Ece061119.qxd The Journal of Engineering Research Vol. 5, No.1, (2008) 71-78 1. Introduction Studies and experience have shown that load model parameters can have a significant effect on the results of dynamic performance and voltage stability of power sys- tems (Millanovic, et al. 1995; Langevin, et al. 1986; Ellithy, et al. 1989; Choudhry, et al. 1990; Choudhary, 1986; Ellithy, et al. 1997 and Craven, et al. 1983; Xu, et al.1994, Vaahedi, el al. 1988; Alden, et al. 1976; Ellithy, et al. 1997). Incorrect parameters of a load model could lead to a power system operating in modes that result in actual system collapse and separation (Craven, et al. 1983; Xu, et al. 1994). Accurate load model parameters are, therefore, necessary to allow more precise calcula- tions of power system control and stability limits which are critical in the planning and operation of a power ___________________________________________ *Corresponding author e-mail: mohahelal39@hotmail.com system dynamics has long been recognized, and it has become clear that assumptions regarding load model parameters can impact predicted system performance. Several efforts have been devoted to load modeling and evaluation of load parameters through field measurements (Xu, et al. 1997; Ohyama, et al. 1985). Analytical approaches to constructing accurate load models have also been considered (Xu, et al. 1997; Berg, et al. 1973). Voltage-dependent load models for composite load repre- sentation are highly recommended by the IEEE working group (IEEE Task Force for Dynamic Performance, 1995) and many utilities (Xu, et al. 1997; Ohyama, et al. 1985; Concordia, et al. 1982). Flexible AC Transmission System (FACTS) controllers based on thyristor controlled reactors (TCRs), such as static var compensators (SVCs) (IEEE Special Stability Control Working group, 1994)) are being used by several Tuning of SVC Stabilizers over a Wide Range of Load Parameters Using Pole-Placement Technique K. Ellithy Department of Electrical Engineering, Qatar University, Doha, Qatar Received 19 November 2006; accepted 1 April 2007 Abstract: This paper investigates the effect of typical load model parameters on the static var compensator (SVC) stabiliz- ers tuning. A proportional-Integral (PI) type stabilizer is considered and its gain-settings are tuned using the pole-placement technique to improve the damping of power systems. Tuning of SVC stabilizers (damping controllers) traditionally assumes that the system loads are voltage dependent with fixed parameters. However, the load parameters are generally uncertain. This uncertain behavior of the load parameters can de-tune the gains of the stabilizer; consequently the SVC stabilizer with fixed gain-settings can be adequate for some load parameters but contrarily can reduce system damping and contribute to system instability with loads having other parameters. The effect of typical load model parameters on the tuning gains of the SVC PI stabilizer is examined and it is found the load parameters have a considerable influence on the tuning gains. The time domain simulations performed on the system show that the SVC stabilizer tuned at fixed load parameters reduce the system damping under other load parameters and could lead system instability. Keywords: Load model parameters, SVC stabilizer, Pole-placement ÜÉ£b’G ™°Vh á«æ≤J ΩG~îà°SÉH ∫ɪY’G øe áØ∏àfl º«≤d ô≤à°ùŸŸG ∫É©ØdG ÒÑeC’G âdƒØdG ¢Vƒ©e hP âÑãŸG ∞«dƒJ »ã«∏dG ~dÉN áá°°UUÓÓÿÿGG âÑãŸG §Ñ°V ≈∏Y ∫ɪMC’G êPɉ ‘ áØ∏àıG º«≤dG ÒKÉJ ádÉ≤ŸG √òg ¢SQ~J :Tuning) (Stabilizers~bh .»µ«JÉà°S’G ádÉ©ØdG Ò¨dG iƒ≤dG ¢Vƒ©Ã ¢UÉÿG êPƒªædG ÜÉ£bG øcÉeG QÉ«àNÉH É¡JÓeÉ©e §Ñ°V ºàj å«M πeɵàdG h Ö°SÉæàdG ≈∏Y »æÑŸG ºµëàdG á«Yƒf ΩG~îà°SG ”Placement)(PoleÚ°ù– ¤G …ODƒJ »àdG øcÉe’G ‘ iƒ≤dG º¶f ‘ OɪN’GPower Systems) (Damping ofQÉÑàY’G ‘ òN’G Öéj ¬fG ~«H .~¡÷G ≈∏Y I~ªà©e ∫ɪM’G ¿G ¢VôØH á°SGQ~dG √òg ºàJ √OÉ©dG ‘h …ODƒj ~b πH iôNG äGÒ¨àe äGP ∫ɪMCG OƒLh ™e ¬àHÉãdG äÓeÉ©ŸG hP ºµëàŸG AGOG ∞©°V ÖÑ°ùj ‹ÉàdÉHh §Ñ° dG ±GôëfG ¤G …ODƒj ɇ .IO~fi ÒZ á≤jô£H ±ô°üàJ ∫ɪM’G ¿G »µ«JÉà°S’G ádÉ©ØdG Ò¨dG iƒ≤dG ¢Vƒ©e ‘ ºµëàdG äÓeÉ©e ᪫b §Ñ°V ≈∏Y ∫ɪM’G êPɉ ‘ äGÒ¨àŸG º«b ÒKÉàd á°SGQO ádÉ≤ŸG Ω~≤Jh .∫ɪM’G ¢ ©H ~æY QGô≤à°SG Ω~Y ¤G ∫ɪM’G Ò¨J ~æY IDhGOG π∏≤j áàHÉãdG äÓeÉ©ŸG hP ºµëàŸG ¿G ¿É«H ” å«M âbƒdG ™e ΩɶædG AGOG á°SGQO ” ~bh .ÒÑc ÒKÉJ É¡d ¿G á°SGQ~dG ÚÑJh πeɵàdG h Ö°SÉæàdG ≈∏Y »æÑŸG .∫ɪMC’G ¢ ©H ~æY QGô≤à°SG Ω~Y ÖÑ°ùj ~b áfG ɪc áá««MMÉÉààØØŸŸGG ääGGOOôôØØŸŸGG.ÜÉ£b’G ™°Vh -»µ«JÉà°S’G ádÉ©ØdG Ò¨dG iƒ≤dG ¢Vƒ©e äÉàÑãe ∞«dƒJ ,∫ɪM’G êPɉ º«b : 72 The Journal of Engineering Research Vol. 5, No.1,( 2008) 71-78 utilities to support the voltage and to increase the capaci- ty of their systems. SVCs with additional signals (stabi- lizing signals) in their voltage control loops have been used to improve the damping of power system electro- mechanical oscillations and to enhance system stability. The additional signals that are generally used in stabiliz- ers (damping controllers) are rotor speed and bus frequen- cy deviations. In recent years, many designs for SVC sta- bilizers have been proposed to damp out the electro- mechanical oscillation mode in power systems (Cheng, et al. 1992; Hsu, et al. 1988; Lee, et al. 1994; Hamoud, et al. 1987; El-Saady, et al. 1998; Hammad, et al. 1984; El- Metwally, et al. 2003; Fang, et al. 2004; Yu, et al. 2001; Farsangi, et al. 2004). The basic limitation of these designs and/or tuning of SVC stabilizers are that the influ- ence of load model parameters has not been taken into account. Almost all of these SVC stabilizers is based on a constant impedance load (fixed load parameters). The constant impedance load representation is not accurate and is not a good approximation in view of the strong influence of the load voltage sensitivity on the dynamic performance of the power system. The parameters of typ- ical loads vary seasonally, and in some cases change over day. Consequently, the SVC stabilizers tuned under con- stant impedance load model may become unacceptable under other load-model parameters. The subject of this paper is to investigate important aspects related to the effect of loads and their parameters uncertainty on tuning of SVC stabilizers. The author has initially addressed this problem in (Ellithy, et al. 1989; Choudhry, et al. 1986). Proportional-integral (PI) type sta- bilizer is considered as the additional stabilizer with the SVC. The gain-settings of SVC PI stabilizer are deter- mined using pole-placement (eigenvalue-placement) tech- nique to improve the damping of electromechanical oscil- lations mode in power systems. The interaction between typical load parameters and the tuning gains of the SVC stabilizer is investigated. Finally, the time domain simula- tions of the system under disturbance conditions are per- formed to demonstrate the effect of the load parameters on tuning of the SVC PI stabilizer. 2. Power System under Study The power system under study is a synchronous gener- ator connected to a large power system, of which the sin- gle-line diagram is shown in Fig. 1. The generator is equipped with IEEE type-1 excitation system. Full order model (7th order model) of the generator is utilized in the analysis and simulations. The load is connected at a gen- erator terminal and the SVC is connected at the mid-point of transmission line. The system parameters and nominal operating point values are given in Appendix. 2.1 Model of SVC with Additional Stabilizer The thyristor-controlled reactor (TCR) type SVC (Chang, et al. 1992; Lee, et al. 1988; IEEE Special Stability Control Working Group 1994; El-Metwally, et al. 2003), shown in Fig. 1, is used in the present study. The model of the SVC with additional proportional-inte- gral (PI) stabilizer is shown in Fig. 2. The stabilizer uses the generator speed deviation (∆ω ) as a feedback signal to generate the auxiliary stabilizing signal ∆Vs (a stabiliz- er output signal) to the SVC. The signal ∆Vs is added to the main input of the SVC to damp out the electromechan- ical oscillations mode. The signal ∆Vs causes fluctuations in the SVC suceptance and, hence, in the bus voltage. If the SVC stabilizer is tuned correctly the voltage fluctua- tions act to modulate the power transfer to damp out the electromechanical oscillations mode. The equation of the SVC controller (Fig. 2) is given by (1) where the auxiliary stabilizing signal (SVC stabilizer out- put signal) ∆Vs is given as (2) where KP and KI are the SVC stabilizer gain settings. The firing control system of the thyristors is represented by a single time constant Tα and gain Kα. The wash out circuit is introduced in the stabilizer to assure no permanent effect in the terminal voltage due to a prolonged error in the low frequency that might occur in an overload and to assure that the wash out circuit will not have any effect on the phase shift or gain on the low frequency. The variable inductive susceptance BL of SVC is a func- tion of the thyristor firing angle α and is given by (3) Vt V Xe Xe V∞ Gen SVC Load Control System B Figure 1. Power system single-line diagram L s ref K B ( V V V) sT α α ∆ = ∆ + − +1 w I s P w sT K V K sT s ⎛ ⎞⎛ ⎞⎟⎜ ⎟⎜⎟∆ = + ∆ω⎜ ⎟⎜⎟ ⎟⎜ ⎟⎜⎟⎜ ⎝ ⎠+⎝ ⎠1 Fig. 2 Block di agram of SVC wi th P I Stabilizer PI Stabilizer Kα 1 + sTα + Σ Vref - V + ∆Vs Vs,min Vs,max BLmax BLmin + + Σ BL0 BL ∆ω + sTw (Kp ) 1 + sTw KI s PI Stabilizer Figure 2. Block diagram of SVC with PI stabilizer L s ref K B ( V V V ) sT α α ∆ ∆= + − +1 w I s P w sT K V K sT s ∆ ∆ω ⎛ ⎞⎛ ⎞⎟⎜ ⎟⎜⎟= +⎜ ⎟⎜⎟ ⎟⎜ ⎟⎜⎟⎜ ⎝ ⎠+⎝ ⎠1 ( )− + = − 2 2 2 L s sin B x π α α π ; ≤ ≤2/π α π 73 The Journal of Engineering Research Vol. 5, No.1, (2008) 71-78 where xs is the reactance of the SVC fixed inductor. 2.2 Load Model This paper follows the recommendation of the IEEE working group (IEEE Task Force on Load Representation for Dynamic performance 1995) and utilities (Xu, et al. 1997; Ohyama, et al. 1985) in utilizing the voltage- dependent load model for composite load representation. Utilities normally perform field tests, or in some cases perform regression analysis to establish system load mod- els to be used for power-flow and stability studies. These models are in the form of (4) where PL and QL are the load active and reactive power; Vt is the load bus voltage; np and nq are the load parameters.; PL0, QL0, and Vt0 are the nominal value of load active power, load reactive power, and bus voltage prior to a disturbance. For small disturbance studies of system damping, the linearized version of Eq. (4) is given by (5) where The load representation given in Eq. (4) makes it pos- sible the modeling of all typical voltage-dependent load models by selecting appropriate values of the load param- eters np and nq. The values of np and nq depend on the nature of the load and can vary between 0 to 3.0 for np and 0 to 6.0 for nq. The load parameters of the composite load (industrial, commercial and residential loads) can be determined by the following equations (Ohyama, et al. 1985; Berg 1973): (6) where Pli and Qli are the active and reactive power of ith component and np, nq are their load parameters. The meas- urement values of the parameters (np, nq) of various kinds of typical power system composite loads are reported in (Xu, et al. 1997; Ohyama, et al. 1985; Concordia, et al. 1982). 3. Design of SVC PI Stabilizer The gain-settings (KP and KI) of the SVC PI stabilizer are determined using the pole placement by moving the eignvalues associated with the electromechanical oscilla- tions mode to a prescribed value on the left-half complex plane. It is well known that improving the damping of these oscillations mode can enhance the damping charac- teristic of a power system. The design procedures and their associated results are given below. 3.1 System without SVC Stabilizer In the design of the SVC stabilizer using the pole- placement technique, the nonlinear equations of the power system are first linearized around an operating point to obtain the state-variables model of the system. In the pres- ent study, the state-variables model of the system is obtained using the component connection model (CCM) technique (Ellithy, et al. 1989; Choudhry, et al. 1986). The equations describe the state-variable model given in (El-Metwally, et al. 2003). The state-variables model of the system is expressed as (7) where X = (∆iq ∆id ∆iq ∆ikkq ∆ikkd ∆ifd ∆δ ∆ω ∆VF ∆Efd ∆VR ∆BL)T is the state-variables vector. The state variables X1 to X7 correspond to the generator, X8 to X11 correspond to the excitation system and X12 corresponds to the SVC. Y = ∆ω, the output signal. U = ∆Vs, the control signal (stabilizer output signal) to the SVC. The system eigenvalues without SVC PI stabilizer (open-loop system) for fixed load parameters np = nq = 2 (constant impedance load) are listed in the first column of Table 1. The eigenvalues associated with the electromechanical oscillations mode of the synchronous generator are depict- ed by the complex pair eigenvalues λ6,7. The damping ratio ζ of this poorly damped oscillations mode without the SVC stabilizer (λ6,7 = σ ± jβ = −0.67896 ± j11.362) is given as ⎛ ⎞⎟⎜ ⎟= ⎜ ⎟⎜ ⎟⎜⎝ ⎠ 0 0 n p t L L t V P P V ⎛ ⎞⎟⎜ ⎟= ⎜ ⎟⎜ ⎟⎜⎝ ⎠0 0 nq t L L t V Q Q V = 0 0 L L p t t P P n V V ∆ ∆ = 0 0 L L q t t Q Q n V V ∆ ∆ t q q d d t V (V V V V ) V ∆ ∆ ∆= +0 0 0 1 ∑ ∑ = = = = 1 1 n nli p pi li i i P n n ( ); P P P ∑ ∑ = = = = 1 1 n nli q qi li i i Q n n ( ); Q Q Q = + dX AX BU dt =Y CX Withou t SVC Stabilizer With SVC Stabilizer ( KP=0.0, KI=0.0) (KP=19.892, KI=178.895) λ1,2 -212.210 ± j842.990 -212.700 ± j842.930 λ3 -98.782 -89.620 λ 4 -72.361 -79.480 λ 5 -38.992 -38.820 λ 6,7 -0.679 ± j11.362 -2 ± j11* λ 8,9 -9.893 ± j14.903 -9.070 ± j14.630 λ 10,11 -0.645 ± j0.837 -0.650 ± j 0.900 λ 12 -10.220 Table 1. System eigenvalues at load model para- meters np = nq = 2 *: Exact pole placement 74 The Journal of Engineering Research Vol. 5, No.1, (2008) 71-78 The damping ratio ζ = 6% for the electromechanical mode is not good enough. The poor damping of this mode can be also seen from the system time response in Figs. 3 and 4. The eigenvalues for this mode should be shifted to more desirable locations by the SVC stabilizer (ie. the SVC stabilizer is needed to improve the damping of this mode). The tuning gains of the SVC stabilizer are described in the following section. 3.2 Determination of SVC Stabilizer Gains using Pole Placement Technique The gain-settings (KP and KI) of the SVC stabilizer will be determined to improve the damping ratio of the electro- mechanical mode by shifting the eigenvalues λ6,7 to desired locations. An expression for the gains has been derived by the author in Ellithy (1997) and is given by (8) λ6= − σ − Jβ is the desired eigenvalue location associated with the electromechanical oscillations mode. D = c [λ6 I - A]-1 B where A, B and C system matrices are given in (7). If the eigenvalues λ6,7 = -2 ± j11 (ie. the damping ratio of the electromechanical mode ζ = 18%) are selected at the desired locations, then the gains KP and KI for the SVC stabilizer can be computed using (8). The results are given in Table 1. The eigenvalues of the closed-loop system (system with the SVC stabilizer) are given in the second column of Table 1. Considerable improvement in the system damp- ing can be expected in view of the closed-loop eigenval- ues. The improvement in the damping can also be seen from the system dynamic performance shown in Figs. 3 and 4. 4. Effect of Load Parameters on SVC Stabilizer Tuning The tuned gains (KP=19.892and KI=178.895) of the SVC stabilizer at the parameters np = nq = 2 are used to check the damping characteristics and stability of the sys- tem under different load model parameters. Based on these fixed gains, tuned at load parameters np = nq =2, the damping of the electromechanical oscillations mode is reduced under other load parameters as shown in Figs. 5, 6, 7 and 9. The tuned gains of the SVC stabilizer at other different load parameters are also used to check the system stability under different load parameters. Based on these fixed gains, the system damping is reduced and the system may become unstable under other load param- − − Without SVC stabilizer ⎯ With SVC stabilizer tuned at np=nq=2 0 1 2 3 4 5 6 7 8 9 10 -8 -6 -4 -2 0 2 4 6 8 10 x 10 -3 Tim e (s ec ) G e n e ra to r S p e e d D e v ia ti o n ( p .u ) Load param eters np= nq= 2 Figure 4. The system dynamic response at load para- meters np = nq = 2 for 50% change in Tm -- Without SVC stabilizer _ Without SVC stabilizer tuned at np = nq = 2 x % σ ζ σ β = = +2 2 100 6 0 0.5 1 1. 5 2 2.5 3 3.5 4 4. 5 5 -8 -6 -4 -2 0 2 4 6 8 10 x 10 -4 Time (sec ) G e n e ra to r S p e e d D e v ia ti o n ( p .u ) Load parameters np= nq=2 -- Without SVC stabilizer _ With SVC stabilizer tuned at np = nq = 2 Figure 3. The system dynamic response at load para- meters np = nq = 2 for 5% change in Tm = −2 21 11 22 11 22 b a b K ga ga a ; = −1 12 11 11 I P b K a K a a where: = − 21 12 2 21 1 a a g a ; ( )( ) =1 real part h b s ( )( ) =2 imaginary part h b s = −1m Tωσ ; = − 2 11a T mωβ σ ; =12a m ; = − −22a m Tωβ αβ ; =22a Tωβ ; = 1 h d ( ) = +2 2 2 T s m T ω ωβ 75 The Journal of Engineering Research Vol. 5, No.1, (2008) 71-78 eters as shown in Figs. 8 and 9. The decreases in the sys- tem damping are caused by the eigenvalues λ6,7, which are associated with the systems electromechanical oscilla- tions mode. In order to improve the damping of the oscillations mode (ie. improving the damping ratio of the eigenvalues λ6,7) over a wide range of load model parameters, the SVC stabilizer gains KP and KI must be tuned. The computed SVC stabilizer gains (KP and KI) for typical load model parameters are given in Figs. 10 and 11. These gains have been computed by (8) with the eigenvalues λ6,7 fixed at the desired locations of -2±j11. From these figures, it can be observed that the variations in the load model parame- ters (np, nq) have a considerable influence on the tuning of the SVC stabilizer. While not reported in the paper, the author has also investigated the influence of load parame- ters when the load is located at the SVC bus. The results obtained indicated no significant departure from the results presented here in so far as the influence of the load parameters on the tuning of the SVC stabilizers. 5. Conclusions This paper has examined the influence of voltage- dependent load models on the effectiveness of the SVC proportional-integral stabilizer for damping the electro- mechanical oscillations mode in power systems. -- With SVC stabilizer tuned at np = nq = 2 - With SVC stabilizer tuned at np = nq = 0 Figure 5. The system dynamic response at load para- meters np = nq = 0 for 50% change in Tm -- With SVC stabilizer tuned at np = nq = 2 - With SVC stabilizer tuned at np = 0.4, nq = 4 Figure 6. The system dynamic response at load para- meters np = 0, nq = 4 for 5% change in Tm -- With SVC stabilizer tuned at np = nq = 2 - With SVC stabilizer tuned at np = 1.2, nq = 2 Figure 7. The system dynamic response at load para- meters np=1.2, nq=2 for 5% change in Tm -- With SVC stabilizer tuned at np = 0, nq = 6 - With SVC stabilizer tuned at np = nq = 2 Figure 8. The system dynamic response at load para- meters np = nq = 2 for 5% change in Tm G en er at or S pe ed D ev ia tio n (p .u ) Time-Sec G en er at or S pe ed D ev ia tio n (p .u ) Time-Sec Time-Sec G en er at or S pe ed D ev ia tio n (p .u ) G en er at or S pe ed D ev ia tio n (p .u ) Time-Sec 76 The Journal of Engineering Research Vol. 5, No.1, (2008) 71-78 The impact of load model parameters on the SVC sta- bilizer tuning gains obtained via pole-placement tech- nique is investigated and it is shown that load models have remarkable influence on the stabilizer tuning gains. The results have also shown that the SVC stabilizer tuned gains under specific load parameters could contribute to the worse damping of electromechanical oscillations and reduce system stability under other load parameters. In particular, simulation with constant active power loads shows system instability when the SVC stabilizer is designed assuming constant impedance load. The results presented in this paper reinforce the need for including the load model parameters in the SVC stabilizers tuning for damping the oscillations mode of power systems. Acknowledgments The author would like to thank Qatar University and Qatar Electricity & Water Company (QEWC) for their support. References Alden, R.T.H. and Zein El-Din, H.M., 1976, "Effect of Load Characteristics on Power System Dynamic Stability," IEEE Trans on Power App. and Syst. Vol. PAS-95, pp. 1762-1768. Berg, G.J., 1973, "Power-System Load Representation," Proc. IEE, Vol. 120(3), pp. 344-348. Cheng, C.H. and Hsu, Y.Y., 1992, "Damping of Generator Oscillations Using an Adaptive Static VAR Compensator," IEEE Trans. on Power Systems, Vol. 7(2), pp. 718-725. 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Zein El-Din, H.M. and Price, W.W., 1988, "Dynamic Load Modeling in Large Scale Stability Studies", IEEE Trans. on Power Systems, Vol. 3(3), pp. 1039-1045. 78 The Journal of Engineering Research Vol. 5, No.1, (2008) 71-78 Appendix System parameters and nominal operating values: Synchronous Generator xd =1.7 xq=1.64 xls=0.15 xkkd=1.605 xkkq=1.526 xffd =1.651 xad =1.55 xaq =1.49 ra=0.001096 rfd=0.000742 rkq=0.054 rkd=0.0131 H=2.37sec IEEE Type-1 Excitation System KA=400 TA=0.05 sec KF = 1.0 TF =1.0 sec KE=-0.17 TE= 0.95 sec Transmission Line x1= 0.15 x2=0.15 Static Var Compensator (SVC) Kα =20 Tα = 0.02 sec Xs = 0.8 αo=1400 BL0=-0.164 Tw = 0.1 sec Vs limit = 0.1 Nominal Operating Values PG =1.0 pfG = 0.85 PL0 =1.25 pfl = 0.5 Vt = 0.976 V = 0.987 V∞ =1.0 δ0 = 43.146 0