Performance of distance protection of e.h.v. feedersutilising shunt - reactor arrangements for arc

suppression and voltage controlAT. Johns., B.Sc, Ph.D., C.Eng., M.I.E.E., M. El-Nour., M.Sc, and

R.K. Aggarwal, B.Eng., Ph.D., C.Eng., M.I.E.E.

Indexing terms: Transmission-line theory, Relays, Waves

Abstract: Digital techniques for modelling the faulted response of any arbitrary linear shunt-reactor compen-sated e.h.v. transmission-line system are described. The methods are specifically developed to meet therequirements of offline or programmable test-equipment-based feeder-protection studies. The essentialdifferences in the faulted response of single and 3-section feeders are established by reference to 500 kVinterconnections involving 4-reactor linear shunt compensators. An extensive study of modern distanceprotection applied to various feeder configurations is reported and the paper concludes with an evaluationof protection performance in a typical sectionalised interconnector of length 550 km.

List of principal symbols

Z Z

C J 0

CO

UQ

7

Zo

= line lengths of feeder having nsections

= length of faulted line section= distance to fault= line lengths of sending-end com-

posite source= line lengths of receiving-end com-

posite source= p.p.s. and z.p.s. shunt capacitance

per unit length of assumed ideallytransposed line

= degree of p.p.s. and z.p.s. shuntcompensation

= magnitude of p.p.s. and z.p.s.inductive susceptance of shuntreactor bank at nominal systemfrequency (1/OJ0LI,1/OOQL0)

= magnitude of p.p.s. and z.p.s.capacitive susceptance of any linesection at nominal system fre-quency, assuming ideal transpo-sition (<LO0Cxl, OJQCQI)

= phase and neutral impedances ofshunt reactor bank

= p.p.s. and z.p.s. inductance ofshunt reactor bank

= nominal system angular frequency= angular freqnecy= any line length lx, l2, etc.= voltage and current transforms= unit matrix= voltage eigenvector matrix= modal propagation constant matrix

YZ1 = Qy~l Q~ lZ = polyphasesurge impedance metrix

Paper 906C, first received 22nd February and in revised form7th July 1980The authors are with the Power Systems Laboratory, School ofElectrical Engineering, University of Bath, Claverton Down, BathBA2 7AY, England

304

0143-7046/80/05304 + 13 $01-50/0

Z

Y

Vt,Vr

s.c.l.SltS2

VL

0

Subscripts

= series-impedance matrix per unitlength of line

= shunt-admittance matrix per unitlength of line

= incident and reflected voltage trans-forms

= sending- and receiving-end main-source impedance matrices

= sending- and receiving-end com-posite-source impedance matrices

= short-circuit level= general form of relaying signals= relaying voltage at voltage trans-

former (v.t.) secondaries= relaying current at current trans-

former (c.t.) secondaries= current replica impedance= sound-phase polarising voltage= ratio of z.p.s. to p.p.s. impedance

of main source= null matrix

a, b, c = phases a, b, ct = transpose of matrix

1 Introduction

The use of shunt compensation for voltage control in longdistance a.c. transmission feeders is a long establishedtechnique1 and recent years have seen increasing world-wide interest in the use of various static shunt reactordevices2 as an alternative to rotating synchronous compen-sators. In the case of static reactors, it is common to use anessentially balanced 3-phase set of reactors which aredirectly connected to the transmission line or are connectedto the system via transformers situated at various pointsalong a complete interconnection.3 Until quite recently,very little had been reported on the performance of distanceprotection applied in such situations. However, a study byFielding et al* revealed that the performance of a distance,relay incorporating the extensively used block-averagecomparator arrangement,5 although satisfactory, wasnevertheless modified somewhat when applied to a relatively

IEEPROC, Vol. 127, Pt. C, No. 5, SEPTEMBER 1980

simple single-section shunt compensated lumped parameterlaboratory model system.6

The work reported in Reference 4 was confirmed to aconsideration of distance relay performances in a systemutilising 3-phase static shunt-reactor compensation of thelinear and saturable types. However, where single-poleautoreclosure is involved, it is commonly necessary toemploy essentially linear 4-reactor arrangements in order toaid the rapid extinction of secondary arcs and therebypermit satisfactory reclosure following transient faults.7*8

In such arrangements, the main jeactors are usually con-nected in star with the common points connected to earththrough a neutral reactor, the parameters of which aredependent on arc extinction times sought, the line para-meters and the degree of steady-state positive sequencereactive compensation effected by the three main reactors.9

Despite the fact that single-pole autoreclosure is beingincreasingly applied globally, the state of knowledge oftypical modern high-speed distance protection, even duringthe initial measuring prefault clearance period, is even morelimited than that relating to applications involving 3-reactorshunt compensation. This paper therefore represents anattempt to rectify the latter deficiency.

It is important to note that, quite apart from any effectthe alternative reactor arrangements may have on relayperformances, the transmission-system configuration itselfcan significantly affect distance relay performances.10 Inparticular, the lower apparent frequencies of the travelling-wave induced components which arise in long line appli-cations are generally more troublesome because they canfall within the bandwidth of the protective relays and signaltransducers and thereby more significantly affect perfor-mance.11 Furthermore, long distance shunt-compensatedfeeders are often sectionalised with protection connectedat the termination of each section, so that, even for faultsclose to a particular relay, the travelling-wave componentsmay still possess a relatively low apparent frequency. Ingeneral, it is therefore to be expected that, irrespective ofthe precise nature of the protective relays used, the vari-ation of distance protection performance with systemconfiguration is likely to be very marked in long shuntcompensated sectionalised arrangements. The firstobjective of this paper is therefore to outline the basisof primary-system digital-simulation techniques which havebeen developed with the foregoing considerations in mindand which have been designed to be sufficiently flexible toenable a larger variety of protection gear application studiesto be performed using offline or real-time programmable testfacilities than has hitherto been possible. In order to obtainmaximum realism, the frequency variance of all line andearth parameters is simulated,12 together with the effectof discrete conductor transpositions as commonly used inlong distance transmission systems.

The second main objective is to report the salientfeatures of an extensive offline study of the performanceof typical crosspolarised mho relays utilising the block-average principle5 >14 when applied to interconnectsinvolving the use of horizontally constructed 500 kV lines.The results of a general study involving single-section and3-section arrangements are presented and the effect of thedegrees of compensation and feeder configurations on bothspeed and accuracy of the relays is established. The paperconcludes with a consideration of the performance ofdistance relays connected at the various locations alonga typical 3-section feeder arrangement operating at specificloading and compensation levels.

2 Basic system model

As mentioned previously, long shunt-compensated feedersare often sectionalised with protection and reactor bankssituated at either end of each section. From a protectionpoint of view, it is particularly important to be able tosimulate faults on any feeder section and to determinethe primary system faulted responses at the points to whichprotective gear is connected. Earlier digital-simulationmethods developed for studying distance relay perfor-mances on relatively simple essentially homogeneousuncompensated feeders12 are clearly not directly applicablein such cases, but they nevertheless form a very usefulbasis for the methods reported in this paper.

Particular emphasis has been placed on providing asimulation which is sufficiently flexible for determiningthe response of a feeder consisting of an arbitrary numberof sections n. Fig. 1 shows the basic arrangement consideredand it is evident that a simulation of faults on the firstsection will involve a solution of an entirely different setof mathematical functions to those involved when simulatingfaults on one of the other sections. The mathematicalprocedures and associated digital computer programsnecessary to provide a realistic simulation of faults on singlefeeder sections12 are in themselves somewhat lengthy and

local outfeeds

I—I) —I—[ 2

1 Basic system model

h-

compositesend ing-end sourceczss]

1 Ic

compositereceiving-source

Fig. 2 Equivalent system model

sending-end sourceCZS]

receiving -end sourceLZR]

Fig. 3 Composite source networks

a Sending endb Receiving end

IEEPROC, Vol. 127, Pt. C, No. 5, SEPTEMBER 1980 305

involved, and it has been necessary to ensure that suchproblems are not compounded to the extent that, in com-puting terms, a rather intractable solution results. With thisvery important factor in mind, the complete arrangementof Fig. 1 is first reduced to the equivalent circuit shown inFig. 2. A composite equivalent source is connected at eachend of the line section on which it is desired to simulate afault, the schematic arrangements of the latter being shownin Figs. 3a and b for the sending and receiving ends,respectively.

It is easily verified that, in order to simulate faults any-where on an ^-section system, each composite source mustpossess at least (n—1) line sections. The line-length data canthen be specified in accordance with the requirements of agiven study so as to fix the section on which it is desiredto simulate a fault. For example, a fault on the midsectionof a three-section feeder (n = 3) is simulated by specifyingthe line-length data such that

h = hsi h = L, h = hRl /.Q-> — Iff) 0'S2 R2

Alternatively, a fault on the line adjacent to the sending-endsource of the same basic system would be simulated byputting lSi=lS2=0,ll=L,l2=lR1, l3 = lR2.

3 Fundamental relationships

3.1 Simula tion of shun t-reac tor banks

Fig. 4 shows the circuit of the four-reactor arrangementconsidered. Although the line sections to which such reactorsare connected are not in practice ideally transposed, it isnevertheless common to assume ideal transposition whendetermining the inductive parameters of the reactors. Thisis the approach followed here so that, in terms of thepositive-phase-sequence (p.p.s.) and zero-phase-sequence(z.p.s.) values of the line shunt capacitance ( Q , Co), theparameters of the shunt-reactor bank when arranged tocompensate one half of any line section of length / are asgiven in eqn. 1:

0)hx = BLI/BC1 =

h0 = BL0/BC0 = 2/(u20L0C0l)

There are a number of factors which determine the degreesof shunt compensation (h0, hx), and for a typical line

Fig. 4 Shunt reactor arrangement

306

they generally lie between, extremes of zero and 1-2.7 9

The line shunt capacitances (Cj, Co) are evaluated in theusual manner from an average sum of all the conductorself and mutual capacitances per unit length of the linesection under consideration. It is evident from Fig. 4that the p.p.s. inductance of the reactor bank Lx is equalto the inductance per phase and that the z.p.s. inductanceLQ ={LP +3Ln). It follows from eqn. 1 that the phaseand neutral parameters of the reactor bank are as givenin eqn. 2.

C,Z)

Ln = 2(/z1C1 -(2)

The resistances RP and Rn are relatively very low, a typicalQ factor of each limb at nominal system frequency (powerfrequency) being 250. If suitable test data were acquired, itwould be possible to include any significant frequencyvariance of the shunt-reactor parameters. However, resortto this degree of complexity is of somewhat questionablevalue in view of the fact that, for distance protective gearevaluation, it is only the components in the spectrum of adisturbance up to about 2 kHz which are of greatestrelevance.10 Reactor impedances consistent with constantvalues of Rp, R,therefore used in the course of this work.

Lp and Ln, as defined in eqn. 3 were

y —1 co

250" + 7 G ^

(3)

Zn = Rn+/o>Ln =1 , . «

1-/ —250 cj0

It is convenient ultimately to combine the shunt-reactorarrangements with the line sections involved and for thispurpose the canonical form of the two port or transfermatrix function defining the arrangement of Fig. 4 (eqn. 4)is particularly useful.

U 0(4)

The difference of the current vectors [I\ —12] defines thecurrent which flows in the reactor [/s] and the latter isseen to be simply related to the impedance matrix [Zs] =[Ys] "' of the shunt reactor by eqn. 5.

= [Zt]

zp+zn zn

zp+zn

Zn

Zn

zn +zr

I So

he}

(5)

The submatrix Ys = [Zs] x which is used in the transfer

matrix representation of the reactor is thus as given ineqn. 6.

IEEPROC, Vol. 127, Pt. C, No. 5, SEPTEMBER 1980

[Ys] =

zP

zP(zp -

+ 2Zn

~Zn

Zn

\-3Z

zP

n )

-Zn

-Zn zP

- z r

+ 2Z

(6)

3.2 Simulation of discretely transposed line sections

In long distance transmission systems, discrete trans-position of the line conductors is often performed atthe termination of each section or at intermediate pointsthereon. It is particularly important to simulate the effectof such transpositions, because they represent an abruptpoint of discontinuity from which incident wave componentsare partially reflected. In consequence, it is to be expectedthat the transient components in distance relaying mea-surands will be affected. Fig. 5 shows a very common trans-position arrangement which has been simulated in the courseof this work. Although this has been drawn only for thefaulted section of the source and line model of Fig. 2,the same transposition arrangements have been used todescribe the unfaulted lines within each composite sourceof Fig. 3.

It has been found useful initially to compute thematrices describing each homogenous length of line so thatthey are uniquely ordered in accordance with the conductorpositions (a, b, c) on the homogeneous section adjacent tothe sending end S. For a midsection fault as shown, thetransfer matrices describing the section between the faultpoint F and the receiving end R are given by matrix equa-tions 7.12

fR-i

'S3

'S3

where

A2f = cosh {i//(2I/3 -x)}, B2f

= sinh{M2L/3-x)}Z0,

= Y0A2fZ0

and

A = cosh {\pL/3}, B = sinh {!///,/3}Z0,

C = Y0BY0, D = YQAZ0

The polyphase propagation constant matrix i// is obtainedby using the voltage eigenvector matrix Q to transform thesystem steady-state voltage differential eqn. 8 into a series ofuncoupled differential equations of the form of eqn. 9.12> 13

Now the products Q'1 exp (± \px)Q define exponentsinvolving the modal propagation constant 7(exp (± yx)),and it follows from matrix function theory that i// is com-puted at all frequencies in the spectrum of interest as theproduct Qy Q'1.

d2Vdx2 = ZYV

= Q

(8)

(9)

Combination of eqns. 7 to form a total line transfer matrixbetween points F and R can be achieved by introducinga transposing matrix M which effects the necessaryjrans-positions by relating the vectors [VR2 IRI]*, [VS3 IS3]*-The transposing matrix is simply deduced by noting thepreviously mentioned manner in which the vectors ineqns. 7 have been ordered, i.e.

(7)

'R2

R2

R7b

RLb

R U

Fig. 5 Discretely transposed line model

IEEPROC, Vol. 127, Pt. C, No. 5, SEPTEMBER 1980 307

Matrix [M] is therefore as given in eqn. 10, so that theoverall line transfer matrix between points F and R isgiven by eqn. 11.

VR2

IRI

~Vf '

TfR

= [M]S 3

(10)

A2f B2f

C2f D2f

[M]A B

C D[M]

AL2

CL2

B L2

DL2 RL

(10

where [M] =

T 0

0 T

and [T] =

0 1 0

0 0 1

1 0 0

By a similar approach, the line-transfer matrix linkingpoints F and S is obtained from eqn. 12.

vf~

where

Aif =

Bif -

~Aif

Cit

~ALl

CLX

= cosh {i//(

= sin!

Bif

Dlf_

BL'

DL}

r/i/VVli

-

—

x-I/3)},

3)

A

C

Vs'

TsL

B

D

Vs

-I~SL_

(12)

_ _Vs

/SL_

=

_ _

Ai Bt

Cx Dx

[M]

3VR

TRL

Exactly similar methods are likewise used to describe theoverall transfer matrices between the fault point and thesending and receiving ends for faults on the first or thirdhomogeneous sections of the discretely transposed linemodel of Fig. 5. Furthermore, in the case of an unfaultedsection of any length / within the composite sources, theline transfer matrix between ends will be given by eqn. 13.

(13)

where

Ai = cosh {i////3},

Bt = sinh{i////3}Z0,

Q = Y0BiY0,

Dx = Y0AtZ0

3.3 Combination of line and shunt reactor banks

For computational purposes, it is convenient to combinethe line sections with the shunt reactors in the mannerillustrated in Fig. 6 to form a line/reactor equivalentcircuit. The situation at the receiving_end _is seen to besuch that the vectors IRL = Ty and T2 —IR- It followsdirectly from the previously developed relationships ofeqns.4and 11 that

Vf

fR

AL2

BL2

L2DL2

VR = V,

IRL =

L2BL2YS BL2YS L2

CL2 DL2

v2 = VR

TR

B, (14)

I 2 = I

compositesendingsource

S T, transposed linesection (x)

I>L1- B

DLI ]L1

fR transposed linesection (L-x)

DL2]L2

compositereceivi ngsourc e

composite

sendingsource

fzss]

c

1

> h line / reactor

equivalentsect i on

'fsF

V r f R

line / reactor

equivalentsection

V"R

compositereceivi ngsource

Fig. 6 Combination of line and shunt-reactor banks

a Actual arrangementb Equivalent arrangement

308 IEEPROC, Vol. 127, Pt. C, No. 5, SEPTEMBER 1980

The transfer matrix eqn. 13 which describes the equivalentline/reactor section linking points F and S is likewisederived from eqns. 4 and 12.

~hs

ALx

CLX

+

+BLX

DLl

Ys

Ys DLX

Vs

rTs

Bx

-T05)

It is likewise possible to obtain an equivalent line/reactorrepresentation for the unfaulted sections within eachcomposite source. In this case, however, the transfer matrixdescribing the transposed line section (eqn. 13) has to bepre- and post-multiplied by the transfer matrix describingthe shunt reactors (eqn. 4) to give the overall equivalentdefined in eqn. 16.

(16)='u

y.

ol

u\

'Ui

\fl

—

[M\

3 U

y,

o"

u_

vR

IR

3.4 Computation of composite source impedances

It will be recalled from Section 2 that each compositesource consists of a cascade of (n — 1) compensated linesections as shown in Fig. 3. The effective impedances ofthe composite sources have to be precomputed over arange of frequencies consistent with the bandwidths ofthe protection and transducer arrangements under study10

and Fig. 7 is useful for illustrating the methods which havebeen developed for so doing. Each line and its associatedterminating shunt reactors is represented by the transfermatrix equivalent in the manner outlined in Section 3.3(eqn. 16). In the course of this work, the impedancematrix of each local infeed/outfeed (Zn_2, Zn_x, etc.)has been estimated from a knowledge of the power fre-quency short-circuit levels and the ratio of zero-phase-sequence to positive-phase-sequence impedance of thesource in question. It is, of course, possible to computethe source matrices corresponding to more complex localsource network models, but, in many applications, thelocal infeed during fault conditions is relatively smalland the considerable extra computational effort requiredcan be avoided without serious loss of realism.

With reference to Fig. 7, the transfer-matrix equation17 defines the response of the line/reactor combination ofthe first source section.

L--XAn-\

A.-1

Vn-07)

hre/reoctcrequivalent[ A p . i , B r _ , ,

n-2I

• r 1 »

I'.re/recctorequivalentsection

'°

rece.v:rg orsendmg-errisource:zR:=r:zs:

" n - J [V,

--2 ' "R: ' s:'

Fig- 7 Composite source equivalent

IEEPROC, Vol. 127, Pt. C, No. 5, SEPTEMBER 1980

Now the total current entering the first section at, say,the receiving end is given by TR = / „ _ ! + [Z n _J " l Vn.xand it follows that the overall transfer matrix of the firstsection, including the local infeeding source of impedance[Zn _ j ] , is as given in eqn. 18.

K-x =

-\ - 1

Cn.x

(18)

Similar relationships are likewise computed to describe theremaining (n — 2) source sections and their respective localinfeeds. The requisite number of transfer matrices requiredto describe a given composite source are then multipliedin the usual canonical manner to finally provide a matrixrelationship of the form of eqn. 19.

(19)

At the main source, the current and voltage vectors arerelated to the impedance matrix [ZR] by Vo = [ZR]T0

and substitution into eqns^ 19yields VR = [ARZR +BR]TQ

and IR = [CRZR +DR]1O. The total composite source-impedance matrix at the receiving end [ZSR ] is then finallycomputed from eqn. 20.

JR.

=AR BR

fR DR_

(20)ZSR = [ARZR+BR][CRZR+DR]-1

Similar procedures are likewise performed to define thetotal composite source impedance [Zss] at the sending end.

4 Fault simulation

The fundamental relationships developed in Section 3 havebeen deliberately formulated in such a way as to effectivelyenable any compensated feeder arrangement to be reducedto the faulted circuit model shown in Fig. 6b. Detailsof the methods of digitally simulating faults on such amodel by using matrix functions and numerically evaluatedFourier transforms are reported in Reference 12. It isworthwhile noting that the latter methods, which weredeveloped for studying very much simpler uncompensatedsingle-section homogeneous feeders, were validated bycomparison with fault throwing tests on an actual system.15

No corresponding field test data have been acquired for thecase of long shunt-compensated feeders, and similar directvalidation of the techniques here developed has not there-fore been possible. However, by deliberately formulatingthe fundamental relationships to reduce the present problemto a previously validated simulation form, it has beenpossible to press closer to actual field test validation thanwould otherwise be the case.

4.1 Parameters of systems studied

4.1.1 Line construction: Fig. 8 shows the typical quad,conductor 500kV line configuration considered. Thepositions of the conductors illustrated correspond to

309

the positions over the first one third of the line sectionfrom the sending end of any discretely transposed section(see Fig. 5). The data for the line are:

(a) phase conductors are 4 x 477 MCM Al alloy,21 -5 mm overall equivalent, 242 mm2 Al equivalent,19/4-3 mm stranding

(b) earth wires are 7/35 mm Alumoweld '(c) earth resistivity is 100 £2 m.

The frequency variation of all earth and conductor para-meters is simulated.

4.1.2 Source and reactor parameters: The ^-factor at thenominal power frequency of 50 Hz was taken as 30 forall p.p.s. and z.p.s. source impedances. In practice, thenormal service loading levels on long compensated feedersare typically between one half to two thirds of the surge-impedance power level, and the corresponding level ofp.p.s. shunt compensation required (/?]) is approximately0-75. For the line in question, the sequence capacitanceratio C0/Ci is approximately equal to 0-572, and theassociated level of zero-sequence compensation h0 requiredto theoretically minimise both secondary arc current andresidual voltages is approximately 0-563.9 The majorityof the studies were therefore performed with the twolatter degrees of compensation but, in studies involvingdifferent levels of p.p.s. compensation, both ht and h0

were chosen so as to minimise the secondary arcing currents.

4.1.3 System configurations: The number of possiblesystem configuration encountered in practice is, of course,very large, but feeders with more than three sectionsbetween main sources are relatively rare. In order to gaina general assessment of both primary-system responses andthe associated distance relay responses, together with theeffects of system configuration and source conditions, etc.,a general study has been performed for the two configura-tions shown in Fig. 9. In the case of the 3-section feeder(Fig. 9b), the local source infeeds were assumed negligibleand faults were simulated on the 300 km midsection. Acomparison of the performance of distance relays protectingan identical line of length 300 km in both single and3-section compensated feeders was thereby possible.The main sources were modelled by the normal lumpedparameter source networks based upon the short-circuitlevels and sequence-impedance ratios at power frequency.Shunt capacitance at the terminating busbars was delib-

erately not included in order to enable the performance ofthe relays to be obtained under conditions of worst casetravelling-wave distortion.11-12

The general study is usefully complemented by a specificstudy of the response of distance protection applied to atypical feeder arrangement operating at specific systemloading conditions. Fig. 10 gives details of the specificsystem studied in which the first-zone operating timecharacteristics of distance relays connected at all linesection terminations (S1RlS2R2S3R3) is examined. Theratio of zero sequence to positive sequence impedance ofeach main and local source was taken as 0-5 and, in thiscase also, the main sources feeding busbars Si and R3

were represented by simple lumped parameter source models.

4.2 Main features of primary system responses

4.2.1 Effect of feeder configuration: Studies of the alter-native feeder arrangements illustrated in Fig. 9 show thatfor given faults and main source conditions, there is a verymarked difference between the response of single-sectionand 3-section feeders. Fig. 11 shows a comparison of theresponses observed at the relaying point S following a solid'a'-earth fault adjacent to S (x = 0). Both voltage andcurrent waveforms are seen to differ significantly in thetwo cases but the most important feature of the responseis that the current waveforms associated with the faulton the 3-section feeder are very considerably more distortedthan is the case for the single-section arrangement. In thisrespect, it will be evident from Fig. 9 that, in the case ofthe 3-section feeder, the travelling-waves of current setup following fault inception successively propagate through

variablesendingsource

variablesendingsource( z s o / z 5 1

variablereceivingsource( z s o / z s r

variablereceivingsource<ZS0/ ZS1

1 6 - 7 m

-12 m

24m

°J*—12 m

110m

i

IIIIII) n i it 1111111 II i II i

Fig. 8 500kVline construction simulated

310

Fig. 9 General system configuration

a Single-section arrangementb 3-section arrangement

100km

s.c.!. = 1500MVA withlocal breaker open

sc I - 200MVA \with local

s.c l.r5000MVA withlocal breaker open

breaker open ~ j ~ 115kV ~Tn5kV

s.c.l. = 100MVA withlocal breaker open

A0MW,20MVAr 20MW,10MVAr

Fig. 10 Specific system configuration

ht = 0-75, h0 = 0-56 for each section

IEEPROC, Vol. 127, Pt. C, No. 5, SEPTEMBER 1980

point S towards S' and are partially reflected from thelatter back through S to produce the relatively high levelsof travelling-wave current distortion observed.

Fig. 12 typifies the differences in the faulted phasevoltage waveforms observed following identical earthand phase fault conditions on single and 3-section feeders.In both cases, the fault is midway between the relayingpoints S and R on the 300 km section (x = 150 km). In thecase of the single-section feeder, the frequencies of thetravelling-wave components are largely governed by thewave transit times between the point of fault and the sourcediscontinuity S of Fig. 9a. They are consequently ofrelatively high frequency by comparison with thoseproduced on the 3-section arrangement where the wavetransit time between the points of major discontinuity(F and S') is longer (see Fig. 9b).

The differences in the transient response of the alter-native feeder arrangements of Fig. 9 is less marked whenconsidering faults at or near zero voltage point-on-wave.

Fig. 11 Faulted response of general configuration for close-upearth fault

'a'-earth solid fault at x = 0; waveforms observed at S (Fig. 9);sending s.c.l. = 5 GVA. receiving s.c.l. = 35 GVA;/i, = 0-75a Single-section feeder (Fig. 9a)b 3-section feeder (Fig. 96)

However, it is important to observe that in the case offaults near peak voltage, the frequency of the travelling-wave distortion in both current and voltage waves associatedwith single-section feeders is relatively high. On the otherhand, maximum voltage faults at a corresponding positionon the 3-section feeder produce relatively low frequencydistortion which in turn will increase the relay measuringtime by an amount which is dependent on the bandwidthof the transducers and protective relay circuits.10'11

4.2.2 Effect of compensation levels: An extensive studyof the arrangement of Fig. 9 has shown that the faulttransient components caused following faults on bothmulti- and single-section feeders are largely independent ofthe level of shunt compensation used. This is somewhatas expected because even for values of hx as high as 1-2,which represents a near maximum practicable upper limit,each limb of the main reactor banks has an inductanceLp typically in excess of 4H. It follows that the shuntreactors present what,for practical purposes, can be regardedas an open circuit to any travelling wave (essentially high-frequency) phenomena. Indeed, it is only the lower-frequency phenomena such as exponential components ofcurrent associated with faults near zero voltage point-on-wave which are affected by the reactors and, even in thiscase, the difference between the faulted response waveformsobtained with and without shunt reactors connected hasbeen found to be small. It is therefore to be expected thatthe transient accuracy of distance relays applied to 4-reactorcompensated lines of a given length will be comparable

/^v

enoo>

JZ

o-200 -

-400 *f a u l t i n c e p t i o n

b

Fig. 12 Faulted response of general configuration for midpointearth-fault

Sending s .c . l .= 5GVA; receivingobserved at S (Fig. 9); hl = 0-75;

= 3-section feeder;= single-section feeder

a 'a'-earth solid midpoint fault (x = 1 50 km)b 'a'- 'b' solid midpoint fault (x = 150 km)

s.c.l. = 35 GVA; waveforms

IEEPROC, Vol. 127, Pt. C, No. 5, SEPTEMBER 1980 311

with that of similar relays connected to an uncompensatedfeeder of the same construction and length. This latterfinding is largely in line with some of the results presentedby Fielding et al. which showed that there was no seriousdegradation in the transient accuracy of a block-averagedistance relay applied to a single-section linear 3-reactorcompensated feeder.4

From a protection point of view, the main effect of thereactors is to increase the steady-state components of thepostfault current levels. This is, of course, due to the factthat, in the compensated case, the reactor bank appears inparallel with the fault loop impedance, thus reducing theimpedance presented to distance relays and thereby causinga slight overreaching tendency. Fig. 13 illustrates theforegoing point with reference to the faulty phase currents

and voltages associated with an 'a'-earth fault on the general3-section model of Fig. 9b. It can be seen that the peakvalue of the voltage waveform observed at S changes veryslightly as the degree of compensation is increased. On theother hand, the peak of the current waveform at a compen-sation hx =1-25 exceeds that at the lower level of compen-sation (hx = 05) by approximately 150 A.

5 Distance protection performance evaluation

The relays investigated are of the crosspolarised mho typeand utilise signals of the familiar phasor form given ineqn.21.14

400-

200-

1 00->

a>enai -200-

S -400

Fig. 13 Typical effect of degree of compensation on primarysystem waveforms for 3-section feeder

Sending s.c.l. = 5GVA; receiving s.c.l. = 35 GVA; waveformsobserved at S (Fig. 96); 'a'-earth solid fault at x — 1 50 km

hx = 1-25,ht = 0-5

248

246

244

242

240O)

a 238

"" 236

234

n o m i n a l r e l a y r e a c h

248

246 -

244 -

242 -

24 0 -

238 "

236 .

2 34

s, = iLzr-vl

+ V,

(21)

The foregoing signals are compared in the well knownblock-average comparator arrangement,5 details of themethods for simulating the response of the mixing andrelaying circuits being given in Reference 10. Each relayis arranged to have a ratio of set to reset voltage of 2and thereby possesses an absolute minimum operatingtime of 10 ms on the nominally 50 Hz system.

The response of first zone relays having a nominalsetting of 80% of the line section in question is considered,and the level of polarisation is 10% of the relevant sound-phase voltage(s). Each comparator has a setting voltageof 0-1 V and, in the case of the general application studyconfiguration shown in Fig. 9, the majority of the responseswere performed for source short-circuit levels of 5 GVA and35 GVA at the sending and receiving ends, respectively. Thelatter conditions give relatively high levels of travelling-wavedistortion12 and consequently enable a near worst caseindication of the performance of the relays connected atpoint S to be obtained.

The nominal transducer ratios were taken as 500/0-11and 1200/1 for the vts and cts respectively. The frequencyresponse of the vts was of the lowpass high-fidelity typeand, in order to indicate the near optimal response from the

0-2 0-4 0 6 1 0 1-2 14 0 2degree of p.p.s. compensation

0 4 0 6 0 8 1 0 10

b

Fig. 14 Variation of reach of earth fault relay with p.p.s. shuntcompensation

'a'-earth solid faults, 'a'-earth relay located at end S of single-sectionfeeder (Tig. 9a)

sending s.c.l. = 5 GVA, receiving s.c.l. = 35 GVAsending s.c.l. = 35 GVA, receiving s.c.l. = 5 GVA

— • — sending s.c.l. = 35 GVA, receiving s.c.l. = 35 GVAfaults at peak of prefault 'a'-earth voltagefaults at zero of prefault 'a'-earth voltage

312 IEEPROC, Vol. 127, Pt. C, No. 5, SEPTEMBER 1980

point of view of minimising relay operating times andensuring reverse fault stability, a cvt high-frequency cutoff( - 3 dB point) of 1 kHz was used.10

5.1 General application study

5.1.1 Measurement accuracy: Fig. 14 illustrates how thedegree of compensation affects the reach of the 'a'-earthrelay at point S in Fig. 9a and, in accordance with theobservations made in Section 4.2.2, the reach is seen toincrease with the degree of compensation. However, evenat an extreme level of compensation corresponding tohx =1-2, the reach does not exceed 247 km which in turnrepresents an overreach of less than 3%. On the other hand,with no compensation (ftj = 0 ) the relays have been foundto operate for faults up to approximately 235 km, which inturn corresponds to about 2% of underreach.

It should be noted that the responses obtained includealso all the errors which are unavoidably encountered inpractice, i.e. residual compensation errors and errors causedby assuming ideal transposition when setting the relays. Itfollows that not all the error observed is attributable to thepresence of shunt compensation. In this respect, it is evidentfrom Fig. 14 that the measurement error solely attributableto compensation does not exceed approximately 5%, afinding which has been found also to apply to the responseof phase-fault relays.

The foregoing findings apply equally to the three-section

140 -

± 100 "

60 "

5 20

1

_

_

• ^

1 1 1

1

jo

rea

a<u

ac

-̂— -^ J l•—]^\__ — — y o

80 120 160 200

fauIt p o s i t i o n , km240

i

1 40

100

60

20

-

-

-

-

JZ

o

"-

aa>

nin

al

I I . I I I I I I I , , fc

20 60 100 U0 180 240b fau l t pos i t ion _ km

Fig. 15 Time-response of earth-fault relay applied to 300 kmcompensated line

'a'-earth solid fault; 'a'-earth relay at end S (Fig. 9); sending s.c.l. =5 GVA; receiving s.c.l. = 35 GVA; /i, = 0-75

= relay applied to 3-section feeder (Fig. 9b) (digitally simu-lated)

= relay applied to single-section feeder (Fig. 9a) (digitallysimulated)

— • — = relay applied to single-section feeder (relay tested on ana-logue test-bench facility)

a faults at peak of pre-fault 'a'-earth voltageb faults at zero of pre-fault 'a'-earth voltage

arrangement and to the relays connected at end R in Fig. 9.For practical loading and compensation levels, no caseinvolving a total error in excess of ± 6% has been observed.It can thus be concluded that there is, for practical purposes,no significant deterioration in the measuring accuracy ofblock-average type relays applied to linear 4-reactor shuntcompensated feeders.

5.1.2 Relay operating times: Fig. 15 shows the timeresponse of the 'a'-earth relay at S for both single and3-section arrangements which are typically compensated ata level of hx = 0-75. In the case of faults which occur nearzero voltage point-on-wave (Fig. 156), the responses arealmost identical and there is, for practical purposes, nosignificant difference between the performances in thealternative configurations. Also shown in Fig. 156 is thetime response revealed from a series of tests on the block-average relay when using a signals derived from a lumpedparameter single-end fed dynamic test bench in which onlythe series impedance of the line was modelled. The modelshunt reactors used had an unrealistically low (Mactorof approximately 7 and, because only the series impedanceof the line could be modelled, travelling-wave componentswere not reproduced. Although faults near zero voltageproduce relatively very low levels of travelling-wave distor-tion, they are nevertheless responsible for the slight dif-ference in the responses obtained near the boundary ofoperation. Despite the fact that the test bench simulation isnot wholly realistic in terms of simulating the primarysystem, the results obtained for zero voltage faults docorrelate sufficiently well with the digitally simulatedresponses to provide a useful independent means of con-firming the latter.

The much higher level of h.f. distortion producedfollowing faults at voltage maximum produces a slowingof relay responses and reference to Fig. 15a shows that,unlike zero voltage faults, there is a marked differencebetween the relay response in the two alternative appli-cations considered. For example, a fault at the midpointof the line gives relay operating times of 20 ms and 30 msfor the single and 3-section feeders, respectively. Further-more, in the case of relay applied to the 3-section feeder,the response for a close-up fault deteriorates to the extentof being approximately 8 ms slower than that for anidentical fault at maximum voltage on the single-sectionfeeder. As mentioned previously, the lower apparentfrequencies of the travelling-waves observed in the case ofsectionalised feeders undoubtedly accounts for the slowerresponse observed in the 3-section arrangement. The preciselevel of travelling-wave distortion present is quite clearlythe main factor which determines the time response. Thisis particularly evident from a comparison of the single-section feeder responses obtained by using the test-benchfacility and the digital simulation (Fig. 15a). As mentionedpreviously, the bench testing programme included only theline series impedances and high-frequency components ofrelaying voltage and current were not therefore produced.The latter limitation largely accounts for the difference inthe responses obtained from the bench testing and digitalsimulation programmes and it further illustrates theimportant part which high-frequency distortion plays indetermining relay responses.

A simplified computer simulation in which only the lineseries impedance was modelled has been performed as partof a partial validation exercise involving a comparisonbetween the relay responses as obtained by dynamic bench

IEEPROC, Vol. 127, Pt. C, No. 5, SEPTEMBER 1980 313

testing and digital simulation. For practical purposes, theresponses thereby obtained were identical with the benchtest results shown in Figs. 15a and b, thus providing evidenceof the realism with which the low-frequency response ofthe relaying circuit has been digitally modelled. Due to thelimitations of the bench test method, similar direct evidenceof the adequacy of the digital simulation in respect ofmodelling the high-frequency response of the relayingcircuits was not possible. However, as part of the processof validating earlier work on the block-average relays,10

some secondary injection tests involving discrete high-frequency components of voltage and current were per-formed. These tests included injecting realistic levels ofdiscrete high-frequency currents into the transformer-reactor circuit,11 and a comparison with the correspondingcomparator responses as obtained by digital modellingrevealed no significant inadequacies in the modellingof the relay circuits. Similar block-average relays wereconsidered during the course of the work here presentedand it has therefore been concluded that the digitalmodelling of the relay circuits themselves is adequate fora realistic indication of performance under field operatingconditions.

The time response of the 'b'—'c' phase-fault relayillustrated in Fig. 16 again shows that there is a markeddifference between the operating time for faults at maximumvoltage on the single and 3-section compensated feederarrangements. For example, for a midpoint fault (approxi-mately 62-5% of the relay reach), the operating times are

1C0

50

1- 2 0

20 60 100 140 180

fau I t posi t i o n km

240

rI'.O

100

60

20

-

_

-

-

-

i i l i i

i

1y /

i i i i i i

1 .c. o

lay

1 a,1 ^

' 1Eoc

1 - ^

20 50 100 HO 180fau! t posi tion _ km

240

Fig. 16 Time response of phase-fault relay applied to 300 km line

'b '- 'c ' solid faults; 'b'- 'c ' relay at end S (Fig. 9); sending s.c.l. =S GVA; receiving s.c.l. = 35 GVA

= relay applied to 3-section feeder (Fig. 96), hl = 0-75= relay applied to single-section feeder (Fig. 9a), hx =0 -75

• = relay applied to single-section feeder (Fig. 9a), hl = 0-75a faults at peak of 'b'- 'c ' voltageb faults at zero of 'b'- 'c ' voltage

approximately 40 ms and 24 ms for faults on the 3-sectionand single-section feeders, respectively. On the other hand,a corresponding fault at the zero of the prefault voltagegives an operating time of approximately 12 ms for bothfeeder arrangements. A comparison of Figs. 15 and 16shows that, irrespective of the configuration involved,the time response for pure phase faults is inferior to thatfor single phase-to-earth faults.

The previously mentioned extent to which the degree ofcompensation affects relay responses is also evident fromFig. 16. It can be seen that, although the phase-faultrelay does not actually overreach its nominal setting in anyapplication, a relative overreaching tendency occurs to theextent that, for the single-section feeder, the reach isapproximately 8 km larger (approximately 3% of therelay reach) with a compensation level of hx ^ 0-75 thanthat obtained for zero compensation. Although not illus-trated, a similar margin of relative overreaching tendencyhas been observed for the 3-section feeder.

5.2 Specific applica tion s tudy

The performance of zone-1 distance relays protecting eachsection of the specific application considered (Fig. 10)is shown in Fig. 17. Both earth-fault and phase-fault relayresponses shown in Figs. 17a and b respectively, indicatethat there is a marked difference in the performance ofthe relays protecting each section. This is particularlyso for faults at peak voltage point-on-wave, there beingjust under one half-cycle of power frequency differencebetween the close-up fault operating time of the earthfault relays connected at points 51 and 53. The corre-sponding difference in the case of phase faults is approxi-mately three-quarters of a cycle of power frequency.

It is important to note that the relay time responses forpeak voltage faults in particular are generally more inversein nature over the whole range of possible fault positionsthan has previously been found to be the case for simplersingle-section uncompensated feeders.10 For example, itcan be seen from Fig. 11b that, in the case of the phasefault relay protecting section S3—R3, the operating

M J2 R2 S3distance to fault from S, , km

I 4-0

en

~ 20

100 200 300 400 500

R, 52 R2 S3 R3

^ di stance to fault from S , km

Fig. 17 Response of relays applied to specific system configuration

System details given in Fig. 10= faults at peak of prefault voltage= faults at zero of prefault voltage

a 'a'-earth solid faultsb 'b'-'c' solid faults

314 IEEPROC, Vol. 127, Pt. C, No. 5, SEPTEMBER 1980

time for a fault 75 km distant from end 53 reachesapproximately 2-5 cycles of power frequency.

The relative differences in the response of the relaysare conveniently illustrated by reference to Fig. 18 whichshows the relative responses of the sending-end relaysfollowing faults at voltage peak. It can be seen that thedifference in responses is much more marked in the caseof phase faults, there being a difference of approximately25 ms between the operating times of the relays at 51 and53 following faults at half the respective relay reaches.

The response illustrated in Fig. 18c for the earth faultrelay at 52 (protecting the 100 km midsection feeder) isuseful for indicating the extent to which the performanceof modern distance relays can be modified in practicalmultisection shunt compensated schemes. It can be seenthat the operating time of this relay always exceeds 20 msand reaches approximately 30 ms for an earth fault at60% of the relay reach. On the other hand, earlier workconcerned with identical block-average relays applied to•a single-section uncompensated400kVfeeder of comparablelength (128 km) indicated a relay operating time of approxi-mately 12 ms for single phase-to-earth faults over the wholeof the range 0—60% of the relay reach.10

6 Conclusions

In this paper, methods are presented for realisticallymodelling practical 4-reactor shunt compensated e.h.v.systems and techniques whereby the models may be usedto determine responses for arbitrary loading, source andcompensation conditions have been described. Thecomplexity of typical shunt-compensated systems hashitherto represented a particularly difficult problem froma computational point of view, but the importance ofemploying very realistic primary-system simulation tech-niques which adequately model the system underconsideration has clearly emerged. The results of this workthus indirectly confirm the desirability of recent trendstowards the use of programmable test equipment as analternative to simpler more conventional approximateanalogue testing techniques, and the digital methods ofsimulation described in this paper are of obvious importancein this context.

The majority of the primary-system simulation studiesutilised an IBM 360/195 computer linked to a Prime 400

40

20

interactive computer facility which in turn was used formodelling the transducers and relay circuits. In computingterms, almost all the total requirement relates to a simulationof the primary system, and typical c.p.u. times of approxi-mately 25 s and 40 s for single-section and 3-section studies,respectively, have been required. The latter times are thoserequired to produce the time variation of the voltages andcurrents at both ends of a faulted line section for a postfaultobservation time of approximately 250 ms. Work is now inprogress to reduce the computing time by optimallystructuring the software and by pre-evaluating and storingmore of those matrix functions which are independent ofboth system configuration and fault position, etc.,Preliminary assessments indicate that, by so doing, thec.p.u. time required will be less than approximately onehalf of present requirements.

Broadly, it has been found that it is the system confi-guration, rather than the precise levels of shunt compen-sation, which is the principal factor which determines theperformance of modern distance protection applied toshunt compensated feeders. For example, it has beenfound that following faults at peak voltage point-on-wave,there is a marked difference between the time responsesin single-section and 3-section configurations. In particular,the relay operating time for close-up faults at maximumvoltage is generally larger in multisection feeders than inotherwise similar single-section arrangements.

It is important to note that the time responses in respectof faults at or near zero voltage point-on-wave have beenfound not to vary significantly with application and further-more they are, for practical purposes, almost identicalwith those obtained in similar uncompensated feeders.

The main effect of the shunt reactors is to cause anincrease in the relay reach of typically 5% over a p.p.s.compensation range of 0 - 1 2 . Such increases are largelyconfiguration independent, and it is concluded that themaximum reach which is likely to occur in a given appli-cation will be some 5% in excess of the reach as obtainedin a similar uncompensated application study. Furthermore,the studies have revealed that the overall error is such thatthe zone-1 reach does not deviate from the nominal reachsetting by more than ± 6%. On this basis, it can safely befurther concluded that there is no serious likelihood ofindiscrimination occurring in schemes employing a nominal80% zone-1 setting.

60

4 0

20

-

/

1 / 1' // // / ,-y / J

/ •

20

fau l t

40

pos i t ion

60

. "1"a

of

80

relay

100

reach

20

f a u l t posi

40

ti 0 n

60

°/o

b

of

80

relay

100

recch

Fig. 18 Normalised time-response of sending end relays in specificsystem configurationFaults applied at peak of prefault voltage

= relay connected at point S,— • — = relay connected at point S2

= relay connected at point 5S

a Response of 'a'-earth relays

b Response of 'b'-'c' relays

IEEPROC, Vol. 127, Pt. C, No. 5, SEPTEMBER 1980315

The specific application study reported in this papershows that there is a significant difference between the timeresponse of the relays protecting each line section. This isparticularly so for faults at maximum voltage point-on-wave,where it has been found that a difference in close-upfault operating times of typically one half-cycle of powerfrequency can occur. Furthermore, it has been found thateven for block-average relays with a theoretically minimumoperating time of one-cycle of power frequency, operatingtimes in excess of one cycle over the whole range of faultcoverage can occur for some of the relays applied to thespecific feeder application studied. In so far as it is possibleto generalise, it can be said that such responses are likelyto meet the requirements of the majority of applicationsbut the system configuration dependent nature of theproblem nevertheless tends to indicate the necessity forindividual application studies in cases where some doubtexists. No serious problem relating to the use of block-average based comparator distance relaying schemes hasbeen found, but it could be unsafe to extrapolate thefindings to existing or proposed distance protection schemesutilising other comparison circuits.

7 Acknowledgments

The authors are grateful for the provision of facilities atthe University of Bath and would like to thank ProfessorJ. F. Eastham for his encouragement. They also acknowledgemany interesting discussions with engineers in industry,particularly at GEC and Kennedy & Donkin ConsultingEngineers. Especial thanks are due to W. H. Parrington ofKennedy & Donkin for his continued help in the provisionof system data. Finally, the authors are grateful to theUK Science Research Council for financial assistance inthe provision of interactive computing facilities at theRutherford Computing Laboratories.

8 References

1 FRIEDLANDER, E., and GARRARD, C.J.O.: 'Long distancepower transmission by alternating current', Engineering, 1942,1, pp. 2-16

2 BARTHOLD, L.O. BECKER, H., DALZELL, J., COOPER, C.B.,NORMAN, H.B., PEIZOTO, C.A., RE1CHERT, K., ROY, J.C.,and THOREM, B.: 'Static shunt devices for reactive powercontrol': CIGRE", Paris, paper 31-80 1974

3 AINSWORTH, J.D., COOPER, C.B., FRIEDLANDER, E.,and THANAWALA, H.L.: 'Long distance a.c. transmissionusing static voltage stabilisiers and switched linear reactors':ibid., paper 31-09, 1974

4 FIELDING, G., CHEETHAM, W.J., THANAWALA, H.L., andWILLIAMS, W.P.: 'The performance of a distance relay appliedto a long distance e.h.v. line with static shunt compensation':ibid, paper 34-02, 1978

5 JACKSON, L., PATRICKSON, J.B., and WEDEPOHL, L.M.:'Distance protection: optimum dynamic design of static relaycomparators', Proc. IEE, 1968, 115, (2), pp. 280-287

6 THANAWALA, H.L., KELHAM, W.O. and WILLIAMS, W.P.:'The application of static shunt reactive compensators in con-junction with line series capacitors to increase the transmissioncapabilities of long lines': CIGRE, Paris, paper 31 -09, 1976

7 KIMBARK, E.W.: 'Suppression of ground-fault arcs on single-pole-swtiched e.h.v. lines by shunt reactors', IEEE Trans, 1964,PAS-83, pp. 285-290

8 HAUBRICH, H.J., HOSEMANN, G., and THOMAS, R.: 'Single-phase auto-reclosing in e.h.v. systems': CIGRE\ Paris, paper31-09 1974

9 KIMBARK, E.W.: 'Charts of three quantities associated withsingle-pole switching', IEEE Trans., 1975, PAS-94, pp. 383-394

10 JOHNS, A.T., and AGGARWAL, R.K.: 'Performance of high-speed distance relays with particular reference to travelling-waveeffects', Proc. IEE, 1977, 124, (7), pp. 639-646

11 JOHNS, A.T., and AGGARWAL, R.K.: 'Discussion on perfor-mance of high-speed distance relays with particular reference totravelling-wave effects', ibid., 1978, 125, (8), pp. 761-765

12 JOHNS, A.T., and AGGARWAL, R.K.: 'Digital simulation offaulted e.h.v. transmission lines with particular reference tovery-high-speed protection', ibid., 1976, 123, (4), pp. 353-359

13 WEDEPOHL, L.M.: 'Application of matrix methods to thesolution of travelling-wave phenomena in polyphase systems',ibid, 1963, 110, (12), pp. 2200-2212

14 WEDEPOHL, L.M.: 'Polarised mho distance relay', ibid., 1965,112, (3), pp. 525-535

15 STALEWSKJ, A.: 'System tests, Sundon-Cowley 400 kV circuit,Sundon 400 kV substation'. CEGB Transmission Division DesignDepartment Report No. 63, 1975

316 IEE PROC, Vol. 127, Pt. C, No. 5, SEPTEMBER 1980