 84-90 runback 83, 94 combined cycle gas turbine Brayton cycle 5,397 configuration 5, 162 control hierarchy 164-7 emissions of 397 modelling of 163-4 popularity of 397 predictive control 187, 367 supervisory control 168-76 thermal efficiency 1, 161 s e e a l s o gas turbine; heat recovery steam generator combustion chamber, gas turbine modelling 48-9 combustion control 6-7 excess air 7, 48 fly ash 244, 248 modelling of 49-50, 354 multiple fuels 326, 351 operational parameters 244 s e e a l s o emissions competition, power system: s e e deregulation component model, power plant air preheater 43 coal mill 43, 64-71 combustion chamber 48-9 compressor 46-7 condenser 46 control valve / damper 35-6, 43 drum 33-5, 56 fan 43 feedwater heater 46, 274-8 furnace 39-42, 49-50 header 36-7 heat exchanger 20-2, 28-33

Index

pump 37-9 subsystem model compressor, modelling of 46-7 computational fluid dynamics 245 burner / furnace design 246 condenser 3 air leakage / tube fouling 375, 382, 409 cooling water temperature 326, 382 modelling of 46 control hierarchy: s e e multi-loop plant control; supervisory plant control control strategy commissioning of 158, 177, 239 decoupling, multi-loop 136, 179, 181-4 interaction, loop 5, 179, 365 saturation 292-3 s e e a l s o adaptive control; feedforward control; LQG control; minimum variance control; neurofuzzy control; PI(D) control; predictive control control action correction, supervisory plant control 186-7 evaporator steam temperature control 142-7 once-through boiler, control of 189-99 control room, power plant information overload 412-13 islands of automation 350 operator training 354, 414 s e e a l s o alarm system; operator advisory system controlled reference value, supervisory plant control 186-7 CCGT supervisory control 169-76 physical model-based predictive control 375-89 convection, heat transfer 6, 21-3, 42, 370-1 see also

damper, modelling of 35q5, 43 data mining 309-10 deaerator 24, 45 decision rules 327 decision trees 327 demand side management 396 deregulation, power system 10-11,395 competitiveness, power plant 389, 395, 401-2 dynamic stability, boiler 132, 159 load-following requirement 179-80, 205 NETA 10, 345, 353 s e e a l s o availability; load-following; maintenance

419

diagnostic system: s e e fault analysis; operator advisory system diffusion, heat transfer 21 distributed control and data acquisition system 350 distributed control system advantages of 13, 80, 391,412-13 configuration 8,410-11 data management 9, 311 islands of automation 350 modelling of 50-1 supervisory plant control 63, 346 s e e a l s o operator advisory system distributed generation 180 disturbances 134, 145, 365, 374-5 feedforward control 137, 153, 215, 218-9 modelling 140, 194, 377-9 rejection 136, 206, 237, 366, 382 drum 3, 368 level control 7, 183, 207, 370 modelling of 33-5, 56, 171 separation efficiency 34 stability 220, 375 drum boiler configuration 3--4, 368-9 control hierarchy 209-13 knowledge-based plant control 221-38 open-loop behaviour 207-8 physical model-based predictive control 375-89 Rankine cycle 1, 18-19 s e e a l s o once-through boiler Dymola, modelling package 19, 52, 188 economiser 3, 181 modelling of 2 5 ~ s e e a l s o heat exchanger efficiency, thermal: s e e thermal efficiency Electricity Act (UK) 10 electrostatic precipitator 244 emissions, stack 2, 11,243, 345 acid rain 11,243 combined cycle gas turbine 397 electrostatic precipitator 244 modelling of coal-fired plant 253-63 gas turbine 48-50, 164-5 monitoring 326, 359-60 NOx advisory system 266-7 NOx formation 248-53 reduction of 244-5, 397 s e e a l s o CO; CO2; NOx; SOx

420

Index

Energy Policy Act (US) l0 Environment Protection Act (UK) 243 environmental regulation 205, 326, 345 legislation 10, 243 see also emissions equivalence ration 252 equivalent availability factor 398 estimation function 299-300 European Commission 11-12 evaporator 3, 133, 182 control of 134-6 LQG feedforward control 137-47 event logging 353,359-60 excess air 7, 48 excitation control, alternator 102 expert system 313, 41i coal mill advisory system 92-7 G2, real-time 354-5 see also operator advisory system extended Kalman filter 379 state estimation 270, 367 failure analysis 407 fan flue gas recycling 183, 369, 371-2 ID/FD 7 modelling of 43 fault analysis 269, 309 coal mill advisory system 92-7 detection of 311-13, 315-16, 327, 329 diagnosis of 270, 313, 396, 410 fault detection model-based 287, 295, 307, 314 statistical-based 313-14 feedwater heater, modelling of 279-87 NOx emissions monitoring 267, 354 predictive maintenance 409-10 principal component analysis 313-25 projection to latent structures 327, 329 see also availability; operator advisory system FD fan 7 modelling of 43 feature selection 310 see also clustering analysis; principal component analysis feedback control advantages of 216, 218-19 see also control strategy feedforward control 213-15 advantages of 135,206, 216, 218-19 commissioning of 239

disturbance rejection 137, 153, 218-19, 382 load-following capability 182, 239, 367 steam temperature control 135, 140-1, 143-7 flue gas pyrometry 153-7 feedwater control 164, 172, 272-3 drum / once-through boiler 4, 183-4 drum boiler 207-13, 219-20 knowledge-based plant control 221-38 once-through boiler 134-6, 143, 158 feedwater heater 8 configuration 271-4 control of 272-3 fault detection 270, 287, 307,409 fouling 375 grey-box modelling 287-95 modelling of 46, 274-8 sensor / valve, malfunction 282-7 state estimation 295-307 steam bleeding 279 tube leaks 279-83, 409 fieldbus internet protocol 293 flame ignition 245 flue gas desulphurisation 11,244, 397 flue gas recycling 183, 369, 371-2 control action correction 190, 195-7 physical model-based predictive control 377, 381-9 see also steam temperature / pressure flue gas temperature, measurement of 153-5 fluid properties air 28 flue gas 28 steam 27 fluidised bed combustion, PFBC 2, 12 forced outage factor 398-9 fouling, heat exchanger 375, 382 Fourier algorithm, voltage measurement 114-16 frequency decoupling, control loop 179, 181,184 fuel calorific value 81, 92, 326 carbon intensity 397-8 selection of 404-5 world reserves, fossil fuels 11 see also combustion control furnace CFD design 246 modelling of 39-42, 49-50 pressure control 39

Index

fuzzy logic 360 coal mill fault diagnosis 93-4 controller design 206 data mining 310 knowledge-based plant control 221-38 local model network 102 membership function 225, 229-30 non-linear modelling 334 steam temperature control 152-3 G2, expert system 354-5 s e e a l s o expert system gain scheduling 137, 192 bumpless switching 142 gas turbine 163 combustion chamber 48-9 compressor 46-7 emissions 48-50, 164-5,397 modelling of 25, 46-9 gasification, IGCC 2, 12 generalised minimum variance control: s e e minimum variance control generalised predictive control: s e e predictive control generation availability data system 398 generator: s e e alternator genetic algorithms 262 controller design 185, 206 gPROMS, modelling package 18, 32, 188 greenhouse gases 11,243, 397 grey-box modelling 245-6, 287-91 advantages of 248, 269 fundamental element 259 HP feedwater heater modelling 292-5 NOx emissions modelling 259-63 structure selection 256-8,289, 292 s e e a l s o black-box modelling; local model network; physical-based modelling H ~ control 185, 206 header 358 modelling of 36-7 heat exchanger fouling 375, 382 metal temperature 369-71,386, 390 modelling of 20-2, 28-33 feedwater heater 46, 274-8 soot blowing 132, 151,326 tube failure, mechanisms 403 s e e a l s o attemperator; steam temperature / pressure

421

heat recovery steam generator 1, 5, 163 heat transfer, mechanisms 6, 21-3, 42, 370-1 burner configuration 382 hierarchical supervisory control s e e supervisory plant control Hotelling's T 2 statistic 316-7 human machine interface 9, 350-1 s e e a l s o operator advisory system

ID fan 7 modelling of 43 independent power producer 10, 397 input-output modelling: s e e black-box modelling integrated gasification combined cycle 2, 12 interaction, control loops: s e e multi-loop plant control intergovernmental panel on climate change (UN) 13 islands of automation 350

k means clustering 335 s e e a l s o clustering Kalman filter 139-40 pf flow estimation 84-5 state estimation 92 s e e a l s o extended Kalman filter knowledge-based plant control 218, 221-4 knowledge-based system coal mill advisory system 92-7 s e e a l s o expert system knowledge discovery in data 310 Kyoto protocol 11

least squares, algorithm: s e e parameter estimation Levenberg-Marquardt, algorithm 256 life, power plant 179, 205 creep 348 estimation of 397 extension of 367, 376, 400, 403 load cycling 397 reduction of 132, 138, 348, 371-2 s e e also thermal stress load cycling alternator problems 406-7 boiler dynamics 207-9, 326, 365 boiler problems 405-6 capacity factor 403

422

Index

load cycling ( c o n t i n u e d ) life, plant 397 turbine problems 405-6 two-shifting, operation 365,390 s e e also maintenance; multi-loop plant control; thermal stress load-following 205, 209 boiler stability 132 deregulation, power system 179-80, 205 feedforward control 213-15, 219, 236, 367 knowledge-based plant control 228-38 limiting factors 142, 367, 370-4 physical model-based predictive control 386-9 ramping rate 235,371-4, 386 steam temperature control 132, 137-8 supervisory plant control 184-5,206, 347-9, 411 s e e also life; load cycling load-frequency control 207-9, 347-8 load line, coal mill 82 local model network alternator excitation control 103-10, 117-27 controller design 108-10 model identification 102-3 low-NOx burner 244, 252 LQ control, coal mill 90-1 LQG control 138-41,367 evaporator steam temperature control 142-7

mechanical terminal 23 thermo-hydraulic and heat transfer terminal 22 thermo-hydraulic terminal 19 type definition 19 validation, submodels 54 s e e also object-oriented modelling modelling: s e e black-box modelling; grey-box modelling; physical-based modelling monitoring, plant performance 351-3, 410-12 association rules 326-7 clustering analysis 310, 313 NOx emissions 245, 266-7 operator interaction 354 principal component analysis 314-18 projection to latent structures 327-9 univariate / multivariate analysis 312-13 s e e also alarm system; fault analysis; operator advisory system multi-loop plant control boiler dynamics 207-9, 365, 370-1 loop decoupling 136, 179, 181-4 loop interaction 5, 179, 365 load-following capability 205-6, 210-11,213-17, 348-9 sliding pressure operation 212-17, 372-3 s e e also supervisory plant control multilayer perceptron, network 255, 335 multiple linear regression 327

maintenance, power plant 407-10 availability factor 398 corrosion 360 load cycling, impact of 405-7 non-destructive evaluation 399 predictive maintenance 407-8, 410 s e e also availability mass/mass control, coal mill 82-4, 86-90 membership function, fuzzy logic 225, 229-30 minimum variance control, generalised 109-10 alternator excitation control 117-27 model-based predictive control: s e e predictive control Modelica, modelling language 18 aggregation, of submodels 25-7 distributed heat transfer terminal 21 heat transfer terminal 22 hybrid system 51

NARMAX model 258 NARX model 246-7 NOx emissions modelling 258-9 non-destructive evaluation 399 NETA, UK electricity market 10, 345,353 neural network model 101,246-7 data mining 310 dynamic network 247, 255 HP feedwater heater modelling 290-302 Levenberg-Marquardt, algorithm 356 multilayer perceptron 255,335 neurofuzzy control 221-38 non-linear modelling 269, 334 NOx emissions modelling 253-6, 354 overfitting 294-5, 336 radial basis function 102, 247, 335 recurrent network 247, 255 spline 247, 335 static network 247, 255

Index

training of 226, 254-6, 302 parameter estimation neurofuzzy control 221 controller design 224-8 feedforward control 222--4, 230-8 membership function 229-30 NIPALS algorithm 328, 335 NO, formation 11,244 fuel 250, 252-3 prompt 250, 252, 262 thermal 250-2, 262 NO2, formation 11,244, 253 North American Electric Reliability Council 398 NOx, emissions 7, 11,243-4 (N)ARX modelling 247, 256-9 acid rain 11,243 advisory system 245, 266-7 CFD modelling 245-6 combustion modification 244, 252, 397 destruction of 248, 253 factors affecting 244-5,253-4, 346 flue gas treatment 244, 397 formation of 244, 250-3 fuel combustion 49-50, 164-5, 248-50 grey-box modelling 248, 259-63 neural network modelling 246-7, 254-6, 354 s e e a l s o environmental regulation see also

O&M, unit profitability 401,413 object-oriented modelling 18, 66-7, 355 distributed parameter models 18, 20-1 lumped parameter models 18, 23 once-through boiler configuration 4, 133, 189-90 control, frequency decoupling 183-4 control action correction 184-5, 190 evaporator control 134-8 feedwater control 134-5, 183 Rankine cycle 1, 18-19, 181 superheater control 4, 136-7, 147 thermal efficiency 4 s e e a l s o drum boiler operator, power plant information overload 412-13 new technology 354 training of 414 operator advisory system 309, 351-3, 410-12 acceptance of 354 coal mill fault diagnosis 92-7 emissions monitoring 266-7,359-60

423

performance monitoring 358 unit startup 356-8 water chemical control 360 optimal control 366-7 orimulsion 404-5 over-fire air 253 ozone 11 parameter estimation 72, 101 coal mill modelling 72 least squares, algorithm 111,225-6 PRBS, excitation 111-12, 118, 143, 191 structure selection 189, 256-8 subspace model identification 189 supervision, onqine 101, 111-12 s e e a l s o Kalman filter; state estimation partial least squares: s e e projection to latent structures petroleum coke 405 physical-based modelling aggregation of submodels 25-7, 53 dynamic decoupling 52-3 fault representation 279 model scheduling 26-7, 76-7 object-oriented 18, 66-7, 355 open problems 56-7 parameter estimation 55, 72, 289, 292-3 validation of 53-6 s e e also black-box modelling; component model; grey-box modelling; Modelica; subsystem model physical model-based predictive control 366-8, 375-7 formulation of 377-80 PI, plant information 352 PI(D) control load-following capability 205-6, 210-17, 348 loop control 13, 347, 365 parameter tuning 90, 210-11 PTx steam temperature control 149-51 sliding pressure operation 21 0-17, 372-3 s e e also multi-loop plant control plant-wide control: s e e supervisory plant control pool, UK electricity market 10, 345 power system stabiliser 110 PRBS, excitation lll-12, 118, 143, 191 observability of 106-7 predictive control advantages of 185-6, 367 CCGT supervisory control 168-76

424

Index

predictive control (continued) coal mill control, multivafiable 90-1 constraints, inclusion of 185, 365 feedforward control 206 formulation of 147-8, 168, 377-80 multivariable steam control 347-9 parameter sensitivity 194-9 physical model-based control 365, 375-89 state estimation-based 380-1 superheater temperature control 147-9 PRESS, statistic 315,329 pressurised fluidised bed combustion 2, 12 primary air 64, 246 coal mill performance 81-2 temperature / pressure of 70-1 principal component analysis fault detection 317-25 feature selection 310 model selection 314-15 multiblock 315-16 non-linear transformation 335 principal component 314 principal curve 340 t scores 314, 317, 320 see also projection to latent structures principal curve 340 procedural rule, fuzzy logic 102, 152-3, 221-3 programmable logic controller 8, 311 see also distributed control system projection to latent structures model selection 327-8 monitoring and optimisation 310, 329-34, 336-9 multiblock 329 non-linear RBF 3 3 4 ~ non-linear transformation 335 see also principal component analysis PTx control, superheater temperature 149-52 Public Utilities Regulatory Policies Act (US) 10 pulverised fuel 7, 243 flow measurement 81 Kalman filter 84-90 pump, modelling of 37-9 pyrometry, flue gas temperature 154 load-following capability 158 steam temperature control 155-7 quadratic programming 380

radial basis function, network 102, 335 radiation, heat transfer 6, 21-2, 42, 370-1 burner configuration 382 Rankine cycle 1, 5, 18-19, 181,397 receding horizon state estimation 295-303 recursive least squares 147 supervision of 11 l - I 2, 118 regression analysis 327 reheater 3, 207 control action correction 190, 195-7 flue gas recycling 183, 190, 369, 371-2 metal temperature, state estimation 370, 375-80, 386 steam temperature control 7, 183, 372, 377 thermal efficiency 371-2 tube failure, mechanisms 403 see also flue gas recycling; heat exchanger; steam temperature / pressure reliability, power plant availability factor 398 subsystem outages 399-400 renewable energy 12, 159 UN targets 13

saturation, actuator 293,367 SCADA 251,354 scheduled outage factor 398-9 secondary air 81,244 self-tuning control: see adaptive control sensor fault detection 311-12 feedwater heater, malfunction 284-7 soft 92, 94, 159 validity index 318 value reconstruction 316-18, 330 sensor fusion 159 simulation, power plant database management 57 dynamic decoupling 52-3 hybrid emulation 113-14, 293 modelling environment 18, 164 numerical integration 52 validation of 53-6, 71-9 see also gPROMS; Dymola; Modelica; object-oriented modelling; physical-based modelling singular value decomposition 335 sliding pressure control 212, 228-9 boiler stored energy 6 gain scheduling 151

Index

thermal stress, reduction of 372, 386 unit startup 182 soft desk 351 soft sensor 92, 94, 159 soot blowing 132, 151,326 SOx, emissions 7, 11,243, 346 acid rain 11,243 flue gas desulphurisation 11,244, 397 PLS modelling of 329-32 s e e a l s o environmental regulation spline, network 247, 335 spot price, electricity 395 startup / shutdown, power plant advisory system 356-8 coal mill 91,132, 155-6 state estimation 270, 366 coal mill advisory system 92-7 HP feedwater heater modelling 295-307 physical model-based predictive control 379, 381-9 state estimation based, generalised predictive control 380-1 state-space model physical model-based predictive control 376-81 subspace model identification 189, 191 steam quality 33 steam tables 27,272, 292 steam temperature / pressure, control of 3, 7, 183, 209-10, 367 control action correction 190, 195-6 evaporator control 134-47 knowledge-based plant control 221-8 load-following 132, 137 metal temperature control of 375,390 state estimation 370, 375-80, 386 model-based predictive control 347-9 once-through boiler 4, 133, 183 physical model-based predictive control 375-81 plant life 132 superheater control 136-7, 147-58 thermal efficiency 132, 158, 372, 391 steam turbine 3 impulse stage 44-5 load cycling problems 405-6 maintenance overhaul 399 modelling of 23, 43-5, 114, 163 reaction stage 44 s e e a l s o life stochastic approximation 270

425

HP feedwater heater modelling 290-1, 301 stoichiometric air-fuel ratio 7, 249 subcritical boiler: s e e drum boiler subspace model identification 189, 191 subsystem model, power plant boiler 19, 28-43, 163 condensate cycle 23-4, 45-6 gas turbine 25, 46-50, 164 steam turbine 23, 43-5, 163 s e e also component model supercritical boiler: s e e once-through boiler superheater 3, 133 control action correction 190, 195-7 flue gas temperature 153-7 fuzzy temperature control 152-4 GPC temperature control 147-9 metal temperature, state estimation 370, 375-80, 386 multivariable temperature control 347-9 PTx temperature control 149-52 steam temperature control 7, 136-7, 183, 367, 372 thermal efficiency 132, 158, 391 tube failure, mechanisms 403 s e e a l s o attemperator; heat exchanger; steam temperature / pressure supervisory plant control 2, 13, 63,346 CCGT predictive control 168-76 control action correction 186-8 control strategies 184-5,206 controlled reference value 186-7 disadvantages of 180, 312 knowledge-based plant control 216-20 load-following capability 205-6, 348-9 multivariable steam control 347-9 physical model-based predictive control 375-81 plant management system 351 thermal efficiency 2, 346 s e e a l s o distributed control system; multi-loop plant control; operator advisory system sustainable development, UN world summit 13 s e e a l s o renewable energy synchronisation, alternator 356 system identification: s e e black-box modelling; parameter estimation t scores 314, 317, 320, 330 testing and validation, models

426

Index

testing and validation, models (continued) design data 54 open-loop / closed-loop tests 55-6 thermal efficiency combined cycle gas turbine 5 factors affecting 158, 326, 382, 399 modelling / monitoring 163, 330, 358-9 once-through boiler 4 sliding pressure operation 6 supervisory control 2, 346 temperature control 132, 371,391 see also monitoring thermal stress 179, 348 load following 132, 136, 185, 371 sliding pressure operation 372, 386 unit startup / shutdown 358,405-7 thermography, infrared 409 Three Mile Island, incident 312 training simulator 414 tramp air 7 transputer 117 tube failure, mechanisms 403

turbine following control 182, 209-11 base-load plant 6 two-shifting, operation: see load cycling unit dispatch 353, 412 United Nations, renewable energy targets 13 valve cavitation 35 modelling of 35-6 VME hardware 117 volatile organic compound 11 voltage measurement Fourier algorithm 114-16 harmonic interference 114 RMS technique 115 white-box modelling 245 see also physical-based modelling