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Internal Fault Simulation in SynchronousMachines

Dharshana De S. Muthumuni,Student member IEEEP.G. McLaren, Fellow, IEEEE. Dirks

University of Manitoba , Canada

Abstract- This paper describes a synchronous ma-chine model that can be used to simulate internal faultwaveforms for power system protection studies. Theneed to develop the machine model in the direct phasedomain is explained and a m ethod to calculate the in-ductances involving the faulty windings is outlined usinga four pole lap wound machine. The machine equationsare then solved using a suitable numerical technique.Comparisons are made betw een t he simulated wave-forms and recorded waveforms to verify the accuracy

of the model.Keywords- synchronous machine, internal faults, re-

laying studies

I . INTRODUCTION

The synchronous generator can be described as oneof the most important pieces of equipment in an elec-trical power system. In an interconnected systemthe proper functioning of the generators is critical inmaintaining an uninterrupted power supply to the cus-tomer. Undesirable conditions can occur inside thegenerator due to faults in the external system, anda l s o due t o faults inside the generator itself. It mustbe properly protected so th at any abnormal conditioncan be rapidly detected enabling corrective measuresto be implemented.The protection of synchronous generators involves theconsideration of more harmful abnormal operating con-ditions than the protection of any other power sys-tem element[l]. As a result the protection scheme ofa generator connected to the system is complicated.The concern that this complicated scheme will oper-at e when it should not is quit e valid. However, eventhough an unnecessary tripping of the generator is notdesirable , the consequ:nces of not tripping it in thepresence of a fault an d damaging the machine are farworse [2]. A prior knowledge of internal fault currentand fault voltage waveforms will be very useful to therelay engineer when designing a method to provide pro-tection for machines. Since these waveforms cannot beobtained using the machine concerned, a mathematicalmodel which can accurately reproduce these waveformswould be very useful in relaying studies.

11. OVERVIEW OF THE AVAILABLE MACHINE MODELS

The machine models available on most of the electro-magnetic transient simulation programs [3] re based

on the two reaction theory and the resulting Parkstransformations [4] [5] [6]. This transformation makesuse of the symmetrical nature of the windings insidethe stator. However, an internal fault divides thefaulty winding into a number of sections. The sym-metry which existed earlier will no-longer be presentbetween these faulted sections and the rest of the ma-chine windings. Thus, the above models cannot be

used in internal fault studies and th e transformationscannot be readily applied in such a situation. Themodel described in this paper is derived on the directphase domain for this reason. A machine model in t hedirect phase domain which is capable of external fau ltsimulation is presented in [7], [8]. The d ata supplied bythe manufacturer can be readily converted to a formwhich can be used in this model [9], [5]There are few machine models available for internalfault analysis [lo], [ l l ] 12], [13]. The method usedin [ lo] and [ l l ] eglects the higher order harmonicsand this leads to erro rs since internal faults give rise tostronger harmonics. The method used in [12] oes notconsider the winding arrangement inside the machine.The methods described in [13] considers a two pole,sinusoidally distributed winding.The method presented in this paper takes into accountthe winding arrangement inside the stator and hencecan be readily used for any type of design. A turn toground fault is considered here but any fault type canbe analyzed in a simiiar manner.

111. DESCRIPTION F THE MACHINE

A synchronous machine can be represented as a systemof s x coupled coils as shown in [5]. Here the damperwinding is represented by two hypothetical windingswhose magnetic axes are at right angles to each other.

The voltage current relationship is governed by the fol-lowing equation [5].

[v1]6z l = - [ ~ l ] t i z 6 [ ~ 1 ] 6 z l x l ] 6 z l (1)

[&]6z l = [LS /n1]6z6[11]6zl (2)

where

The elements in the inductance matrix [Lsynl], andthe matrix [RI] are known from the dat a supplied by

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v. RESULTS ND COMPARISONSOnce the inductance matrix is known, the system infigure 3 can be solved. In the case of a turn t o groundfault th e h a 1 system can be expressed by a matrixequation of the order 8 and wil l have the followingform. It can be solved using a suitable numerical tech-nique.

This reduces to

The method outlined in the earlier section was ap-plied to obtain the inductance parameters of a 10 KVAsalient pole type machine with six poles. A number offaults were applied on the stator wihding and the re-sulting waveform recordings were compared with those

obtained from simulations. Three cases are show in figures 5, 6 and 7.

ow Im 1 4 1111

A B t . U l l l , l l l l ~ l u h m p

Fig. 6. Two phase fault between phases A and B.

Fig. 7. Phase A to ground fault with a 15 Ohm groundingresistance.

VI. CONCLUSIONS

A method t o calculate internal fault currents in syn-chronous machines has been presented. A machinemodel in the direct phase domain has been developedand its accuracy has been tested using recorded wave-forms.

REFERENCES[ l ] Protection of synchronous gererators, IEEE catalog number

95 TP 102[2] G. C. Parr , Generator stato r phase fault protection, IEEE

catalog number 95 TP 102[3] EMT DC users manual, Manitoba HVDC research center

publication.[4] R.H. Park, Two Reaction Theory of Synchron ous Machines,

AIEE Transactions, 48:716 730, 1929.[5] P.M. Anderson, A.A. Fouad, Power System Control and

Stability, The Iowa State University Press, 1977.[6] A.E. Fit zgerd d, Charles Kingsley, Stephen D. Umans, Elec-

tric Machinery, McGraw - Hill 1990.[7] P. Subra maniu m, O.P. Malik, Digital Simulation of a Syn-

chronous Generator in Direct Phase Domain, Proc.Iee, Vol.118, No 1, Jan. 1971.

[8] J.R. Marti, K.W. Louie, A Phase Domain SynchronousGenerator Model Including Saturation Effects, IEE E trans-actions on-Pow er System s, V01.12, No. 1, Feb 1997.

[9] M. Rafian, M.A. Laughton Determination of synchronousmachine phase co-ordin ate parameters, Proc. IE E, Vol. 33,No. 8, August 1976.

[ l o ] V.A. Kinitsky Determination of intem al fault curren ts ansynchron ous machines, IEE E Transacti ons PAS, Vo1.84, No.5, May 1965

[ l l ] V.A. Kinitsky Digital comp uter calculation of internal faultcurrents in a synchronous machine, IEEE TransactionsPAS, Vo1.87, No. 8, August 1965.

[12] A.I. Megahed, O.P. Malik, Simulation of Intema l Faultsin Synchronous Generators, IEEE Transactions on PowerSystems, July 1996

Internal faults in synchronousmachines, IE EE Transac tions on energy conversion. (to bepublished)

[14] V.A. Kinitsky Inductances of a portion of the armaturewinding of synchronous machines, IEEE Transactions PAS,Vo1.84, No. 6, May 1965.

[15] B.R. Prentice, Fundamental Concepts of Synchronous Ma-chine reactances, AIEE Transaction s, 56(supp l l 716 721,1 9 2 9 .

[13] Peter Reichmeider et el.

APPENDIX A

a 1 b l E a2 b2 d

Toplayer NO of+ipathr = 2 NO ofmic~ 4

o m m h p r No ofslots = 4

Fig. 8 The w inding diagram.

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