00092947-damping of synchronous generator by static reactive power compensator with digital...

8/12/2019 00092947-Damping of Synchronous Generator by Static Reactive Power Compensator With Digital Controller

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Damping of synchronous generator by staticreactive power compensator with digital controllerC. J. WU, PhDY.-S. Lee, ME

Indexing terms: Generators, Control equipment and applications

Abstract: A static reactive power (VAr) com-pensator (SVC), constructed by fixed capacitors(FC) snd thyristor controlled reactors (TCRs), isdesigned and implemented to improve thedamping of the synchronous generator. A digitalpropotional-integral (PI) controller is synthesisedby the Motorola M68HCll single chip micro-processor board to modify the reactive powercompensation of the SVC from adjusting the con-duction angle of the thyristors. The SVC is placedat the generator bus terminal with the speed devi-ation (Am) as the feedback signal for the PI con-troller. The pole assignment method is used todetermine the gains of the PI controller. Resultsfrom digital simulation and the implementationtest show that the SVC with the PI controller cangreatly enhance the damping of the system oscil-lation caused by disturbances. Although the PIcontroller is designed at a special operation point,it can also provide a good damping effect at otheroperation conditions. The voltage profile of thegenerator is also improved by the SVC.

List of symbols= rotor speed= torque angle= conduction angle= d- and q-axis terminal voltage= generator terminal voltage and current= reference voltage for generator= d- and q-axis component of voltage behind= real power and reactive power= resistance and reactance= reactance of static reactive power com-= inductive susceptance of static reactive power= capacitive susceptance of static reactive= electrical torque= mechanical torque= per unit output voltage of the exciter= gains of the PI controller= constant matrices

transient reactance

pensatorcompensatorpower compensator

Paper 8148C Pl, PlO), first received 18th September 1990 and inrevised form 2nd April 1991The authon are with the Department of Electrical Engineering,National Taiwan Institute ofTechnology, 43 Keelung Road, Section 4,Taipei, Taiwan 10772, RepublicofChinaIEE PROCEEDINGS-C, Vol. 138, No. 5 , SE P T E M B E R 1991

M , DTwT, = sampling timeK,,&TLo,Tb0= d- and q-axis armature-winding transientK,, K , = thyristor gain and time constantSubscriptsd, q = d-axis, q-axis1 IntroductionStatic reactive power (VAr) compensators (SVCs), whichare constructed by thyristor controlled reactors (TCRs)and fixed capacitors (FCs), are finding a wide employ-ment in the power industry [I-23. Many applications ofthe SVC have been suggested in the literature, such asreactive power compensation for the arc furnace [3],reduction of transmission line loss [4], expansion of thetransfer capacity of transmission line [MI , stabilisingthe load bus voltage [7-91, and balancing the load buscurrent [lO-Il]. The SVC has also received great atten-tion in the damping of a power system [12-171. It canprovide a supplementary damping torque for the syn-chronous generator and increase the damping of systemoscillation. However, in the literature there are fewpapers with an implementation test report about thedamping effect of an SVC [15-17]. The dynamic per-formance of a radial distribution line is improved bythree SVCs in Reference 17. Only the study in Reference16 considers the damping effect on the generator, but thefrequency response approach design method used in thecase studied is too rough.Owing to the remarkable advances in electronic tech-niques, the microcomputers/microprocessors are alsoused in the power industry, such as digital relay [18], thedigital power system stabiliser [19], and the automaticmeter reading system [20]. If a digital controller is syn-thesised by a software program on the microprocessorboard, some advantages can be obtained. The controllercan be any type and the parameters of the controller canbe set at any value. Also the parameters of the controllerwill not drift due to the temperature effect. A micro-processor board will be used in this paper to construct adigital controller for the SVC.In this paper, a 5 kVA SVC test unit is installed in thelaboratory. The SVC is placed at the generator bus ter-minal. A digital proportional-integral (PI) controller issynthesised by the software program on a MotorolaM68HC11 single chip microprocessor board [22-231.With the speed deviation Ao)s the feedback signal, thePI controller can modify the reactive power output of the

427

=moment constant and damping coefficient=washout time constant of the PI controller= exciter gain and time constant

open-circuit time constant


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SVC and supply a damping torque to the synchronousgenerator. The gains of the PI controller are determinedusing the pole assignment method by placing the electro-mechanical mode at the prespecified position. Resultsfrom the digital simulation and implementation test showthat the SVC with the PI controller can greatly improvethe damping of the synchronous generator. Although thegains of the PI controller are designed at a special 0pe.r-ation point, it can also provide a good damping effect atother operation points. In the dynamic period, thevoltage profile at the generator bus terminal is alsoimproved because the SVC can provide a reactive powermodulation to the system.

2 Problem formulationThe system considered in this paper can be described bythe diagram as shown in Fig. 1, where a synchronousgenerator is connected to the infinite bus through thetransmission line with a load placed at that bus. The syn-generator transmission in fi ni te

mFig. 1ator bus renniMlSingle machine infinite bus system with SVC placed at gener-

chronous generator is a salient pole type with damperwinding on the rotor shaft and driven by a large DCmotor . An SVC is placed at the generator bus terminal toincrease the system damping. The field current of the syn-chronous generator is supplied by a static exciter with theblock diagram as shown in Fig. 2. Electric power isdelivered from the generator t o the load through a trans-mission line. All the system data are given in Appendix 8.

ref I - Ve I K O I Efd -I 1 t sT,Fig. 2 Static exciter

The dynamic behaviour of the generator can bedescribed by the two axis model [ 21 ] . All the nonlineardifferential equations are(1)( 2 )(3)(4)5 )

15= T, DO - T J / Ms = Ob W )E f d = [ - E f d Ko ( f vI/K

= [ - E : - X , - X b ) I J / T ~ .pq = [E/d - Eq + x d - X&) Id] /T; ,

where= EdId + E; I - X h- Xd)IdIg

t:= ( V i + V yv = E:, - R , I d - X b I ,V = E : - R , I , + XLId

428

The SVC is designed and implemented to support thereactive power compensation. The SVC s constructed by12-pulse thyristor controlled reactors (TCRs) and fixedcapacitors (FCs) as shown in Fig. 3.The TCR is con-

compensated busI v I'i nductor apacitor

control systemFig. 3

TCR FCOne line diagramof SVC with T C R s and FCs

nected to the compensated bus through a triple windingstransformer. The conducting of the reactors is controlledby the thyristor with continuous symmetric firing signals,such that the TCR with the FC can provide a continuousamount of reactive power compensation to the powersystem. The equivalent susceptance of the reactor can beobtained from the fundamental component of the currentpassing through the reactor in each phase [ I ] The rela-tion between the equivalent susceptance BL of the reactorand the conduction anglea f the thyristor sa - in aBL(a)= ___nXL

where X , is the physical reactance of the reactor.3 Design of PI contro ller using pole assignmentmethodA PI controller is used to control the compensation valueof the TCR as shown in Fig. 4.The nonlinearity in eqn. 6is removed by a linearised circuit [I], and the TCR canbe represented by a simple transfer function. To deter-mine the gains of the PI controller, all the nonlinear dif-ferential equations are linearised at the initial operationpoint. The linear system state equations are

X ( t ) = A X ( t ) + BU( t ) (7)Y ( t )= C X ( t ) 8)

Fig. 4 Transferfunction representationof S V Cwhere X = [Am, A A E f d ,A , AE;, ABL]' is the statevector, U = AKm is the control signal, Y = Am is theoutput signal, and A, B, C are constant matrices. Becausethe sampling period of the microprocessor is only 1ms,which is very small compared to the low frequency oscil-lation period [ 21 ] , we can directly design the digital PIcontroller on the s-plane.Taking the Laplace transform of eqns. 7 and 8, we get

sX( s ) = A X ( s )+ BU(s)Y ( s )= C X ( s )

(9)

C(SI- A ) - ' B U ( s ) (10)IEE PROCEEDINGS-C, Vol. 138 No. 5 SE P T E M B E R 1991

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Also the control signal from the PI controller can be r e presented by a set of three phase transmission line, load boxes, a speedencoder, AID and D/A convertors, and a digital PI con-troller which is synthesised by the M68HCll micro-processor board.( s )= H(s)Y(s)

1 +sT,It is easy to see that the characteristic equation of theclosed loop system is [24]

1 - C(s l - A) - 'BH( s) = 0 (12)If1 s the system eigenvalue to be assigned, we have

(13)Assume that the value of T, is given, we need to assign apair of eigenvalues to obtain the values of K, and K .Because the behaviour of the generator is dominantlyrepresented by the electromechanical mode, we mustassign this mode at the prespecified position. Let 1 and1, be the pair of eigenvalues of electromechanical modeto be assigned, we can get two linear algebra equationsfrom eqn. 13 with two unknowns K, and K, By solvingthis pair of algebra equations, we can obtain the desiredgains of the PI controller.

At the initial operation point P = 0.8 and Q = 0.6 P.u.,we arbitrarily assign the eigenvalues of the electro-mechanical mode atI 1 = -4.1 + 26

The gains of the PI controller are calculated.K = 5.5K , = 64.5

Table 1 shows the eigenvalues of the system with andwithout SVC. It is observed that the electromechanicalmode of the system with SVC is exactly at the prespeci-fied position. The damping of the synchronous generatoris greatly improved by the SVC. To examine the dampingeffect of the SVC when the load condition is changed, theelectromechanical mode at different operation points isshown in Table 2. It is known that the SVC can alsoimprove the system damping at other operation points.Table 1:Svstem eigenvaluesItems With out SVC With SVC

~ ~

A -1 9.87 +/70.41 -1 9.88 +/70.89A -1.67*j26. 19* -4.1 +j26.0*A -1 1.7 -11.6AS , -97.89 +j25.9* Electromechanical modeTable 2: Electromechanical mode at d i f fe rent opera t ionooints

~

Operation point Witho ut SVC With SVCP = 1 . 2 , 0 = 0 . 8 -1.549tj26.841 -2.78tj26.0P =OB, = 0 . 6 -1.673tj 26.193 -4.1 +j26.0P =0.5. 0 ~ 0 . 2 2.896+;25.631 -5.3+i25.614 5 kVA test unitThe generator system diagram is shown in Fig. 5andconsists of a 5 kVA synchronous generator, a set of SVCswhich are constructed by TCRs and FCs, a static exciter,IEE PROCEEDINGS-C, Vol. 138, No. 5 S E P T E M B E R 1991

primemachi ne

encoder+ . I I > > Iq M 6 8 H C 1 1 E load\svc

Fig. 5 5 k V A test unit4.1 Microprocessor boardThe Motorola M68HCll is an HCMOS single chipmicroprocessor board and is suitable for the applicationof real time control. With the diagram shown in Fig. 6,the organisation data of the microprocessor board are asfollows.

M68CH11

Fig. 6 Block diagram o f M 6 8 H C l I microprocessor boardhardware:

a) 12k bytes ROM(b) 512 bytes EPROMc) 512 bytes RAM(d) 8 bits impulse arithmetic unite) 8 bits A/D convertor and data channelf) eal time interrupt request(g) enhanced 16 bits timea) enhanced M6800/M6811 instruction setb) 16 x 16 integer and fraction divisionc) with bit operation(d) with wait modee) with stop mode

4.2 Digital PI controllerThe digital PI controller is synthesised by the softwareprogram on the microprocessor board, with the speeddeviation as the input signal.The speed error signal is

software:

e ( t )=O(t)- a (14)where w is the rating synchronous speed and o ( t ) is thefeedback rotor speed. The input signal to the micro-429


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0 002 0 002-2a a. 0001 =- 0 001-0 9s o 0 -0v vu(1I

U-0001 0 001-VI

- 0 002 - 0 0 0 2

processor is the sampled error signal time series e kT),k = 0, 1, 2, .. , where k is the sampling instant and T isthe sample period. Let the output control signal of themicroprocessor be u(kT).Consider that the microprocessor wants to performthe digital computation of the PI controller. The controlsignal at the continuous time domain isu(t) = K,e( t ) + K , d t 15)

The integration term in the last equation is written asZ ( t )= [d~)WJ dr + Z ( t J (16)1:

We can use the trapezoidal integration rule here. At thetime interval [ k - 1)T, k q , the definite integration ineqn. 16 is approximated byrT d t ) -o d t( k - I ) T

E T / 2 [ o ( k T )+ o [ ( k - 1)77] w,T (17)Then the discrete time domain representation of eqn. 16is

ZC(k + 1)77 = T/2Co kT) oC(k - 11771+ Z ( k T )- w,T (18)The discrete version of u(t) is written as

u[ (k + 1)T] = K , [ d k T ) - WJ + K , Z [ ( k + 1)T] 19)4.3 12-Pulse TCRTo reduce the harmonic current caused by the TCR, theconnection type of the TCR must be well arranged. Theconduction angle of the thyristor in each phase issymmetric to cancel all the even harmonic currents. The

LI

, , , , . , ,

reactors are divided into two separate groups, each groupof reactor is a TCR. The A connection type of the reac-tors in each group can let all the triplen harmonics beabsent from the line current. The TCRs are connected tothe compensated bus through a triple windingsY - Y/ Y - A connection transformer. There is a 30phase shift between the voltages and currents of the twoTCRs, and the 5th and 7th haronic currents are elimi-nated from the primary-side line current.

0 002 0 002QC. o o o l 4 0 0 0 1 ~

; o c (r

P

c9

0I 0:0 001 g - 0 001-0VI

-0 0020 002

5 Digital simulation and implementation testresultsTo demonstrate the damping effect of the SVC, digitalsimulation and implementation test results of the systemwith and without SVC are compared at three differentoperation points. The simulations are taken on an IBMPC/AT using a fourth-order Runge-Kutta routine [26].The step size is 1 ms. In the experiment procedures, thegenerator is first brought up to the synchronous speed bya DC motor, and the terminal voltage is raised to therated voltage by an appropriate exciter output voltage.Step load change is made by changing the equivalentadmittance of the load box.The dynamic behaviour of the synchronous generatoris examined by a 0.2 p.u. load change at three differentoperation points. Figs. 7, 8 and 9 show the rotor speeddynamic responses of the digital simulation at the oper-ation point (P = 1.2, Q =OX , (P = 0.8, Q = 0.6) and(P = 0.5, Q = 0.2), respectively. The settling time xdefined by A d t ) < O.ooOo5 p.u. for t > T of the systemoscillations with and without SVC is compared in Table3. It is observed that the SVC can greatly improve thedamping of the synchronous generator. Figs. 10, 11, and12 show the speed dynamic responses of the implementa-tion test at three operation points. The system settling

I A+-\

t i m e , saFig. 7(I Without SVC b Wi t h S V C

Dynamic response o simulation results at P = 1.2 and Q = 0.8t i m e , s

b

t i m e , sa

Fig. 8II Without SVC

Dynmnic response of simulation result at P = 0.8 and Q = 0.6b With SVC

t i m e , sb

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0 1 2 3 Ltime, sa

Fig.9LI Without SVC

Dynamic response ofsimulation result at P = 03 and Q = 0 3b With SVC

73

0 1 2 3 L

0001.C0:-0001-2- 0 0 0 2

time, sb

I c 0001-

g 0-0 L: 0oG-l-0

U

VI

-0 002, ' . . . , . .

0 002 0 0023

3

c 0 001-9

1. 0 001.. -

2 00-Ug -0001- ;0 001-VI

1 1 20 2 3-0 002time. s time. s

-0002 . . . . , 'a b

Fig.10a Without SVC

Dynamic response of Implementation test result at P = 1 2 and Q = 0 8b Wllh SVC

0 002 I 00021

0 1 2 3 Latime, s

Fig. 12a Without SVCIEE PROCEEDINGS-C, Vol. 138 No. 5, SEPTEMBER 1991

Dynamic response ofimplemen tation test result at Pb With SVC

0 001

0-

-0 001-t-0002* . , ,

0 1 2 3time. sb

= 0 3 and Q = 0.2

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Table3: Set t l ing t ime of the rotor speed deviat ion(simulat ion)Operation Settling time s)point Without SVC With SVC

1 08- 1 08-3a 1 OL- ;06 :. I00-- $ 1 00-

: 84-- 0 9 6 - = 0 96-> 0 92- 1 0 2-

F 0 88-E -84-0807 . . . . . . . 0 8 0 i

0- 0 .p o 88: -

P = 1.2. Q = 0.8 3.75 1.45P = 0.8, Q = 0.6 2.05 1 oP = 0.5, 0 0.2 1.25 0.75

9 I . . I . .

Table 4: Set t l ing t ime of rotor speed deviat ion (imple-mentat ion test)Operation Settling time (s)

108 -a 104 -3g 100:-0 0 9 6- 0 9 2 -

0 88-> -0 .

0 EL0807

point Without SVC With SVC

. . . . . . .

P = 1.2. a = 0.8 3.25 1.75P = 0.8, = 0.6 1.75 1.1P = 0.5, Q = 0.2 1.3 0.8

1 08.a1 0 4 .3 .g 1 00:

096.- 0 92-> -

0 88-0 84.080 -

time is also compared in Table 4. Figs. 13, 14 and 15show the terminal voltage responses of the implementa-tion test at three operation points.

. . . . . . .

Several observations are obtained.(a)Both in the digital simulation and in the implemen-tation test, the SVC can provide a supplementarydamping torque for synchronous generator and improvethe system dynamic behaviour.(b) From Figs. 13-15, the voltage profile of the gener-ation is improved by the SVC.c ) Although the PI controller is designed at a specialoperation point, it can also provide good damping effectat other operation points.

0 92-- 0 88-cE3 0 8 4

6 ConclusionAn SVC is designed and implemented in this paper toimprove the damping of a synchronous generator. Thepole assignment method is used to determine the gains ofthe PI controller by placing the electromechanical modeat the prespecified position. The PI controller is simple instructure and easy to synthesise by the software programon a Motorola M68HCll single chip microprocessorboard. Digital simulation and implementation test resultsshown that the SVC with the PI controller can greatly

Fig. 14o Without SVC

Voltage profile ofimplementation test result at P = 0.8 and Q = 0.6b With SVC

0 8 4;;8 0 time. sb

Fig. 15(1 Without SVC432

Voltag e profile ofimplementation test result at P = 0.5 and Q = 0.2b With SVC

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enhance the system damping. Although the PI controlleris designed at a special operation point, it can alsoprovide a good damping effect at other operation condi-tions.The studied system in this paper is a single machinepower system. By the modal control theory [24], The PIcontroller can provide two degrees of freedom. The elec-tromechanical mode can be assigned at an arbitrary posi-tion by the PI controller. If more modes are to becontrolled, another PI controllers with different feedbacksignals such as current and electric power are needed. Ina multimachine power system, many SVCs may beneeded. Co-ordination tuning of the controllers of SVCsmust be done such that all the synchronous machines inthe system have good damping.7 References

1 MILLER, T.J.E.: Reactive power control in electric system (JohnWiley Sons, 1982)2 IEEE Var management working group report.: Bibliography onreactive power and voltage control, IEEE Trans., 1987, PWRS2,pp. 361-3703 COX, M.D., and MIRBOD, A.: A new static Var compensator foran a rc furnace,IEEE Trans., 1986, PWRS-1, (3). pp. lCL1204 LIN, C.E., CHEN, T.C., qnd HUANG, C.L.: Optimal control of astatic Var compensator for minimization of line loss, Electr. PowerSyst. Res., 1988, 15 pp. 5 1 4 15 BYERLY, R.T., POZNANISK, D.T., and TAYLOR, E.R.: Staticreactive compensat ion for power transmission systems, IEEETrans., 1982, PAS-101, pp. 3997-56 CHOI, S.S. STEWART, J.R., SINGH, B., CARRINGTON, P.F.,GODDARD, E.M., and CARTER, C.E.: Performance esting of along distance radial static Var compensated transmission systemand validation of simulation results, IEEE Trans., 1988, PWRS3,pp. 1509-15717 CHENG, SJ., MALIK, O.P., and HOPE, G.S.: An expert systemfor voltage and reactive power control of a power system, IEEETrans., 1988, PWRS 4, pp. 1449-14558 PAZIUK, L.A., CHIKHANI, A.Y., and HACKAM, R.: An expertmicroprocessor controlled voltage regulator for energy conservationand demand deduction in distribution feeders, IEEE Trans., 1989,PWRD4, pp. 2222-22289 HAMMAD, A.E., and EI-SADEK, M.Z.: Prevention of transientvoltage instabilities due to induction motor loads by static var wm-pensators, IEEE Trans., 1989, PWRS4, pp. 1182-119010 GYUGYI, L., OTTO, R.A., and PUTMAN, T.H.: Principles andapplication of static th yristo rantr olled shunt compensators, IEEETrans . , 1978, PAS-97, pp. 19351945GUETH, G., ENSTEDT, P., REY, A., and WENZIES, R.W.: Indi-vidual phase control of a static compensator for load compensationand voltage balancing and regulation, IEEE Trans., 1987, PWRS2,pp. 898-90512 OBRIEN, M., and LEDWICH, G.: Static reactive-power com-pensator con trols for improved system stability, IEE Proc. C, 1987,134, pp. 38-4213 PIERRE, D.A.: Nonl inear Var control for damping multivariab leswing equations, IEEE Trans., 1988, PWRS-3, pp. 1033103814 OBRIEN, M., and LEDWICH, G.: Placement of static com-pensators for stability improvement, IEE Proc. C, 1985, 132, pp.3 3515 GERIN-LAJOIE, L., SCO m, G., BREAULT, S., LARSEN, E.V.,BAKER, D.H., and IMECE, A.F.: Hydro-Quebec multiple SVCapplication control stability study, IEEE Trans., 1990, PWRD-S,pp. 1543-155116 SAWA, T., SHIRAI, Y., MICHIGAMI, T., SAKANAKA, Y., andUEMURA, Y.: A field test of power swing damping by static Varcompensator, IEEE Trans., 1989, PWRS 4, pp. 1115-1120

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17 RAMOS, A.J.P., and TYLL, H.: Dynamic performance of a radialweak power system with multiple static Var compensator. Paper 89WM 183-5 PWRS, presented at the IEEE/PES 1989 Wintermeeting New York18 OHURA, Y., et al . : A digital distance relay using negative sequencecurrent, IEEE Trans., 1990 PWRDS, pp. 79-8419 MALIK, O.P., HOPE , G.S., CHENG, S.J., and HANNCOCK, G.:A multi-micro-computer based dual-rate self-tuning power systemstabilizer: Paper 86 JPGC 652-2, presented at the IEEE/PES 1986Joint Power Generation C o d , Orgon20 LANCASTER, J.T., WEBB, M.R., MYERS, J.A., and PRIEST,K.W.: Semi-automatic meter reading, I E E E T r m . , 1987,PWRD-2, pp. 6 7 1 4 7 721 ANDERSON, P.M., and FOUAD, A.A.: Power system control andstability Iowa State University Press, Am-, Iowa, 1977)22 LIPOVSKI, G.J.: Single and multiple chip microcomputer inter-facing (Prentice-Hall, 1988)23 MOTOROLA: M68HCll evaluation module users manual(Motorola Inc., 1988)24 KAILATH, T.: Linear systems (Pnntice-Hall, 1980)25 IEEE: IEEE standard proadum for obtaining synchronousmachine parameters by standstill frequency responses testing. IE EEStandard 115A. 198726 CARNAHAN, B., LUTHER, H.A., and WILKES, J.O.: Appliednumerical methods (Wiley, 1969)

8 Appendix: system dataThe followung data of the synchornous generator aregivenrated kVA = 5 kVArated voltage = 220 V, Y onnectionexcitation voltage = 45 Vstator current = 13.5 Afield current = 3 Apower factor = 0.9 laggingrated speed = 1800 RPMpole number = 4The parameters of the synchronous generator can beestimated by the IEEE 115 A standard test procedures[25]. All the system data are as follows:Generator (P.u.)

X,= 2.3 P.U.

Td,= 0.26 s

x 2.1 p.u.

Tio= 0.21 sXd= 0.421 P.U. Xq= 0.421 P.U.

M = 1.48 s D = 0.12 P.U.R , = 0.04727 p.u. ob 371 radJsec

Exciter PA)K , = 175 T.= 0.04 s

Transmission line (P.u.Re = 0.02 P.U. X , = 0.4 P.U.

Initial operation point (PA)P = 0.8 Q = 0.6 & = 1svcT = 1 ms T , = 1 ms K, =2 5

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00092947-damping of synchronous generator by static reactive power compensator with digital...

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