torsional oscillations in alternators1

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237EEE Transactions on Energy Conversion, Vol. 13, No . 3, September 1998APPLICATION OF STATCOM FOR DAMPING TORSIONAL OSCILLATIONS IN

SERIES COMPENSATED AC SYSTEMSK.V. Patil J. Senthil J. Jiang R.M. Mathur

Department of Electrical EngineeringThe University of Western OntarioLondon, Ontario, Canada - N6A 5B 9dbs t r ac t - This paper presents the results of a study onthe application of the recently developed FACTS device,Static Compensator (STATCO M), for th e damping of tor-

sional oscillations that occur in a series compensated acsystem. The IEEE first benchmark system is consideredfor this study. In ordter to suppre ss unstable torsionalmod e oscillations, STATCOM with PI controller to reg-ulate the bu s voltage, and with an auxiliary signal derivedfrom the generator speed deviations is employed at thegenera tor terminal. Eigenvalue analysis techniq ue is usedfor small signal analysis, and optimization of the controlsystem parameters is done through step response studies.In addition, dynamic performance of the nonlinear systemwith optimized STATCOM controller is evaluated under athree-phase fault. Results from the analytical and digitalsimulation studies reveal the technical feasibility of usingSTATCOM for damping of turbine-generator torsional os -cillations in series compe nsated ac syste ms.

Keywo rd s - Torsional oscillations, Series compensa tion,STATCOM

I. INTRODUCTIONSeries capacitor compensation is employed in electric

power systems to raise the power transmission limit oflong EHV lines. This however may lead to the phe-nomenon of subsynchrcmous resonance (SSR). SSR oc-curs when a natural frequency of a series compensatedtransmission system aligns with the complement of oneof the torsional modes of the turbine-generator. Undersuch circumstances, the turbine-generator oscillates at afrequency corresponding to the torsional mode frequency,and unless corrective achion is taken, the torsional oscilla-tions can grow and may result in the failure of the turbineshaft [l].The first experience of such an interaction oc-curred at the Mohave substation in 1970. Since then ,several countermeasureti for damping of torsional oscil-lations, such as use of excitation control [2], Static Var

PE-568-EC-0-01-1997 A palper recommended and approved by bythe IEEE Electric Machinery Committee of the IEEE PowerEngineering Society for publication in the IEEE Transactlons onEnergy Conversion. Manuscript submitted August 23, 1996, madeavailable for printing J anuary 8, 1997

Compensator (SVC) [3], [4], [5], NGH scheme [6], staticphase-shifter [7], super conducting magnetic energy stor-age (SMES) [8] etc., have been suggested in the literature.

The availabili ty of high power gate-turn-off thyris tors(GTO) have recently led t o the development of a newequipment called Static Compensator (STATCOM) [9],[ lo] . STATCOM is a second generation FACTS equip-ment based on voltage source inverter. STATCOM usesself commutating devices like GTOs and is an advancedform of SVC. The operat ing and functional characteristicsof STATCOM are however different from those obtainedusing SVC. The major advantages of STATCOM over theconventional SVC are, significant size reduction due to re-duced number of passive elements, and ability to supplyrequired reactive power even at low bus voltages [ll].

This paper examines the application of STATCOM fordamping torsional oscillations in series compensated acsystem. The IEEE first benchmark system [12] has beenmodeled with STATCOM at the generator terminal. TheSTATCOM considered is a voltage source inverter, andis equipped with a PI-controller that regulates the gen-erator terminal voltage. The PI controller has an addi-tional input derived from the generator speed deviations.The voltage controller and speed feedback gains are de-termined by eigenvalue analysis an d step response studiesof the linearized system. Time domain simulations usingthe nonlinear system model are also carried out t o demon-str ate the effectiveness of the proposed scheme under thecondition of a three-phase fault at the infinite bus.

11. SYS TEM MODELI NGThe one-line diagram of the IEEE first benchmark

model [12], with STATCOM connected at the generatorterminal is shown in Fig. 1-a. In order t o develop a mathe-matical model for the studied system, the electric networkequations as given in [5] are used. The STATCOM and itscontroller are modeled as given in the next section. Thegenerator is represented by the d- an d q-axis equivalentcircuit with one damper winding an d field winding in thed-axis, and two damper windings in the q-axis [13]. Th emechanical system comprises six masses, i.e., the high-pressure turbine (HP), the intermediate pressure turbine(IP), two low pressure turbin es (LPA and LPB), th e gen-erator (GEN),and the exciter (EXC) as shown in Fig. 1-b.

0885-8969/98/$10.00 0 1997 IEEE


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0

Mechanical damping is assumed to be zero for all massesto represent the worst damp ing conditions. The generatoris equipped with a static excitation system. The config-uration for the static excitation and the governor systemare taken from [14]: The system dat a and the initial oper-ating conditions of the system are given in the Appendix.

32% I 46.5% I 59.25% I 72.25%0.168fj 10.0810.113fj 10.991 0 . O f i 11.851 -0.31fi 12.75

Etp t 0.14 0.02 j0.50 Xc j0.06 ,*--wW-mm A T m;1 0

1

Generator

-0.OOlrj 99.37 0.006rtj 99.70 0.0 44 fj 100.63 6 .5 3 fj Q8.79

.............................. :STATCOM(a)

(b)Fig. 1. (a)Network for SS R Damping Studies, (b ) Six-Mass Rotor

in addition to an electromechanical mode (mode 0). TheIEEE first benchmark system is characterised by fourunstable torsional modes. Each of these modes has itslargest SS R interaction at a certain value of the seriescompensation X , [5]. Without STATCOM, the real partof the eigenvalues corresponding to the various torsionalfrequencies vary in magnitude and become unstable atdifferent levels of series compensation as shown in Fig. 2.For each of the critical compensation levels at which thereal part of the eigenvalue is maximum (indicating worstdamping) , he corresponding torsional and electrical modeeigenvalues of the system without STATCOM are listedin Table I. From Fig. 2 it can be seen that modes 1 ,2 ,3and 4 become unstable at various values of X ,. The ob-jective is to da mp all these torsional modes by employingSTATCOM at the generator terminal.

2 0.OOlfj 127.05 0.006kj 127.11 l .Z l&jl Z6.g8 0.004fjl26.903 I 0.017-fj 160.811 2.2Q fj16 0.4Q ~0.0 17rt j60.251 0.002rtj160.41

TABLE IFIRSTB E N C H M A R KIGENVALUES

4

HP IP LPA LPB GEN EXC IModel % ComDensation Level

2.135fj203.0 1 0. 01 5f j 202.58 0.0 02fj 202.73 -O.OOl&j202.80Combining the equations of mechanical system, genera-

"6-'TE

5 1E-Bf j 298.18 -1E-5fj 298.18 -1E-5hj 298.18 -lE-5fj29 8.18

- K cos Os -K sin Os

WORSA S Ls

L , L ,1

_ --U0 -_, ~ [;I]

--.5Kcos6, 1.5Ksin0,- -- cs c, %C, -

. -compensated transmission line results in a set of 27th or -der nonlinear differential equations without STATCOM.These differential equations a re then linearized around anoperating point to obtain the linear differential equationswhich are then used to obtain the system eigenvalues.

8 (99 rad/s)Mode 1

'-60 10 20 30 Percent0 Compensation0 60 70 80 90 100Fig. 2. SS R Modes of First Benchmark Model

The six-mass model of Fig . 1-b has five torsional modes

111. STATCOM MODELThe st ate space model in R- I frame ( the synchronously

rotat ing frame of reference) for th e STATCOM circuit inFig.1-a can be written as below. It is to be noted tha tthe per unit system adopted for modeling the STATCOMcircuit is the same as for the rest of the system.

\


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240TABLE I11

FIRSTBENCHMARKIGENVALUESITH STATCOM VOLTAGECONTROLLERND SPEEDDE VI AT I ONEEDBACK

Mode

0

% Compensation Level32% I 46.5% I 59.25% I 72.25%

-3.3485: 2.621-3.398fj 2.701-3.484%j 2.801-3.716rtj 2.921 -1.0045j 99.14 -1.442fj 99.25 -2.256kj100.50 0.284fj101.20

~

3

bu t also increases the system damping considerably (referTable 111). This reduces the torsional oscillations.It is to be noted th at the eigenvalues listed in Tables I1and I11 are with STATCOM controller gains specified innext section.

-0.718+j160.73 0.215fj161.33 0.018fj160.97 0.041fj160.86

V. SELECTION OF CONTROLLER GAINSThe STATCOM controller model as shown in Fig. 4

has three gains, the proportional gain K,, the integralgain Ki , and the speed feedback gain K,. The objectiveis t o design a single controller which can be used t o dam pall SSR modes at all compensation levels.

Eigenvalue analysis is used to obtain the range of K p ,Ki and K , fo r which the system is stable. It is foundthat the system is stable for -6.25 5 K p 5 -1, -132 5Ki 5 0 and 4 5 K , 5 11. From these K p ,K ; and K ,values, final gain parameters are then selected by carryingout the step response test on the system and ensuring thatthe system settling time and the overshoot in generatorspeed is low. Th e final values of K,, Ki and K, thusobtained are -1, -1.25, and 8 respectively. For these gains,the plot of generator rotor angle and generator speed fora 10% step increase in V,,f for 72.25% compensation isshown in Fig. 5.

VI. DIGITA L SIMULATIONTo support the results of the eigenvalue analysis given

in Tables I1and 111, time domain simulation based on non-linear differential equations of the system under a three-phase fault at th e infinite bus is performed. A set of non-linear differential equations are solved using the fourth -order Runge-Kutta algorithm. All system nonlineadticsare included in the model. The three-phase fault is ini-tiated at 0.2 second, and the fault duration is 5 cycles(83 ms). Plots of the generator rotor angle, generatorelectrical torque, LPB-GEN shaft torque, generator ter-minal voltage, and the phase difference angle are given inFig. 6 for the case with STATCOM under voltage controlbut with no speed deviation feedback. For the case with

5

Rotor Angle (degrees)

i50

0 1 2 4 5 6 7 8 9 10

-lE-5hj298.18 lE-5rtj298.18 lE-5fj298.18 lE-5fj298.18

50

Llv ' ' ' ' ' ' ' ' ' I0 1 2 4 5 6 7 8 9 10

I,'Generator Speed (pu)Speed 1pu =377 ad/:

0 950 1 2 4 5 6 7 8 9 10

Fig.5. 10 % Step Change in V,,, for 72.25% Compensati on2000 Generator Rotor Angle (dag)1000

n"0 1 2 4 5 6 7 6 9 1020

011\11 ,

0 1 2 4 5 6 7 8 9 10-20200

4Generator Terminal Voltage (pu)

-0 1 2 3 4 5 6 7 8 9 10I Phase Difference Anale fded I00

-2000 1 2 3 4 5 6 7 8 9 10Time,s

Fig. 6. SimdationResults with only STATCOM Voltage Controllerfor 72.25% Compen sation

STATCOM under voltage control and with speed devia-tion signal, in addition to th e above plots, plots of real andreactive components of STATCOM current are also givenin Fig. 7. These results are for X,=0.505 pu, which corre-sponds to a compensation level of 72.25%. For other crit-ical compensation levels (i.e., 32%, 46.5%, and 59.25%),for the case with STATCOM with voltage controller and


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241reveal that STATCOM with the voltage controller andauxiliary signal derived from generator speed deviationis effective in damping torsional oscillations at all criti-cal compensation levels. Simulation was carried out forother compensation levels as well. Results for these cases(not given in the paper) reveal that STATCOM with thevoltage controller and auxiliary speed signal is effective indamping of torsional oscillations.From the plots of generator rotor angle in Figs. 6 and7 it can be seen that immediately after the applicationof the faul t, the generator rotor angle decreases for a fewtenths of a second before increasing. This is due to thepresence of STATCOM. As soon as the fault is created,the generator terminal voltage transiently drops to zerofor a few tenths of a second. The STATCOM voltagecontroller tries to boost the voltage by supplying reactivepower. In this process, the STATCOM draws real power(refer plot of STATCOM real current in Fig. 7) to keepthe dc side capacitor charged [16].From the plots of I # R and I*I in Fig. 7 it can be seenthat, in steady state, is^ is nearly zero, and id^ has avalue of 0.35 pu. Since the STATCOM bus voltage E,is considered as 0.95, the pu MVA of STATCOM is 0.33.This implies that the size of STATCOM required wouldbe of the order of 30-35% of the generator MVA rating.

0

10050 -0 1 2 3 4 5 6 7 8 9 10

0 1 2 3 4 5 6 7 8 9 10-5

1 2 3 4. 5 6 7 8 9 10bener atdr Termitb.1 Voltade (pu) '1

0.5-

0 I0 1 2 3 4 5 6 7 8 9 10STATCOM React ive Current (pu)

"0 1 2 3 4 5 6 7 8 9 1050

-5

STATCOM Real Current (pu)

0 1 2 3 4 5 6 7 8 9 10

I0 1 2 3 4 5 6 7 8 9 10Time,s4 0 L 1 '

Fig. 7. Simulation Results with STATCOM Voltage Controller andSpeed Deviation Feedback for 72.25%Compensation

Shaft Torque (pu),32% comp0 -0 1 2 3 4 5 6 7 8 9 10-5

, IShaft Tdique (p i) , 46.5% comp0

--O 1 2 3 4 5 6 7 8 9 10

',l1 'ShaftTorque (pu),59.25% comp ' ]0

I0 1 2 3 4 5 6 7 8 9 10T i m e s

-5 '

Fig.8. LPB-GEN Shaft Torques for other Critical CompensationLevels with STATCOM Voltage Controller and Speed DeviationFeedback

speed deviation feedback,plots of LPB-bE?N shaft torqueonly are given in Fig. 8. Examination of these results

VII. CONCLUSIONSIn this paper, a new concept of using STATCOM to

damp the torsional subsynchronous oscillations in addi-tion to controlling the voltage in power system has beenproposed. The concept is verified by means of eigenvalueanalysis and detail time domain simulations under a se-vere three-phase fault at the infinite bus. Application ofthis concept to the IEEE first benchmark system provedthat STATCOM, provided at the generator terminal andequipped with both voltage controller and an auxiliarysignal derived from generator speed deviation is effectivein damping the torsional oscillations at all compensationlevels.

ACKNOWLEDGMENTSFinancial support for carrying out this work was re-

ceived from the National Science and Engineering Re-search Council, Canada. The authors are thankful toProf. R.K. Varma for the discussions they had with him.

REFERENCESA. A. Fouad and K.T. Khu, "Subsynchronous resonance Bonesin the IEEE benchmarkpower system",IEEE Trans . ,PAS, vol.97, no. 3, pp. 754-762,1978.A. Yan and Y.N. Yu, "Multi-mode stabilization of torsionaloscillations using output feedback excitation control", IEEE! hns . , P A S, vol. 101, no. 5, pp. 1245-1253, 1982.T.H. Putman and D.G. Ramey, "Theory of the modu-lated reactance solution fo r subsynchronousresonance",IEEE! h n s . , P A S , vol. 101, no. 6, pp. 1527-1535, 1982.


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242[4] 0 .Wasync.uk, Dam ping subsynchronous resonance using re-active power control, IEEE Trans . ,PAS, vol. 100, o. 3,pp .

1096-1103,1981.A.E. Hammad an d M. El-Sadek, Application of a thyristorcontrolled var comp ensato r for damp ing of sub synchronous os-cillations in power sy stem , IEEE Trans . ,PAS, vol. 103, o. 1,pp . 198-212,1984.N.G. Hingorani, A new scheme for subsynchronous esonancedamping of torsional oscillations and transient to rques-part 1IEEE Trans . ,PAS, vol. 100, no. 4, p. 1852-1855,1981.M.R. Iravani and R.M. Mat hur, Dampingof subsynchronousoscillations in power sy stem using a stati c phase-shifter, E E ET r ans . ,P W R S , vol. 1,no . 2,pp . 76-83, 1986.[8] C-J. Wu and Y-S. Lee, Application of simultaneou s activean d reactive power modulatio n of sup er conductiong magne ticenergy storage unit to damp turbine generator subsynchronousoscillations, IEEE Trans . ,EC, vol. 8, o. 1,pp . 63-70, 1993.C.D. Schauder and H. Meht a, Vector analysis and control ofadvanced static var compensators, IEE Proc.- C, vol. 140, o.

4, p. 299-306,1993.[lo] L. Gyugyi, Dynamic compensatio n of ac transmissionlines bysolid-state synch ronous voltage s o u r c e s , IEEE Trans .,P W R D ,vol. 9,no. 2,pp . 904-911,1994.[ll] C.W. Edwards P.R. Nannery K.E. Mattern E.J. Stacey andJ. Gubernick, Advance d sta tic var generator employing gtothyristors, IE E E ~ a n e . , P R D ,vol. 3, o. 4, p. 1622-1627,

1988.[12] EEE SSR Task Force, First benchmark model for computersimulation of subsy nchronous resona nce, IEEE Trans . ,PAS,vol. 96, o. 5,pp . 1565-1570,1977.[13]P. Kundur, Powe r Sys te m Stabi l ity and Control , McGraw-Hill,Inc., New York, 1994.[14]Y.N. Yu, E lect r ic P ow er Sys t em Dynamics , Academic Press,New York, 1983.[15] S. Svensson an d K. Mortensen, Damping of subsynch ronousoscillations by an hvd c link - an hvdc simulator study , IEEETrans . ,PAS, vol. 100, o. 3, p. 1431-1437,1981.[16] J.B.Ekanayake and N. enkins, A three-level advanced sta tic

var compensator, I E E E T r a n s . , P V R D , vol. 11, no. 1, pp .

[5]

[6]

[7]

[9]

540445,1996.APPENDIX

SYSTEM PARAMETERSBase MVA =892.4, Base kV =500

Rotor Spring Mass System [12]

HP-IPIP-LPA

LPA-LPBLPB-GENGEN-EXCGEN

0.1555890.858670.884210.8684950,0342165

19.30334.92952.03870.8582.822

Synchronous Generator [12]Xd ~ 1 . 7 9U Xi =0.169 PU Xi=0.135 PUX, 1.79 pu Xi =0.228 pu Xi =0.200 puTi0=4.3 s Ti0=0.032 s Ti0=0.85 sT;b=0.05 s XI =0.13 PU Ri ~ 0 . 0

I

Turbine and Governor 1121. 1141

F x p = 0 . 3 TCH 0 . 3 KG = 25F1p = 0.26 TRH~ 7 . 0 TSR=0.2 sFLPA =0.22 Tco =0.2 s TSM=0.3 sFLPB ~ 0 . 2 2

Exciter and Voltage Regulator [14]K A =200TA=0.02 sTE=0.002 s

EFD m a x =7.3EFDmin =-7.3

STATCOM Circuit and Controller [9]R,=0.01 pu X,=0.15 pu Rp =128 puC,=0.013 pu Tm=0.0024 s K ~ = 0 . 0 1

Initial Operating ConditionsGenerator real power =0.9 puInfinite bu s voltage =1 puGenerator terminal vo ltage,Et= l puSTATCOM bus voltage,E, =0.95 pu

Definition of Percent Compensation [ 5 ]x 100Compensation= xc0.14 +0.5 +0.06

where, 0.14 is the sending end transformer reactance, 0.5is the transmission line reactance, and 0.06 is the equiva-lent system reactance at infinite bus.

BIOGRAPHIESK.V. Pati1 received his M.Tech degree from the Indian Insti-

tu te of Technology (IIT ) Kanpur in 1991. From 1991-1995 e waswith Bhara t Heavy Electricals (BHEL), New Delhi. Currently heis working towards his Ph.D at the University of Western Ontario,London, Canada. His research intere sts are in t he are as of Controlsystems, and power system dynamics and Control.J. Senthil received the P h.D degree from IITKanpur in 1991.

&om 1992-1995 e was with BHEL, New Delhi. Curren tly he isemployed a s a post docto ral fellow in th e Electrical Eng ineering De-partme nt at th e University of Western Ontario, London, Canada .His research interests are in th e areas of Power System Dynamicsand Control.J . Jiang completedhis Ph.D in 1988 rom the Department ofElectrical Engineering, University of New Brunswick, Re der ict on,Canada. Currently he is a n Associate Professor in th e D epartmentof E lectrical Engineeringat the University of Western Ontario , Lon-don, Ca nada. His research interes ts are in the ar eas of control sys-tems, power system dynamicsand controls,andsignal processing.R.M. Mathur received the P h.D degree from th e Universityof Leeds in 1969. From 1969 o 1987 he w a s with the Departmentof Electrical Engin eering at the Unversity of Manitoba, Canada.Since July 1987 he is th e Dean, Faculty of Enginee ring Science atthe University of Western Ontario , London, Canada. His researchintere sts are in areas of Elect rical Machines and Power System s.Prof. Mathur is t he recipient of th e IEEE Centennial Medal, and isa Fellow of the Academy of Engineering, C anada.
http://wasync.uk/http://wasync.uk/http://wasync.uk/


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243Discussion

Z. Yao and V.Rajagopalan (Chaire de rechercheindustrielle Hydro-Qukbec-CRSNG, UniversitC duQuebec,Trois-Rivieres, Quebec, G9A 5H7, Canada) :

The authors have presented an interesting paper onapplication of STATCOM for damping torsionaloscillations in series compensated ac systems.However, this STATCOM is ihstalled at the terminal ofthe generator just for improving damping to torsionaloscillation. We would like to know how this can bejustified if an excitation clontrol can do the same job [l ].

Furthermore, the STATCOM controller design based onthe averaged model (see page 2) usually is not valid forstability analysis of the same system with a detailedrepresentation of STATCOM.

To explain this, we suppose the authors use a 12-pulseSPWM technique. Although this topology would encountersome other technical problems because of high switchingfrequency (12x60 = 720 Hz), we would like just to showthe problem of control performance.

Since the controller cannot do anything during thewidth of a pulse (see Fig. l), the STATCOM and the powersystem can be considered somehow discretized. Thesampling period is more than 1 millisecond.

Thus, a question is raised : how can this controllerwhich is designed based on a continuous model stabilize adiscrete system with a large sampling period ?

1

0-1 I .

1 1

0 0.002 0.004 0.006 0.008Time (s )

Fig.1 :Pulse generation for an SPWM inverter[l] A. Yan and Y. N. Yu, Multi-mode stabilization of

torsional oscillation using output feedback excitationcontrol, IEEE Trans. on PAS, Vol. 101, No . 6, 1982,pp . 1527-1535.

Manuscript received February 18, 1997

K.V.Pati1, J.Senthi1, J.Jiang and R.M. Mathur:The authors tha nk th e discussers for their interest in thispaper and their valuable questions and comments. Firstbench mark model is characterized by four unstable tor-sional modes which are excited because of four differentseries compensation levels as shown in Fig.2 of this paperor as given in [ 5 ] . The idea is then to design a unique con-troller which can damp out all these four unstable modes.In [2] suitability of the multiple signal outp ut feedback ex-citation control for multi-mode stabilization of torsionaloscillations is examined. However excitation controllermay not effectively damp all torsional modes for certainpower system configurations. For such situat ions differ-ent methods such as use of static var compensator [3,4,5],NGH scheme [6 ] ,static phase shifter [7],super conductingmagnetic energy storage [8]are discussed in the literature.Furthermore, in this paper it is shown that a STATCOMequipped with voltage controller alone is not sufficient todamp all modes (refer Table 11).The generator speed de-viation feedback along with STATCOM voltage controllernot only reduces the frequency of oscillations of the elec-trical mode, but also increases the damping (refer Table111), hus stabilizing all torsional modes at all critica l com-pensation levels.

Our past experience shows that as far as improvingdamping is concerned, the best location for any device em-ployed for such a purpose is the generator terminal [17,18].

The STATCOM is used t o regulate the bus voltage bycontrolling the instantaneous reactive power at the pointof connection. Th e STATCOM model is developed consid-ering the fact tha t t he instantaneous power at the ac- anddc-terminals of th e inverter is equal. We do not see whythe STATCOM controller designed based on this principleis not valid for stabil ity analysis of th e same system with adetailed representation of STATCOM. The approach fol-lowed in HVDC, SVC systems is similar. The controlleris designed based on continuous system model and tunedwhile performing simulator studies. Also in [9]experimen-tal results of the dynamic response of the instantaneousreact ive current controller of an ASVC are shown. Herethe controller was designed based on this same principle.[17] Nelson Martins, L.T.G. Lima, Determination of

Suitable Locations of PSS and SVC for DampingElectro-mechanical Oscillations in Large Power Sys-tems , Proc. of Power Indust ry Computer Applica-tion Conference, pp. 74-82, May 1989.

[18] M. Sainath Moorty, Generalized Design of Damp-ing Control, M.S. Thesis, The University of WesternOntario, April 1990.

Manuscript received September 23, 1997.

torsional oscillations in alternators1

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