Source: https://ja.scribd.com/document/313392439/A-New-Optimal-AVR-Parameter-Tuning-Method
Timestamp: 2019-04-19 14:29:39+00:00

Document:
characteristics of linearized “on-line” system model.
affect the power system dynamic response and stability.
off-line model may not give the optimal performances in online conditions.
for the parameter tuning of AVR has been introduced .
Seoul National Uni versity, Kwanak-gu, Shinlim151-742, South Korea (e-mail: blues kilm@koreamail. conl).
Moon is with Seoul National University, Kwanak-gu, Shinlim151-742, South Korea (e-mail: simoon@plaza,snu.a c.kr).
Lee is with Seoul National University, Kwanak-gu, Shinlim151-742, South Korea (e-mail: ljoho@powerlab. snu.ac.kr).
of linearized on-line power system model is presented.
= I [ ~ETr ~J”. So in order to verify the relationships between the characteristics of frequency-domain and on-line performance with generator on-line condition. A V.. LINEARIZED EXCITATION Generator parameters MODEL . Ah A(z r AS al2 *13 ‘21°0000 A ~ fd _ “31 ’32 a33 @id a41 ’42 ’43 A@.x . the system performances are greatly influenced by its operating level and the parameters of the external system . 3-c./ AVref) indicative of the speed of the transient response of the system .0 1.27 Exciter parameters .5 A V. v v.673 0.00 (C) 2001 IEEE . 1555 0-7803-7031-7/01/$10. I.12 0. R.. and could be converted into the transfer-function form @E.00 © 2001 IEEE 1. load are linearized and arranged in state-space form .0 0.1 41. L. K.. 2 .A ‘lq + K63A v2q (2) ‘6Avfd +’61A ‘ld In the above equations. 120. na this paper.” 4 T’ d . 0.5 Operating Conditions K .q “5I ’52 a53 A @2q _a61 ’62 a63 ’14 ’15 a16 al I ‘t= ‘5A6 + ’34 a44 a54 ’64 ’35 ’45 ’55 a65 bO 11 00 A. relative stability of a excitation control system is measured in terms of the gain margin and phase margin.158 0. Fig. f V“. L SYSTEM PARAMETERS III. ST.198 1. 0-7803-7173-9/01/$10. K. Detailed description of this excitation system model is described in .2 R& + jX& . Detailed equations for the coefficients in the above equation are given in .“ K. sK.. It should be noted that simultaneous optimization of all performance indices is not possible. the relationships of both characteristics with IEEE ST2A type exciter at three different operating conditions are shown in Fig.673 0. 1 + sT. I I. . 3b.0 0. v. c! 0.5 L.3 0.By combining the above equation (3) with (l)-(2).15 1. the variation of mechanical input torque ATMis neglected.. various case studies have been performed with different type of excitation systems at wide operating range..5 0. i.. A I#fd ATM “36 0 ’32 AY.power angle of the generator As shown in the Fig. .158 0. phase margin and gain margin are also the measures of relative stability at the generator on-line conditions. when the generator is connected to the power system.* . It is clear that the large crossover frequency is indicative of the fast rise time at all operating conditions.728 0.0 Q. which is calculated by operating condition. to facilitate frequency-response analysis.15 0.5 . high phase margin and high gain margin for the stable operation are not compatible with large crossover frequency for fast response. T..thevenin’s equivalent impedance of transmission system This excitation system utilizes the rate feedback loop to provide excitation control loop damping. 3-a. complete system dynamic equation is obtained. 0.. In addition. As an example.158 0.d + 00 AEFD ’46 [1 00 “56 Av. and Fig. In v. L: 0. the crossover frequency OC is still the indicative of the speed of the transient response.q a66_@2q . and the crossover frequency Uc is + ‘62. A&. KE where. v.19 K.09 T.2 23.at~on system is-shown in Fig.0 0- IV. 0. L:. T“ do 1..] T’ 2. IEEE ST2A excitation system is used to verify the proposed tuning method. T. When the synchronous machine is connected to the power system.45 0. K.. the product point on the main control path is changed by the gain VB.05 1.0 ‘“ TA Case 1 Case 2 Case 3 F. ~ P f[I. 0.5 0. 2.0 El =1. As shown in the Fig 3-c. 5 E . ‘x 11 1+ sT. The complete state equations could be obtained by compounding above state equation and state equation of excitation system.6 0. RELATIONSHIPS BETWEENTHECHARACTERISTICS OFTHE FREQUENCY-DOMAIN ANDTHEON-LINEPERFORMANCES (1) When the generator is open-circuited.673 7. TABLE. which is discussed in the next section. as shown in the Fig.. In this paper. IEEE ST2A RateFeedb ?ck type Excitation System K. 3..06 0. L. Generator and exciter parameters and operating conditions used in this example are given in Table. IN & o- F. ATMrepresents the prime mover torque variation and AEFDrepresents the the excitation voltage variation due to AVR action. For the purpose of linear analysis. T“ H 5:. T. j L ‘ Linearized state-space form equation of this excitation system is given in (3). The block diagram of the ST2A exc. x.8 0.3.
Relationships between the characteristics of frequency domain and time domain Fast excitation response to terminal voltage variations is required for improvement of transient stability .M of off-line system model 2 40” (4-2) G. for example the excitation control system stabilizer gain KF. Gain margin has the characteristic of monotonously increase as increase of some parameters. Consequently. Detailed description of the routine is given in [9. excitation control system response shows more oscillatory response caused by lack of damping torque as the load-angle is increased. at these large load-angle conditions. From the various case studies. 3. that are not applicable in the real exciter. Unfortunately. When the load-angle is so large. Although the high crossover frequency makes the system response fast. minimum phase margin and gain margin of the off-line model 0-7803-7173-9/01/$10.00 (C) 2001 IEEE . to determine the suitable weighting value of phase margin for the different operating conditions. Both phase margin and gain margin can be used in the object function to solve the compromise problem. In addition. may be obtained when the gain margin is considered in the object function. it is hard to determine the proper weighting value analytically. Therefore. Maximize (coC+ WXPM) of on-line system model (4-1) Subject to where. more value of phase margin is needed as the load-angle is increased. the minimum phase margin of the on-line model is also considered as constraints.45 50 OIc [rad/see] 55 60 65 70 Phase Margin[degree] (b) (a) 1. So the normalizing factor to reduce the numerical value of phase margin to the reasonable range must be considered in the object function. Therefore. 3. V. w P.00 © 2001 IEEE are considered as constraints (4-2) and (4-3) . various case studies have been performed with different types of excitation system at wide 1556 0-7803-7031-7/01/$10. the crossover frequency should be high.10. OBJECTFUNCTIONANDOPTIMIZATION TECHNIQUE In this paper. load-angle and exciter type. the constraint (4-4) for the well-damped stable operation is not satisfied any longer. the system response and performance indices used in the object function are affected by many factors. In this method. So very large values of parameter sets. it recluces the damping of system oscillations. Consequently. such as system configuration. constrained optimizatic. An effective way to solve this problem is to provide a power system stabilizer.5 20 25 Q. gain margin has an adverse characteristic that is not applicable to the optimization technique. The numerical value of phase margin is much higher than the numerical value of the crossover frequency as shown in Fig. an approximation is made of the Hessian of the Lagrangian function using a quasi-Newton updating method and ~~QP sub-problem is solved at each iteration.M of off-line system model >6 dB (4-3) P. to guarantee the stable operation at the generator on-line condition. Object function and constraints that are used in the proposed method is shown below (4). it is more reasonable to use the phase margin in the object function.1 1]. To guarantee the stable operation of obtained parameter set. 10]. phase margin with proper weighting value is also included in the object function. To solve the comprc)mise problem between fast response and stable response. to satisfy the stable operation (4-4). In addition. 65” of phase margin of on-line system model guarantees the well-damped stable operation. system response shows so oscillatory response because of the lack of damping torque [6. For the fast excitation response. at the generator off-line commissioning phase. it leads to reduce the phase margin and gain margin of the frequency response. Therefore. the compromise between the fast excitation response and the welldamped response is needed for stable operations. etc.the weighting value of the phase margin High crossover frequency for fast response can be inherently obtained from this object ftmction because of the nature of optimization technique. 3’0 3’5 [rad/see] (c) Fig.8]. This is then used to generate a QP sub-problem whose solution is used to form a search direction for a line search procedure. Therefore.n technique is used to solve the compromise problem and Sequential Quachatic Programming(SQP) method is used to solve the constrained optimization problem [9. However. Therefore.M of on-line system model > 65” (4-4) .
V. Resulting suggested values of two basic type of excitation systems are summarized in the table. = 0. which is used in the simulation.673 0.2 II 0°-500 \ 0. the gain ‘A is assumed unadjustable to provide the good steady state performance and the excitation system stabilizer time con stant T. OPER. = 0.00 (C) 2001 IEEE V.79 ‘%0 [see] [see] 3.71 0/0 LOa’-@7ssF Weighting value Load-angle Tuning Method Settling Time (Syo) 2.: : I 2 r I 1 4 .195- 0.3 to prevent the excessive crossover frequency.7” ) 1 10 .015 1. < Q.1-0.70 and 45.00 © 2001 IEEE 0.Analytical .5 0.010 1.020 The case study with ST2A exciter with two different operating conditions has been performed to verify the performance of proposed tuning method.030 1. Table.2. II. 6 45. is the 3°/0 step change of the AVR reference value at 0. Simulation results are given in Table. V.1-0.7° ) operating range.000 0 2 4 6 8 In time (see) TABLE. In thlls case.056 malytical Method K. PERFORMANCElNLXCESOFBOTHPARAMETERSET( 6 = 13.5 parameter ‘reposed Method K.158 0.3” ~ As shown in the Table. 0. The parameter that is tuned by analytical method using off-line KF = 0. OPERATINGCONDITION Operating Conditions E.e. III.1 1.. III and Table. IV.200 –~ ~~ o. 4 and Fig.3.7” lY. the weighting values of the phase margin are chosen to 0.7 0.0. Therefore.0 0.1 (see] 1. is 1.3 II 50°-60” I 0. Test signal.210 h TABLE.3 I 50°-60° 0.0 0.067 Over shoot Rise Time 8. To verify the performance model is improvement of parameter set that is tuned by proposed method. Block diagram of 2 Q Ur ST2A exciter is shown in Fig. ~ Q.9 see] 8.9 0. 5. the load-angles of each case are 13.603 13. L Table.067 .025 VI.210 0. time-domain simulation is performed on both parameters using the reaI-time simulator . VI. 8 L 0. . 0-7803-7173-9/01/$10. I I TABLE.205- . Fig. --------.TABLE. HI and Table [V show the operating conditions that are used in this case study.0. XE J 0.190 I o 1 .5 sec..–I 6 method I i3 time (see) Fig.035 II 600-65~J 1.15 and 0.2 I I 20°-50° ] 0.2.2 1. 1. II SOGGESTEDWEIGHTINGVALUES FORPROPERTONING (Rate feedback) I 0°-200 I 0. CASE STUDY 1. 2. 0.4.ATINGCONDITION Operating Conditions x. Simulationresults(3%stepchangein 1557 0-7803-7031-7/01/$10.005 also found to be untunable at 1 sec. Generator parameters and Exciter parameters usedl in this case study are given in Table.06 R. d = 13.30 respectively.0.
They also show some more oscillatory but well-damped response of electrical torque. CONCLUSIONS This paper presents an AVR parameter tuning method using optimization technique with frequency responses of on-line system model. “Development of a new on-line Synchronous Generator Simulator using Personal Computer for Excitation System Studies. Jung-mun Kim. Jan/Feb 1977. pp. IEEE Std. W. 4. Vol. Bollinger. 435-441. 4. A Fast Algorithm for Nonlinear Constrained optimization Calculations. 3. C.. Vol. Vol. 1997. rise 0-7803-7173-9/01/$10. and M. Aug. F. No. ed. 6. 1991. K. “Concepts of synchronous machine stability as affected by excitation control. S. VO]. 3.785-791. Numerical Linear Algebra and optimization. The proposed tuning method find the optimal parameters that maximize the object function in order to improve the voltage response at on-line conditions and satisfy the constraints in order to guarantee the stable operation of both the generator on-line conditions and the generator offline conditions. Power $irrenrs. 13. 1.C~.J. In addition. Kook-Hun Kim. Table. pp. Concordia. Seog-Joo Kim. Simulation results (3% step change in V. No. “A Generator Transfer Function Regulator For Improved Excitation Control. and Evaluation of the Dynamic Performance ojExcitation Control Systems.” IEEE Trans. TABLE. Since this method needs no additional compensators. Power Apparatus and Systems. P. PAS-88.2-1990. 4 and Fig. Powell.3° )  As shown in the Table.00 (C) 2001 IEEE . Fig. REFERENCES 10 time (see)          o 2 4 6 8 10  time (see)  Fig. 421. No. 13. IEEE Std. Ghazizadeh. P. 1969. as the proposed method uses the on-line system model. 316-329. m=] a 2 4 6 8 VIII. C. 2. Vol. VI. pp. 630. F. No. M. Rodolfo J. PERFORMANCEINDICESOF BOTHPAILAMETERSET( J = 45. Power Apparatus and Systems. PAS-96. Gill.” IEEE Trans. M. Testing.. Vol. Springer Verlag. 1. pp.time and settling time than the response of the parameter that is tuned by analytical method. 1998. 1842-1848. Wright. Lecture Notes in Mathematics. Addison Wesley. R. 762-767. 1978. “Tuning Synchronous Generator Voltage Regulators Using On-line Generator Models. The system responses c)f the tuned parameters increase the performance of the terminal voltage response and maintain the well-damped performance of the electrical torque. So the efforts for performing tradeoffs between fast response and stable operation are greatly reduced. December 1988.5-1992. “Complex Root Compensator – A New Concept For Dynamic Stability hmprovernent. GA.5. IEEE Recommended Practice fbr Excitation System Models for Power System Stability Studies. deMello. Kundur. pp. the parameters tuned by this method show more optimal responses than tuned by traditional method using offline model at the operating condition. ~ = 45. 421. Koessler. Power Apparatus and Systems. Raczkowski. JongMoo Lee. So-Hyung Kim. Lalonde. New York: McGrawHill.D. Numerical Analysis. Power System Stability and Control. Apr. Watson. 32-37. vol.” IEEE Trans. the optimal parameter sets of conventional AVRS are readily obtained at the various operating conditions.” IEEE Trans. Jong-Bo Ahn. M.” IEEE Trans. E. the parameters that are tuned by proposed method show more optimal responses than the parameter that is tuned by conventional analytical method. pp. Power Systems. “Techniques for tuning excitation system parameters.3° VII. 1994. 11-Do Yoo. P. H. Vol. Seung-111 Moon. They show smaller overshoot.” IEEE Trarw Energy Conversion. PAS-93. Hughes. May 1998. V. V1. Nov/Dec 1974. No. 5. 1558 0-7803-7031-7/01/$10. Matlab optimization toolbox user’s guide. Murray. Massachusetts: MathWorks. No.00 © 2001 IEEE IEEE Guide for Identification.
E. He received the B. His research interests include analysis. degree in electrical engineerinj~ from Chonbuk National University. Jonghoon Lee (S’2001) was born in Kunsan. Korea in 1971. Korea in 1976. S. control and modeling of the power systems and the flexible AC transmission systems. degrees from The Ohio State University in 1989 and 1993.E.D. Korea. He is the MS. he is an Assistant Professor of Electrical Engineering with Seoul National University in Korea. in 1962.00 © 2001 IEEE 1559 0-7803-7031-7/01/$10. Korea in 1985 and the M. degree from Seoul National University. and Ph.E. candidate of Electrical Engineering with Seoul National University in Korea.00 (C) 2001 IEEE .S.S.E. S.IX. and M. He received the B. Currently. His research interests are control and modeling of the power system dynamics Sermg-11Moon (M’) was born in Soon-chon. Korea in 2000. He received his B. Joong-Moon Kim (S’2!000) was born in 1m-sil.S. Currently. BIOGFL4PHIES. Korea in 1996 and 1998. degree in Electrical Engineering from Seoul National University.D. he is a Ph. candidate and his present research interests are the voltage stability and the control of the HVDC transmission systems. respectively. 0-7803-7173-9/01/$10.

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