breaker were studied. Considerable differences wereobserved, the major one of which was that far lessdistortion of the wave occured with 3-pole simultaneousclosure energisation.

The effect that different energisation source repre-sentations had on the wavefront duration of travellingwaves was investigated. Small amounts of series inductance,IOJUH or so, at the energisation circuit breaker causedconsiderable increase in wavefront durations. Smallamounts of shunt capacitance, or additional cables con-nected to the energising busbar, give effects similar toinfinite busbar conditions. From these results it wasconcluded that in high-speed transient studies care has tobe taken in representing the energising source correctly.

6 Acknowledgements

The authors would like to thank C.B. Cooper of theElectrical Engineering and Electronics Department atUMIST for his interst and encouragement in this work, andare grateful for the facilities provided in the UMIST PowerSystems Laboratories.

References

1 HYLTEN-CAVALLIUS, N., and ANNESTRAND, S.: 'Distortionof travelling waves in power cables and on power lines'. CIGRE,Paris, 1962, paper 325, Appendix III

2 STAVNES, ).: 'Attenuation of travelling waves in high voltagecables'. CIGRE, Paris, 1960, paper 316

3 HEATON, A.G., and MELAS, E.: 'Capacitance, attenuation andcharacteristic impedance of a 132 kV power cable at variousfrequencies', Proc. IEE, 1970, 117, (4), pp. 761-765

4 BREIEN, O., and JOHANSEN, I.: 'Attenuation of travellingwaves in single-phase high-voltage cables', ibid., 1971, 118, (6),pp. 787-793

5 WEDEPOHL, L.M., and WILCOX, D.J.: 'Transient analysis ofunderground power transmission systems. System-model andwave-propagation characteristics', ibid., 1973, 120, (2), pp.253-260

6 BROWN, G.W., and ROCAMORA ,R.G.: 'Surge propagation inthree-phase pipe-type cables, part 1-unsaturated pipe', IEEETrans., 1976, PAS-95, pp. 89-94

7 WEDEPOHL, L.M., and MOHAMED, S.E.T.: 'Multiconductortransmission lines. Theory of natural modes and Fourier integralapplied oto transient analysis', Proc. IEE, 1969, 116, (9), pp.1553-1563

8 DORNY, C.N., and MATHIAS, R.A: 'Finite-difference methodsfor determining capacitance relationships among arbitrarilyshaped conductors', IEEE Trans., 1971, PAS-90, pp. 876-881

9 RACE, H.H., HEMPHILL, R.I., and ENDICOTT, H.C.: im-portant properties of electrical insulating papers', Gen. Elec.Rev., 1940,43, pp. 492-499

10 TEGOPOULOS, J.A., and KRIEZIS, E.E.: 'Eddy current distri-bution in cylindrical shells of infinite length due to axial currents,Part 1; Shells of one boundary', IEEE Trans., 1971, PAS-90,pp. 1278-1286

11 SILVESTER, P.: impedance of non-magnetic overhead powertransmission conductors', ibid., 1969, PAS-88, pp. 231-238

12COMELLINI, E., INVERNIZI, A., and MANZONI, G.: 'Acomputer program for determining electrical resistance andreactance of any transmission line', ibid., 1973, PAS-92, pp.308-314

13 POPOVIC, B.D.: introductory engineering electromagnetics'(Addison-Wesley, 1971), p. 492

Distribution of switching surges in the line-endcoils of cable-connected motors

R. E. Adjaye and K. J. Cornick

Indexing terms: Machine insulation. Machine windings, Surge protection, Surges

Abstract: When specifying the winding insulation of electrical machines it is necessary to know the electricalstresses to which the winding will be subjected. In the case of interturn insulation the most severe stressesare caused by steep-fronted voltage waves produced by circuit-breaker closure. To some extent such steep-fronted waves are reduced in severity by the time they reach the machine terminals by distortion and attenu-ation in the cable connecting the machine to the circuit breaker. In the studies described the interturnvoltages in the line-end coils of cable-connected machines are evaluated. The equivalent circuits for themachine winding, the cable, and the energising source are obtained and compounded into an equivalentcircuit for the complete system. The interturn voltages in the line-end coils of the machine are obtainedfrom solutions of this equivalent circuit. Studies are made with a number of different cable lengths and types,and for a number of energisation source representations. Single-pole and 3-pole simultaneous closure ofthe circuit breaker are considered. The use of series inductors at the circuit breaker, or shunt capacitors atthe motor terminals, for reducing the severity of the interturn voltages is also investigated. The results ob-tained indicate that the type of cable insulation and the length of cable are both significant in influencingthe magnitude of interturn voltages. Energisation source impedance has a large effect. Comparison of series-inductance and shunt-capacitance methods of surge protection reveals that both methods are effective, butthat both produce other unwanted effects.

List of principal symbols

Zm = series impedence matrix per coilYm = shunt admittance matrix per coilY. = source admittance matrix

Paper T302 P, first received 9th May and in revised form 10thNovember 1978Dr. Adjaye ,and Mr. Cornick are with the Power Systems Laboratory,University of Manchester Institute of Science and Technology,PO Box 88, Manchester M60 1QD, England

ELECTRIC POWER APPLICATIONS, FEBRUARY 1979, Vol. 2, No. 1

YL = terminal admittance matrix/ s = equivalent-current-generator column matrixV = voltage column matrix

A,B = 2-port admittance-matrix parametersLs = leakage inductance of transformer or equivalent

source inductanceLc = inductance associated with circuit breakerC = equivalent stray capacitance of transformer and

busbarZc = surge impedance of cable

11

0140-1327/79/010011 +11 $01-50/0

Z' = equivalent surge impedance of cableLm — series inductance associated with motor terminal

capacitor connecting lead

1 Introduction

Under steady-state voltage conditions the voltage distri-bution in a machine winding is linear and the interturnvoltages are low. Under fast transient-voltage conditionsthe voltage distribution is nonlinear and the interturnvoltages can be very high. Consequently, the interturninsulation of the winding has to be designed to withstandthe stresses caused by fast transient voltages and for thispurpose the interturn voltages developed under theseconditions need to be evaluated.

To obtain a general understanding of how high interturnvoltages are produced in machine windings under transientconditions it is convenient to regard the winding as a trans-mission line. The transient voltage waves propagate into thewinding with a certain velocity, and the winding has acertain wave transit time. The wavefront of the transientcan be regarded as being distributed along a length of thewinding whose wave transit time is equal to the wavefrontduration of the transient. From this it follows that theshorter the duration of the transient wavefront the shorteris the length of winding over which this wavefront is distri-buted and, consequently, the greater will be the voltagedeveloped, per unit length of winding or, per turn. Experi-mentally, it has been found that as transient voltagespropagate into machine windings the wavefront durationof the transient increases.1 The result of this is that themost severe interturn voltages occur at the line end of thewinding.

The transient voltages that occur most frequentlyduring the service life of a machine are those caused byswitching operations. The wavefront duration of suchtransients, which are caused by the premature breakdownof the gap between the closing contacts of the supplycircuit breaker, can be exceptionally short. Tests carriedout2 on a machine/cable/circuit-breaker system indicatedvoltage transients at the machine terminals with wavefrontdurations as short as 0-2 jus.

Invariably the machine will be connected to its supplycircuit breaker by a length of cable. This supply cablebehaves as a complex transmission line and it has thecharacteristics of wave propagation and wave distortion.The wave-distortion characteristic has the effect of pro-longing the wavefront duration of the transient voltagearriving at the machine terminals and it therefore has aconsiderable effect upon the magnitude of the interturnvoltages. Consequently, when the interturn voltages at themachine terminals have to be evaluated, it is necessary totake into consideration the wave-distortion characteristicsof the cable. In brief, the cable and the machine cannot beconsidered as independent elements but have to be con-sidered together as forming a single system when evaluatinginterturn voltages in the line-end coils of the machine.

Economically, it is undesirable to insulate all machinewindings for the worst possible transient conditions. It ismore convenient to produce a standard design that willwithstand most transient conditions and then apply protec-tive measures in systems where transient conditions areexceptionally onerous. One such protective measure thathas been recommended3 is to slope off the front of thetransient voltage wave appearing at the machine terminals

to 10/us or more. However, before undertaking such, orany, protective measures it is first necessary to ascertainwhether protective measures are necessary and, if necessary,whether the 10/us recommendation for wavefront durationis satisfactory.

The present paper will deal with the problem of evalu-ating the interturn and intercoil voltages in the line-endcoils of cable-connected motors. Initially, the character-istics of the cable and machine will be considered, and herethe results of a complementary paper,4 dealing with thewave propagation characteristics of the cable, will beutilised. The cable and machine elements will then be con-sidered as a compound system and mathematical solutionsfor the transient performance of the system will be derived.Using the transient solutions formulated, studies are madeon a cable/machine system. Variations in the parameters ofboth machine and cable are examined and the effect thatthese variations have on the interturn voltages will be indi-cated. Other variables studied will be the source-sideimpedance of the energising circuit breaker and the modifi-cation of this impedance to give less onerous conditions.The techniques available for sloping off the transientvoltage waves arriving at the machine terminals will bestudied and the efficiency of the various techniques com-mented on.

2 Machine-winding representation

2.1 Equivalent network of machine winding

To evaluate the surge voltage response of a machine windingit is first necessary to devise an equivalent circuit for thewinding. The response of the equivalent circuit can then beobtained by the usual methods of network theory. It is inthe appointment of an equivalent circuit that the greatestdifficulty lies, for a balance has to be struck between anaccurate equivalent circuit that would be extremely difficultto solve mathematically and one which is an oversimplifi-cation and leads to inaccurate results.

The machine winding has similar characteristics to anartificial transmission line in that it consists of a chain ofseries-connected coils each of which has series inductanceand shunt capacitance. In a machine winding, however, thecoils are distributed around the machine stator with theresult that the first coil and the last coil are in close proxim-ity. This leads to the condition whereby coils which areremote, in the direction of propagation of the surge, arephysically in close proximity. As a consequence of this,the mutual inductive coupling factors between coils be-comes complex. The same situation occurs with capacitancecoupling between coils; but capacitance coupling is muchweaker due to the intercoil capacitance values being small.

Under surge voltage conditions the effective self induc-tance of a coil differs considerably from the 50 Hz value.Initially, the self inductance arises from flux which is con-fined mainly to paths outside the high-permeability ironcore by eddy currents set up in the core. The eddy currentsare set up by the high-frequency components of the incidentsurge and will therefore be more predominant with steeplyrising surge voltages. Gradually, the flux will penetratedeeper into the core but, during this time, the reluctanceof the flux paths is constantly changing. For calculationpurposes it is therefore necessary to consider self induc-

12 ELECTRIC POWER APPLICATIONS, FEBRUARY 1979, Vol. 2, No. 1

tance as a factor which varies with time of application ofthe surge.

Similar considerations apply to the mutual-inductancecoupling factors existing between coils. However, due tothe limited extent of flux penetration into the core, theflux linkage from one coil to a coil in a neighbouring slotis very small. Thus the mutual coupling between coils undersurge voltage conditions is likely to be very small.

Unlike the case of transformer windings the capacitancebetween coils is very low due to the fact that each coil isembedded in a slot which acts as an earthed boundary.Hence, the intercoil capacitance is usually limited to thatin the endwindings and is very small. On the other hand,and again due to the fact that the coil is embeded in theslot, the coil-to-earth capacitance is large.

Based on the foregoing general characteristics thefollowing assumptions and simplifications are made whenderiving the equivalent circuit of the winding:

(a) It is in the line-end coils of the machine winding thatthe highest interturn voltages exist under surge voltageconditions. Therefore, the time duration for the study willbe limited to that corresponding to the period of time ofpropagation of the surge voltage through these coils.Typically, a study time of 5 JUS will be adequate for mostmachine windings. As a consequence of this time interval,the final equivalent network for the winding need only beaccurate in representing the surge phenomena in thewinding for this time period, and so only the high-frequencyproperties of the winding need be considered.

(b) The turns of coils in the same slot are very closelymagnetically coupled and hence the voltage distributionwithin a coil is linear. This result has been confirmedexperimentally by Wellauers in tests on voltage distri-butions in coils subject to very-high-speed surges. The basicunit, or cell, in the equivalent circuit for the winding willtherefore be a coil. The interturn voltage can then easilybe derived from the coil voltage on a pro rata basis.

For voltage transients with extremely short wavefrontdurations, say 0-25//s and less, the voltage distributionwithin a coil will be nonlinear.8 Under such circumstancesthe assumption of linearity used in the present work willgive interturn voltages slightly lower than might be ex-pected in practice.

(c) As a consequence of (a) there will only be a veryshort time available for the build-up of magnetic flux inthe core of the machine. The mutual magnetic couplingbetween coils of one phase winding, or between coils ofdifferent phase windings will therefore be very small andwill be neglected. It is usually considered6'7 that, to a firstapproximation, an effective series inductance is adequate.This assumption will also be made in the present analysisand an effective frequency-dependent series inductancewill be used. The frequency-dependent characteristic willtake into account the time-varying nature of the fluxpaths.

(d) The capacitive coupling between coils of one phasewinding and between coils of different phase windingswill be very small and will be neglected. The series capaci-tance between turns in a coil and between the coil and thecore is of prime importance and will be taken into consider-ation.

(e) Due to the short study time, the steepness of thesurges, and the high frequencies involved, the dielectriclosses of the capacitance elements will be represented. Thisis a factor that has hitherto been neglected in such studies.

(Z)The presence of eddy currents and skin effectsrenders the series resistance of the coils frequency depen-dent. Consequently, corrections for these effects on theseries resistance values will be made.

The equivalent network for the winding is then a com-bination of three isolated single-phase networks, as shownin Fig. 1, within which, and on a coil basis

Rs = series resistanceLs = effective series inductanceCs = series capacitanceRs = resistive loss element associated with Cs

Cg = shunt capacitanceRg = resistive loss element associated with Cg

2.2 Machine parameters

The machine data used in the studies to follow is that of a3-3 kV 3-phase 429 kW (575 lip), 12-pole squirrel-cageinduction motor with a double-layer lap winding havingtwo circuits in parallel per phase.8 As there are six polepairs, the coil arrangement can be considered to be made upof six coil groups, each of four coils.

At very high frequencies, the magnetic flux is primarilyconfined to air paths within the slot and the series induc-tance of a coil approaches its 'air-cored' value. To obtainthe air-cored inductance of a coil with the dimensions givenin Fig. 2 calculations, based on the work of Lawrenson,9

were carried out. From these calculations the air-coredinductance for the coil was found to be 111-8/uH. Theinductance of the coil in the slots of the motor wasmeasured and found to be 340juH at 1 kHz.8 A logarithmicvariation of the effective series inductance from the 1 kHzvalue to the air-cored value at 100 kHz was assumed, and isshown in Fig. 3. Experimental work on this aspect ofmachine-coil inductance variation with frequency is verysmall, and so the particular variation shown in Fig. 3 wasthat obtained from tests on iron-cored transformer coilsby Li.10

The coil-to-ground capacitance Cg and the effective end-to-end capacitance of a coil were found experimentally8 tobe 910 pF and 60 pF, respectively.

Because of the lack of detailed information on thecharacteristics of the winding insulation, it was assumedthat the dielectric characteristics of the interturn and slotinsulation would be similar. Typically for the coil-groundinsulation an epoxy mica dielectric might be used and forthis material, the expression for the relative permittivity hasbeen given as11

= 4-8-/1-344 0)In view of the lack of information on the characteristicsof such insulation with frequency it was assumed that thevalue given is independent of frequency.

To account for the variation in series resistance Rs withfrequency, the expression13

(2)

was used, in which,

Rs — resistance at a given frequencyR50 = low-frequency value of resistance based upon

conductor resistivity, conductor dimensions,uniform-current distribution

/ = frequency

ELECTRIC POWER APPLICATIONS, FEBRUARY 1979, Vol. 2, No. I 13

2.3 Two-port equivalent network of machine winding

On a coil basis the series impedance matrix Zm and theshunt admittance matrix Ym are both diagonal and aregiven by

(3)

and, with reference to Fig. 1, the values of Y and Z aregiven by

(4)

(5)

Z = Zx (R

in which

Z, = Rc/(l-Q+jcoCsRc)

and

Y = (l-0+jcjCeRg)/Rt (6)

The equivalent propagation constant for the network will be7 = {ZY)xn and the surge impedance will be Zo = (Z/Y)in.Also Yo = \/Z0. The 2-port network A and B parametersfor a coil, or a number of coils in cascade, are then given by

A = Yo coth ny

B = Yo cosech«7

where n = number of coils in cascade.In the present study, it is only the voltages in the first

four coils nearest the line terminal that are of significance.For this reason the individual 2-port networks are used forthe first four coils only while the 2-port networks for the

remaining 20 coils are compounded together into a single2-port network. The resulting network for solution is thengiven in Fig. 4.

3 System representation

3.1 Machine-cable-source representation

A typical busbar-and-load system is shown in Fig. 5, inwhich, in addition to the cable-connected motor, there areother cable-connected loads and a compensation capacitor.In the complementary paper4 it was shown that when anumber of cables, or a capacitor, are connected to theenergisation busbar then the busbar behaves very closely toan infinite busbar. However, it was also shown in the comp-lementary paper that small values of inductance or capaci-tance at the circuit-breaker terminals could seriously affectthe energisation transient. For ease of network manipu-lation the source network was considered as an idealconstant-current generator in parallel with a source admit-tance. By changing the value of the source admittancevarious values of busbar impedances could be accommo-dated.

The equivalent cascaded 2-port equivalent network ofthe entire system, machine-cable-source, can now berepresented as shown in Fig. 6. In this Ys represents thesource-admittance network. The admittance YL representsa terminating network at the machine neutral and is usedso that the earthed or unearthed neutral condition can beeasily represented.

The cable 2-port network is that applicable to a3-3kV,3-phase belted-type polyethylene cable and is derived in thecomplementary paper.

phase 1

phase 2 neutral

phase 3

Fig. 1 3-phase motor winding equivalent network

14 ELECTRIC POWER APPLICATIONS, FEBRUARY 1979, Vol. 2, No. 1

3.2 Solution methods

For illustration, only the derivation of the voltage acrossthe first two coils in the machine winding will be given. Themethod can be extended to cover a greater number of coilsif required. It must be remembered however, that themachine model suggested is valid only for the first fewmicroseconds of the transient and this will impose an upperlimit on the number of coils studied.

Fig. 2 Winding diagram of 3 k V induction motor*

a Winding diagramb Slotc Coil overhang detailsCapacitance at 50 Hz:

capacitance of one coil to earth C« = 910 pFcapacitance between ends of coil Cs — 60 pF

Inductance at 1 kHz:self inductance of each coil L« = 0-34 mH

300

ia.

200

•E 100

2 U 6 8 10log of frequency, Hz

Fig. 3 Coil inductance variation with frequency

Lx = 3 4 0 M HLa = 111-8/uH

With reference to Fig. 6, and starting from the sourceend of the network, the following matrix equations can bewritten,

Source:

Cable:

Coill:

Coil 2:

-B

A2

\-B2

Ac

-Bx

-B2

A2

(7)

(8)

Remaining coils: \—

(10)

V*

V5

(11)

The A and B parameters of coil 1, coil 2 and the remaining22 coils are formulated as in Section 2.3, while the A and Bparameters for the cable are formulated in the complemen-tary paper.

At the neutral-end of the motor winding

-Is = YLV5 (12)

Assembling eqns. 7—12 and resolving, it can be shown(Appendix 8.1) that the voltage at the line side of the

terminal

neutralterminal

coin

A -B"

L-B A

coil 2

A -B'

-B A

coil 3

A -B"

-B A

coiK

"A -B

-B A

coils 5-24

~A" -Br

I-B- A'

Fig. 4 Equivalent 2-port network for machine winding

contactor power cable

circuit-breaker

motor

o-O-load

-load

-load

static\\-% capacitor

Fig. 5 Typical distribution system

circuit-breaker terminals Vx, is related to the source currentby the equation

Vx = (YB+Ae-BeTxyxIt

where

Tx = (Ac + Y^y1 Bc

(13)

(14)

Since all the parameters in the right-hand side of eqn. 13are known, the sending-end voltages could be obtained. The

ELECTRIC POWER APPLICATIONS, FEBRUARY 1979, Vol. 2, No. 1 15

coil voltages are calculated by backward substitution intothe following equations:

V2 = Tx

V, = T2

V, = T3

where

T2 = (A

T, = (A

The voltages

Vex = V

Vc2 = V

V\

v2y3

X-Y2)-1BX

2-Y3ylB2

across coils 1 and 2 are then given by:

1 - ^ 2

2~V3

(15)

(16)

(17)

(18)

(19)

(20)

(21)

The solutions to the foregoing equations were obtained byFourier transform methods in order that frequency-dependent elements could be fully represented. In thestudies illustrated the frequency range for the Fourierintegral was 100 kHz to 100 MHz. This very high upperfrequency limit together with an integration time step of001 JUS was found to give adequate definition of the fasttransients. A maximum observation time of 3JJLS was usedin the studies.

busbar cablemotor

I3-I3 h-kcoil 2

A2 -B2

LB 2 A 2

Fig. 6 Machine-cable-source: system and representation

4 System studies

4.1 Direct energisation of motor

An initial study was made on the motor-winding represen-tation alone. This was done to determine what effect therepresentation of a frequency-dependent series inductance,and a dielectric with a loss component, had on thetravelling-wave characteristics of the winding. For thisstudy the equivalent network of the 3-3 kV motor, Fig. 2,was considered energised from an infinite busbar and undersingle-pole closure conditions.

Three studies were made (Fig. 7). In the first, (i), theseries inductance was taken as the 1 kHz measured value,the series resistance zero, and the dielectric loss free. In thesecond, (ii), the series inductance was frequency dependent,the series resistance was appointed according to Section2.2, and the dielectric loss free. In the third, (iii), the sameparameters were used for the second study but the di-electric was assumed to have a loss component.

From the comparison of studies in Fig. la, a number ofmajor differences are evident. By comparing Figs. 7a(i) and(ii) it is apparent that the frequency-dependent inductancehas the effect of increasing the speed of propagation and

16

leading to a shorter wavefront time at the end of coil 1.This is to be expected for the frequency componentsdefining the energising wavefront corresponding to thisrange of frequencies the series inductance will be low.

From the comparison of the studies, Figs. 7a(ii) and(iii), the effect that the loss component of the dielectrichas on wave propagation is clear. Coil voltage oscillationsare heavily damped and the wavefront duration is slightlyincreased.

coili coil2 coil3 coiKTV

V

1-5

OHO

1.0-5

0-5 V0 15time.us

a

20 2-5

10

a 085In 0-6

0/Ol2 02o

1 2 3 4coil number

b

Fig. 7 Effect of machine parameters on waveshape and peakvoltages

er = 4-8, Rs = 0, Ls = 0-34 mHer = 4-8, Rs = /?(w), Ls — L(u>)e = 4 - 8 — / 1-344, Rs = 7 ? ( C J ) , Ls =

To determine the voltage appearing across the line-endcoils of the winding the results of studies shown in Fig. lawere extended to the first four line coils. The effect thatparameter variations have on the intercoil voltages is givenin Fig. 1b. It is here seen that changing the series inductanceto a frequency-dependent parameter has little effect onintercoil voltages but the inclusion of dielectric lossesaffects a 50% change at coil 4. What may be thought to besurprising is that coil 1 suffers the same intercoil voltageindependent of what parameters are used. This feature ishowever due to the fact that for this study the winding isbeing directly energised with a 1 p.u. infinitely steep-fronted surge wave. Consequently with the coils having afinite wave propagation time the voltage across the firstcoil must reach 1 p.u. independent of parameters.

A further study was made under direct-energisationconditions in order that the results might be brought ontoa more realistic basis and at the same time compared withexperimentally derived results. The experimental testsfor comparison were those carried out by Parrott8 on the3-3 kV induction motor mentioned earlier. For these tests,a test wave with a 016 jus wavefront duration was used and

ELECTRIC POWER APPLICATIONS, FEBRUARY 1979, Vol. 2, No. 1

for comparison purposes this was the wave used in thecomputer studies. The results of the computer studies aregiven in Fig. 8, and the comparison between these resultsand the experimental results is given in Fig. 8b. Agree-ment between the two sets of results is reasonable with thegreatest difference appearing in the results for coils 2 and3. It is suggested that the error could be caused by theneglect in the present work of intercoil magnetic coupling,and the assumed value of er.

V5

STos1

0-5 10 V5time, us

a

20 25

energised from an infinite busbar. Three lengths of cable,30 m, 100m, and 300 m were used in these studies; theselengths being typical of practical conditions.

Initially, single-pole closure energisation studies wereundertaken and typical of these studies are the resultsshown in Fig. 9. This figure indicates that due to the differ-ent modal velocities in the cable, on single-pole closure thewave arriving at the machine terminals (Fig. 9a) has a com-plex wave front pattern and that it is difficult, if notmeaningless, to talk of wavefront duration. The defor-mation of the wave as it passes through the first four line-end coils is also shown. The wave delay and wavefrontelongation as the wave passes through a coil can be clearlyseen. It is in the first coil that very nearly all of the higher-frequency components of the voltage wave at the machineterminals are removed and it is across this coil that thehighest coil voltage exists.

103ci.-= 0-88J 0-6

computationalresults

Parrottsexperimental

results

coil numberb

Fig. 8 Voltages across line-end coils: comparison of computerresults with field test results

l=100m

20

oco 10o>5 05a»

I °-0-5

3

CL

b0/ena

1-Op.u.

motorterminal

<vo

coilicoil 2

coil 3 coil 4

coilicoi!2

coil 3coil 4

Fig. 9 Voltages to ground and across line-end coils in a cable-connected motor: single-pole closure

4.2 Energisation of a cable-connected motor

4.2.1 Single-pole closure. To determine what effect cablelength has on the magnitude of the interturn voltages,studies were made on a cable-connected motor system

VOp.u.

20

Q.•o 1 5

oeno~Z 1 0S1

g 05CL

'300m100 m

30m

1 2coil number

1 5

V0

I 0-530m100m300m

1 2 3coil number

Fig. 10 Peak voltages to ground and across line-end coils: effect ofdifferent cable lengths: single-pole closure

Typical voltages developed across the line end coils areillustrated in Fig. 9b, and from this it will be noted thatacross coil 1 a voltage of 105 p.u. is generated. Of furtherinterest is the fact that in coil number 2, although thevoltage developed is not as great in magnitude as that incoil 1, the slower and steadier waveform might be assevere as far as the insulation is concerned.

The results of the studies on single-pole energisationwith three lengths of cable are summarised in Fig. 10. Inbrief, the magnitude of the voltage to ground, developed atthe machine terminals, is virtually independent of cablelength. However, the voltages developed across the line-endcoils are strongly dependent upon cable length, ranging

ELECTRIC POWER APPLICATIONS, FEBRUARY 1979, Vol. 2, No. 1 17

from 1-5 p.u. with a 30m length of cable down to 0-8 p.u.with a 300 m length of cable. Also, and as anticipated, thevoltages developed across a coil decrease the further thecoil is from the line terminal.

4.2.2 Simultaneous 3-pole closure. A set of studies similarto the foregoing set were made with simultaneous 3-poleclosure. For these studies one pole was assumed to close ata voltage of 10 p.u. and the other two poles at —0-5 p.u.This type of closure could possibly be due to the triggeredclosure mechanism mentioned in the complementarypaper.4

I =i00m

fcn2 10

2 0-5o

1-Op.u.Q

,-motor terminal

coil!

t imersa

10

10

Fig. 11 Voltages to ground and across line-end coils in a cableconnected motor: simultaneous-pole closure

Waveforms which are typical of these studies are givenin Fig. 11. The first feature of significance in these wave-forms is that the motor terminal-voltage waveform displaysdistinct travelling wave characteristics. The travelling wavesset up by simultaneous pole closure constructively interfereto give a more defined wave-propagation characteristic tothe cable. The crest value of the motor terminal voltage ofi-9p.u. is however slightly greater than that caused bysingle-pole closure. Because of the mode of wave propa-gation under this type of energisation the wavefront dur-ations of the voltages, at the motor terminals and at eachjunction of the first four coils, are shorter than thoseobtained in the single-pole closure condition.

Typical voltages developed across the first two line-endcoils are shown in Fig. lift, and the oscillatory nature ofthese voltages is clear. The very nature of this voltageoscillation, and as an example the swing from +1-5 p.u. to— 1-5 p.u. across coil 1, could in itself cause insulationproblems. Fig. 12 summarises the results of the 3-polesimultaneous closure studies.

18

4.3 Energisation of a cable connected motor: Influenceof protective measures

Two methods can be used for reducing the interturn vol-tages of cable-connected motors. The first is the methodproposed by the AIEEE3 which recommends a shuntcapacitor connected at the motor terminals. The second isthe use of a series-connected inductor at the circuit-breakerend of the cable.12

10 p.u<hrO

2 0

a O 5

30m

1coil number

201-

3 15

10

.0-5

300 m100 m

30m

1 2 3 4coil number

Fig. 12 Peak voltages to ground and across line-end coils: effectof different cable lengths: simultaneous-pole closure

Analytically the work involved in adding a shunt capaci-tor or a series inductor into the study formulation is verysmall. The series inductor is considered as an additionalcomponent in the energisation source representation anda shunt capacitor is added into the shunt admittance matrixof the motor.

4.3.1 Shunt capacitor. The effect of connecting a shuntcapacitor at the machine terminals is highly effective(Fig. 13). The wavefront duration has been increased by a,0-25/uF capacitor from about 0-5 jus (Fig. 9) to almost10/is, Fig. 13. The corresponding voltage developed acrosscoil 1 has been reduced to 0-15 p.u., Fig. 136.

The results of studies obtained when a number of differ-ent values for the shunt capacitor are used are given inFig. 14. Here it can be seen that the effect of adding a

ELECTRIC POWER APPLICATIONS, FEBRUARY 1979, Vol. 2, No. 1

0-5 /iF capacitor is to reduce the coil voltages almost ten-fold and that capacitor values of only 0-1 /iF make afivefold reduction. On the other hand it must be noted thatthe effect of the shunt capacitor is to produce a greaterovervoltage to ground at the machine terminals, Fig. 14a.Values increase from l-6p.u. without a capacitor to a maxi-mum of l-95p.u. with a 0-5/iF capacitor. Here a compro-mise might have to be made between a low interturn vol-tage and a high winding-to-ground voltage.

When a shunt capacitor is to be used at the motorterminals, it will be connected by a short length of cable.This cable represents an additional inductance in series withthe capacitor and effectively reduces the protective value ofthe capacitor, as described by Shankle.2 A further studywas therefore carried out with a 1 juH inductor, corres-ponding to approximately a i m length of capacitor-connecting cable, in series with the capacitor. The resultsof these studies are also shown in Fig. 13a, and indicatethat the motor terminal-voltage waveform has high-speedtransients, A and B, superimposed. These results are in

VOp.u.

UlOOm

£ 2 0ft

* 0 5o

A B

U 6time, is

Fig. 13 Voltage waveforms in a capacitor protected cable-motorsystem: single-pole closure

agreement with those obtained experimentally by Shankle.2

High-speed transients are also noticeable on the intercoilvoltage waveform patterns, (Fig. 13b).

4.3.2 Series inductor. In recent studies on vacuum inter-rupter energisation transients, the use of a series inductoras a means for increasing the wavefront duration of tran-sient voltages has been proposed.12 These experimentalstudies indicated that an inductor of several microhenrieswould be adequate for this purpose. Consequently, a studyusing the configuration shown in Fig. 15 was made using a10/xH series inductor.

Immediately apparent from the results of these studies(Fig. 15a) is the effect the inductor has on wavefrontelongation of the voltage wave appearing at the motorterminals. However, the first coil voltage is still very highat 0-7 p.u. (Fig. 156). Values of series inductor of lOO^Hand 500 JUH were then considered and the results of thesestudies, together with studies using a 10/uH value and a zerovalue, are given in Fig. 16. It is seen in Fig. 16b that to have

the same effect on interturn voltages as a 0-5 /xF capacitora series inductor of 500 /iH must be used. Also, that, ingeneral and within certain limits, the value of intercoilvoltages decrease with increasing value of series inductor.Similar considerations also apply to the magnitude of thewinding-to-ground voltages (Fig. 16a).

Again, a compromise must be achieved between a seriesinductor that reduces the intercoil voltages to a tolerablelevel and one that may cause serious system oscillations.

1-Op.u.O

20

Q.

! ' 5

eno

| 1 0

I 05

Fig. 14 Peak voltages in a capacitor protected cable-motor system:effect of capacitor size: single-pole closure

VOp.uQ

l=i00m

LrlO^H

10 V5time.ps

15

g > 5| S 0 5

05 10 1-5timers

bFig. 15 Voltage waveforms in an inductor protected cable-motorsystem: single-pole closure

ELECTRIC POWER APPLICATIONS, FEBRUARY 1979, Vol. 2, No. I 19

5 Discussion and conclusions

Studies have been carried out for the purpose of evaluatingthe distribution of energisation transients in the line-endcoils of cable-connected motors. The studies were based ontaking into account all system parameters including thoseof the energisation source and interconnecting cable. Solu-tions to the network problems were obtained by Fouriermethods in order that parameters which were frequencydependent could be fully considered.

An equivalent circuit for the machine winding wasproposed that takes into consideration the dielectric losscomponent of the insulation and an equivalent seriesinductance that is frequency dependent. It should bestressed that this equivalent circuit is applicable only forthe short time period corresponding to the surge wavepropagating through the line-end coils. Reasonable agree-ment was obtained from the results of studies on thisequivalent circuit and experimental results. It was con-cluded that in such studies it is important to include di-electric loss and frequency-dependent inductance.

VOp.,£

2-Ot-

en

O

ai

2 VO•5

Ia05

10

o 2a

1 2coil number

b

L.uH— 0-10

-100•500

2 3coil number

Fig. 16 Peak voltages in an inductor protected cable-motor system:effect of inductor size: single-pole closure

Energisation studies, which included a length of cablebetween the machine and the energising busbar, indicatedthat for single-pole circuit-breaker closure conditions thevoltage-to ground at the machine terminals was indepen-dent of cable length. However, the voltage across the firstcoil was strongly dependent upon cable length, varyingfrom 1-5 p.u. with a 30 m length of cable down to 0-8 p.u.with a 300 m length of cable. Similar studies for simul-taneous 3-pole closure conditions revealed that the voltageto ground in the machine winding, and the voltage acrossthe line-end coils, were greater than for the correspondingsingle-pole closure conditions.

It should be noted that sequential-pole closure, acondition not treated in the present work, will generallyproduce higher voltage transients than those caused bysingle-pole and simultaneous-pole closures.

The effectiveness of either a shunt capacitor connectedat the machine terminals, or a series inductor at the circuit-breaker, for protection purposes has been fully demon-strated. With both methods, and with a suitable value, themagnitude of the intercoil voltages in the line-end coils canbe reduced tenfold. However, when using either method,care has to be taken that no circuit oscillations are set upby the addition of the protecting element. In addition ithas been demonstrated that in the case of the shunt capaci-tor care must be exercised when locating the capacitor;long capacitor leads give rise to voltage transients thatcould be harmful to the machine winding. It is suggestedthat, in the present system studied, a capacitor to extendthe wave front duration at the machine terminal to IOJUSwould be very conservative and a smaller value, say 0-1 JUFwould be as effective.

In brief, the voltage developed in the endwindings ofcable-connected motors depend upon the machine windingparameters, the length and type of interconnecting cable,the type of busbar configuration and whether a single-poleor 3-pole energisation is usual. A shunt capacitor or seriesinductor can be used to substantially reduce the interturnvoltages although with either method secondary unwantedeffects are produced.

At the present moment, and on the basis of the presentstudies, it would be unwise to generalise from the results.The problem is complex and involves a large number ofparameters. For the purpose of generalisation it would benecessary to carry out many more studies covering a widerange of machine and cable, types and sizes.

6 Acknowledgments

The authors would like to thank C. B. Cooper of theElectrical Engineering & Electronics Department at UMISTfor his interest in this work, and are grateful for the facilitiesprovided in the UMIST Power Systems Laboratories.

7 References

1 MONNET, M. M.: 'Distribution of impulse voltages through thewindings of electrical machines'. Rev. Gen. Electr., 1958, 67,pp. 507-519

2 SHANKLE, D. F., EDWARDS, F. R., and MOSES, G. L.: 'Surgeprotection for pipeline motors', IEEE Trans., 1968, IGA4,pp. 171-176

3 AIEE committee report. 'Impulse testing of rotating machines',AIEE Trans, 1960, PAS-79, pp. 182-188

4 ADJAYE, R. E., and CORNICK, K. J.: 'Wave propagationcharacteristics of three-phase distribution cables', see p. 1

5 WELLAUER, M.: 'The voltage stresses in the entrance coils ofwindings on the occurrence of surge voltages of different steep-ness'. Bull. Oerlikon, 1947, 27, pp. 1823-1830

6 RUDENBERG, R.: 'Performance of travelling waves in coils andwindings', AIEE Trans., 1940, 59, pp. 1031-1045

7 LEWIS, T. J.: "The transient behaviour of ladder networks of thetype representing machine and transformer windings', Proc. IEE1954, 101, Pt. II, pp. 541-553

8 PARROTT, P. G.: 'Surge voltage distribution in line-end coils ofhigh-voltage motor windings', ERA Report 5224, 1967

9 LAWRENSON, P. J.: 'Calculation of machine end-windinginductances with special reference to turbogenerators', Proc.IEE, 1970, 117, (6), pp. 1129-1134

10 LI, K. K.: "The parameters of transformer windings for surgedistribution purposes'. M.Sc. Dissertation, UMIST, 1971

11 FARMER, E.: 'The insulation of large electrical machines'.BEAMA electrical insulation conference, 1970, Paper 1

12 MURAI, Y., NITTA, T., TAKAMI, T., and ITOH, T.: 'Protectionof motor from switching surge by vacuum switch', IEEE Trans.,1974, PAS-74, pp. 1472-1477

13 HELLER, B., and VEVERKA, A.: 'Surge phenomena in elec-trical machines' (Iliffe, 1968), p. 368

20ELECTRIC POWER APPLICATIONS, FEBRUARY 1979, Vol. 2, No. 1

8 Appendixes

8.1 Circuit-breaker voltage in terms of source current

From Fig. 6, the following matrix equations for the systemcan be written:

or

Source: Is = YSVX +1

Cable:

Coill:

Coil 2:

/i

It

-h

hh

u

Ac -Bt

Bc A,A, ~

l~Bx A,

-B2

L /J I-B2 A2\ \YARemaining I—/J [ A% —>coils:

Neutralconnection: — 7S = YLVS

Expansion of eqn. 26 gives

- / s = -B3V4+A3V5

By substitution from eqn. 27

Eqn. 26 again gives

-U = A3V*-B3V,Substituting eqn. 29 into eqn. 30 gives

/4 =or

h =where

B3-A3}V<

Y3 = B3(A3 + YLy1 B3-A,

From eqn. 25

74 = -B2V3+A2V*

(22)

(23)

(24)

(25)

(26)

(27)

(28)

(29)

(30)

(31)

(32)

(33)

(34)

or

Substituting eqn. 32 into eqn. 34 and simplifying results in

V, = (A2-Y3ylB2V3 (35)

(36)

(37)

where

T3 ••

= T3V3

= (A2-

Expanding eqn

_ / = A2

- nr1

.25

V3-B2

B2

(38)

Substituting eqn. 36 into eqn. 38 and simplifying reducesto

h = (B2T3-A2)V3 (39)or

I3 = Y2V3 (40)

where

Y2 - B2T3~A2 (41)

From eqn. 24

73 = -BXV2 +AXV3 (42)

Substituting eqn. 40 into eqn. 42 and simplifying gives

K3 = (Ax-Y2)'1 BXV2 (43)

ELECTRIC POWER APPLICA T1ONS, FEBRUAR Y 1979, Vol. 2, No. 1

V3 = T2V2

where(44)

(45)

(46)

T2 = (Al-Y2)~lBl

Expansion of eqn. 24 gives

-I2 = AlV2-BlV3

Substituting eqn. 43 into eqn. 46 results in

-I2 = {Al-Bl(Al-Y2ylBl)V2 (47)

Let Yx be the admittance seen at the motor terminals.Then

- h = YXV2 (48)where

(49)

(50)

(51)

(52)

(53)

From eqn. 23

I2 = -BCVX +ACV2

By substitution of eqn. 48 into eqn. 50

V2 = (Ac + Yxyl BCVX

orV2 = TXVX

where

T — (A + Yx)~l Bc

By expansion from eqn. 23 and using eqn. 52

I, = (AC-BCTX)VX (54)

Substituting eqn. 54 into eqn. 22 gives:

7S = (YS+AC-BCTX)VX (55)

Hence the circuit-breaker voltage in terms of the sourcecurrent is

Vx = {Ys+Ac-BcTxyl Is (56)

The presence of any additional equipment at the lineterminals of the motor (with Yr as its diagonal admittancematrix) alters the motor input admittance matrix equationto:

Y, = {Ax-BX(AX-Y2yl BX+YT (57)

8.2 Design details of cable and motor

Cable3300 V, 3 x 95 mm2, plastic-insulated, stranded-aluminiumconductors, double-steel-wire armoured

Motor8

Type: Vertical squirrel-cage motorLine voltage: 3KVWinding connection: StarRating: 520KVA,429kW(575 hp)Poles: 12Bore diameter: 95-25 cm (37-5 in)Core length: 41 -9 cm (16-5 in)Stator slots: 144Rotor slots: 120Coil pitch: 83-3%Length mean turn: 1 -8 mLength per circuit: 349 mStator slot dimensions: 0-99 cm x 6-05 cmStator conductordimensions: 025 cm x 0-61 cmTurns per stator coil: 8

21