a new optimal avr parameter tuning method

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A New Optimal AVR Parameter Tuning Methodusing On-line Performance Indices of

requency domain

Joong-Moon Kim, Studenl Member, IEEE, Seung-11 Moon, Member, IEEE and Jonghoon Lee,Student Member, IEEE

Abstract-- AVR parameter tuning for voltage control of powersystem generators has generally been done with the “off-lineopen-circuit model” of the synchronous generator. When thegenerator is connected on-line and operating at rated loadconditions, the AVR operates in an entirely different environmentfrom the open-circuit conditions. This paper describes a newmethod for AVR parameter tuning for on-line conditions usingparameter optimization technique with frequency responsecharacteristics of linearized “on-line” system model.

As the proposed method uses the online system model, thetuned parameters show the optimal behavior in the on-lineoperating conditions. Furthermore, as this method considers theperformance indices that are needed for stable operation asconstraints, the performance of the tuned parameter guaranteesthe stable operation.

Index Terms Excitation System, Parameter Tuning,Automatic Voltage Regulators, Parameter Optimization,Linearized model

I. INTRODUCTION

c ONTROL parameters of the excitation system greatlyaffect the power system dynamic response and stability.For the proper tuning of these parameters, analytical methodusing frequency response techniques on the open-loopexcitation control system with generator off-line have beenwidely utilized [1,2]. Since the AVR operates in an entirelydifferent control environment when the generator operated inon-line condition, the parameter set that is tuned by using theoff-line model may not give the optimal performances in on-line conditions.

A frequency domain technique, using on-line generatormodel obtained from the detailed transient stability program,for the parameter tuning of AVR has been introduced [3].Although this method intends to improve the terminal voltageresponse with on-line operating condition, it can not yield theparameter set for optimal performance at various operatingconditions. Many researches to improve the performance of

voltage control characteristics of the AVR using additionalcompensators such as pole-zero canceling compensator andG.T.F.Regenerator Transfer Function Regulator) have beenperformed [3,4,5]. In spite of the improvements, thesemethods do not easily applicable to the already installedconventional AVRS.

In this paper, a new AVR parameter tuning method usingparameter optimization technique with the frequency responseof linearized on-line power system model is presented.Parameter optimization technique inherently reduces theefforts to performing tradeoffs between the performanceimprovements and the stability. In addition, since this methodneeds no additional compensator, the optimal parameters ofconventional AVRS are readily obtained at the variousoperating conditions. Relationships between the performanceindices of the frequency domain and the on-line time domainperformance are described. Object functions to acquire theparameter set that produce the fast and stable responses atvarious operating conditions are also proposed, Case studiesperformed with two basic types of exciter models at different

loading conditions, to verify the performance of proposedtuning method.

II. LINEARIZEDON-LINESYSTEMMODEL

Fig. 1, shows the overall system configuration that is usedfor parameter tuning.

o-

Fig. 1. Overall system configuration

1----

7;

Large ~system ~

L----------

Joong-MoonKimk with Seoul National Uni versity, Kwanak-gu, Shinlim-dong, Seoul 151-742, South Korea (e-mail: blues kilm@koreamail. conl).

Seung-11 Moon is with Seoul National Universi ty, Kwanak-gu, Shinlim-dong, Seoul 151-742, South Korea (e-mail: simoon@plaza,snu.a c.kr).

Jonghoon Lee is with Seoul National University, Kwanak-gu, Shinlim-dong, Seoul 151-742, South Korea (e-mail: ljoho@powerlab. snu.ac.kr).

Based on Park’s equations, generator model whichincorporates one d-axis amortisseur and two q-axisamortisseurs is used in the system model. The system dynamicequations including swing, generator, transmission line and

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load are linearized and arranged in state-space form [6].

Ah A zr al I al2 13 ’14 ’15 a16 bOAS A; 11

‘21°0000 00

A ~ fd _ “31 ’32 AI fda33 ’34 ’35 “36[1

ATM0 ’32

(1)@id a41 AY,d’42 ’43 a44 ’45 ’46 + 00 AEFDA@,q “5I ’52 a53 a54 ’55 “56 Av,q 00

A@2q _a61 ’62 a63 ’64 a65 a66_ @2q .0 0-

‘t= ‘5A6 ‘6Avfd + ’61A ‘ld + ‘62,A ‘lq + K63A v2q (2)

In the above equations, ATMrepresents the prime mover

torque variation and AEFDrepresents the excitation voltage

variation due to AVR action. In this paper, the variation ofmechanical input torque ATMis neglected. Detailed equations

for the coefficients in the above equation are given in [6].The complete state equations could be obtained by

compounding above state equation and state equation ofexcitation system, which is discussed in the next section, andcould be converted into the transfer-function form @E,/ AVref

to facilitate frequency-response analysis.

III. LINEARIZED EXCITATION MODEL

In this paper, IEEE ST2A excitation system is used toverify the proposed tuning method. The block diagram of theST2A exc;at~on system is-shown in Fig. 2 [7].

By combining the above equation (3) with (l)-(2), thecomplete system dynamic equation is obtained.

IV. RELATIONSHIPSETWEENTHECHARACTERISTICSFTHEFREQUENCY-DOMAINNDTHEON-LINEPERFORMANCES

When the generator is open-circuited, relative stability of aexcitation control system is measured in terms of the gainmargin and phase margin, and the crossover frequency Uc is

indicative of the speed of the transient response of the system[1]. When the synchronous machine is connected to the powersystem, the system performances are greatly influenced by itsoperating level and the parameters of the external system [8].So in order to verify the relationships between thecharacteristics of frequency-domain and on-line performancewith generator on-line condition, various case studies havebeen performed with different type of excitation systems atwide operating range. As an example, the relationships of bothcharacteristics with IEEE ST2A type exciter at three differentoperating conditions are shown in Fig. 3. Generator andexciter parameters and operating conditions used in this

example are given in Table. I.

TABLE. L SYSTEMPARAMETERS

Generator parametersT’ T“o T’ T“ H K,,

5:; 0.05 1;; 0.;5 3.5 0.0,,L, L:, L; i, L: ‘“ L,

1.8 0.27 0.198 1.728 0.45 0.09

5 v..“ E

f

;

na.”

K v 41+ sT,

11 ‘x STv.

v, o-V“.,.

KsKI 1 sT,

.I,. . v, IN F,x .

f[I.] PF,. Fig. 2. IEEE ST2AFeedb ?ck type Excitation System

Rate-

This excitation system utilizes the rate feedback loop toprovide excitation control loop damping. Detailed descriptionof this excitation system model is described in [7].

A V,

I

A ,. =

A V,.

[ ~ETr ~J”, T, j L ‘

Linearized state-space form equation of this excitationsystem is given in (3). For the purpose of linear analysis, theproduct point on the main control path is changed by the gainVB, which is calculated by operating condition.

Exciter parametersK, TA KE T. T, K,,

120.0 0.15 1.0 0.5 0.0 1.19K, K, T,.

2.5 0.5 1.0Operating Conditions El=1.0

~ Q, R. x, c

Case 1 0.15 0.06 0.158 0.673 7.2Case 2 0.3 0.12 0.158 0.673 23.1Case 3 0.5 0.2 0.158 0.673 41.6

where, R& +jX& - thevenin’s equivalent impedance of

transmission system

d - power angle of the generator

As shown in the Fig. 3-a, the crossover frequency OC is

st ill the indicative of the speed of the transient response, whenthe generator is connected to the power system. It is clear thatthe large crossover frequency is indicative of the fast rise timeat all operating conditions. In addition, as shown in the Fig. 3-b, and Fig. 3-c, phase margin and gain margin are also themeasures of relative stability at the generator on-lineconditions. It should be noted that simultaneous optimizationof all performance indices is not possible. As shown in the Fig3-c, high phase margin and high gain margin for the stableoperation are not compatible with large crossover frequencyfor fast response.

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OIcrad/see] a)

45 50 55 60 65 70

Phase Margin[degree] b)

1,5 20 25 3’0 3’5

Q, [rad/see] c)

Fig. 3. Relationships between the characteristics of frequency domain and time domain

Fast excitation response to terminal voltage variations isrequired for improvement of transient stability [6]. For the fastexcitation response, the crossover frequency should be high.Although the high crossover frequency makes the system

response fast, it leads to reduce the phase margin and gainmargin of the frequency response. Consequently, it reclucesthe damping of system oscillations. Therefore, thecompromise between the fast excitation response and the well-damped response is needed for stable operations.

V. OBJECTFUNCTIONANDOPTIMIZATIONECHNIQUE

In this paper, constrained optimizatic,n technique is used tosolve the compromise problem and Sequential QuachaticProgramming(SQP) method is used to solve the constrainedoptimization problem [9, 10]. In this method, an approximationis made of the Hessian of the Lagrangian function using a

quasi-Newton updating method and ~~ QP sub-problem issolved at each iteration. This is then used to generate a QPsub-problem whose solution is used to form a search directionfor a line search procedure. Detailed description of the routineis given in [9,10,1 1].

Object function and constraints that are used in theproposed method is shown below (4).

Maximize (coC+ WXPM) of on-line system model (4-1)

Subject to P.M of off-line system model 2 40” (4-2)G.M of off-line system model >6 dB (4-3)P.M of on-line system model > 65” (4-4)

where, w - the weighting value of the phase margin

High crossover frequency for fast response can beinherently obtained from this object ftmction because of thenature of optimization technique. To solve the comprc)miseproblem between fast response and stable response, phasemargin with proper weighting value is also included in theobject function. To guarantee the stable operation of obtainedparameter set, at the generator off-line commissioning phase,minimum phase margin and gain margin of the off-line model

are considered as constraints (4-2) and (4-3) [1]. In addition,to guarantee the stable operation at the generator on-linecondition, the minimum phase margin of the on-line model isalso considered as constraints. From the various case studies,

65” of phase margin of on-line system model guarantees thewell-damped stable operation. When the load-angle is so large,the constraint (4-4) for the well-damped stable operation is notsatisfied any longer. Therefore, at these large load-angleconditions, system response shows so oscillatory responsebecause of the lack of damping torque [6,8]. An effective wayto solve this problem is to provide a power system stabilizer.

Both phase margin and gain margin can be used in theobject function to solve the compromise problem. However,gain margin has an adverse characteristic that is not applicableto the optimization technique. Gain margin has thecharacteristic of monotonously increase as increase of someparameters, for example the excitation control systemstabilizer gain KF. So very large values of parameter sets, that

are not applicable in the real exciter, may be obtained whenthe gain margin is considered in the object function, Therefore,it is more reasonable to use the phase margin in the objectfunction.

The numerical value of phase margin is much higher thanthe numerical value of the crossover frequency as shown inFig. 3. So the normalizing factor to reduce the numerical valueof phase margin to the reasonable range must be considered inthe object function. In addition, excitation control systemresponse shows more oscillatory response caused by lack ofdamping torque as the load-angle is increased. Therefore, tosatisfy the stable operation (4-4), more value of phase marginis needed as the load-angle is increased.

Unfortunately, the system response and performanceindices used in the object function are affected by manyfactors, such as system configuration, load-angle and excitertype, etc. Consequently, it is hard to determine the properweighting value analytically. Therefore, to determine thesuitable weighting value of phase margin for the differentoperating conditions, various case studies have beenperformed with different types of excitation system at wide

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operating range. Resulting suggested values of two basic typeof excitation systems are summarized in the table. II.

TABLE, II SOGGESTEDWEIGHTINGVALUES FOR PROPERTONING

Weighting valueLoad-angle

(Rate feedback) LOa’ @ ssF

ITABLE, V, PERFORMANCElNLXCESOFBOTHPARAMETERSET 6 = 13,7° )

ITuning Over Rise SettlingMethod

parametershoot Time Time Syo)

‘reposed 8.7 0.71 2.9Method K, = 0.056 0/0 see] [see]malytical 8.9 0.79 3.1Method K, =0 .067 ‘ 0 [see] see]

I 0°-200 I 0.1-0.2 II 0°-500 \ 0.1-0.2 I

I 20°-50° ] 0,2- 0.3 II 50°-60” I 0.2- 0.3 I

50°-60° 0.3- 0.5II 600-65~J

VI. CASE STUDY

The case study with ST2A exciter with two differentoperating conditions has been performed to verify theperformance of proposed tuning method. Block diagram of

ST2A exciter is shown in Fig. 2. In thlls case, the gain ‘A isassumed unadjustable to provide the good steady state

performance and the excitation system stabilizer time constantT,

is also found to be untunable at 1 sec. Generatorparameters and Exciter parameters usedl in this case study aregiven in Table, L Table, HI and Table [V show the operating

2Q

Ur

1.035

1.030

1.025

1.020

1.015

1,010

1.005

1.000

0 2 4 6 8 Inconditions that are used in this case study.

time see)

TABLE. III. OPERATINGCONDITION

Operating Conditions< Q, E, R, XE J 0.210

0,2 0.06 1.0 0.210 0.603 13.7” h

TABLE. lY. OPER,ATINGONDITION0.205-Operating Conditions

~ Q, 8 L x, 6 .,

0.5 0.1 1.0 0.158 0.673 45.3”

~ 0.200–~

As shown in the Table. III and Table, IV, the load-angles of ~~

each case are 13.70 and 45.30 respectively. Therefore, theweighting values of the phase margin are chosen to 0.15 and0.3 to prevent the excessive crossover frequency. The o.195- 1 ;

parameter that is tuned by analytical method using off-line

- : r

--------- Analytical methodmodel is KF = 0.067 [2]. To verify the performance .:

improvement of parameter set that is tuned by proposed I,.–- 1

0.190 I I 1 I Imethod, time-domain simulation is performed on both o 2 4 6 i3 10parameters using the reaI-time simulator [12]. Test signal, time see)which is used in the simulation, is the 3°/0 step change of theAVR reference value at 0.5 sec. Simulation results are given Fig.4. Simulationesults(3 stepchangein V,e, , d = 1 3.7” )

in Table. V, Table. VI, Fig. 4 and Fig. 5.

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TABLE. V1. PERFORMANCEINDICESOFBOTHPAILAMETERSET J = 45.3°

m=]

a 2 4 6 8 10t ime see)

o 2 4 6 8 10t ime see)

Fig. 5. Simulation results (3 step change in V,C~ ~ = 45.3° )

As shown in the Table. V, Table. VI, Fig. 4 and Fig. 5, theparameters that are tuned by proposed method show moreoptimal responses than the parameter that is tuned byconventional analytical method. The system responses c)f thetuned parameters increase the performance of the terminalvoltage response and maintain the well-damped performanceof the electrical torque. They show smaller overshoot, rise

time and settling time than the response of the parameter thatis tuned by analytical method. They also show some moreoscillatory but well-damped response of electrical torque.

VII. CONCLUSIONS

This paper presents an AVR parameter tuning method usingoptimization technique with frequency responses of on-linesystem model. The proposed tuning method find the optimal

parameters that maximize the object function in order toimprove the voltage response at on-line conditions and satisfythe constraints in order to guarantee the stable operation ofboth the generator on-line conditions and the generator off-line conditions. So the efforts for performing tradeoffsbetween fast response and stable operation are greatly reduced.In addition, as the proposed method uses the on-line systemmodel, the parameters tuned by this method show moreoptimal responses than tuned by traditional method using off-line model at the operating condition.

Since this method needs no additional compensators, theoptimal parameter sets of conventional AVRS are readilyobtained at the various operating conditions.

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

VIII. REFERENCES

IEEE Guide for Ident ification, Testing, and Evaluation of the DynamicPerformance ojExcitation Control Systems, IEEE Std. 421.2-1990.Rodolfo J. Koessler, “Techniques for tuning excitation systemparameters,” IEEE Trarw Energy Conversion, vol. 3, No. 4, pp.785-791,December 1988.K. Bollinger, R, Lalonde, “Tuning Synchronous Generator VoltageRegulators Using On-line Generator Models,” IEEE Trans. PowerApparatus and Systems, Vol. PAS-96, No. 1,pp. 32-37, Jan/Feb 1977.Raczkowski, C., “Complex Root Compensator – A New Concept ForDynamic Stability hmprovernent,” IEEE Trans. Power Apparatus and

Systems, Vol. PAS-93, No. 6, pp. 1842-1848, Nov/Dec 1974.M. S. Ghazizadeh, F. M. Hughes, “A Generator Transfer FunctionRegulator For Improved Excitation Control,” IEEE Trans. Power irrenrs, Vol. 13, No. 2, pp. 435-441, May 1998.P, Kundur, Power System Stability and Control, New York: McGraw-Hill, 1994.IEEE Recommended Practice fbr Excitation System Models for PowerSystem Stability Studies, IEEE Std. 421.5-1992.deMello, F, P,, C, Concordia, “Concepts of synchronous machinestability as affected by excitation control,” IEEE Trans. PowerApparatus and Systems, Vol. PAS-88, No. 4, pp. 316-329, Apr. 1969.M.J.D. Powell, A Fast Algorithm for Nonlinear Constrainedoptimization Calculations, Numerical Analysis, ed. GA. Watson,Lecture Notes in Mathematics, Springer Verlag, Vol. 630, 1978.P, E. Gill, W. Murray, and M. H. Wright, Numerical Linear Algebra andoptimization, Vol. 1 ,Addison Wesley, 1991.

Matlab optimization toolbox user’s guide, Massachusetts: MathWorks,1997.Seung-111Moon, Kook-Hun Kim, Jong-Bo Ahn, Seog-Joo Kim, Jong-Moo Lee, So-Hyung Kim, 11-DoYoo, Jung-mun Kim, “Development ofa new on-line Synchronous Generator Simulator using PersonalComputer for Excitation System Studies,” IEEE Trans. Power Systems,VO]. 13, No. 3, pp. 762-767, Aug. 1998.

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systems,

IX. BIOGFL4PHIES,

Joong-Moon Kim (S’2 000) was born in 1m-sil,Korea in 1971. He received his B.S. and M.S. degreein electrical engineerinj~ from Chonbuk NationalUnivers ity, Korea in 1996 and 1998. Currently, he isa Ph.D. candidate of Electrical Engineering withSeoul National University in Korea. His researchinteres ts are control

system dynamics

and modeling of the power

Sermg-11Moon (M’) was born in Soon-chon, Korea,in 1962. He received the B.S.E.E. degree from SeoulNat ional Universi ty, Korea in 1985 and the M.S.E.E.and Ph.D. degrees from The Ohio State University in1989 and 1993, respectively. Currently, he is anAssistant Professor of Electrical Engineer ing withSeoul National University in Korea. His researchinterests include analysis, control and modeling ofthe power systems and the f lexible AC transmission

Jonghoon Lee (S’2001) was born in Kunsan, Koreain 1976. He received the B.S. degree in ElectricalEngineering from Seoul Nat ional Univers ity, Koreain 2000. He is the MS, candidate and his presentresearch interests are the voltage stability and thecontrol of the HVDC transmission systems.

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a new optimal avr parameter tuning method

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