Reference Power Systems Protection Handbook

Reference Protection Handbook

CHAPTER 1 The Principles of Power-network Calculations By C. H. LACKEY. INTRODUCTION

point in the circuit to which the voltage is related. E ah therefore means the voltage of phase-a relative to phase-b; E an means the voltage of phase-a relative to neutral-no It is essential, if confusion is to be avoided, that the nomenclature decided upon shall be most rigorously applied. If this is done, interphase-voltagevectors, which sometimes give trouble, become quite simple. There are six for the three phases, namely E.ab and E ba , E bc and E cb , E ca and E ac ; and these are shown In fig. 2.

The use of calculator-boards for the evaluation of network currents and voltages is established practice, and results in a great saving of time as compared with direct calculation. The manipulation of a calculator-board may not demand great skill on the part of the operator, or require a full knowledge of the principles involved, but the interpretation of the results and a full realisation of the nature of the problem to be solved and its implications do require a sound knowledge of the basic principles of calculation. Apart from this, a calculator-board is often not available, or the problem may be simple enough for direct solution. Engineers associated with the design and performance of power-supply systems should so equip themselves as to be able to predict current and voltage values under both normal and abnormal conditions: a clear understanding of the basic principles of fault-calculations is of paramount importance in this connection. Attention is devoted here mainly to the principles of faultcalculation, but it should be understood that many of the principles, such as those of vector-algebra and networkreduction, are equally applicable to load-studies. Fault-calculations have come to be regarded as the prerogative of experts, and as operations requiring rather exceptional skill. Experience is without a doubt a necessary adjunct to speed, but no great skill or mathematical ability is necessary for the proper understanding and solution of most problems. The subject will be considered under the following four headings: Vector- Representation. Vector-Algebra and Impedance-Notations. Network-Reduction and the Calculation of Balanced Faults. Symmetrical-Component Methods. The approach will be practical rather than theoretical, and some elementary background knowledge will be assumed.

fen

\-----E""

Ebn

E'a

+

---<

VECTOR-REPRESENTATION There can be no doubt about the value of vectors for the pictorial representation of alternating currents and voltages, and every effort should be made to cultivate their use. Difficulties have arisen in the past due to (a) lack of established nomenclature, and (b) inconsistency in the use of conventions. Figs l(a) and I(b) show the nomenclature recommended. First, there is a vector-label, E or I for example, meaning simply voltage or current; second, a suffix, as for example in E, meaning the voltage of phase-a; and third (for voltage-vectors especially), a second suffix, as for example in E ah , indicating the other

FIG.

I.

The polarity of all vector-quantities is positive, and the positive direction is away from the source of supply, as shown in fig. I(a). This applies to neutral-currents and earth-currents as well as line-currents. On this basis the currents in a 3-phase 4-wire system, for example, are

Ian + Ihn + len = -In· The current in a circuit, multiplied by the impedance of the circuit, is the voltage driving the current through the circuit. It is not the voltage-drop, which is -IZ, as shown

10

in fig. 3. Positive phase-sequence is a-b-c, negative phase-sequence a-c-b. Vectors of zero phase-sequence are in phase with one another. Three examples will be given to illustrate the conventions. (al

bb

,a)

E..b

4'

Ecb Drivins·voltar·'

Eax

f,

,, ,, I

,

to.

(b)

.

--3-0:'- a

I

Ex..

I I I

b

Eba

Eac

(b'

E'b.. Eca

c

Eab

\

Voltage--drops.

\

\ \

,0'

\ f

I

----L_O

bx

I I

(cJ

I

/ I

'0

FIG. 3. Ebc (e)

FIG. 2.

Example 2.-Phase-to-phase fault.

In fig. Sea) a generator is shown feeding a line with a short circuit at F between phase-b and phase-c. The current I be is driven by the interphase-voltage E be , and ~he current Ieb is driven by the voltage E eb . Since the Impedance of the circuit is largely reactive, the currents lag behind their respective driving-voltages by an angle ~, as shown in fig. S(b). The reactive and resistive voltage-drops in the generator phase-b, namely -IbX g, lagging behind I b by 90°, and -IbR g, in phase-opposition to I b, reduce the p~a~e-to-neutralvol~age of this phase from E bn to VbnSimIlarly, the reactIve and resistive voltage-drops in phase-c reduce the phase-to-neutral voltage from E bn to Ven . The reactive and resistive voltage-drops in the line, -IbX1 and -IbR I for phase-b, and -leX, and -IeRI for phase-c, reduce the interphase voltage at the fault to zero (neglecting fault-impedance). The voltages to neutral of phase-b and phase-c at the faults are identical, a~d eq~al to V Fn , the arrow-head of V Fn lying at the mid-pomt of the line joining E bn and E en . Although phase-a does not carry any fault-current, the magnetic linkage between phases causes a voltage-drop and the phase-to-neutral voltage becomes Van'

Example l.-Earth-~ault in a resistance-earthed system, taking capacItance-current mto account.

Fig. 4(a).shows a resistance-earthed generator feeding a system wIth star and delta capacitance, and with a fault to earth as F in phase-a. The current in phase-a has three components; one through the circuit, phase-a, the fault, and the neutral-earthing resistor, another through phase-a, the ~ault, and capacitance C b to phase-wire-b, and the thud, through phase-a, the fault, and capacitance Ce to phase-wire-c. The voltage driving the component Ian (i.e. the one through the neutral-earthing resistor) is the phase-to-neutral voltage E an , and the current is for all practical purposes in phase with the voltage, as shown in fig. 4(b). The voltages driving the other components are E ab , and E ae and since the !mpedanc~ of the circuits traversed by these components IS predommantly capacitative, they lead their respective voltages by nearly 90°, as shown by vectors lab and Iae . The resultant current in phase-a la' is the vector sum Ian as shown in fig. 4(b).

+ lab + lac' 11

Example 3.-Two-phase-to-earth fault in a solidly-earthed system.

It should be noted that the phase-a driving-voltage vector is horizontal in all the vector-diagrams. It is fairly usual to draw it vertical; but the horizontal position is to be preferred, because it is commonly used in symmetrical-component work. It simplifies calculation by eliminating an operator-j term; that is to say, the voltage of phase-a is E an + jO, whereas if the vector is vertical the voltage of phase-a is 0 + jEan. It is therefore well to accustom oneself to make the phase-a voltage-vector horizontal. It will bear emphasis that vectors are of very great value in bringing electrical conditions into the mind's eye, and so in aiding the user to understand his problem and the significance of calculated results.

Fig. 6(a) shows a generator feeding a line with earth-fault at F in phase-b and phase-c. The fault-currents in phase-b and phase-c may each be considered as comprising two components, namely a phase-to-phase component, as in a phase-to-phase fault (fig. 5), and a phase-to-earth component. In fig. 6(b), I he and leh are the phase-to-phase components, and I hn and len the phase-to-earth components. The total currents in phase-b and phase-c are therefore I h = I he + Ihn' and Ie = leh + len' and the total earth-current is Ie

=

I hn

+ len'

The generator-voltage E hn can be resolved into the two components E'he and E'hn at right angles to each other as shown. Similarly, the voltage E en can be resolved into the two components E'eh and E'en' The two component vectors E'bn and E'en are coincident. The voltage-components E' be and E'eh are each equal to one-half ofthe interphase-voltages E be and E eh , and each is completely absorbed by driving the corresponding interphase-currents Ihe and Ieb . These currents lag behind their associated voltage by the angle 0. The voltages E' bn and E'en are absorbed by driving the earth-currents Ibn and len' which in a solidly-earthed system lag behind their voltages by approximately 70°.

EGb (not to scale)

~>

1\

-IeRg GENERATOR

" n

t

Ecn

X

l-l~

'I

I

b

~cn

-IcH

"' "'

\

"' "'

Veb

I

Ie

"'"'

_ _--;;;j,.:::::......:=-='""=-==-:="'=--::-:;~Eon Von

NEUTRl\l l:ARfHING

RESl5TOR

lb

(a)

Ebn

Vb.

Ebt.

10.

(not to scale)

(b)

I I

FIG. 5.

I

\(Ub ,

\

,

VECTOR-ALGEBRA AND IMPEDANCE NOTATIONS

\

Vector-Algebra All students are familiar with the elementary principles of vector-algebra, such as the expression of an inductive impedance in the form Z = R + jX, and the rationalization of expressions as in the following example:

FIG. 4.

12

GENERATOR Zg

z.e Ib

1\

The scalar value of this is IZI = YR2 + X 2, and X/R = tane Hence R = IZI cose, and X = Izi sine.

a. I.

F

----+ Ie

c.

tIe

~

(a)

Substituting these values in equation (1) gives Z = Izi (cose + j sine).

• Eeb (NOT TO SCALE)

It is proved in standard mathematical text-books that

cose + j sine = .i e .

II

Ee~

. --IrE'cb'T Eeb

Substituting .i 8 in the equation for Z gives Z = IZI .i e

I

Ie

len

(2)

This is known as the exponential method of specifying a vector. leI.

An impedance-vector has been taken by way of example, but the same principles hold good for current, voltage, or any other vectors. The physical significance of a vector expressed exponentially is perhaps not so obvious as when it is expressed in rectangular coordinates, but the exponential form is sometimes easier to manipulate in division and multiplication. The rules are the same as for ordinary algebra. Thus AXx AV = A(x + y) and AX/AY = A (x-y).

Ea.n

I

Ibe ' I

i

I

I I I

E'bc..E~C

: Ebn I

If we take a voltage-vector E = lEI .i e . and a current vector I = II cie" then EI lEI .i e , x III Je, EI III .j(e, + 8,), and E/I lEI Je./ III Je, = (I EI / III )J(e, - e,)

I

Ebc( NOT TO SCALE)

(b) FIG.

E

I Z

E I

I

6.

5 + JIO 2 + j3 5 + JIO 2 + j3 40 + j5 13

Consider also the following. Let Z = Z,Z2Z3/z..ZS. X

Expressing this exponentially, we have Z = Iz,1 .i e , x Iz21 .i e , x IZ3! .i e , Z.I .i e, x IZsl .i e ,

2 - j3 2 - j3

I

Iz.. Zsl , IZ 1 IZ./ IZ 31 x .j(ed ed ed - e, - e,) IZ·IIZs/ e 1 ZTI .i , (3)

It is not proposed to go into details of this part of the

work; we shall rather devote our attention to one or two important aspects that experience shows are not so well understood. where

These are: (a) the exponential method of specifying a vector; (b) vector-operator-a; and (c) the resolution of parallel impedances.

Algebraically, and in rectangular coordinates, an inductive impedance is expressed as

+ jX

T and e

I z,1 Iz21 Iz31 1z..IIZs! ' (e, + e2 + e3 - e. - es).

The evaluation of IZTI and e is merely arithmetrical, since all the components are plain numbers. If it is desired to give the final value of Z in rectangular coordinates, i.e. R and X, it is easy to do so, because R =IZTI cose, and X = IZTI sine.

The exponential method of specifying a vector

Z = R

1Z I

(1)

13

called operator j. Any vector-quantity multiplied by j is thereby rotated 90° anti-clockwise. If any vector, say a current vector, II Ea, is multiplied by vector I.i e , we get I.i(a e). The length of the vector II is unchanged, but its inclination to the reference-line is increased from a to (a + 8). Thus to multiply a vector by U 12 lJ" means simply that its angle to the reference-line is increased by 120°, i.e. the vector is turned through 120° counterclockwise; and multiplying by l. j240' turns the vector through 240°. The quantity l.i 120' is called a 120°-operator, and is usually denoted by the small letter a. Operator U240' is then a'.

A little reflection will show that equation (3) can be written down at once for any division of vector expressions, without the preliminary steps indicated above.

I

Take now a numerical example, and suppose that it is required to evaluate the following expression in terms of Rand X. Z = Z,Z./Z.Z.Zs, where Z, = 2 + j3, Z. = 4 - j2, Z. = 3 + j4, Z. = 2 + j2, Zs = 2 - j4.

In rectangular coordinates, a = I.i120'= cosl20° + jsinl20° = -0.5 + jO.866 a' = I.i240'= cos240° + jsin240° = -0.5 - jO.866

Writing the expression in exponential form gives Z =IZTI .ie, where IZTI =

\z,\z·1

IZ·I

IZ.I IZsl

Operators a and a' are used in symmetrical component work (as described later) as a simple means of rotating vectors through 120° and 240° respectively.

and 8 = 8, + 8. - 8. - 8. - 8s. Then

IZ,I = V2'

+

3' = 3.60 8, = tan- 1

3/2 = 56°

The resolution of parallel impedances

If a circuit comprises impedances in parallel, the total impedance is obtained from

IZ·I = V4' + (-~. = 4.471 • = tan- -2/4 = _27° /Z·I = V3'

+

4' = 5.00: 8. = tan- 1 4/3 = 53°

IZ.I = V2'

+

2' = 2.82 8. = tan- 1 2/2 = 45°

I

I

_1_ = ~1_ + _1_. + _1_ + Z Z, Z. Z.

..

Thus, for three impedances in parallel, 1 Z2Z. + Z.Z, + Z,Z. Z Z,Z.Z. Z = Z,Z.Z. Z.Z. + Z.Z, + Z,Z. In working out an expression of this kind, each impedance must be put in its vector from (R + JX) or Z I .i e . A simple alternative procedure, which is specially advantageous for more than two circuits, is as follows. Let R, + jX" and R. + jX•. 1 ~+~ Then z, Z. Z 1 + R. + jX.

/Zsl = V2'+(-4)' = 4.47 : 8s = tan- 1 -4/2 = _63° 3.6 x 4.47 = 0.25, 5 x 2.82 x 4.47 8 56 - 27 - 53 - 45 + 63 = _6°. Z IZTI .i e = 0.25.j(-6') R Izi cos8 = 0.25 cos (_6°) = 0.25 x 0.99 = 0.249. X IZ/ sin8 = 0.25 sin (_6°) = 0.25 x (-0.1) = - 0.026. Hence Z = 0.249 - jO.026. IZTI

I

The time saved by this method is well exemplified in star/delta transformations, where the expressions Z,Z,/Z" Z,Z,/Z" and Z,Z'/Z, require to be evaluated. Here the calculations of IZ,I ' Z.I, IZ.! ' 8" 8., and 8. for the first expression are equally applicable to the other two, whereas with rectangular coordinates there is nothing common to the three calculations.

Rationalise each term separately:

I

_1_ = 1 x R,-jX, + R, + jX, R,-jX, R. + jX. Z R, - jX, + R. - jX.

R,' + X,'

X

R.-jX. R.-jX.

R.' + X.'

R, + R. _j ( X, + X. ) R,'+ X,, R.'+ X.' R,~+ X,, R.'+ X.' The first two terms, consisting of resistance divided by the sum of the squares of resistance and reactance, are called the "conductance" of the circuit, and such terms are denoted by the small letter g. Similarly, quantities

Vector-operator-a

Two methods of expressing a vector have been mentioned, namely the rectangular-coordinate method, e'f' Z = R + jX, and the exponential me!h~ e.g. Z = ZI.-I e . In each of these the quantity j = V-I, and is

14

ohms to a voltage-base other than that to which they belong in practice. In this connection students are doubtless familiar with the concept of transformer equivalent impedance, referred to the primary or to the secondary winding. In the same way any impedance can be transferred from one voltage-base to another. The transferred impedance must of course have a value different from the natural impedance, in order that its effect in the circuit may be the same. The criterion so far as these calculations are concerned is that the same proportion of the driving-voltage shall be absorbed by the new value of the impedance. Expressed algebraically, I1Zl/El = hZ2/E2, where the suffix (1) indicates the initial or natural conditions, and suffix (2) the new-voltage-base conditions. From the above identity,

like the last two terms, involving reactance divided by the sum of the squares of resistance and reactance, are called the "susceptance" of the circuit, and are denoted by the small letter b. The last expression may thus be written as:

liZ = gl + g2 - j(bl + b2), and, generally, for any circuit involving a number of parallel impedances: liZ = gl + g2 + ga + -j(bl +b2 +ba + ) = G - jB, where G = gl + g2 + ga + . . and B = bl + b2 + ba + Thus Z

= _1_ , which, when rationalized, G -jB

gives, Z

+ jB G + B2 G

(4)

2

Zl Z2 Za Z.

= = = =

2 4 3 2

+ + -

X Zl El h E2 X ~ X Zl El El (because the current must be inversely proportional to the voltage)

j3, j2, j4, j2.

=

g2 = ga = g. =

2 22 + 4 42 + 3 32 + 2 22 +

32 22 42 22

=0.154 bl = =0.200 b2 = =0.120 ba = =0.250 b. =

3 22 + 32 -2 = 42 + 22 4 = 32 + 4 2 -2 = 22 + 22

(

~:

)

2

X

Zl

(5)

Taking transformer-impedance by way of example: Z, = Zp(E,/E p)2 and Zp = Zs (E p /E s )2, where ZIand Zp are the total equivalent impedances of a transformer referred to the secondary and primary sides respectively, and E s and E p are the secondary and primary voltages. Suppose that it is required to transfer the impedance of a 33-kV overhead line (say 8.6+ j 11.4 ohms) to a voltage-base of 6.6-kV. Z33-kY= 8.6 + j11A Zhh-kY =(8.6 + j11A) (6.6/33)2 = 0.344 + jOA56

Then gl =

~ x ~

Z2

The use of this equation for determining the impedance of parallel circuits can be a great time-saver, and reduces the problem to little more than simple arithmetic. Consider, for example, four parallel impedances as follows:

0.231 0.100 0.160 0.250

Per-cent-notation

G = gl+g2+ga+g. = 0.724 B = (bl+b2+ba+b. = 0.041 Z =

G + jB G 2 + B2

The percent impedance of a circuit, or of a piece of equipment, is the impedance-drop in the circuit, or in the equipment, when it is carrying a specified current, expressed as a percentage of the line-to-neutral voltage. Thus, % impedance ZI x 100, (6) line-to-neutral voltage where Z is the ohmic impedance of the circuit or equipment, and I is the specified current. In practice, MVA is invariably used instead of current in connection with per-cent impedance; this is permissable because MVA is proportional to current for a given voltage. Further, when specifying the per-cent impedance of. for example, a transformer or a generator, it is usual to give it for its rated current (MVA). Thus a 15-MVA transformer may have its impedance given as lOper-cent at 15 MVA or a

0.724 + jO.041 (0.724)" + (0.041)2

0.724 + jO.041 = 1.38 + jO.078 0.526 Impedance-Notations There are three ways of expressing the impedances of the various components of a network, namely (I) in ohms, (2) as a per-cent value, and (3) as a per-unit value, and in each case the expression may be in vector or in scalar form. Ohm-notation

The only matter to which attention need be drawn in connection with ohm-notation is that of relating the

15

30-MVA generator may have an impedance of 20 per-cent at 30 MVA. When using percent impedances, it is frequently necessary to transfer them from their natural MVA-base to some other MVA-base. Since the per-cent impedance-drop is directly proportional to current, and therefore to MVA, we have a very simple proportionality for such transfers, as follows: % impedance at MVA (A) = % impedance at MVA (B) x MVA (A) MVA (B)

approximate result is required, it is sufficient to treat the impedances as scalar quantities, and so make the additions, subtractions, and so on purely arithmetical. If however, such a simplifying assumption is not permissible, ohmic impedances must be expressed in their R + jX or IZI .j6 form, and per-cent and per-unit impedances in per-cent or per-unit resistance and reactance drops, as given above in equations (8) and (9). Relations between impedance-notations

It often happens that the impedances of networkcomponents are not all given on the same basis; for example, cable and line impedances are usually given in ohms, whereas transformer and machine impedances are usually given in per-cent or per-unit values. The same basis must obviously be used for all the components of the network, and so it becomes necessary to transfer some impedances from the given basis to the basis chosen for the calculations. We shall therefore derive expressions for the relations between the three notations, in order that such transfers from one basis to another may readily be made.

For example, if a generator has an impedance of 15 per-cent at 50 MVA, its impedance at 100 MVA is % impedance (100 MVA) = 15 x 100 = 30% 50 Per-unit-notation

The per-unit impedance of a circuit, or of a piece of equipment, is the impedance-drop in the circuit, or in the equipment, when it is carrying a specified current, expressed as a decimal fraction of the line-to-neutral voltage.

Let Z =impedance per phase of the circuit or of the equipment, in ohms, I =any given current per phase, in amperes, E =the rated line-to-line voltage, in kV, and M = 3-phase MVA based on E and I (M = V3EII1000). From equation (6), ZI % impedance x 100 = v'3ZI 1000E 10E

Thus, P.U. impedance ZI line-to-neutral voltage

.................(7)

Obviously the only difference between per-unit and per-cent impedance is that the former is the one-hundredth part of the latter. The 15-MVA transformer mentioned above has a per-cent impedance of lOper-cent and a per-unit impedance of 0.1. The rule for transferring a per-cent impedance from one MVA base to another, as given above, is clearly applicable also to per-unit impedances.

v'3 1000M v'3E '

Now I % impedance

and therefore, substituting for I

v'3z x 1000M 10E 100ZM -,

Vector-expression of per-cent and per-unit impedances

v'3E (10)

E2

If the ohmic impedance Z is written in its vector-form

R + jX in the expressions given above for per-cent and per-unit impedances, we have the concept of per-cent or per-unit resistance and reactance.

and Z

% imp. x E2 100M -ZM -,

Similarly, P.U. impedance =

E2

Thus, % impedance _ _ _--=Z=I x 100 line-to-neutral voltage

and Z

(11)

P.U. imp x EO

(12)

(13)

M

= (RI x 100) + jJSL x 100) ... (8) Ean Ean where Ean is the line-to-neutral voltage.

For example, a 20-MVA transformer with lOper-cent impedance (at 20 MVA), and a rated voltage of 33kV, has an ohmic impedance, from equation (11), of

Similarly, P.U. impedance= RI + jJSL (9) Ean Ean When all the impedances in a network are known to have, or may be assumed to have, the same, or approximately the same, power-factor, or when only an

2 Z33-kV = 10 X 33 - 5.44 ohms. 100 x 20 A 20-MVA generator with a per-unit impedance of 0.125 (at 20 MVA), and a rated voltage of 11 kVhas an ohmic impedance, from equation (13), of

16

NETWORK-REDUCTION AND THE CALCULATION OF BALANCED FAULTS

=

0.125 x 11" - 0.76 ohm 20 A 132-kV overhead line with an impedance of 12 ohms has a percentage impedance on a basis of 100 MVA, from equation (10), of ZIl-kV

An electrical power-network, from the point of view of fault-calculations, is merely an arrangement of series and parallel impedances between the source of supply and the fault. For the calculation of the total fault-current, the network is reduced to a single equivalent impedance between the source and the fault. For a radial network, the process of reduction is simply the addition of the various generator transformer, and line impedances. An example of this is given in fig. 7(a) and 7(b), the impedances in 7(b) being shown in ohms, per-cent, and per unit values. The value of the 3-phase fault-current is derived by dividing the line-to-neutral voltage by the equivalent impedance in ohms. If per-cent or P.U. impedances are used. Base MVA x 100 Fault MVA ----'------,------,--, or Total per-cent impedance Base MVA Fault MVA Total P.U. impedance In all these calculations the assumption is made that the impedance-values are identical for each phase, and so only one phase need be calculated.

100 x 12 x 100 - 6.9, 132 2 and the P.U. impedance is 0.069. % impedance =

rv V

GENEP~TOR

I IOMVA:IS.l'

GENERATOR 2 IOMVA:12'S!

- ....--T--....-

OVERHEAD LINE OF COPPER CONDUCTORS 0-1 SQ. IN. PER PHASE

LOADS ~T II kVAND 33kV OMITTED AS NOT RELEVANT TO THE PROBLEM

-..,..

T2

z" (0'43 +j 0-57).a PER MILE

...._

33kV

S1

S MVA:

2

IIkV

Example of radial system

From fig. 7(b), the impedance of the equivalent circuit is 0.774+j2.131 ohms at 6.6 kV.

6·6k'/

MI~ES

Hence the fault-current

0·2 SQ. IN. P. I. L C_ CABLE Z~(o·215+JO'122)1l.PER MILE

FAULT

IF =

6600/Y3 575 - j1590 0.774 + j2.131 If only the numerical value of the current is required,

(a)

j 68

0+jO'5S

O+jl00

a+J \-0

0+

= YR2 + X 2

Z

ZPU.

0.774 2 + 2.131" = 2.27 ohms, and

= Y

IF = 6600/Y3 - 1690 A. 2.27

0+jO·Z97

The current in the 33-kV line is

79+ j 105

TRANSFORMER

1

0+ j a-43b

IF33 = 1690

x

6600 =340 A. 33000

x

6600 11000

Similarly

0-79+ j 1-05

LINE

0-344+jO-456

IFll = 1690 --!--

33-kV BUSBAR

1020 A.

Current in generator 1 0+j160

O+jl'6

TRANSFORMER 2

OtjO'69B

II 99+jS6

0-99+)0-56

CABLE

=

_--=Z=2__ X IFI Z, + Z2

0.545 x 1020 = 463 A. 0.655 + 0.545

0·43+ jO'Z44

Similarly 178+j469 17S+j4'S9 TOTAL F TOTAL

(b)

0774+jZ-131

12 =

Zl Zl

FIG_ 7.

17

+ Z2

X IFll

_ _0_._65_5_ _ x 1020 = 557 A. 0.655 + 0.545 It is important, if the phase-angles of the generatorimpedances Zl and Z2 are not equal, that each shall be 6 form. expressed in its R + jX or The voltage at the 33-kV busbars is the line-to-neutral voltage plus the voltage-drop between the source and the 33-kV busbars. The impedance to the 33-kV busbars in ohms at 6.6 kV is Z =(0+jO.298) + (0+j0.436) + (0.334+j0.458) =0.334 + j1.l92 The current in amperes at 6.6 kV is IF6.6 = 575 - j1590. Hence the impedance-drop = - IZ = -(575 - j1590) (0.344 + j1.192) = -(2099 + j144).

IZI % = Y178 2 + 489 2 = 519% The 3-phase fault MVA = 100 x 100 519 = 19.3 MVA. The fault-current MVA x 1000 IF6.6 = V3 x 6.6 19.3 x 1000 1690 A, as before.

Izl.i

Y3 x

Expressing this as a vector quantity,

e

= tan- 1

100 x 100%= 17.2 MVA. 528% With vector-impedances, as above, the MVA is 19.3. The error resulting from the assumption of equal phase-angles is therefore

V6." = Y3X Y1716 2 + 1442 = 2980 V on a 6.6 kV basis. The actual line-to-Iine volts V33 = 2980 x 33/6.6 = 14,900 V.

Error % = 19.3 - 17.2 19.3 = 10.65%

Now, using the per-cent impedances figures of fig. 7(b), the total per-cent impedance on a 100-MVA basis = 178 + j489.

e

0·67+ i 6·\ 0·4 + j 3·62

o 24+jO·75 1·75+jO·9 0·Z4+jO·75 0-4+ j 3·62 ~.

1·36+j 1·36

'·75+jO·9 (a.)

o 55+j0224

l

~~~~el /·08 +jO·S5

0·55+1 C224

\

(d)

= 70°, and

= 1690 cos70 - j1690 sin70 = 578 - j1590, as before. The procedure for P.D. impedances is obviously exactly the same. It is frequently permissible, if vector-results are not required, to assume that the phase-angles of all the impedances are the same. If this is done in the preceding example, a total scalar impedance of 582% is obtained on an MVA basis of 100. The three-phase fault MVA is then

The scalar line-to-line volts.

145+ jO·8

489 178

IF6.6

The phase-to-neutral voltage at the 33-kV busbars, expressed on a 6.6 kV basis, = (E + jO) + IZ = (6600/V3 + jO) - (2099 + j144) = 1716-j144.

175+ j09

6.6

I (e)

FIG. 9.

18

x 100

An error of such an amount is often quite permissible, and because of the relative simplicity of scalar impedances they should be used wherever vector results are not required, and where great accuracy is not important.

equivalent star-group (say ZAB, ZBC' and ZCA) as follows: ZAB =

_ _Z_A_Z_B_ _ ZA + ZB + Zc

(14)

ZBC =

- -ZBZC ---

(15)

ZA An example of an interconnected network

ZCA =

Consider now a simple interconnected network, as shown in fig. 8. Let it be supposed that a three-phase fault occurs at sub-station C, and that it is required to determine the currents in all branches of the network. Fig. 9(a) is the impedance-diagram for the network of fig. 8. In fig. 9(b) the impedances of the two parallel cables, each 1.75 + jO.9, have been resolved into the single impedance Zl = 0.87 + j0.45, and the four series-impedances of the 66-kV line and transformers have been resolved into the single impedance Z2 = 1.28 + j8.74. Z2 is in ohms at 33 kV, i.e. the actual ohms at 66 kV of the line have been multiplied by (33/66)2, and the transformer-impedances have been calculated on a

+

ZB

+

Zc

(16)

_ _Z_cZ_A_ _ ZA + ZB + Zc

(o.)

20MVA

"_ ..........__..,..1.oooo-33kV

(b)

B

FIG.

Applying this to the delta-group ZA' ZB, Zc of fig. 9(b) gives the equivalent star-group ZAB, ZBC' ZCA of fig. 9(c). For example:

D

ZAZB

ZAB = ZA F

FIG.

10.

8.

=

+

ZB

+

Zc

(1.75 + jO.9) (1.45 + jO.8) (1.45+jO.8) + (1.36+j1.36) + (1.75+jO.9.) 0.55 + jO.224.

Similarly ZCA = 0.439 + jO.371, and

33-kV basis. Although these steps have simplified the impedance-network, the delta-group of impedances ZA, ZB, and Zc is not amenable to reduction by the laws of series and parallel impedances; but it can be replaced by an equivalent star-group. Any delta-group of impedances (say ZA, ZB, Zc in fig. 10) is related to the

ZBC = 0.53 + j0.416.

The network may now be reduced to fig. 9(d), and further, by combining the parallel impedances, to fig. 9(e), and finally to fig. 9(f) which shows it as a single equivalent impedance of 2.3 + j7.17 in ohms at 33 kV;

19

and the total three-phase fault-current may be determined thus: phase-to-neutral voltage IF = equivalent impedance 33,000

V3 X(2.3

leaving a junction must be equal. Refer to fig. 11, which is an enlarged diagram of this part of the network, and consider the junction between ZB' Zc, and Z2' First assume a direction for the current I c ; it is immaterial which direction is chosen so long as it is indicated clearly,

+ j7.17)

= 775 - j2420 amperes.

ASSUMED DIRECTION FOR Ie

To find the current in each branch of the network, we must now work back from the equivalent impedance to the original network, dividing up the total current IF between the various branches according to their respective impedances. From fig. 9(d) the currents in the branches Zx and Zy are obtained by the ordinary rule for parallel circuits thus: Ix =

z,

z,

-

Z X If, where Z is the impedance of Zxand Zy Zx in parallel = 1.08 + jO.~5 (fig. 9(e)),

= 1.08 + jO.85 = (775 _ j2420) =

Iy

1.31 + jO.82 917 - j2078.

_ -Z

-

Zy = =

X

FIG. 11.

IF since the result is related to the direction chosen. Suppose that Ie flows from left to right as shown in fig. 11. Then I B , or I c + 12 I B - 12 (12 = I y of fig. 9(d)) Ic (145 - j890) - (-142 - j342) 287 - j548.

1.08 + jO.85 x (775 - j2420) 1.81 + j9.15 - 142 - j342.

The distribution of current in fig. 9(d) is now determined. The next step is to find the currents in the delta ZA, ZB, Zc, of fig. 9(b), corresponding to those of the equivalent star ZAC' ZBC' ZCA of fig. 9(c). There are two steps in this, namely first finding I Aand I B, and then finding I c . To find I A and I B, equate the voltage-drops between equivalent star and delta terminals as follows: IBZ B = IABZ AB + IBcZBc (see fig. 9(c)), where lAB = If = 775 - j2420, and I Bc = ly = - 142 - j342. Hence I B (1.75+jO.09)

The result may be checked by considering the junction of Zj, ZA' and Zc. Thus (again referring to fig. 11). I, I A + I c , or Ic II - I A (I, = Ix of fig. 9(d)) (917 - j2078) - (630 - j 1530) 287-j548. The current in each of the two cables on the left-hand side of fig. 8 is one-half of the current in impedance ZI of fig. 9(b). Thus

(775 - j2420) (0.55+jO.224) + (-142-j342)(0.53+ j0.416), from which I B = 145 - j890. =

Icables

Similarly, IAZ A = IABZ AB + IcAZ cA (see fig. 9(c)) , where lAB = If = 775 - j2420 as before, and I CA = Ix = 917 - j2078.

=

~ 2

=

917 - j2078_ 458 - jl039. 2

Similarly, the current in each of the generators is one-half of the total fault-current, since in this example the generators have equal ratings and impedances. Thus

Hence I A (1.45+jO.8) = (775 - j2420) (0.55+jO.224) + (917 - j2078) (0.439 + jO.371), from which I A = 630 - j1530.

Im!e

=

l!:.2

= 775 - j2420_ 387 - j1210. 2

The total current and the current in each branch of the network have been calculated, and the results are summarized in fig. 12. The impedances ofthe 66-kV line and its associated transformers were reduced to ohms at

To find the current Ie in the branch Zc, remember that the sum of the currents flowing into any junction is zero, or, in other words, the total currents entering and

20

33-kY, and the actual current In the 66-k Y line therefore Ibh-kv I, x 33/66 (-142 - j342) x 33/66 -71-jI71.

method is usually more convenient than the per-cent. The per-unit method is usually preferred for synchronous-machine studies in general and for calculator-work. (iii) When vector-impedances are to be used, there is little to choose in fault-current and fault-voltage calculations between ohms, per-cent, and per-unit notations, unless most of the data happen to be in a particular notation. In this case, the student should, to begin with. use the notation thatcomes most naturally to him.

IS

This is the value given in fig. 12.

SYMMETRICAL-COMPONENTS METHOD Basic Relations

~-jI71

The basic principle of symmetrical-component theory is expressed in the following relations: I" = 1"0 + 1"1 + I,,:, (17) Ih = I ho + Ihl + Ih :, (18) Ie = Iell + lei + Ie:' (19) where I". I h , and Ie' are the phase-currents, and (i) components with suffix '0' have zero phasesequence. (ii) components with suffix '1' have positive phase-sequence, and (iii) components with suffix '2' have negative phase-sequence.

B

F

Using operator a, these relations can all be expressed in terms of phase-a as follows: (20) I a = laO + I al + I,,:, I h = laO + a 2 I ai + ala:' (21) Ie = 1"0 + alai + a 2 I"2 (22) Equations (21) and (22) for the phase-b and phase-c currents can be expressed in another way as follows:

TOTAL FAULT-CURRENT

775 -

j 2420

FIG. 12. Choice of impedance-notation

Having now referred in greater detail to the three notations in use, we may consider their relative spheres of application. (i) A decision must be made on whether or not it is permissible to use scalar values of ohms, per-cent, or per-unit. For phase-to-phase faults, or for phase-toearth faults in solidly-earthed systems, and where only the magnitudes of fault-currents and fault-voltages are required (i.e. not their phase-angles), scalar impedances are very often permissible, and negligible errors result from their use. The reason for this is either that the phase-angles are very similar (for example the impedances of generators and transformers are mostly reactive), or that one kind of impedance predominates. (ii) When scalar impedances are permissible, per-cent and per-unit values are usually preferred to ohms, unless most of the data are in ohms. The advantage of per-cent and per-unit values is that they can be added together irrespective of voltage, whereas ohmic values have to be brought to a common voltage-base. As between per-cent and per-unit there is nothing to choose for fault-current calculations. When voltages are involved, and when it is necessary to calculate voltage-drops, the per-unit

EQUATION (21): I b = laO + a 21al + ala:' = lao+ (-0.5 - jO.866)la1 + (-0.5 + jO.866) la2 = laO - 0.5 (Ial + la2) - jO.866(Ial - Id

..

...................... (23) (22): I c = laO + alaI + a 2 1a2 = laO + (-0.5 + jO.866) lal + (-0.5 - jO.866) la2 = laO -0.5 (Ial + Id + jO.866 (Ial - la2) · (24) EQUATION

Corresponding terms in equation (23) and (24) are identical, apart from the signs of the j terms, and this simplifies the calculations of phase-b and phase-c currents. These relations between phase-values and component values hold good for phase-to-neutral voltages as well as for currents. Calculation of the sequence-components

The utility of the basic principle expressed in equation (20), (21), and (22) above depends on knowing the

21

sequence-component currents lao, lab and la2' The first step in the calculation of these is to determine the impedance of the network to their flow. This is not necessarily the same for currents of each sequence. There are two reasons for this: first, that the impedance of the generators, transformers, and so on may not be the same for all sequence-currents, and, second, the path through the network, from the source to the fault, may not be the same for each. It is therefore necessary to have a network-impedance diagram for each phasesequence component. These diagrams are generally referred to as the sequence-impedance networks. A simple line-diagram of the network is prepared, showing the generators, transformers, lines, and so on with which the calculation is concerned, and the position of the fault. The positive-sequence impedance-diagram contains the impedances of all the parts of the network between the source of supply and the fault; and the values of the individual impedances (ohms, per-cent, or per-unit) for the generators, lines, and so on are the ordinary star-impedances as used in three-phase fault-calculations. The only voltages generated (by normal machines) are positive sequence (a, b. c), and therefore the generator voltages are placed in the positive-sequence network. Fig. l3(a) is a single-line diagram for a simple network comprising two generating-stations with interconnectors, and with a fault (of some kind) at F. Fig. 13(b) is the corresponding positive-sequence impedance-diagram. It is usually assumed that all generator internal voltages are equal in magnitude and phase. On this basis the four generator-terminals 1, 2, 3, and 4 are all at the same potential, and the diagram can be simplified by joining these points and using a single source of e.mJ. E, as in fig. 13(c). This impedance-diagram has two terminals, namely the neutral-terminal N I and the fault-terminal Fl' Consider now the impedance of the network to the flow of negative phase-sequence currents. The impedance-diagram is the same as for positivesequence. The impedances of transformers, lines, and so on to negative-sequence currents are the same as their positive-sequence impedances, but for generators the negative-sequence impedance is only about 70 per cent ofthe positive-sequence impedance. Further, there is no generated voltage in the negative-sequence network, because, as stated above, positive-sequence voltages only are generated. Fig. 13(d) is the negative-sequence impedance-diagram of the network of fig. 13(b). The two terminals of the diagram are N z and F 2 • In considering the impedance of the network to the flow of zero-sequence currents, it should be remembered that the three zero-sequence currents are by definition equal in magnitude and phase. They can only flow, therefore, when the fault provides an exit from the phases whereby they can return to the system-neutral. Such an exit is provided only when the fault is between one or more phases and earth, and the system-neutral must be earthed so that the return-circuit to the neutral is complete. Thus zero-sequence currents flow only in earth-faults, and they traverse only those

N. .---- - - - - - - - - - - - --:-----0- - - - - - - - - - - - - - - - - - - - I

e I

e,

I

3

2

Fl

e,

4

(b)

I

ej>--: :

e~--'

EoN,

r------ ----- - ---.- -- --8-------- - ----- - ---- - --,

:

:

F,

(ej POSITIVE-SEQUENCE NETWORK 2

~~ ~ ro

'---------'-:

Fz

(d) NEGATIVE-SEQUENCE

NETWORK

~ (e) ZERO-SEQUENCE NETWORK

FIG.

13.

parts of the network directly connected to earthed neutrals. The zero-sequence impedances of the generators, transformers, and lines are often quite different from the positive-sequence and negative-sequence impedances. Neglecting the values of the impedances, the zero-sequence impedance-diagram for the network of fig. 13(b) is as shown in fig. l3(e). The neutral-point of generator 4 is not earthed, and so the impedance of this N,

o e

Zz

Z,

FIG.

22

14.

Zo

Referring to the diagrams of fig. 15, we may now calculate the sequence-component currents as follows (E is the phase-to-neutral voltage): Earth fault: (see fig. 15(a)). E ......................(25) lao = I al = I az = Zo + Z, + Z2 Phase-to-phase-fault: (see fig. 15(b)). E ................................................(26) Z, + Z2 I az = -I al (27) lao = O. Two-phase-to-earth-fault: (see fig. 15(c)).

machine does not appear in the zero-sequence network. There is, further, no generated voltage in the zero-sequence network, because, as stated above, only positive-sequence voltages are generated. The two terminals of the zero-sequence diagram are No and F o. If the values of all the impedances in the positive, negative, and zero sequence diagrams are known, each may now be reduced to a single equivalent impedance. The positive-sequence diagram now becomes the single impedance Zj, the negative-sequence diagram Zz, and the zero-sequence diagram Zz, as shown in fig. 14. All that is now required to enable Iaj, I az , and lao to be calculated is a knowledge of the voltages impressed across the impedances Zj, Zz, and Zoo Since the only voltage in the three impedancediagrams is that in the positive-sequence diagram, the negative-sequence and zero-sequence impedance diagrams must be connected in some way with the positive-sequence diagram in order that negative-sequence and zero-sequence currents may flow. The question is how the diagrams should be connected, and it can be shown that the answer depends on the kind of fault, i.e. whether it is phase-to-earth, phase-to-phase, two-phase-to-earth, or three-phase, a different connection applying for each. The methods of connection for each kind of fault are shown in fig. 15(a) to 15(d). For an earth-fault all the three diagrams are connected in series; for a phase-to-phase-fault the positive-sequence and negative-sequence diagrams are connected in parallel; for a two-phase-to-earth-fault all the three diagrams are in parallel; and for a three-phase-fault there is only the positive-sequence diagram. The correctness of these connections is proved in books dealing with the theory of symmetrical components.

N,

N,

t,

r,

~

...

1.,

'2

F,

NZ

t

1.. F,

ca.) hnh·f<\ul~

F,

\b)

(do.)

P~.l$e ·to· phA$e .fl>Ult

1""I.-ee-pr,a.-:.e-falllt

~N E

t,

r

Z,

...

"

TWO-;l~./t5t·

'.

tc· euth-fa.vIC

FIG,

Z,

(30)

(31)

The six steps are: (i) Determine (by inspection) the sequenceimpedance diagrams (the zero-sequence diagram is required only for faults involving earth). (ii) Fill in the values of the sequence-impedances. (iii) Reduce the diagrams to their equivalent impedances ZI' Zc, and Zo. (iv) Connect the equivalent impedances together in accordance with figs. 15(a) to 15(d), according to the kind of fault.

N2

...

-E

(29)

I az = O. lao = O. Attention should again be drawn to the important convention that all vectors are for the positive direction; that is to say, they represent quantities acting away from the source towards the fault. This applies equally to the symmetrical-component vectors of the fault-current, and therefore the values of I al , and I az , and lao derived above are for the directions neutral-to-fault, as indicated by the arrows in figs. (15a) to 15(d). These relations are obviously very simple indeed, and therefore the symmetrical components of currents for any of the four kinds of faults mentioned above are easy to determine when the sequence-impedances are known. When the components of current are known, the actual phase-currents are obtained by addition, in accordance with equations (20), (21), and (22), or with equations (20), (23), and (24).

Z2

FZ

•

I al =

(28)

Z2 Zo Z2 + Zo

Zo Z2 + Zo Z2 lao = -Ial X Z2 + Zo Three-phase-fault: (see fig. 15(d)).

z,

Z2

Z, +

I az = -I al x

N,

NZ

E

I al =

15.

23

GENERATORS ~,

N,

1'4, 0

0

19kv

p

19kv

)2,6

)2'6

j 14

J 13

J IS

1'4, 0

0

19kv

19kv

1'4,

j 1·3

J14

1 15

pI

j 18

jl33

j 20 Q,

Q

R,

)24 <) :::1

"

F,

F,

(a)

FIG.

16. N,

1'4,

(v) Calculate the sequence-component currents, using equations (25) to (31) according to the kind of fault. J '·9

(vi) Find the current in each phase at the fault by adding the sequence components in accordance with equations (20), (21), and (22), or with (20), (23), and (24).

j 14

j 19

N,

j095

J 14

j 15

)15

jl8

An example

Consider the network of fig. 16, and suppose that it is required to determine the current in each feeder with a two-phase-to-earth fault in the b-phase and the c-phase at F. Fig. 17(a) shows the positive-sequence impedancediagram, with it various stages of reduction to the equivalent positive-sequence impedance, 0 + j13·3 ohms. In the second stage, the delta-group of impedance j8, j20, and j12 are replaced by their equivalent star j4, j6, and j2.4, using the delta-star transformation equations. Thus the equivalent-star impedance at junction Q, is 8 x 20 = 4 ohms, Z= 8 + 20 + 12 at junction R I 20 x 12 = 6 ohms. Z= 8 + 20 + 12 and at junction F I 8 x 12 = 2.4 ohms. Z= 8 + 20 + 12 Similarly, figs. 17(b) and 17(c) show the reduction of the negative-sequence and zero-sequence diagrams to the equivalent impedances Z2 = j13, and Zo = j24.9

]24

) 24

(b)

jO'7

j28

j07

130

jO'7,

po

j28

j48

j42 j 24·9

i 48

(c) FIG.

24

i 36

17.

The impedance of generator G z does not appear in the zero-sequence diagram, since it neutral-point is unearthed. The equivalent positive, negative, and zero-sequence impedances are now combined for the two-phase-toearth-fault as shown in fig. 15, and the sequencecomponent currents la l, laz, and lao calculated as follows: lal

E

Z2XO ----Z2 + Zo 19000

-I al

~-j 870

-1435~

~ - j435

P, -)468

~-j402 ~

• -j468. -j402

Q,

i27

~- )402 R,

0 - j870

=

j13 x j24.9 j13 + j24.9

~ -j870

~-j870

Zo Zz

+

Zo

·870 x j24.9 J j13 + j24.9 -I al

~-j870

~ -j468~ -j870

E

= -------

j13.3 +

E

1

N, 0 E

N, 0 E

N, 0

N, 0

0 + j57!.

=

Z2

+ Zo

j870 x

j13

j 13

0 + j299.

=

+ j24.9

F,

F,

F,

(b)

(C)

(d)

FiG. 19. delta-impedance. Thus for the left-hand impedance of the delta I x j8 = (-j468 (j4) + (-j870) (j2.4) = 3952

----

Z2

F, (a)

and I =

3952 = 0 - j495, j8 and for the right-hand impedance of the delta I x j12 = -(j402) (j6) + (-870) (j2.4) = 4492

These are the total values of the positive, negative, and zero sequence currents through the equivalent impedances, as shown in fig. 18, and they must now be divided throughout the sequence diagrams according to the relative impedances of the several branches.

a nd I =

4492 = 0 - J·375 j 12 . For the current in the centre-impedence of the delta. equate the current flowing towards either of the two junctions to zero, i.e. taking the right hand junction. (-j402) + Ix - (-j375) = 0, or Ix = j402 - j375 = j27. This value is correct in sign only from the assumed direction of the current Ix. which was from left to right. If the opposite direction were taken. the result would be -j27. The two generator-impedances are equal and, the current in each is therefore -j870/2 = -j435. This completes the current-distribution in the positive-sequence diagram. The distribution in the negative-sequence diagram is similar. because the positive-sequence and negative-sequence impedances of the feeders are the same. The values of the negative-sequence currents are difficult from those of the positive-sequence currents. because the total negative-sequence current is 0 + j571. whereas the total positive-sequence current is 0 - j870. The negative-sequence currents in the branches can therefore be obtained simply by multiplying the positive-sequence branch-currents by 571/870 , and changing the sign of the j operators to plus instead of minus. The result is the negative-sequence-current distribution diagram of fig. 20.

lao

~

z,

2, FIG.

J299

20

18.

Consider first the positive-sequence diagram. The positive-sequence current of value 0 - j870 flows through the equivalent impedances as shown in fig 19(a).In the left-hand branch of fig. 19(b) the current is 21 21 + 18

I = (0 - j 870) x = 0 - j468, and in the right-hand branch.

I = (0 - j870) x

18 21 + 18

-------

= 0 - j402. This settles the distribution in the positive-sequence diagram as far as fig. 19(c). The current in the delta of fig. 19(d) is obtained by equating the voltage-drops in two star-legs to that in the corresponding

25

Then la = lao + lat + la2 = j138 + (-j402) + j264 = 0 I b = lao - 0·5(l al + Id - jO·866(lal - la2) ......................(eqn 23) = j138 - 0.5(-j402 + j264) -jO.866 (-j402 - j264) = j138 + j69 - 576 = -576 + j207. Ie = lao - 0.5(1al + la2) + jO.866(1al - la2) = j138 + j69 + 576 = 576 + j207 The currents in any branch are found in exactly the same way.

N,

N,

J 285

t

t

G1 G2

)285

P,

+J 571

1

306

• J 264

+

R,

f,

f,

FIG. 20. Similar considerations to those for the negative-sequence-current distribution apply also to zero-sequence currents. The positive-sequence and zero-sequence impedances of the feeders are not equal, but they bear (in this example) a definite relation to o~e another, i.e.Zo/Z, = 2·0. (This is practical; the ratIO varies with different networks). It follows therefore that in this example the ratios of the branch-currents in the zero-sequence diagram are the same as those in the positive-sequence diagram, although their values ar.e different, because the total zero-sequence current IS o x j299 as compared with 0 - j870 for positive-sequence. The zero-sequence currents in the branches are therefore obtained in this example by multiplying the positive-sequence brach-currents by 299/370 , and changing the sign of the j operators from minus to plus. The result is the zero-sequence current distribution diagram of fig. 21.

Distribution-factors

In the preceding example the branch-currents were found by taking the total current for each sequen~e diagram and dividing it between the branches 10 accordance with their respective impedances. An alternative procedure is to take a total fault-current of unity in each sequence diagram, instead of the actual value and divide this between the branches in the same way. ' The branch currents so obtained are called distribution-factors, and the actual current in each branch is equal to the distribution-factor multiplied by the total fault-current. If the calculation is for only one kind of fault, e.g. a phase-to-phase-fault, there is little, if any, advantage in calculating distribution-factors, since it is just as easy to calculate the branch-currents directly as to find the distribution of unity current and multiply the total current by the distribution factors. When, however, the currents in the branches are required for various kinds of faults, e.g. phase-to-earth, phase-to-phase, and two-phase-to-earth, the distribution of the total fault-current in the sequence-impedence diagrams has to be calculated for each kind. It may then be quicker, instead of doing this, to calculate the distribution of unity current in each diagram, i.e. to find the distribution-factors, and then to multiply these by the total sequence-component currents in each diagram, as determined by the kind of fault. In other w~rds, distribution-factors are applicable to faults of all kmds, and therefore save time when more than one kind is involved in the problem.

No

G,

t ]299 Po

)161

t

-R

t1138 Ro

Qo

6f

o

Fo

Voltages at any point in a network

FIG. 21.

As was mentioned earlier, the phase-to-neutral voltages at any point in a network are expressed in exactly the same relationships as the currents.

The distribution of the sequence-component currents is now completely determined, and the phase-currents in any branch can be found by applying the equations (20), (21), and (22) or equation (20), (23), and (24). Suppose, for example, that the value of the phase-currents are required in the branch PRo From fig. 19, lal = -j402. From fig. 20, la2 = j264. From fig. 21, lao = j138.

Thus E a = E ao Eb Ec

26

= =

+ E al + E a2 (32) 2 E ao + a E al + aEa2 ·······································(33) E ao + aE al + a 2 E a2 ·······.·· .. · · · · (34)

Alternatively, E b and E e may be expressed as E b = E ao - 0.5(E a1 + Eaz) - jO.866 (E a1 - Eaz) ....(35) E e = E ao - 0.5 (E a1 + Eaz) + jO.866 (E a1 - E a2 ) •. (36) The calculation of the phase-to-neutral voltages at any point in a network is therefore merely a calculation of the sequence-component voltages E ao , E ab and E a2 , and a combination of them in accordance with the equations just given. The sequence-component voltages at any point are determined by subtracting the impedance-voltage between the source and the point from the drivingvoltage. The driving-voltage in the positive-sequence diagram is the normal phase-to-neutral voltage, but in the negative sequence and zero-sequence diagrams it is zero, because, as has been said, only positive-sequence voltages are generated in normal systems. The following example will make the procedure clear. Fig. 22 shows the positive, negative, and zero sequence

~I

Phase-to-neutral voltages: E a = E ao + E a1 + E a2 = 209 + 17868 + 541 = 18618 + jO. E b = E ao - 0'5(E al + E a2 ) - jO.866 (E a1 - Eaz) .............(eqn 35). = 209 - 0.5(17868 + 541) -jO.866 (17868 - 541) = 209 - 9204 - j15000 = -8995 - j15000. E e =E ao - 0.5(E a1 + E a2 ) + jO.866 (E a1 - Eaz) (eqn 36). = 209 - 9204 + j15000 = -8995 + j15000 Voltages at fault-point F Sequence component voltages (i) Positive sequence: From fig. 22(a), E a1 =19000-(-j870 x j13.3) = 19000 - 11580 7420 + jO (ii) Negative-sequence: From fig. 22(b), E a2 = 0 - (j571 x j13) = 7420 + jO (iii) Zero-sequence: From fig. 22(c), E ao = 0 - (299 x j24.9) = 7420 + jO. Phase-to-neutral voltages: E a = E ao + E a1 + E a2 = 7420 + 7420 + 7420 = 22260 + jO. E b = E ao - 0.5(E a1 + E a2 )-jO.866 (E a1 - E a2 ) = 7420 - 0.5(7420 + 7420) -jO'866 (7420 - 7420) = O. E e = E ao-0.5(E a1 + E a2 )+ jO.866(E a1 -E a2 ) = 7420 - 0.5(7420 + 7420) +j.866 (7420 - 7420) = O. The voltages at any other point in the network are found in exactly the same way.

N,

19kv

jH. !-j435 -j435+ j2·6 ,

j299+ j07

P,

19kv

A

F,

F,

Fa

--

j13 N, Q---'VII\r-O F,

--

j24'9

jiB

N,O",~F,

--

NoQ--J\lV\r-<) Fo

-j870

j 571

j299

(a)

(b)

tel

FIG.

22.

diagrams of the previous example, with values of branch-currents and branch impedances. Suppose that it is required to determine the three phase-to-neutral voltages at points P and F. Voltages at point P Sequence component voltages: (i) Positive-sequence: From fig. 22(a), E a1 = 19000 - (-j435 x j2.6) = 19000 - 1132 = 17868 + jO. (ii) Negative-sequence: From fig. 22(b), E a2 = 0 - (j285 x j1.9) = 541 +jO. (iii) Zero-sequence: From fig. 22 (c), E ao = 0 - (j299 x jO.7) = 209 + jO.

Earth-current, residual current, and residual voltage

It was said earlier that there could be no zero-sequence current unless the fault provided an exit from the phases whereby the current could return to the system-neutral, i.e. the fauh has to involve at least one phase-condurtor connected to earth, and the system-neutral had to be earthed to complete the circuit. No such reservations were required for positivesequence and negative-sequence currents, which flow to all faults, whether to earth or not. It follows that the only currents in the earth-return circuit are the zerosequence components, i.e.

27

-(laO + I bo + leO), where Ie is the total earth-current, = - 3Iao (37) The minus sign is used because of the convention that all currents act away from the source; this convention is illustrated with respect to the zero-sequence and earth currents in fig. 23. The vector sum of the three line-currents at any point in the network is sometimes called the residual current. Thus I, = I a + I b + Ie (laO + I bo + leO) + (lal + Ibl + lei) + (Ia2 + I b2 + Id· Ie

Residual current is usually measured by three current-transformers connected in parallel, as shown in fig. 24(a), and residual voltage by a broken-delta winding on a three-phase voltage-transformer, as shown in fig. 24(b).

=

I.

a

-+

-rb

c

C

J

Til'

Iao+lbo+1co

~

10.0

__ Ibo

lao

Ibo

-...b-

leo

/

: b 'FAULT I

_leo

c' I

,,:

-

1

(L)

lb'

_

I

FIG.

I

24.

Ie' -(Iao+ lbo+ Ico)

i

Ie

L-.

_~

• - 3 lao

~

Faults in phases other than those for which the basic equations are established

.__.J

(b)

(a)

FIG.

The methods of connecting the diagrams for the four main kinds of faults, as given in fig. 15, and the equations that follow for the calculation of the sequence components, are based upon earth-faults in phase-a, phase-to-phase-faults between phase-b and phase-c, and two-phase-to-earth faults between phase-b and phase-c and earth. The procedure holds good for these

23.

The components in the last two brackets are balanced, and by definition their sum must be zero Therefore lao + I bo + leo 3I ao (38) Here Lao is the zero-sequence current flowing at the point in the network under consideration. The current I, may therefore equal the total earth-fault current in magnitude, or only part of it, if there is more than one path to the fault; and it may sometimes consist of capacitycurrent only. The residual voltage at a point in a network is the vector sum of the three line-to-earth voltages. I,

=

=

oy

80

co

R

R

bO

R

8/0Y

b

o

o OY

E ao is the zero-sequence voltage at the point under consideration. Residual currents and residual voltages are used in protective schemes for the detection of earth-faults.

8o---<>Y

o

80

E ae + E be + E ee = (E ao + E bO + E eo ) + (E al + E bl + Eel) + (E a2 + E b2 + Ed As before, the resultant of the last two components is zero, and therefore E, = E ao + E bO + E eo = 3E ao · =

ob

<

o

Thus E,

..o

R

o

0<

La.)

Lb)

FIG.

28

25.

precedure in the calculation of fault-currents and fault-voltages, and, as was stated earlier, some of the principles are also applicable to load-distribution and other studies. Many fault-conditions (or prospective fault-conditions) are completely soluble by the methods described, but it should be understood that conditions can and do arise in practice to which the formulae and the procedure given herein are not immediately applicable. Two examples of this are cross-country earth-faults and broken-conductor faults. The details of procedure for the calculation of these and other special conditions is outside the present scope. Sometimes it is merely a matter of extending the principles described above, but sometimes additional concepts are necessary. Whatever the problem may be, however, a proper understanding is necessary of the basic principles dealt with in the foregoing exposition.

conditions only, i.e. phase-a must always be the faulty phase for earth-faults, and phase-b and phase-c must always be the faulty phases for phase-to-phase-faults and two-phase-to-earth-faults. If the phase-marking of a system is R, Y, B, for example, and a calculation has to be made for an earth-fault in phase-Y, this phase is phase-a for the purpose of the calculations. Phase-B then corresponds to phase-b, and phase-R to phase-c. The various correspondences between the calculations-phases a, b, and c, and the named phases R, Y, and B, are shown in fig. 25(a) for earth-faults, and fig. 25(b) for phase-to-phase faults and for two-phase-to-earth faults.

CONCLUSION These notes have covered many of the basic elements of

29

CHAPTER 2 The Use of the Network Analyser in the Solution of Unbalance Problems By J. B. PATRICKSON. and a number of different types of "vector computor" are used to speed up what can be a very tedious set of calculations. When all three phases of the problem system are set up on the analyser, all quantities are read directly on the analyser instruments and no subsequent calculations are necessary. In the following sections an attempt will be made to illustrate the use of the analyser in the solution of problems involving 3-phase unbalance. Methods involving 3-phase modelling and symmetrical components will be discussed and examples given to illustrate procedure in both cases. It will be assumed throughout that all are familiar with the principle formulae and manipulation of symmetrical components, and an attempt will be made to interpret these in terms of physical phenomena. In view of the fact that an intimate knowledge of the a.c. network analyser is confined to a relatively small number of engineers the first part of the paper is devoted to a brief general description of the features of the typical modern network-analyser which are involved in unbalance-problems. Subsequent parts dealt with the use of 3-phase model networks and the application of the theory of symmetrical components to the network-analyser. In these parts, only the less complex cases are dealt with as a thorough grasp of the fundamentals in the simple cases opens the way to the tackling of the more complex cases.

SUMMARY The network analyser has made possible the routine investig~tion of m~ny unbalanced-power-system problems whIch were hItherto untackled because of the tedious calculations involved. The mathematical analysis of the majority of such problems has been well established for a number of years now but for only the less complicated problems was it feasible to apply paper analysis, the more complicated networks involving too much effort. The introduction of the method of symmetricalcomponent analysis answered the need for a simpler mode of attack and it was soon apparent that a familiarity with the method made it possible to visualize the processes involved in quite complicated unbalanced conditions. This has been described as "the symmetrical-component outlook" and the acquiring of this "outlook" constitutes a major advance towards the understanding of the phenomena of a 3-phase unbalance. There is a great similarity between the method of symmetrical-component analysis and Fourier analysis as applie? to the solution of problems involving nonsInusOIdal wave forms. In both cases an appreciation of the physical significance of the method leads first to an understanding of the problem and secondly to a facility for the evaluation of the problem. In this paper the two distinct advantages to be obtained from a knowledge of symmetrical-component analysis will be stressed and it will be shown that, when a network analyser is used, the "symmetrical-component outlook" is in many cases more important than the use of the method for the actual evaluation of the effects of the unbalance. This is because the analyser "looks after" the calculation but the problem must be correctly posed to the analyser and the results correctly interpreted. The solution of unbalanced 3-phase conditions is not always best obtained on an analyser by using symmetrical components and frequently the actual 3-phase network is "modelled" on the analyser and the unbalance applied in the same way as in the power-system. When two or more unbalances simultaneously exist or when the problem involves partially unbalanced reactances in each of the three phases of a power-system, even the symmetrical-component method may become too cumbersome and 3-phase modelling may be a more profitable approach. It is important to realise that when the method of symmetrical components is used on the analyser, only the quantities associated with the reference phase are read directly. The quantities associated with the other phases must be calculated from those of the reference phase. This latter calculation usually takes much longer than the actual reading of the reference-phase quantities

Part I. THE CONVENTIONAL A.C. NETWORK ANALYSER GENERAL The simplest a.c. network analyser to describe and understand is what is termed the "conventional" a.c. network analyser. In this analyser the impedances of the power system being studied are modelled using specially designed variable inductors, capacitors, resistors, and transformers. Any desired "scaling factor" may be used in the model system as regards ohmic value and frequency but the phase-angle of all impedances must be strictly observed. Generally, the frequency is fixed in anyone design and scaling of ohmic value is applied. The variable impedances can be interconnected in any manner and the network so formed energized by means of voltage generators of continuously-variable phase and amplitude.

Impedance Scaling It is usual to scale the impedance values to conform to "percentage" notation or "per-unit" notation because the majority of analyser problems are more easily solved

30

using these notations and most analyser impedances and meters are correspondingly calibrated. A familiarity with percentage (or per-unit) notation is assumed and it will merely be noted that the percentage impedance (Z%) of any branch (of impedance Z ohms) in a network is Z% =

type of connection. Consider that it is required to measure the vector current in a particular branch of a network and that per-unit notation is used. The amplitude of the current is measured by the current-meter and this current is passed through the current coils of both the wattmeter and the varmeter. The voltage-coils of both the wattmeter and varmeter are connected in parallel and fed from a "reference" voltage which is fixed in phase and amplitude. The actual phase-angle of this reference is chosen as convenient and the amplitude is fixed exactly at 1 per-unit (i.e. 100%). The wattmeter reads (VI cos 8) and, if V is fixed at unity, it reads (I cos 8) where 8 is the phase-angle between the current I and the reference voltage. The value (I cos 8) is the real part of the current I referred to the axis fixed by the phase-angle setting of the reference voltage. The varmeter similarly reads the imaginary part of the current. In this way, any current can be read in cartesian form; I = a + jb If the phase-angle instrument is used to measure 8 direct, the current can be expressed in the polar form: 1=111 L8 where III is read on the current-measuring meter.

MVA . Z ohms. 100 (kV)2

where "MVA" is the base quantity to which all impedances are referred and "kV" is the phase-to-phase voltage of the part of the system in which Z ohms is connected. Per-unit notation is similarly defined except that there is no factor of 100.

Measuring Equipment Most analysers are fitted with four main measuring instruments. There are: (a) Voltmeter. (b) Current-measuring meter. (c) Single-phase wattmeter. (VI cos 8) (d) Single-phase varmeter. (VI sine 8) Each meter has a number of 'ranges' and the scales of each are calibrated in percentage or per-unit according to how the impedances are calibrated. The meters can be connected to any point in the network analyser. When percentage notation is used on the network analyser, its meaning is clearly illustrated. If, for example, a voltage of 100 per cent is applied across an analyser resistor of 100 per cent, the current-meter will read 100 per cent and the wattmeter will read 100 per cent. There is no reactive power in this case. If this analyser resistor represents a particular resistor in a 132-kV system and the base chosen is 100 MVA, the meter readings would be interpreted as follows: 100% voltage 132 kV phase-to-phase 100% currenf _

If a reference current is passed through the currentcoils of both the wattmeter and varmeter, any voltage may be read in cartesian or polar form in exactly the same way. When quantities are being measured in sequence networks, the cartesian form is preferable as corresponding quantities in each sequence-network must be added to give the true reference-phase quantity. This referencephase quantity is then transformed to polar form. With a good vector computer, it is possible to read from it the final quantities in polar or cartesian form with the minimum of effort. If the unbalanced problem· is modelled in 3-phase form, the voltages and currents of any phase at any point can be read directly in cartesian or polar form. The real and reactive power at any point can be read in all cases by using the wattmeter and varmeter in the normal way.

3

100 x 10 = 435 amperes per \/3 x 132 pnase

100% watts 100 megawatts. Other quantities are interpreted similarly, the percentage voltage and percentage current changing their meaning according to the voltage of the part of the system in which measurements are taken. An instrument to measure relative phase-angle is also usually included and this can be used to measure the phase-angle between any voltage and current, or the phase-angle between either of these quantities relative to a reference. This instrument usually indicates phaseangle direct in degrees.

Part II. SOLUTION BY MEANS OF 3-PHASE MODELS INTRODUCTION When the power-system problem is modelled in 3-phase form it is necessary to simulate, accurately to scale, all the parameters of the power system. The major items in a power-system are: (a) Overhead lines and cables. (b) Reactors. (c) Transformers, regulators, etc. (d) Rotating machinery. Of these, the last is the most difficult to simulate

Use of Instruments With the above instruments it is possible to measure all the quantities requried in the solution of unbalance 3-phase problems. In many instances the wattmeter and varmeter are not used as such but are connected to measure the real and imaginary components of either the voltage or the current. The following illustrates this

31

network while the transformers method preserves the identity of the three phases on both sides ofthe network. The former can be used when the equipment is connected between the three phases and neutral and the latter when the impedance is a "series" impedance such as the series impedance of an overhead line or bank of reactors. Referring to fig. l(a), the self impedance of each phase (Zp) is, with

accurately on the analyser because of its complicated nature (involving rotating parts), and because the parameters vary with time, mainly due to armature-reaction effects. All these items are characterized by the fact that each phase has self-impedance and, between phases, mutual impedance to an extent depending on the equipment. It should be borne in mind that the self and mutual impedance of the three phases of an equipment are the basic impedance-parameters and that the sequence impedances are derived from them. In many instances, when the 3-phase model has been set up on the analyser, its validity may be checked by measuring the three sequence-impedances. When the actual self and mutual impedances are not known, the sequence impedances may be used to derive these parameters. In many instances this is the case, as present-day practice is to quote the sequence impedances of an equipment rather than the basic parameters. In almost all cases, the self impedances of each phase and the mutual impedances between phases are different for each phase due to asymmetry in construction of the equipment. These differences are usually small and the average value of the impedances can be taken and symmetry assumed. In some instances, of course, the different per-phase impedances must be represented on the analyser, and this can lead to a degree of complication which makes the process very tedious except for the smaller problems. In fact, the process of 3-phase modelling is invariably confined to the small problems, since the representation of all self and mutual impedances in a large network demands a very large number of analyser impedanceunits. In the following sections, the use of 3-phase models will be discussed and illustrated and every attempt will be made to draw attention to the reationship between the basic parametta"s and the derived sequence parameters.

Za=Zb=Zo Zp=Za+Zm,

and the mutual impedance between phases (Zpp) is symmetrical, and Zpp=Zm.

Exactly the same values are obtained using three perfect transformers as in fig. l(b). The impedance Zm is reflected equally into each phase and again Zp=Za+Zm Zpp=Zm·

The circuit of fig. l(c) is electrically equivalent to fig. l(b) but uses one less transformer. Fig. led) illustrates the use of a single four-winding

transformer of equal turns per winding. This arrangement is equivalent to that of fig. l(b) or l(c) but is obviously more econimical as regards transformers. The above network can be used to represent many 3-phase circuits either by using a number of networks each representing an individual equipment or by using one network to represent a section of a power-system involving many different equipments. It is interesting to examine these networks as regards their sequence impedances. Looking at fig. l(a), if positive-sequence voltages are applied to the three upper terminal (with the lower terminal at neutral potential) the point P will be at neutral potential and the impedance of each phase is Za. Thus, Za in the network is the positive-sequence impedance (Zd. Za is also the negative-sequence impedance (Zz). If zero-sequence voltages are applied to the upper terminals, the impedance of each phase becomes: Za+ 3Zm·

Representing the Basic Parameters

This is most readily seen by re-arranging the network of fig. l(a) so that the single impedance Zm is replaced by three parallel impedances each of value 3Zm as in fig. 2(a). When this has been done, the points X, Y, Z are equipotential points for zero-sequence applied voltages and may be opened to form the network of fig. 2(b) where it is obvious that the zero-sequence impedance per phase (Za) is:

Throughout the following discussion, the three phases of all equipment are assumed to be symmetrical as regards impedance. The self-impedance of the three phases of an equipment are easily represented using the resistors, inductors, or capacitors of the analyser set to the appropriate value. The mutual-impedance between phases can be represented by the inclusion of an impedance common to all phases or by the use of "perfect" transformers of unity turns-ratio connected between phases and to an impedance which represents the mutual impedance. The perfect transformers have a very low excitation-current and negligible resistance and leakage-reactance. Fig. l(a) shows the use of a common impedance to represent the mutual impedance and fig. led) illustrates the use of perfect transformers. It will be seen that the common-impedance method results in the loss of the identity of the three phase connections on one side of the

ZO=Za+ 3Zm·

The network of fig. l(a) thus has equal posltlvesequence and negative-sequence impedances and a zero-sequence impedance which depends on the value of Zm, the mutual impedance. The zero-sequence impedance can be made greater or less than the positivesequence impedance by making the impedance of Zm of opposite sign to that of Za. Thus, if Za is inductive, Zm can be made capacitive. There are obvious limitations to this manipulation when resistors are involved. The network of fig. l(b) is equivalent to the above

32

Za

Zb

p

Zm

ZI =Z2=Za Zo=Za+3Z m

ZI =Z2=Za Zo=Za+3Z m

(h)

(a)

ZI =Z2=Za Zo=Za+3Z m

Zj =Z2=Za Zo=Za+ 3Z m

(d)

(e)

FIG.

1.

DIAGRAMS REPRESENTING 3-PHASE SELF AND MUTUAL IMPEDANCES.

network except that as the 3-phase terminals are available at each end of the network it can be used to represent, say, a bank of reactors with mutual impedance between phases, or 'the series impedance of a 3-phase line or cable. The impedance offered to positivesequence and negative-sequence current is:

nected with an impedance 3Zm. The impedance offered to positive-sequence and negative-sequence currents is the excitation impedance of each transformer, which is so high as to constitute an open-circuit. The impedance offered to zero-sequence currents is 3Zm13=Zm per phase, i.e. ZO=Zm. Fig. 4 shows a further arrangement using the fourwinding transformer of fig. led) with the fourth winding open-circuited. Under positive-sequence or negativesequence conditions this transformer introduces zero impedance into each phase because the total flux in the magnetic circuit is zero. The impedance per phase offered to zero-sequence currents is, however, so large as to be infinite in the practical case, the actual impedance being governed by the excitation impedance of

Z\=Z2=Za,

and that to zero-sequence currents is: ZO=Za+ 3Zm.

Figs l(c) and led) behave in an exactly similar manner. A furthet arrangement of impedance and perfect transformers is given in fig. 3. Here the second winding of each two-winding transformer is open-delta con-

33

They are thus applicable to all but equipments involving rotating parts such as the induction motor etc. where the positive-sequence and negative-sequence impedances differ considerably. In many cases, however, they can be used to represent synchronous motors and generators without excessive error. Overhead Lines

An overhead line has both series and shunt impedance. The series impedance constitutes the resistance and inductance of line and the shunt impedance the capacitance of the line. The shunt leakage resistance can usually be neglected in the absence of corona. In this case it is convenient to consider the series and shunt impedances separately and to choose the simulating network by examining the self and mutual impedances of each phase conductor. The validity of the final 3-phase model can then be checked by measuring the sequence impedances.

(a)

If each conductor is considered singly as constituting an "earth-loop", the conductor forms the "upper" part of the loop and the earth-return the "lower" part as shown in fig. 5. The earth-return is common to all phases. The self impedance (Zp) of each "earth-loop" could be measured directly by applying a voltage at one end (with the other end connected to earth) and measur-

(h)

FIG.

2.

ZERO-SEQUENCE IMPEDANCE OF FIG. I(a).

the transformer. The transformer thus acts as an opencircuit or short-circuit in each phase depending on the sequence voltages and currently involved. If, as in fig. I(d), an impedance Zm is connected to the fourth winding then an impedance 3Zm is reflected into each phase under zero-sequence conditions. This network can be used in the approximate representation of 3-phase transformers etc. when, as is usual, only the sequence impedances of the transformer are known, and the complex self and mutual impedances are unknown. In the following section, some examples of the use to which these circuits can be put is illustrated.

FIG.

3.

THREE-PHASE DELTA NETWORK.

I _Jr I

I!I~~ di~

Representing Power-system Equipment General

The networks described in the previous section can be used, either singly or in combination, to represent many equipments encountered in power-systems. Their use is confined, however, to those cases where the positivesequence and negative-sequence impedances are equal.

FIF. 4.

34

o

c

FOUR-WINDING TRANSFORMER WITH FOURTH WINDING OPEN-CIRCUITED.

,I

--------0

CONDUCTOR b

r-i I

CONDUCTOR c

I

CONDUCTOR a

- - -0

Zpp

-+-Zp

r " ' E , . . - - - - - - - - - EARTH·RETURN - - - - - - - - ; ; , . . . ,

FIG.

5.

BASIC PARAMETERS OF AN OVERHEAD LINE.

ing the resulting current with the other conductors open-circuited. The impedance measured is Zp. In a similar manner, the mutual impedance Zpp between the separate earth-loops can be measured. These two parameters can be calculated by the method due to Carson with good accuracy. The network of figs l(b), l(c), or led) can be used to represent the series impedance of the overhead line. The self impedance Zp is then Zp=Za+Zm, and the mutual impedance between conductor loops is: Zpp=Zm. In the previous section it was shown that the positivesequence and negative-sequence impedances of this network were: Zj=Z2=Za, and the zero-sequence impedances: ZO=Za+ 3Zm· Expressing these derived quantities in terms of the self and mutual impedances of the phase conductors: Zj=Z2=Zp-Zpp Zo=Zp+2Zpp . It can be shown that these values of the sequence impedances in terms of the self and mutual impedances hold for all types of overhead-line construction. The addition of an earth-wire merely changes the value of the self and mutual impedance, the form of the equations remaining unchanged. In fig. 6 the network is drawn with the impedances marked in terms of Zp and Zpp with the alternative notation in Zj, Z2, and Zoo The network of fig. led) is used as a basis. The shunt capacitive-reactance of the line can be considered in exactly the same way. Each conductor has self-capacitance to earth which is measured with all conductors completely open-circuited and there is also mutual capacitance between the three conductors. These values can be measured or calculated, and if the values are expressed in terms of self and mutual capacitive-reactance (Xp and X pp ) at the power-

frequency a strict analogue holds with the series impedances Zp and Zpp and the same network can be used to represent them. Fig. l(a) is the most convenient form to use and it will be seen that the self capacitive-reactance X p is represented by Xp=Za+Zm, and the mutual capacitive-reactance X pp by Xpp=Zm. By analogy with the case of the series impedances Zj=Z2=Xp-Xpp , and Zo=Xp+2Xpp . This is illustrated in fig. 7 where the two notations are again given. When all phases are considered symmetrical the circuit of fig. 7 is preferred to the usual capacitive circuit using eight capacitors in star and delta connection both because of the smaller number of capacitors involved and because the self and mutual capacitances are more readily visualised. The series and shunt networks can now be used to simulate the 3-phase overhead line as in fig. 8 where the line is represented as a 7f' section, half the capacitance being connected at each end. In long-line problems a number of such sections are used to represent the line. The above argument can be extended to include the case of the double-circuit overhead line. Considering the self and mutual series inductance and resistance only, fig. 9 shows the network used as the model. In this network, the mutual impedance has been split, forming an impedance divider which is adjusted to give the correct mutual impedance between the conductors of one circuit and the mutual impedance between the conductors of the two separate circuits. The mutual impedance between the two circuits is effective only for zero-sequence currents flowing in one or two circuits and is termed the zero-sequence mutual impedance, designated Zoo. It should be noted that the only resistor in the mutual branch is that common to both circuits and is the resistance of the earth-return of the overhead lines.

35

1r

l

= c:3J Zp--Lpp

L o ZI=Z2=Zp- Zpp Zo=Zp+2Z pp

FIG.

6.

THREE-PHASE SERIES EQUIVALENT OF AN OVERHEAD LINE.

Fig. 10 shows the associated capacitance net-work for the double-circuit line and includes the mutual capacitance between the two circuits. This network is combined with that of fig. 9 in the same way as for the single-circuit line (fig. 8).

return. Knowing these reactances it is necessary to form a 3-phase model which has the same reactances. One form of this is shown in fig. 12. The analyser "perfect" trans-

3-phase Transformers

r

0

In the previous section, it was shown that a 3-phase model of the overhead line could be built up from a consideration of the self and mutual impedances of each phase conductor. These quantities are readily calculable and their use leads to a good understanding of unbalance in 3-phase lines. When dealing with power-transformers however, it is generally not possible to build up a 3-phase model from the self and mutual impedances as these are not normally quoted. The sequence impedances are generally given for any transformers and it is from these that the 3-phase model is designed. The positive-sequence and negative-sequence impedances are identical in powertransformers and the zero-sequence impedance varies with the type of transforI)1er. When modelling power-transformers the basic networks detailed at the beginning of Part II are used to form, in most cases, a composite 3-phase network. In all cases, the power-transformer magnetizing impedance can be neglected and, for clarity, the winding resistance will be neglected here. Considering first the star-delta transformer of fig. 11(a) with the starred windings connected to earth, the sequence impedances are as illustrated in fig. 11(b). The positive-sequence and negative-sequence reactances are identical and the zero-sequence reactance of the delta winding is infinite due to the lack of an earth-

x,

1

0 i

I

1

I

--L

Ti

L

X p -- X pp

I I

I

X o XI -3-

1

~ X pp

I

XI X2 =X p--X pp Xo~Xp FIG.

7.

I 2Xp~

THREE-PHASE CAPACITIVE EQUIVALENT OF AN OVERHEAD LINE.

formers T I and T z are necessary to ensure the correct reactances. Note that T 1 comprises three separate units and that T z is a four-winding transformer. For positivesequence of negative-sequence currents flowing from star-winding terminals to delta-winding terminals the only reactance is that marked XI. This is because the

36

I o I 3

.----_/~-----,

o

I

-~-T~

o-------1>-----t-----~-~ -F~-T

I

1\<

,(

XO-XI

2

3

)

:1 !

I -iFIG.

8.

THREE-PHASE

1r

SECTION OF A SINGLE-CIRCUIT LINE.

o

~----v

CIRCUIT I FIG.

9.

"

y,----

CIRCUIT 2

THREE~PHASE SERIES EQUIVALENT OF A DOUBLE-CIRCUIT LINE.

37

r_--x,I 1 1

CIRCUIT

CIRCUIT 2

,_---A.---.. . .

x.l

A

1 1

FIG. 10.

THREE-PHASE CAPACITIVE EQUIVALENT OF A DOUBLE-CIRCUIT LINE.

analyser transformer T 2 offers no reactance to positivesequence and netative-sequence currents, and the transformer T l offers infinite reactance. For zero-sequence currents passing from the earth connection to the "star" terminals, the per-phase reactance is: Xl

+ 3

....- - _ . "

Part III. SOLUTION USING THE PRINCIPLE OF SYMMETRICAL COMPONENTS GENERAL In Part II, the solution of unblanced problems using 3-phase models was discussed and these models were used to illustrate the relationship between the basic per-phase parameters and the sequence impedances. In the following discussion, the only impedances used are the sequence impedances but, where possible, the effects using these impedances will be interpreted in terms of physical quantities. When the analyser is applied to the solution of unbalanced problems using symmetrical-component theory, the general pattern of connection of sequence impedances is unchanged from that when the problem is solved by calculation. Each sequence network is "set up" on the network-analyser in single-phase form and the networks are interconnected as one would interconnect them if a calculation were being made on paper. The networks are energized and readings taken in each to establish the positive-sequence, negativesequence, and zero-sequence currents and voltages. The quantities are those associated with the reference phase and, as outlined in Part I, these can be read in cartesian form by energizing the current or voltage coils of the wattmeter and varmeter from and independent source. Straightforward addition of the reference-phase quantities in each network yields the true phase-quantities of the reference phase. The quantities associated with the other two phases must now be calculated from those of the reference phase in the same way as when calculating results.

(Xo-Z l ) = X o.

3 There is no path for zero-sequence currents in the delta winding due to the infinite per-phase impedance of T 2 offered to zero-sequence currents. The 3-phase model of a star-delta-star transformer is built up in the same way but the fact that both starred windings can be earthed leads to a more complicated network. Fig. 13(a) shows the star-delta-star transformer with both star windings earthed. The positive-sequence and negative-sequence reactances are identical and each star winding has a zero-sequence reactance which is low as a result of the delta winding. Zero-sequence currents flowing in one star winding will induce zero-sequence voltages in the other star winding due to leakage-flux linkages, and for complete modelling this should be included even though the effect is normally small. Fig. 13(b) shows the sequence reactance of this transformer. The coupling between the two star windings is apparent. Fig. 14 shows how these two sequence-impedance networks may be combined to form a single 3-phase network. Again, a combination of analyser "perfect" transformers is used and it will be seen that the correct sequence impedances can be measured at all terminals.

38

(a)

0>------------'

X,=X2

1fOTIO!

1..-------0

0

X,=X 2

tQOOO'1 . . - - - - - - - 0

0

POSITIVE.SEQUENCE AND NEGATIVE.SEQUENCE IMPEDANCE

X I =X 2

~' - - - - - - - - 0

0

(h)

Xo ----0

C

Xo ----0

Xo ----0

ZERO·SEQUENCE IMPEDANCE

FIG. 11. DIAGRAMS REPRESENTING (a) Star-Delta Power-Transformer and (b) Sequence Impedances.

XI

XI

STAR WINDING

DELTA WINDING

XI

3 (X o- X,)

FIG. 12. THREE-PHASE EQUIVALENT OF STAR-DELTA TRANSFORMER.

39

As mentioned previously the latter process is usually carried out using a vector computer and can be very rapidly completed. A vector slide-rule can be used, but a fair amount of manipulation is still necessary. When symmetrical-component calculations are made on paper, much of the time is spent in sequence-network reduction, a necessary prelude to the interconnection to the sequence networks to conform with the type of fault or unbalance being investigated. The interconnected networks are then used to establish the total unbalance currents and voltages and their sequence components at the point of unbalance. Knowing these, it is then necessary to establish the distribution of current and voltage

in each network to determine the true distribution in terms of phase quantities. Thus, most of the time is taken in reducing the networks and in calculating current-distribution through them, both of these operations having little connections with the principle of symmetrical components. When a network-analyser is used for the same problems, no circuit reduction is necessary and the current and voltage distribution is read directly in each network. The calculation of actual phase-quantities is also rapidly accomplished using the vector computer. This freedom from calculation enables more time and thought to be devoted to studying the underlying princi-

'-----"""'0

STAR

STAR

WINDIf\JG

WINDING 'b'

0

'01'

c--------i

'--------;0

(il)

XI

Xl

roOQ\-

0

XI

0

0

Xl

romrXl

0

rzJOO'

0

POSITIVE-SEQUENCE AND NEGATIVE·SEQUENCE IMPEDANCE

XI

0

X OOl

Xob

-1JOO'\

roQOI

0

"

Xoj

/\0;1

X OOl

Xob

roo

0

OJ ---D

XoOlb

Xo01b

f

ZERO-SEQUENCE IMPEDANCE

Xo01b

(hi

FIG.

13.

DIAGRAM REPRESENTING

(a) STAR-DELTA-STAR POWER-TRANSFORMER. AND (b) SEQUENCE IMPEDANCES.

40

FiG.

14.

THREE-PHASE EQUIVALENT OF STAR-DELTA-STAR TRANSFORMER.

currents and voltage are at once apparent. Using an analyser the phase-to-neutral voltage of each phase would be 1 per-unit and, say, the value of each resistor 1 per-unit. The current in the faulty phase is then 1 per-unit and is zero in the other two phases. The voltages at the points R', Y', B' will be undisturbed and, at the faultpoint, the red voltage is zero and the other two phases are at nominal voltage. It is obvious that this system could be modelled on the analyser and the above quantities read directly but the solution could equally well be obtained by symmetrical-component methods. Without evaluation, two facts are apparent. At the fault-point, the red voltage is zero and the yellow and blue voltages are of normal phase and amplitude. Secondly, current flows in the red phase only. These voltages and currents are illustrated in fig. 16. Fig. 17 shows the same circuit drawn in a different way. The fault is removed and voltage-generators have been connected to all three phases at the fault-point. The horizontal sets of three generators are adjusted to give respectively a positive, negative, and zero sequence set of 3-phase voltages and each is adjusted until the vertical summation in each phase gives: Red-to-neutral voltage = zero; Blue-to-neutral voltage = normal voltage; Yellow-to-neutral voltage = normal voltage. Fig. 18 shows one possible adjustment of the generators to comply with the above conditions. The positive-sequence generators are 2/3 per-unit amplitude and are "out of phase" with the negative-sequence and zero-sequence generators, the latter being 1/3 per-unit amplitude. The circuit is now completely balanced in a

pIes behind the interconnection of sequence networks and this has led in many cases to methods which are suited particularly to the network-analyser.

Physical Representation of Symmetrical Components The essence of symmetrical-component theory is that any configuration of three vector quantities can be represented uniquely by three sets of "balanced" vectors, these sets being designated positive-sequence, negative-sequence, and zero sequence quantities. The vector quantities are usually those associated with voltage and current. This fact in itself is of limited use in numerical analysis unless it can be applied to the solution of unbalanced problems and the importance of symmetrical components is due solely to the fact that the balanced resolution of unbalanced vectors leads to a simple analytical method applicable to many cases of practical interest. The widest and most direct application is to the analysis of fault-conditions, i.e. single-phase to earth, phase to phase, and phase-to-phase to earth. In this section it is shown how the unbalance currents and voltages can be considered as being generated by sets of sequence-voltage sources at the point of unbalance. Referring to fig. 15, this sketch shows three singlephase resistors fed from a 3-phase "infinite busbar" (i.e. zero-reactance source). There is no mutual impedance between phases. The system is subject to a single-phase fault to earth (red phase) and is so simple that the

41

B'

w'-------------
8

y'

r--+--+------~---~Oy

FIG.

15.

SIMPLE SINGLE-PHASE UNBALANCE.

3-phase sense but behaves as if the original inbalance due to the fault still exists. Fig. 19 confirms that the vertical summation of these generator voltages is correct. Thus, if these nine generators are connected in place of the fault, the system as a whole behaves in the same way as if the fault were connected. The voltages across the yellow-phase and blue phase-resistors is zero and the current in these phases is therefore zero. The voltage of the red phase at the fault is zero and the two other phases are at normal voltage. If now we apply the principle of superposition to fig. 16 to determine the currents flowing in the circuits as a result of all nine generators, we can treat each set of generators of the same sequence separately and obtain the sequence currents. The three sequence impedances of the resistors are identical and equal to 1·0 per-unit since no mutual impedances exist. Taking first the zero sequence generators, the zero-sequence current per phase is as shown in fig. 20 which should be read in conjunction with fig. 18. Taking. now the negative-sequence generators alone the currents will be as in fig. 20. When considering the positive-sequence generators, there are two sets to consider, that of the source as well as the added generators. The net positive-sequence voltage is the vector sum and this, with other sequence voltages, is given above the resulting positive-sequence current in fig. 20. From fig. 21 it is seen that the correct currentdistribution is obtained but care must be taken with vector conventions; driving voltages and voltage-drops must be identified. This simple example illustrates the physical signifi-

cance of the sequence voltages and currents and shows that a solution can be obtained using 3-phase models and first principles. Any of the 3-phase equivalent circuits discussed in Part II could have been used in place of the three resistors thus catering for different positive, negative, and zero-sequence impedances. Sequence currents can in this way be looked upon as being driven by the artificial generators at the fault-point. The most complex problem can be treated in this way but obviously the treatment would be tedious. When the impedance offered to currents of the three sequences is different in size and phase-angle it is almost impossible to choose the correct "mixture" of sequence voltages for the artificial generators so that they simulate the voltages with the fault applied. In all cases involving singie-phase-to-earth faults it is the current sequence-components which make the solution unique. The relative phase and amplitude of these are always known from the fact that there is current in the faulty phase at the fault-point and none in the other two phases. Consideration of this leads to the conclusion that in all cases, independent of the sequenceimpedances of the faulty network, the current sequence-components are as shown in fig. 20 where all components are of equal size and the reference (faulted) phase-components are in phase. The sizes and relative phase-angle of the voltage sequence-components at the fault-point are governed by the sequence impedances of the network. Fortunately, for the direct faults it is possible to connect the sequence-impedance networks in the prescribed manner to determine the sequence voltages at the fault-point and the sequence currents flowing at the fault-point.

42

VB' 1'0

}---~-VR'

, 1·0

f

Vy'

Vy

VOLTAGES AT R'y'B' FIG.

VOLTAGES AT RYB

16.

1'0

""

VOLTAGES AND CURRENTS OF FIG.

]Y

0

IB

0

CURRENTS THROUGH RESISTORS

15.

y' R'

R

/.

Vy ,

/' \

,,

~

.

1

,

'

~-

,,

...

~

VOR

'1

V,y

,

~

(,"-:~I

,

V2R I.

A..,.I

., ....

l

'IVIB(~\I

" ' .

r'-.J ;

"

~

''

. .......

V2 B,'""-')

.i

..

, /

~

"I'~,y (~\: ... ... , \

VIR

,... : \

FIG.

17.

PHYSICAL REPRESENTATION OF FIG.

Fig. 22 shows the familiar connection for a singlephase fault. The circuit applies only to the reference phase, in this case the red phase. It was seen that, in this phase, the sum of the sequence voltages should be zero at the fault-point. This is satisfied in fig. 22 by the closed-loop connection. Note that the individual sequence vQltages are not specified; only the summation to zero is known in the general case. It is further known that

"

\

I""\.J I

... ...' '

15.

at the fault-point current flows in only the reference phase. This indicates that the other two phases carry no current and, as stated above, there is only one set of sequence currents which will satisfy this condition. Thus, the loop-connection is correct for all single-phase-toearth faults and it will solve for all reference-phase quantities no matter how complicated the network may be. The same approach, for say, phase-to-phase faults can

43

V1B V1B

z3 Z 3

VIR

¥

V1R

~ 3

t

.l

3

VOR

"'"

VOY

"" '"

3

V1Y

VoB

V1Y POSITIVE-SEQUENCE FIG.

18.

3

1.

NEGATIVE·SEQUENCE

1 3

ZERO·SEQUENCE

SEQUENCE VOLTAGES AT THE FAULT·POINT.

•

RED PHASE RESULTANT IS;

YELLOW PHASE RESULTANT IS:

19.

~~ '\0

1 0

ZERO FIG.

BLUE·PHASE RESULTANT IS:

SUMMATION OF SEQUENCE VOLTAGES AT THE FAULT·POINT.

J

VOR~ 1

VOY~ 1

VOB~ 1

IOR~ 1

IoY~ 1

IoB~ NET POSITIVE FIG.

20.

NET NEGATIVE

NET ZERO

SEQUENCE.COMPONENT VOLTAGES AND CURRENTS.

ZERO

1,0

ZERO

- - - - - -.. v ------,/

RED·PHASE CURRENT FIG

21.

YELLOW·PHASE AND BLUE·PHASE CURRENTS SUMMATION OF SEQUENCE CURRENTS.

44

be made and the significance of the parallel connection of the sequence-networks is apparent. In this case the known conditions at the fault-point which have to be satisfied by the artificial generators are: Yellow-phase and blue-phase voltages are identical; Yellow-phase and blue-phase fault-currents are equal and opposite; Red-phase fault-current is zero. As there is no fault-connection to earth, no zerosequence currents are involved and fig. 23 shows the sequence currents with, in fig. 24, the summation. Note here that to satisfy the conditions for the phase currents at the fault, there is only one possible arrangement of the two sequence-currents to give no current in the reference phase and equal and opposite currents in the other two phases. Similar conditions can be drawn regarding the sequence voltages, and the phase-to-phase-to earth fault yields to similar treatment. It should be borne in mind that when the sequence networks are connected together in a particular fashion, the composite network so formed has no true physical significance. It can be looked upon as forming a computational aid in solving for the sequence currents and voltages. The composite network is thus a form of 'analogue computer' into which the constraints are fed in the form of voltage and current equations which define the unbalance. The majority of faults (i.e. phase-to-phase, one or two open conductors, and so on) can be solved by the conventional series of parallel connection of impedance networks. These are "complete" phase unbalance cases in the sense that the impedance of one phase is infinite or zero in a series or shunt sense. When the impedance of one phase is finite and different from that of the other two, these two connections are again valid but when all three phase impedances are different, more complicated connections have to be devised, some of which demand the use of "unilateral" mutual impedances. Solutions involving two simultaneous faults or "unbalances" are, in general, of this form.

F

N

F

N

Ro= "0

N FIG.

22.

F

SINGLE-PHASE-TO-EARTH CONNECTION.

In the following section, the methods usually adopted will be outlined for these routine studies. Routine Investigation of Unbalanced Faults

The most direct method of solution is to set up on the analyser all sequence-impedance networks and to interconnect them in the established manner. This method is applicable to all networks but physical limitations of the analyser usually prohibit its use when the network is large. The large number of analyser impedance-units required by this method is the usual limiting factor. It is usual with large networks to set up on the analyser each sequence-impedance network in turn and to measure voltages and currents in each separately. When dealing, for example, with the negative-sequence network one unit of fault-current is passed through the network from the neutral plane to the fault-point. All branch currents are now measured as a proportion of the total fault-current and the phase-angle is measured relative to that of the total fault-current. The latter is usually made zero degrees for ease of reference. In this way the vector distribution of the total faultcurrent through the three networks is established, usually for a number of fault-positions. This distribution is expressed as a "distribution factor" and each branch has three such factors in the general case, one in each sequence network, for a particular fault position. A large number of analyser readings is, of course, entailed by an extensive network and the data obtained so comprehensive as to become unmanageable in many cases. The distribution factors obtained for each network are universal and can be used for all types of fault. The total fault-current for each fault-point can be determined by using three simple equivalent impedances connected in the usual way according to the type offault being studied. Knowing the total fault-current, the sequence currents previously measured as distribution factors in each branch can be "scaled" from the values

Application using the Network Analyser General

In the previous sections, a physical picture of the working of the method was given for one case of a direct fault and it was indicated that the other faults could be interpreted in the same way. In applications using the analyser, the conditions.at the fault or unbalance must always be examined first and, from these conditions the sequence-impedance networks are then interconnected to satisfy the conditions at the unbalance point. In many cases, the analysis of unbalance follows an analyser power-flow study coupled with an investigation into circuit-breaker 3-phase performance. The results of these studies dictate the interconnection of the system for normal operation. Earthing and protection arrangements are then considered and a series of studies made to examine the performance of the system under faultconditions.

45

hR .......--------\

\

Ity

POSITIVE

[2Y

NEGATIVE

FIG. 23.

SEQUENCE CURRENTS FOR A PHASE-TO-PHASE FAULT·.

ZERO

Jy YELLOW-PHASE CURRENT

RED-PHASE CURRENT

FIG. 24.

BLUE-PHASE CURRENT

SUMMATION OF SEQUENCE CURRENTS.

obtained using the assumed unit value for this faultcurrent. The above method enables each phase current in each network-branch to be evaluated as well as all neutral currents and the total fault-current. In many instances, it is only necessary to know the zero-sequence-current distribution through the network for the purpose of, for instance, earth-fault protection-grading or mutualinterference problems. When this is the case, only the zero-sequence impedance-network need be set up on the analyser and the "distribution factors" are then measured as described above. Only the lumped equivalent impedance of the positive-sequence and negativesequence networks is required to determine the total fault-current. The positive-sequence equivalentimpedance is usually obtained during the load-flow studies which frequently precede the unbalance studies. The negative-sequence equivalent-impedance can, in the majority of cases, be taken as equal to the positivesequence value but special measurement may be essential when large induction motors are involved or faults adjacent to power-stations are being studied. It should noted that while it is usual to evaluate the branch currents in terms of amperes-per-phase, the "distribution factors" alone often yield valuable information

and can, for instance, show to what degree the sequence voltages developed at the fault cause unbalanced voltages and currents at points in the system remote from the fault.

Special Methods

A number of special methods are used but all these are derived from the basic methods described above. Numerous 'dodges' are often resorted to for the purpose of simplifying calculations which must eventually be made when the unbalance currents and voltages have been measured. For example, the equivalent circuits of equipments such as impedance relays can be set up on the analyser and, with the analyser meters connected to the output terminals of the equivalent circuit, the input terminals are connected to the appropriate point in the power-system network. The analyser meters thus responding the same way as would the actual equipment, and much valuable information regarding the performance under complex unbalance conditions can be so obtained. This technique can be extended to deal with many other unbalance problems including those associated with induction motors.

46

CHAPTER 3 D. C. Primary Transients in Power-Systems By F. L.

HAMILTON.

INTRODUCTION This article is intended as a study of simple exponential d.c. transients which is necessary for understanding the behaviour of current-transformers and protective systems in the transient state. This latter subject will be dealt with in a subsequent artiele. Faults on power-system components and interconnections are mostly of a sudden nature and, because of this, are accompanied by transient components of current. These may last only for a few cycles of system frequency but, even for this short duration, they may affect the performance of fast-acting devices such as circuitbreakers and protective gear. The transient currents may be oscillatory or of a unidirectional type. The oscillatory types are mostly of high frequency unless they are concerned with large values of capacitance, such as series capacitors. These oscillatory current-transients do not usually last long enough to affect protective gear and they do not constitute a current-transformation problem. Extreme conditions of current and high frequency may, however, create an insulation problem on the current-transformer secondaries and on the associated relay equipment. The exponential transient, with which this article is concerned, is of importance both in circuit-breaking and in protective gear. In the latter, the large current levels and the low-frequency character of this transient create difficulties in accurate current-transformation. Familiarity with the d.c. primary transients can be of great value in application problems, in the assessment of test circuits, and in the interpretation of test-data such as oscillographic records. The basic phenomena are simple and are treated in most text-books, but some of the finer points are not always appreciated by many engineers in relation to practical problems.

current zero, while the maximum transient is given by switching at a prospective current maximum. The rate of decay of the transient is determined by the time-constant L/R, which is also directly related to X/R or the circuit Q factor, or to the circuit power-factor or phase-angle. It is not necessary, in practice, to have more information than the basic time-constant of the circuit, the prospective steady-state current, and the "point-on-wave" of making the circuit. The form of the transient is the same for all switching points except in respect of polarity and initial starting value. The familiar "off-set" or fully asymmetrical current is shown in fig. 2(a), which gives maximum d.c. transient. Also shown in 2(b) and 2(c) are oscillograms of switching 30° in advance and 30° later than prospective current maximum. Note the initial minor loop for the advanced making.

Some Useful Properties of Exponential Current Some of the properties of the exponenial can be useful both in the analysis of test-results and in the interpretation of test-data and oscillograms. The more interesting of these are described below. Time-constants

The time-constant can be shown mathematically as being the time when the transient is reduced to lie (36'8%) of the initial starting value. In addition, it can be shown that the tangent to the exponential at zero time intersects the time axis at a value equal to the timeconstant. These are shown in fig. 3. Another property of the exponential which can be of value in this respect is that the ratio of currents at equal successive intervals of time is constant and equal to e--.'lt/T. Each of the above properties can be used for the evaluation of timeconstants but, because of practical errors of measurement, the average result of more than one method is usually preferable. A table is given in fig. 4 of the corresponding values of time-constant, phase-angle. and circuit power-factor for various ratios of X/R at 50 cis. Fig. 5 gives typical values of X/R for the various components in a power-system. These of course are only typical but are sufficiently correct for most purposes. However, it should be remembered that, in practice, we are concerned with the overall time-constant of the circuit which may be somewhat complex and contain a number of components in different configurations. Allowance has to be made for this in evaluating the effective X/R of the total fault-current which is the quantity usually under consideration. These effects, together with the influence of arc-voltage on effective X/R, are dealt with later.

Basic Switching Exponential There are a number of different ways of explaining or deriving the basic exponential d.c. transient which accompanies the making of a circuit containing linear resistance and inductance as shown in fig. 1. The basic mathematical analysis gives the required solution as: -tiT i = I.sin (wt + a -~) - I.sin (a -~) e I being the peak value of the steady-state current. The transient term is of initial amplitude equal to that of the starting value of the prospective steady-state current, and is of opposite polarity to satisfy the requirement that total current must start from zero with inductance in the circuit. The case of zero transient is obtained if switching takes place at a prospective steady-state

47

e = E sin (wt+ IX)

E sin (wt

+ IX) ~I sin (wt

FIG.

+ IX -


1. BASIC CIRCUIT.

48

(a) Full asymmetry.

(b) 30" in advance.

(c) 30° later.

X/R::!!: 16. FIG.

2.

ASYMMETRIC CURRENT WAVEFORMS.

1·0

i2

i3

,(

'2

-:- = -:- =

e- bt!T

e

ot

6t

FIG.

T (m.secs)

X/R

i 1 2 4 8 10 12 14 16 18 20 22 24 26 28 30

1·59 3·18 6·36

12·72

<

25·44 31·8 38·16 44·5 50·9 57·2 63·6 70·0 76·3 83·2 89·6 96·0

III

26·5° 45·0° 63·5° 76·0° 82·8° 84·3° 85·3° 86·0° 86·5° 86·8° 87·25° 87·4° 87·6° 87·8° 88·0° 88·2°

T 3.

EXPONENTIAL TIME-CONSTANT.

Log/Linear Plotting

Cos III

The exponential waveform has the useful property that when it is plotted on a log/linear scale the result is a straight line. This is a useful way of obtaining exponential curves, particularly for data purposes. Typical data curves on this basis are shown in fig. 6. Linear plotting of exponentials is most easily done using the constant ratio of successive values already referred to.

·895 ·707 ·446 ·242 ·123 ·099 ·082 ·07 ·061 ·054 ·05 ·045 ·042 ·038 ·035 ·033

Values of Transient-current Peaks

It is often necessary, for the purpose of assessing contacts, circuit-breakers, and protective gear, to know the values of current-peaks in an asymmetric waveform. The theoretical upper limit of twice the steady-state peak current is only achieved with extremely long timeconstants outside the range normally met in practice. For the case of peak values of current, maximum values are obtained, not with maximum d.c. transient, but with the slightly lower transient current occurring when the circuit is made at voltage-zero. Although the transient is lower in this case, the peaks occur earlier,

FIG. 4. CORRESPONDING X/R, TIME-CONSTANT, AND CIRCUIT PHASE-ANGLE VALUES IN 50 cis SYSTEMS.

49

Component

Voltage (kV)

Range of X/R

11-15

30-120

11 or 15/ 132-275

20-40

Large generators for transmission

Transformers for transmission and primary distribution

275/66--132 132/66 66/6--33

30-35

Value depends on % reactance required for system reasons

Transformers for distribution

3·3-33

5-10

-

30-120

Depends on throughput and economic design of losses

3·3-6·6 11-22 33-132 275

0·16--1·0 0·2 -2·0 1·0 -5·0 2·0

Largely depends on rated current. Larger values tend to be obtained with large-section single-core types

11-22 33-66 132 275

i-2! H-3 2! 4 9 9 15

Generators alone

Generator Transformers

Reactors

Cables

Overhead lines

400

FIG 5.

Remarks Generally large generators at high X/R, but these are usually combined with transformers

Reactance values kept low for regulation reasons

Depends on rated current 2 2 2 4

x x x x

·175 ·4 ·4 ·4

in" conductors in" conductiors in" conductors in" conductors

TYPICAL RANGES OF X/R (50 cIs SYSTEMS).

giving the slightly increased values of peak current. The values of the first peak of current are plotted against X/R in fig. 7. Values are given for the first peak for switching at both voltage-zero and at prospective maximum current, but it can be seen that the difference is only significant at relatively low values of X/R. The first currentpeak is an important value for the rating of a contact. Other points which may be of importance on a transient-current waveform are at times of about 50ms and 7Oms. These are the approximate times which fast circuit-breakers and protective gear would take to achieve contact-separation. Values for these times are also given in fig. 7. The values of d.c. component can of course be obtained by subracting 1 per unit from the values given by these curves.

ably valid for larger time-constants it should be appreciated that there is theoretically always a minor loop associated with this condition. Fig. 8 shows an analysis for this particular effect. The total current is the difference of the exponential and cosine wave and the minorloop effect can be seen by plotting an exponential current and cosine current together. The shaded area represents the minor loop in duration and magnitude. It can be seen from this that the duration of the minor loop is significant for X/Rs between 2 and 8 but that the amplitude of the minor loop is not greatly significant for X/Rs above 4. This effect is pointed out because it can be important in assessing accurately the switching point particularly of low X/R circuits and also because this part of the waveform is frequently shown in an expanded form on some oscillographic records. The existence of this minor loop would also be important in protectivegear devices responsive to polarity of current and position of current-zero. There is no minor loop at all in the other important case of switching the circuit at voltage-zero.

Minor Loop on Fun Asymmetry

It is quite common to see sketches of oftset current waves with maximum d.c. transient not showing any minor loop at the commencement. While this is reason-

50

Time of First Major Peak on Full Asymmetry

cally this is not exact but the accuracy is quite sufficient for all practical purposes. The exact time of occurrence of the first major peak and its value can be obtained by plotting curves of d.c. exponential, sin wt, and d.c exponential/X/R. Again the disparity is most noticeable

It is quite common to estimate the peak-value of a loop, particularly the first major loop, by adding the peak-value of the steady-state current to the instantaneous values of the d.c. component at that point. Theoreti-

I

e

! ~f

I~

I

f\1

I

!

I \

I

I

N I

i

I

I

1\.

1\ ,x

'I

O· I

~

i

I

t

i

2:

~

I

i -H~" ~ I

i

[I

I

,;

borx -i--------+----+-[--+-+-i-R'--'-t-=--r-8-;

f

". R= 6

i

I I

II

1',

I!

Ii

I

I

5

10

15

10

20

30

il'-r-.x

Pl'I

0= 4

i "

'I

IllJl '

i

IU

I-+---tl---+-------i ._--l-r----.----\r-...---------=t"-.'--+-+-+-----+-+_ ....

_-+-'--+--,,'......

Ii i ' !' I I '"

1- =

R

---H~

20

25

30

t (m. sees)

1·0

I

0·5 e

FIG.

6.

40

50

LOG/LINEAR PLOTS OF EXPONENTIALS.

51

60

t (m. sees)

=r=r I I I I I '1~~=t=t=1~t;t:t:~+=~~~t:f:$=Fff=t=~~t:t=t=t _Io--'i""""'"

2·0r

I

f I I 1transient

--+--I---l---l~f-::"I~f---~+--+-+---+-+-+-+--+--+--+--+--

/\

1--

--+--+-+--+--+-- c-

I stead y-state --+--+_Ai9"~--I---l--lC-A_t t-I._0t-m_st-f0i-r_mra_xrim.-+um-+t_r.a-+n_si-+e_nt-+--+--+-. I .5

1--_ --1--1-'

-+-~-J

~+-+-+--J.n/~~q===*===*=t=1 FO~ s~it~h in1g ~t-+--+--+-+--+--+--lJ-~J:.:::.J=..::t-=!-=+--:[-J

~V vo I,ta g e ze ro !.-' :.- :.- :.- r-:.-- :.--:---:.--~ I . 4 ~t-t-+/~+-+-+-+-+-+-+-+-+-+--+-'+-~~-+-+-+-+-+--+:::;;;"-;''''''''-"'f~-+-+--+-._j----

~'(J

I

II

: :

~

50 ms

V

V~V"""

V

V

f.--+-/+~JIH--+-+--+--+--+--1-/-+/--+V-+-V~/-+v-+/-+-/-+/--I:..,...q--+--+-·+----,

-_

~-+--r-+--+-_.

1

i/ I 1.1

I

1/

I I

04 -03

V

/3

1/

1---

c ..

: I

:

I

I

'

_1._1 2

j.' c--- .-

IJ

4

,

-

- -

'-

.

.

1--+--1---

.

·-P~-8 V V

-+--,--t--+---i-¥---\--+---+-+---+--iL---4-

1/

I :

I

._.- -- -

f··-

+--1,".-

I

-I---+--+---+·---{-I

- - f - _.

·02 _.

·01

2

l::= tv )/----+~I It..-JL i-i1 II· ~~ "-- --+--r--- --~-f!----

:~.

. OS

V/,~70 m,

/

:L

V

\

... -., - --- .-'

6

8

10

FIG.

15

7.

PEAK VALUES OF CURRENT.

52

20

25

30

·61----·51----

·4

·31----

·2

·1

' - - - - _ .._----

3

2 FIG.

8.

4

m. sees

INITIAL MINOR LOOP WITH MAXIMUM D.C. TRANSIENT.

on time-constants in the range of 2-4 but comparison between values of peak current obtained accurately from this construction and the additive method used for fig. 7 gives negligible errors, as shown on the constructional diagram, fig. 9.

bered of course that there will will be a discontinuity when the resulting total current passes through zero. The expression is given for the resulting transient current which is still exponential in waveform but which is asymptotic to a horizontal line through kX/R. An approximate evaluation of the increased rate of decay due to the presence of the arc is given by the equivalent time-constant T T' =

Effects of Arc-voltage The presence of an arc-voltage in series with the circuit has a pronounced effect on the waveform of the resulting transient current, even for relatively low values of arc-voltage. It is not possible, of course, to calculate accurately the effects for complex arc-waveforms, but a common case is that of a relatively small arc-voltage of rectangular waveform. The general circuit is shown in fig. 10 and the resulting total current can be obtained by superimposing the currents resulting from the two separate voltage-sources, one being the normal prospective tra'nsient current without arcing and the other being the current resulting from the replacement of the arc by an equivalent squarewave generator. It must be remem-

(1 + kX/R) In this expression X/R is the natural value of the circuit and k is the per-unit value of arc-voltage referred to the peak sinusoidal voltage. An example of the extent of this increase is obtained by taking the X/R= 15 and k= 1/25, T' being equal to ·625T. The complete waveform of current for this particular case is plotted in fig. 11. During the first loop the resultant current is obtained from the transient expression shown in fig. 10. At currentzero the arc-voltage is restarted with opposite polarity.

53

I· 0 . . . - - - - - - - - - , - - - - - - - r - - - - - - - r - - - - - - - - , - - - - - - - ,

-

-

~

-

"·1

\

;1f

-tiT

-

e X./ \ f - - - - - - - - - - 1 , - - - - - - - I - - - - - ) : ( for T=2 ---+-------t--+--1 \

\

R

\

,

..... 6·]0 Correction

for~ = R

i....£.

2

= 6·YO ~

-+ I peak --

·22

+

·22

-1-

cos 6·YO ·99

= 1·21 compared with 1·2 from fig. 7. The error will reduce with increasing XjR.

·01 ~-------l

--f----·------f----·----fi

----j----------+---------I1

t---------t---------t--------.---------~--------_+__--------_t1

f - - - - - - - - - f - - - - - - - - - - t - - - - - - - - - - - - --------+-------.-"11

f - - - - - - - - - - + - - - - - - - - + - - - - - ---------+----------+--------11 f-------------- ----------+-----------.- ---------+-------------"11

7

6 FIG.

9.

8

ACCURATE METHOD OF ASSESSING FIRST MAJOR PEAK.

54

9

10

m. secs ---">0-

L

R

'7 It

I

L

R

ea

L

R

)

+

ANALYSIS FOR EFFECT OF ARC-VOLTAGE i

1·0

p.u.I

= I ( e -tiT - cos wt)

e. it = I ( e-tiT I cos wt ) - R

E~IX.

If

e

a

(I _e -tiT)

= kE = kIX,

then. for 1st loop. it

=

I[ e- t/T - cos u,t] -k

= I [{ e

PRO PECTIVE TRANSIENT CURRENT WITH ARC (I st LOOP)

e -t/T(1 .

.L

'

-tiT

(I + k~)

r; [I k~

-

e- t/T ]

}- cos wt]

~~-TRANSIENTCURRENT

WITHOUT ARC

=

e- t/T

k?S)-k ~ __--\,.-__~... R R

O-+------~~---_.:."f....----------"

"

---7- t

""

"" " ",

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

-k ~ f - - - - - - = - - - - - - - R FIG.

10.

-

....1-

T

EFFECT OF ARC-VOLTAGE ON THE RATE OF TRANSIENT DECAY.

55

.............. _

In addition the decay transient of the current i', which was the ultimate value of the previous arc-voltage transient current, has to be taken into account. Subsequent loops are obtained by repetition of this process. Fig. 12 shows the approximate correction factor for various values of X/R and arc-voltages.

is only about 2 or 3 for very-high-voltage lines with bundle conductors. In practice, therefore, the total circuit-current under short-circuit conditions will usually involve impedances having different X/R values and this should be taken into account when evaluating the transient currents. There are four basic circuits, which, when analysed, can usually cover most practical cases. These are as follows.

Mixed Circuits In general, the concentrated componets of a powersystem such as generators, transformers, and reactors have X/R values which are greater than those of cables and ovehead lines, although- in the latter case the factor

Series Impedances

This is shown in fig. 13 and represents, in general terms, the common case of a fault beyond the switching

Total current with arc-drop

1·0

OI-l----------H::...:.----II-<;:;--=:--------1rr"'----~r_----

-- ---;..--/'

.6 (I -

j'

e- t/T ) /

·61-----------+_

FIG.

11.

EFFECT OF CONSTANT ARC-VOLTAGE ON FULL-ASYMMETERY WAVE-FORM.

Natural X/R = 15 e a = 1/25E.

56

[~J

25

[~r

I

[I +

k

~J

[~J

20

I -

k

k = ea/E

50 I

k

15

40

k

= ---I

k

= --

k

-

k

---

k

-

30

10

I

25 I

20 I

15 I

10

5

~

i<-

~

5

FIG.

12.

10

_:_':=__---

15

20

Total circuit -

13.

25

ApPROXIMATE CORRECTION-FACTOR FOR VARIOUS VALUES OF

or relaying point, the fault being fed by predominantly generator and transformer plant. The fault-current, apart from reducing as the fault is moved out along the line, will have a reducing X/R value

FIG.

~-----~--

X

R

Xl

+

R1

+ R2

X/R

30

AND ARC-VOLTAGES.

Simple Shunt Circuit

This is as shown in fig. 14 and is representative of a close-in busbar-fault, with two types of infeed to the busbars. Generally, part of the fault-MVA will be derived from generators and transformers having an effective X/R value about 30-40, and the remainder will be infeeds from the system, having X/R values approximately that of the lines, i.e. of the order of 3-15. This results in two components of fault-current, each with a transient corresponding to its own particular X/R value, and an initial magnitude corresponding to the respective steady-state value. ParaUel/Series Circuit

X

= -----2

This is an extension of the previous case of mixed infeeds, but has the complication of a common length of line between the fault and switching point, as shown in fig. 15. The line impedance is mutual to the two infeeds and the solution is therefore more difficult. A degree of simplification is possible if one infeed, i.e. that due to line infeed, has the same X/R as the line impedance between switching point and fault as will generally occur in practice. Analysis of this case shows that the total fault-current has two exponential transients, one at the X/R value lying between that of the line and that of the

SIMPLE SERIES-CIRCUIT.

since the line X/R is less than that of the source. The equivalent X/R of the total fault-current is easily obtained by dividing the total circuit-reactance by the total resistance. Curves relating equivalent X/R with various busbar MVAs and line-Iengths-to-fault are given for various system-voltages on pages 25 and 26 of R.R. 174. (A Reyrolle Review Reprint).

57

generator-transformer X/R. The exact value of this latter X/R, and the magnitude of each component of the transient have been evaluated for a range of impedance-ratio values in figs 16 and 17. These are based on an X/R of 30 for ZI and an X/R of 9 for Zz and Z3 which are the approximate figures for the 275-kV system. The values obtained from these curves are interesting since they show that, for a wide range of practical cases, x' is substantially below the maximum value of 30, and the proportion of current having a transient of the minimum X/R=9 is large. A simple example is when

7I FIG.

14.

~=~=1

SIMPLE SHUI'T-CIRCUIT.

Zl Z3 This is the case of a station, in which the total shortcircuit MVA is divided equally between generator/ transformer plant and line-infeed from the system, the fault for a 275-kV 15,000-MVA level being about 15 miles from the busbar. In this example, ·75 of the faultcurrent has an X/R = 9 and ·25 has an X/R= 17. The curves can be used to evaluate the total d.c. component of fault-current,- or to determine current-transformer requirements. Shunt Resistance

This simple case, shown in fig. 18, sometimes gives rise to difficulty because of the use of such circuits to produce the 50-cycle conditions equivalent to a series circuit. Since this equivalence is only valid at the one frequency, 50 cycles, a completely different currenttransient can be expected in each case. On making, the current is immediately established in the resistance, with no transient, and the current in the inductance is accompanied by a normal exponential transient. This transient is not, however, related in time-constant to the original circuit power-factor, but only to the natural X/R of the inductive branch. This transient will be considerably longer than the equivalent series circuit for the same overall power-factor.

Three-phase Faults TOTAL FAULT-CURRENT TRANSIENT

;2-3 at

X

Ii: of

Three-phase transients will be of the general form of the single-phase cases already covered. As the starting values of the prospective steady-state currents add up to zero, so also will the three d.c. transients summate to zero at all times. With three phases, however, there is always a higher probability of experiencing asymmetry of fault-current in the system. There will, theoretically, always be a minimum of 86% asymmetry in at least one or more phases. Some differences arise with sequential closure of the different phases of the circuit, but these tend to be of academic rather than practical interest.

x2 X (i-c) i I at - between R

_L_~==~::::::::::::::~~;~~~X I

and x2

FAULT TRANSIENT IN Z2

Conclusions Analysis of the d.c. transient arising from faults on a power-system shows that the basic exponenital form is applicable, with some modification, to most practical systems. These modifications can be important in the evaluation of the practical fault-conditions needed to assess the realistic requirements of equipment such as current-transformers and protective gear. It is hoped

-_"---1\ I

.•. ci I

FIG.

15. TRANSIENT CURRENTS IN PARALLEL/SERIES CIRCUIT.

58

x

to

_

-

rl Y

=

~

ZI

Z~ ~

2

l..--- ~

l-- ~ l---

-

1·0

0·8

~

/ V

~

V I.-'"

V

17

Xl

I-'" ?'

---

o· 3

r-.....

I/'

/

V

/

/

/

/

--

" -

V

V

I

V ·4

·5·6

FIG. 16.

·8

COMPLETE

~

v~ L

1·0

X/R

,

/

V

1/

J

/

J

/ I I I

/

1I

0·2

·2

/

/

VI V l.I V " / I I

'/

V ~ ~~ I

~

V

V ~

VV

/

0·4

I

/

/

V /

~

V

Vv ~I Vv

V

l.--"

0·5

/

vv/ v v V V VV,V

/

io"'" ~ I---"

v

= 12

Xl

~

V

/

./

i-""" ~~

~

0·6

0·'

/

=9

~9 R

4

10

V

X

-

3)r-1

Z2

=

Xl

30

/

2

VALUE (xl FOR CURRENT

59

il.

15

Xl

=

Xl

= 18

XI

~=

Xl

=

21 24

Xl

=

27

4

f---i 2

~------

1·0i----

·99 0·1

2

FIG.

17.

PER-UNIT VALUE OF TRANSIENT CURRENT IN TOTAL FAULT-CURRENT AT LINE X/R.

60

4

between the busbars and the fault and this will have the same X/R as the line-source input. This particular case can be solved with a minimum of mathematics, if certain circuit concepts are borne in mind. The general circuit is shown in fig. 19. The steady-state currents will be divided in the ratio I1/Iz=ZZ/Zl and the resulting transient components in each loop must satisfy this division. From inspection, two loops exist with Z3 as the mutual impedance. It was previously pointed out that the exponential current in a circuit comprising impedances of the same time-constant does not generate any external voltages. It is possible, therefore, for the loop ZZZ3 to carry an exponential of the line time-constant without interreaction with the loop ZIZ3, and this is one of the transient currents. The other transient, involving ZI, must intereact with Zz and will be of a time-constant intermediate between that of the generators and that of the line, and be distributed so as to satisfy both the inter-reaction and the initial starting requirements.

X T=-

rw Transient Current Distribution

Let II and I z be the steady-state components of current in the two loops. The transients i 1 and iz will distribute as shown in fig. 20. Total transient current =(1 - c) i 1 + i z, wherec=

~ ZZ+Z3

i 1 must start with initial value = IJ, iz must start with initial value = lz + elJ, and the total transient with II + I z.

FIG.

18.

SHUNT-RESISTANCE.

z) E

that the data provided in this article will help in this respect, because there is always the possibility that the over-simplification which results from lack of working data may give rise to excessively pessimistic requirements. '

APPENDIX Circuits of Mixed Time-constants Detailed Analysis and Alternative Presentation

As previously discussed, many practical systems can be reduced to the form shown in fig. 15. This constitutes one input source of predominantly generator and transformer characteristics, and another in which line characteristics predominate. Also, there will be a length of line

FIG. 19.

61

Thus, the per-unit of current at the line time-constant

And the effective Q of this series circuit will be

1+c!l = A = Iz+cl i Iz+11

___ Iz =

x

II 1+ Iz

=

ZI

+ Z'

~+£ XI

Xz

or, expressed in terms of

x

Xz

(z

Xz

+ 1) +1

Presentation

The above expressions can be shown as in figs 16 and 17. However, more generalised data-curves relating the values to the various fault-MVA levels at the busbars and at the line are more useful and are shown in figs 21, 22, and 23. Independent variables are obtained involving three short-circuit levels such that

x = Y

The intermediate time-constant of the transient i 1 can be readily obtained from fig. 20. Total impedance seen by this transient

Zz Z3 ZZ+Z3

MVA at the busbars from line-source MVA at the busbars from generator-source

Intermediate time-constant

= Zl +

Total MVA at the fault Total MVA at the busbars

Fig. 21 shows the per-unit value of fault-current at the line time-constant for various values of X and Y. Fig. 22 shows the dependent variable z plotted against various values of x and y. Fig. 23 gives the intermediate X/R (Q value) for various values of this dependent variable z.

= Zj+Z'.

62

1·8

·l·~-

---~

i

6'"

I

II

I I I

I

<:(

1·6

I ·4

--1 t-----+--t----+-+----~~-

1·2 w U a:: w:) Uo a:: V> :)a:: 00 V> Iw< 1·0 za:: - w -'z ::E w O\.:J a::::E ""0 V> a:: a:: .... 0·8 ela:: :) < ell ell

V>

I- :) < ell < ::E< > ::E II >-

0·6

0·4

0·2H--+-+-+-~1£_-~:....-_t-~~-_+----_::::l:_-~--_!

A = 0'\

o

0·4

0·2

X A

=

21.

0·8

MVA AT FAULT MVA AT BUSBARS

=-_,= + I

FiG.

0·6

~ Y

FRACTIONAL D.C. COMPONENT OF LINE TIME-CONSTANT (T)

FRACTIONAL D.C. COMPONENT OF LINE TIME-CONSTANT.

63

/·0

I ·8.----.----,-

I ·6 t------+----t-----+---+---+---+--t-----tc--+--t---

1·4 t - - - - - - - \ l - - - - -

W

u

1·2

'" uo

w::::>

::::>", "'''' 00 "'I-

W<

z'" - W ....I

'·0

Z L W

o~

"'L u.

o

"'''' <'" "'u.

co",

0·8

:>< co

II

>-

1·0

X= z FIG.

22.

=

MVA AT FAULT MVA AT BUSBARS

Y+X I-X

GRAPH FOR DETERMINiNG Z IN TERMS OF X AND

64

y.

6

5 I--

Z

UJ

Z

0Q.. I:

0

4

U UJ

I--

I-- Z

< < I-0 V) UJ I: Z

ex: 0 UJ

I--

z

LL

0

UI UJ

3

I:

i= UJ

I-- Z

Z

...J

c;(

I--

V)

z

2

0

UI UJ

I:

i=

"

x I"" x

Xl

X2

x

GENERATOR SOURCE TIME-CONSTANT LINE TIME-CONSTANT

z+1 __ z_ + I

-=---X2

XI!X2 FIG.

23.

TIME-CONSTANT OF INTERMEDIATE COMPONENT.

65

CHAPTER 4 Current-transformers in Relation to Protective Gear: Steady-state Considerations By F. L.

HAMILTON. ary impedance is reduced, and the circuit can be considered as current driven as shown by fig. 2. On this basis, the primary resistance and leakage reactance may be omitted to give the simplified current-driven circuit shown. In most cases, current-transformers are of the ringcore type, with toroidal secondary windings and symmetrical primary windings. For these, the leakage reactance of the secondary winding is very small and may be omitted from the equivalent circuit. With unsymmetrical primary windings, incomplete winding of the core, and built-up cores, the secondary leakage-reactance may be high and, in extreme cases, comparable to the secondary load, in which case it must be included in the equivalent circuit. These two categories of current-transformers are defined in B.S. 2046 (Protective Transformers) as lowreactance and high-reactance current-transformers, and different testing and application techniques are required for each type. Low-reactance types are generally preferred for use in protective systems. The shunt impedance ZM of the equivalent circuit represents the magnetizing and iron-loss impedances of the transformer and it is convenient to consider these as a linear reactance in shunt with a linear resistance for many calculations where high accuracy is not required. It is important to remember, however, that these impedances are non-linear and must be considered as such when accurate calculations in the unsaturated region are required or when operation in the saturated region is being considered. For the case where the shunt impedance ZM is considered linear, a further variation of the equivalent circuit is possible by using Thevenin's Theorem, as shown in fig. 3. This gives an equivalent circuit which is voltageenergized. It is important to realise that the voltages

INTRODUCTION The wide application of current-transformers to powersystem requirements presents a scope greater than can be dealt with in a single article. As part of a course on protective-gear, this article deals with some of those aspects which are of interest to protective-gear engineers, both designers and users, and which are concerned with the behaviour of current-transformers in protective-gear circuits. From consideration of such aspects it is possible to obtain a better understanding of the problems and difficulties which arise in the design and application of protective gear. Whenever possible, a complicated mathematical approach has been avoided in favour of graphical analysis. The use of some mathematics is, however, inevitable and a reasonable knowledge of this and of basic electrical circuit theory has been assumed. The importance of the current-transformer needs no emphasis. The device is basically a very simple one but its behaviour, particularly under saturated and transient conditions, is rather complex. These conditions are of particular interest in the design and understanding of modern protective-gear.

Equivalent Circuits The use of equivalent circuits can be invaluable in the study of curren-transformer problems and full use should be made of these techniques. The basic equivalent circuit of a current-transformer is shown in fig.! and is similar to that of a power-transformer. The effective impedances of the current-transformer imposed on the primary energizing system are invariably small compared with the natural impedance of the primary system, even under fault-conditions when the prim-

N sec.

Zs

turns

RpN2 XLPN2

Rs XLS

ZM Zs FIG.

1.

Primary resistance Primary leakage-reactance Secondary resistance Secondary leakage-reactance Shunt magnetizing impedance Secondary load

}

Rererred to secondary

level

EQUIVALENT CIRCUIT OF CURRENT·TRANSFORMER.

66

RpN'

XLpN'

Rs

XLS

Zs

EpN ZpN2

FIG.

2.

l Primary

system-voltage impedance referred to secondary level.

Ip,N

r and

Rs

XLS

SIMPLIFIED CURRENT-ENERGIZED EQUIVALENT CIRCUIT OF CURRENT-TRANSFORMER.

developed across ZM in this circuit are theoretical and do not occur in the actual current-transformer windings. This circuit gives the same value of secondary current in the load and the same errors as that in fig. 2.

tic circuit, the quality of iron, the cross-sectional area of iron, and the number of secondary turns. Most of these factors are affected by the space available for accommodating the current-transformer and the design factors are such that, for a given space, there is an upper limit of accuracy which can be attained for a particular secondary burden and primary rating. This maximum accuracy can be increased by the use of high-permeability low -low steels for a part or the whole of the core. The accuracy is also dependent on the secondary loadimpedance and will be increased as this impedance is reduced. In the limit, the value of accuracy on short circuit is determined by the secondary-winding resistance and leakage reactance. Many protective currenttransformers operate under conditions approaching this. The value of secondary turns will be related to the number of primary turns, the transformation ratio, and the rated secondary-current. When the rated primarycurrent is below about 300 amperes, the number of secondary turns, especially with a 5-ampere secondary rating, may become too low to achieve a particular accuracy with a bar-primary (single-turn) so that multiple primary turns must be used. The effect of secondary turns and rated secondary current is considered in more detail later.

Design Factors and Steady-state Performance Accuracy

The main criterion of performance is the accuracy with which the primary current is reproduced in the secondary circuit with respect to both magnitude and phase-angle. This steady-state performance is expressed in terms of 'Ratio error' and 'Phase-angle error,' defined as: Ratio error =

[_NI~Ip]

100%

Phase-angle error = "y in fig. 4 (+ ve when Is vector leads IplN vector as shown). Considering the simple equivalent circuit shown in fig. 2, a given primary current will be divided between the shunt impedances ZM and (Rs + X LS + Zs) in accordance with their relative magnitudes and phase-angles as shown in fig. 4. Thus the accuracy of output for a given total secondary impedance will be governed by the value of ZM' This is directly ~elated to the length of the magne-

Rs

XLS

Zs

FIG.

3.

VOLTAGE-DRIVEN EQUIVALENT CIRCUIT OF CURRENT-TRANSFORMER.

67

The saturation-factor is dependent, to a large extent, on the same factors which govern the accuracy and, for a given space, primary rating, and core material, there will be an upper limit to the saturation-factor which is attainable. Although saturation effects the greatest departure from linearity, most magnetic steels are fairly non-linear over most of the working range, giving typical voltage/ current characteristics as shown in fig. 5(a). There is generally a region of low initial permeability followed by a region of high permeability and finally the region of low permeability resulting from saturation. Such nonlinearity results in harmonic components of magnetizing currents even in the unsaturated region. The type of curve shown in fig. 5(a) is associated with a core of homogeneous cross-section, such as obtained with a ring-core comprising either annular stampings or spiral-wound strip. Cores of the built-up type using overlapped butt construction exhibit an effect of two-stage saturation, as shown in fig. 5(b). This is due to saturation at the butt joints, where the cross-section is halved and the flux-density is about twice that in the remainder of the core. This results in an equivalent air-gap line before total saturation is reached. Built-up cores are not often used for main current-transformers, except at low voltage, but they are generally used for auxiliary currenttransformers. The hysteresis loop is such that harmonics are produced due to the hysteresis-loss current, i.e. the shunt resistance representing the iron losses is really a nonlinear resistance. In order to produce sinusoidal ironloss currents, the hysteresis loop would need to be elliptical in shape (see fig. 6). Both these effects make the vector combination of magnetizing and loss currents with the primary and secondary currents, as in fig. 4, an approximate process of convenience. The inaccuracies involved are not great, however, and for most protective-gear purposes may be neglected below the region of saturation.

jp/N

Vs

Vs

Ratio error Phase error

FIG.

4.

_n_

-(IMsin0

+ IlL cos 0)

Ip/N

y lead 1M cos 0-IJL sin 0 Ip/N

x

1000

10.

radians.

SIMPLE EXPRESSIONS FOR ACCURACY.

Saturation and Non-linearity of Iron

The main departure from linearity in the shunt impedance ZM occurs when the core flux reaches saturation. This is accompanied by a rapid reduction of ZM and a large increase in errors. It is important to know the secondary current at which this departure from reasonable accuracy occurs. It is often defined by Saturation Factor, which is the multiple of rated current up to which the current-transformer is accurate for a specified secondary burden. The correlation of accuracy, burden, and saturation-factor is used in B.S. 2046 as a convenient method of specifying the general capabilities of a current-transformer.

Design-data Curves

The characteristics of various typical materials used for current-transformer cores are conveniently shown in the design-data curves in figs 7a, b, and c. Log/log scales

V

volts

Ie

UNSATURATED

REGIO~,

REGION

Ie amps FIG. 5(a).

NON-LINEARITY OF ZM'

68

:=J

Total Saturation /

I

""

I I I

Equivalent Air-gap line

Equivalent Air-gap -:.~

I

L:""''" "b""JOO",~_ FIG. 5(b).

TWO-STAGE SATURATION-STACKED CORE.

are used to maintain accuracy over a wide range of values. These curves are based on Lm.S. ampere-turns and peak flux-density at a frequency of 50 HZ and are normally given for a sinusoidal voltage, the current and thus the ampere-turns containing harmonics. This is a compromise which is generally justified in practice and is referred to again in the following section on 'Basic Performance Data.' The curves are expressed in unit values and the separate values of magnetizing and iron-loss ampere-turns are given so that it is relatively easy to relate them to a specific design-problem. For example, to calculate the phase-angle error and ratio error for a 300/1 Stalloy current-transformer having LMP = 25 in, a cross-section of 3 in", and a secondary-winding resistance of 1·0 ohm, assume a range of secondary currents up to 20 amperes and a burden of 7·5 ohms/60°.

FIG.

6.

Area = 19·4 sq cm LMP = 63·5 cm Total secondary impedance Z

=

1+7.5/60°

= 8.0/54°.

Total secondary voltage from which B M where B M I sec

ZXl sec (r.m.s.) = 4.44 B M A f N 10-8 = 620 I sec lines/cm" = Peak flux-density, and = secondary Lm.S. current. =

300 IlL

= ·212 ATlL/cm, where

1M and IlL are the Lm.S. magnetizing and iron-loss components of exciting current.

EFFECT OF HYSTERESIS ON WAVE-SHAPE OF MAGNETIZING CURRENT.

69

o 5,...---,...----,.---,..---,..----,..------,

0'2· E

u

c: ~

'"

0 I

~

<>

0..

E

«

'05

.,;

Grain-orientated Silicon-iron

E ~

'015" SPIRAL CORE '02

~'-:--.-L~~.~ 200

500

1000

2000

5000

10000

Peak Flux-density - Gauss

1.0 r - - - - - , - - - , . - - - , - - - - r - - - - , - - - , . . - - - - - - . - - ) " ! - . . . ,

o 5 r----j---t---L----.l.---.L....--+----r---b'-~(b) Hot-rolled Silicon-iron '03" RING STAMPING

o2 E

u

0·1

c:

'" ~ <>

0..

05

E

«

E cr:

'02

·01

(cj Nickel-iron (Mu-metal) '015" SPIRAL CORE

200 500 I Peak Flux-density-Gauss

20

FIG.

7.

CORE-MATERIAL CHARACTERISTICS.

70

10000

For various values of I'e<> values of BM and thus 1M and are obtained, the ratio and phase errors then being calculated. The values of ratio error and phase-angle error are shown plotted in fig. 8 for a range of currents up to 20 amperes. By reducing the number of secondary turn from 300 to 292, the ratio-error curve would be referred to the new axis through a (see fig. 8), and the effective error would be reduced over most of the working range, but would not affect appreciably the phase-angle error. Turns compensation is used to increase the accuracy of metering current-transformers but it is rarely necessary for protective current transformers, although it is often done to make these also suitable for metering. It will be seen from the above example that the: region of low initial permeability results in a considerable reduction in accuracy at low currents. This region is important in both metering and protective currenttransformers as it limits the lower value of current for which high accuracy may be obtained.

instrument current-transformers and are not normally required for protective current-transformers. For protective current-tranformers, a suitable ratiocheck with zero burden and rated current is usually made to check the turns ratio, which is an important factor in protective systems, particularly those of the balanced type. In addition, the excitation-currents are measured (see 'Open-circuit Excitation Curves' below) since, in this type of application, this is considered to be sufficient indication of the expected accuracy under working conditions. Special ratio-tests are seldom called for.

Basic Performance Data

These are used to define the volt/ampere characteristics of the shunt-impedance ZM' They may be predicted from the basic data curves in fig. 7 and/or by actual measurement on the current-transformer. The predicted or measured open-circuit excitation characteristic of a particular current-transformer may be used as a data curve for general design-purposes, as shown in fig. 9. The scale factors of the two coordinates are obtained from the core dimensions and secondary turns. The phase-angle of the exciting current and the secondarywinding resistance are often shown on the same sheet. The knee-point voltage (see the following sub-section) can also be shown as it is independent of the scale factors.

IlL

Internal Resistance

This also may be important in the operation of balance systems of protection. Whilst it can usually be predicted with sufficient accuracy, the measurement of this is done as a routine test. Open-circuit Excitation Curves

Performance can be predicted from a knowledge of the design parameters, the connected burden, and the characteristic curves of the core material, as shown in the previous section. A production current-transformer will generally be tested to show that it falls within a specific class and that the predicted performance is obtained. B.S. 81 and B.S. 2046 give details of the classes and the tests which are normally called for. Accuracy

Accuracy can be checked by bridge methods against standard transformers for the required secondary burdens. Such tests are usually associated with metering and

.... 0 .... ....

%

UJ

-I

0 .;::;

-2

'"

a::.

%

0

-3 -4

10

Secondary Current ·20A

+1

--:;o..c;..-------+..------=-..o;;;:--.L--i 0' 10 Secondary Current (new aXis)

20A

mins

40 L

g

30

UJ

~

20

'"

..r::: 0-

10 0

+2

~---l~:_t-__t-_+---,O

Secondary Current 20A

-10

FIG.

8.

ACCURACY CURVES FOR WORKED EXAMPLE.

71

-I

-2

R.m.s. Volts Volts

Kv

....,

CSA

rr:-4

N

x

119

x

-N

LMP

~

39

1'0

30

"0

>

119

0·8

..to

\\

.",

c

0'6

V>

0'4

0 u

.,

c

in

10 0'2

Material : Dimensions: Std. LMP Winding

Stalloy.

4" x 51" diams x 2·k" deep. 39 em. Std. CSA : 11·4 sq. em. 119 turns 14 S.w.g,

0

0

'·5A

"0 R.m.s. Secondary Current

FIG.

9.

TYPICAL STANDARD OVERCURRENT EXCITATION CURVE.

(4)

Volts

150

.----------r----------...."."-------.-~

rl~:::~IE] 100

., ::l""

"0

>

..to

"c: 8., V> ~

"

v

50

'y

.,

c:

Stalloy Core: St" x 7~" dlams )( 3' deep

a.

0

Secondary VVlndlng' 300 turns (I) & (2) Average-reading Instruments (3) & (4) R.m.s.-reading instruments

o .\.L----------'-----------'----50 o 100

150 A.T

EXCiting Ampere-turns

FIG.

10.

OPEN-CIRCUIT EXCITATION CURVES USING VARIOUS TEST-METHODS.

72

These curves are widely used for protective currenttransformers as, for a low-reactance current transformer, they contain all the information necessary to assess the capabilities of a current-transformer and its consistency with others of the same nominal design. It is important to appreciate, therefore, that the form of this curve is affected by the methods of test, the instruments used, or the basic data curves from which it is derived. This is illustrated in fig. 10, which gives a series of excitation curves for the same current-transformer for different test-conditions. The first curve (1; is for average values of voltage and exciting current for applied sinusoidal voltage. The second curve (2) is similarly for average values but is for sinusoidal current. Considering curves (1) and (2), the average value of voltage, regardless of waveform, depends on the average flux-change, which depends on maximum flux and hence on peak magnetizing-current. Two points on these curves, (a-a') of equal average voltage, would have the same peak magnetizing-current. The current of curve (1), being peaky, will have a smaller average value than that of curve (2) and so will lie to the left. The Lm.S. value of a quantity is very dependent on wave-form, and this is noticeable in curves (3) and (4). Taking the sinusoidal-voltage case (3), the Lm.S. value of the peaky magnetizing current will be greater than its average value but will still be less than that of the sinusoidal current, and this curve will thus lie between (1) and (2). For similar values of sinusoidal current (b-b') the average voltage being the same, the Lm.S. value of the peaky voltage will be very much higher, raising the level of this curve as shown. This sinusoidal current/Lm.s. curve gives the impression of a higher saturation level. Curves of average values are shown because many average-reading instruments of the rectifier type are in general use, these being scaled in terms of 1· I times average value, which gives the true r.m.s. value only for a sine wave. It should be noted that all the curves coincide in the unsaturated region because both current and voltage are approximately sinusoidal. The curve normally used for protective gear is No. (3) i.e. sinusoidal voltage with r.m.s. reading instruments, and most design-data curves, e.g. those in fig. 7 and fig. 9, are given for this condition. This is valid in most applications of low-impedance schemes with linear burdens since the secondary current, and thus voltage, is nearly sinusoidal. For high-impedance schemes the voltage may become very peaky on internal faults and curve (4) is more applicable. However, this is not gen~ral1y used even for high-impedance systems, the addItional voltage obtained being considered .as an add~tional safety-factoL In any case, the validity of using a curve would depend upon whether the relay used is responsive to Lm.S. values or average values.

SO%i IO~.v

KNEE POINT

o

> u

a

Exciting Current

FiG.

11.

KNEE-POINT VOLTAGE.

materials except, perhaps, mumetal. It is difficult to define this transition, and use is made of the so-called 'knee-point' voltage for this purpose. It is generally defined as the voltage at which a further 10 per cent increase in volts requires a 50 per cent increase in excitation-current as shown in fig. 11. For most applications, it means that the current-transformer can be considered as approximately linear up to this voltage. This voltage does not necessarily correspond to that given by the saturation factor and its associated burden, but will be of the same order.

Special Requirements for Protective Current-transformers Instruments and meters are required to work accurately up to currents of the order of full load only. Accuracy is not rquired above this and saturation may, in fact, be advantageous in limiting the overload imposed on a secondary burden. Saturation could therefore take place at secondary currents above about 150 per cent of normal rating but, in many cases, it will be considerably in excess of this because of the iron section needed to obtain the required accuracy. This is not necessarily so when high-permeability core-materials are used. Protective gear, on the other hand, is concerned with a wide range of currents from fault-settings to maximum fault-currents which may be many times normal rating. While larger errors may be permitted in protective current-transformers it is extremely important that saturation should be avoided whenever possible in order to eliminate gross errors. The widely differing requirements of current-transformers for instruments and for protection usually mean that it is advisable to provide separate transformers for these two duties. In smaller classes of switchgear, however, economic limitations may require that instruments, such as ammeters, are energized from the protective current-transformers. An acknowledgement of the special requirements of protective current-transformers is given by B.S. 2046, which is concerned with the specification of currenttransformers for non-balance systems of protection. B.S. 81, for Instrument Transformers, is under-going revision and may in future utilize some of the methods of

Knee-point Voltage

The transition from the unsaturated region to the saturated region of the open-circuit exitation characteristic is a rather gradual process in most of the core

73

accuracy and to saturation-factor. As most currenttransformer specifications seem to favour the 5-ampere level and as the I-ampere level is often preferable from protection design considerations, it is worth while reviewing the significance of the secondary level in more detail. As previously pointed out, the main requirement associated with protective current-transformers is that they should maintain their ratio with a prescribed accuracy for primary currents greatly in excess of the rated current. This factor is important in both slow-speed and high-speed protective systems and in both balance and non-balance systems. For slow-speed balance systems the required saturation-factor is determined largely by the steady-state stability conditions, but a much higher saturation-factor will generally be required for highspeed balance-systems due to the transient fluxes occurring in the current-transformers under fault-conditions. In some high-speed non-balance systems, such as distance protection, transient effects may have to be taken into account and similarly high saturation-factors will thus be needed. This requirement of high saturation-factor has become an important aspect of modern protectivesystems. The level of performance required of protective-systems has increased and system conditions have become more severe. In order to achieve adequate protective-systems it has been necessary to reduce the VA requirements to as Iowa value as possible and, in some cases, to a value which is low compared with the internal burden of the current-transformer and the external lead burden. With these considerations in mind, for high-speed low-VA protective gear a I-ampere secondary level is very desirable except for those current-transformers having primary ratings sufficiently high to give the required saturation-factor with a 5-ampere secondary. At these higher primary ratings the physical problem of

specifying performance given in B.S. 2046. It should be noted that B.S. 2046 is concerned with currenttransformers for protective systems such as overcurrent, earth-fault, and distance. In the latter case, special consideration may be necessary for high-performance high-speed distance. The requirements associated with balance systems of protection are so various and so dependent upon the particular protective system that it has not yet been considered advisable to attempt to standardise this type of current-transformer. However, the methods of specifying and defining output used in B.S. 2046 are applicable to current-transformers for balance systems and are to be preferred to those used in B.S. 81. In addition to the current-transformer tests specified in B.S. 2046, balance systems of protection would require conjunctive testing of some form either as type-tests or individual proving-tests.

Choice of Secondary Rating Though B.S. 81 and B. S. 2046 give a preferred value of rated secondary current of 5 amperes they permit a I-ampere or O· 5-ampere level to be used where (a) the number of secondary turns is so low on a 5-ampere winding that the ratio cannot be adjusted within the requisite limits by the addition or removal of one turn, and (b) the length of the secondary connecting-leads is such that the burden due to them, at the higher secondary current, would be excessive. Requirement (a) may be largely associated with metering applications, as the precise transformation-ratio of protective current-transformers is not particularly important so long as the current-transformers are all the same. It has already been pointed out that the number of secondary turns can have a marked effect on the capabilities of a current-transformer both in respect to Volts

150

'" ~ o

100

>

RCT=

300

FIG.

600A Primary Rating

12.

I-AMPERE SECONDARY.

74

In. (at 300A)

Winding drop

Volts

150

r--_.. .====~~==========

100 o

>

c o .;:;

Saturation Factor = 30

RL= I Jl

~

..

~

50

o·oaJ1.

Vl

Ro=0·04J1. (at 300A) Relay volts

o

600A

300

Pri mary Rat; ng

FIG. 13.

5-AMPERE SECONDARY.

5-ampere secondary level as shown below. Peak open-circuit voltage for I-ampere sec. VI = Kalp.n. Peak open-circuit voltage for 5-ampere sec. V s = K7alp.n/5 where K and ex are constants for given core-material, and n is the number of turns of a I-ampere secondary. VS/V I = 1·4.

winding I-ampere secondaries would, in any case, favour a 5-ampere secondary. The following analysis may help to bring out the particular problems involved in choosing the secondary level. Fig. 12 shows the saturation-voltages plotted against primary rating (and thus secondary turns) for a barprimary current-transformer of core-section 'a' and secondary rating of 1 ampere. Also plotted are the various voltage-drops, which would occur at a multiple of the primary rating, given by the saturation-factor. Typical values are given from which it is seen that, for a primary rating of 300 amperes and a saturation-factor of 30, a core-section of 3 square inches would be required. For a 600-ampere primary-rating the core-section required would be 2 square inches, since the required saturationvoltage is only 50 per cent greater and there are twice as many secondary turns. Fig. 13 shows the equivalent ca~e for a 5-ampere secondary rating, the VA in the winding and load being the same, but the lead burden being kept at the same ohmic value. It can be seen that, in order to give the same saturation-factor, a core-section of about 7 times that used in the I-ampere current-transformer would be required. Such a current-transformer would be difficnlt to accommodate and would often be impracticable. In many cases it would be necessary to accept a currenttransformer with a much smaller saturation-factor in order to permit accommodation. One of the points often quoted in favour of the 5-ampere secondary level is that it does not give rise to such high peak-voltages when the current-transformer is open-circuited. This is not always so if the lead burden is significant and if the same saturation-factor is provided in both cases. In fact, in the cases shown in figs 12 and 13, a higher open-circuit peak-voltage is possible with the

Some Steady-state Problems Fault Settings

In applying protective gear, it is important to be able to assess the primary fault-setting in relation to the minimum level of fault-current to be expected. This is relatively easy in relay-systems where the reflected relay-impedance is small compared with the effective value of ZM, the shunt exciting impedance, as it will be sufficiently accurate to refer the actual relay settingcurrent to the primary by the turns-ratio of the feeding current transformer. Such conditions will probably apply to overcurrent relays, some earth-fault relays, and some low-impedance differential relays. The value of relay-impedance may not be low compared with exciting impedance, however, in the case of low-set earth-fault relays, high-impedance differential relays, and lowimpedance differential relays in protective-systems where there are many current-transformers connected in parallel. Where this arises, the primary fault-setting must be obtained by referring the vector addition of total exciting-current and secondary relay-current to the primary by the turns-ratio as shown in fig. 14. The above general calculation will be sufficient for most cases, but it is applicable to a given ratio of current-transformer and a given relay-setting. It some-

75

Simple Case of Two Current-transformers in Balance

The simple case of two current-transformers and a differential relay is shown in fig. 18. The separate equivalent circuits of the two transformers are connected as shown for through-fault conditions where tQe primary currents 'in' and 'out' are equal. This equality will exist on the secondary level, provided the turns-ratio of the transformers is the same, and the return current-paths may be omitted, a simplified equivalent circuit being obtained as shown. It can be seen that the relay is connected across a bridge formed by the burdens and the exciting impedances. The condition for no unbalance current is given by R]/R z = ZMdZMZ' It is thus possible to obtain theoretical balance for differing current-transformer designs and loading by satisfying this requirement. This condition is only true when ZMl and ZMZ have similar phase-angles.

4~)'

Ip

N( 1/+

I'

Secondary output of feeding current-transformeJ,

-> ->\ ( IR + 3 IE . FIG.

14.

FAULT-SETTINGS.

times happens that the best choice of these parameters has to be made in the design stages to give a minimum primary fault-setting. In the first case, many relays such as overcurrent and earth-fault have a range of settings obtained by providing a tapped operating-coil. The VA burden at the relay-setting will remain constant, but the ohmic burden will vary and so will the accuracy of the currenttransformer if its design is fixed. The primary faultsetting will be given, as shown in fig. 15, by the vector sum of exciting current and relay current. Expressing primary setting as a function of relay-setting will give:

[piN

Is

I p = N«VA/ZMIs) + Is) The minimum value of Ip is given when VA/ZMI s = Is i.e. when the exciting current and relay current are equal. This is shown in fig. 16 for the case when the phaseangles of ZM and ZR are equal. When the phase-angles are unequal the same condition, i.e. ZM! = !ZRI ' gives a minimum primary-setting but the vector sum of the two currents must be taken. Another problem is the case where the turns-ratio of the current-transformer is variable and the relay-setting is fixed, as shown in fig. 17. A similar condition, = ZRI, is required for minimum primary-setting, the turns-ratio being chosen to satisfy this relationship.

Ip/N VA

Is + IE IS(ZMIE)

Ip/N

Is

FIG.

15.

+ .',1A . ZMIs

FAULT-SETTING:

FIXED CURRENT-TRANSFORMER RATIO. CONSTANT RELAY - VA.

I

I

IzMI

Steady-state Balance

The value of unbalance current in the relay-circuit of a balanced group of current-transformers carrying steady-state through-fault current is important in slowspeed systems of protection as it will determine the upper limit of stability. Even where care is taken to avoid saturation, some unbalance is to be expected where current-transformers of different design or loading are used. The equivalent circuit is particularly useful in obtaining an estimate of the unbalance which will result with a particular arrangement.

VA ZMIs

Is FIG.

76

16.

VARIATION OF FAULT-SE1TING WITH RELAY-SETTING.

Is

ZMcxNZ IpjN

kNZ

Is

+ IE

I + ISZR S

kNz

IS(N+;~)

Ip

For minimum Ip ZR

N

kN

i.e. ZR=kNz=ZM. FIG.

17.

MINIMUM FAULT-SETTING: FIXED RELAY-SETTING, VARIABLE CURRENT-TRANSFORMER RATIO.

When RdR z and ZMljZMZ are not equal, it is possible to calculate fairly easily the resulting unbalance current. Using Thevenin's theorem the voltage across the relay circuit, when this is open-circuited, is determined. The unbalance current is calculated by applying this voltage to the relay impedance and exciting impedances as shown in fig. 19. It should be noted that, for accuracy, ZMl and ZMZ are complex values, but some simplification is possible if they are of the same phase-angYe. In this type of calculation it is normally sufficiently accurate to assume that the impedances ZMl and ZMZ are linear, and some average values for these are obtained from the excitation curves in accordance with their respective approximate working levels.

ZMZ as shown in fig. 20. The approximate expression for out-of-balance current is also shown. For small unbalance ZMZ must be kept small with respect to 2Mb which is an advantage in tranformer protection where the high-voltage current-transformer is usually much inferior to the low-voltage one. This particular arrangement can be considered in terms of the ampere-turns on the inferior currenttransformer. The secondary current of the good current-transformer is sufficiently accurate to supply secondary ampere-turns to the inferior currenttransformer which almost balance the primary ampereturns. The small unbalance does not result in appreciable output, because of the low value of ZMZ' This approach leads to the name "Magnetic Balance."

Principle of Magnetic Balance Single-phase Balance of Multi-terminal Group

It can be seen from fig. 18 that, if the value of ZMZ is small compared with 2Mb the value of R z must be made small compared with R I . The limit of R! will be when there is no external lead burden and it be~omes equal to the winding resistance. This value of R z may be still too large for balance and to eliminate it from the relay connection an additional winding is provided on current-transformer 2 so that, in the equivalent circuit, the relay may be considered as being connected across

N

The use of equivalent circuits can be extended to the case of a number of current-transformers in a balance group under divided through-fault conditions as shown in fig. 21. When the exciting impedances and lead burdens are different the calculation is tedious although it involves simple circuit-calculations. In most cases, some simplification is possible. For example, if all the current-transformers are of the same

N

[p

[p

FIG.

18.

EQUIVALENT CIRCUIT FOR SIMPLE CURRENT-BALANCE.

77

Interposing Transformers

Vca-Vcb

v

Vca

FIG.

The transformers can be inserted into the equivalent circuit as shown in fig. 24, and calculations of unbalance are possible though more laborious than in the simple case. Generally speaking, their inclusion should be avoided unless essential to some feature of the protective system, wither as a summation-transformer or to change the level of current. There is usually some minimum required core-volume relative to the main current-transformer volume and this will depend on the particular duty. They have a special application in some modern systems of protection where the burden of the relay equipment is low compared with the lead burden. By reducing the current level and mounting the interposing transformers close to the main current-transformers the overall burden may be reduced and better performance obtained with a relatively small interposing transformer. In fig. 25 this condition would be given as follows: Voltage required from main current-transformer without interposing transformers =IpIN (R 1 +R 2) Voltage required from main current-transformer with interposing transformer = IplN (R 1 +R 2/n 2 +2r). Voltage required from secondary of interposing transformer = IplNn (R z+rn 2 ). The relative values of Rio R z, and r will determine whether any advantage is gained from fitting interposing transformers. It should be noted, however, that if it were practicable to obtain the overall ratio of Nn on the main current-transformer itself, this would be the better arrangement.

Ip

"- N'

Vcb

J'_

v

£"

Ip

Rl

(ZMl ) }Rl)

(Rl +R2)

Z

N' (ZMl +Z102)'

MI Ip RIZM2-R2ZMl -N'-'-ZMI + ZM2

19. SIMPLIFIED CALCULATION OF UNBALANCE CURRENT.

design and loading the equivalent circuit is reduced to that shown in fig. 22 and it can be seen that balance is obtained assuming the exciting impedances are linear. This would not be strictly correct and the calculation should be made taking the mean values of ZM from the exciting curve according to the respective working levels as shown in fig. 23. The divided fault condition, however, is normally capable of being reduced to the simple form of two current-transformers in balance, making the calculation of unbalance a simple matter.

FIG

20.

Steady-state Saturation

The Importance of A voiding Saturation When the primary current and secondary burden are such that the required secondary voltage is in excess of the knee-point voltage, a current-transformer will produce a secondary current of distorted waveform. This secondary current will contain a high proportion of odd

SlMPLE ARRANGEMENT OF MAGNETIC BALANCE.

78

[p/3

[p/3

R.

~-;;--J\NV'v-- ......----lp/3 N

[p/N

_·---,.----JV..,.,..--r-----,~--'ffl'--_--__+--

[p/3 N

---+---+-_ [p/3N

"'--"N\......

FIG.

21.

CURRENT-BALANCE WITH MORE THAN TWO CURRENT-TRANSFORMERS-DIVIDED FAULT.

---~

.r-"""R...,....

Ip/3N

... ·[p/3 N

·--r-"""'V---..,..----r:-""".,.....-~--__+-L-"\",.,~--__t---t_.

FIG.

22.

SIMPLIFIED EQUIVALENT CIRCUIT-DIVIDED FAULT.

R

FIG.

23.

\p/3 N

R/3

DIVIDED FAULT. ALLOWANCE FOR MEAN VALUE OF

79

ZM'

N

N

Ip_/N~n,--,.-~",R",'n"".--_-.._..J'I"'Rrv,"-_-.._.J\JR"l"'-_ _r--JvR."nv'\.-_-r_I;LN n

FIG.

24.

EQUIVALENT CIRCUIT INCLUDING INTERPOSING TRANSFORMERS.

harmonics, will have a larger ratio-error, and may have zero-points considerably displaced from those of the primary current. Such steady-state saturation must, in general, be avoided up to the maximum value of through-current in balanced and phase-comparison systems of protl~ction. In high-speed protective systems the requirements for transient conditions, discussed later, automatically cater for this. In non-balance systems the results of saturation, while not so serious, still require some consideration. The harmonic content and limitation of output may modify time/current characteristics of overcurrent relays, directional relay characteristics, and the accuracy of distance protection. As with any non-linear system, calculation of the effects of steady-state saturation is not simple. It is not often that exact computation is required or justified, and as the effects will depend on the type of circuits and relays connected to the secondary winding actual test and observation are generally necessary. However, an understanding of the mechanism of steady-state saturation is worth-while and the following sections describe the effects obtained with simple secondary loads of resistance, reactance, and capacitance.

that the violent distorti.on takes place at a current about half the value corresponding to saturation in the previous two cases. This is because the non-linearity in the open-circuit impedance of the current-transformer is such that the incremental inductance in gradually reducing at flux densities above half the saturation-level. Ferro-resonance causes the cyclic peak of currentdistortion at such levels, this current-peak being due to the flux level in the inductance being driven beyond its normal level, giving saturation and consequent discharge of the capacitor through this saturated inductance. In the oscillgrams shown, the distortion is of relatively short duration and the waveform recovers to normal. The results given by the graphical analysis are for conditions of high current for which saturation could be normally expected. Because of the risk of resonance and distortion, the use of a capacitive burden is not common. Where it is used, care must be taken to design to much lower values of maximum flux-density than would normally be acceptable. There are other problems associated with capacitive burdens in relation to transient response which make them undesirable. I:n

Saturation with Capacitive Burden The combination of capaCIty and non-Imear inductance is known to produce complex waveforms through the action of what is known as "ferro-resonance." The solution of these problems is difficult, even with the simplification of two-stage excitation characteristics. The general shape of the waveform is as shown in fig. 29 where it appears derived from graphical analysis and fig. 31(c) which reproduces the actual oscillograms, 9 and 10. Oscillogram 10 shows some general agreement with the graphical result but the interesting feature about it is

rn'

N

FIG.

25.

INTERPOSING TRANSFORMER AND LEAD BURDEN.

80

Ie with L, Ie with L,

Is

t =

-

I

-Is ~.-

TIME

01 I

I

L,

FIG.

26.

1

L,

L,

GRAPHICAL CONSTRUCTION SHOWING SATURATION WITH RESISTIVE BURDEN (FINITE SLOPE IN SATURATION).

high value and short duration will occur as the primary ampere-turns cross the zero, from the negative to positive saturation-levels and vice versa as shown in fig. 30. If the saturation-level of ampere-turns is small compared with the peak primary ampere-turns, the peak value of voltage will be directly proportional to the peak primary ampere-turns, since the primary current has an approximately constant slope in this region. Oscillogram 11 (fig. 32) shows this waveform for a low-loss mu-metal core but it will be noticed that the pulse of voltage is displaced from the primary current-zero and has dissimilar leading and trailing edges. This is due to the effect of the hysteresis loop. Fig. 32 shows a construction which takes this into account and which agrees closely with the flux and voltage waveforms shown in oscillogram 11. It can be seen that the hysteresis effect does not materially reduce the value of peak-voltage.

Peak-voltage on Open-circuit or High-resistive Burden

The peak-voltages developed in the secondary winding do not generally present any problem provided that saturation does not take place. In recent years, however, attention has been given to the risk of high peak-voltages in current-transformers which have been inadvertently open-circuited on load or, under fault-conditions, in current-transformers which feed high-impedance relays. In both cases, considerable saturation takes place with consequent high peak-voltages. These are usually more of a problem in modern high-performance currenttransformers, particularly those of the post-type, with multi-turn primaries. For the conditions referred to, the peak primary ampere-turns are greatly in excess of the ampere-turns required to saturate the core. In the simple case, neglecting secondary load and iron losses, a pulse of voltage of

81

Is

v

Js

FIG. 27.

I,

SATURATION WITH RESISTIVE BURDEN (ZERO SLOPE IN SATURATION).

IplN

JJ 'IB L

Ip/N

LB

Ip/N

t FIG. 28.

SATURATION WITH REACTIVE BURDEN (ZERO SLOPE IN SATURATION).

82

Saturation with Resistive Burden

A simplification is obtained if the slope of the excitation curve is assumed to be zero in the saturated region. The transient when changing into the daturated region then disappears. The resulting waveshape is shown in fig. 27. It can be seen from the analysis and the oscillograms of progressively increasing primary current that the distortion resulting from saturation is generally in the form of a loss of the trailing part of the half-cycles of secondary current. This gives rise to a general loss of output, considerable harmonic content, and a possible large shift in the zeroes of the secondary current. This latter effect is especially important with respect to phase-comparison systems of protection. It is sometimes wrongly assumed that such protection is more immune from the effects of saturation than differential protection. This, as can be seen, is not necessarily the case.

The effect of saturation when the burden is a pure resistance is shown by the graphical analysis of a simple case (see fig. 26) and by the oscillographic records 1-4 (see fig. 31). The waveforms of secondary current and exciting current in fig. 26 are obtained by assuming a two-stage excitation curve for the current-transformer with constant slopes in both the saturated and unsaturated regions. The analysis is started at any point in time and the circuit conditions are changed when the exciting current passes through the values corresponding to the onset of saturation. With this type of change, a connecting exponential transient involving the magnetizing inductance and the secondary resistance must be included at each change. The transient in the unsaturated region is assumed to be long and is approximately equivalent to a constant offset in the exciting current. In the saturated region, the transient is of short duration.

Prospective

Is

-Is-I--

,~o~

--

TIME -;+0

-I.,

Jp/N.

.-

~

181

,

t'

I FIG.

29.

SATURATION WITH CAPACITIVE BURDEN (ZERO SLOPE IN SATURATION).

83

.. Current, Ip=",It

ls......--+~~-

-

- - - - - - --'''''--_____

B-H Curve

TIME..-

'" V = -k",I -JIo._--J

FIG.

30.

OPEN-CIRCUIT PEAK-VOLTAGE, IGNORING LOSSES.

Saturation with Inductive Burden

tained with a slow decay by the inductance of the load. Successive oscillograms of increasing primary current are shown in the oscillograms 5-8 (see fig. 31) which line up with the graphical waveform. It can be seen that the effect of saturation, in this case, is to lose the peaks of the secondary-current waveform, leaving zeroes relatively unchanged. Phase-comparison systems would be less affected by saturation of this type than differential systems. This is useful in some phase-comparison systems where the main secondary burden may be largely reactive due to the use of sequence networks.

Similar analytical methods may be used in the case of an inductive burden, the exciting current having a different phase-relationship from that of the resisitive case. Again, connecting transients are required but in this case the time-constant in the saturated region will not be zero, but will be determined by the Z/R ratio of the burden and the current-transformer-winding resistance. The resulting contruction is shown in fig. 28 and it can be seen that the secondary current does not drop to zero when the current-transformer saturates, but is mainC.T. and Load Data

0

+-_~_

Jp = 125

Ip

~

250

1p

~

500

Ip = 1000

Ip

~

250

(p

~

500

jp = 1000

60

Ip

50.,

N = 300

(a) Resistive Burden. Ip

(] N

~

00

125

50,.,

300

(b)

Reactive Burden. Ip~

b

N

~

~

125

50,.,

300

(c) Capacitive Burden. FIG.

31. eRO records showing effects of steady-state saturation. (Primary and secondary current-traces superimposed).

84

-

TIME

B-H Loop

FIG.

32.

OPEN-CIRCUIT PEAK-VOLTAGE, ALLOWING FOR HYSTERESIS.

The effect of the eddy-current iron-loss is to give an expression for peak-voltage as follows:

In most practical cases, the effect of eddy-current iron-loss or secondary resistive-loading must be taken into account. As the eddy-current loss can be represented by a shunt resistance in the equivalent circuit, its effects will be the same as a secondary loading resistance. Fig. 33 gives the mathematical and graphical solution to this problem. It can be seen that the transient generated in the shunt reactance and loading resistor slows down the rate-of-change of flux, alters the waveform of the secondary voltage, and reduces it peak value. Analysis for various values of resistance shows the dependence of the time-constant, and thus the peak value of voltage, 'on the resistance; but the area of the secondary voltage-wave remains substantially constant, as one would expect. Oscillogram 12 (fig. 33) shows the practical results obtained by loading the secondary winding with various values of resistance, starting initally with the open-circuit condition of oscillogram 11 in fig. 32.

v=

Kl~

The value of K depends on the core dimensions, lamination thickness, type of material, etc. B also depends on some of these but it is 'generally a fractional index ranging from about 0·4 to 0·6. Design-data curves have been evolved to enable peak-voltages to be estimated with corrections for external resistive loading, but there is still some disagreement between the calculated figures and the test figures. Practical testing of transformers is difficult as it is necessary to preserve a sinusoidal waveform on the primary and this requires high-power test-supplies. Calculation methods are of considerable value, therefore, and work is going on to improve their accuracy.

Differential Equation: dimidt

Solution: 1m =

.

I w t-

iR

=

i-i m

=

---"'-.! [ rx

FIG.

33.

rx w It

ocI[ 1_ e -rx(t + to)] W

-rx(t I-e

PEAK-VOLTAGE WITH HIGH-RESISTANCE SHUNT.

85

+ rx i m =

+ to)]

CHAPTER 5 Effects of Transients in Instrument Transformers By F. L. HAMILTON. INTRODUCTION Curren~-transformers and voltage-transformers play an important part in the operation of modern powersystems. They provide the link over which information is derived from the main high-voltage system for the purpose of measurement, control, and protection. Measurement and control are generally concerned with the longer-term steady-state conditions and transients will not be of any great significance. Protective equipments, particularly the modern highspeed types, are concerned with instantaneous conditions. The performance of current-transformers and voltage-transformers is therefore of considerable importance to protective gear at all times and particularly under conditions of fault on the primary system. The subject of the transient response of instrumenttransformers is therefore dealt with in this article, with particular reference to its effect on protective gear. The transient response will be the same in relation to instruments and meters but its significance will be less.

long duration and impose onerous conditions on current-transformers and are thus of considerable importance. The emphasis in this article is therefore given to this type of current-transient. Voltage-transients

Transients in voltage wave-forms can occur due to primary faults or to switching operations. They are generally of the form of a step-function representing a sudden change in voltage and may be accompanied by highfrequency oscillations due to the reactance and capacitance of the primary circuit. Again, these oscillations are of relatively short duration and are not of great significance to secondary apparatus. In some cases, where the phase-angles of lines and power-system components are not equal, the flow of d.c. exponential fault-current can give rise to d.c. exponential voltages and these may have to be taken into consideration. Fig. 2 shows how those d.c. voltages may occur under fault-conditions.

Primary and Secondary Transients

Secondary transients

Transient conditions are set up in the power-system whenever it is dlstu:cbed, either by the occurrence of a fault or by the re-arrangement of connections, for example, by switching operations. These transient conditions give rise to transient voltages and currents which, under idealised concitions, should be reproduced accurately in the secondary circuits of voltage and current transformers. Since practical voltage-transformers and currenttransformers are far from ideal, transients receive considerable modification in passing through them and it is the errors and imperfections so caused which are of interest to protective-gear engineers. In general, it is sufficient to consider the response of current-transformers with respect to current-transients on the system and of voltage-transformers with respect to voltage-transients.

Besides the secondary reproduction of the primary transient, secondary transients may be generated in the internal and external circuits of instrument transformers under rapidly changing conditions. These secondary transients may be extremely important and will depend upon the design parameters of the transformer and the nature of connected secondary burden.

Reproduction of Transients in Voltage-transformers Voltage-transformer devices at present in use are of two main types: (a) A conventional transformer having primary and secondary windings and a magnetic circuit of high permeability. (b) A capacitor-transformer device using a capacitor voltage-divider, a tuned circuit, and an auxiliary transformer of conventional type. The two types are widely different in their characteristics and respond to transients in different ways. The response of the capacitor voltage-transformer (CVT) is of considerable importance since this type of transformer is being applied almost universally at systemvoltages of 132kV and above.

Current·transients

The main forms of current-transient which may occur in a power-system are: (a) D.C. components of exponential form such as those which are produced at the start of fault conditions (see fig. 1.). Similar currents can be produced under load conditions by the switching of reactive circuits. (b) High-frequency oscillatory currents caused by switching operations or restriking conditions in circuit-breakers. The latter type of transient is generally of short duration and is not of major significance to the secondary equipment. D.C. components, however, are of relatively

Transient response of wound voltage-transformers

The transient response of wound voltagetransformers is generally good, and the secondary reproduction of the transient primary wave-form is substantially correct.

86

Ils Xs - COMPONENTS OF SOUIlCE IMPEDANCE UP TO IlELAY POINT

ilL XL-COMPONENTS OF IMPEDANCE BETWEEN IlELAY AND FAULT

I

t_ -1. ~'AXIMUM PRIMARY TRANSIENT CURRENT ~I. T T

co

EFiLCTIVE PR:MARY TIME CONSTANT •

INITIAL VALUE OF CURRENT

FIG

1.

~ (X~ + X~) w(

-R V

( S + RLl

S

+

L)

[J I ,w1 22 1 T •

PRIMARY D.C. EXPONENTIAL CURRENT TRANSIENT.

In general, the design requirements for normal steady-state accuracy are low winding resistance and leakage reactance compared with the connected burden. These, together with relatively low working fluxdensities tend to minimise the problems of transient reproduction. A detailed analysis is not often necessary, but some general consideration of the effects is of interest. The most common primary transients likely to be impressed up on a voltage-transformer are caused as follows: (a) Energisation or de-energisation of the transformer at normal voltages- equivalent to a circuit being switched in or out. (b) Sudden increase of voltage to a value above normal. This can occur on a system with insulated or resistance-earthed neutral with voltagetransformers connected between line and earth. (Increased voltage is V3 time normal). (c) Collapse of voltage from normal system-voltage to fault voltage. This happens when a fault occurs on the primary system, the fault voltage depending on the system constants and the type and position of the fault.

Recovery of voltage from the fault voltage to normal system-voltage- which occurs when the fault is cleared by operation of circuit-breakers. (e) A d.c. exponential voltage which may occur under (c) if the system impedances have different time-constants.

(d)

Transient voltage at R :;:. v

dt SolVIng, y

Ie

Ie

- t

T

[

RL -

XL (RS ' RL)] ----:-(XS ; XL)

-.1 [mRL m -.

For one important case RS

~

RS ]

T

V.

_m_ _ . (m

+ 1)2

~. XL

ThiS gives a maximum Initial value of v when m =

FIG.

87

where m

a

Vo SL

Ie. Xs

•

I

I,

XL [RL usually being small with respect to XL

2.

D.C.

l

EXPONENTIAL VOLTAGES.

Vs

R

SWITCH ON

SWITCH

OFF~

'm

rp

< > - /--/VV\N'--~---""'---<:>

R - - ; . - Vs

L

- L_ _- - - J L - - - - - o

c;- /

[r Note

If voltage collapses due to fault, then T2

~

<<

R]

TI

FLUX

V2 (N.B. V 2

TRACE INVERTED) (a) FIG.

3.

(b)

(c)

SWITCH-ON AND SWITCH-OFF TRANSIENTS (WOUND YOLTAGE-TRANSFORMERS- LINEAR CASE) WITH TYPICAL OSCILLOGRAPH RECORDS, A, B, AND C.

88

In the case of switching-in a voltage-transformer, the transients are similar to those in power transformers, the main transient appearing as an exponential magnetising-current, with possible consequent doubling of peak flux-density at the start of the transient. The output voltage is not unduly affected and, with the small frame-sizes of such transformers, the transient timeconstants are fairly short being of the order of one or two seconds. At the switch-off point the magnetising current will decay exponentially through the connected burden and iron loss resistance, and will produce a small d.c. ouput-voltage depend on the relative values of magnetising current and load current. The basic forms of the switch-on and switch-off transients are shown in fig. 3 together with typical oscillographic records a, b, and c. If a voltage-transformer were designed to work at relatively high flux-densities similar to those of a powertransformer, some distortion of output wave-form would take place due to transient saturation and this would be exaggerated further if there were initial remanence in the core of the same polarity as the transient flux rise. The increased magnetising current under such conditions could cause appreciable volt-drops in the primary resistance and leakage reactance, as shown diagrammatically in fig. 4 and associated oscillograms d and e. These results are exaggerated in order to enhance the effects. The effects of transient flux rise would be further increased in the event of a rise in voltage above normal, as in the case of an earth-fault in (b) above. Considerable attention is given to the avoidance of serious saturation in voltage-transformers, especially where this might lead to non-linear resonance (ferroresonance) between the neutral inductance of the transformer and the capacity of the associated primary system. This phenomenon was occasionally experienced some years ago, in the circumstances shown in fig. 5. Such conditions can lead to high over-voltage harmonics (neutral inversion). Designing for low flux-densities and resistance loading of secondary windings have eliminated this problem. In practical voltage-transformers, the windings have distributed capacity to earth between layers and between HV and LV windings. This capacity, in conjunction with the transformer reactances, can produce oscillatory transients at the switch-on and switch-off points in addition to those described above. They are generally of high frequency and short duration and are not usually significant, although it is well to appreciate that they can occur. Examples are shown in fig. 6 and oscillograms f and g. The case of reduction or restoration of voltage, during or following a fault condition are generally similar to those described for switch-on or switch-off. However, when a fault occurs on the primary, the voltagetransformer primary winding is effectively shortcircuited and the flux at the instant of fault will die away exponentially. Rapid restoration of the voltage may occur while this flux still exists so that some increase in the peak flux-densities might be expected on this account.

The condition of a d.c. exponential voltage on a wound voltage-transformer is fortunately not too severe in practice. The solution for transient secondary voltage and magnetising current is shown in fig. 7. It can be seen that the secondary output has an exponenital voltage in addition to the 50 cis voltage, this transient changing polarity at the point of maximum d.c. magnetisation. The value of d.c. magnetisation will depend on the power-system parameters and the secondary loading. If typical values are inserted in the expressions derived in fig. 7 it will be seen that the maximum d.c. flux-density is not much in excess of, and may be even less than, the normal steady-state peak flux density at full voltage. With the use of normal flux densities, saturation can usually be avoided. Summarising, it can be said that, with the normal designs to be expected in practice, the transient response of wound-type voltage-transformers is very satisfactory. The most serieous phenomenon which might occur is that of ferro-resonance and this is generally avoided by the use of relatively low flux-densities and as much resistance loading of the secondary as is practicable, either directly as secondary load or in the form of a loaded tertiary-delta winding. Transient response of capacitor voltage-transformers

The primary voltage transients to be considered are those already described for wound voltage-transormers, but the capacitor voltage-transformer has far more complexities because it is basically a tuned circuit and can generate transients of its own during rapidly changing conditions. In order to consider the response of this device, it is necessary to consider the basic circuit and its method of operation. Fig. 8 shows the general layout with the equivalent circuit in its reduced simple form. In this equivalent form it can be readily seen that the capacitor volage-transformer has the elements of a band-pass filter. The band-width and cut-off frequencies depend on the choice of design parameters, but with many standard designs the power-system frequency is in the region of mid-band. Under shock excitation, such as occurs with sudden change of primary voltage either under fault conditions or switching conditions, the device will ring at two frequencies, one below the supply frequency e.g. 8-16 cis and the other above the supply frequency, e.g. 200-300 cis. The former oscillations are between the series capacity and the magnetising reactance and the latter are between the series reactance and the leakage capacitance. The magnitude of the transients will depend on the particular point-on-wave at which the voltage change occurs. The duration of the transients will depend on the amount of damping present i.e. the iron and copper losses of the various components and, in particular, the value of resistance in the load. The most pronounced effects will be experienced when the voltage is suddenly reduced, e.g. on the occurrence of a fault, since in this case the transient may be superimposed on a relatively small power-system voltage. Under these conditions, relays such as distance or directional relays may be modified in their performance. The restoration to normal voltage after a fault is not

89

'm _Vp

_v,

R

L

sao v

/

I

analysis

],.k'/

~

,

Typical values used (or

3

)00

R

-

1m

S:lt

\ r-Jorm:ll pC'Jk s.s

1

m

'm -

Vp & V,

'm

i m ptak

------

t

.-."

~alurated

I

; value i m

(

•

/

t

\

\

/

normal

(stead Y ltc1lei m

\

\ \

('~lle f

00 )'

j~l

- -;- /~

p('zk)

\ i m during ~

saturation

/

I

I

i

.~.

/

\

~!

I

4.

/

. dun ngsa1uratlon

\

/

\

I

/

\

........ J

',./

Tinle·consunt T2 in satllrated region =.::.'=

FIG.

I

'vc prospective im

i

~

/ 1~ .
/

- - - - ",---" -+

'm

t

;' \

/

/

_.i-

IOO~. 3 ~

0'005 sec.

WOUND VOLTAGE-TRANSFORMERS-SWITCH-ON TRANSIENT WITH SATURAnON; SEE OSCILLOGRAMS D AND C.

90

R 0---

y 0---

B

0---

EARTH

Lw

EAR1H

B "-

"-

"-

"-

"-

NG

"-

"-

"-

R

EARTH /

/' ./ ./

./ ./ ./

Y

The neutral earth-point is moved outside the system-voltage

~.

Note the voltage between N G and Earth is not of fundamental frequency. Under normal condition I/Cw < < Lw, but if saturation takes place series resonance may occur between the saturated inductance on one phase and the capacitive inductance on the other phase, with consequent high voltages and displacement of the neutral. FIG.

5.

NEUTRAL INVERSION-BASIC EFFECT.

91

"

r - - - - -," ,- - - - - l "

1 I

1

-

-,- 1

~vs

I 1 1

'p

'p

"

_v.

(f)

(g)

FIG. 6. WOUND VOLTAGE-TRANSFORMERS-EFFECT OF WINDING CAPACITY (SEE ALSO OSCILLOGRAMS F AND G). THE FREQUENCY OF THE H.F. OSCILLATION IS APPROXIMATELY THAT OF THE CAPACITY AND PRIMARY LEAKAGE REACTANCE FOR THE CASE OF COLLAPSE AND RESTORATION OF VOLTAGE.

92

-, v---=voe

T

T T

=

__

Assume rs &

t

Let va

~

~

kY (see fig. 2), where Y

-va (-~). e T ~ 1m + L rP Vp

Xs

«<

R.

x p < < < LW,and neglect iron loss

system time-constant

. dim -d t

~ ~

. gives . . ~ (v- o ) ( e-~t -e-~t) . Solved, thIS 1 m ~ Q.t'-~ rp

rp

I

f'

peak value of normal voltage.

~ ~-L'

(Usually ~> > ~).

Solution for maximum value of im, I

., I If ~ < <

~, i'm ->

k( ~P p

)

m

~

kY ( Y --fp

)I-y , were h Y

~

~-

CI.

1m , where 1m ~ peak steady-state magnetising current at normal voltage.

For maximum case of fig. 2 and for 70 line, Xs 0

m

XL

~

XL --

RL

k Max. i'm

~ l!f(~:)lm

=

it (2:~)lm ~

7.

tan 70°

~

TIl

(m-t-ff2

2·75 RL

•

XL

I

n

0·5 1m

Maximum d.c. excitation for example shown FIG.

~

~

50% peak a.c. excitation at normal voltage.

WOUND VOLTAGE-TRANSFORMERS- RESPONSE TO D.C. EXPONENTIAL.

93

0

I

1

CH X N:I

y

CL

BASIC ARRANGEMENT OF CAPACITOR VOLTAGE-TRANSFORMER

R,

em

VOUt

Vln~

FIG.

8.

Equivalern leakage capacity

EQUIVALENT CIRCUITS OF CAPACITOR VOLTAGE-TRANSFORMER.

94

consequent overvoltages, distortion of output voltage, and perhaps sustained flashover on the protective gap. Record (j) show the results of this effect which has been deliberately exaggerated in an experimental transformer. The avoidance of the above conditions is essential and practical designs of capacitor voltage-transformers are arranged to have low working flux-densities in both the reactor and the transformer. Since it is necessary to maintain as high a degree of damping in the circuit as possible, the maximum permissible resistive burden should be used.

quite so significant, the transient being superimposed on the normal working voltage. The damping may well be an important factor and it is better that capacitor voltage-transformers be resistance loaded up to their rated burden in order to improve the transient performance. Typical oscillograph records of capacitor voltage-transormer wave-forms are shown in fig. 9 for the various conditions of collapse and restoration of voltage. Little difference is observed beween the conditons of voltage being switched on or off and the conditons of collapse or restoration. This is understandable when considering the equivalent circuits, the difference being only in the inclusIOn or omission of the highvoltage capacitance. In the case of the d.c. exponential primary voltage, the device being essentially a band-pass filter will not reproduce the d.c. voltage very faithfully and this transient will be attenuated very rapidly. There will, of course, be the usual oscillatory transients at the commencement due to the shock excitation. The response to this type of transient is shown in record (h), the oscillogram being taken by switching in at the fault voltage in order to avoid confusion with transients due to collapse of voltage. The lower capacitor of a capacitor voltagetransformer is provided with protective spark gaps which may flash over under impulse conditions on the primary circuit or for short-circuit conditions on the secondary circuit. Flashover in the former case is usually of short duration, but one may expect transients to be set up in the capacitor voltage-transformer circuit due to this shock and these transients are similar to those already described. The conditions may be made more severe by repeated shock excitation under intermittent flashovers. Most of the transient conditions in capacitor voltagetransformers can produce flux densities in the step-down transformer in excess of normal, but the condition of flashover at the spark-gaps can produce.the most severe increase, e.g. as high as 3 times normal. This increase, added to possible effects due to remanence. may cause the transformer to work in the non-linear region of its magnetic circuit. Such conditions can give rise to transient or even sustained ferro-resonance between the capacitance and the transformer shunt reactance, with

FAULT APPLIED BY CLOSING S

Xs

WOUND

V.l.

C.V.1.

(h)

Summarising, there are far more possibilities for distortion of the secondary wave-form to occur in capacitor voltage-transformers than in conventional wound-type voltage-transformers. Care in design and loading can reduce these, but the natural ringing of the circuit under transient conditions is to be expected. The effects of such ringing are not usually very great in practice, their duration not being very long. Where relays are used, they are generally operated by currents derived from the secondary voltages and the high-frequency transients at least will be considerably reduced in terms of the current produced in the reactive circuits of relays. The many advantages of the capacitor voltage-transformer at higher voltages, both for economy and safety reasons, make its use desirable even when its transient characteristics are somewhat inferior to that of a wound voltage-transformer.

Rl

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FIG.

9.

CAPACITOR VOLTAGE-TRANSFORMER TRANSIENT RESPONSE.

96

through various stages of simplification. The final simple circuit is possible because, in most cases, toroidal-wound ring cores are used and the leakage reactance may be neglected. The complete subject of current-transformer transient performance including saturation, nonlinearities, balanced working, and the effects of various types of burden is too large to be dealt with here, but the basic phenomena may be brought out by considering the secondary currents and exciting currents of a currenttransformer when working with. a simple resistive load.

Transient Response of Current-transformers The most important transient condition 10 be considered in the operation of current-transformers is the d.c. exponential current which generally occurs with a primary fault. In order to simplify the problem of under"tanding the behaviour of current-transformers under such conditions, it is necessary to look at (he currenttransformer in terms of its simplified equivalent circuit. Fig. 10 shows the basic circuit of a curren [-transformer

SY~TEM VOLT AGE lp ~ SYS EM IMPEDANCE

~2

is very small with respect to system impedance

EQUIVALENT CIRCUIT REFERRED TO SEC. LEVEL rp

x,

r,

Rj

For ring-core type, further simplification gives: r,

Rj

Fo,- transient investigation of magnetising current: Ip/N

R

l

Xm

Wi rs ZL FIG.

10.

where R includes winding resistance, iron loss, and burden.

Shunt magnetising reactance. Iron loss resistance. Secondary winding resistance. External burden.

EQUIVALENT CIRCUITS FOR CURRENT-TRANSFORMERS.

97

~W""

(",(

CAS~

PRIMARY TRANSIENT

R

~ 1

~ I cos Nt-Ie -xt

rt.

~

~

Primary time constant.

dim. dt + ~ 1m

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-(;d

Secondary time-constant

),

With reasonable approximations the solution is: im

~

I. ~-. sin Nt N

I ( _~) (e -~t -e -rt.t) rt.-i" Q

I

I

V

V

Steady-state term

(CX~1l ) I

""

Transient term

,--

"

-(-~)I OC-i!

VT\ -/_/,/_1_-_,->,,,""\--/ -------------.-' I - '-' . / He~dy·Slate 1m

\

,, \.

J

,

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/

/ \

/

/

\ , h,

!.l.c.

FIG.

11.

n.

[~] I..c

TRANSIENT MAGNETISING CURRENT (NO SATURATION).

98

Basic form of magnetizing-current

Basic form of the secondary current

The general problem of a transient primary-input current to the equivalent circuit is shown in fig. 11. The primary current contains two terms, the d.c. transient current and the a.c. steady-state current. The magnitude and polarity of the d.c. transient will depend on the instant of time at which the fault occurs. In the interests of simplicity, the condition of maximum primary transient is taken. The time-constant, and thus the duration of this transient, will depend on the effective X/R ratio of the primary circuit. This is assumed to be fairly large, i.e. 10 or more, as is often the case in practice. The expression for the magnetising current may be solved and takes the form shown. The total magnetising-current has two terms, the steady-state term and the transient term. Some simplification and approximations are made in order to bring out basic principles. The transient magnetising-current is in the form of the difference of two exponential terms, having the same initial value, but having different time-constants. One has a time-constant equal to that of the primary circuit and the other equal to that of the secondary-circuit resistance and shunt inductance. In most cases, the latter is long compared with the former. From this point arises one important fact, that the transient conditions in the current-transormer core may persist after the d.c. primary transient has disappeared. The general form of the secondary magnetising-current, including both transient and steady-state components, is shown in fig. 11. It will be noticed from this that the rise of transient exciting current is largely dependent on the primary timeconstant whereas it decays largely in accordance with the secondary time-constant. In the simple idealised case where the shunt inductance is linear, the flux in the current-transformer core would be of exactly the same form. The form of the magnetising current and flux transient gives the key to the transient performance of currenttransformers. If the expression is solved for the maximum value, it can be shown, with suitable approximations, that this value is related to the steady-state value by the expression:

The form of the secondary current can be obtained readily as the difference between primary current referred to the secondary level and magnetising current. This is also in the form of a transient component and steadystate component. The transient is again the difference between two exponentials, one having the primary time-constant and the other the secondary timeconstant. The initial values, however, are unequal, giving the initial transient secondary current equal to that of the referred primary current. The general form of this transient is shown in fig. 12. It can be seen to be generally similar to the primary current, but reduced by the value of the magnetising current, and is of changing polarity. The point at which the secondary transient crosses zero corresponds to the point at which the magnetising current is equal to the referred primary transient current, i.e. all primary transient is expended on exciting the core. This also corresponds to the point at which maximum transient excitation takes place and in a linear system, the point at which maximum transient flux-density occurs.

The effect of inductive burden

The case of an inductive burden often occurs in practice. It can be shown that, for most practical cases, the maximum value of transient flux-density is dependent only on the resistive component of the secondary burden. The steady-state component of flux is, of course, dependent on the total secondary impedance. The considerations given to the resistive burden are therefore applicable. Capacitive burdens are considerably more complex and are difficult to analyse. In most cases, capacitive burdens are avoided because of the difficulty of preventing ferro-resonance and they are thus not of great practical significance.

Effect of iron saturation

As already mentioned, the high d.c. flux densities produced under transient conditions frequently lead to saturation of the magnetic circuit. Such saturation causes non-linearities in the shunt inductance, which lead to drastic modification to the linear case previously considered. Quantitative analysis is difficult as with most nonlinear systems, but, with certain simplifications, an understanding of the effects may be obtained. The greatest simplification is to assume that the shunt impedance is a two-stage inductance with the characteristic shown in fig. 13(a). This is further simplified if the second-stage inductance is taken as zero, as in fig. 13(b). This characteristic is approached in such materials as mu-metal and greatly facilitates the study of transient effects. Fig. 14 shows, for a resistive burden, the magnetising current and prospective fluxes under transient conditions for the linear case, i.e. with no saturation, only the

~(Iac). Rp As the value of Xp/Rp may be quite large, i.e. 5-30 according to system conditions, it can be seen that the peak transient flux-density may be very much larger than the steady-state value, and that the effective primary time-constant determines this value. Bearing in mind the fact that the steady-state value lac may be many times (up to 100) that which occurs under normal load conditions, the transient condition imposes a very high flux-density in the iron circuit of the currenttransformer, and transient saturation will be experienced in many cases. The consequence of such saturation will be further referred to later.

99

GENERAL fORM Of SECONOARY CURRENT fL

-

I

COSt' + I [S 0:- ~

Steady State Term

-~, e

t

l 13 e-ex ]

ex

0:-

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1/13 TRANSIENT SEC. CURRENT

FIG.

12.

FORM OF CURRENT-TRANSFORMER SECONDARY TRANSIENT OUTPUT.

The most important aspect of the region ot saturation of the core can only be appreciated when both the d.c. transient component and the a.c. steady-state component are considered together. This is shown in fig. 15, the prospective values without saturation being shown dotted. The combined a.c. and .d.c. flux curve will enter the saturation region at some point, and again all the primary input is by-passed through the saturated shunt inductance. However, due to the cyclic variation in the primary input, the core will come out of saturation for some period of each cycle. This can be appreciated by the fact

d.c. component being considered. This condition WIll exist until the magnetising current reaches the value corresponding to saturation. At this instant the inductance becomes zero and the total primary current becomes expended on exciting the core, the secondary output disappearing. This condition will last until the primary transient current has reduced to the value corresponding to the saturation point. From this point onwards, the core comes out of saturation and the coreflux decays in a transient largely decided by the secondary time-constant. The secondary transient in this region is of negative polarity.

100

v

v

(.)

",

"

(b)

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, , , , ,

_ _ _

_ _ _ _ _ _ _

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FIG. 14.

D.C.

/

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m

- -------__ -----.. -.......

-

TRANSIENT ONLY-EFFECT OF SATURATION.

101

Primary and Secondary currents are approximately equal except for unshaded areas occurring when the core uturates.

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FIG.

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CURRENT-TRANSFORMER TRANSIENT RESPONSE WITH SATURATION-RESISTIVE BURDEN.

Remanence

that the negative loops of primary current require a negative flux change, i.e. reducing flux. The flux will reduce from saturation for the duration of the negative loop and again start to increase as the positive loop commences. It is easily seen that there will be a period of non-saturation on the positive loops as shown in fig. 15, such that the area on the positive side is equal to that of the negative loop. The secondary output wave-form will thus be distorted by loss of the output on the positive loops during the period of saturation. As the primary transient decays, the wave-form becomes more symmetrical and less of the positive output is lost until eventually the core fails to saturate. Note that it is the trailing edge of the positive loops which is lost during saturation. This is shown also in oscillogram record (k). With a reactive burden it can be shown, in a similar way, that the top part of the wave-form is lost during the saturated period. This condition is shown in oscillogram record (l).

From the preceding considerations, it can be seen that transient saturation is difficult to avoid under practical working conditions and that the errors and transient distortion produced can be considerable. This is so even when the full range of core flux is available. The presence of remanent flux in current-transformer cores can considerably increase these problems. Ring-core current-transformers have low reluctance cores with no air-gaps and the loop characteristics are such that remanant flux densities of from 6000 gauss (Stalloy-type materials) to 8000-9000 gauss (cold-rolled grainoriented steel) are easily obtained. Such conditions can occur, for instance, after a transient has been experienced. Instead of the transient flux decaying to zero, it will decay to the remanent flux-density. This can remain in the core because the fault is cleared fairly quickly and, in most cases, the a.C. component of fault-current or load-current will generate such a small minor BH loop

102

(k)

that the remanence is not destroyed. Remanence can exist in a core under load conditions almost indefinitely. It will give rise to small steady-state-&rors which may be significant to high-accuracy metering. The most important effect, however, is in connection with a further transient of the same polarity. The transient flux now rises from the remanent value of flux and the effective flux change before saturation will be much less. Saturation will take place earlier and the effects will be more pronounced. A transient of opposite polarity will, of course, benefit from remanence and the saturation effects be reduced.

circuits when reactive burdens are used. Such voltages are of short duration due to the rapid decay of the transient but flashovers have been experienced in the secondary circuit, which is normally adequate for 2-kV test. The iron-losses in the core at these frequencies are effective in reducing the voltages somewhat but the voltage may still be high compared with 2-kV.

CONCLUSIONS From the limited considerations of transients given in this article, it can be seen that they are of considerable importance in relation to high-speed devices such as relays and instantaneous measuring devices such as oscilloscopes. The functioning of relays under transient conditions is a problem for protective-gear engineers, but the correct interpretation of oscillograph records may be of wider interest. In this latter case, it is often useful to be able to distinguish between the actual conditions existing in the primary system and those effects which may be introduced by the instrument transformers. It is hoped that this brief survey will help in both cases.

Effects of high-frequency transients

High-frequency current transients can occur on the primary of a current-transformer due to sudden switching, restriking, etc., where the primary system can oscillate between inductive and capacitive members. The conditions are particularly pronounced in some cablesystems. This current transient can be reproduced in the secondary circuits and, because of the initial magnitude of the current and the high frequency involved (e.g. 30 kc/s), high voltages may be set up in the secondary

103

CHAPTER 6 Transformer protection By B. DAKERS INTRODUCTION Types of Fault and Effects

The increasing demand for power on distribution and transmission systems throughout the world has resulted in transformers of very large capacity. Whilst this has certain economic advantages in maintenance as well as installation and running costs, it creates the very real danger that a transformer fault will cause a large interruption to power supplies. In general, transformer breakdowns are relatively few, but repair and replacement of large transformer units means considerable expenditure and time, and further, if faulted units are not cleared quickly and selectively can cause serious damage and power system stability problems. Protective schemes applied to transformers thus play a vital role in the economics and operation of a power system. The percentage cost of protection compared with the capital cost of the transformer being protected is extremely small making it totally uneconomic to apply anything less than a complete scheme of protection, to large transformer units. This of course is not true of smaller transformer units where their loss may not be so important to system operation. For these units the protection applied must be a balance against economic considerations. The following notes give some guidance on the protection schemes manufactured by Reyrolle Protection Limited for application to transformers. It will be concluded from these notes and published literature that Reyrolle Protection Limited manufacture a complete range of relays to protect transformer units.

To design a protective scheme it is necessary to have an intimate knowledge of the faults that have to be detected. With regard to transformers fig. 1 shows the types of fault that can be experienced. 1. Earth fault on H.V. external connections. 2. Phase to phase fault on H.V. external connections. 3. Internal earth fault on H.V. windings. 4. Internal phase to phase fault on H.V. windings. 5. Short circuit between turns H.V. windings. 6. Earth fault on L.V. external connections. 7. Phase to phase fault on L.V. external connections. 8. Internal earth fault on L.V. windings. 9. Internal phase to phase fault on L.V. windings. 10. Short circuit between turns L.V. windings. 11. Earth fault on tertiary winding. 12. Short circuit between turns tertiary winding. 13. Auxiliary transformer internal fault. 14. Earth or phase to phase fault on L.V. connection of auxiliary transformer. 15. Sustained system earth-fault. 16. Sustained system phase to phase fault. Earth Faults

The following conditions must exist for earth fault current to flow:A path exists for current to flow into and out of the windings i.e. zero-sequence path.

....'1. r---------------------------, WINO,...,.

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FIG. 1.

TRANSFORMER FAULTS

104

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FIG. 2b. VARIATIONOFFAULTCURRENTON DELTA AND STAR SIDES OF TRANSFORMER FOR FAULT ON STAR WINDING.

I. ,I.

tI

~

FIG.

~

2c.

FAULT CURRENT MAGNITUDE AND

DISTRIBUTION FOR EARTH FAULT ON DELTA WINDING.

~

lU

Star Connection -

~

The fault current in this case is primarily determined by the earthing resistance. The value of earth fault current is directly proportional to the position of the fault in the winding the curve being as shown in fig. 2b.

.r 5:>

t

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. I-

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4-

Delta Connection -

~

0

0·2

FIG.

2a.

K-

0·4

0·"

0·8

FAULT CURRENT DISTRIBUTION & MAGNITUDE

FOR EARTH FAULT NEAR STAR POINT OF A 33KV 50MVA TRANSFORMER.

That ampere turns balance is maintained between the windings. The magnitude of earth fault current is dependent on the method of earthing, i.e. solid, resistance or transformer, and transformer connection, i.e. star or delta. Star Connection -

Earthing Transformer

Fault current in this case is determined by the impedance of the earthing transformer windings. The distribution is as shown in fig. 2c. The above earth fault currents, particularly in the case of solid earthing, flow through the transformer coils causing them to try to assume a circular shape and thus produce very high mechanical stresses which are proportional to the square of the current. In resistance earthing the fault current is much reduced but consideration must be given to the possibility of flashover particularly if the resistor is of the liquid type.

t. 0

Resistance Earthing

Phase Faults

Phase faults have a similar effect to that of an earth fault on a solidly earthed transformer since current is only limited by transformcr winding impedance.

Solid Earthing

Transformer Connections and Fault Current Flow

The distribution of fault current for this configuration is shown in fig. 2a. It is only dependent on transformer winding impedance and thus is not directly proportional to the position of fault. The reactance decreases very quickly so that fault current is actually highest for a fault near the neutral point.

Under fault conditions, currents are distributed in different ways according to the winding connections. An understanding of the various fault current distribution is essential for the design of balanced differential protection, the performance of directional relays and setting of

105

o 3I o

31

l'

o

SUPPLY

3I

Jr

o

FIG.

3a.

FLOW OF FAULT CURRENTS IN TRANSFORMER WINDINGS.

applying the rule that the ampere turns produced by the fault currents flowing in the transformers secondary windings are balanced by equivalent ampere turns in the primary windings.

overcurrent and earth fault relays. Figures 3a and 3b show some typical examples. The current values shown are for transformers with equal phase voltages on primary and secondary side. The currents are devised by

106

r---------------I I

I

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1-

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FIG.

3b.

FLOW OF FAULT CURRENTS IN TRANSFORMER WINDINGS.

Having a knowledge of the various connections and characteristics of transformers in terms of type of fault and current expected on internal fault to give operation and external faults to define stability limit, we can proceed to the methods employed to detect faults and the Reyrolle Protection range of relays for this purpose.

mers are generally based on the current balance principle of magnitude comparison of currents flowing into and out of the transformer. This principle can be used to protect the transformer windings separately or as an overall unit. However, in the latter case as we shall see later, certain refinements are necessary. To explain the basic principle consider a single phase arrangement as shown in fig. 4. It will be seen that under

Current Balance Principle The differential protective schemes applied to transfor-

107

quiescent conditions, magnetizing conditions, normal load and through fault conditions that current circulates between the two current transformers which results in no current flowing in realys Rl and R2. This is a stability condition. If we now consider an earth fault at 'X' shown in fig. 4d it is seen that the balance is disturbed and current flows in relays Rl and R2. As fault 'X' approaches 'Z' the transformer acts as an auto-transformer so that 12 increases and 11 decreases. The resultant current is sufficient to operate the relay for all positions of 'X', and therefore the whole of the windings can be protected using this principle. When the system is resistance earthed (fig. 4e) 12 decreases as 'X' approaches 'Z'. As a result the amount of winding protected depends upon the relay sensitivity, i.e. fault setting.

The main problem experienced in designing a current balance scheme is ensuring stability on through faults which cause unequal saturation of the C.T.'s during the first few cycles after the fault initiation. This is overcome by using a relay of high impedance, as our type 4B3, which has a high value stabilising resistor connected in the relay circuit. This scheme has now been in use for many years, the simplicity in application being that the performance of the protection on both fault setting and stability can be calculated with certainty. This is shown in fig. 6.

Three-phase

Where R = Maximum lead resistance X = CT secondary resistance This is based on the assumption of a worst condition when one current transformer completely saturates and ceases to transform any part of the primary fault current, whilst the other CT continues to transform accurately. If the setting voltage of the relay is made equal to or greater than this voltage the protection will be stable for currents up to the through fault current level used in the

Stability

For a given through fault current (I) the maximum voltage that can occur across the relay circuit is given by: VR = _I_(R + X) N

Extending the foregoing principle to three-phase transformers the connections will be as shown in fig. 5. Since both of these schemes only protect the transformer on earth faults within the zone covered by the C.T. 's; this scheme of protection is known as "RESTRICTED EARTH FAULT PROTECTION". The Reyrolle Protection relay designed for this application is the type '4B3'.

..... Sl

PI

52

P2.

PI

lIm.

PI

-

-

P2.

P2. RI

b.

g..

-

.

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Y

A

~II X

i2-

P2.

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l~1

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e

d. FIG.

LI

1.1

PI

c.

PRINCIPLES OF SEPARATE WINDING CURRENT BALANCE SCHEMES.

108

~

51

LOAD S2.

calculation. The knee point voltage of the C.T.'s is designed to be at least twice this value in order to ensure high speed operation of the relay.

This may be necessary when the CT excitation currents and relay current give a primary setting too low in relation to CT steady state errors.

LINE

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en

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FIG. 5a.

b.

lb

RESTRICTED EARTH FAULT PROTECTION STAR CONNECTED WINDING.

c..

Fault Setting

This is given by:IFS = N (IR + IA + IB) Where IR = Relay circuit current at setting voltage lA, IB = CT excitation currents at relay setting voltage N = CT ratio. The primary fault setting can be adjusted to the level required by adjustment of the relay circuit current using resistors connected across the relay circuit.

FIG. 6. PRINCIPLE OF MERZ-PRICE CIRCULATINGCURRENT (OR CURRENT-BALANCE) PROTECTIVE SYSTEM:- USING HIGH IMPEDENCE RELAYS.

Type 483 Relay

The circuitry of our type 4B3 relay is shown in fig. 7. The operating element is a type B61 d.c. attracted armature relay energised from a full wave rectifier. The capacitor, in conjunction with the resistors, forms a low pass filter circuit. The function of this is to increase the setting in relation to harmonic frequencies thus retaining stability under high frequency currents which can be produced in certain installations during switching. The variable resistor R2 to R6 enables the voltage setting to be adjusted and the non-linear resistor Ml limits the

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----..0_------

E1LMlJlT TVPE-OUol ~-R------O

RESTRICTED EARTH FAULT PROTECTION DELTA CONNECTED WINDING.

FIG. 7.

109

4B3 RELAY CIRCUIT.

peak voltage output from the C.T.'s during internal fault and so protect the secondary wiring which otherwise may flash over and short circuit the relay resulting in failure to trip. Summarising: separate winding current balance schemes are:(a) Unaffected by load current, external fault or magnetizing inrush currents. (b) Unaffected by the ratio of transformer (c) Complete winding can be protected with solidly earthed neutral but not when resistance earthed. (d) Will not detect phase faults (three-phase protection) shorted turns or open circuits.

ever, any mismatch in C.T.'s will result in unbalance current which will flow in the relay circuit. Since most transformers are equipped with tap changing the design of an overall scheme for three phase transformers must take account of this mismatch under through fault conditions. Therefore, the application of an overall differential scheme to three phase transformers requires a biased relay to maintain stability during:(a) Tap Changing (b) Magnetizing inrush conditons, when switching transformer on or when subjected to sudden loss of load. In both of these cases the out of balance current tending to flow through the relay circuit may be several times the basic fault setting. The method employed to ensure that the relay remains stable under the above conditions is by means of bias windings. The application of a biased relay is shown in fig. 9, where it will be seen that the bias is arranged to give an operating setting which is always greater by a suitable margin than the expected maximum spill current. Usual practice is to arrange the bias characteristic as a slope of at least twice

Overall Differential Protection The current balance principle can also be applied in an overall unit protection to cover both primary and secondary windings. Fig.8 illustrates the principle in terms of single phase. This shows that an overall scheme is effected by magnetizing current and internal fault current and remains balanced under normal load or through fault current providing c.T. ratios are matched. How-

PI

SI

PI

P2

52

P1.

51

PI

~

S2

P2

R b.

Q.

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------Q51

---+tMH---aS2

FIG.

8.

PRINCIPLE OF OVERALL CURRENT BALANCE SCHEMES.

110

SI

current, thereby preventing the relay from operating during magnetizing conditions. One thing to be considered with "harmonic bias" is that harmonics are also present during internal faults due to C.T. saturation. To ensure that the relay will operate under all internal fault conditions the harmonic bias unit should preferably be designed to use only second harmonic which predominates in a magnetizing surge. Both of the above factors have been very carefully optimised in the design of Reyrolle Protection type 4C21 'Duo-bias' relays.

the slope of the spill current characteristic. During internal faults the whole of the available secondary current will pass through the relay operating circuit. Usually the secondary current will pass through part of the bias winding so that it will produce what is sometimes referred to as "self bias" and causes an increase in setting. If for example the current required to operate will be as indicated by curve 4. Relay operation occurs at the point where curve 3 crosses curve 4. The points to be considered in setting a biased relay are therefore:(a) The graph of current required to operate under external fault conditions must be well above the graph of anticipated spill current. (Fig. 9b) (b) The available operating current under internal fault conditions must be well above the graph of current required to operate. (Fig. 9d)

Type '4C21' Overall Biased Protection Relay

Figure 10 shows a single phase diagram of the '4C21' relay. Under load or through fault conditions, the C.T. secondary currents circulate through the primary winding of the bias transformer. The rectified output of this transformer is applied to the bias winding on a transductor via a shunt resistor. Out of balance current flows from the centre tap of the primary winding of the bias transformer energising the transductor input winding and the harmonic-bias unit. The input winding and output winding of the transducter are inductively linked, but there is no inductive

Harmonic Restraint

The second reason, already mentioned, for using a biased relay for overall transformer protection is that operating current may flow during a magnetizing surge. This current is known to contain a high percentage of second and higher harmonics. It has been found convenient to use these harmonics and connect them into bias

..,. :

PoWU-T~fo/trtfR

(c.)

& ~ Ra.Ay SIA~- tlfZc.ulT

o -=

FIG.

9.

~·Of!«Art.lftlll'"

ApPLICATION OF RESTRAINT BIAS TO POWER·TRANSFORMER PROTECTION.

111

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FIG.

10.

DUO-BIAS RELAY -

linking between these and the bias-windings. So long as the protected transformer is sound the transductor bias-winding is energised by full-wave rectified current which is proportional to the load or through-fault current, and this bias-current saturates the transductor. Out-of-balance currents in the transductor inputwinding, produced by power-transformer tap-changing or by current-transformer mis-match, superimpose an alternating m.m.f. upon the d.c. bias m.m.f., as shown in fig. 11, but the resulting change in working flux-density

SINGLE PHASE.

is small and consequently the output to the relay is negigible. If the power-transformer develops a fault, the operating-m.m.f. produced by the secondary faultcurrent in the transductor input-winding exceeds the bias-m.m.f. resutling in a large change in working fluxdensity. This allows transformer coupling to be effective between the input and output windings and thus operation of the relay. Relay-operation cannot occur unless the operating-

112

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FIG.

11. FLUXES DUE TO OPERATING AND BIASING AMPERE-TURNS.

Earth Fault Sensitivity

When a power-transformer is resistance-earthed, the current available on an internal earth-fault for operation of a differential protection may be relatively low and the percentage of the winding protected against earth-faults may be inadequate. This is a fundamental point and applies to all differential protections. In these circumstances it may be necessary to add some separate form of earth-fault protection. Consider the delta/star-connected transformer shown in fig. 13 in which the star-connected winding may be connected to earth through a resistor. Suppose that a fault occurs at a point F, p% from the neutral end of the winding, and that the neutral-earthing resistor is rated to pass the full-load current of the star-connected winding with a terminal fault. If the fault is fed from the delta side of the transformer then the current in the primary winding of the faulty phase is:Ip

m.mJ. exceeds the bias-m.m.f.; and as the bias-m.mJ. is proportional to the load or through-fault current, the required operating-m.m.f. - and hence the required operating current - is also proportional to the load or through-fault current. Fig. 12 shows the operating characteristics of the relay with the 20%, 30% and 40% percentage-bias slopes corresponding to the 20%, 30% and 40% shunt-resistor tappings. The harmonic-bias unit is a tuned-circuit which responds to the second-harmonic component of the magnetizing current. When magnetizing inrush-current flows through the relay-operating circuit the rectified output of the harmonic-bias unit is injected into the transductor bias-winding and restrains the relay.

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can be combined with the overall protection as illustrated in fig. 14. A current transformer is required, of course, on the neutral-to-earth connection. The advantage of the restricted earth fault relay is that it is energized from a current transformer which "sees" the whole of the fault current and not just the primary side equivalent of the fault current. Where the system is solidly earthed an overall transformer protection with a setting of about 30% would give complete phase-to-earth fault protection of the delta winding and about 80% of the star winding. In that case additional restricted earth fault protection is not required for the delta winding, but if it is fitted to the star winding it may detect faults much nearer to the neutral end of the winding. On star windings at 132kV and above, it is usual practice to fit restricted earth fault protection. In addition to overall protection it is usual practice to protect all but the smallest transformers against interturn faults using a Buchholz relay. Severe faults are detected from the resultant surge in oil and low current faults by the measurement of accumulation of gas produced. Back-up protection is normally provided by IDMTL overcurrent relays, although in recent years this has taken the form of a two-stage scheme. This comprises one IDMTL relay energised from the C.T.'s on the H.V. side, the source of infeed. Operation of this relay trips the L.V. breaker and starts a time-delay relay. The setting of this time-delay relay is such that it does not operate before the L. V. breaker trips. If the fault persists the time-delay relay trips the H.V. breaker. Since IDMTL relays have a relatively long reset time an instantaneous overcurrent relay with a fast reset is connected in series so that the time lag is de-energised as soon as the fault is cleared.

On the other hand a restricted-earth-fault relay on the star-winding would be energised by the fault-current passing through the earthing resistor via a neutral current-transformer, that is by p

x

Full-load secondary current

100 Using the given expressions, the amount of winding protected can be plotted graphically against the faultsetting, as shown in fig. 13. This demonstrates that a restricted-earth-fault relay is a much more efficient device for the detection of winding earth-faults than a differential relay; and, in addition, to cover a reasonable percentage of the winding, the latter would need to be extremely sensitive. This, however, is impracticable because of the limitations imposed by out-of-balance current, due to tap-changing, current-transformer mismatching, and power-transformer magnetization. Although tests on Duo-bias protection have shown that separate high-set overcurrent relays are not required to ensure tripping under heavy internal fault conditions, some customers still demand them. Care must be taken in setting high set relays because their speed of operation may cause them to have significant transient overreach. Some care must also be exercised in choosing the current transformer ratios and connections. The current transformer ratio must compensate for the difference in primary and secondary currents of the Transformer and their connections must compensate for the phase difference. Fig. 14 has illustrated a typical example. The restricted earth fault relay can be operated from a completely separate set of line current transformers or it PIbf1AllY

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In the case of banked transformers separate overcurrent back-up protection is usually preferred. The most usual questions asked on the application of protection to transformers are:1. What advantage does an overall scheme have over a scheme of separate over-current and earth fault. 2. What is the minimum size of transformer to which an overall scheme should be applied. Considering question 1, overall protection gives instantaneous clearance of phase faults, has a high through fault stability whilst retaining a low fault setting and is inherently discriminative. Against this the degree of protection afforded by IDMTL overcurrent relays is very limited since the relay must be set above emergency loading conditions which often means a setting of 200% rating. In addition the time setting may have to be high in order to grade with other overcurrent relays on the system.

Clearly, therefore, the application of an overall scheme must be considered in relation to the risk of phase to phase faults. Considering question 2, this is entirely a matter for the user to decide in relation to loss of supply and consequently loss of revenue. In the experience of Reyrolle Protection overall schemes are usually applied to all transformers of 1OMVA and above.

Auto-Transformer Protection Fig. 15a indicates the scheme used to protect autotransformers. Each phase winding forms a three-ended primary zone and is protected, therefore, by three C.T.'s, one at each end, connected to form a circulating current system. Three such systems share a common neutral lead and form a complete phase and earth-fault protection of the transformer.

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TYPICAL ARRANGEMENT OF DIFFERENTIAL PROTECTION WITH SUPPLEMENTARY EARTH-FAULT PROTECTION.

115

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ApPLICATION OF SIMPLE (UNBIASED)

OVERALL DIFFERENTIAL PROTECTION TO

275/132 kY.

AUTO·TRANSFORMERS.

116

pivoted floats carrying mercury switches contained in a chamber. This chamber is connected in the pipe which connects the top of the transformer tank to the oil conservator. Under normal conditions the Buchholz relay is full of oil, the floats are fully raised and the mercury switches open. This device relies upon the fact that an electrical fault inside the transformer tank will be accompanied by the generation of gas and, if the fault current is high enough, by a surge of oil from the tank to the conservator. Gas bubbles due to a core fault will be generated slowly and collect in the top of the relay. As they collect, the oil level will drop in the relay and the upper float will turn on its pivot until the mercury switch closes. This is used to give an alarm. Similarly, incipient winding insulation faults and interturn faults which produce gas by decomposition of insulation material and oil may be detected. Such faults are of very low current magnitude and the Buchholz relay is the only satisfactory method of detection. Serious electrical faults, such as flashover between connections inside the main tank generate gas rapidly and produce a surge of oil. This causes the lower float to be forced over about its pivot, causing the lower mercury switch to close. This is arranged to trip both the H.V. and L.V. circuit-breakers. In addition to the above, serious oil leakage will be detected initially by the upper float which will give an alarm and finally by the lower float, with will disconnect the transformer before dangerous electrical faults result. The Buchholz relay is thus a versatile protective device and for certain types of faults the only protection available. However, the time of operation of the surge

It should be noted that all the C.T.'s are of the same ratio and that there is no magnetizing inrush problem since the inrush appears as a through-fault as far as the protection is concerned. Fig. 15b shows the arrangement of the auto-transformer protection when, as is commonly the case, the transformers are arranged in pairs banked on the H.V. side to a single 275kV switch. Five sets of C.T.'s now form the complete circulating current system, a single set of three relays (one per phase) being provided for the pair of transformers. The isolator auxiliary switches shown in the C.T. secondary circuits ensure that the isolation of either transformer disconnects its C.T.'s from the remaining C.T.'s and relay, so avoiding any possible interference with the latter when work is carried out on the isolated transformer. It will be evident that since both transformers are protected by the one scheme, discrimination between the transformers is impossible. This is sometimes overcome for earth-faults within the transformer by the provision on each transformer of a simple frame leakage "tank earth" indication relay, Type 'Bl' or "CF1' depending on setting required.

Directional Overcurrent Protection Directional overcurrent relays are usually employed to provide discrimination on phase faults for two parallel transformers where there is no source on the L.V. side. An analysis of the various fault conditions has shown that a 90° connection 4SO maximum torque relay is the best arrangement.

Buchholz Relay This device is illustrated in Fig. 16. It consists of two

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16.

USE OF BUCHHOLZ GAS & OIL ACTUATED RELAY.

117

Several methods of intertripping are available, but we will only consider those generally used.

float for a fault well down the winding may be appreciable (of the order of 0·5 second). For severe electrical faults on large transformers, the Buchholz relay therefore serves as a back-up to other faster forms of protection.

Fault Throwing

If pilot cables are not available or considered too expensive to be used for intertripping purposes, then intertripping can be achieved by means of fault throwing switches. This scheme is restricted to cases where the fault level is below certain limits. The transformer protective relays first trip the L.V. circuit-breaker. This immediately operates a fault throwing switch which is a spring-operated switch (generally single-phase) which applies single-phase to earth fault to the associated H. V. feeder. Feeder protection at the remote end then operates to trip the associated circuit-breaker.

Intertripping Schemes In order to ensure operation of both the H.V. and L.V. circuit-breakers for faults within the transformer and feeder, it is necessary to operate both circuit-breakers from protection normally associated with only one. The technique for obtaining this facility is known as intertripping. The necessity for intertripping arises from certain types of faults producing insufficient fault current to operate the protection associated with one of the circuit-breakers. These faults are:Incipient faults in transformer tank, which, as we have seen, operate the Buchholz relay associated with the L.V. breaker but fail to operate the protection associated with the H.V. breaker. Earth-faults on the L.V. winding of transformers which have resistance earthing.

Post Office Pilot Intertripping

Hired Post Office pilots are normally used to transmit a coded intertripping signal initiated by the transformer protective relays and arranged to trip the remote circuit-breaker. A complete Post Office pilot intertrip-

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119

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ping scheme can provide coded intertripping in both directions for duplicate feeders, using a single pair of pilots.

Type of Transformer

Other Forms of Protection

1. Distribution

Rating) 5MVA

Depending upon the transformer connections and circuit configuration other forms of protection such as the type 'B37' neutral displacement relay and type Bl or CF3 or TJM60 relay for standby earth fault protection may also be required. Each circuit must be considered as a unit and the protection assessed accordingly.

General The degree of protection provided for any particular arrangement depends to a great extent upon the size and functional importance of the unit. A further important factor is economics. The following table gives a guide to the protection applied to the various forms of transformers usually associated with power system installations: Reyrolle Protection have had many years of experience in the design and application of relay schemes for the protection of transformers and any advice required for a particular installation will readily be given.

Type of Protection IDMTL O/C REF.

Relay On TJMIO each 4B3 Winding

2. Distribution Rating ( 5MVA

Overall Differential 4C21 REF. each Winding 4B3

3. Two-Winding Transmission

Overall Differential REF. each Winding IDMTL O/C SBEF

4C21 4B3 TJMIO CF3 or TJM60

4. Gen/Transformer Overall Differential REF. each Winding H.V. IDMTL O/C L.V. IDMTL O/C SBEF

4C21 4B3 TJMIO TJMlO CF3 or TJM60

5. Auto Transformer Overall Circulating 4B3 Current

120

CHAPTER 7 Proving Test of Duo-bias Transformer Protection INTRODUCTION The use of unit systems of protection is now almost standard practice in all important electrical power systems. Most unit systems are of the balanced class and are based on the assumption that under through-fault conditions the currents entering and leaving the protected zone are equal to one another, or bear some fixed relationship to one another. In applying unit protection to power-transformers two special problems arise, namely, the unbalancing effect of tappings on the transformer windings which cause the relationship between the magnitudes of the input and output currents to vary, and the magnetizing inrush current which occurs when switching on a transformer with its output side opencircuited or very lightly loaded. The first problem is usually dealt with by employing bias or restraint on the relays so that the current required to operate the protection increases roughly in proportion to the straightthrough fault-current. The second problem presents much greater difficulty. It can be dealt with by introducing time lags, as in conventional systems such as that using our type-TJG relay, or by methods which in some way or other differentiate between normal internal-fault currents and magnetizing inrush currents in such a way that the protection operates for the former but not for the latter. One difference between these two currents, which may be used for the purpose mentioned, lies in their wave-forms, fault-currents being nearly sinusoidal, whereas magnetizing currents contain appreciable second harmonic. The duo-bias system of transformer protection derives its "magnetizing" stability by taking this into account.

2ND-HARMONIC FILTER

F

RELAY

FIG.

1.

DUO-BIAS DIFFERENTIAL PROTECTION WITH TRANSDUCTOR RELAY.

rectified and fed into the d.c. control-winding on the transductor thus biasing the protection in the same way as does straight-through fault-current. Fig. 2 shows the interconnections between the relays in the protection of a three-phase transformer. It should be noted that the outputs of the three filter-units are paralleled and fed through the transductor biaswindings of all three phases connected in series, thus ensuring adequate restraint in all relays under conditions of magnetizing inrush.

GENERAL PRINCIPLES OF DUO-BIAS TRANSFORMER PROTECTION The principles of duo-bias protection are now fairly well known. It is a Merz-Price system with biasing to take care of tap-changing, and harmonic restraint to counteract the effect of magnetizing inrush currents. A schematic diagram for one phase of a three-phase transformer is shown in fig. 1. It differs from most other differential systems of transformer protection in that the relay is fed from the secondary winding of a transductor, the primary winding of which is connected across the pilots in the usual way. Biasing is obtained by d.c. excitation of the transductor via a separate d.c. controlwinding which is fed from an auxiliary transformer in series with the pilots. On internal faults the transductor acts more or less as a transformer but on external faults the saturation of the transductor core by the d.c. control-winding prevents the unbalance current present in the pilots from being transferred to the relay. With magnetizing inrush currents the harmonic-restraint circuit has appreciable second-harmonic output. This is

TESTS ON DUO-BIAS PROTECTION Research and exhaustive testing are continually finding new ways of improving the performance of protective systems generally. The Reyrolle Research and Certification Laboratories are very fully equipped for work of this kind and the majority of system conditions can readily be simulated. For transformer protection, however, a fundamental difficulty exists in connection with the production of magnetizing inrush currents which represent service conditions sufficiently accurately. It is therefore desirable to supplement laboratory tests on transformer differential-protection with tests on site. It is not often that facilities for site tests are available but through the courtesy of the Central Electricity Author-

121

CURRENT- TRANSFORMERS ON PRIMARY

POWER· TRANSfORMER

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TRANSFORMERS

OPERATING WINDING

TRANSDUCTORS

RElA '(

SMOOTHING WINDING

SECOND-HARMONIC FIL TERS

FIG. 2.

PROTECTION OF A 3-PHASE TRANSFORMER

injection as described below.

ity, Eastern Division, it was possible to test the duo-bias system thoroughly at their Rayleigh Transforming Station recently and these tests, together with comprehensive laboratory tests, have fully proved the performance of the system. Before dealing with the site tests we give a brief outline of the laboratory tests.

Primary-injection Tests

In order to simulate site conditions as closely as possible, a number of laboratory tests were made using circuits incorporating 500-kVA and 2500-kVA powertransformers. For the majority of the tests the transformer had a 3-phase rating of 500-kVA, 660/48 volts, with delta/star windings. On the H.V. (delta) side three 25/1 currenttransformers (i.e. 200/1 using 8 primary turns) were connected in star, and on the L.V. (star) side three 600/1 (i.e. 347/0· 58) current-transformers were connected in delta. With these ratios the steady-state unbalance current was negligible. To simulate power-transformer ratio-changes (due to tap-changing) of plus and minus 12!%, the number of primary turns used on the H.V. current-transformers was altered from 8 to 9 and 7 respectively. Fig. 4 shows the magnetization curves of the currenttransformers used in these tests, but other currenttransformer designs have also been tested. Fault-settings without through-load were measured in terms of the H.V. current, and were less than 36% for all phase-to-phase and phase-to-earth faults, the variation in the settings obtained for the six fault-conditions being less than 5%. These figures applied for faults on both the H.V. side and on the L.V. side of the power-transformer. The effect on the fault-settings of 100% three-phase load (using the circuit shown in fig. 3) is shown in fig. 5,

Secondary-injection Tests

A large number of tests were made using secondaryinjection circuits, and these provided data on the transductor and filter characteristics, and the ratings of components. A detailed investigation of the percentage-bias characteristic showed that the overall relay performance was almost unaffected by phase variations between the bias and the operating inputs to the transductor, and that the settings were similar irrespective of whether the inputs were switched or slowly increased. Further tests were made to determine the effects of harmonic content and frequency variations. The operating-time of the protection at three times the setting of the relays was shown to be approximately 60ms. with no through-load current, and 85ms. with full-load current. Furthermore, it was proved that the asymmetry of the fault-current made little difference to the operating-time, the actual times varying by only 5ms. between fully symmetrical and fully asymmetrical conditions. The detailed data obtained by means of low-current testing techniques were confirmed by tests using primary

122

PHASE·SHIFTER

VARIAC

CURRENTTRANSFORMERS

H.V

CURRENTTRANSFORMERS

REACTORS

RELAYS

FIG.

3.

TEST-CIRCUIT LOAD AND FAULT CONDITIONS.

from which it is apparent that the phase-angle between fault and load is unimportant in deciding the sensitivity. Tests also proved correct operation with high values of fault-current and current-transformer burden (such that the current-transformers saturated). The operating-time

of the protection is shown in fig. 6. The stability of the protection under through-fault conditions, the fault being applied on the secondary (L.V.) side after the transformer had been energized, was proved under normal and maximum tap-change conditions with H.V. current-transformer burdens of up to 8 ohms. Fig. 7 shows a typical record of the relayoperating current and L. V. primary current, the latter corresponding to approximately 15 times the currenttransformer rated-current. The record shows the safety margin at an extreme tap-change position, and illustrates clearly that the relay output, resulting from the magnetizing current of the power-transformer prior to closure onto the fault on the L.V. side, is low relative to the relay operating-level. Tests were also made to demonstrate the stability when the H.V. side was energized with an external fault already applied on the L.V. side, and to prove that repeated fault-current asymmetry did not prejudice the stability of the protection. Tests to prove the performance under conditions of magnetizing inrush current were made in the laboratory on the 500-kVA transformer and also on the 2,500-kVA 6'6-kV 3-phase transformer. For the former, the ratio of the H.V. current-transformers was 200/1, and peak currents of up to 6·1 times the current-transformer rating were obtained, the time-constant of the magnetizing inrush current-decrement being 35ms (X/R = 11). These tests were made with repeated point-on-wave switching, and the protection remained stable throughout, oscillograph records showing that the value of the transient relay-operating current never exceeded half that required for operation. A further test was made using current-transformers of ratio 25/1, when the protection remained stable with a peak magnetizing-current equivalent to approximately 30 times the currenttransformer rating. Similar tests were made on the 2,500-kVA transformer using 100/1 and 200/1 current-transformers of

300

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FIG. 4. MAGNETIZATION CURVES OF THE CURRENTTRANSFORMERS USED IN PRIMARY-INJECTION TESTS.

123

90"

NO-LOAD FAULT-SETTING

180

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FIG_

5.

RED-PHASE-TO-EARTH FAULT-SETTING WITH

differing designs. Peak surges of up to 14 times the current-transformer rating, and time-constants of 105ms. were obtained on these tests.

100

PER CENT 3-PHASE LOAD.

ditions are independent of source-impedance and transformer size. Stability under conditions of magnetizing inrush current is, however, dependent upon both the magnitude and the time-constant of the inrush current. The laboratory tests demonstrated the stability of the protection with heavy inrush currents, but the timeconstants of these inrush currents were much shorter

Site Tests

The characteristics of duo-bias protection concerned with fault-settings and stability under through-fault con-

120

100

0

0

\

\

'-

0

0

10 OPERATING·CURRENT IN TERMS OF MULTIPLES OF FAULT-SETTING

FIG.

6.

OPERATING-TIME OF DUO-BIAS PROTECTION.

124

I.V· SIDE.

FIG.

7.

RELAY-OPERATING CURRENT AND PRIMARY CURRENT UNDER THROUGH-FAULT CONDITIONS.

cerned with the output of a particular currenttransformer (which will be higher the 'better' the current-transformer) and not with the balancing of the outputs of current-transformers. Across the output of each power-transformer was permanently connected a 150-kVA auxiliary transformer, the secondary winding of which was opencircuited. The magnetizing-current of this transformer would produce very little bias, and did not therefore affect the validity of the tests. Throughout the tests Dudell oscillograph records were taken of the primary-current and relay-current in each phase, and the harmonic-bias current was recorded

than those usually associated with large powertransformers. The site tests at Rayleigh were made, therefore, to prove stability with an inrush current of long time-constant. The tests were made on 30-MVA and 60-MVA 132/22-kV transformers (see Table 1 opposite) using the current-transformers available on site. The magnetization-curves of these current-transformers are shown in fig. 9. It should be noted that these currenttransformers have a much higher knee-point than those which would normally be supplied for duo-bias protection. The use of these current-transformers does not, however, ease the test-condition, since here we are con-

FIG.

8.

CURRENTS DURING MAGNETIZING SURGE.

125

Table I-Data of Rayleigh Transformers Reference

T3

T2B

Rating

30 MVA: ON/OFB-cooled (15 MVA ON-rating)

60 MVA: ON/OFB-cooled (30 MVA ON-rating)

Connection

Star-Delta

Star-Delta

Voltage

132/33 kV

132/33 kV

Impedance

10·3%

12·4%

Ratio of associated H.V. currenttransformers

150/0·5

250/0·5

J_

on a moving-film cathode-ray oscillograph. Fig. 8 is a typical record and shows that the relay-current is well within the operating-level of the relay. Whereas the laboratory tests were made with control of asymmetry, thus permitting testing always under the most severe conditions of primary-currents, such control was not possible on site, and a large number of switching operations were necessary. A total of 69 switching operations were made during these tests. In many tests the harmonic bias was deliberately reduced below its normal level by altering the primary turns on the harmonic-bias reactor, the bias produced being in direct ratio to the number of primary turns. Although the harmonic bias was reduced to ! of its normal value protection still remained stable. Some of the more significant results are given overleaf in Tables 3 and 4. Examination of the results given above (and of the oscillograms taken) show that: (a) The greater the inrush current the greater the harmonic bias produced. (b) The greater the harmonic bias the less the relay current for corresponding inrush currents. (c) The continuation of the asymmetrical wave due to the longer time-constant did not produce any adverse effect on the stability of the protection.

1100

/

1000

V

V

./~ C.T. RATIO

150/0-5 D.C. RESISTANCE S'O In

1/

)v 00

REF.T2B CT. RATIO 250,.'0'5

D.C. RESISTANCE 3-5n.

I

'J

I

CONCLUSION From the laboratory and site tests described it can be concluded that: (1) Duo-bias protection is stable with through-fault currents of at least fifteen times the rated current of the current-transformers with magnetizing inrush surges having maximum peak values exceeding any likely to be found in practice, and also that it is stable with magnetizing surges having time-constants of at least 6 seconds. (2) The fault-settings of the protection are less than 40 per cent of the current-transformer rating with

200.

'00

600

'00

1000

CURRENT mA (I-I TIMES AVERAGE)

FIG. 9.

MAGNETIZATION-CURVES OF THE CURRENTTRANSFORMERS USED IN SITE-TESTS.

no through-load, and less than 60 per cent of the current-transformer rating with 100 per cent three-phase through-load. The phase-angle between the load-currents and the fault-currents is unimportant.

126

Table 2-Site-testing Data Transformer No:-

T3

T2B

Steady-state Magnetization-current

3·4 A (approx.)

Time-constant Normal lead-burden Current-transformersRatio Secondary turns D.C. resistance Excitation curve

6 sees (approx.) 6 ohms/phase

Red and blue phases-II A (approx.) Yellow phase 6 A (approx.) 2 sees (approx.) 4·6 ohms/phase

150/75/0·5 (used as 150/0·5) 295 of 19 s.w.g. 5 ohms Fig. 9

250/0·5 495 of 19 s.w.g. 3·5 ohms Fig. 8

Table 3---Results of Tests on Transformer T3

Nominal turns on harmonic-bias reactor (per cent)

Leadburden (ohms/phase)

Peak primary current

(% of operating-

(A)

current)

Relay-current

Harmonicbias current (rnA)

Red

Yellow

Blue

Red

Yellow

Blue

100

8

340

195

115

38

30

39

12

100

6

15

15

15

Negligible

9

10

Very small

57

8

100

190

125

45

46

38

57

8

30

30

50

6

14

8

33

8

120

50

125

20

26

24

8 Very small 2

Table 4-Results of Tests on Transformer T2B Nominal turns on harmonic-bias reactor (per cent)

Leadburden (ohms/phase)

Peak primary current

(% of operating-

Relay-current

(A)

current)

Harmonicbias current (rnA)

Red

Yellow

Blue

Red

Yellow

Blue

100

4·6

490

330

220

25

30

18

35

100

4·6

230

320

140

21

18

34

28

57

4·6

570

410

230

31

38

32

29

57

6·6

340

180

160

30

25

28

9

33

6·6

570

320

220

36

56

No record

8

33

6·6

110

120

170

29

33

27

Very small

(3) The operating-time of the protection is less than 100 milliseconds at 3 times the setting under all conditions of load and fault-current asymmetry, and is less than 65 milliseconds at 3 times the setting for internal faults with no through-load. (4) The correct performance of the system is unaffected by the presence of harmonics higher than the second, and by departures from the nominal

frequency greatly exceeding anything likely to occur in practice. These additional tests and appreciable operating experience with duo-bias protection have provided valuable confirmation that this system of transformer protection is basically sound in principle, and that it can be applied with confidence to the largest and most important transformers in service.

127

CHAPTER 8 The Requirements for Directional Earth Fault Relays By F. L.

HAMILTON AND

N. S.

ELLIS.

SUMMARY

Impedance Values Generator/Transformers. Zj = Zz = 23%. Zo = 10%.

This report deals with the conditions under which directional earth fault relays may be required to operate in conjunction with distance protection relays. Variations in system conditions which might occur in practice are related to the current settings, relay characteristics and forms of polarising. The results are plotted graphically in order to assist in the application of this type of relay.

Primary values. (Total impedance of generator/ transformer portion of busbar MVA rating). 1500 MVA Busbars Z, = Zz = 18·15 ohms, Zo = 8·05 ohms 2500 MVA Busbars Z, = Zz = 11·1 ohms, Zo = 4·8 ohms 3500 MVA Busbars Z, = Zz = 7·93 ohms, Zo = 3·43 ohms

GENERAL The investigations on which this report is based were made in connection with Distance Protective Schemes using a single directional earth-fault relay to control the operation of plain impedance relays for earth faults. The results, however, are of general interest in respect to the application of Directional Earth Fault relays to solidly earthed systems where the polarising winding is energised from a residual voltage transformer, provided the appropriate range of system conditions and characteristics is taken into account. This report deals with the particular case of a typical 132 kV system.

Secondary values. (On basis kV/ll0 VT). 1500 MVA Busbars Zj = Zz = 7·7 ohms 2500 MVA Busbars Z, = Zz = 4·62 ohms 3500 MVA Busbars Z, = Zz = 3·3 ohms

of 500/1 CT and 132

Zo = 3·33 ohms Zo = 2·0 ohms Zo = 1·43 ohms

Grid-Infeed. This is taken as overhead line impedance where Z, Zz and Zo = 2·5 Zl·

SYSTEM IMPEDANCES In the typical 132 kV system chosen, the relaying point is associated with busbars having 3,500, 2,500, or 1,500 MVA rating, the voltage transformer ratio being 132-kV-II0-volts and the current transformer ratio being 500/1. The station is assumed to have a local generating capacity and a proportional grid infeed. For example, in the case of 2,500 MVA breaking capacity, the generators have a load capacity of 360 MVA and the grid in-feed a short-circuit capacity of 1,000 MVA. The lines are assumed to have Z, =Zz = 0·7 ohm/ mile and Zo = 2·5 Zj. For convenience, the calculations are made on the basis of equivalent secondary voltages, currents and impedances. The impedances obtained from the maximum fault MVA will represent the minimum source impedances. In practice, the actual source impedances will vary over a range of values, the maximum of which will correspond to the minimum plant condition. The impedance encountered between the relaying point and the fault will be directly proportional to the distance from the fault to the relaying point, provided there are no in-feeds of fault current between these two points. This condition has been assumed in this analysis.

Primary values. (Total impedance of grid infeed portion of busbar MVA rating). 1500 MVA Busbars Zj = Zz = 29·3 ohms Zo = 72·5 ohms 2500 MVA Busbars Z, = Zz = 17·4 ohms Zo = 43·5 ohms 3500 MVA Busbars Z, = Zz = 12·4 ohms Zo = 31·0 ohms Secondary values (On basis kV/ll0 VT). 1500 MVA Busbars Z, = Zz = 12·1 ohms 2500 MVA Busbars Zj = Zz = 7·25 ohms 3500 MVA Busbars Z, = Zz = 5·18 ohms

of 500/1 CT and 132

Zo = 30·2 ohms Zo = 18·2 ohms Zo = 12·9 ohms

BOUNDARY CONDITIONS FOR OPERATION Taking an earth fault relay, the current circuits of which are energised by the residual current of the line C.T.'s and the voltage circuits of which are energised from the open delta voltage of the V.T.'s, the

128

- - -

GRIO-IN-F=£to

/32 K.V.

~

63·5'1.

FIG. leA) EQUIVALENT CIRCUIT.

To ~

63·5v fbt.-ARISINC, VOLfAG-£

ON !<E1JJ,Y ~ Vp

FIG. 1(B) SEQUENCE NETWORK FOR EARTH FAULTS.

129

= 3ID Zso

two quantities on the relay are:Voltage = V p = 3IoZ so Current = IE! = 31 0 The circuit conditions being investigated are represented in equivalent form in figs. l(a) and l(b), the parameters which are varied being the impedances Zu, Zu, ZLO and ZSl' ZS2 and Zso. The boundary conditions may be explored by:(a) First considering terminal earth faults, i.e. Zu, Zu, ZLO = 0, and varying ZSb ZS2, Zso down to their minimum value, i.e. maximum MV A. (b) Secondly, keeping ZSb ZS2, Zso at their minimum value and varying Zu, Zu, ZLO up to the maximum value to be considered. (c) Lastly, keeping Zu, Zu, ZLO constant at the maximum value to be considered and varying ZSb ZS2, Zso up to the maximum value to be considered, i.e. minimum plant conditions.

the relay is required. This will normally be decided by the maximum stage 3 setting, which may be of the order of 100-200 miles. The lower limits of these boundary lines are marked off corresponding to various line lengths for the stage 3 setting. (c) Distant Faults with Increasing Source Impedance The voltages corresponding to the lower limit of the boundary lines in (b) above are the lowest at which the relays are called upon to operate. It is of interest to note that these low voltages also correspond to small currents, i.e. the relay is not called upon to operate at low voltages and heavy currents. The currents at this lower limit are not, however, the minimum at which the relay should operate. These will be obtained by keeping the fault at the maximum chosen distance from the relaying point and following the appropriate curve to the line MQ, or a line parallel to this if the maximum source impedance is less than that corresponding to 250 miles of line. Whilst the current will reduce during this process, the voltage will rise again because of the increasing zero sequence impedance of the source. The current corresponding to a fault at the limit of reach and with maximum source impedance will give the minimum pick-up current of the relay. It will be noted that this minimum current value of the relay occurs with reasonable voltage, i.e. tends towards the minimum operating current with full volts. The boundary lines for 200 mile and 100 mile reach are shown in fig. 2 scaled against equivalent line lengths of source impedance. The maximum length of 250 miles corresponds to a range of about 30 referred to a minimum stage 1 setting of 8 miles. The curves shown through 'm' and 'n' are typical and presume a proportional reduction of generating plant and grid infeed down to about 20% power, and then further reduction of input with no local generation. Other conditions will not produce much deviation from these curves.

(a) Terminal Earth Faults Whilst terminal earth faults at the relaying position do not produce low polarising voltages in the relay, they form one boundary line enclosing the zone of operation of the earth-fault relay. For terminal faults Zu = ZL2 = ZLO = 0, the variation in relay voltage and current will depend entirely on the source impedance. Referring to fig. 2 showing the relation between relay volts and current in log/log form, the points A, B, C, give the relay voltages and current for the three maximum MVA's. For the condition of a terminal earth fault with increasing source impedance, the boundary here will be A, B, or C towards Q. It should be noted that at small currents on this boundary, conditions are such that the predominating impedance is that of overhead line, where Zo = 2·5 Zj, i.e. no generators in, and the residual voltage will rise above 63·5 volts. These boundary lines are typical, but will vary slightly according to the proportionality of line impedance to machine impedance. The boundary lines thus formed represent the upper limit of the voltage/current zone experienced by the relay.

RELAY CHARACTERISTICS The voltage/current characteristics for particular phase angles may be superimposed on the boundary diagram of residual voltage and current shown in fig. 2. The characteristics of two such relays are shown.

(b) Earth Faults beyond the Relaying Point with Minimum Source Impedance (Maximum MVA) In this case, the effect on the relay voltage and current of moving the fault away from the relaying point is shown. It should be noted that the condition of minimum source impedance is taken. The boundary line for this will obviously go through the Point A, B or C according to the appropriate maximum MV A. The relationship for relay volts and current is V p = 3IoZ so = IEFZ SO, and as Zso is constant (at its minimum value) this boundary line will be a straight line through A, B or C at 45° to the axis. The lower limit of this boundary line will depend on the maximum distance of the fault for which operation of

Type USE Relay

As used in XZA protection, having a nominal maximum torque angle of 30° and which consumes 3 VA in the voltage circuit at 63·5 volts. The characteristics for this relay are shown with 30°, 60° and 90° between polarising voltage and current. The basic equation for volts and current are of the general form VI = const, so that on log/log scales, the characteristic is a straight line at 45° to the axes. Comparator Relay

Such as obtained with the use of a rectifier bridge polarised relay arrangement. The maximum torque angle for the relay is 60°, and the VA for the voltage

130

/00

~---_-.:Q~:;o=======::;;::::===:;Z:====:;;;;;:~--=::::=-----------

60

c

~

.30 ~

~

2D

u

~

V)

.J

~

~

10

~

0

'vP ~

~.

~

r

~ ~\O ~ (J'/'

(j"l

~O~ -t-Q Q't-q,.~~ \9

~

5'0 4-'0

cJ>~

.i'

,3-0

/"'0

-\0> -

CDMP R.ELAY

'66° -

UNCOMPE.N:jATE 0

·5 ~---=---:-----:-----:-----A-::----;:;-~""';"""7---:-~--""'7-:-----r:---.",..-.-.2. -3 -4 -6 /-0 2-0 3-0 ,"'0 S-o 10 () 30 /(ESIOUAL Sf{. wttENr

/32 KV - 50L-(0 EARTHEO SYSTE.M - cr.: LINE

Z, :::Z1. = Q-7.o.../mile

FIG.

2

Zo:: 2:5"z.,

VT

DIRECTIONAL ElF RELA YS FOR DISTANCE PROTECTION.

131

500/1

= 132KV/llo

circuit corresponding to the characteristic shown would be 30. The theoretical characteristic for such relays is formed by two straight lines parallel to the axes. In practice, the corner so formed is rounded off, as shown in the characteristics. The characteristic may be compensated to give the increased voltage at higher currents by the unbalancing of the current inputs in favour of the restraint side of the comparator.

(d) The comparator type of characteristic is more

amenable to application and can give reasonable coverage with reasonable VA in the voltage circuits. (e)

The particular property of the hyperbolic relay characteristic which gives operation at very low currents at high voltages, and at very low voltages for very high currents may be a definite disadvantage in relation to possible spurious operation. The possibility of such operation would be increased considerably if the characteristic were lowered by consuming more VA in the voltage circuit, and it must be borne in mind that the voltage can increase to about 105 volts. The present relay characteristic gives operation at 105 volts and 0·1 ampere.

(1)

Current polarising from neutral current transformers would overcome some of the weaknesses of the hyperbolic relay characteristic. The required degree of current polarisation may be obtained from the curves in fig. 2. For example, to obtain complete operation for the whole boundaries given by A, a, m, the required minimum operation is 2 volts, 0·7 amperes, but actual operation is 13 volts, 0·7 amperes. The additional polarising effect from 0·7 amperes must be eqivalent to 11 volts (assuming the fault current and polarising current to be equal). If no allowance is made for increasing VA on the polarising circuit due to the requirement of two polarising windings, the VA in the current polarising circuit would be

INTERPRETATION OF RESULTS In order that the relay should operate satisfactorily under all practical system conditions, its voltage/current characteristic should lie between the axes and the area enclosed by the boundary lines appropriate to the particular application. It should be appreciated that the phase angle between polarising voltage and current will vary between 90° and 50° for the various system conditions. For example it is nearly 90° when the source is predominantly machine and transformer impedance (i.e. along lines aA, bB, cC of fig. 2) and nearly 50° when the source is predominantly line impedance (i.e. along the other boundary lines).

CONCLUSIONS From a consideration of the relay characteristics and boundary conditions, the following conclusions may be drawn. (a) The directional earth fault relay is not called upon to operate with low voltage and heavy current. (b) With the hyperbolic characteristic such as is obtained with Beam relays, it is difficult to cover a range of system conditions at low voltage and low current. (c) Although the USE characteristic might be lowered, this would require considerable VA on the voltage circuit. For example, to give a coverage comparable with that of the comparator relay would require

)'x

_1_= approximately 3 [11 \63.5 0·72 0·2 VA at 1 ampere, which is a reasonably low figure. Current polarising is not, however, always practical as it requires a neutral point to be available and in use near to the relaying point. The use of current polarising will require some care in relation to the choice of phase angle for the relay as the residual capacity currents will cause phase shifts between the residual C.T. current and the neutral C.T. current.

Y

3VA x [ 15 = 300 VA. \ 1.5) Generally, it can be considered that the hyperbolic characteristic is basically not particularly suited to this type of application.

132

CHAPTER 9

The Performance of Distance-Relays

By F. L. HAMILTON and N. S. ELLIS. INTRODUCTION

x

x

A variety of relays are used in protective systems of the distance-measuring class, typical forms being plain impedance, mho, ohm, reactance, and directional relays. All these come under the general description of distance-relays and are characterised by having two input-quantities respectively proportional to the voltage and current at a particular point in the power-system, referred to as the relaying point. The ideal forms of such relays have characteristics which are independent of the actual values of voltage and current and depend only on the ratio of voltage to current and the phase angle between them. The ideal characteristics are thus completely specified by the complex impedance Z=V/I. The impedance Z can be shown on a complex diagram having principal axes of resistance and reactance. The form of this function for the commoner types of characteristics is illustrated in fig. 1. Operation of the relay occurs in the shaded areas and no operation takes place in the unshaded areas. The boundary curve represents marginal conditions and is referred to as the "cut-off impedance". Practical distance-relays depart from the ideal and have characteristics which depend on the actual values of the input voltage and current. An approximation to the ideal is obtained only over a specific range of input quantities. Inside this range the relay will have errors which are acceptable, and outside the range it will have excessive errors and may not even operate. The operating-time of the relay will be variable and dependent on the individual magnitudes of the input quantities, being, for example, long for small inputs near the cut-off impedance and short for large inputs well within the cut-off impedance. The complete performance specification of a practical relay should thus include information on these aspects in addition to the ideal polar-characteristic such as is illustrated in fig. 1. In the past, various methods of specifying performance have been adopted to meet these difficulties. None of these, however, en'lbles the performance of the relay to be related easily to the requirements of the power-system and most do not facilitate comparison of different relays. It is the purpose of this article to outline methods which have recently been developed to overcome these difficulties and to outline the principal factors affecting the performance. The testing of distance protection is also considered and test-procedures outlined which are directly related to the new methods of specifying performance.

~,

l(a) PLAIN IMPEDANCE

." l(e)

REACTANCE

FIG.

1.

~" I (d)

DIRECTIONAL

IDEAL POLAR CHARACTERISTICS OF DlSTANCE- RELAYS.

the simplified diagram of fig. 2. Zs represents the source impedance from the relaying point P back to the generators and ZF the fault impedance of the powersystem from the relaying point to the fault. Both are supplied from the open-circuit system-voltage E. The current and voltage at the junction of the two impedances are proportional to those applied to the relay via the current and voltage transformers at the relaying point. The source impedance Zs depends on the amount of generating plant available behind the relaying point and is directly related to the short-circuit MVA available at the relaying poing. This will vary according to system conditions but it will normally be possible to assign an upper and lower limit to the short-circuit MVA and hence to Zs. The fault impedance ZF is proportional to the distance of the fault from the relaying point. The ratio of the voltage and current applied to the relay is always equal to ZF, but the actual values are determined by both Zs and ZF. Consider a fault at the nominal cut-off impedance of

P.- -Relaying point. Zt-.- - Fault impedance. ZS.--Source impedance.

Performance Requirements as Dictated by the Power-system The requirements for a particular distance-relay can be assessed in relation to the power-system by reference to

FIG.

133

2.

E.-- Normal system voltage. l.--Current at relaying point. Y.-Voltage at relaying point.

BASIC CIRCUIT OF POWER-SYSTEM UNDER FAULT- CONDITIONS.

the relay. The impedance ZF is thus fixed and will normally correspond to 80 per cent of the line protected. The voltage at the relaying point is then determined only by Zs. For a very large MVA source, i.e. small Zs, this voltage will approach the normal system-voltage. For a small MVA source, i.e. large Zs, the voltage will only be a fraction of the normal voltage and will be determined by the ratio Zs/ZF' A practical relay is required to work correctly between these limits of voltage. Since the top limit is normally fixed by the system-voltage it is usually necessary only to specify that the relay will work down to some minimum voltage Vm' Apart from the magnitude of the impedances Zs and ZF it is necessary to consider their phase angle. This determines the time constant of the primary transients which will occur in the voltage and current waveforms when a sudden fault is applied. With high-speed relays this factor becomes of great importance as the relay is required to measure correctly during the transient period. Since relays are generally connected to a three-phase system the problem is more complicated than that shown in fig. 2, as different types of faults can occur. The problem can, however, always be reduced to the simple case for a particular fault though it may be necessary to use different values for the source impedance according to whether the fault is to earth or between phases.

tv=:j

I DISTANCEt: RELAY

4>.\DIRECT CONNECTION

I: N

I

C (b) TRANSFORMER CONNECTION

FIG.

3.

RELATION BETWEEN VOLTAGE-TRANSFORMER BURDEN AND PERFORMANCE.

setting and hence the minimum voltage-setting is proportional to ~, all other parameters being constant. The general expression relating the voltage range, the voltage-transformer burden, and the basic relay-setting is thus of the form a:.

v~

w.

Factors affecting Relay Performance

Compensation of relays

Voltage-transformer Burden and Relay Sensitivity

A simple distance-relay element which has linear characteristics will have a curve relating applied voltage and current oftheform shown in curve (a) of fig. 4. With zero applied-voltage a certain minimum current known as the pick-up current is required to cause operation. With increasing voltage the operating-current increases

The optimum performance that can be obtained from a given relay is directly related to factors such as the burden on the voltage-transformers at nomal systemvoltage and the minimum operating-current of the basic relay-element. The relation between performance and voltage-transformer burden is illustrated in fig. 3. A relay is represented in fig. 3a which has a voltagetransformer burden Wand operates correctly from the normal system-voltage down to a minimum voltage V m • If transformers of ratio N: 1 are inserted in the input circuit as shown in fig. 3b the normal setting of the relay is unaltered because the ratio VII is unaltered. The minimum voltage is reduced to VmiN but the voltagetransformer burden is increased to W.N". If the useful performance-range of the relay is expressed as the ratio of normal system-voltage to minimum voltage for correct operation, this is related to the voltage-transformer burden by E a:.

Vm

vw.

The burden of the current input circuit is related in a similar manner to the voltage range of the relay. Normally this is not so important as the voltage-circuit burden, the main difference being that the voltage circuit is energised continuously whereas the current circuit is only energised to any extent during fault-conditions. The voltage range of the relay is also closely bound up with the setting in milliwatts (w) of the basic relayelement. For a particular relay the minimum current-

Ip

1m CURRENT

Jp.-Minimum

FiG.

134

pick-up current. Im.-Minimum current for correct operation.

4.

SIMPLE RELAY CHARACTERISTIC.

voltages and currents. The extra voltage range has only been obtained, however, at the expense of using the relay in a very delicate state below the nominal minimum setting. This introduces problems of variation of setting with friction, of long operating-times, and of general mechanical instability. Voltage compensation is therefore to be preferred to current compensation.

linearly. If the nominal impedance-setting is as shown by the dashed curve (b), the cut-off impedance will always be less than the nominal impedance, the percentage error becoming progressively smaller as the inputs are increased. If limits of permissible error are assigned as indicated by the dotted curves (c) and (d), then the relay characteristic must lie in the shaded area to be of practical use. It can be seen that for the example illustrated the minimum current at which the relay can be used is appreciably larger than the minimum pick-up current.

Presentation of Accuracy General

In the previous section the errors in a relay have been assessed in relation to a graph of voltage against current plotted on linear scales (figs 4, 5, and 6). Such a graph does not enable the errors to be determined directly and also has limitations in that the lower end of the scales is very cramped. Alternative methods are briefly reviewed in this section and indication given of merits and demerits of each form.

..,w <{

f-

-'

o

>

/

/

Existing Methods

CURRENT FIG.

5.

The first modification to the basic graph of voltage aginst amperes on linear scales is to replace the linear scales by log. scales. Constant ordinates on the graph now represent constant percentage-errors and difficulties associated with the cramping of scales at the lower value are removed. In order that the errors may be measured directly it is preferable to plot the per-unit impedance as a function of current or voltage. Per-unit impedance is the ratio of cut-off impedance to the nominal impedance setting of the relay, i.e. per-unit impedance of 1 is fully accurate. In this case the per-unit impedance can be plotted on a linear scale and the current or voltage on a log scale. A comparison of the different methods is given in figs 7 and 8. The most useful of these two final methods is that using current, as the minimum pick-up current can easily be obtained. By using current x nominal impedance in place of current as the independent variable, the curves are made more general. The maximum point now corresponds to the normal system voltage. Such graphs provide the most

VOLTAGE-COMPENSATED RELAY CHARACTERISTICS.

In order that the relay may be utilised to full advantage, compensation can be added to produced a curve of the form shown in fig. 5. This compensation may take the form of a non-linear impedance in the voltage circuit of the relay to prevent the voltage-input being effective until a value is reached which corresponds to the product of the minimum pick-up current and the nominal impedance setting.

..,w <{

f-

-'

o

>

CURRENT FIG.

6.

RELAY CHARACTERISTICS WITH CURRENT COMPENSATION.

f-

Z

::>

a: w

Cl.

Compensation can also be obtained by introducing a step in the current-input to the relay. The resulting curve is then of the form shown in fig. 6. At first sight this is attractive and enables the relay to operate down to lower

2

5

10

20

50

10C

CURRENT-AMPS FIG.

135

7.

ACCURACY OF CURRENT GRAPH.

It is again convenient to plot y on log. scales and x on linear scales as shown in fig. 10.

'"

U ZI'O

----

«

-----------

8a. ~

!: Z J

a: '"a.

f-

Z

2

5

10

20

J

50 100

a: a.

VOLTS

FIG.

8.

'"

ACCURACY OF VOLTAGE GRAPH.

H '5 1·0 2'0

convenient method for plotting the results of steady state tests and enable characteristics of relays to be compared and assessed quickly.

5

10

20

50

RANGE-y

FIG.

10.

ACCURACY OF RANGE GRAPH.

Per-Unit Impedance versus Range Presentation Polar Characteristics

The per-unit impedance versus current x nominalimpedance method, while enabling relays to be assessed as individual items, is not readily applicable to assessing the requirement or perfomance of a relay in relation to a power-system. On a power-system, conditions are normally such that at a particular time, the source MY A and the length of protected line are known, the variable factor being the position of fault. At other times the source MY A may have different values. Information on the performance of the relay is required in terms of the length of line at which cut-off takes place as a function of source MY A. Ideally this length is constant. These two variables may be generalised in terms of per-unit fault position (x) and "impedance range factor" 0') where x= ~

andy

=

Zrv

The accuracy-range curves referred to previously can be plotted for various values of phase angle between voltage and current. Normally only the curve at the nominal angle and either side of this angle is required. A general idea of the relay performance outside this region is best given by a series of polar characteristics taken for fixed values of current. It would be theoretically possible to take such curves at fixed values of range (y) but in practice such elaboration is unjustified.

Operating Time of Relays

~

The variation of cut-off impedance with system conditions is not in itself adequate for applying distanceprotection. It is necessary to know the operating-time of the relays as a function of both fault-position and system-source conditions. In the simplified theory of distance-protection, a constant low operating-time of say 60 ms is assumed for the zone-l relays which extend to 80 per cent of the protected line. A further constant time of say 300 ms is assumed for the zone-2 relays up to ISO per cent of the first feeder. In practice the operating-time of a relay may become very long for fault-positions near the cut-off impedance. If the effect is very marked the zone-2 relay may operate before the zone-I relay. thus reducing the effective zone-l cut-off impedance. It is therefore important to present information as regards operating-time which can be readily applied to the evaluation of such effects. Conventional methods of presenting operating-time are considered below. One common method is to plot operating-time as a function of current for specified values of voltage. a series of curves being obtained as in fig. I I. This is difficult to relate to system-conditions. An improved form is shown in fig. 12. Operating-time is here plotted as a function of fault-position. curves

Zrv

and the symbols have the significance shown in fig. 9. The impedance range factor is conveniently referred to a~ range.

FIG.

9.

BASIS FOR IMPEDANCE-RANGE FACTOR

The variables x and yare related to the voltage and current applied to the relay by x x +y

v or

x -

E Z,

. E V

x +y

y

IZrv

136

.

The per-unit impedance/range curves (see fig. 10) already described are a particular contour curve in which the operating-time is infinite, i.e. operation of the relay is marginal. Similar curves can be plotted for a given operating-time and will be of similar shape. By plotting a series of curves in this manner a contour graph is obtained as shown in fig. 13. The outside curve represents the boundary between operation and nonoperation and thus shows the cut-off impedance. Successive curves approaching the origin give decreasing operating-times as the inputs to the relay are increased. The time of operation for a particular set of systemconditions is obtained directly from the graphs by finding the fault position (x) and the range (y) corresponding to the available source MVA and interpolating between contours. The curves can be extended to cover resetimpedances and reset-times as shown in fig. 14, without any difficulty.

400

E w 300 ~

t-

~ 200

i= c(

a:

:t

100

o

o FIG.

2 3 CURRENT

11.

4

TIME v. CURRENT GRAPH.

being given for various values of current. The faultposition is expressed on a per-unit basis, a value of 1 corresponding to the nominal cut-off impedance. It is necessary to use great care in evaluating such curves since a judicious choice of current values can give the impression of good performance as regards operatingtime. Closer examination may show that curves are concentrated in the region corresponding to large inputs to the relay. By replacing the constant current by constant range a set of curves corresponding to a given set of systemconditions is obtained. These are more easily applied. The general form is very much as for the constantcurrent curves of fig. 12.

1·0

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FIG.

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CONTOUR TIMING CURVES.

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1·0 PER UNIT FAULT POSITION

FIG.

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oQ. t-

TIME v. FAULT-POSITION GRAPH.

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II.

RANGE-y

Contour Presentation FIG.

With the methods of presenting operating-time so far described it is necessary to provide a separate curve to show the per-unit impedance range characteristics. It is thus necessary to have two separate sets of curves describing the performance of a relay. With the contour method described below only one set of curves is used to give complete information on both accuracy and operating-time.

14.

EXTENSION OF CONTOUR METHOD TO RESET CURVES.

System Application Contours The contour method of presentation can be extended to cover a complete scheme of distance-protection com-

137

prising a number of relays with different nominalimpedance settings and extra time-lag relays. In this case the nominal impedance used in the assessment of range and cut-off point is taken as that corresponding to the complete length of the protected line. All relaycharacteristics are then plotted on this basis. Overall timing contours are assessed from the individual contours for each relay and only composite curves need to be drawn as shown in fig. 15. Since the performance of the overall protection may be quite different for different types of fault it will normally be necessary to have a series of diagrams covering the principal types of fault such as phase-to-earth, phase-to-phase, and three-phase. The three-phase-fault condition is of particular interest as in most forms of distance protection the direc-

CUT-OFF IMPEDANCE

l'OI====~=========::::::::::".....r-----__-"COOms

RANGE-y

FIG.

16.

THREE-PHASE CONTOUR CURVES.

2' 0 f - - - - - - - - - - - - - - - - -

Test Methods ~

Cl

A method of testing distance-protection has been developed in parallel with the method of presentation described which tests the protection under conditions closely approaching actual conditions. In essence the method consists of providing a mimic three-phase system with source impedances in which relays can be connected to the junction of source and line impedances. Contour curves are thus obtained directly in terms of calibrated impedances without recourse to measurements of voltage and current, thus eliminating one source of errors immediately. The phase angle of the source impedances can be altered, thus enabling desired transient conditions to be set up. The test-bench which enables such tests to be made is described in the following article.

ZONE 2 CUT-OFF

:t

r----_-J.1~200

m.

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FIG.

15.

Typical Characteristics

SYSTEM APPLICATION CHART.

Typical curves for a medium distance relay using the methods outlined are given in fig. 17. These were taken on a polarised mho zone-l earth-fault relay used in our type- H distance-protection. The two sets of curves relate to conditions of minimum and maximum transient. It is of interest to note the effect of the transient on the timing contours and also that with this particular relay the boundary curves are identical. The latter feature indicates that transient over-reach effects are negligible.

tional feature fails for faults at or near the relaying point. The forms of characteristic obtained is indicated in fig. 16. It will be noted that the fraction of the line which is unprotected for particular source conditions on the power-system is obtained directly from the curves. This information is very difficult to obtain from the existing methods of specifying performance.

138

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CONTOUR CURVES TAKEN ON PROTOTYPE MHO RELAY AS USED IN TYPE-H DISTANCE-PROTECTION. CURRENT TRANSIENT AND (b) MAXIMUM CURRENT TRANSIENT.

139

(a) NO

CHAPTER 10 Developments in Bench Testing Facilities for Protective Gear By F. L.

HAMILTON, AND

N. S.

ELLIS.

INTRODUCTION

(d) Provision of facilities for close control of the

The testing of protective-gear systems and their constituent components calls for test-equipment of a rather specialised nature. The requirements of modern protective-gear systems have increased the complexity and cost of such equipment and the amount of testing to be done has necessitated a speeding up in the procedure of tests. The tests which may be necessary on protective-gear equipment are somewhat varied but, in general, will fall into one or more of the following categories.

(e)

test-conditions and parameters. Rapid rate of testing.

General-purpose Test-bench for Protective-gear General

An overall view of the test-bench is shown in fig. 1. The main primary circuits for the test bench are supplied from the 440-volt 3-phase mains, with alternative arrangements for taking this supply from a three-phase variable-frequency machine when necessary. The maximum current which is taken by the primary circuits is of the order of 120 amperes but, as tests at these currents are of a limited time-duration, the supply need not be rated continuously at this current. When the primary currents are of the order of 10 amperes these may be used on a continuous basis. The main primary circuits are shown diagrammatically in fig. 2, from which it can be seen that the threephase supply is applied, by a "fault-making" switch, to two sets of variable impedances per phase, one of which represents a generating source impedance and the other the impedance of a line. The current-transformers, of which there may be up to four per phase, can be connected in various combinations according to the particular fault distribution which it is required to reproduce. The primary circuit has two main functions: (a) To provide primary currents in various combinations of current-transformers, with control of overall time constant, the point of wave at which the fault is applied, the type of fault, and the duration of fault. This function is required when the bench is used for tests where only current is of significance. (b) To provide variable current and voltage conditions at a relaying point with control of time constant, duration of fault, point-of-wave, and type of fault. This function is required when the bench is used for the dynamic testing of relays and protective-systems which require both current and voltage, e.g. distance protection. The equipment required for the above basic functions lends itself to many other test applications which require controlled current and/or voltage conditions. The various units which make up the complete test-bench are described in more detail overleaf.

Investigatory

These include those tests which may be essential on circuits and components during development projects. The scope of these test may be large, as they often explore a variety of effects, design factors, parameter changes, etc. Tests of this type may also include investigations into more fundamental problems, such as the transient response of current-transformers and the effect of this on various protective-systems. The information obtained from such investigations is often used to check the soundness of new ideas and provide practical design-data upon which new experimental equipment may be based or by which existing designs may be modified to improve their performance. Performance Testing

The overall performance of protective-systems, relays, and the like is an important aspect of protectivegear testing. Tests of this type may be concerned with experimental and production prototypes or with the certificiation and type-testing of new protective-gear equipment or relays. In the past, a large amount of the testing referred to above has required heavy-current rigs, which are costly and limited in flexibility. Such heavy-current rigs require extensive machine supplies, the demands upon which are so great that they often form a considerable limitation to the number of investigations which may be undertaken. The protective-gear test-bench described in this article was developed in order to replace the conventional heavy-current and secondary-injection equipment in many types of testing particularly those concerned with investigatory work on experimental projects and prototypes. The main requirements borne in mind in the design of the equipment are as follows: (a) Extreme flexibility of test circuit and conditions. (b) Rapid setting up of equipment. (c) Use of a.c. mains as the source of power.

Source and Line Impedances

One of the main requirements of test-equipment of this type is to obtain current and voltage transients of the

140

FIG. 1.

r I

,---1-

01

VIEW OF TEST-BENCH.

MASTER TIMING

CONTROLLED - - SWITCHING SE~UENCE UNIT

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II CURRENT I I VARIABLE TRANSFORMERS" • VARIABLE MAIN SOURCE I MAKE I FAULT IPRIMARY IcONTACTORIIMPE DANCE tRIMARY-VARIABLE ISWITCH I IMpLE';AENCE ISELECTORSISHUNTS L c.EC~1 ~M~ ~5~MP:..L _ _ 1 ..1 1_ _

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FIG.

2.

SCHEMATI

ARRANGEMENT OF PRIMARY CIRCUITS.

141

I

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order of those which may occur in practice. The source impedances are designed with maximum X/R values of the order of 30 and these produce current-transients which are large enough to be comparable to those obtained with generator and transformer impedances in CONNECTION

cIS

REACTANCi AT 50

UNIT '8 3·0

',0

12·0

24'0

49·0

96·0

X/R (0) FOR ALL CONNECT IONS. 35

(a)

~

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UNIT '9'

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0 Z

{} 0 Z

0

3'0

12'0

49·0

6'0

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36·0

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(h)

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§ 0 Z

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4·0

5·34

0

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practice. The line impedances are designed with a maximum X/R of about 10 which corresponds to that of a typical 275-kV line. Resistance can be inserted to reduced this X/R value to about 2·6 which corresponds to that of a typical 132-kV line. The reactors in both source and line impedances are air-cored so that they are completely linear. Two source-reactors are provided for each phase, each having four sections. These two units are provided with switches so that their sections can be connected in a number of ways and the resulting impedances connected singly, in series, or in parallel to give a total sourceimpedance per phase, variable in relatively close steps between 2 ohms and 144 ohms. This arrangement is shown in fig. 3. The X/R values can be made constant over this range of source-impedance. An earlier version of the bench uses the simpler method of a tapped reactor with manual plug-selection but this has the disadvantage of a varying value of X/R over the range of impedances. Source-impedance is not normally included in the neutral connection, but where tests require a higher value of zero-sequence impedance in the source, the source-impedance of one phase may be connected in the neutral connection. This is permissible, since such tests will invariably be concerned with single or double phase-to-earth faults where one phase is not in use. A neutral link is provided so that resistance may be connected to simulate systems which have a resistanceearthed neutral. Three line reactors are provided in each phase and in the neutral. These represent, when all are in series, a line of approximately 3·5 ohms, the sections being 0,5,1·0, and 2·0 ohms respectively (at 275 kV). By shorting out various sections, the impedance between the relaying point and the fault can be varied from 0-3·5 ohms in steps of O· 5 ohm. The neutral line impedances are half the value of the phase line impedances, giving a typical value of Zo/Z\ = 2· 5 for the line. The arrangement of the line reactors are shown in fig. 4.

0---0

5, 52 S3 Imped •.mce of line units: Phase 0 to 3 -5 ohms in 0-5 ohm steps "'itll phase-angles of 70

Neutral

FIG.

0

2'56

2'9

9·0

10·6

16'0

to 85 .

0 to 1·75 ohms in 0-25 ohm steps with phase-angles of 60 or 70

4.

ARRANGEMENT OF LINE IMPEDANCES.

"Make" Switch and Main Contactor

The function of the main contactor is to connect the voltage-supply to the test-bench a short time (about i sec.) before application of the fault and to interrupt the fault-current after the required duration of the fault. With this arrangement, the main primary circuit is normally dead and is only made alive for the minimum required time. The main contactor is of the heavy industrial type and is capable of interrupting repeatedly the maximum currents at very low power-factors.

32·0

(c)

FIG. 3. SOURCE REACTORS, SHOWING (a) CONNECTIONS, (b) RANGE OF SOURCE IMPEDANCE WITH UNITS IN SERIES, AND (c) RANGE OF SOURCE IMPEDANCE WITH UNITS IN PARALLEL.

142

The "make" switch is required to apply the fault at a particular "point-on-wave", so that high speed and consistency of operation are essential. Experience has shown that telephone-type relays with heavy-duty contacts can perform this duty with comparative ease. The arrangement adopted is shown in fig. 5. One telephonetype relay with two parallel heavy-duy contacts is used per phase, and two auxiliary relays, energised in parallel with these, provide synchronised contacts for timing, interlocking, etc. The standard contacts have been modified by the addition of a momentum transfer-device with practically eliminates contact-bounce. Very consistent operation is thus obtained and wear on these contacts is negligible. The relays are energised from the master control-unit as will be described later.

also provides the facilities for interlinking the primary circuits of the current-transformers to form the various arrangements required. A tapped section of 10 per cent of the secondary turns enables the ratio of some of the current-transformers to be controlled by ± 10 per cent in steps of 2 per cent. The arrangement permits tests up to a current which is equivalent to 30 times the currenttransformer rating at fairly high values of X/R. The amount of influence which the secondary burdening exerts on both the magnitude and time constant of the primary current is relatively small with modern low-VA protection and the arrangement is a fairly close approximation to a current source over the whole range of currents. Typical arrangements of the current-transformer circuits are shown in figs 6a, 6b, and 6c. It should be noted that the reversing-switch in the primary circuits of some current-transformers enables rapid change-over between a single-end-fed internal fault, a double-end-fed internal fault, and a throughfault, when balanced-current systems of protection are being tested. The provision of both I-ampere and 5-ampere secondaries on the current-transformers enables relays and protection for either rating to be tested. Alternatively, one secondary can be used as a search coil while the other is in use, or can be used for the injection of d.c. or a.c. ampere-turns into the current-transformer to simulate certain conditions.

Current-transformers

Up to twelve current-transformers can be energised from the primary circuit in various combinations. They are of typical bar-primary design having normal 300/1 and 300/5 secondaries. Four primary windings are provided to enable the overall transformation-ratio (and thus secondary current level) to be varied over a wide range in close steps. These windings are in the proportion 1 : 3 : 9 : 27 giving primary turns by addition or subtraction of 2-80 in steps of two. Selection of the primary turns is by means of a manual plug board which

Voltage-transformers

FIG.

5.

These are provided so that the voltage windings of relays may be connected to the relaying point, i.e. between the source and line impedances. They are of normal accuracy, suitable for burdens up to 75 VA, and are of ratio 440/110 volts, open-delta windings being provided for relays requiring residual voltage connection. The primary windings of these voltage-transformers may be connected via a selector-switch to a number of positions as follows: (1) Continuous 440-volt supply. This is of use during those tests and adjustments where a continuous voltage-supply is necessary. (2) The source side of the "make" switch, so that the relays are energised at normal voltage prior to the application of the fault-current. This represents the condition, in practice, of a fault occurring on a line which is in service. (3) The line side of the "make" switch, so that the relays are energised by the fault-voltage simultaneously with application of the fault-current. This represents the condition, in practice, of a faulted line being switched into service. The general arrangements of the voltage-transformer connections is shown in fig. 7. It can be seen from this that the current taken by the voltage-transformers is fed through the current-transformers. This is not completely desirable, but with the normal voltage-transformer burdens used in practice the reflected impedance of the

"MAKE" SWITCH ASSEMBLY.

143

voltage-circuits is so large compared with the line impedance that the resulting errors are negligible. This connection is preferable to that in which the currenttransformers are on the line side of the voltagetransformers, since in this case the small voltage-drop across the current-transformers is imposed on the voltage-circuits. This voltage-drop becomes significant when testing with terminal faults close to the relaying point with heavy currents.

PLUG CONNECTIONS

r I AMP

REVERSING SWITCH

'MAKE' SWITCH

MAIN CONTACTOR

\

"-.

(a)

LX FIG. 7.

/

SELECTION OF VOLTAGE-TRANSFORMER CONNECTION.

Master Control-unit I AMP

(b)

(c)

FiG. 6. CURRENT-TRANSFORMERS SHOWING (a) ARRANGEMENT OF TYPE-A UNIT, (b) ARRANGEMENT OF TYPE-B UNIT, AND (c) A VIEW OF TYPE A AND B UNIT.

144

The master control-unit provides the following features: (I) A safety time-lag of about! second between closing of the main contactor and operation of the "make" switch. Interlocking contacts on the contactor and "make" switch ensure that the circuit is always broken by the contactor. (2) 360° control through a "selsyn" and thyratron circuit for selecting the point-on-wave at which the "make" switch closes its contacts. This is accurate and consistent within about 1° or 2°. (3) A timing circuit which controls the duration of the fault-current. Extreme accuracy of interruption of the circuit is not possible but the duration of fault may be adjusted from short faults of the order of 3 loops up to long faults of the order of seconds. (4) A variable pulse which can be used for triggering an oscilloscope at any point in the fault-sequence. This means that the whole of the fault may be observed on a slow time base or that any part of the fault or associated phenomena may be recorded in an expanded form by using a fast time base. This feature is extremely valuable, espeically when used with an oscilloscope equipped with a long persistence tube. Full advantage may be taken of the rapid testing-rate as photographic records may be kept down to a minimum. The general arrangement of the lastest type of control-unit which has been developed is shown in block form in fig. 8. The unit is shown withdrawn from the panel in fig. 9 which also shows the unit construction of the Dekatron counter stages. These are made withdrawable so that units can be easily replaced or interchanged. The selsyn unit provides a variable-phase supply to an electronic squaring circuit from which a pulse-forming circuit is energised. The 51-cycle oscillator may be used as an alternative to the phase-shifter and this provides

MAIN SUPPLY

- 200 V0~----o
PHASE SH IF TER

r-----., SQUARING CIRCUIT

--

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PULSE FORMER

+ SOV DC

n I

PRIMARY

100 ms COUNTER

1000ms COUNTER

D

C-MAIN CONTACTOR D-MAKE SWITCH BASIC

10 mS COUNTER

INTERNAL STOP SELECTOR

TRIGGER SELECTOR

CIRCUIT

~ LOCAL: ) PUSH 4:gV

A

FIRING UNIT

FIRING UNIT

C FIRING UNIT

MAKE' SWITCH 'D'

RE LAY • E'

AUX 11iARY CIRCU ITS CRO. TRIGGER FIG.

8.

BLOCK DIAGRAM OF CONTROL-UNIT.

the facilities for random point-on-wave switching which is sometimes required. The pulse-forming circuit develops a train of pulses at 10 ms intervals which, when taken from the phase-shifter, are locked to a selected point-on-wave of the main supply-voltage. The pulse train actuates a 3-decade "dekatron" counter unit which gives a maximum overall time of 10 seconds. The counter system is arranged to start always on a pulse corresponding to the negative going half-cycle of voltage out of the phase-shifter. Thus the firing unit for the make switch, which is selected to a fixed SOO-millisecond point on the second decade, always fires at the correct pointon-wave which is indicated by the phase-shifter. The firing unit of the make switch contains a thyratron which is triggered at the correct point, discharging a condenser through the "make" switch coil. Fast consistent operation of the "make" switch is thus obtained. The trigger control for the oscilloscope can be selected to any point in the pulse train thus enabling it to be up to t second in advance or 9t seconds later than the firing point of the make switch. This enables the beginning of the fault to be observed or any point after to be expanded on a fast time base. For complete convenience in this respect, a variable 10-20 milliseconds delay is fitted to the trigger circuit to enable triggering to be effected at points between the pulses of the main pulse train. The internal stop selector is also capable of being selected to any pulsc in the train and this is used to trip

the main contactor. The duration of fault may therefore be controlled in IO-millisecond steps from about 2-3 loops up to 9t seconds. Facilities are also provided for stopping the sequence, i.e. tripping the main contactor, from a protection relay under test. The whole test-sequence is automatically controlled from one push-button, the equipment automatically resetting when this button is released.

Fie;. 9.

145

VIEW OF CONTROl.-UNIT.

B

Ancillary Equipment Apart from the facilities offered by the main primary circuit, current-transformers, voltage-transformers, control-unit etc., certain auxiliary equipment has been included in the bench in order to extend its use and provide greater flexibility. The main items are described below: Phase-shifters

A variable-phase supply is a frequent necessity in both protective-systems and relay-testing and this facility has been incorporated in the test-bench. The normal rotary phase-shifters have limitations which make them unsuitable for such use and a special static phase-shifting transformer has been built. The arrangement is as shown in fig. lOa and is basically a tapped three-phase transformer energised from the same power-supply as the main primary circuits. The taps are so arranged that the manual plug-selection of the output circuits on the phase-shifter panel provides a 240-volt supply adjustable in 100 steps through 3600. The plug-selection provides a visual indication of the phase-angle selected. The turns on the various secondary taps are so arranged that output-voltage remains constant independent of its phase-angle. Variac transformers can be inserted in the output to give control of the output-voltage. Two plugselector systems are provided so that two variable-phase supplies may be obtained. The phase-shifter is capable of delivering currents of the order of 10 amperes without significant phase-shift so that there is no zero-correction necessary and the selected phase-angle may be referred to the main supply-voltage. Practice has shown that control in 100 steps is adequate for most tests. Where closer control of phase-angle is necessary an external autotransformer unit has been designed, as shown in fig. lab, which gives control between the 100 positions in steps of

440V MAINS INPUT

ta)

250 V OUTPUT

(b)

FIG. 10. PHASE-SHIFTING TRANSFORMER, SHOWING (a) ARRANGEMENT FOR 100 STEPS, AND (b) THE ATTACHMENT FOR I ° STEPS.

Auxiliary A.C. and D.C. Supplies

In view of the large number of electronic instruments in use which require mains supplies, a number of mains sockets are provided on the bench. These can also be used for auxiliary voltage supplies of fixed phase-angle. A II a-volt d.c. supply which can be used for repeatcontactors is provided on the bench. A repeat-contactor with seal-in contacts and lamp-indication is a built-in feature for relays with no repeat-contactor incorporated.

0

1

•

Voltage Simulators

It is sometimes advantageous to use the main current circuits of the bench to energise the current circuits of a relay, but to use voltages which change in a predetermined way (independent of the bench circuits) on application of the fault-current. A voltage-simulator unit has been designed for this purpose. Potentiometers in each phase-to-neutral voltage enable the voltages on each phase to be adjusted to a particular value to which they will fall from normal voltage when the current is applied.

Timing

A portable electronic timer is normally used in conjunction with the bench. The provision of contacts synchronised with those on the "make" switch ensure easy measurement of overall operating-times of relays and protection. Auxiliary contacts on the main contactor provide similar facilities for measuring the release times of relays on de-energisation.

Primary Shunts and Meters

The primary circuits are provided with current-shunts so that the primary current-transient may be observed by oscilloscope. A multi-range ammeter is provided together with current-transformers so that the steadystate current in any phase or the neutral may be measured. An operations-counter is provided so that the number of operations may be logged. This is useful both from the test and maintenance aspects.

Oscillographic Work

The facilities for triggering oscilloscopes on singlestroke operation enable transient phenomena to be readily investigated on the bench. The ability to repeat shots under controlled test-conditions in conjunction

146

Some of the applications for which the test-bench has been used are described below.

the overall time of operation for faults within the zone may be determined for various source conditions and for varying degrees of transients. With suitable interconnections it has been possible to explore the effect of reversal of current-flow when a switch opens under fault. The effect of the zerosequence impedance of transformers and the efficacy of earth-fault compensation has also been investigated.

Differential Protection

Relays

Most of the protective-systems based on currentbalance of current-transformers can be explored. Protective-systems with up to four terminals can be tested on a three-phase basis, and those with up to twelve terminals on a single-phase basis. The steadystate and transient balance of current-transformers are readily checked by the equipment. The examples of oscillograms shown in fig. 11 illustrate how clearly the problems of transient balance of current-transformers may be demonstrated. These records also show the considerable time constants obtainable and the consistency of point-on-wave switching.

Tests on individual types of relays may be made with or without the effects of current-transformers. Some examples are as follows: (a) The dynamic characteristics of instantaneousrelays with off-set current-inputs. (b) Timing characteristics of overcurrent relays and overshoot measurements. The effect of currenttransformer saturation on time of operation of overcurrent-relays. (c) Dynamic tests on directional-relays.

with long persistence tubes reduces photography to a minimum. It is usually only necessary to photograph traces when permanent records of a particular trace are required.

Typical Application

CONCLUSION The illustrations in this article apply to a new design of test-bench just nearing completion. A previous prototype design has been in use for three years and has proved invaluable. It is of interest to note that nore than 100,000 operations have been done on the earlier testbench with practically no maintenance. The principles developed in these test-benches have been applied to the testing of production-equipment, and a bench of similar type is being supplied to the C.E.A. It is also of interest to note that the equipment developed and the methods used are finding application to University research. For example, a bench of this type is being constructed at Manchester College of Technology for use in post-graduate research and as demonstration equipment, the major items being supplied by Reyrolle.

Distance Protection

Individual distance-relays or complete distanceprotection schemes may be tested in a very realistic manner with extreme rapidity. The provision of line and source impedances affords a realistic relaying point for distance-protection, the source-impedance being varied to simulate the system plant conditions and the line impedance varied to simulate the fault-position. Fine control of the impedance relay setting is effected by means of primary and secondary adjustments on the current-transformers, thus enabling the accuracy of the relays to be determined under switched conditions in addition to ordinary static bench-test. The effects of the primary transients on accuracy is important with highspeed systems and this may be readily explored. Also,

147

TISl

I.

Primary current
lp

Maximum unbalance curren\.

TISI

TIS I

2.

J.

Primary current transient reversed.

L

Unbalance current practically zem.

Ip

Repeat of Test 2.

L

Small unbalance current as remanence builds up.

T~s I

4.

Ip

Repeat of Test 2. Maxinlunl unhalance current Lstahlished.

Tics I 5.

L

Ip

Primary current transient reversed.

i.

Unbalance current practically zero.

Ip

FIG. 11. ZERO-SEQUENCE TESTS ON BALANCED EARTHFAULT PROTECTION WITH LOW-IMPEDANCE RELAY.

148

CHAPTER 11 Distance Protection of Feeders By N. S.

ELLIS.

INTRODUCTION

x

A variety of relays are used in modern schemes of distance protection as produced by different manufacturers. These can be classified according to the theoretical polar characteristics and the type of comparator used in the basic relay element. There are only a limited number of characteristics in general use. These are normally referred to by the terms, plain impedance, ohm, reactance, directional, mho, and polarised mho characteristics. Any type of comparator can be used to produce any type of characteristic. Thus while there appear to be an exceptionally large number of relays in use, all with individual characteristics, in fact the number of types is restricted. All distance relays are characterised by having two input quantities respectively proportional to the voltage and current at a particular point in the power system, referred to as the relaying point. The ideal forms of such relays have characteristics which are not dependent on the actual values of voltage and current but only on their ratio and the phase angle between them. These ideal characteristics which define the conditions for marginal operation are thus completely specified by the complex impedance Z where Z = VII. The impedance Z can be shown on a complex diagram having principal axes of resistance and reactance. The modulus ZI) of Z when plotted as a function of the phase angle (8) of Z completely defines the relay characteristics. The locus of the impedances presented to the relay by the power system can be superimposed on this same diagram. Thus the locus of faults is a straight line through the origin inclined at the angle of the line of impedance to the resistance axis. This is illustrated in fig. 1. Other system conditions such as load currents and power swings can also be represented and are considered later.

LOCUS OF FAULTS ON FEEDER

---f--.l--------- R

'X

FIG.

1.

=

Phase-angle of Feeder Impedance.

IMPEDANCE DIAGRAM FOR SYSTEM FAULTS.

x

(I

OPERATION OCCURS INSIDE SHADED AREA

BASIC POLAR CHARACTERISTICS Plain Impedance The plain impedance characteristic shown in fig. 2 is the simplest in use and consists of a circle with centre at the origin. Operation occurs in the shaded area inside the circle. The significance of this is that the relay operates below a certain impedance level, which is independent of the phase angle between voltage and current.

FIG.

2.

PLAIN IMPEDANCE CHARACTERISTIC.

admittance instead of impedance diagram, gives a straight line. The more general case where the circular characteristic of the plain impedance case is offset by varying amounts is known as the "offset mho" characteristic. Different degrees of offset mho characteristics are shown in fig. 4. Offset mho relays used in practice are intermediate in characteristic between a plain impedance and a mho characteristic and do not normally take the completely offset form of fig. 4b.

Mho and Offset Mho A class of relays is used in which the characteristic is again circular but is not now centred on the origin. The term "mho" is given to the particular case where the circumference of the circle passes through the origin as shown in fig. 3. This term was originally derived from the fact that the mho characteristic when plotted on an

149

x

The polarised mho characteristic is identical to the mho characteristic. There are, however, important practical differences between relays with the two types of characteristics. It should also be noted that the term 'polarised mho' is not in general use and has been introduced in order that the two types may be distinguished. In most of the literature, the term 'mho' is used indiscriminately and a close study is necessary to determine which type of relay is used.

Directional The characteristic is a straight line passing through the origin as shown in fig. 5. Operation takes place on one side of the line as indicated by the shading. X FIG.

3.

MHO CHARACTERISTIC.

x ----~---r'---7''_7'_7'_7'_7'-----R

/

FIG.

5.

DIRECTIONAL CHARACTERISTIC.

Ohm and Reactance FIG.

4a.

The characteristics of this group are also straight lines but they do not pass through the origin. One of the most commonly used forms is the reactance relay shown in fig. 6a in which the characteristic is parallel to the resistance axis. Operation occurs for reactances less than this value. Another is the ohm blocking relay in which the characteristic lies parallel with the locus of the feeder impedance as shown in fig.6b.

OFFSET MHO CHARACTERISTIC.

x

BASIC COMPARATOR DEVICES General Comparators are conveniently divided into two groups according to whether a comparison is made of the amplitude of the two input quantities or of the phase-angle between them. In practice the two types may be made to give exactly similar results and the arrangements of circuits may be similar. It is important to recognise the distinction however as similar circuits used with the two types of comparators will in general give different relay characteristics. Thus, for example, as will be shown later, the circuit used to produce a directional characteristic with an amplitude comparator is identical to that used to produce a plain impedance characteristic with a phase angle comparator.

---j-----------R

FIG.

4b.

ALTERNATIVE OFFSET MHO CHARACTERISTIC.

150

x

OUTPUT

Sr(S

(S,)

/

FIG.

6a.

R

FIG.

7.

REPRESENTATION OF IDEAL AMPLITUDE (OR PHASE-ANGLE) COMPARATOR.

finite amount for an output to be obtained. The equation is then modified to:

REACTANCE CHARACTERISTIC.

I

1f(So)1 > K + f(Sr)1 (2) The function (f) is the same for both inputs and for most devices is either a linear or square function i.e. the signal is either of the form S or S'. Over the working range of the relay it is always necessary for the constant K to be negligible so that the simplified equation (1) may be used. This may be achieved in practice either by making the input quantities very large or by modifying one of the inputs so that a further constant which is equal and opposite to K is effectively added to the equation. It will be noted that the above expressions are independent of the angle between the complex inputs.

LOCUS OF FEEDER IMPEDANCE

x

Phase-angle Comparator The general case may again be conveniently represented by the 'black box' of fig. 7, the two inputs signals now being designated by Sl and S2' The conditions for operation in the ideal case may now be written as:

------'-,-O""""-',-+-'',,---,f-------- R

FIG.

6b.

~

2

< Y

<~

-

(3)

2

where y is the angle by which Sl leads S2' In this case, the operation is independent of the magnitude of the two input quantities. With practical comparators, it is necessary for the inputs to exceed a finite value before operation can be obtained and the expression becomes:

OHM CHARACTERISTIC.

Amplitude Comparators

f(1 SII,1 S2/' cos y) > K. In the simplest case, this function merely involves the product of the three quantities, i.e.

The general case may be conveniently represented as in fig. 7 by a 'black box' with two pairs of input terminal and an output which may take the form of an electrical or mechanical signal. The two alternating input quantities may be either voltage or current according to the particular device in question. If the two inputs are denoted by an operating signal (So) and a restraint signal (Sr), then the conditions necessary to obtain an output can be expressed as: soe.1 sri (1) With all practical comparators it is necessary for the operating signal to be in excess of the restraint signal by a

Isdls21 cos y > K.

Practical Amplitude Comparators Beam Relay

One of the earliest comparators used, which is being gradually superseded, is the balanced beam relay. In this relay, two magnetic circuits are arranged to act at opposite ends of a beam as illustrated in fig. 8. Assuming that

I

151

angle between inputs. So far as is known, it is not used in any modern scheme of distance protection. This type of comparator should not be confused with the induction disc or cup phase-angle comparators described later. In the former the driving torque is the sum of two separately derived torques, whereas in the latter the two compared quantities combine in the production of a single torque.

the turns are equal on the two coil systems and that the magnetic circuits are similar, operation is obtained when +K (5) 01

11 2>11,12

It is necessary to ensure that the operating and restraining forces are adequately smoothed as otherwise there is a tendency for the beam to follow the pulsating forces and violent chattering may be set up. This is

Moving-Coil Relay'3

CJ

A moving-coil relay (see fig. 10) with two operating coils, the general construction of which is similar to that

RESTRAINT FIG.

8.

OPERATE

BALANCED-BEAM AMPLITUDE COMPARATOR.

particularly the case when the two inputs are 90° out of phase. It is difficult to design this comparator to work safisfactorily over a large range of input quantities due to the rapid increase of force with input-currents. The beam must be designed to withstand the large forces corresponding to maximum input and yet must also be sufficiently light to enable a small control force K to be used. The comparator is also very susceptible to positional errors as the operating force increases rapidly with change in position of the beam. The main application of this type nowadays lies in the provision of cheap starting elements with limited range and accuracy requirements.

OPERATE AND RESTRAINT COILS FIG.

MOVING-COIL AMPLITUDE COMPARATOR.

of a loudspeaker movement, is currently used by one manufacturer. With this unit, operating and restraining forces are proportional to the input currents. This, together with the high basic sensitivity of the movingcoil relay, enables a reasonable range to be obtained before thermal overloading limits the maximum values of input currents. As the forces are independent of the position of the coil the unit does not suffer from positional errors and also has a reset value equal to the operating value. An alternative form of relay similar in principle to an ordinary ammeter movment can also be used. In practice this form is currently used only in . conjunction with the rectifier comparator.

Induction Disc

By providing two entirely separate driving mechanisms on an induction disc as shown in fig. 9, an amplitude comparator is obtained. This unit suffers from most of the disadvantages of the beam relay with regard to range of operation but has not the positional errors, as the forces are independent of the actual position of the disc. It is much less efficient however and is slow in operation. There is also interference between the two magnetic circuits, which produces errors dependent on the phase

RESTRAINT

10.

Rectifier Comparator'·

A comparator circuit consisting of two bridge rectifiers and a sensitive output relay is shown in fig. 11. A moving-coil relay is normally used as the sensitive element, both axial and rotary types being currently used. The unit is capable of operating over a large range as the sensitive relay never obtains large restraint or operating inputs, these being limited by the action of the rectifiers to a value in the region of 3 to 5 times the relay-setting.

OPERATE

Transductor 12

FIG.

9.

The transductor can be used as shown in fig. 12. The output winding of the transductor is directly coupled to an input winding to which is applied the operatingcurrent input. The restraint input is rectified and applied to the bias winding of the transductor. The unit is inher-

INDUCTION-DISC AMPLITUDE COMPARATOR.

152

~

OPeRATE INPUT

RESTRAINT INPUT FIG.

11.

LEAF SPRING

RECTIFIER-BRIDGE AMPLITUDE COMPARATOR.

ently sensitive but has certain disadvantages associated with the transient response. It is not currently used by any manufacturer. FIG.

Polarised Moving Iron"

A large number of relays are in use which employ a magnetic circuit and an attracted armature. These are of two types, one of which is not sensitive to the direction of the d.c. flux in the magnetic core and is not suitable as a comparator. The other type has a permanent magnet somewhere in the magnetic circuit and will only operate for a given sense of the d.c. input to the coil system.

13.

POLARISED MOVING-IRON COMPARATOR.

direction, the armature releases under the action of a mechanical spring. The relay must be reset by hand or by an auxiliary set of relays which complicates the overall scheme of protection.

Practical Phase-Angle Comparators Induction Disc

A torque is obtained by the interaction of the fluxes from the two magnet circuits which act in close proximity on the copper disc as illustrated in fig. 14. The unit has a very low sensitivity and suffers from interaction between the two magnetic circuits. It is also difficult io balance and there is a tendency for spurious torques where only one input is applied. It is currently used in directional elements where high performance is not required.

OPERATE INPUT

RESTRAINT INPUT FIG.

12.

TRANSDUCTOR AMPLITUDE COMPARATOR.

Relays of this type can be used as comparators by having double coils, one being used for the restraint input and the other for the operating input. Since the coils are on a common magnetic circuit, there is a certain amount of mutual coupling between the two inputs, which must be considered in the design of a relay with such a comparator. One type which is in use is illustrated schematically in fig. 13. An armature is held in an operated position in a loop magnetic circuit due to remanent flux. When the flux in the magnetic circuit is in the correct

FIG.

153

14.

INDUCTION-DISC PHASE-ANGLE COMPARATOR.

x

Induction Cup'

The induction-cup comparator is illustrated in fig. 15. It is an improved version of the induction disc phaseangle comparator just described. It is more efficient, can work over a larger range of input quantities, and has very little interaction. The forces are proportional to the product of the input quantities. In order to limit the torque produced at high inputs, a clutch mechanism is sometimes inserted between the contacts and the cup.

FIG.

INPUT 2

Is]

15.

IMPEDANCE DIAGRAM FOR

I z I<

1.

If now the sum and difference of two input quantities SI and S2 are fed to the comparator such that So=SI + S2 and Sr=S]-S2, the equation for operation becomes:

INPUT I FIG.

16.

+ S21 > IS]-S21·

If ~I = w where

w is complex quantity with

S2

INDUCTION-CUP PHASE-ANGLE COMPARATOR.

angle y, this equation can be written as

Iw 1/

+ >1w-ll. This can be seen to represent a straight line on the imaginary axis through the origin as shown by the graphical construction of fig. 17. This however, is the characteristic of the ideal phase-angle comparator and can be expressed alternatively as

Electronic Relays

Experimental comparators have been produced using valve circuits 1" 15. Many of these have been very crude and lacking in accuracy, while others, though accurate, have been exceptionally complicated. None of them has found practical application as yet apart from experimental insallations. Present indications are that the transistor 18. 19. 20 offers a lot more promise here and may well be applied in the not far distant future in applications where exceptional range is required and for very high speeds. It will be noted that electronic comparators have been described under the heading of phase-angle comparators. This is deliberate as they lend themselves far more readily to this than to the amplitude comparator.

DERIVATION OF IDEAL CHARACTERISTICS Relation between amplitude and phase-angle comparators The expression for marginal operation of the ideal amplitude comparator has been given previously as: ISol>lsrl This can be written as:

FIG.

IMPEDANCE DIAGRAM OF

I w + 1I> I w -

1I

The combination of an amplitude comparator and ideal transformers is thus exactly equivalent to a phaseangle comparator and is illustrated in fig. 18. It can be shown that the converse, as illustrated in fig. 19, is also true.

where z = -Sr'So The characteristic of z on a polar graph is a circle as indicated in fig. 16. 1..Iz~

17.

1

154

AMPLITUDE COMPARATOR

PHASE·ANGLE COMPARATOR

I I

FIG.

18.

EQUIVALENCE OF PHASE-ANGLE COMPARATOR TO AMPLITUDE COMPARATOR PLUS IDEAL TRANSFORMERS.

Plain Impedance Characteristics

In general, therefore, any characteristic which can be produced by one comparator can also be produced by the other comparator with a different combination of the input quantities. The required relations are given below: or So=Sj + Sz and Sr=Sj-SZ, or Sj

So + Sr and Sz= So

2

From what has already been done, it is fairly easily seen that a plain impedance characteristic can be produced by applying a quantity proportional to the system voltage as the restraint input, and a quantity proportional to the system current as the operating input in an amplitude comparator. The system voltage and current considered are those associated with the faulty phase or phases.

Sr'

2

Derivation of Characteristics General

Thus

Having shown the equivalent of the two types of comparators it is convenient to take each characteristic in turn and consider first in each case that comparator which most simply produces the desired results.

or

I

11l2: ~I Zr

where So = I and Sr =

I:£ I <1 where Z = .~I Zr AMPLITUDE COMPARATOR

PHASE·ANGLE COMPARATOR

1

(VOLTAGE)

V\J'\JI.I ~-,

FIG.

19.

EQUIVALENCE OF AMPLITUDE COMPARATOR TO PHASE·ANGLE COMPARATOR PLUS IDEAL TRANSFORMERS.

155

~, Zr

The overall equation becomes:

The phase-angle of the impedance Z has no effect on the ideal characteristics. In practice, however, it may be significant where non-ideal comparators are used in which the characteristic is not an exact circle.

I~ I

Z-nZrLSI Zrl· This can be seen to represent a circle by the graphical construction of fig. 21. The difference between the complex impedances Z, represented by the line OA, and nZr represented by the line OC, is constant and equal to if the locus of A is a circle with centre at C and radius

From the previous analysis, it is again easy to see that a directional characteristic is obtained directly from a phase-angle comparator by making one input proportional to the system current and the other to the system voltage.

IZrl

IZrl·

~< (8 - ,8)-:s~where Sj = I,

2-

I
which reduces to:

Directional Characteristic

Thus -

-nI

-2

v

Z;;-' A

the angle of Zp is ,8, and the angle of Z is 8. The phase-angle of Zp determines the angle of the perpendicular to the characteristic as indicated in fig. 20. The magnitude of Zp has no effect on the characteristics in this case.

IZ, I

FIG. 21.

FIG. 20.

TO

IZ -

nZ r

I = I Z,I·

For the particular case in which n = 1, the circumference of the circle passes through the origin. It should be noted that this does not give a true directional action for very small impedances which are obtained for faults near the relaying point. The corresponding inputs in the case of the phaseangle comparator are obtained as:

DIRECTIONAL CHARACTERISTIC.

The corresponding inputs to the amplitude comparator become:

S 1-

I - ~, Zp Zp and the overall equation for the amplitude comparator is:

So

CHARACTERISTIC

= I + ~and S, =

(1-n)1+ V/Zr and S2= (1+n)I - V/Zr 2 2

Ohm Characteristic

The ohm characteristic is obtained with the amplitude comparator by feeding the voltage signal into each side of the comparator and the current into the operating side. The inputs are given by V So=I +--. Z,

Offset Mho Characteristic

An offset mho characteristic is obtained with an amplitude comparator by taking a plain impedance relay as described and feeding a fraction of the operating current into the restraint input. Thus the two inputs are now given by:

_ V

S,---. Z, The overall equation thus becomes

So = I, and S, = -v- - nl. Z,

I ~ I < 'I 156

+

iI

and

Izi


to multiply both inputs by the same terms and consider the phase relation between the following two modified inputs

This represents a straight line as illustrated in fig. 22. The perpendicular to this line from the origin is equal to Z,/2. The phase-angle (ex) of Z, controls the angle at which the characteristic is inclined to the axis.

S'J= ~ '!:Lz, and S'2=Zr-Z, V r Zp The simplest case is where the input S' Jcan be taken as a scalar quantity times the impedance Z. (This is equivalent to assuming that the polarising and restraint currents are in phase.) This can be seen to represent a circle by the graphical construction of fig. 23. The major diameter of this circle is the impedance Z,. The condition that the angle between (Z) and (Z,-Z) is a rightangle is that the locus of (Z) is a circle centred on (Z,) as a diameter.

x

---+-----~~--

FIG. 22.

CHARACTERISTIC OF I Z

R

I < I Zr + ZI·

The more general case in which the voltage signal injected into the operate side of the comparator is not equal to the restraint signal results in an offset mho characteristic. This form of offset mho relay has practical limitations and is not in general use. The corresponding inputs for the phase-angle comparator are: _ I V I and SJ--+--. S2= 2 2 Zr

FIG. 23.

POLARISED MHO CHARACTERISTIC.

In the more general case where the polarising and restraint currents are displaced by an angle (y) the characteristic is still a circle but of the form shown in fig. 24. The angle between (Z) and (Z,-Z) is now (90 _y) on one side of the impedance Z, and (90°+ y) on the other side. 0

Polarised-Mho Characteristics

This characterisitic is most easily obtained using the phase-angle comparator. One input is taken from a suitable reference voltage which will be termed the polarising voltage (Vp ). The other is taken as the difference between voltage and current. The two inputs can thus be written down in the form.

Sl=~' Zp

Z-Zr

So=I-~.

Zt Generally, the polarising voltage can be related to the restraint voltage by an angle (~such that

~=IC~ Vr The ratio C can have any value. To analyse the behaviour of this relay it is necessary to determine the conditions for there to be a ::+::90° shift between the two input-signals SI and S2. It is convenient

FIG. 24.

157

GENERAL CASE OF POLARISED MHO.

In practice it is usual to work with the particular case of polarising and restraint currents in phase, though small angular shifts are used to some extent to swing the characteristic round. The performance of a practical relay deteriorates as the angular shift is increased. The corresponding inputs in the case of the amplitude comparator become So =~ + 1 - -V-r , Zp

Zr

andS=~ -1+ ~ r

Zp

Zr

MODIFIED CHARACTERISTICS General

E =30"

E =15'

Modified polar characteristics can be obtained in a number of ways. In general, these have found very little application up to the present. A brief survey of the various methods is given in this section.

E =0°

FiG.

26.

MODIFIED IMPEDANCE CHARACTERISTICS.

Modified Two-input Phase-angle Comparator A phase-angie comparator can often be arranged so that the cut-off angles are some angle less than 90°. The equation can thus be rewritten as

This results in modified forms of the various characteristics. These are shown in figs 25-27 for the directional, plain impedance, and polarised-mho relays. The offset mho and ohm characteristics are of identical shape to the plain impedance and directional relays respectively but with offset axes.

'---;---t- E ~ 30°

E = 15° /

x FIG,

27.

MODIFIED POLARISED MHO.

\ \

The flattened form of polarised mho and offset-mho characteristics are used by one manufacturer, the flattening being at right anles to the locus of the system fault.

Three-input Amplitude Comparator -------:~::__------

An amplitude comparator can be be made with three inputs·. This can be represented by an equation

R

Isrli ± Isr21

E =0° FIG.

25.

<

I Sol

.

Elliptical characteristics are obtained by making the inputs as follows: SrI=V-ZA I Sr2=V-ZB I So=Zc I, and using the additive arrangement.

MODIFIED DIRECTIONAL CHARACTERISTIC.

158

Iv -

v-

I Zcll,

Thus ZAI/ + I ZBII < which can be rewritten as

PERFORMANCE OF PRACTICAL IMPEDANCE-MEASURING RELAYS General

I

IZ-ZAI + I Z-ZBI < Zcl The characteristics are shown in fig. 28 and can be deduced from the property of the ellipse that the sum of the distance from the two foci to a point on the curve is constant.

The ideal polar characteristics so far described are independent of the actual values of current and voltage applied to a distance measuring relay and depend only on the ratio of the input quantities. Practical distance relays depart from the ideal and have characteristics which depend on the actual values of voltage and current. An approximation to the ideal is obtained only over a limited range of input quantities. Inside this range the relay will have errors which are acceptable, and outside this range it will have excessive errors and may not operate. The operating time of the relay will be variable depending on the individual magnitudes of the input quantities, being for example long for small inputs near the cut-off impedance and short for large inputs well within the cut-off impedance. The complete representation of a practical relay has thus to include information on these aspects in addition to the ideal polar characteristics.

x

/

/

/

Z-ZA j

/ /

/

/

/

I

I

/

Performance requirements of Power System

/

The requirements for a particular distance relay can be assessed in relation to the power system by reference to the simplified diagram of fig. 30. Z, represents the

------f-------R

Zs FIG.

28.

r FIG.

•, •, I I

Z-ZA, "

,"

J--

,,

.-

,

. ..

,

) Za

Z-Za

--- ------

ZA FIG.

29.

30.

BASIC CIRCUIT OF POWER-SYSTEM UNDER FAULT CONDITIONS.

source impedance from the relaying point (P) back to the generators and Zj the fault impedance of the power system from the relaying point to the fault. Both are supplied from the open-circuit system voltage (E). The current and voltage applied to the relay via the current and voltage transformers at the junction of the two impedances are proportional to those at the relaying point. The source impedance (Z,) depends on the amount of generating plant available behind the relaying point and is directly related to the short-circuit MVA at the relaying point. This will vary according to the system conditions but it will normally be possible to assign upper and lower limits to the short-circuit MVA and hence to Z,.

I

, ,,

P

ELLIPTICAL CHARACTERISTIC.

Using the subtractive arrangement and similar inputs a hyperbolic characteristic is obtained as shown in fig. 29. Relays have been constructed using these comparators but have not found any application as yet.

, ,,

I

HYPERBOLIC CHARACTERISTIC.

159

The fault impedance (Zf) is proportional to the distance of the fault from the relaying point. The ratio of the voltage and current applied to the relay is always equal to Zr, but the actual values are determined by both Zs and Zf. Consider a fault at the nominal cut-off impedance of the relay. The impedance Zf is thus fixed and will normall correspond to 80% of the line protected. The voltage at the relaying point is then determined only by Zs. For a very large MVA source, i.e. small Z" this voltage will approach the normal system voltage. For a small MVA source, i.e. large Z" the voltage will only be a fraction of the normal voltage and will be determined by the ratio Zs/Zf' A practical relay is required to work correctly between these limits of voltage. Since the top limit is normally fixed by the system voltage, it is usually necssary only to specify that the relay will work down to some minimum voltage V m' Apart from the magnitudes of the impedances Zs and Zf it is necessary to consider their phase-angle. This determines the time constant of the primary transients which will occur in the voltage and current waveforms when a sudden fault is applied. With high speed relays this factor beomes of great importance as the relay is required to measure correctly during the transient period. As relays are generally connected to a three-phase system, the problem is more complicated than that shown in fig. 30 as different types of fault can occur. The problem can always be reduced to the simple case for a particular fault though it may be necessary to use different values for the source impedance according to whether the fault is to earth or between phases.

..

....V

Zr A

--

.. Ir

~

FIG.

31.

10 AMPLITUDE COMPARATOR (CURRENT)

I 1">

PLAIN IMPEDANCE RELAY.

Compensation of Characteristics

It will be noted in the above example that the minimum current at which the relay can be used is appreciably greater than the minimum pick-up current. In order that the relay may be utilised to full advantage, compensation can be added to produce a curve of the form shown in fig. 33. This compensation may take the form of a non-linear impedance in the voltage circuit of the relay to prevent the voltage input being effective until a value is reached which corresponds to the product of the minimum pick-up current and the nominal impedance setting.

E

Factors affecting Relay Performance Characteristics of Simple Relay

(b)

The various factors affecting the performance of a relay are most easily explained by taking a simple example such as the plain impedance relay based on the amplitude comparator. Considering a linear comparator comparing current signals, a circuit of the form shown in fig. 31 could be used. The relevant equation for operation is

V

Vm

These characteristics are shown in fig. 32 (curve a). With zero applied voltage a certain minimum current known as the minimum pick-up current (ip) is required to cause operation. With increasing voltage the current required increases linearly. At large inputs the impedance setting of the relay approaches Zr which is taken as the nominal setting of the relay. If limits of permissible accuracy are assigned as indicated by the line (b) and (d), the relay characteristic must lie within the shaded area to be of practical use. The useful working range of the relay thus lies between the minimum voltage V m and the normal system voltage (E).

FIG.

32.

CHARACTERISTICS OF SIMPLE RELAY.

Compensation may also be obtained by introducing a step in the current input to the relay. The resulting curve is then of the form shown in fig. 34. At first sight this is attractive and enables the relay to operate down to lower voltages and currents. The extra voltage range can only be obtained, however, at the expense of using the relay

160

A relay is represented in fig. 35a which has a voltage transformer burden Wand operates correctly from the normal system voltage down to a minimum voltage Vm' If transformers of ratio N: 1 are inserted in the input circuits as shown in fig. 35b, the normal impedance setting of the relay is unaltered because the ratio VI is unaltered. The minimum voltage is reduced to VmN but the voltage transformer burden is increased to WN'. If the useful performance range of the relay is expressed as the ratio of normal system voltage to minimum voltage for correct operation, this is related to the voltage transformer burden by:

v

a:

Vm

VW.

---

FIG.

33.

W

VOLTAGE COMPENSATED.

DISTANCERELAY

in a very delicate state below the normal minimum setting. This introduces problems of variation of setting with friction, of long operating times, and of general mechanical instability. Voltage compensation is therefore to be preferred to current compensation.

(a)

WN

2

I: N

. - - - - - - - - - , NI

]IIINV

DISTANCERELAY

I: N

IIC

(b)

Direct Connection. Transformer Connection.

(a) (b)

v

FIG.

35.

RELATION BETWEEN VOLTAGE-TRANSFORMER BURDEN AND PERFORMANCE.

FIG.

34.

The burden of the current input is related in a similar manner to the voltage range of the relay. Normally this is not so important as the voltage circuit burden, the main difference being that the voltage circuit is energised continuously whereas the current circuit is only energised to any extent during fault conditions. The voltage range of the relay is also closely bound up with the sensitivity of the basic relay element. For a particular relay the minimum current setting and hence the minimum voltage setting is proportional to ~, when w is the sensitivity expressed in milliwatts, all other parameters being constant. The general expression relating the voltage transformer burden and the basic relay setting is thus of the form

CURRENT COMPENSATED.

V.T. Burden and Relay Sensitivity

The optimum performance that can be obtained from a given relay is directly related to factors such as the burden on the voltage transformers at normal system voltage and the minimum operating current of the basic relay element. The relationship between performance and voltage transformer burden is illustrated in fig. 35.

E VOl

161

a:

jlW

\ W

The maximum voltage that can be applied to a given relay is often limited by thermal effects. The designs may thus be chosen so that the voltage corresponds to the normal system voltage. This can be achieved by the use of voltage-matching transformers or in most cases by the suitable choice of turns level on the relay coils. With a given sensitivity of relay element, this places a fundamental restriction on the maximum obtainable range. Exactly similar limitations occur due to mechanical forces and saturation of magnet circuits.

design of the impedance element it is possible to minimise the effects of the transients and still maintain a fast operating time. Theoretically a relay can be made free from transient effects by the correct use of a 'replica impedance'. In essence the principle is to ensure that the transient inputs are identical on both sides of the comparator. This is achieved by deriving a restraint current from the voltage through an impedance which is equivalent to the impedance of the faulted line. The transient components of operating and restraint currents are then identical.

Distortion, Operating Time and Transients

PERFORMANCE SPECIFICATION OF IMPEDANCE MEASURING RELAYS Cut off Impedance

Distortion of Characteristics

Review of Methods of Presentation

!he operating torque of a relay is in general of a pulsatIng n~t~re due to the alternating nature of the input quantItIes. When the operating and restraint inputs are in phase in an amplitude comparator, this is not normally of great consequence as the restraint and operating torques pulsate together and there is only a small residual pulsating torque on the relay element. If the operating and re.straint inputs are not in phase, however, very large pulsatIng torques are set up. These may cause distortion of the characteristics. For example, with a balanced beam relay, violent chattering commences and the setting becomes indeterminate. The effects may be minimised by electrical or mechanical 'smoothing', but this tends to increase the operating time of the relay. Because of this, it is normal to arrange that measurement ~s made w~en the inputs are approximately in phase In any partIcular design of relay. Apart from the fact that greater accuracy and consistency is obtained the operating time is in general smallest along this axis.

Under the heading 'Factors Affecting Relay Performance' the errors in a relay were assessed in relation to a graph of voltage against current plotted on linear scales (figs 32, 33, and 34). Such a graph does not enable the errors to be determined directly and also has limitations in that the lower ends of the scales are very cramped. Alternative methods are reviewed briefly in this section and indication given of the merits and demerits of each form. The first modification to the basic graph of volts against amperes is to replace the linear scales by log scales. Constant distances on the graph now represent constant percentage errors and difficulties associated with the cramping of scales at lower values are removed. In order that errors may be measured directly, it is preferable to plot the per-unit impedance as a function of current or voltage. Per-unit impedance is the ratio of cut-off impedance to the nominal impedance setting of the relay, i.e. per-unit impedance of I is fully accurate. In this case, the per-unit impedance can be plotted on a linear scale and the current or voltage on a log. scale. A comparison of the different methods is given in figs. 36 and 37. The most useful of the two final methods considered is that using current, as the minimum pick-up

Thermal, Mechanical and Saturation Limitations

Operating-time

The operating-time of a distance relay is dependent on a number of factors and cannot be simply assessed. The factors involved are: magnitude of individual inputs, ratio of inputs, phase angle between inputs, and transient components of each input. In order that fast operating-times can be obtained it is necessary to use light movements with low mechanical inertia. This conflicts with the requirements for 'smoothing' and some compromise is always necessary.

'"0f------7'""""'======== I.>J

U

Z

«

a I.>J 0-

f Transients

'Z=

When a fault occurs on a power system a transient d.c. component exists in both current and voltage inputs to the relay. These transient components may cause 'overreach' of the impedance measuring elements, i.e. transient operation for impedance in excess of the steady state setting. The transient components may alternatively cause an increase in operating-time. By correct

::J

d: LlJ

O-l-r---L.,-----;--r--r---,--...;-2 5 10 20 50 100 CURRENT (AMPERES)

FIG. 36.

162

PER-UNIT IMPEDANCE/CURRENT GRAPH.

Ls

1'0 w U

Z

-<

0 w

~

L I-

Z

:::>

FIG.

38.

BASIS OF RANGE FACTOR.

d::.

""


2

5

10

20

50

100

VOLTS

37.

FIG.

w

PER-UNIT IMPEDANCE/VOLTAGE GRAPH.

U

~ 1·0 I:===:=:========:::::~--

ow

1I-

current can easily be obtained. By using current times nominal-impedance in place of current as the independent variable, the curves are made more general. The maximum point now corresponds to the normal system voltage. Such graphs provide the most convenient method for plotting the results of steady-state tests and enable characteristics of relays to be compared and assessed quickly.

~

.... Z :>

~ w

1I-

'1 FIG.

Per-unit Impedance versus Range Presentation 17

The per-unit impedance versus current times nominal-impedance method, while enabling relays to be assessed as individual items, is not readily applicable to assessing the requirements or performance of a relay in relation to a power system. On a power sytem, conditions are normally such that at a particular time, the source MVA and the length of the protected line are known, the variable factor being the position of the fault. At other times, the source MVA may have different values. Information on the performance of the relay is required in terms of the length of line at which cut-off takes place as a function of source MVA. Ideally this length is constant. These two variables may be generalised in terms of per-unit fault position (x) and 'impedance range factor' (y) where

39.

·2

'5 "02"0 5 10 20 RANGE 7j

50

PER-UNIT IMPEDANCE/RANGE GRAPH.

Polar Characteristics

The accuracy range curves referred to previously can be plotted for various values of phase-angle between voltage and current. Normally only the curve at nominal angle and either side of this angle is required. A general idea of the relay performance outside this region is best given by a series of polar characteristics taken for fixed values of current. It would be theoretically possible to take such curves at fixed values of range (y) but in practice such elaboration is unjustified.

Operating-time of Relays General

x

=

ZF and y ZN

= ~,

The variation of cut-off impedance with system conditions is not in itself adequate for applying distance protection. It is necessary to know the operating-time of the relays as a function of both fault position and system source conditions. In the simplified theory of distance protection, a constant low operating-time of say 60 mS is assumed for the zone-1 relay which extends to 80% of the protected line. A further constant time of say 300 mS is assumed for the zone-2 relays up to 150% of the first feeder. In practice the operating time of a relay may become long for fault positions near the cut-off impedance. If the effect is very marked the zone-2 relay may operate before the zone-1 relay thus reducing the effective zone-1 cut-off impedance. It is thus important to present information as regards operating time which can be readily applied to the evaluation of such effects.

ZN

and the symbols have the si~I).ificance ~hown in fig. 38. The 'impedance range factor IS convemently referred to as 'range' and this sliortened form will be used from now on. The variables (x) and (y) are related to the voltage and current applied to the relay by

v

=

(~:

y)

E

V orx = IZN

It is again convenient to pilot y on log scales and x on linear scales as shown in fig. 39.

163

Review of Methods

Various methods of presenting operating-time characteristics are in current use by various manufacturers. One common method is to plot operating-time as a function of current for specified values of voltage, a series of curves being obtained as in fig. 40. This is difficult to relate to system conditions. An improved form is shown in fig. 41. Operating time is here plotted as a function of fault position, curves being given for various values of current. The fault position is expressed on a per-unit basis, a value of 1 corresponding to the nominal cut-off impedance. It is necessary to use care in the evaluation of such curves, it being possible for all the curves to represent large inputs to the relay. By replacing the constant current by constant range, a set of curves corresponding to a given set of system conditions is obtained. These are more easily applied and assessed. The general form is very much the same as the constant current curves of fig. 41.

w

I:

i=; o

z

~

«c<: w

0..

o

1'0

PER·UNIT FAULT POSITION FIG.

41.

TIME/FAULT-POSITION GRAPH.

The per-unit impedance versus range curve already described is a particular contour curve in which the operating-time is infinite, i.e. operation of the relay is marginal. Similar curves can be plotted for a given operating-time and will be of similar shape. By plotting a series of curves in this manner, a contour graph is obtained as shown in fig. 42. The outside curve repres-

Contour Presentation

With methods of presenting operating time so far described it is necessary to provide a separate curve to show the per-unit impedance versus range characteristics. It is thus necessary to have two separate sets of curves describing the performance of a relay. With the contour method described below, only one set of curves is used to give complete information on both cut-off impedance and operating time.

H

z0 o

400

1'0

~ VI

o

10

0..

~

....J

u

~

~

«

LL

300

...J ...J

I: '1 '2

LoU

I: 200

5

I

2

RANGE

~

5 10 20

50 100

Y

o

z

FIG.

f=

~

42.

CONTOUR TIMING CURVES.

100

u.J 0...

o o

2

ents the boundary between operation and nonoperation and thus shows the cut-off impedance. Successive curves approaching the origin give decreasing operating-times as the inputs to the relay are increased. The time of operation for a given set of system condtions

4

CURRENT FIG.

40.

TIME/CURRENT GRAPH.

164

Linear Comparator

The linear comparator has a characteristic as illustrated in fig. 44. It will be seen that the setting is constant in terms of either input and that the curve has a discontinuity at the point where the two setting lines cross. Curves at different phase-angles between inputs are parallel, the settings becoming higher as the phase-angle difference is increased.

System Characteristics · I .2

·5

I

3

RANGE FIG.

43.

Plain directional relays are normally only applied for earth-fault distance protection and are energised from residual voltage and current at the relaying point. Phase-fault directional relays are practically always made in the form of crude polarised mho relay and can be treated by the methods developed for impedance measuring relays. It is thus only necessary to determine the relation between residual current and voltage at the relaying point for various source and line conditons to obtain the requirements for practical earth-fault dirctional relays. The general form of these requirements can be seen from a consideration of the simplified system of fig. 45(a) in which a single-phase-to-earth fault is consi-

5 10 20 50 100

!I

EXTENSION OF CONTOUR METHOD TO RESET CURVES.

is thus obtained directly from the graphs by finding the fault position (x) and the range (y) corresponding to the available source MVA and then interpolating between contours if necessary. The curves can be extended to cover reset impedances and reset times as shown in fig. 43 without any difficulty.

PERFORMANCE OF PRACTICAL DIRECTIONAL RELAYS General As directional relays have no impedance setting the methods of specifying performance described for impedance-measuring relays are not generally applicable. Only the contour timing curves are of any application and these are normally considered in relation to an overall scheme in which impedance and directional relays are used in conjunction. This aspect is discussed later under the heading "System Application Charts". So far as the directional relay is concerned, the main information required is the relation between voltage and current for marginal operation of the relay. This must then be related to the voltage and current available under various system conditions.

(a) \ (b)

'i , \IiI sonl-- ! !'\I 1---+ i

20

v

Voltage-Current Characteristics

!

~.--t---t----t---t

!

,

I

I

5!

I

I

IO~-i~'i

I

-"--r~~(C~)-

Square-Law Comparator

The characteristics of directional relays in use nowadays can be divided into two groups, the square-law and linear comparator. These have appreciably different characteristics. The square-law comparator has an equation of the form.

2 I

·---1 . .-----+------+-~"",,.---t------+ i i , ... ! -! I L-....J __~_______' _ _______'__

..l----:""_____'

I

II I

lSI Sz cos e > K At a fixed value of the phase-angle between inputs this is the equation of a rectangular hyperbola. Thus if the characteristics are plotted on log.-log. scales the locus is a straight line as illustrated in fig. 44. Curves taken at other angles will also be straight lines parallel to the original line.

(a) (b) (e)

FIG.

165

2

5

10

20

50

Square-law comparator. Modified square-law comparator. Linear comparator.

44.

SQUARE.LAW DIRECTIONAL RELAY.

100

SOURCE IMPEDANCE

LINE IMPEDANCE

Zso

Z/o

Z"

Z/.

8-D------10~;

tva

D-----r-17 .J

SINGLE PHASE-TO-EARTH FAULT (a)

100 50

J----I------+---+_-r--I-----.'<---+~L-+__r_-+__r'_'---___+_r'_'_______'

J:-L---l.'<--~ 0

20

10

5 In

to-

..J

0

> ..J

2

-<

:::> 0

V;

w

'" '5 In

.,

L---L-----.l

..J

..J

1:

1:

~

1:

0 0

0 0

0

N ""

""

N

.I

W

W

..J

·2

In

In

W

.L--'------.l_---'--'-----.l_---'-'-_---'-_ _-'--_ _--'--_----'

'5

I

2

5

10

20

RESIDUAL CURRENT (AMPERES)

Source

Boundary curve shown for: 100-2500 MY A. Line 100 miles. (b)

FIG.

45.

ApPLICATION OF DIRECTIONAL RELAYS.

166

50

100

MI LES

dered. For this system the following relations can be shown to apply: Residual current =31 0 =

ZSI(2+ Zso)+ Zf1 ZSI Residual voltage=3V= -3Zso 10 ,

POLARISING SUPPLIES General In the previous descriptions of impedance measuring and directional relays, reference has been made to three input quantities to the relay. These were operating current, restraint voltage, and polarising input. The first two determine the complex impedance (Z) measured by the relay and are derived from the voltage and current associated with the fault. The third quantity is essentially a reference for determining the phase-sense of the operating current and may be derived from a variety of quantities. The requirements for the polarising input may be summarised as follows: (a) The phase-angle of the polarising input should be fixed relative to the restraint voltage. (b) The magnitude of the polarising input is unimportant so long as it is never zero, e.g. for terminal faults, when the restraint voltage is zero the polarising input must still exist. In practice it is not possible to satisfy these two requirements completely. The different methods in use for polarising suffer from limitations and are discussed in the following sections.

(2+~) Zf1

Considering the above expressions it can be seen that low voltages and currents are obtained together with a low source-impedance and a large line-impedance. The boundary line within which the voltage and current must lie can be plotted on a voltage/current diagram as in fig. 45(b) if limits of source and line impedance are known. In this diagram a particular type of system is chosen by way of example in which the source has a ZO/Zl ratio of 0·5 and the line has a Zo/Z ratio of 2·5. Similar curves can be drawn for other examples. Considering a particular case of a 100 mile line and source which can vary between 100 MVA and 2500 MVA the area in which the directional relay must operate is indicated in chain-dot. From considerations of these curves and those given in fig. 44 for the two types of comparators it can be seen that the area covered by the square-law comparator is far wider than is necessary. Under conditions of one large and one small input to the relay the setting will tend to be excessively sensitive. This introduces difficulty with regard to spurious operation on small out-of balance quantities under three-phase fault conditions. In some practical relays using square-law comparators the characterisitics have been modified slightly to the shape indicated by curve (c) of fig. 44 to help overcome these defects. The linear comparator is not affected to the same extent by these effects.

Faulty Phase Voltage If the same voltage is used for polarising as is used for the

restraint voltage and the comparator input is derived through similar impedance, the polarising signal disappears when the fault impedance is low and thus this method of polarising is not of practical use. It is worth noting however that the phase-angle relation is always satisfied. A combination of faulty phase voltage with some other input is thus sometimes used to minimise phase-angle errors.

Phase-Angle Characteristics A general picture is best achieved by plotting phaseangle characteristics on a polar diagram in similar fashion to the ideal characteristics. Curves taken at constant voltage and constant current are both useful to cover the full field of the relay. A typical curve is shown in fig. 46.

FIG.

46.

Faulty Phase Voltage with Memory

POLAR CHARACTERISTIC OF DIRECTIONAL RELAY.

167

If, instead of applying the faulty phase voltage through a similar impedance to the restraint impedance to provide a polarising input, an alternative impedance consisting of a tuned circuit is used, it is possible to maintain a polarising signal for a short time after a fault occurs. Thus in the case of a terminal fault the polarising input will be maintained sufficiently long for operation of the relay to occur. This method, which is straightforward in principle, is widely used in America by one manufacturer in this country. The two ideal requirements laid down previously are not satisfied completely. From application considerations, the most serious drawback is that the arrangement is not effective when a line is energised. The relay being initially de-energised the 'memory' is ineffective under this condition. The disadvantage can be overcome completely by using busbar instead of line voltage-transformers. The polarising current does not maintain a constant phase relation to the faulty phase voltage. When the fault occurs the phase-angle of the faulty phase voltage

alters whereas the memory circuit maintains a current at the original phase-angle. The value of this shift is given in Table 1 which summarises phase-angle shifts for all the various methods of polarising. The amount of this shift is not excessive and can be tolerated. It is mentioned mainly because the fact that it exists at all is not always appreciated. A further and more serious cause of phase-angle shifts is due to variations in the supply frequency. The resonant circuit always resonates at a fixed frequency whereas the supply frequency may vary between certain limits. In this country these limits are laid down as 47 to 51 cycles. The error due to this cause is cumulative.The phaseangle shift increasing with each cycle. To avoid trouble it is essential that the 'memory' is restricted to about three cycles at the most. This implies that the relay must be very fast.

Healthy Phase Voltage A polarising voltage can be obtained from one of the healthy phases or between two phases. Numerous alternatives are possible depending upon whether the relay in question is an earth or phase fault relay. The phase-angle shifts associated with the principal methods in use are given in Table 1. The main disadvantage of this method is that in the event of a three phase terminal fault the polarising voltage disappears. This risk is normally accepted in this country and no special measures are taken to cover this condition apart from the back-up feature provided by zone 3 of the protection. In a number of cases in America it has been possible to use high-set overcurrent relays which can protect for this type of fault.

Table 1 Phase.Angle between Polarising and Restraint Voltage.

The phase-angle by which the polarising voltage leads the restraint voltage is tabulated for various types of relay connections and system connections. These cover the principal types of fault and limiting values of the source conditions. Under the column headed "Source", the first letter indicates whether the source impedance is large with respect to the fault impedance, letter L-Large, or small, letter S. The following figures give the phase-angle of the source impedance in degrees. The column headed K s gives the ratio of zero sequence to positive sequence impedance of the source impedance. The corresponding value for the fault impedance is taKen as 2· 5 in all cases. The phase-angle of the line is taken as 60 degrees. In the main part of the table the firstletter denotes the magnitude of the polarising voltage, i.e. Large-L, small-S, zero-a. The second figure is the angle by which the polansing voltage leads the restramt voltage. Relay Connctions Restraint Vr Operating Ir Polarising Vb Restraint Vr Operating Ir Polarising-Vo Restraint Vy-B b

Type of Fault

Source Value

Ks

S,L, 60 L, 90 L,90

-

S, S, L, L, L,

2·5

60 90 60 90 90

2·5 0·5 1·0

t-l

2·5 0·5 1·0

R-N L, L, L, L,

120 134 139 150

S, 0 S, 30 L, 0 L,30 L,30

R-Y-N B-R-N Y-B-N Y-B R-Y-B L, 120 L, 120 L, 180 L,169

L, 120 S,120 S,60 S,82

S, 300 S, 330 L, 300 L, 90 L, 19

S, 60 S,90 L, 60 L,90 L, 101

S,L, 60 L, 90 L, 90

-

-

-

-

2·5 0·5 1·0

-

-

-

-

-

-

-

-

S,L,60 L,90 L,90

-

-

-

-

2·5 0·5 1·0

-

-

-

-

-

-

-

-

-

-

2·5 0·5 1·0

-

-

-

Operating 1y- I b Polarising Vb-Vr

S,L, 60 L,90 L, 90

-

-

-

Restraint Vy-Vb Operating I,-I b Polarising Vy-Vb (Memory)

S,L,60 L, 90 L,90

-

-

-

-

2·5 0·5 1·0

-

-

-

Operating Iy-Ib Polarising Vr Restraint Vy-Vb Operating Iy-I b Polarising Vr-Vy Restraint Vy-Vb

168

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

L, S, S, S,

120 120 120 120

0,0,0,0,0,-

L, 90 L,90 L, 120 L, 120

L,90 L,90 L, 120 L, 120

L,90 S, 90 S, 90 S,90

L, 120 L,90 L, 120 L, 120

L, 120 L,90 L, 120 L, 120

L, 120 S, 120 S, 120 S,120

L, 240 L,270 L, 300 L,300

L, 240 L,270 L, 300 L, 300

L, S, S, S,

L,O L,O L,30 L,30

L,O L,O L,30 L,30

L,O L,O L,30 L,30

240 240 240 240

Residual Voltage

impedances. In this first zone tripping is instantaneous. The second zone reach is set to a point outside the end of the protected line but short of the end of the next line in the system. The second zone thus extends from the end of the first zone to the second zone cut-off and covers the remote line terminal. In this zone, tripping is delayed sufficiently to co-ordinate with the operating-time of a circuit-breaker on a zone-l fault. An external fault will thus be cleared by the circuit-breaker of the adjacent line section before a tripping impulse is received on the protected line. The two zones described are sufficient to establish a complete scheme of protection. It is customary however to provide a third zone as back-up protection. This is set to extend into the third line and has a long time-delay of the order of 2 to 5 seconds. It is important to realise that the operating times indicated by the diagram of fig. 47 are ideal times and are not obtained in practice. Near the cut-off points of the various zones the times increase rapidly. Reference should be made to the later section on "System Application Charts" for practical timing curves.

The residual voltage, i.e. zero sequence voltage, at the relaying point can be used for polarising all the earthfault relays. The phase-angle is automatically correct for an earth-fault on any phase for the appropriate relay. On two-phase-to-earth faults, however, the shift in angle is excessive for use with polarised mho relays. This limitation does not exist with an earth-fault directional relay in which the operating current is derived from the residual current of the main system and this arrangement is commonly used. The method suffers from the disadvantage discussed earlier under "Healthy Phase Voltage" above that no polarising is obtained for a three-phase terminal fault. There is a further practical limitation in that under conditions of long lines and low sourceimpedances the residual voltages may become very small. Relays can be designed to operate with this small voltage but there is always the possibility of spurious operation due to out-of-balance voltages appearing in the residual voltage. This point has been discussed more fully under "System Characteristics".

Residual Current Application to Three-phase System

If a transformer neutral is available at the relaying point a polarising current can be obtained from a currenttransformer connected to respond to neutral current. The available current may be small if the neutral current is shared by a number of transformers and may also vary with system operating conditions. Normally the method can be used and overcomes the limitations of very small signals under conditions of long lines and low sourceimpedances. The main practical drawback is that a transformer neutral may not be available for all system conditions.

In a three-phase system a wide variety of faults can occur, i.e. phase-to-phase, phase-to-earth, two-phaseto-earth, and three-phase. Some duplication of relays is thus necessary in order to provide complete protection. A number of methods can be adopted and are listed below. (i)

SCHEMES OF DISTANCE PROTECTION Principle

Multiplicity of relays to cover all fault conditions. Six sets of relays are required for the three possible phase-to-phase faults and the three possible earth-faults. Other faults are covered by one or more sets of relays. This method involves the most equipment but is also the most reliable. It is generally adopted by nearly all manufacturers for all important applications.

(ii) Three sets of relays are sometimes used, which can be switched to measure either phase-to-phase or phase-to-neutral quantities. The relays are normally connected for phase-to-phase fault measurement and are switched to earth-fault measurement by a residual current-detector. Difficulties arise due to spurious residual currents and on changing faults. The arrangement is not in common use.

Up to the present distance-relays have been considered as individual units and their performances assessed in terms of the single-phase voltage and current applied to the relay terminals. In developing an overall scheme of distance protection it is necessary to provide a number of relays to obtain the required discrimination. The method adopted in all medium and high performance schemes today is known as the three-zone scheme. Considering this in relation to a single-phase system in which only one type of fault can occur, the principle is illustrated in fig. 47. A number of distance relays are used in association with timing relays so that the power system is divided into a number of zones with varying tripping times associated with each zone. Thus the first zone extends from the relaying point to a point just short of the far end of the protected line. The first zone reach is normally set to between 80% and 90% of the line, the margin being allowed to cover inaccuracies in the relays and assessment of the system

(iii) One set of relays is used and can be switched to anyone of the six measuring conditions. This phase selection is normally accomplished by over-current and residual current relays, but may be supplemented by under-voltage relays. The phase-selection relays restrict the application to lower voltage and relatively unimportant lines. The same difficulties are experienced with changing faults but are generally accepted as a reasonable risk in this particular application.

169

ZONE·) BACK-UP RELAY

I

I

ZONE-2 RELAY DISCRIMINATING TIME

H---

-----t-

CIRCUIT-BREAKER OPERATING-TIME

FIG.

47.

(C)

TYPICAL STEPPED TIME/DISTANCE CHARACTERISTIC.

(iv) A method by which one set of relays can be used for all faults by the use of static sequence networks has been considered. ,. The basic principle is to derive the various sequence components of voltage and current at the relaying point and make use of the relation that

Phase-fault relays-Phase-to phase voltage. Difference between phase currents. Earth-fault relays-Phase-to-neutral voltage. Phase current plus k times residual current (31 0 ) where

IV I I -lv 2 I -Iv o I III I + 11 2 I + kil o I

~-,-1

k

= _Z~l

_

3

This is reasonably accurate so long as the phase-angle between source and line impedances is small. Special methods have to be adopted however for two-phase-to-earth faults for which the expression does not apply. This method has not been used in practice.

and Zo and ZI are the positive and zero sequence impedances of the protected line. It can be shown that all relays measure positive sequence impedance for all appropriate fault-conditions. The reason for the added component in the earth-fault relays is that currents flow in the sound phases of the system in the event of an earth-fault due to the various zero sequence paths via transformer neutrals. The presence of these sound-phase currents induces a voltage into the loop formed by the faulty phase and ground causing an error in measurement. The added current component is proportional to these currents and compensates for them.

Earth and Phase Fault CompensationS Having provided six sets of relays it is still necessary to arrange the inputs in order that correct measurement is obtained under all conditions. A typical arrangement is shown in fig. 48. It can be seen that the quantities applied to the various relays are as follows:

170

COMPENSATIONTRANSFORMERS

RELAYS

n

I----_-~-~

f--_-~

For Red Relay

I

where FIG.

48.

+ 3n l o + Iz +

=

IR

I

=

11 It

+

12

k

=

1

+

3n, or

I

+

(I

+

3n) I

klo n =

k-l. -3-

CURRENT COMPENSATION.

CHARACTERISTICS OF COMPLETE SCHEMES General

Phase-Fault Schemes Directional and Plain Impedance Relays

The overall characteristics are shown in fig. 49. There are three identical sets of relays for the three types of phase fault and one set only need be considered. The direction of the fault is determined by a directional relay and three separate impedance relays are used to determine the zone I, 2 and 3 cut-off points. The tripping areas for the three zones are thus as indicated by the shaded areas. The d.c. circuits associated with the relays are shown in fig. 50. Operation of the directional (D) and third zone impedance element (Z3) start a timing relay (T) which permits tripping after a time-lag (T3). Tripping in a shorter time is obtained if the zone-2 impedance relay (Z2) has also operated. Direct tripping is obtained if the first zone relay (ZI) operates. One of the difficulties associated with this arrangement is the co-ordination between the directional and the zone-I impedance relays. Under external-fault conditions on an inter-connected system it is possible for a

The characteristics of complete schemes of protection are conveniently expressed in the form of ideal polar characteristics of similar form to those previously considered for single relays. The arrangements adopted for phase faults and earth faults are conveniently studied separately, different combinations of the various schemes being used in practice. The principal forms in current use are considered in the following sections.

ZONE 1 - - - ZONE 2 - - - - - -ZONE 3 - - - -

+ D

FIG.

49.

DIRECTIONAL AND IMPEDANCE CHARACTERISTIC.

FIG.

171

50.

D.C. CIRCUIT.

Polarised Mho and Plain Impedance

B

A

e[~""'"-,.---~~.]e--~7

C ~

--

AFTER C OPENS

FiG.

51.

~.

FAULT ~

In the arrangement just described four relays are used. An obvious simplification is to use only one impedance relay instead of three and change the setting by the appropriate timing relays to obtain the second and third zones. If this is done, starting must be by means of the directional element only. A plain directional element is liable to operate under load conditions, however, and such an arrangement is not very satisfactory. By using a modified directional element, which is in effect a crude form of polarised mho relay with very inaccurate settings, this difficulty is overcome. The arrangement is shown in fig. 52. It should be noted that the circle shown for the polarised mho relay can vary widely and does not give a precise cut-off point. The general operation of the scheme is similar to that previously described and the same problems are encountered as regards directional control. With long heavily loaded lines, the inaccurate setting of the polarised mho relay is not adequate to distinguish between load and fault conditions. The polarised mho relay can be made more accurate and provide the zone-3 setting. This simplifies the arrangements for changing the settings on the impedance relays and makes the scheme of wider application. In practice, however, the limitations as regards operating time usually mean that the scheme using off-set mho and polarised mho relays described later is used instead.

D - -INITIAL

CONDITION FOR SUDDEN

REVERSAL OF CURRENT.

sudden reversal of current to take place when one circuit-breaker opens. Unless the timing of the directional and impedance relays are carefully co-ordinated this can result in spurious tripping. The condition is illustrated in fig. 51. There are two conditions which must be satisfied. (i) At terminal A the directional relay will initially restrain and the zone 1,2, and 3 impedance relays operate. When circuit-breaker C opens the directional relay will operate and the zone 1 and 2 impedance relays reset. It is thus essential that the reset of the zone-l impedance relay is less than the operating time of the directional relay.

Polarised Mho and Reactance"

With very short lines difficulty is experienced on arcing faults due to the resistive component of the arc-drop being added to the line impedance drop. In an attempt to overcome this difficulty, reactance measuring relays have been used instead of impedance measuring relays.

(ii) At terminal B the directional relay, zone-2 and zone-3 impedance relays will operate initially. When circuit-breaker C opens the directional relay will restrain and the zone-l impedance relay operate. It is thus essential that the directional relay resets before the zone-l impedance relay operates. Thus both directional and impedance relays require slow operating and fast reset times. The "slow" is, of course, a relative term, as the operation must still be fairly fast if the protection is to be in the high-speed class.

ZONE I ZONE 2 ZONE 3

To avoid this race between contacts some manufacturers adopt the practice of directional control. In this the impedance relays are short-circuited until the directional relay operates. This cuts out condition (i) completely. Of the two, this is the more onerous condition. It can be shown that condition (ii) cannot in fact arise at all if both lines are the same length, because the zone-l impedance relay can never operate during the second stage of the fault. This applies for any source conditions at either end of the lines. The condition can arise if the line AB is shorter than the line CD as may be possible on a more complex system. Since in any case it is likely that the impedance relay would then be operating marginally with long time, the condition can normally be disregarded as a practical risk.

FIG.

172

52.

POLARISED MHO AND IMPEDANCE CHARACTERISTIC.

A polarised mho starting relay is used which also provides the zone-3 setting, the reactance relay being set for zone-l cut-off. The setting of the reactance relay is altered by the timing relay to give the zone-2 cut-off. The impedance diagram for this arrangement is shown in fig. 53. The same problems as regards directional control arise as discussed under "Directional and Plain Impedance Relays" above. An alternative solution adopted by one American manufacturer is to open the trip circuit by means of an auxiliary element if the reactance relay has not operated within 30 mS after the polarised mho relay. To prevent a permanent lock-out of the trip circuit in the event of slow operation of the reactance relay, a further auxiliary relay reconnects the trip-circuit if the reactance-relay contacts remain closed for 15 mS.

ZONE I ZONE 2 ZONE 3

I

FIG.

54.

OFFSET MHO AND POLARISED MHO CHARACTERISTICS

(ii) The tripping area associated with zone-l is small. This is of help in respect to power swings. (See the section "Power Swings" on page 29). (iii) The area associated with the starting relays is small. This is a help in cases where it is difficult to distinguish between load and fault conditions.

ZONE I ZONE 2 ZONE]

Earth-Fault Schemes Single Directional and Separate Impedance Relays

A single directional relay is used which is energised by zero-sequence voltage and current at the terminal. This is adequate for both directional properties and starting, there being no difficulties associated with spurious operation on load currents. Separate impedance relays are used in each phase and are normally used for all three impedance settings by alteration of settings. The arrangement is illustrated in fig. 55.

FIG. 53. POLARISED MHO AND REACTANCE CHARACTERISTICS.

The use of reactance relays is falling out of favour with some manufacturers nowadays and their use has been discontinued. There are two main reasons for this: the first is the preference for schemes in which zone-l tripping is determined by one relay only in order to obtain maximum speed. The second is that technically it is very doubtful whether the use of reactance relays actually improves matters when all system conditions are taken into account. This aspect is discussed more fully later in the section "Arc Resistance".

Offset Mho and Polarised Mho.,

ZONE I ZONE 2 ZONE 3

4.

This arrangement is shown in fig. 54. Zone-l is determined completely by a polarised mho relay and zone-2 is obtained by alteration of the settings of this relay. An offset mho relay is normally used for starting the timing relays and for the zone-3 back up. This is set with the backwards reach about 10% of the forwards reach. The main features of this arrangement are as follows: (i) The maximum possible speed is obtained for zone-l faults.

FIG.

173

55.

DIRECTIONAL AND IMPEDANCE CHARACTERISTIC.

Single Directional and Separate Reactance Relays

ZONE I

Reactance relays are sometimes used instead of impedance relays for zone-l and zone-2 cut-off points. Due to the large area covered by the reactance characteristic associated with the directional characteristic an extra impedance relay is added to restrict the tripping area. This can be seen from fig. 56. This relay is normally used to give the zone-3 cut-off point.

ZONE 2 - - - - - - ZONE 3

-._.-

Offset Mho and Polarised Mho

With long lines and high source MVA difficulty is experienced due to the very low polarising voltage available at the relaying point. This can be sometimes overcome by using current polarising but this is not always possible. A further difficulty is that a fairly low currentsetting is required for the operating current of the directional relay. With the long untransposed lines which are becoming common nowadays, the zero-sequence current produced on a three-phase fault may be large enough to operate the relay. As the phase angle is indeterminate this could result in spurious tripping. In such cases, an identical scheme can be used to that already described in the section headed "Offset Mho and Polarised Mho" on page 26. This overcomes the difficulties just described and also enables the faster operatingtimes to obtained.

FIG.

56.

57.

ARC-RESISTANCE AND PLAIN IMPEDANCE.

DIRECTIONAL AND REACTANCE CHARACTERISTIC.

NnSCELLANEOUSPROBLEMS Arc Resistance4 The effective resistance of an arcing fault is difficult to assess accurately. The voltage does not vary uniformly with current and the waveform is considerably distorted. The effect on the protection is also dependent on the line length and spacing and imponderables such as the arc length which is dependent upon wind velocity and other variables. Published information on the subject gives a figure for the drop of

FIG.

- t - - - - - - - - - - , - ---'- - ----.....I -

-

V=drop in volts. L=length of arc in feet. I= current in amperes. It is generally accepted that the effects become pronounced with lines of 10 miles or less at the higher voltages, and distance protection is not normally applied to very short lines. It is of interest to compare the errors produced by the three types of relay characteristic in common use, i.e. impedance, reactance, and polarised mho for various system conditions. For this purpose it is not necessary to

J-FIG.

174

58.

ARC-RESISTANCE AND REACTANCE.

know the value of arc resistance accurately as relative performances are being considered. In the simplest case in which there is only an in-feed to the fault from one line terminal the reactance relay has no errors, the impedance relay has fairly large errors, and the polarised mho relay is intermediate, the exact values depending upon the angle chosen for the characteristic. Normally the axis of the circle will be lined up along the axis of the line but as can be seen there is a definite advantage to be gained by setting the axis of the circle to a smaller phase-angle. These conditions are illustrated in figs 57-60. Normally there will be a feed into the fault from both ends of the protected line. If the two in-feeds have the

FIG. 61.

FIG.

59.

MODIFIED ARC-RESISTANCE AND PLAIN IMPEDANCE.

ARC-RESISTANCE AND MHO.

-~

----------~ FIG.

60.

MODIFIED ARC-RESISTANCE AND REACTANCE.

same phase-angle there will be no difference in the relative performance of relays. The actual effects of the arc resistance will be accentuated slightly due to the larger current in the arc. If, however, there is a phase shift between the two in-feeds, as is quite likely when large blocks of load are being transmitted on the system, conditions are changed. The voltage across the arc can now appear to have a reactive component. When viewed from one line terminal this appears as a positive reactance and when viewed from the other as a negative reactance. The effect on the various relays is illustrated in figs. 61-64. It will be noted that the reactance relay is now worse than the polarised mho relay.

30"

FIG.

62.

ARC-RESISTANCE AND MHO WITH A SHIFT IN ANGLE.

175

SOURCE IMPEDANCE

LINE IMPEDANCE ---------

lOCUS OF POWER

-------f'-f---------:~.;:..:.=-.::...: SWING

SOURCE IMPEDANCE

FiG.

FiG.

63.

-------

65.

Locus

OF POWER SWING.

MODIFIED ARC-RESISTANCE AND MHO.

Double Circuit Lines

FIG.

64.

With double circuit lines there is an appreciable zero sequence mutual coupling between the two circuits. The impedance seen at the relaying point at the end of one line is thus dependent on the current flowing in the other line due to the induced mutual voltage. The apparent impedance may become either larger or smaller depending on the direction of current in the unfaulted line. The relay may thus tend to under-reach or over-reach respectively. The amount of this over-reach or under-reach is dependent on the line parameters, source and line impedances, and position of fault. For a particular line configuration it is possible to plot a graph as shown in fig. 66 in terms of the two range factors and the fault position. The main axes are the range values of the source impedances at the two ends of the double circuit line, Le. the values YA and YB are equal to the ratio of the respective source impedances to the impedance of one line. The various lines on the graph represent the actual cut-off point of the zone-l relays assuming that these have a nominal cut-off of 80% of the line length. Thus, knowing the values of the source impedances the cut-off point can be estimated by interpolating between contours. It should be noted that the maximum amount of overreach is restricted to the total length of the line and the cut-off point can never extend outside the line length. This can be shown to be independent of the line parameters and the actual value chosen for the zone-l cut-off point. It is thus unnecessary to provide any form of compensation for these effects in practice.

MODIFIED ARC-RESISTANCE AND MHO WITH A SHIFT IN ANGLE.

Power Swings2 , 8 Distance protection, not being a true unit protection, is affected by power swings on the system and can operate under these conditions. The locus of a power swing can be illustrated on the polar diagram as shown in fig. 65. It will be noted that the locus is at right angles to the general direction of the line impedances. In general terms the mho types of characteristics are less susceptible to operation on power swings due to their narrower characteristics. If the system actually goes out of step of course these relays will also operate. Because of this special measures are sometimes taken to block operation during a swing. In general, these work on the time interval between the operation of successive relays to determine if a swing or a fault exists.

Setting Adjustments Distance-measuring relays must be set to correspond to the actual length of the protected line. These initial setting adjustments may be made on either the voltage or current inputs to the relay. In order that the performance of the relay can be maintained for all values of

176

~:_zo xx~

y A="?-A9

Zo

YB=~~~

~y~/ez'----- J LJ POINT

K=2'66 H= ·53

-/ FAULT

100

V

,LIMIT OFn c 0-69 ATYA+o 50 Ya ~oo

~/

I~ /~

rf\J

20

5

./

~ L..---

'/

/V

'05

'02

/

'0 I

·01

'02

V '05

/

V /

/

/ / 1/

C>'

,/ ~~~ V

iP

",>x,1

lA3~ -,/

'Y0~

/ /

V

/

/ / /

I

/ / / / / V

I '1

/V

/V

+~ 'l~ ~~/ / 0/~~"

:/

V/

I

/

/

?,O

/ /

/

~ It /

/

>'B

--

/ r(I-

,-/

V

/

/

",

/

~

[7

-/

2

·5

/

c:s~

V

--

10

/

'5

2

5

V~ l'

r(V)

/

/

LIMIT OFn= 1

>'A- 00 >'B- 0 10

20

~ SO

100

>'A FIG.

66.

CUT-OFF IMPEDANCE OF ZONE-l RELAY FOR VARIATION IN SOURCE IMPEDANCES.

setting the adjustments must be made on the current input circuits. This follows directly from the considerations of an earlier section headed "Characteristics of Simple Relay" in which it was shown that the range of a relay is dependent on the burden on the voltagetransformers. Any alteration to the voltage input affects the range of the relay. It is common practice therefore to make the main initial adjustments in the current circuit and to make only fine adjustments or zone-2 settings in the voltage circuit.

Transient Response of Current-transformers and Voltage-transformers Current-transformers With any form of distance protection it is necessary to ensure that steady-state saturation of the currenttransformers does not take place when system conditions are such that the relays are operating near the cut-off impedance. This normally does not present any

177

2f--------------------

ZONE- 2 CUT-OFF

:r:

I-----__~

-------1200 m$

f-

\

t,)

Z

U.J ..J

Z

::::; I

ZONE-I CUT-OFF

\

:. .:_

[,.::,-~-~-~_:...:_:-_=-=-_=-_=_.:::_~_ =-=-=...::-=-=-=-='-='-=--\--------~-'---------

t:

\

z

::> I

c>:: U.J

0..

-5

2

5

RANGE

10

20

so

100

Y

- - - COMPOSITE TIMING ------- ZONE-I RELAY TIMING - - - - ZONE-2 RELAY TIMING FIG.

67.

SYSTEM APPLICATION CHART.

difficult design problem. With high-speed protection it is also necessary to ensure that transient saturation does not occur under the same system conditions. This may present difficulties with units having a high burden in the current circuits.

System Application Charts The contour method of presentation of distance relay characteristics already discussed can be extended to cover the performance of a complete scheme of distance protection comprising a number of relays with different nominal impedance settings. In this application of the method it is convenient to take the impedance corresponding to the complete length of the protected line as the nominal impedance ZN' All relay characteristics are then expressed on this basis and composite contours drawn representing the performance of the complete schmem, as illustrated in fig. 67. As the performance of the protection may be quite different for different types of faults it will normally be necessary to have a series of diagrams covering the principal types of fault, e.g. phase-to-earth, phase-to-phase, and three-phase faults.

Voltage-transformers

Electromagnetic voltage-transformers do not present any problem as the primary voltage is reproduced faithfully in the secondary winding. With capacitor voltagetransformers, transient voltages occur in the secondary whenever a sudden change of primary voltage takes place. These transient components consist of two damped oscillations, one at a frequency higher than the normal mains frequency and one at a lower frequency. The order of these frequencies is 200 cis and 12 cis respectively. The effect of these transients will depend on the particular type of relay in use. Normally there is a slight reduction in operating-speed of the protection. Cases have occurred however in which mal-operations have occurred with half-cycle protection in which this cause has been suspected.

Special Applications Distance relays may be applied to the protection of transformer feeders and to tee'd feeders. In recent years protective schemes employing distance relays and a carrier link between feeder ends have been used to an increasing extent in order to provide high-speed clearance over the complete length of line.

178

BIBLIOGRAPHY The following bibliography is not intended to be exhaustive of the literature on distance protection. It has been chosen so that further study may be made of topics dealt with in this paper. To assist in this respect number references have been given throughout the text to relevant papers. Further references will be found in the bibliographies given in the various papers listed. 1. GUTTMAN, Behaviour of Reactance Relays with Short-Circuit fed from both Ends, Elektrotechnische Zeitung, 1940. p.514 (in German). 2. CLARKE, Impedances seen by Relays during power Swings with and without Faults, ALE.E., 1945, p.372. 3. HUTCHINSON, The Mho Distance Relay, ALE.E., 1946, p.353. 4. WARRINGTON, Application of the Ohm and Mho Principles to Distance Relays, ALE.E., 1946, p.278. 5. LEWIS & TIPPETT, Fundamental Basis for Relaying on a Three-Phase System, ALE.E., 1947, p.694. 6. DEWEY & MCGLYNN, A New Reactance Distance Relay, ALE.E., 1948, p.743. 7. GOLDSBROUGH, A New Distance Ground Relay, A.LE.E., 1948, p.1442. 8. WARRINGTON, Graphical Method for Estimating the Performance of Distance Relays during Faults and Power Swings. ALE.E., 1949, p.608 9. BRATEN & HOEL, A New High Speed Distance Relay, C.LG.R.E., 1950, Paper 307.

10. NEUGEBAUER, The use ofRotating Coil Relays and Rectifiers in Protection, Elketrotechnische Zeitschrift, 1950, August. (In German). 11. The Effect of Coupling Capacitor Potential Devices on Protective Relay Operation, A.LE.E., 1951, p.2089. 12. EDGELEY & HAMILTON, The Applications of Transductors as Relays to Protective Gear, Proc.LE.E., 1952, August. 13. RYDER, RUSHTON & PEARCE, A Moving Coil Relay Applied to Modern System of Protection, Pro.LE.E., 1950. 14. BERGSETH, An Electronic Distance Relay using Phase Discriminator Principles, ALE.E., 1954. 15. All Electronic One Cycle Carrier Relaying Scheme, Four papers, p.161-186, ALE.E., 1954. 16. GIBSON, Improvements in Electric Protective and/or Fault Locating Systems for Polyphase Alternating Current Power Transmission Network, British Patent 743,323, 1956. 17. HAMILTON & ELLIS, The performance of Distance Relays, Reyrolle Review, No. 166, 1956. 18. BERGSETH. A Transistorised Distance Relay, ALE.E., 1956. 19. ADAMSON & WEDERPOHL, Power System Protection with Particular Reference to the Application of Junction Transistors to Distance Relays, Proc.LE.E., Part A, October, 1956. 20. ADAMSON & WEDERPOHL, A Dual-Comparator Mho-Distance Relay using Transistors, Proc. LE.E., Part A, August, 1956.

179

CHAPTER 12 An Introduction to Distance Protection By D. ROBERTSON. BASIC PRINCIPLES It is as well to remind ourselves at the beginning that distance protection does not measure distance but actually the impedance between the relay and the fault. However, the impedance of a feeder is related to its length so that if the impedance per unit length of a feeder is known the protection can in effect measure the distance to the fault. H is fundamental to the requirements of discrimination that distance protection measuring characteristics for direct tripping need to be directional. Also because tripping is determined by measurement of the impedance to the fault, fundamental accuracy is necessary rather than comparative accuracy as required by differential protection. Thus a concept of zones of protection naturally develops where the first zone of measurement is that part of the protected feeder impedance to which the distance really can be set without any possibility that relay errors, instrument transformer errors or errors in estimation of the power system impedances will cause mal-operation. Typically a figure of 80% of the protected feeder length is chosen as first zone and many installations are operating successfully using this zone 1 setting criteria. The advent of more accurate relays both basically (i.e. better steady state accuracy) and dynamically (i.e. little or no transient over-reach) has encouraged use of 90% of protected feeder impedance for zone 1 settings by some users, but most authorities prefer to accept the better performance as increasing the safety factors, considering that 80% of feeder impedance gives adequate coverage. There is some justification for increasing the percentage coverage for phase fault relays but for earth fault relays the uncertainty of determining the zero sequence impedance makes it undesirable to change from the well established 80% value. The remainder of the feeder is protected by zone 2 which is set typically at 120% of the protected feeder impedance. This means that zone 2 will operate for busbar faults and faults at the busbar end of adjacent feeders. This allows the zone 2 to provide busbar protection in its own right or to act as back up to a busbar unit protection. Also the zone 2 acts as back up protection in the important area at the busbar end of adjacent feeders where, in general, a relatively high fault incidence may be expected. Discrimination between zone 1 and zone 2 is traditionally provided by a definite time lag relay which can be made to be very precise and relatively unaffected by climatic and electrical environmental conditions. Thus the grading of zone 1 and zone 2 is simple becausc it is only one step and only the circuit breaker operating time has significant variation.

A third zone of protection is traditionally provided which is not directional, this has special duties which depend on the type of scheme and facilities required. Because it is available for these duties it can also be used as a second stage of back-up protection covering typically the next feeder in the forward direction and the busbars and a small percentage of the feeder in the reverse direction. Impedance settings of this zone 3 are sometimes dictated by the zone 3 other duties and may also be limited by load impedance. Time settings of the zone 3 back-up have to take account of any I.D.M.T.L. relays which may be providing back-up for other equipment. This leads to the difficulty of grading inverse characteristics with definite time lag characteristics. However, the zone 3 time lag may always be set long enough to provide a back-up to the I.D.M.T.L. back-up if co-ordination ofthe two is a problem. Individual relays may be used for each zone and the six basic types of fault may each have an associated relay. With this arrangement a three zone distance protection requires 18 relays. There are two ways of reducing the number of relays; first, common relays may be used for zone 1 and zone 2; this is referred to as a zone switched relay. Secondly, a common measuring relay may be switched to the appropriate current and voltage signals by fault detecting relays; this is referred to as a phase switched relay. This concept of zones with increasing settings and time lags to give discrimination gives a very comprehensive protection scheme when viewed from the total power system aspect. In addition when the various zones are programmed with other equipment to provide the full facilities of which a modern distance protection is capable, the fact that it is all provided from one set of C.T. cores makes distance protection very attractive. Schemes of distance protection were originally built up from discrete relays of various characteristics with interconnection being done at the panel building stage. The need for faster and more sensitive distance relays has been met by using semi-condl'~tor designs which allows greater sophistication in the interconnection of the various relays. However the inclusion of the relay interconnection within the composite relay case can be a disadvantage if the overall relay design is not flexible enough to cater for the varieties and options within the various types of scheme. The inter-face between supplier and user is especially important in this respect because communication of the complexities and their possible options is not easy and changes introduced late in manufacture or on site while although unavoidable in some circumstances are not to be recommended.

180

x 10

30

20

]j

FIG.

......=!:::=o_",------

--~

2.

CIRCULAR POLARISED CHARACTERISTICFAULT CONDITIONS. W is ratio of minor to major axis

--+_R

=

ZN : NZN

x FIG. 1. CIRCULAR POLARISED CHARACTERISTICBALANCED CONDITIONS APPLICATION - ZONE I AND ZONE 2.

W~----,---

w ~ 0.354

1-+-\--'\---- w

x

I--f---\---- w

1----+--

~

0.5

~ 0.6

w

~

0.75

w

~

1.0

------'......",.-\-\-+---f----''--+-h'---f---,f----- R

___.......

+-_...1.-

----,(-

R

FIG. 3. CIRCULAR OFFSET CHARACTERISTIC BALANCED CONDITIONS AND FAULT CONDITIONS APPPLICATION - ZONE 3 POWER SWING BLOCKING.

FIG 4. CIRCULAR/ SHAPED OFFSET CHARACTERISTIC BALANCED CONDITIONS AND FAULT CONDITIONS APPLICATION - ZONE 3 POWER SWING BLOCKING.

TYPE OF RELAY

Further development produced a relay with a basic characteristic of a circle whose diameter is the relay setting and whose circumference passes through the origin of the R and X axes as illustrated in fig. 1. This was termed Mho relay because of the fact that the Mho characteristic when plotted on an admittance instead of an impedance polar diagram gives a straight line. The Mho relay is clearly directional and the characteristic angle is at the diameter of the circle which originates at the origin of the R and X axes. This characteristic is

Distance relays are generally classified by their characteristic as defined by a polar characteristic using resistance and reactance axes. Thus a plain impedance relay will operate when the ratio between the voltage applied to it and the current applied to it is a set value (setting) irrespective of the angle between the current and voltage. This characteristic is a circle with radius equal to the relay setting and centre at the origin of the R and X axes.

181

generally designed with a polarising signal derived in part from the sound phase voltage (conventionally referred to as Polarised Mho relay). With this type of polarising signal, during unbalanced fault conditions, when the faulted phase voltage can have significant phase difference from its reference but the sound phase voltages will not have changed their phase angle, the characteristic will change to that shown in fig. 2. The extent to which the characteristic is changed is dependent upon the relationship (magnitude and phase angle) between the faulted phase voltage and the sound phase voltage. This, in turn, is dictated by the magnitude of the source impedance in relation to the nominal measured impedance. Hence the various curves for different values of SIR (system impedance ratio). For balanced faults (i.e. 3-phase) the relay characteristic is the circle as in fig. 1 because all voltages are affected equally and remain in balanced phase relationship. Fig. 3 shows a modified impedance characteristic which is called the offset Mho characteristic and is used to supplement polarised Mho relays to provide definite operation for close up balanced faults where the polarised Mho relay is not sure to operate. The offset Mho characteristic develops from the requirements to have a large reach in the forward direction to use as a starter and overall back-up without encroaching too much on the load transfer of the feeder. The load impedance generally will be centred around the resistive axes and thus the offset Mho relay gives better discrimination with load whilst providing sufficient reverse coverage to ensure operation for close up faults in the forward direction (line earth bars left on) or reverse direction (busbar faults). Where very long starter or back-up reach is required, shaped characteristics need to be applied and these are x

represented typically by the characteristic in fig. 4. This off-set element can be set to a variety of characteristics from the conventional off-set Mho circle to a narrow waisted characteristic by choice of simple links within its printed circuit. It is particularly useful when used as shown in fig. 5 where the links for the top half of the characteristic are chosen to give a reasonably broad coverage to allow for errors in the power system data, fault resistance etc. and the lower half of the characteristic is chosen as the narrowest to give very good discrimination with load impedance.

R

X

1,0

FIG.

1.5

6.

DIRECTIONAL SHAPED CHARACTERISTIC BALANCED CONDITIONS TYPICAL APPLICATION - ZONE 1 AND ZONE 2 SHORT AND MEDIUM LENGTH LINES

One of the problems encountered by distance protection is the possibility of relatively large values of fault resistance in earth faults. This is obviously related to the length of line or magnitude of impedance being protected because the fault resistance is determined by the voltage, current and physical make-up of the fault. To eliminate resistance from the distance relay measurement on short lines, reactance relays may be used. This type of relay characteristic is effectively a straight horizontal line at the relay setting value above the R axes. Theoretically a reactance relay will operate when a certain reactance is reached without any limitation as to the resistance involved. However, all reactance relays will have limits and generally they are controlled by other characteristics such as an off-set Mho starter to keep their reach within reasonable limits. The use of two relays to provide a composite characteristic has always produced problems of contact racing, (if not in the operate mode quite often in the reset mode) and fig. 6 shows a reactance form of characteristic developed from a shaped Mho characteristic thus giving a directional reactance characteristic produced by one element.

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FIG. 5. CIRCULAR/SHAPED ASYMMETRICAL OFFSET CHARACTERISTIC BALANCED CONDITIONS AND FAULT CONDITIONS APPLICATION - ZONE 3 POWER SWING BLOCKING.

182

x

factor to compensate for the mutual effect. Obviously with this arrangement if the current returns via the sound phases there is no residual current and hence no compensation. Thus, in this case, the earth fault relays basic setting is the same as the phase fault relays. Under three-phase fault conditions there will be no residual current and no mutual effect so the earth fault relays will measure correctly. The phase fault relays will be energised with phase to phase voltage which is equal to phase to neutral vol+age times V3 and the currents will be the difference of the two phase currents which in the case of a three phase fault are displaced 120° in phase and will therefore give a V3 times factor on the current per phase. Hence both earth fault and phase fault relays will measure three-phase fault conditions correctly.

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FIG. 7. DIRECTIONAL SHAPED REACTANCE CHARACTERISTIC FAULT CONDITIONS.

Because this characteristic is derived from the polarised Mho characteristic it retains the change in characteristic during unbalanced conditions as shown in fig. 7.

FAULT TYPES AND QUANTITIES APPLIED TO RELAYS

SCHEME ARRANGEMENT From the previous section, it is obvious that different types of fault require different input quantities fed to the relay and in full distance protection schemes it is conventional to provide relays for each main type of fault. Thus in each zone of protection six relays would be provided, red-yellow, yellow-blue and blue-red for phase faults and red, yellow and blue for earth faults. These would be connected directly to the appropriate current and voltage signals to measure their designated faults To obtain individual measurement in each zone for each type of fault a three zone full distance protection would therefore use eighteen relays (or more correctly eighteen measuring elements because with semiconductor design, the inputs and output tripping and logic circuits are often commoned and the dedicated element for each fault type resolves to a simple printed card). The use of eighteen elements is regarded as unjusitified economically for distribution systems and schemes with less elements are readily arranged by, in the first stage, using common relays for the first two zones by switching settings on completion of the zone 2 time lag. This results in using 12 relays in a full scheme, 6 relays for zone 1/zone 2 and 6 relays for zone 3. This is possible because the zone 1 and zone 2 relays are of the same type (i.e. directional distance) and the zone 3 relays are non-directional. Where schemes use the same type of relay for all zones, the setting can be switched twice or more, however, there is a requirement always for an independent set of relays to start the timing sequence. These detect that a fault exists and therefore have to be set to cover the complete range of all zones. The above schemes are referred to as zone switched schemes and a further reduction in number of relays (or elements) can be achieved by employing the technique of phase switching. Phase switched distance relays generally use only one master measuring relay and three starting relays and are referred to loosely as switched distance schemes. A typical switched distance arrangement is shown in fig. 8. Because this relay is a semi-conductor design all currents and voltages are fed to the elements via isolating transformers. The current transformers perform the additional duty of providing the replica impedance so

Because the power system has three phases which are carried on conductors in relative close proximity, the effective fault impedance of the conductors is made up from self and mutual impedance. Thus the fault currents in each conductor inter-act with the other two conductors and incorrect measurement would occur if compensation was not included to allow for this. With phase to phase faults the fault driving voltage is clearly the phase to phase voltage and the fault impedance does not include mutual effects because equal and opposite currents are flowing in the two conductors which cancel out any induced voltages. It is conventional therefore with phase to phase distance measurement to apply to the relay phase to phase voltage and the difference of the two phase currents, (because these are in phase opposition the difference results in twice the value of one phase current) which results in a measurement of one conductor impedance without any mutual effect. (Self impedance minus mutual impecance which is equal to the positive sequence impedance.) With phase to earth faults the driving voltage is clearly phase to neutral voltage and considering that the earth fault current could all return to the sending end via the earth path, considerable mutual effects can be present. This results in an earth fault impedance 1· 5 - 2 times the impedance measured by the phase fault relays. This can be compensated for simply by an increase in setting of the earth fault relays but for the fact that in some cases the earth fault current may return on the unfaulted phases (i.e. the sound phases). Thus if the earth fault relays are arranged to measure the increase in earth fault impedance caused by mutual effects by a simple increase in fault setting, this must be cancelled if the earth fault current returns via the sound phases. This can be achieved by feeding a signal to the earth fault relays derived from the sound phase current, and is referred to as sound phase compensation. An alternative compensation for earth fault relays is to feed an additional current signal to the relay which is derived from the residual current in the C.T.'s so that the current which is flowing back to source via earth is identified and can be fed to the relay with an appropriate

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will reflect the primary impedance to be measured to the relay at a level dependent upon their ratios Thus the impedance presented to the relay: Vp x Ct Ratio Zs = V s Ip Is VT Ratio

that they provide to the measuring elements the current signal as a voltage equal to I times the relay setting and phase shifted to correct for the line angle. Thus the current transformer in the relay has an angle setting and an impedance magnitude setting. Residual compensation is provided for earth faults and a second residually connected transformer feeds a neutral starter which switches the voltages from delta to star when an earth fault is detected. Offset Mho starters are used and these select the correct voltages and currents to the measuring element dependent on the fault condition they detect. They also start the zone timing which increases the setting of the main measuring element. These schemes which save in relay equipment are economical for application to voltages as low as 11 kV but have the disadvantage of the dependence on the starters to detect the correct type of fault. Sound phase currents, load current and complex fault conditions can cause incorrect measurement and this would only result in incorrect indication in a full scheme but it could result in incorrect tripping in a switched scheme if the measuring element was provided with incorrect measuring quantities. However, provided the worst case can be analysed, the use of shaped characteristics (fig. 5) will allow wide application.

x

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Line Impedance In the general case, the source impedance is significant and during a fa:.Jlt, less than rated voltage is applied to the relay; as the source impedance increases, the voltage applied to the relay reduces to a point at which the relay cannot measure accurately. It is important to understand and allow for this limitation in applying distance relays. A typical relay is shown in block diagram form in fig. 9. This is a semi-conductor design using a phase angle comparator fed by amplifiers but a limit is placed on the sensitivity obtainable because of the linearity of the current transducers, among other things. Thus all distance relays have a lower limit at which accurate meas-

OVERALL RELAY PERFORMANCE Of necessity relays are fed from the power system by current and voltage transformers and these transformers 184

THREE INPUT COMPARATOR

composite characteristics in fig. 10 and fig. 11 where fig. lOis for the condition of minimum transient current and fig. 11 shows the increase in time of operation caused by maximum off-set current transient. The insignificant transient overreach (i.e. little difference in the two boundary of operation characteristics) which is typically obtained from semi-conductor designs should be noted. The third input shown in the typical relay block diagram in fig. 9 is a useful stabilising device for line dropping conditions. Line dropping can cause operation of distance relays with consequent difficulty when autoreclosing is being used. The third input is also used for shaping characteristics.

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One of the main objections to the use of distance protection is the fact that because of inaccuracies in the relay and in the determination of power system data, the high speed zone 1 protection can only be applied to operate for faults within the first 80-90% of the feeder. This leaves a proportion of the feeder at each end which can only be protected by zone 2 of the remote distance protection and unless additional equipment is used final clearance of faults in these areas is delayed by zone 2 time. The additional equipment used with the distance protection is generally some form of end to end signalling which ensures high speed operation for all faults between the two associated distance protections and, of course, stability for faults outside the protected zone. This effectively gives distance protection a unit scheme type of operation. Before describing the various forms of end to end signalling, a diversion describing extended reach schemes is worthwhile because these are the most economical method of providing the high speed clearance over the whole length of the feeder which is a basic requirement for auto-reclose schemes. The basic scheme of extended reach operation is arranged by setting the high speed zone 1 relay to overlap the adjacent feeder as shown in fig. 12(a). Thus a fault in the overlap areas as represented in fig. 12(a) will trip circuit breakers A, C and D. During the dead time the auto-reclose relay will switch the zone 1 setting of the distance relay to 80% of feeder impedance giving therefore the conventional stepped time distance protection scheme as shown in fig. 12(b). Upon reclosing, circuit breaker A will remain closed, circuit breaker C will trip high speed and circuit breaker D will trip in zone 2 time. Of course, if the fault is transient, all circuit breakers will reclose successfully. At the end of the auto-reclose reclaim time the zone 1 setting of the distance relays are switched back to the extended reach as in fig. l2(a). Thus the scheme provides the high speed tripping at both ends for all fault positions as required for the high speed auto-reclose sequence. The disadvantages are that faults in the overlap area will trip a healthy feeder as well as the faulty feeder causing additional circuit breaker operations, and will give final clearance of one end in zone 2 time. These

OUTPUT

urement is maintained and this can be defined by voltage limits. However, a powerful method of measuring distance protection performance uses the ratio between source and nominal measured impedance, this is termed system impedance ratio (S.I.R.). This value can be plotted against the accuracy of the relay and the time of operation in relation to fault position is shown in the

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FIG. 12. tances a permissive scheme must gate with zone 3 which because of its greater reach is less secure. However, an alternative is to use the received signal to accelerate the change of setting so that the zone 2 reach is made effective as soon as the signal is received. This system may be classified as an acceleration scheme and is slower than the permissive scheme because the zone 2 relay only starts to operate after the signal is received. Thus a faster signalling channel may be used for an acceleration scheme because the time of operation of the zone 2 element is a safeguard against short pulses of interference. Very short feeders require the use of overreach schemes because the distance relay settings may not be low enough to match the line. Also with short lines the fault resistance, which is determined by line configuration, earthing and rated voltage, will be higher in relation to a conventional relay setting of 80% of line impedance so that an overreach scheme may be used to increase the effective fault resistance coverage. The simplest form of overreach scheme is that using the zone 2 to signal the remote end zone 2 to trip. Thus tripping at each end is dependent on a signal from both ends. This scheme requires two independent signalling channels because the permissive signal from one end must not be confused with the permissive signal from the other end. Because the received signal in the permissive overreach scheme has the same action as in the permissive underreach scheme, the two schemes can be combined as shown in fig. 14. This, of course, can only be achieved when independent zone 2 relays are available and the zone 1 settings are low enough to set to 80-90% of the line impedance.

factors must be taken into account when assessing the economics of the scheme. In choosing the form of end to end signalling to be used the fundamental fact that the faster the signalling channel, in general, the more susceptical it will be to interference must be considered. The assessment of how much the worst fault condition may interfere with a given signalling scheme is not simple and therefore the various types of scheme have developed to suit particular requirements as developed from experience in service. The simplest form of end to end signalling is to use a plain intertripping channel to signal to the other end that a fault has been detected in zone 1 and therefore the other end should trip directly. The problem with this arrangement is that interference at any time will directly trip the circuit breaker and therefore the signalling channel must be very secure and therefore generally slow. To improve the security of the end to end signalling system, it is gated with a local relay and this allows a faster signalling channel to be used because operation is dependent upon both the signalling channel and the local relay. One form of this scheme is shown in Fig. 13 where the signal to the other end is sent by the zone 1 which is set to its conventional underreach setting (8090% of feeder impedance). The received signal is permitted to trip if zone 2 has operated and hence this scheme is caJled the permissive underreach scheme. In a switched zone distance protection the received signal cannot be gated with zone 2 because it does not exist as a separate relay and the zone 2 setting will not be effective until after the zone 2 time lag. Thus in these circums-

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A particular problem of overreach scheme is when a healthy circuit in parallel with the faulted circuit first detects the fault in one direction and, on opening of a circuit breaker in the faulted circuit, then detects the fault in the opposite direction. This is the classical reversing fault condition and may be allowed for by delaying the tripping logic a short time to allow the establishment or reset of the end to end signalling in relation to the operation and reset of the overreaching distance relays. Signalling channels for end to end signalling have traditionally been provided by power line carrier equipment operating over the protected line and it is obvious that in order to receive a permissive signal or acceleration signal the power line carrier equipment is required to transmit through the primary fault. Experience has shown that this is a viable system but doubt still remains in some minds and the alternative system of using the signal to stabilise the remote end is thus favoured. These schemes are referred to as blocking schemes and generally require more complex relaying. A simple blocking scheme is shown in fig. 15 where the signal is sent to the other end if zone 3 operates and zone 2 does not operate, thus indicating that the fault is in the reverse looking portion of the zone 3 characteristic and signalling that the overrreaching zone 2 at the other end is not to operate. The basic problem of this scheme caused by racing of the zone 3 and zone 2 contacts is overcome by the short time lag relay (STL) and provided that the blocking channel has a fast reset a reasonable scheme is possible. However, the problem of relative relay sensitivities could cause incorrect operation at marginal fault levels.

An external fault within the reach of the remote zone 2 relay must be blocked by operation of the local zone 3 relay which will detect the fault within its reverse reach. If the zone 2 relay is intrinsically more sensitive than the zone 3 relay low level faults can operate the zone 2 and not the zone 3 thus giving mal-operation for·a low level external fault. To correct this the zone 2 may be made less sensitive than the zone 3 relay but this may cause blocking of an internal fault which could operate the zone 3 relay and not the zone 2 relay at the low infeed end thus giving a blocking signal and causing failure to trip. This is the basic dilemma of simple blocking schemes and the reason why blocking schemes tend to be more complex. The classical blocking scheme uses elements for blocking which can only operate for external faults e.g. directional elements looking into the reverse direction. The scheme is shown in fig. 16 where it can be seen that the reverse directional element (ZIR) sends its signal to block the remote end provided the local end zone 2 has not operated, also a special 3 phase detection gate sends a blocking signal to cover the condition when the polarised Mho directional relays may not have correct polarising signals. Tripping is dependent on operation of both zone 3 and zone 2 which ensures that the blocking signal is more sensitive than the tripping signal because the zone 3 is not as sensitive an element as the reverse measuring element. Where a full complement of elements (24) is incluGed in the relay, independent zone 1 high-speed tripping can be included. This is a very powerful scheme and the blocking mode can be regarded as complementary to

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ANCILLARY FEATURES Line Check

Polarised Mho relays require a voltage signal to ensure operation and the severe condition of a bolted 3-phase fault can cause failure to trip because the voltage at the primary of the V.T. is too low to give relay operation. The bolted 3-phase fault is caused by earth bars being left on a circuit when it is closed. A special feature can be provided for the special problem of the bolted 3-phase fault. The zone 3 or starting relays are invariably not dependent on voltage for operation and can thus be relied on to detect the bolted 3-phase fault. Because this type of fault can only occur when closing-in, the zone 3 or starting relay can be made to trip directly for a certain time after closing-in and this feature is referred to as line check. The switching of the time lag to give direct trip from zone 3 or starting relays may be achieved by an additional contact on the closing control (d.c.line check) or by an undervoltage relay which detects that the line has been de-energised (a.c. line check.)

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The distance relay is dependent on being provided with the correct voltages for operation and also to maintain stability. Operation due to load current is likely if the voltage signal is lost due to fuses blowing or being removed. Supervision of the voltage signals to the distance protection is therefore very important because the whole operation of the distance protection is dependent

DUAL CIRCULAR POLARISED MEASURING ELEMENT BALANCED CONDITIONS TYPICAL APPLICATIONS FORWARD - ZONE I AND ZONE 2 REVERSE- START FOR PROTECTION SIGNALLING OR REVERSE DIRECTIONAL FIG. BACK·UP (ZONE 4)

17.

189

x

with the attendant difficulties in ensuring stability, considering that it has to detect the difference between loss of voltage due to a primary fault and loss of voltage due to voltage transformer supply failure. Power Swing Blocking

Any sudden power system disturbance results in transient changes in the generator angles caused by changes in the power demand and the inertia of the generators. With substantial power system disturbance the generators can swing in this way until their apparent impedance is contained within the distance relay characteristic thus causing tripping. On transmission systems where power swing is a likely condition, distance protection can be fitted with power swing blocking which detects the power swing and blocks all the distance measuring relays. A typical power swing blocking arrangement is shown in fig. 18. A relay which matches the zone 3 characteristic is used with a time lag to detect the difference between a power swing and a fault. A power swing changes the impedance slowly from operation of the power swing element to operation of the zone 3 element, so that the power swing timing element can time out and block all the distance measuring relays. On the other hand a fault will effectively operate both the power swing element and the zone 3 element simultaneously resulting in blocking of the power swing element and thus resetting of the power swing timing element.

LOCUS OF APPARENT IMPEDANCE DURING TYPICAL POWER SWING

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Directional Earth Fault

Certain power systems have a problem of high resistance earth faults and, although the distance relay has much better fault resistance coverage than is apparent from consideration of the simple characteristics, the use of sensitive directional earth fault relays is the only solution when very high earth fault resistance is present. The directional earth fault relay is essentially an overreach element and therefore if it is required for high speed tripping it must be used in one of the overreach types of scheme i.e. permissive over-reach or blocking. In a classical blocking scheme dual elements similar to the dual Mho elements would typically be used.

D.C. CIRCUIT - POWER SWING BLOCKING RELAY

FIG.

18.

upon the reliability of the voltage transformer output. Two basic forms of voltage transformer supervision are used, one which give an alarm only and therefore has no special high speed requirement and the other which is made fast enough to prevent the distance relays operating when a voltage is lost. With the high speed of distance protection measurement (typically 15 milliseconds) the voltage supervision scheme to prevent distance protection operation must be extremely fast

190

CHAPTER 13 Polarised mho distance relay New approach to the analysis of practical characteristics By L. M.

WEDEPOHL.

SYNOPSIS

INTRODUCTION

The use of the polarised mho distance relay for the protection of high-voltage lines has become widespread. Up to the present time, the relay has been thought to be of limited use in the protection of short lines, owing to its relatively small reach for arcing faults. However, recent practical tests have shown that the actual performance is considerably better than that predicted by theory. A new analysis is therefore developed in this paper which shows that the polarised mho relay has an offset characteristic, in the case of unbalanced faults, which encloses the origin and hence enhances the relay reach in the direction of the resistive axis. The degree of offset is a function of the source/line impedance ratio of the system to which the relay is connected. It is shown that the theory developed is in good agreement with results obtained in practice. It is shown in an Appendix that the theory also covers the cases of crosspolarised directional relays and polyphase impedance relays, both classes of relay having an offset characteristic. The paper concludes by discussing the implication of the results. It is noted that the polarised mho relay has most of the benefits of the reacatance relay, while retaining the advantages of being inherently directional and insensitive to load currents and power swings. It is also noted that, by using this method of analysis, the reach for lines with series capacitance may be predicted.

In the past two decades, the use of polarised mho distance relays for the protection of high-voltage transmission lines has become widespread, because of their inherent property of being simultaneously an impedance and a directional measuring element. This type of relay is associated with a number of advantages and drawbacks, and these have in the past been used as a basis for assessing its merits relative to other schemes of feeder protection. It is inherently directional and has the virtue that of all distance relays it is least sensitive to power swings. 1 On the other hand, by virtue of its constrained characteritic, it is rather insensitive to resistive components in the fault impedance and is, for this reason, of limited use in the protection of short lines, when resistance due to fault arcs may be appreciable compared with the line impedance. In these applications it is customary to specify reactance relays' or differential schemes of protection. The fault-arc problem is further aggravated by the fact that the polarising voltage, derived from an unfaulted phase or a tuned circuit, may be out of phase with the fault voltage. Recent measurements have been made to investigate the sensitivity of polarised mho relays to faults with simulated arc resistance, and it has been found that the results are not consistent with the present theory. The relays are found to be capable of operating in the presence of fault-arc resistances which considerably exceed the values predicted by simple theory; the situation improves as the source/line impedance ratio increases. As a result of these measurements, a new analysis of the polarised mho relay was developed, and it is the purpose of the paper to describe this, together with presentation of results and consideration of their practical implication.

List of symbols V R , V y , V B = phase-neutral voltages of red, yellow and blue phases, respectively, at relaying point I R , I y , I B = phase currents E= phase-neutral generated voltage on red phase II = positive-sequence current 12= negative-sequence current 10 = zero-sequence current K, KJ, K 2= relay constants Zn, ZnJ, Zn2= relay impedance constants 8= angle of Zn ZL = positive-sequence line impedance ZLO= zero-sequence line impedance Zs= positive-sequence source impedance Zso= zero-sequence source impedance p= Zso/Zs q= ZLO/ZL a= - i + ij\13 or /120

SIMPLIFIED THEORY OF POLARISED MHO RELAY It is well known that the characteristics of all distancerelay functions may be obtained by using either an amplitude or phase-comparing measuring element. The relationships in the polarised mho relay are more readily understood by considering the operation of the phase comparator. Identical characterisitcs may be obtained from both comparators if the following transformations are observed:

Sx = i(SI + S2) Sy = !(SI - S2)

0

191

Sl = Sx + Sy Sz = Sx - Sy where Sx and Sy are the operate and restraint input signals to the amplitude comparator, and Sj and Sz are the two inputs to the phase comparator. The criterion for operation of the two relays is Sx ,:;; Sy and -tr/2 ~ cP ~ Tr/2 where cP is the phase angle between Sl and Sz. The basic phase-comparator input quantities for a polarised mho relay are Sl = V p Sz = IZ n - V where V p is the polarising voltage and V and I are voltage and current at the relaying point. The corresponding inputs to the amplitude comparator to give identical characteristics are Sx = !(Vp + IZ n - V) Sy = HVp - (IZ n - V)] Fig. 1 shows the basic input arrangement for a mhoconnected phase-angle comparator. The two quantitites which are compared in phase are Sl = V Sz = IZ n - V or

where

V Zs

The relative phase angle between Sl and Sz is not disturbed if they are multiplied by the same quantity, i.e. (Zs + Zd/E. The two vectors to be compared in phase are therefore

Sf = S2 =

ZL Zn - ZL

The vector diagram is shown in Fig. 2, and it is clear that the locus of ZL is a circle with Zn as diameter. In practise, the mho relay is not suitable as a directional element, since a finite value of Sl is required in order to effect operation, so that the origin is outside the relay characteristic, and there is no protection against terminal faults. The problem is solved in the polarised mho relay by making Sl = V p , where Vp is in phase with V but not proportional to it so that for terminal faults,

x

EZ L + ZL • R

E FIG.

Zs

Sz =

+

ZL

MHO-RELAY CHARACTERISTIC.

when V = 0, phase comparison can be effected. In this case,

E(Zn - Zd Zs + ZL

Sf

The criterion for operation is that

- TrI2 ~ ~ /So

2.

=

Zp

S2 = Zn - ZL

.:S Tr/2

where Zp is a vector of constant magnitude but in phase with ZL' The vector diagram is shown in Fig. 3, from which it is clear that phase comparison of Zn - ZL with Zp is the same as ZL, because these latter two impe-

~-

x

ts'--",_v_ _

----1

Phas~1-------s:Iz

comocr~_~

-v

I

n

R

FIG. FIG

1.

BASIC CONNECTION FOR MHO RELAY.

192

3.

BASIC POLARISED-MHO-RELAY CHARACTERISTIC.

dances are in phase: consequently, the 'polarised mho' characteristic is identical with the 'mho' characteristic, except that the origin in this case is a well defined point. The problem is in selecting a suitable polarising voltage V p' and three basic solutions are adopted in practice. V p is either derived from the fault voltage V through a resonant circuit tuned to system frequency (memory) or from an unfaulted phase through a suitable phase-shifting circuit (sound-phase polarising): alternatively, a combination of part sound-phase and part faulted-phase polarising is used. The last two methods do not solve the problem in the case of 3-phase faults, when an unpolarised mho characteristic is obtained, and operation for close faults once more becomes indeterminate. In practice V p and V are not in phase for terminal faults, because of the characteristics of the system, prinicipally unequal source-impedance/line-impedance angles. By considering a number of boundary conditions, Ellis3 has shown that, in most cases, a suitable choice of sound-phase polarising voltage gives rise to errors in phase of less than 1 SO between V p and V. The effect of phase shifts between these two voltages modifies the relay-imput equations to the following:

mho relays to systems are interested in the maximum negative value which ex: can attain, since this corresponds to a minimum value of R. Typically, () = 75°, and, if a = - 15°, R = O. This case is illustrated in Fig. 5, together with a typical range of system impedances superimposed on the diagram, including the effect of fault-arc resistance. It may be seen that the relay coverage under

= Zn -

R

4.

CHARACTERISTIC OF POLARISED MHO RELAY WITH PHASE SHIFT BETWEEN Zp AND ZL.

tic, and the diameter D lags Zn by a and has a magnitude sec a. For a = 15. sec a IS 1·035, which is a negligible increase. The polar equation of the mho circle is

IDI = IZnl

IZI

SI = Zne

IZnl

cos (cjJ - () + a) sec a where cjJ and () are the angles of ZL and Zn, respectively. The value of Z when cjJ = 0, i.e. the relay reach in the resistive axis for terminal faults, is R = Znl cos (() - a) sec a Engineers concerned with the application of polarised =

a

= - 15

arc-resistance conditions is rather poor. The effect shown in Fig. 5 is most severe in the case of short lines and low fault currents, corresponding to high source/line impedance ratios, and has detracted considerably from the appeal of these relays in this case. Warrington' has shown that, in these circumstances, a reactance relay is more suitable as a distance-relay element, despite the added complexity of the arrangement, since separate directional elements must be provided. In order to verify these conditions in practice, a series of measurements was made on a practical polarised mho distance relay, and marked disparities between theory and practice were noted. The reach in the resistive axis for terminal faults was found to be greater than expected, and it increased as the source/line impedance ratio increased. These results are presented and discussed in Section 7. The reason for the disparity between theory and practice is in assuming that V p and V are in phase or separated by a fixed angle a. In practice, this only applies when ZL and Zn are in phase. Deviations become progressively more severe as ZL moves around the polar diagram, and it is possible under certain conditions for a to equal 180°. In the Sections to follow, a more rigorous analysis of the operation of the polarised mho relay is presented, in order to take this effect into account. In Section 3 it will be seen that, in the case of the polarised mho relay, the input quantities to the relay take the most general form, i.e.

ZL

Zp and ZL have the same phase, and the angle between V p and V is accounted for by the additional rotation a. From the relationship in the vector diagram shown in Fig. 4, it is seen that Zn is achord of the mho characteris-

FIG.

POLARSED MHO CHARACTERISTIC

() = 75

S{ = Zp ~

S;;

5.

FIG.

S2

=

+

KZ L

Znl - ZL

It is shown in Appendix 12.1 that the locus of ZL at the boundary of operation of the relay is a circle, and a simple construction is developed which relates the position of the circle in the complex plane to the three constants Znh Zne and K.

I

193

ANALYSIS OF POLARISED-MHO-RELAY CHARACTERISTIC FOR PHASE-TO-PHASE FAULTS

VBR is not used in practice, because the vector position is such that inductive phase shift is required to achieve the correct phase relation with V yB , and this raises practical problems. There are no further advantages to be gained by this choice, and it will not be considered.

The system is shown schematically in Fig. 6, together with the sequence impedance diagram. The operation of a relay connected between yellow and blue phases is E_

Derivation of polarising voltage for phase-fault relay element

O---l\.Jv~ Zs ZL

R

The three practical cases are considered below for the derivation of the polarising signal SI' (a) SI = KIV YB + KZV R This is a case of mixed polarising, where K z is complex with an angle of approximately -90°. For later simplification, we write K z = -jY3K2. K I is generally real and approximately equals 1. Subsituting for VYB and VR and simplifying, SI = E(a 2 - a)[KIZ L + K2(Zs + ZL)]/(Zs + Zd

a2E _ r--~\,I\/'\I"------'\/\JVe---,y

oE_

SI = KIV YB + KzV YR K 1 is as before. For convenience in this case we write K z = K2 /60°. Substituting for the voltages and simplifying, SI becomes (b)

E(a 2

-

a)[KIZ L + K2Z L + (Y3/2)K2 /30 Z s]/(Zs + Zd 0

FIG.

6.

EQUIVALENT CIRCUITS FOR SYSTEM WITH PHASE FAULT

This is the case of a memory relay, where KIVYB is initially the interphase voltage prior to the fault, which then decays exponentially to the fault voltage. K I may have a small angle, owing to the resonant frequency of the tuned circuit not coinciding with the system frequency. In this case,

considered. The voltages and currents in each phase are VR

E

E (2a 2 ZL - Zs) 2(Zs + Zd

Vy VB V YR V YB IR Iy IB

E (2aZL - Zs) 2(Zs + ZL) E[(a 2 - I)ZL- I'SZs]/(Zs + Zd E(a 2 - a)ZJ(Zs + ZL) 0 E(a 2 - a)/2(Zs + Zd -

which is the signal just prior to fault occurrence. These three cases cover those generally used in practice. The general characteristics for the three types of mho relay may be obtained in the manner detailed in Appendix 12.1. The signal Sz in each is the same; SI takes the three alternative forms described in (a), (b) and (c) above. In order to obtain the general form of input signal Si and Sl, all input signals will be multiplied by the vector

Iy

Iy - I B E(a2 - a)/(Zs + ZL) The measuring signal for a polarised mho phase-fault relay is Sz = (Iy - IB)Zn - V YB which, in this case, is Sz = E(a 2 - a)(Zn - Zd/(Zs + Zd There are three possible practical alternative choices for polarising voltage: (c) combination of V YB and V R (b) combination of V YB and V YR (c)

(Zs + Zd/E(a2 - a) The input signals for the three cases then become (a) Si = K2Z s + (K I + K2)ZL Sl = Zn - ZL (b) Si = (Y3/2) /30° K2Z s + (K I + K2)ZL Sl = Zn - ZL (c) Si = KIZ s + KIZ L Sl = Zn - ZL

memory circuit associated with V YB'

194

Characteristic of polarised mho phase-fault relay The relay characteristics for the forward direction of power flow in the three cases are shown in Fig. 7. In all cases, the origin is enclosed by the relay characteristic, the degree of offset of the relay in the third quadrant being principally a function of the source-impedance

Polarised K j V YB +K z V R

Q

x

R R Q

K2 'Z n

b

1

Polarised K j V YB + K z V YR

x

--R

~IJ--

0=00

c

FiG. 7.

Polarised K j E YB (memory)

b

POLARISED MHO PHASE-FAULT-RELAY CHARACTERISTICS FIG.

8.

CHARACTERISTICS OF POLARISED MHO RELAY FOR CASE (a) OF SECTION 3.1

a Zs = 0

The relationship between the three general constants Znb ZnZ and K is given in Table 1.

bZs=oo

vector Zs and the constant K z. When Zs = 0, the characteristic always passes through the origin. The construction for this special condition for case (a) is shown in Fig. 8. By virtue of the construction for the relay characteristic, the diameter subtends an angle of 90 at the origin, which must therefore lie on the relay characteristic. Also shown in Fig. 8 for the same case is the construction for the special condition Zs = <Xl in case (a). It is evident that the characteristic is a straight line through Zn perpendicular to KzZs. From the foregoing, it would appear that the directional feature of the relay has been lost, since the origin is enclosed by the relay characteristic. This interpreta-

Table 1 Relationship between vectors

0

Case

Znj

Zn2

K

(a)

Zn

KzZ s

K j + Kz

(b)

Zn

(Y3/2)Kz /30 Zs

K j + Kz

(c)

Zn

KjZ s

Kj

0

195

ongm lies outside the relay characteristic, which is almost entirely in the third or negative-impedance quandrant. Only in the special case of Zs = 0 is it permissible to identify negative impedance and reverse power, since the characteristics for both directions of power flow are then identical.

R

ANALYSIS OF POLARISED MHO RELAY FOR EARTH FAULTS In this case, operation of a relay connected beween the red phase and earth is considered. The sequence diagram is shown in Fig. 10. I)

E/[(2 + p)Zs + (2 + q)Zd

11

I z = 10

Where Zso

FIG. 9. POLARISED-RELAY CHARACTERISTICS. CASE (a) OF SECTION 3.1; REVERSE-POWER-FLOW CONDITIONS

VR

= pZs and ZLO = qZL E - Zsl\ - Z,l z - pZ,lo E[(2 + q)Zd/[(2 + p)Zs + (2 + q)Zd E[(2 + P)a 2 Z s + (2 + q)a 2 ZL + (1 -p)Z,]I[(2 + p)Zs + (2 + q)Zd

tion follows from the fact that negative impedance in the forward sense and positive impedance with reverse power flow are normally identified. This assumption is not valid. In the case of reverse power flow, the relayinput equations change, owing to the new vector relationship between voltage and current. Typically, in case

E((2 + P)aZ, + (2 + q)aZL + (1- p)Zs]/[2 + p)Zs + (2 + q)Zd E(a 2

-

a)

3E/[(2 + p)Zs + (2 + q)Zd

(a), the equations become

Sl S2

=

K2Z s + (K I + K2)ZL Zn - ZL

= -

In the case of an earth-fault relay, the measuring current is a combination of phase and zero sequence to give correct measurement impedance, i.e.

The vector construction for this case is shown in Fig. 9. It may be seen that the characteristic is totally different from that for forward power flow. In particular, the

1m

IR + [(Zul/Zd - 1]1 0 E(2 + q)/[(2 + p)Zs + (2 + q)Zd

[1

The measuring signal in the case of an earth-fault relay is

E(2 + q)(Zn - Zd/[(2 + p)Z, + (2 + q)ZLJ

FIG.

10.

In this case, there are four practical cases of polarisingvoltage signal Sl to be considered: K1V R + KeV B, K1V R + KeV yB . K1V R (memory) and K1V R + KeV RB •

SEQUENCE DIAGRAM FOR PHASE-EARTH FAULT

196

Derivation of polarising voltage for earth-fault relays 5/ = KIV R + K 2 V B Writing for convenience K 2

(a)

K IVR

+

K 2V B

= K~

-

/-120°,

E[KI(2 + q)ZL + K~(2 + p)Zs + K~(2 + q)ZL + ~(1 - p)Zs~] ...

-

(2 + p)Zs + (2 + q)ZL E(2 + q){K2[(Y3 ~

+ Y3p ~)Zs/(2 + q)] + (K[ + K2)ZL} (2 + p) Zs + (2 + q)ZL

Writing K 2 = -

jK~,

E(2 + q){[Y3K~(2 + p)Zs/(2 + q)] + (K I + Y3K2)Zd (2 + p)Zs + (2 + q)ZL KjE =

E(2 + q){[K I(2 + p)Zs/(2 + q)] + KIZ L} (2 + p)Zs + (2 + q)ZL

E(2 + q){[Y3K~(cl!E + p)Zs/(2 + q)] + (K j + Y3K2)ZL} (2 + p)Zs + (2 + q)ZL

reason. The same arguments regarding extrerr,e limits of Zs apply, i.e. zero and infinity. In the former case, simple mho-relay characteristics are obtained and, in the latter case, reactance-relay characteristics.

Characteristic of polarised mho earth-fault relay element The input quantities S{ and S2 for the four cases are obtained by multiplying 51 and 52 by [(2 + p)Zs + (2 + q)Zd/(2 + q)E I.e. (a)

S{

52

RELA Y CHARACTERISTICS UNDER 2-PHASE-TO-EARTH FAULT CONDITIONS

Y3K2[( j- 30° + p LlQ~ )ZsJ(2 + q)] + (K[ + K2)ZL = Zn - ZL

=

(b) S{ = Y3K2[(2

Owing to the complexity of the voltage and current relationships, it is not possible to describe the characteristics in terms of the simple basic quantities as has been done in other cases. However, the following general observations may be made: (i) When Zs = 0, all characteristics are simple 'mho' circles through the origin. (ii) When Zs = 00 , the characteristics are straight lines whose angles of inclination are functions of Zs, as before. The choice of the type of sound-phase polarising is of some importance, since the vectors are subject to severe phase shifts. A danger exists when Zs is large that, if K2Z S is too far in the fourth quadrant, overreach for arcing faults will be experienced. The basis for selection of sound-phase polarising described by Ellis" is valid in this case, since the phase shifts described in his paper are in fact related to the effective position of K2Z S on the mho characteristic. In general, the preferred choice of 'sound phase' for a phase-fault element is VB for a RY relay while the preferred phase for a RE relay is also VB' It is important to note that the RE relay measures correctly

+ p)ZsJ(2 + q)] + (K[ + Y3K~)ZL

(c)

S{ = K j [(2 + p)ZJ(2 + q)] + K1Z L 52 = Zn - ZL

(d)

S{ = Y3K~Zs[( /- 60°

+ p)/(2 + q)] + (K[ + Y3KDZL

It may be seen that cases (a) and (d) are almost identical if K2 in the second case has a leading angle of 30°, while cases (b) and (c) are similar. The characteristics for cases (a) and (b) are shown in Fig. 11. The general appearance is similar to that for the phase-fault relays. The condition for reverse power is similar to that previously described for the phase-fault elements, and the characteristics are not plotted for this

197

x

(iii)

Sj

KjE

S2

S{

E(Zn - Zd/(Zs KjZ s + KjZ L

S2

Zn - ZL

+ Zd

The two characteristics are shown in Fig. 12. The angle of K~ has purposely been exaggerated to show the lack of coincidence between Zn and the diameter in this case.

1J:s~'---+---~-R

a

x

I

/.--- -~+i /

i.

!

/ /

I/!

!

Y

I

I!.

/ . I

il// / ! ~/ Yi",f,;:c- / ! /1JIi1 ~ ~/ 1/ /Cz~/

~ it /

rt:f----+---R

1

1.

/

i

.1\.,1::/

o /

ti

~/

b

FIG.

11.

*,~,0

G

x

!

POLARISED MHO EARTH·FAULT·RELAY CHARACTERISTICS a POLARISED S,

b POLARISED S,

= K1VR + K2VIl = K,V R + K2VYB --_R

for both RYE and RB E faults. In the former case, the characteristic encloses the origin as in the case of the simple earth fault, while in the latter case the origin is indeterminate, because VB falls to zero with VB, and a simple mho characteristic is obtained.

FIG 12. POLARISED MHO EARTH·FAULT-RELAY CHARACTERISTICS DURING '·PHASE FAULTS a POLARISED K,VR + K2V B b POLARISED K[ER (MEMORY)

RELAY CHARACTERISTIC UNDER BALANCED-FAULT CONDITIONS With the exception of the memory relay, the characteristics will be simple 'mho' circles, the origin being indeterminate. The diameter may not coincide with Zn if K2is not real. The behaviour of a RE relay polarised from VB and the same relay with memory are considered below:

PRACTICAL RESULTS Tests were carried out on a polarised mho phase-fault relay using the rectifier-bridge moving-coil principle. Polarising was as for case (0) of Section 4.1. and the constants of the relay were () (angle of Zn) = 60°, K 1 = 1.42 and K2 = 0'14/-15". A set of polar curves is presented in Fig. 13. These were obtained by connecting a relay to a 3-phase test bench and varing the line impedance together with simulated fault resistance. The curves are normalised. in that all vectors are divided by Zn. It follows that Z,/Zn = Y is the system-impedance range factor. The curves are presented for a number of such factors. The curves are not circles about the major diameter, since in this particular type of relay the criterion for operation is that the angle between the two signals S[ and S, is 75° rather than SlO°, so that the relay characteristic consists of the arcs of two

EZ,/(Z, - Z,) aEZ,/(Z, - Zd E/(Z, - Z,)

o (ii)

I

S, S2

S; S2

E[K,Z, - K2Ztl/(Z, + Z[) E(Zn - Zd/(Z, + Zd K,Z, - K2Z r Zn - Z,

198

characteristic which is independent of system conditions, i.e. ZL = Zw In the past, in certain cases, the setting of a polarised mho relay for line angles other than that of Zn has been specified in terms of the simple trigonometrical equation Zs = Zn cos (0 - ¢), where Zs is the setting for a line angle 0 - ¢ displaced from that of Zn. It may be seen from the analysis in this paper that the equation is not valid and that errors in setting may arise if this approach is used. If an accurate knowledge of the setting is required, the angle 0 - ¢ should not exceed 10°. In the case of lines with series capacitors, this condition cannot be met and the setting becomes indeterminate.

circles with the major diameter becoming a chord. If the reach in the resistive axis is critical, this effect could be taken into account. The theoretical curves are also given, and, apart from the disparity in reach in the resitive direction for the reason stated, the agreement between theory and practice is good.

ASSESSMENT OF THE CAPABILITIES OF THE POLARISED MHO RELAY In the past, it has been customary to use polarised mho relays for relatively long feeders, while reactance relays have been preferred for short lines where arc resistance x

CONCLUSIONS

nominal angle 60·

1·0

Owing to disparities between theory and practice in predicting the performance of polarised mho relays, a new theoretical analysis was undertaken, the treatment being presented in Section 1 of this paper. The charactenstics of the polarised mho relay for a number of well known connections are shown to have an offset in the negative-impedance quadrant in the case of unbalanced faults, thus providing added reach in the direction of the resistive axis. In particular, the reach for arcing-terminal faults is far greater than would be expected from a simplified analysis. Negative impedance and reverse power flow should not, in general, be identified, since the characteristic for reverse power flow is different from that for forward flow. It is shown that, for unbalanced faults, the polarised mho characteristic for reverse power flow is a circle lying almost entirely in the negative-impedance quadrant and not enclosing the origin, so that die relays are directional. The characteristics of crosspolarised directional relays are in accord with the general theory as shown in Appendix 12.2. For unbalanced faults, the origin is included within the relay characteristic for faults in the forward direction and lies outside it for faults in the reverse direction. In this case, the relay characteristic is a straight line. The polar characteristics of polyphase directional impedance relays may be obtained by the same general method (Appendix 12.3) and are in accordance with the results for single elements. The advantages of the reactance relay for short lines are not as great as may be expected from a simplified analysis, and the polarised mho relay may be favoured, because of its ability to adapt itself to the system conditions; i.e. increasing its reach in the resistive axis for arcing faults on short lines, whilst retaining the virtue of insensitivity to impedances due to load currents and power swings. If an accurate knowledge of the settings of a polarised mho relay is required, the angles of the nominal impedance Zn and the line impedance ZL should not differ by more than 10°. The setting in the case of lines with series capacitance may be determined for certain specific plant conditions but cannot be specified in the general case,

~-----d;::l::---tl.:""-_~-O-...L..:-'::'~.L----1:L5=--R

Zn

FIG.

13.

COMPARISON BETWEEN THEORETICAL AND EXPERIMENTAL RESULTS Y = Zs/Zn - 0 - experimental - - - - theoretical

has been a problem. This latter solution has not been ideal, because of the need for a directional-control element and an impedance element for preventing undesired operation on load current. From the analysis presented in this paper, it may be seen that, when the source impedance is large compared with the relay setting, the polarised mho characteristic is similar to that of a reactance relay, and the advantage of the latter becomes marginal. The condition of a very short line with arc resistance usually implies that the sourceimpedance/line-impedance ratio is high, and it follows that the polarised mho relay has the virture of automatically adapting itself to system conditions. Load current is not a problem, since in this case of balanced current flow, the characteristic is the classical mho circle. Generally the likelihood of a 3-phase arcing fault is small, and the lack of reach in this case would not be a serious drawback. The analysis also enables an assessment of reach to be made for faults which lie in the fourth quadrant. This may be necessary in lines which have series-capacitor compensation, and in the past it has been difficult to predict the relay behaviour in this case. A further important point which should be noted is that there is only one point on the polarised-mho-relay

199

since it is a function of the system sourceimpedance/line-impedance ratio. Finally, it should be noted that the analysis in this paper is based on the assumption that the faulted line is energised from one end of the system only. The analysis in the more general case does not lend itself readily to a simple geometrical interpretation. In this case, it would be more appropriate to study specific cases with the aid of a digital computer backed by practical results obtained from a test bench. This does not detract from the analysis in the paper, however, since the main effect of an interconnected system would be to alter slightly the amplitude and phase of the voltage derived from the unfaulted phases and to include reactive effects in the arc-resistance voltage, which is purely resistive in the simple case. The general form of the characteristic would remain unchanged. The comparison with earlier analysis is in any event valid, because this was invariably based on the assumption of a power feed from one end of the system only.

K

=

D/B

ZL = V/I

and A, B, C, D and K are, in general, complex. The boundary of relay operation is defined by the condition that S; and S2 should be displaced in phase by 90°. The vector diagram is shown in Fig. 14, the vectors Sf and S2 being represented by AB and DC, which are at

ACKNOWLEDGEMENTS The author wishes to thank A. Reyrolle and Co. Ltd. for permission to publish this paper. Thanks are expressed to Mr. F. L. Hamilton (Engineer-in-charge of research), and Mr. J. B. Patrickson (Deputy Engineer-in-charge of research) for helpful discussions during the preparation of this paper, and to Mr. T. H. Potts for carrying out the practical tests.

FIG. 14.

GENERAL VECTOR DIAGRAM FOR PHASE COMPARATOR OE = ZnZ/K

REFERENCES 1. WARRINGTON, A. R. VAN C.: 'Application of the ohm and mho principles to protective relays', Trans. Amer. Inst. Elect. Engrs., 1946,65, p.378 2. WARRINGTON, A. R. V AN c.: 'Reactance relays negligibly affected by arc impedance', Elect. World, 1931,98, p.502. 3. ELLIS, N. S.: 'Distance protection of feeders', Reyrolle Rev., 1957, (168), p.16 (which is chapter 11) 4. WARRINGTON, A. R. VAN c.: 'Protective relays, their theory and practice' (Chapman and Hall, (1962) p.285

right angles on the relay boundary. Since it is the locus of point B which is of interest, a point E is described, so that triangle OCD is similar to triangle aBE. The ratio between sides is OC/OB = K, so that corresponding sides of the two triangles are in the magnitude ratio K and separated in phase by 8, the angle of K. The corresponding sides EB and CD intersect at X, and the angle BXC is 8. By definition, AB and DC are at right angles; angle XBY is therefore 90° - 8 and angle ABE is 90° + 8. Since A and E are points fixed by Zn I, ZnZ and K and are not functions of ZL, AE must be a chord of the relaycharacteristic circle. A diameter of the circle must be AF, such that ABF is a right angle, and therefore angle FBE is 8. Since A is also on the characteristic circle, FE must subtend the same angle at B as at A, so that angle FAE is 8. Finally, FEA is a right angle, since it is subtended by the diameter. This diagram provides the basis for a simple construction for the general circle. It is noted that ZL = Znl is a point on the circle; the vector diagram is drawn for this special case in Fig. 15. Here B and A are coincident, since Znl = ZL and OC = KZ L =KZn1 . E is the same as before. The phase of the zero vector AB must be at right angles to DC (= ZnZ + KZ n1 ). The triangles OCD and OAE are similar, as before. A diameter is obtained by describing F so that angle FAE is8 and angle FEA is a right angle as before. A new point M is fixed so that MA is equal and parallel to OC (= KZ n1 ), and G is fixed so that MG is

APPENDIXES 12.1 General distance-relay characteristic The most general input to a 2-terminal phase-angle comparator is Sl = AI - BV Sz = CI + DV The relative phase angles are not disturbed if both signals are divided by BI to give S; Znl - ZL

S2

ZnZ - KZ L

where Znl

AlB

ZnZ

C/B

200

equal and parallel to DO (= zd. OH is drawn perpendicular to OA (= Znl), and it remains only to show that HF is parallel to MG and GFA lies on a straight line. This is done by noting that triangles OAH and EAF are similar (equal angles 8 and one right angle), and consequently triangles AHF and AOE are similar, since there is an equivalence in translation from H to 0 and F to E. However, triangles OAE and MAG are similar, and therefore MAG and HAF are similar, so that F lies on AG. The final construction of the general characteristic is shown in Fig. 16. Vector K is also shown for clarification.

K <1,0)

FIG.

16.

CONSTRUCTION FOR PHASE-COMPARATOR POLAR DIAGRAM (GENERAL CASE)

12.2 Directional relays 'Crosspolarised' directional relays may be explained in terms of the analysis described for polarised mho relays. The analysis will be performed for one particular connection, but the extension to other connections is obvious. Consider a phase-comparing relay of the type previously described, in which SI = IpZ n and S2 = V YB 90°, this being the so-called 'quadrature' directionalrelay connection. A number of faults need to be considered, i.e. RY, RB, RE and R YB. RY fault SI E(l - a2)Zn/2(Z, + Zd

L

/G FIG.

15.

S2

Y3E(!Y3Z s LlQ:.

SI

Zn /30°/2

SI

tY3Z, /30°

+ Zd/(Z, + Zd

+ ZL

RB fault GENERAL VECTOR DIAGRAM FOR PHASE COMPARATOR ZL ~ Zn

Since the construction will be used repeatedly in the text, it is worth while summarising the steps: I. Vector Znl is drawn from the origin. 2. Vector KZ nl is drawn to meet the extremity of the Znl vector. 3. Zn2 is drawn in such a position that the extremity touches the beginning of vector KZ nI. 4. Vector Zn2 + KZ I11 is formed by joining the beginning of ZI12 to the extremity of KZ nl (and incidentally ZI1I)' 5. A line is drawn from the origin perpendicular to ZI1I to intersect KZ nI. 6. From the point of intersection with KZ I1I , a line is drawn parallel to ZI12 to interset ZI12 + KZ I1I . 7. The vector diameter of the relay characteristic is drawn from the final point of intersection to the extremity of the ZI1I vector.

SI

E(l - a)Zn/2(Z, + Zd

S2

Y3E(!Y3Z, L~30° + Zd/(Z, + Zd

S;

Zn

S2

tY3Z,

L-

30°/2

1-

30°

+ ZL

RE fault SI

EZ n/[(2 + p)Z, + (2 + q)Zd

S2

(a 2

S;

Zn/Y3 (2

S2

Zsl(2 + p)/(2 + q)] + ZL

-

a) /900 E

+ q)

RYB fault SI

EZ I1 /(Z, + Zd

S2

Y3EZ L/(Z, + Zd

S;

ZI1/ Y3

S2 201

The characteristics are shown in Fig. 17, where it can be seen that they are similar to those of the polarised mho relay, except that in this case the diameter is infinite. The general characteristic is a straight line through

either be in phase or in antiphase at the boundary of operation. The same characteristic could be realised with a cos ¢ comparator, if a relative phase shift of 90° were introduced between the two signals. It has been indicated! that a phase comparator with this connection gives correct impedance measurement for interphase faults between any pair of phases but gives no protection against 3-phase faults. However, the polar characteristic for various fault types is not described. The polar characteristic is obtained for the possible fault types as shown below.

x

znt2Q" -2

Fault between phases Rand Y 2

(1 - a )E (Zn - Zd Zs + ZL

k---------- R J3Z

m"

(1 - a 2 )E [Zn _ (1-a)(Z,+Zd + Z]. Z, + ZL [ 2 1 - a2 2]

5 2

a

s;

x

S;

Zn - ZL !Zn - Zs( !-60° -

n - ZL 1- 60°

, zZn

1-

+

!j ,/ v 3Zs -

ZL

60°

---<_R

---....,j,L--

b

FIG.

17.

CHARACTERISTIC OF CROSSPOLARISED DIRECTIONAL RELAY 1I RY fault h RB fault

a

the modified Zs vector, perendicular to the modified Zn vector. Again the origin is included within the relayoperating characteristic for forward power flow and is outside it for reverse power, except in the case of a 3-phase fault, when the characteristic passes through the origin. For the cases considered for this particular connection, the characteristic rotates through ±30°, depending on the type of fault. This is a well known effect and is taken into account when specifying the angle of ZI1"

b

c

12.3 Polyphase directional impedance relays There is a certain class of relay connection which gives rise to polyphase directional impedance characteristics.' The characteristics of one of these will be described below. The two input signals to a phase comparator in this case are SI = (lR - ly)ZI1 - V Ry and S2 = (lR - lB)ZI1 - V RB The only practical realisation of this relay described in the literature' makes use of an induction-cup movement, so that the criterion for operation is that Sl and S2 should

d

FIG.

18.

e

POLAR CURVES FOR POLYPHASE MHO RELAY 1I RY fault h RB fault c YB fault d General dlaractcristic. all phase faults. forward power flow e General characteristic. r('\erse power flo\\.

202

12.3.3

It is important to note that the criterion for operation is S\ and S2 in phase or antiphase. If S/ \ is advanced 60° to become S2, the criterion for operation becomes 60° < a < 240° where a is the angle of S:; relative to S; and S; = Zn - ZL S"2 = lcZ /60° - lcY3Z - ZL 2n~ 2 s 1-30°

- lcY3Z /30° S"2 = lcZ 2 n /-60° 2 s~ where, as before, the operating criterion is 60° < a < 240°. The characteristic is once more an offset circle through Zn, as shown in Fig. 14c. The vector chord in this case is !Zn( /60°- !600)-!Y3Zs (/-30°- L1Q':) = !jY3(Zs + Zn) As before, the vector chord subtends 60° in the major quadrant, so that the diameter is Zs + Zn, and the characteristic is identical with that for the previous two cases. The characteristic for all phase faults for forward power flow is shown in Fig. 18d and for reverse power flow in Fig. 18e.

The polar characteristic is shown in Fig. 18a. It is seen that the characteristic is an offset 'mho' circle with the Zn - (iZn

L.2.!r... -

!Y3Zs 1-30°) = !Y3(Zn + Zs) /-30°

vector as a chord. It is clear that the chord subtends an angle of 60° to the right and 120° to the left of the chord. The diameter must therefore be the vector D = C LlQ:. sec 30°, where C is the chord; i.e. D = Zn + Zs. For reverse power, the diameter is D = - Zn + Z" and, as in previous cases, the characteristic lies almost entirely in the third quadrant and the origin is outside the relay circle.

12.3.4

2-phase-earth faults

As before, a geometrical presentation of the polar characteristics is complicated, but it is readily seen that the vector Zn is on the relay characteristic, and it may be assumed that the main effect in this case is for the degree of offset in the negative-impedance quadrant to be modified, while retaining accuracy of setting in the positiveimpedance quadrant.

12.3.2 Fault between phases Rand B

In this case, the two signals become, after manipulation, S'{ = !Zn /-60° - !Y3Zs 1+30° - ZL

S2

Fault between phases Y and B

In this case, the two input signals are S"1 = lcZ 2 n /60° - lcY3Z 2 s /-30°

12.3.5

Zn - ZL The criterion for operation is, as before, 60° .::: a < 240° where a is the angle of S2 relative to S/I. The polar characteristic is shown in Fig. 18b. In this case, the vector chord is Zn - (!Zn /-60° -!Y3Zs /+30°) = !Y3(Zn + Zs) /30° =

3-phase faults

In this case, S\ and S2 are equal in magnitude. S\ is proportional to (1 - a 2 ) and S2 to (1 - a), so that there is a permanent restrain condition; no operation can take place. 12.3.6 Comparison of the relay characteristic for different fault types

It has been shown that, in the case of each type of phase fault, the relay characteristics are identical, with diameter Zs + Zn. The connection thus yields a true poly-phase polarised 'mho' phase-fault element which is insensitive to 3-phase balanced conditions.

Applying the same reasoning as for a RY fault, the diameter is Z, + Zn, and the characteristics are identical in the two cases.

203