Digital simulation of fault autoreclosure sequencesWith particular reference to the performance evaluation

of protection for EHV transmission linesA.T. Johns, B.Sc, Ph.D., C.Eng., M.I.E.E., and R.K. Aggarwal, B.Eng., Ph.D., C.Eng., M.I.E.E.

Indexing terms: Power systems and plant, Power system protection, Power transmission, Circuit breaking

Abstract: The successful development of EHV transmission-line protection increasingly depends on a detailedsimulation of power-system faulted responses. In consequence, increasing use is being made of programmabletest equipment in which the primary-system responses are simulated digitally. Previous work on digitallysimulating faulted-system responses has been concentrated very largely on the initial faulted period prior tothe initiation of an autoreclosure sequence. The implications of incorrect operation of protection at any timethroughout the process of fault clearance are, however, often serious, and the paper is therefore concernedwith detailing methods of frequency-domain simulation which have been developed to greatly extend thecapability of computer-based simulation methods in their application to protective-gear testing. Problemsassociated with the simulation of various network time nonlinearities are overcome, and the new methodsenable both 3-phase and single-pole autoreclosure to be simulated. The paper concludes with a presentationof some simulation studies relating to a short 500kV interconnection which is subjected to various transientand sustained fault conditions.

List of principal symbols

e, v, i, = instantaneous (time) variation of voltages andcurrent

= time

h(t — T) = delayed unit step function =0,t<T

l,t>T

E,V,I

zss,zSR

RF

Q7

ZoX

LT(J0O

waSCL

= frequency transform of voltages and current= sending and receiving-end source impedance

matrices= fault-resistance matrix= voltage-eigenvector matrix= propagation-constant matrix= QyQ-1

= Y~l = polyphase surge-impedance matrix= distance to fault (from sending end)= line length= matrix transpose= nominal angular system frequency= angular frequency= frequency-shift constant= short-circuit level

Subscriptsa,b,c = phases a, b and cS,R — sending and receiving endsF = fault point

1 Introduction

The demand for more detailed and accurate modelling tech-niques for predicting the faulted response of EHV transmissionsystems is steadily increasing. This is particularly so in the fieldof power-system protection, where recent years have seen theemergence of equipment that measures from much more ofthe detail within the faulted-system waveforms than hashitherto been the case [1 ,2] . Such developments partiallyaccount for the gradual trend towards the use of program-

Paper 1396C, first received 19th September 1980 and in revised form6th May 1981The authors are with the Power Systems Laboratory, School of Elec-trical Engineering, University of Bath, Claverton Down, Bath BA2 7AY,Avon, England

mable test equipment [3]. The advantages of computer-simulation techniques are particularly well known. Althoughintrinsically less realistic in terms of simulating system transi-ents, conventional analogue relay test benches neverthelessadmirably meet the requirements of studies where it isrequired to simulate the whole process of fault inception, faultclearing and autoreclosure. In this sense, computer techniquesare at a relative state of infancy, in that the vast majority ofthe work reported has been concerned solely with methods ofsimulating conditions in the initial measurement period priorto fault clearance [4, 5] . Some limited progress has, however,been made to the extent of providing digital simulationswhich cover part of both single-pole [6] and 3-phase autore-closure sequences [7].

A prime objective of this paper is to report progress in thedevelopment of frequency-domain simulation techniqueswhich are sufficiently flexible to cope with the wide range ofcomplete fault sequences encountered in practice. Modalcomponent techniques are used which avoid the necessity formaking simplifying assumptions such as frequency-invariantline surge impedances, constant modal voltage vectors andmodal wave velocities. The methods therefore avoid anyuncertainties which arise as to the effect such approximationsmay have on the accuracy of simulation. Furthermore, themethods developed here are particularly powerful in that theyenable the source networks to be changed without any funda-mental change to the computational procedures and hencesimulation software.

The simulation of faults and subsequent clearance involvesa very large number of successive time nonlinearities. These arehandled relatively easily when using time-domain methods.However, when using frequency-domain analyses, any onesuch nonlinearity involves a change in the system matrix [8].

This paper reports the basis of methods which have beendeveloped to overcome this problem and gives details of thecomputational methods used. The paper concludes with apresentation of the results of several interesting studies of theresponse of a short uncompensated 500 kV line of the typewidely used in many parts of the world.

2 Basic system model

Fig. 1 illustrates the basic arrangement studied. With thisparticular model any type of earth fault can be treated bysimulating the closure of the appropriate switches at the fault

IEE PROC, Vol. 128, Pt. C, No. 4, JUL Y 1981 0143-7046/81/040183 + 13 $01.50/0 183

point. Fault break off or release is likewise simulated byopening the appropriate fault point switches in series with thetotal fault-path resistances (RFa,RFb,RFc). The modellingof any fault-path nonlinearities, e.g. time-variant secondary-arcing phenomena in single-pole autoreclosure schemes, isbeyond the scope of the present paper, and the commonlymade assumption of a constant linear fault-path resistanceis followed. Pure interphase faults are likewise modelled by anappropriate interconnection of fault resistances and switches.However, the earth-fault case illustrated in Fig. 1 adequatelyserves to illustrate the method. Opening, and subsequentreclosure, of the circuit breakers is likewise simulated by theoperation of the appropriate switches, according to thesequence associated with any type of autoreclosure cycleunder consideration.

circuit-breaker/ poles

arbitrary sending-end j \ arbitrary receiving-end

I switches operate on fault" " inception/release

Fig. 1 Basic system arrangement

3 Simulation techniques developed

It is important to note that, even in the case of 3-phase autore-closure, simultaneous opening of the breaker poles is rarely, ifever, obtained in practice because interruption is usuallyeffected close to the respective current zeros. Pre-arcingconditions can likewise occur on reclosure to producesequential pole closure effects; in this respect it is worthnoting that nonsimultaneity in modern circuit breakers istypically in the region 2—3 ms, and the simplifying assumptionof simultaneous pole reclosure can threfore often be invokedwhen evaluating protection performance.

The latter considerations, together with the fact that thereare a variety of possible autoreclosure schemes, gives rise toan extremely large number of possible sequences of operationof the various switches and hence network time nonlinearities.The scale of the problem is such as to make it impractical todevelop discrete mathematical procedures for simulating eachpossible sequence. In addition, the digital-computer storagerequirement for implementing the large number of discreteprograms which would be required if such an approach wereused, is prohibitive. A further, very significant, problem is thatit is not always possible to predefine the precise sequence ofevents pertaining to a particular study. For example, the timesat which the currents in each pole of a particular circuitbreaker approach zero, as distinct from the time at which the

breaker contacts separate, depend on the system response tofault inception and to any previous pole openings. The analy-ses detailed in this Section represent the outcome of anextensive study to evolve mathematical modelling techniqueswhich satisfactorily overcome the foregoing problems andwhich, thus, greatly extend the capability of modern digitalsimulation techniques in their application to power trans-mission systems.

3.1 Underlying principlesThe time nonlinearity caused by the operation of any breakerpole, or fault inception etc., is simulated indirectly by replac-ing each switch in Fig. 1 with a parallel connection of nhypothetical current generators. For example, in the case ofthe fl-phase breaker pole at end S, the equivalence depicted inFig. 2 illustrates the method. The total current through thisbreaker pole is given by the sum / S l a + zS2a . . . +

n

ah isk°-

•Sa

Fig. 2 Simulation of network time nonlinearities

a a-phase breaker pole at end Sb Equivalent using parallel current generators

Now the individual components of current are arranged sothat, for any period of time during which the pole is open, thesummation is zero, i.e. iSa = 0. Conversely, during any periodswhen the pole is closed, the summation 2 iSka is arranged

fe=1such that eSa = 0.

An understanding of the manner in which the parallel-current-generator injection technique is applied in the simu-lation of faults and their clearance is best achieved by con-sidering a sequence on the simple hypothetical single-conduc-tor system of Fig. 3a. Now suppose it is required to simulatethe fault sequence defined in Table 1.

With the breaker initially in the closed position and thesystem operating in the steady-state, there are thus five dis-tinct circuit states. Now the number of current generatorsnecessary for performing any given sequence always corre-sponds to the number of possible circuit states n so that, forthe simple illustrative example under consideration, fivehypothetical generators are connected at the breaker andfault points as shown in Fig. 3b.

The equivalent arrangement of Fig. 3b can be solved bysuperposition, and is thereby decoupled into the five separatecircuits shown in Figs. 3c—g. The circuit of Fig. 3c effectivelydefines the steady-state response of the system, i.e. theresponse for all time up to Tx. As such it is solved with the

Table 1 : Simple transient sequence

Time t (with respect toany arbitrary datum)

7",

Event fault breakerinception interrupts

current

fault breakerbreak off recloses(or release)

184 IEEPROC, Voh 128, Pt. C, No. 4, JULY 1981

sinusoidal source voltage as the forcing function. Becausesuperposition is being used, and the source driving voltage isincluded in the response of Fig. 3c, the remaining superim-posed circuits (Figs. 3d—g in the present example) are solvedwith all source voltages set at zero. A further consequence ofsuperposition is that the circuit breaker and fault-point volt-ages (es,eF) and currents (JSJF)

m t n e actual network ofFig. 3a, are given by eqns. 1 and 2, respectively:

s 5

= Z esfe, is = Z 'sfe=i fe=i

eF = IF = Z lFk

0)

(2)

It will be evident that there are an infinite number of combi-nations of currents and voltages within the superimposedcircuits of Figs. 3c—g which, when summed in accordance

Fig. 3 Simplified illustrative system

a Physical arrangementb Equivalent using parallel current generatorsc Steady-state circuitd—g Superimposed circuits

with eqns. 1 and 2, could provide a simulation of the overallsystem response. However, the computational proceduresare greatly simplified, and more easily implemented, if thesuperimposed circuits are arranged to become active in suc-cession as each circuit change takes effect. Mathematically,this is equivalent to constraining the voltages and currentswithin each superimposed circuit according to eqn. 3.

~ eF2 = IS2 = l>2 = 0,

= eF3 = 'S3 =

eS5 — eF5 —

t < T,

t < T2

t < T3

t < T«

(3)

In order to conform with the sequence defined in Table 1, it isnecessary to constrain the voltage across the circuit breakerand the current through it according to the followingequation:

es = 0,

is = 0,(4)

The fault-path voltage and current are necessarily likewiseconstrained according to

eF = 0,

iF = 0,

t < t < T3

3 < t < Ti(5)

It is now evident that the constraints of eqns. 3—5 demandthat the steady-state and superimposed circuits are constrainedwith the currents and voltages indicated in Figs. 3c-g.

The computation proceeds with a solution to the circuitof Fig. 3c in which eSi = iFX = 0 to conform with the pre-fault steady-state condition. The value of eFl thus obtained isthen used to calculate the suddenly applied voltage [eF2 =— eFlh(t—Ti)] driving the first superimposed circuit ofFig. 3d. The resulting solutions to the circuits of Figs. 3c and3c?, then enable the driving current for the second superim-posed circuit of Fig. 3e [iS3 = — (isi + zS2)Mf ~ ^2)] to bedetermined as a prerequisite to its solution. Dependent sol-utions are likewise performed on the remaining superimposedcircuits of Figs. 3/and 3g, by applying the current and voltage[i>4 = - (.h 1 + *>2 + *>3)fc(f - T3] and [ess = — (eSi +eS2 + ess + es*)h(t - T4)], respectively.

It will be appreciated from the foregoing simplifiedexample that the techniques are readily generalised to dealwith any arbitrary system configuration. Once the predisturb-ance steady-state system response has been obtained, a seriesof standard de-energised-circuit models, with a hypotheticalcurrent generator connected at each breaker and fault point,are solved in succession, as and when each circuit changeoccurs. Injection into the superimposed circuits is made at thepoint at which the particular change occurs. In the case ofbreaker closure or fault inception, the injection is specified interms of a suddenly applied voltage equal and opposite to thesum of all previously computed superimposed and steady-statevoltages at the point in question. Where breaker opening orfault break off is involved, the injection is conversely specifiedin terms of a suddenly applied current which is, likewise, equaland opposite to the sum of all previously determined superim-posed and steady-state currents at the point in question.

The method of solution outlined above enables the pre-viously mentioned problems relating to the time of occurrenceof the various network nonlinearities to be overcome; e.g.suppose the time T2 in Table 1 had represented the time ofbreaker-contact separation and current interruption sub-sequently occurred at the first current-zero crossing there-after. Now the method of formulation developed is such that

IEEPROC, Vol. 128, Pt. C, No. 4, JULY 1981 185

the summation /S1 + /S2 represents the current through thebreaker for all time up to current interruption, and it followsthat the actual time of interruption is then obtained as thetime of the first zero-crossing of is t + iS2 after T2.

It will be apparent that, for any arbitrary system configur-ation, the summation of the steady-state circuit and all preced-ing superimposed circuit responses represents the completesystem response for all times up to the time of occurrence.ofthe next circuit change. Where necessary, the time data arethus determined dynamically within the program by examin-ing the summation of all previously computed responses at thecompletion of any intermediate stage.

The assumption of zero arcing voltage across the breakercontacts is implicit to the above detailed methods of represent-ing the process of current interruption. However, the extracomplexity involved in simulating the effect of a finite arcingvoltage is somewhat questionable in view of the fact thatmodern circuit breakers produce arcing voltages of typically1—2% of the nominal system voltage. For example, a modern550 kV breaker has an arcing voltage in the range of approxi-mately 7 to lOkV when interrupting a fault current of lOkA.

3.2 Frequency-domain simulation of double end-fed feedersDuring the process of fault inception and clearing, a trans-mission system is subjected to a wide range of frequencyvariations, and it is important to ensure that the response isevaluated over the whole frequency spectrum of importance.In order to take account of the frequency variation of thetransmission-system parameters, it is therefore necessary toimplement the simulation techniques outlined in Section 3.1in the frequency domain. The basis of the methods for obtain-ing the steady-state response of the full system model of Fig. 1are covered elsewhere [4], and these will not therefore beconsidered in detail.

The standard superimposed circuit of the full system model(Fig. 1) is represented in the frequency domain by the circuitof Fig. 4. It will be evident from the foregoing that, in order toeffect a complete simulation, it is necessary to solve a total ofn — 1 such circuits. The suffix k, as previously defined, relatesto the kth superimposed circuit (k = 2, . . ., n), and the basicrelationships of eqns. 6 and 7 are seen to describe the circuitat each end of the line and at the fault point, respectively.Furthermore, the line sections on each side of the fault aremost conveniently represented in terms of the polyphase2-port or A, B, C, D parameters defined in equation 8 [4]:

(6)

vRk = zSR.VFH

= EFk R - EFk

VSk

rSk

VFH

IFRH

A

C

A2

c2

Bx

Dx

B2

D2

I7Fk

TFSH

vRk

TR]

(8)

where

Ax = cosh{i//x}, Bi = sinh [\}JX]ZO,

Cx = YOBXYO, Dx = I^Z.

A2 = cosh {\}/(L —x)}, B2 = sinh [\}J(L — x)]Zo,

C2 = YOB2YO, D2 = YOA2ZO

The three foregoing relationships effectively define a set ofsimultaneous equations relating transforms of the kth super-imposed-circuit transform currents to the associated transformvoltages across each hypothetical current generator and theycan be arranged in the alternative form

hk

TRk

YA

YD

YG

YB

YE

YH

Yc

YF

Yj

(9)

Each of the submatrices in the admittance relationship of eqn.9 is defined in terms of the basic parameters (RF,Ai,Zss

etc.) of the system at any spectral frequency of interest. It isimportant to note that each submatrix within the whole is a3 x 3 matrix and that each subvector (EFk,IFk etc.) is a3 x 1 column vector representing the voltage or currenttransforms of the individual phase conductors, e.g.

(7)

The 9 x 9 admittance matrix of eqn. 9 is essentially a universalrelationship which can be computed and stored at all spectralfrequencies of interest at the outset of a particular simulationstudy. As such, it enables a solution to any of the superim-posed-circuit models to be obtained in a particularly economicmanner from a digital processing point of view.

In order to illustrate the computational procedures involvedin a full system study, consider simulating an c-earth fault onthe actual system of Fig. 1. The initial value of the steady-stateprefault voltage between the a-phase conductor and earth atthe point of fault (eF i a ) is first determined by means of thesteady-state-circuit study. Now if the fault occurs at somearbitrary time Tx, the time variation of the forcing voltage inthe first superimposed circuit (k = 2) will, in accordance withthe previously developed methods, be given by eF2a =— eFyah(t — Ty). Because the prefault condition is ajteady-state one, the frequency-domain forcing voltage EF2a is

de -energisedsending -endsource IZcc I

de-energisedreceiving -endsource | z s R |

Fig. 4 Frequency-domain superimposed-system model

186 IEEPROC, Vol. 128, Pt. C, No. 4, JULY 1981

readily evaluated as the Fourier transform of an analytical timefunction of the form — V sin (u>of 4- P)h{t — TO. The twosound-phase fault point currents 0>2b>*F2C) anc* the sixbreaker-pole voltages eS2a^bfi,

eR2a,b<c a r e all identically zero,and there are therefore a total of nine known transformvalues which enable the standard matrix relationship of eqn. 9to be solved in the frequency domain for the remainingvoltages and currents. Details of the latter process will be givenin Section 3.2.1.

Suppose now that the next circuit change to occur iscurrent interruption in say the 2>-phase at the remote end atsome arbitrary time T2. In accordance with the previouslydeveloped theory, the forcing function for the second super-imposed circuit (k = 3) is therefore given in the time domainby IR 3 b = ~ OR ib+iR2b)h(* — T2).

N o w t n e currentcomponent iR i b is an analytically described sinusoidal currentavailable following the initial solution to the steady-stateprefault circuit. The component iR2b, on the other hand,contains transient components and is therefore a nonanalyticalfunction whose time variation has to be determined from thefrequency spectrum IR2b obtained following the foregoingsolution to the first superimposed circuit. In common withprevious work [4, 5,8] a digital evaluation of the half-rangeinverse modified Fourier transform integral has been used forthe latter purpose, and the forcing current iR3b is therebyobtained.

The next stage of the computation involves finding theFourier transform of the current iR 3 b . This is achieved in oneof two ways. First, if the time difference (T2 — Ty) is rela-tively large and such that the current iR 2 b attains a periodicform at time T2, then the current iR3b is also periodic, andtherefore becomes an anlytically defined forcing currentwhose Frequency transform IR3b can be directly defined. Onthe other hand, if the time difference T2 — Tt is such thatiR2b still contains transient components at time T2, thefrequency transform current TR3b has to be obtained bydigitally evaluating the modified Fourier transform integral ofeqn. 10. The first approach is usefully adopted wheneverapplicable, because this reduces computational effort byavoiding the necessity for numerically evaluating the integralof eqn. 10. A simple test to determine whether or not aparticular forcing current or voltage is periodic in form istherefore included to ascertain which of the alternativemethods of finding the associated frequency transform isapplicable. In this respect it is worth noting that in manystudies the time between successive changes in circuit states isso long that the direct approach is automatically applicable.For example, in delayed 3-phase autoreclosure schemes, deadtimes of the order of 10 s or more are commonplace, and theforcing function to simulate breaker reclosure (in this case avoltage) will, for all practical purposes, always be periodic inform:

J.oo

i- oo

(10)

It is important to note that iR3b = 0, t <T2, and that thelower limit of integration in eqn. 10 is limited to time T2.Furthermore, it is only necessary to simulate the systemresponse up to a finite observation time, and it is thereforealso possible to reduce the upper limit of integration in orderto increase the efficiency with which this and other similarintegrals are digitally computed. In theory, the integral needonly be evaluated up to the desired observation time, but ithas been found that when so doing, the resulting digitallyevaluated frequency spectrum can oscillate about the actualfrequency spectrum and thereby degrade the accuracy ofsimulation. This effect is analogous to Gibbs' oscillations

which can similarly occur when digitally evaluating inverseFourier integrals to obtain time responses [10]. An extensivestudy of this latter problem has shown that when using anoptimum value of frequency-shift constant a, the upper limitof integration necessary should be about twice the value of theobservation time.

For the_ third circuit state, the nine known transformvalues are IR3b,£S3a,b,c =^R3a,c = EF3a = TF3bx = 0 andthese are again used in conjunction with matrix equation(eqn. 9) to obtain all remaining transform values for this step.

The above detailed processes are likewise applied in thesolution of all succeeding superimposed circuits necessary tocomplete the fault clearing sequence involved.

3.2.1 Superimposed-circuit solution problem: It will be notedfrom the foregoing that each superimposed circuit has to besolved for a combination of both voltage and current trans-forms. Such a solution is not ordinarily straightforwardbecause the nine known transform values lie within both thecurrent and the voltage vectors of eqn. 9, which, in conse-quence, cannot therefore be solved directly. There are clearlya vast number of combinations of the nine known transformswhich can arise, and it is impractical, if not impossible, toovercome the problem by computing all the matrix operationsnecessary to provide a solution for each possible superimposedcircuit. This problem is further compounded by the necessityto perform a solution to each circuit at a number of discretefrequencies within the spectrum of interest.

The foregoing problem, which has hitherto been one ofconsiderable magnitude, is effectively overcome by virtue ofthe manner in which the simulation processes have beenformulated. Specifically, advantage is taken of the fact thatthe formulation is such that there are always eight zero-valuetransforms associated with each de-energised circuit, and it isshown in Appendix 9 that a solution is thereby effected bysimply inverting a submatrix derived from the full admittancematrix of eqn. 9. This approach always yields a solution forall transform values within any arbitrary superimposed circuitand is simply implemented in a standard procedure involvingminimal computational effort.

4 System configuration studied

A typical short 500 kV horizontally constructed line havingthe mean spacings shown in Fig. 5a, has been considered. Theline length of 100 km is sufficiently low not to demand theuse of shunt reactor arrangements for reducing secondary-arccurrent and recovery-voltage levels during single-pole switching[11], and a direct comparison of both 3-phase and single-phase autoreclosure-system responses is therefore possible.

Source side networks rarely comprise only localised gener-ation, and, in general, the busbars at either end of the lineoften terminate other lines, which in turn are remotely termin-ated in equally complex source networks. Because the compu-tational methods developed in this paper enable the sourcesto be defined in terms of impedance matrices (ZSS,ZSR), anyarbitrary source configurations can be incorporated by pre-

.computing the latter matrices at all frequencies of interest. Achange in the source side networks is thus readily effectedwithout any fundamental change to the simulation software.In effect, a change in the sources therefore represents only achange in the program data, a feature which is fundamental toall frequency-domain methods, and which is particularly usefulin practice in that one basic simulation package then effec-tively satisfies the requirements of any arbitrary sources andline configurations.

The overall system arrangement simulated in the course ofverifying the methods developed in this paper is shown in the

IEEPROC, Vol. 128, Pt. C, No. 4, JULY 1981 187

single line diagram of Fig. 5b. The number of possible systemarrangements is vast, and the specific line and source modelsused are chosen to provide a general appreciation of thesalient features of both transient- and sustained-fault clearancesequences in schemes employing high-speed single-pole anddelayed or high-speed 3-phase autoreclosure. Each equivalentlocal generation source Gi — G5 is represented by the usuallumped-parameter networks based upon symmetrical SCLcontributions, the ratio of ZPS to PPS impedances ZS O/ZS 1,and the reactance to resistance ratio XIR at power frequency.

Fig. 5 Line and system configuration studied

a 500 kV line configurationPhase conductors are 4 X 477 MCM Al, 242 mm2 Al equivalent;19/4.3 mm stranding; earth wires = 7 X 35 mm AW; earth resis-tivity = 100 Om; frequency variance of all line and earth parametersis included [4]

b System configurationAll 500kV lines (including sources) of length 100 km; ZSo/Zg, =0.5 and X/R = 30 for all equivalent sources (G, — G,); symmetricalSCL for sources: Gi = GA = Gs = 15GVA, G2 - 5GVA, G3 =10GVA

The effect of metering and protection transducers on thesystem responses has not been simulated, and the resultstherefore represent the true primary-system responses aswould be viewed through ideal burdenless voltage and currenttransducers having a distortionless (linear phase) lowpassfrequency response. This assumption also aids the validationprocess in that the responses obtained are not complicated bythe additional presence of transducer relaxation transients orother forms of distortion. The methods developed in thispaper enable any desired degree of detail in the system wave-forms to be obtained by computing responses over an appro-priate range of frequencies [4]. However, nearly all protectiondevices employ prefiltering arrangements which limit thebandwidth of information processed to below typically 2 kHz.In these circumstances, spectral components above the latterfrequency do not significantly affect relay performance, and itis sufficient to compute the primary system responses over thislimited frequency range [12]. In so doing, the computationaleffort expended in performing a given simulation study is

usefully reduced, and this approach has therefore been usedwhen computing the responses presented in this paper.

5 Simulation studies

In delayed-autoreclosure schemes, the dead times usually liebetween 5 s and 20 s, whereas, in high-speed autoreclosuredead times of 0.5—1 s are common. The present studies assumedead times between the latter figures, and a linear 0.512 faultresistance is taken. The prefault busbar voltages at S and R arein phase and of magnitude 500 k\^, the reference directions ofvoltage and current being as indicated in Fig. 5b. The preciseinstant of current interruption in each phase is somewhatindeterminate, in that it depends on the type of circuit breakerused and its characteristics. Interruption will only rarely occurexactly at a zero crossing following breaker contact separation,and the possibility of current chopping near a prospectivecurrent zero cannot be precluded. The studies here presentedsimulate current chopping at one sample step (0.25 ms) beforea prospective zero crossing. In the majority of applications theinstant of reclosure is not precisely controlled to produceoptimum pole reclosure for minimising switching-surge over-voltages.. This is taken to be the case for the studies herepresented; various instants of simultaneous contact makewithout prearcing being simulated. In the case of the single-pole autoreclosure studies presented, the most commonsequence, involving single-pole tripping for single phase-to-earth faults followed by 3-phase tripping under sustainedfault conditions, is considered.

In practice, breaker separation is not absolutely simul-taneous at both ends. Nevertheless, the protection and breakerarrangements in EHV applications usually operate in aunitised-type mode, so as to produce near simultaneousclearance. Furthermore, in high-speed autoreclosure, anattempt is made to achieve simultaneous reclosure at bothends, although again, absolute simultaneity is rarely achieved.The number of relative separation and reclosure times possibleis clearly vast and, although the techniques described enablethe small degree of nonsimultaneity associated with specificapplications to be simulated, the assumption of simultaneouscontact separation and reclosure in high-speed schemes canusefully be invoked for many studies. This latter approach willtherefore be adopted here.

The precise instant of transient fault break off is dependenton a number of factors [12]. In this respect, field experiencerelated in the literature suggests that, provided the arc currentis limited to approximately 20 A RMS on a steady-state basis,arc extinction will occur. In the course of these studies, faultbreak off has been taken to occur at the first zero crossing inthe fault-path current following a peak-to-peak current of lessthan 56 A (2 \/2 20).

5.1 Delayed 3-phase autoreclosureFig. 6 shows some results for a typical transient-faultsequence. With reference to Fig. 6a, it can be seen that, duringthe initial post-fault period, the travelling wave caused by faultinception passes through end S and returns as an attenuatedreversed-polarity wave after approximately 0.7 ms. This isas expected because it is evident that a large proportion of anywave incident at S subsequently travels along the single infeed-ing line S—Gi where polarity reversal occurs, the relativelysmall generating source G2 having little effect. Anotherinteresting feature of the responses concerns the behaviour ofthe sound-phase voltages immediately following currentinterruption at T2. For example, it can be seen from Fig. 6bthat the c-phase is the first to clear. However, the c-earthvoltage continues to increase negatively until clearance occurs

188 IEEPROC, Vol. 128, Pt. C, No. 4, JULY 1981

Fig. 6 Delayed 3-phase autoreclosure transient fault simulation

a-earth midpoint fault (x = 50 km); Tl = fault inception (5 ms); T7 = breaker contacts at S and R separate (65 ms); T3 = fault break off (~ 80 ms);TA = breaker at end S recloses (5.15 s); T, = breaker at end R recloses (7.2 5 s)© a-phase® 6-phase® c-phasea Voltages on line side of breaker at end Sb Line currents at end Sc Voltages on line side of breaker at end Rd Line currents at end R

IEEPROC, Vol. 128, Pt. C, No. 4, JULY 1981 189

also on the faulted a-phase (see Fig. 6a). The reason for this isthat, following clearance at ends S and R, the c-phase conduc-tor carries a net trapped charge, but is otherwise isolated, toeffectively form the tapping point of a capacitor divider chaincomprising the capacitance between the a- and c-phases andthe total c-earth phase capacitance. A voltage proportional tothat associated with the as yet still energised a-phase is there-fore superimposed on an essentially steady trapped chargevoltage on the isolated c-phase. The effect of current choppingon the faulted-phase voltage is clearly evident from Figs. 6aand c. The current chopping induced voltage sets up a seriesof travelling waves in transit between the now open-circuitedline ends and the as yet remaining short-circuited fault point.With reference to Fig. 5b, the switching surge components setup following reclosure at end S propagate from S to the as-yetopen-circuited end R and return through S towards Gt wherethey experience polarity reversal. The transit time as observedat ends S and R is therefore principally associated with adistance of wave travel equal to 400 km, i.e. a transit time ofapproximately 1.3 ms, as indicated.

Reference to Figs. 6b and d shows a significant time lagbetween clearance of the current in the faulted and soundphases. In this respect, it is worth noting that such effects mayassume major importance in determining the performance ofultra-high-speed protection equipments measuring from datawindows of less than 10 ms. The source-side voltages at end Rare shown in Fig. 6e. These are, of course, identical with theline-side values (Fig. 6c) prior to opening of the breakers attime T2 • Fig. 6/ shows the behaviour of the fault-path voltageand current. The faulted-phase conductor is totally isolated

after clearance, but the energy stored therein continuesdischarge through the fault path to ground in the characteristicoscillatory manner shown. At fault break off, the smallamount of energy remaining in the faulted phase establishes asmall steady trapped charge voltage of approximately lOkV.The voltage across the transient-fault path subsequentlyrecovers to normal after closure of the breaker at end S.

Fig. 7 shows the system response following a sustaineda-earth fault. With reference to Figs, la and b, it can be seenthat sound-phase voltages continue to change in the period T2

to approximately T2 + 10 ms. This is owing to the previouslymentioned effect in relation to the transient-fault sequence. Inthis respect it is worth noting that the voltage along thefaulted conductor when the remote end is energised variesfrom around zero to two thirds of the nominal system voltageat the fault point and remote ends, respectively. There is,therefore, a substantial net superimposed coupling voltagebetween the sound and fault phases which, in turn, accountsfor the variations in the sound-phase voltages at S immediatelyfollowing times T2 and T6. A similar variation in the sound-phase voltages is not observed following T4, because at thistime the breaker poles at the remote end are open. It is ofinterest to note from Fig. 1b that, in the initial fault periodT\—T2, sound-phase currents of around 2kA are forced toflow. This phenomenon is principally due to a faulted-phasecurrent infeed from end R, which, by virtue of electro-magnetic coupling between the faulted and sound-phaseconductors, forces substantial cophasal sound-phase currentsto flow. This latter effect cannot occur subsequent toreclosure at time T3 because the end R breaker is then open.

Fig. 6 Delayed 3-phase autoreclosure transient fault simulation

e Line currents at end R/ Voltage across and current in fault path F voltage current

190 IEEPROC, Vol. 128, Pt. C, No. 4, JULY 1981

5.2 High-speed 3-phase autoreclosure sequenceFig. 8 shows the results of a typical zero-voltage study involv-ing high-speed clearance of a pure interphase fault. It can beseen from Fig. 8a that the total time from current interruptionto fault break off is approximately 0.025 s. It is of interest tonote that the time for fault break off to occur is about fourtimes that observed under the transient single-phase to earthfault conditions considered in Fig. 6. The foregoing consider-ations tend to indicate that it is the system behaviour follow-ing pure interphase faults which is likely to dictate the lowestpractical 3-phase autoreclosure dead times.

5.3 Single-pole autoreclosure sequenceFig. 9 shows a typical transient-fault-sequence simulation. Theeffect of electromagnetic coupling between the faulted andsound phases is again evident during the initial faulted periodTi—T2. In this case, the faulted-phase current induces avoltage in the sound phases over the whole line length and thisin turn causes relatively large sound-phase currents to flow inantiphase with the faulted-phase current as indicated inFig. 9b. Fig. 9c shows the system behaviour at the faultpoint, the most significant feature of the response being thecharacteristic manner in which the voltage across the arc path

€ 0 -

-«©-15.2

-«©- -89-

\

- 3 L

r\ , / \

Fig. 7 Delayed 3-phase autoreclosure sustained-fault simulation

a-earth close-up fault (x = 0); T, = fault inception (5 ms); 7\ = breaker contacts at end S and R separate (45 ms); T3 = breaker at end S recloses(5.086s); 7\, = breaker contacts at end S separate (5.126s); Ts = breaker at end R recloses (15.166s); T6 = breaker contacts at end R separate(15.206 s); key as in Fig. 6

a Voltages on line side of breaker at end Sb Line currents at end Sc Voltage across and current in fault path F voltage current

IEEPROC, Vol. 128, Pt. C, No. 4, JULY 1981 191

behaves following fault break off at T3. This form of responseis characteristic of short-line single-pole autoreclosure appli-cations in which shunt reactors are not connected. In conse-quence, the possibility of restriking of the arc path cannot beprecluded. Fig. 9cl shows a detailed simulation of the currentin the fault arc path under conditions where, due to restriking,extinction of the secondary arc is delayed beyond time T3 atwhich the arc current conforms to the assumed extinctioncriterion. The uncertainties underlying fault-path behaviourin single-pole autoreclosure are particularly well known, andthis is undoubtedly an area where further work might usefullybe done. Some recent work has been reported on frequency-domain simulation of 4-reactor shunt compensated systems[14], and these methods could, if necessary, be applied inconjunction with the techniques developed in this paper. Fig.10 shows the results of a study involving a sustained faultcondition. In this case, the sustained mid-point fault causes thevoltage on the line side of the breaker at R to ring down tonear zero voltage during the dead time T2—T3. Unsuccessfulautoreclosure at the latter time causes final 3-phase interrup-tion to occur at time T4.

6 Conclusions

Methods have been developed which considerably extend thecapability of frequency-domain techniques in their applicationto the simulation of EHV transmission systems. Particularemphasis has been placed on evolving methods of simulation

that are suitable for simulating any arbitrary autoreclosuresequence. Previous problems relating to simulating the variousnetwork time nonlinearities, and the random sequence inwhich they can occur, have been overcome by means of astandard matrix array, relating conditions at all points ofpossible nonlinearity within the network. In this way, asimulation of autoreclosure is effected in a situation thatwould otherwise lead to a computationally intractable andinefficient solution. Furthermore, the methods developedenable realistic source-side networks to be incorporated andthese can be easily changed to suit the requirements of aparticular study without any fundamental change to thecomputational procedures or the software to implement them.It is clear that for practical line and source configurations, avariety of wave transit times occur and that no single domi-nant travelling-wave frequency can be identified. In somemethods of analysis it is commonly necessary to assume theexistence of a single dominant travelling-wave frequency. Suchan assumption is not of course required when using the fre-quency-domain methods developed in this paper, and anyuncertainties regarding the effect such approximations have onsimulation accuracy therefore are avoided.

Aspects of the system responses which might ultimately befound to affect the performance of both present and futuregenerations of transmission-line protection include theobserved delay in clearance on the faulted and sound phasewhich occurs under some conditions and the relatively low-frequency distortion produced following reclosure. The work

0.65 170

Fig. 8 High-speed 3-phase autoreclosure transient-fault simulation

Remote-end 6-c-phase fault (x — 100km); 7", = fault inception (5 ms); T2 — breaker contacts at S and R separate (65 ms); T3 = fault break off(~ 9 5 ms); T4 = breakers at ends S and R reclose (0.625 s); key as in Fig. 6

a Voltages on line side of breaker at end Sb Line currents at end S

192 IEEPROC, Vol. 128, Pt. C, No. 4, JULY 1981

6

A

nU

-4

-6

-8

:

-

_0.05

-

' 1T

0.15time.s

d

(firstzero-crossing following peak-peakT-, current <56.7A)

instant of a-phase currentinterruption at end S

Fig. 9 Single-pole autoreclosure transient-fault simulation

Remote-end a-earth fault (x = 100 km); TL = fault inception (5 ms); T2 = a-phase breaker poles at S and R separate (65 ms); T3 = fault break off(~ 105 ms); T4 = a phase breaker poles at S and R reclose (0.57 s); key as in Fig. 6

a Voltages on line side of breaker at end Sb Line currents at end Sc Voltage across and current in fault path at F voltage currentd Detailed simulation of secondary-arc current under conditions of delayed arc extinction

IEEPROC, Vol. 128, Pt. C, No. 4, JUL Y1981 193

underlines longstanding uncertainties relating to the behaviourof the fault arc paths following single-pole fault clearance. Thisis undoubtedly an area for further work involving both field-test investigations and associated simulation techniques.However, the findings of this paper indicate that following3-phase autoreclosure, fault-path discharge is so rapid as tomake the necessity for more complex fault-path models ratherquestionable.

7 Acknowledgments

The authors are grateful for the provision of facilities at theUniversity of Bath and the provision of computing facilitiesby the UK Science Research Council. They also acknowledgemany useful discussions with engineers in UK manufacturingand consulting industry.

8 References

1 CHAMIA, M., and LIBERMAN, S.: 'Ultra-high-speed relay for ehv/uhv transmission lines - development, design and application',IEEE Trans., 1978, PAS-97,pp. 2104-2116

2 JOHNS, A.T.: 'New ultra-high-speed directional comparison tech-nique for the protection of e.h.v. transmission lines', IEE Proc. C,Gen., Trans. & Distrib., 1980, 127, (4), pp. 228-239

3 PAULL, C.J., WRIGHT, A., and CAVERO, L.P.: 'Programmabletesting equipment for power-system protective equipment', Proc.IEE, 1976, 123, (4), pp. 343-349

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

5 JOHNS, A.T., and EL-KATEB, M.M.T.: 'Developments in tech-niques for simulating faults in e.h.v. transmission systems', ibid.,1978, 125, (3), pp. 221-229

6 AGGARWAL, R.K., and JOHNS, A.T.: 'Simulation of electricaltransient phenomena associated with single-pole autoreclosure of

short e.h.v. transmission lines'. Proceedings of the XIV univ. powerengineering conference, Loughborough, 1979, paper 7B.2

7 AGGARWAL, R.K., and JOHNS, A.T.: 'Digital simulation tech-niques for testing line protection relays during 3-phase auto-reclosure'. IEE Conf. Publ. 185, 1980, pp. 250-254

8 WEDEPOHL, L.M., and MOHAMED, S.E.T.: 'Transient analysis ofmulticonductor transmission lines with special reference to non-linear systems', Proc. IEE, 1970, 117, (5), pp. 979-988

9 BALSER, S.J., EATON, J.R., and KRAUSE, P.C.: 'Single-poleswitching - a comparison of computer studies with field testresults', IEEE Trans., 1974, PAS-93, pp. 100-107

10 DAY, J., MULLINEX, N., and REED, J.R.: 'Developments inobtaining transient response using Fourier-transforms: Gibbs'phenomena and Fourier integrals', Int. J. Electr. Eng. Educ, 1965,3, pp. 501-506

11 CARLSSON, L., GROZA, L., CRISTOVICI, A., NECSULESCU,D.S., and IONESCU, A.I.: 'Single-pole reclosing on e.h.v. lines'.CIGRE, 1974, paper 31-03

12 JOHNS, A.T., and AGGARWAL, R.K.: 'Performance of high-speeddistance relays with particular reference to travelling-wave effects',Proc. IEE., 1977, 124, (7), pp. 639-646

13 FUKUNISHI, M., ANJO, K., TERASE, H., OZAKI, Y., YANO, K.,and KAWAGUCHI, Y.: 'Laboratory study on dead-time of high-speed reclosing of 500 kV systems', CIGRE, 1970, paper 31-03

14 JOHNS, A.T., EL-NOUR, M., and AGGARWAL, R.K.: 'Perform-ance of distance protection of e.h.v. feeders utilising shunt-reactorarrangements for arc suppression and voltage control', IEE Proc. C,Gen., Trans. & Distrib., 1980, 127, (5), pp. 304-316

Appendix 9: Superimposed-circuit solution

With reference to Section 3.2, there are always eight knownzero-value transforms associated with any superimposedcircuit. For the purposes of illustration, let it be assumed thatthe circuit change which the fcth superimposed circuit rep-resents_is one in which the eight zero-value transforms areE E E J s k a > a n d hkb,c The latter are then

Fig. 10 Single-pole autoreclosure sustained-fault simulation

Midpoint a-earth fault (x = 50 km); Tt = fault inception (5 ms); T2 = a-phase breaker poles at ends S and R separate (45 ms); T3 = a-phase breakerpoles at ends S and R reclose (0.526 s); T4 = a-, b- and c-phase breaker poles at ends S and R separate (0.586 s); key as in Fig. 6

a Voltages on line side of breaker at end Sb Line currents at end S

194 IEE PROC, Vol. 128, Pt. C, tfq. 4, JULY 1981

placed within admittance-matrix eqn. 9 which, when writtenin extended form, is

F V V V V V V

21 J 22 *23 * 24 •» 25 - ' 2 6 -̂ 27

^ 3 1 ^ 3 2 ^ 3 3 ^ 3 4 ^ 3 5 ^ 3 6 ^ 3 7

41 •« 42 -» 43 •'44 •* 45 -'46 r 47^ 5 1 ^ 5 2

^ 6 1 ^ 6 2

I n\ -* 72

81 r 82

91 r 9 2

es

5^53 ^54 ^55 ^56

^63 ^64 ^65 Y,

V V V* 73 * 74 •« 75

^ 8 584

94

57 -^58

^ 6 7 ^ 6 8

^ 7 6 ^77 ^ 7 8

^ 8 6 ^ 8 7 ^ 8 8

9s 97

With reference to eqn. 11, all rows and columns that corre-spond to zero-value transforms in the voltage vector can beremoved to produce the reduced matrix relationship of eqn.12. This in turn is inverted to produce eqn. 13:

0

0

0

Ika

Y22

Y32

Y<2

Y12

Y23

Y33

Y43

Yn3

Y2*

Y34

Y44

Yn

Y21

Y31

Y*

Ynn

J* ret

F kc

ESka

ERka

(12)

98

Yn

Y29

Y39

F49

Ys9

Yeo

Y19

Y&9

Y99

0

EFkb

E~Fkc

Eska

0

0

ERka

0

0

Ska

•Z22 Z23 Z24 Z

Z 7 7 732 ^-33 ^ 3 4 ^

Z42 Z43 Z44 Z

7 2 '74

27

37

47

77

0

0

0

TRka

(11)

(13)

Now IR ka is the ninth known transform which in turn enablesthe voltage vector in eqn. 13 to be determined. Furthersubstitu_tion_ of_ the resulting known J voltage vector[EFkbEFkcESkaERka\

T into the full admittance matrix ofeqn. 11 enables the remaining current-transform values withinthe fcth superimposed circuit to be obtained.

IEEPROC, Vol. 128, Pt. C, No. 4, JULY 1981 195