Simulation of Unified Static VAR Compensator and Power System Stabilizer for arresting- Subsynchronous Resonance S. A. Khaparde IEEE, Senior Member, Dept. of Electrical Engineering Indian Institute of Technology, Bombay, India V. Krishna IEEE, Student Member, Dept. of ECE Illinois Institute of Technology, Chicago. Abstrac+- In the literature, co-ordination of Static Var Compensator (SVC) and Power System Stabilizer (PSS) using generator speed deviation or modal speeds as stabilizing signals is shown to damp the system oscillations. Though such schemes are able to damp the SSR modes for small disturbances, they are unable to damp transient SSR due to large disturbances. Here in this report improvement in the control aspect of the SVC at the midpoint of the transmission line is suggested. This scheme attempts different auxiliary signals that include Line Current, Computed Internal Frequency, Bus Angle deviations. A system of configuration similar to IEEE First Bench Mark model is considered, eigen value analysis has been carried out, and results indicate that Bus Angle deviation signal as auxiliary control signal for SVC was able to damp most of the modes leaving some of them still oscillatory. The main feature of the proposed work is to use combination of deviation in speed and electrical power output of the generator as input signals to PSS which operates simultaneously along with SVC. Such simultaneous PSS and SVC scheme is found to improve the damping under large disturbances i.e. the growth of system oscillations is arrested. The simulations are carried out on PSCAD. The efficacy of controllers to damp SSR under steady state and faulted conditions where one of the torsional modes gets excited is presented and discussed. self excitation have been proposed using composite speed signals and torsional monitoring devices. It was concluded that the control strategies are unable to damp other modes of oscillations. In [71, a new simple concept was introduced where generator speed deviation was used as auxiliary stabilizing signal for SVC, in addition to voltage control action. It was shown later in [SI that the generator speed signal as auxiliary stabilizing signal will actually undamp the torsional modes when the system is subjected ‘to large disturbances. In[9]. SVC has been used at the midpoint of the transmission line for damping SSR and for the improvement in the power transfer capability. A few stabilizing signals have been shown to damp SSR through linearized eigen value analysis. But it was not shown whether the signals are capable of damping torsional modes through time domain analysis. Power System Stabilizers(PSS) have been used in Power Systems to damp the inertial modes of oscillations of turbinegenerators[ 101. h[I I] generator speed based PSS has been used and it was shown that torsional oscillations are damped, but the disturbances considered are small. In[ 121, D. C. Lee et al. have proposed a new scheme for PSS, which uses deviation in generator speed and electrical power output of the generator as input signals. It was shown that the inherent disadvantages of using speed based stabilizers can be eliminated with this scheme. The coordinated scheme proposed in [SI,based on modal speeds, has been shown to damp the torsional oscillations effectively for small disturbances, however €or large disturbances the scheme can arrest only the growth of oscillations and satisfactory damping is not achieved. Here in this paper a new simple concept is introduced with simultaneous operation of PSS and SVC. The SVC is at the midpoint of the transmission line. The PSS model that has been used is similar to the one presented in [ 121. The auxiliary signal used for the SVC is the angle deviation at the SVC bus and has been derived locally. As customary, to alleviate the damping, the measured signals are passed through torsional filters before they are input to the controller. The study has been canied out on the system considered in[9], which is similar to IEEE FBM. This configuration has been taken because the results presented in this paper can be validated with that model as it has shunt compensation at the midpoint of the transmission line. The investigations carried out indicate that the proposed scheme can effectively arrest the growth of the oscillations under I. INTRODUCTION Subsynchronous Resonance is a Power System phenomenon where the electric power system exchanges its energy with turbines at one or more frequencies below the synchronous frequency, when the electric network is compensated with series capacitors. The problem of torsional interaction has been [ 1,2,3] identified to take place when the electric resonant frequency is near the complement of one of the torsional mode frequencies of the turbine-generator shaft system. In addition to torsional modes the inertial mode is also excited as a result of disturbances. In recent years, great deal of attention has been focused on mitigating SSR with the use of Static Var Compensators (SVC), which were previously used only for voltage regulation purposes and for damping the inertial mode of oscillations[4,5]. In [6] two new methods to damp SSR by 0-7803-3713-1/97 $10.00 0 1997 IEEE 302 Authorized licensed use limited to: INDIAN INSTITUTE OF TECHNOLOGY BOMBAY. Downloaded on December 4, 2008 at 06:23 from IEEE Xplore. Restrictions apply. , faulted conditions also. The analytical results have been verified by the time domain simulations with the use of Manitoba HVDC center's PSCAD. The proposed concept has been implemented also on IEEE FBM and the results of the test case 1 -T[ 13]are presented. 11. SYSTEM MODEL A. Power System Description. The network configuration that has been used for study purpose is given in Fig.1. Figure 1 shows a steam turbine driven synchronous generator supplying power to an infinite bus through a long distance series compensated transmission line. A Fixed Capacitor -Thyristor Controlled Rectifier (FCTCR) combination which works as Static Var Compensatory system is considered at the mid point of the transmission line. The total system model can be derived by clubbing the individual subsystem models, which are explained later. Fig. I. System Configuration used for study. B. Mechanical System model The mechanical system has been described using the 'multiresonant mass model' (all modes model)[ 121. This model is considered because it includes the effect of the zeroth mode and accounts for the coupling between different modes. Each major rotating element is modeled as a massless rotational spring with its stiffness expressed by a spring constant. Viscous damping of each mass and shaft is represented by a dash pot damping. The equation of the i' mass of the n-mass rotating system is given by where M is Inertia constant, D is damping, K is spring constant, T, and T, are mechanical and electrical torque. Equations for all the masses can be written and can be linearized around the operating point, and are transformed to D-Q axis[9], which is synchronously rotating reference frame. The state and output equations in the state space form can bq given as XM = AM. XM + BMI. UMI +BM2. UM2 YM = CM. XM (2) where XM =[AS, AZi2 Aa3 AS4 AS5 A66 A o , A o 2 A o 3 Ao, A o s A% 1' 303 UMl = [AID AIQIt, UM2 = [A& Ab ]I, YM = [ A& A u 5 1' where A6s and Aos are angle deviations and speed deviations of masses 1 to 6 respectively. The variables in UMl and UM2 are explained later in Rotor model. C. Synchronous machine model. Synchronous machines can be modeled in varying degrees of complexity depending upon the purpose of the model and usage. The model reported in [9] has been used in this paper and is found to be suitable for torsional dynamic studies. The machine is split at the air gap which is its natural boundary. It includes a field winding and a damper winding on d axis and two damper windings on the q axis. 1). Stator Circuit model. In this model, the stator of the synchronous generator is represented by a dependent current source (I, ) in parallel with the subtransient inductance L,' [9]. This stator model is combined directly with the transmission network model which is explained later. I, =[ I, I, I, 1' = I, c + I, s (3) where c'=:fi [ cos(e) cos(e-2~13) cos(e+ 21113) 1 st = fi [ sin(e) Sin(e-2~0) sin(e +2n13) J &,I, are components of dependent current source along d and q axis ,respectively. 8 is the rotor angle. Superscript t indicates transpose. 2). Rotor circuit model. The flux linkages in the rotor associated with the different windings are defined as follows $f =alWf+%Whfblvf+b2id $h =a3Yf +a4Wh+b3id q g = Wg \Vk E Wg + % %Wk+ bSfq Wk+ b61q (4) where vf is field excitation voltage. id,iq are d and q components of the machine terminal currents. All the constants a and b are defined in [9]. Then the currents have to be transformed to D-Qframe. The state equation of rotor circuit can be obtained after linearizing as follows XR = AR.XR + BRl.UR1 +BR2.UR2 + B W . U W (5) where XR = [ AWf AWh AWk 1' URI = [A6 Ao UR2 = A V , uR3 = [AiD AiQ]' 6 and o are the angle and angular speed of the generator respectively. The components of the dependent current source, along d-q axes respectively expressed as Id=CIWf +C2\11h' r q = c 3 Y g +c4\11k (6) The currents are transformed to D-Q frame as r0, I ~ The . linearized output equations of rotor circuits is obtained as YRI- CR1.XR +DRl.URl r, YR2=CR2,XR +DW.URl+DEU.UR2 +DR4.UR3 (7) where YR1= [AID AIQ]', YR2= Ykl D.Excitation System IEEE type 1 excitation system [14] has been used for studies. The system is based on dc rotating machine and is consistent with the model provided for the IEEE FBM. The terminal voltage of the generator is the input to the excitation system. transmission line is modeled as a lumped parameter PI circuit on both sides of FC, and the symmetric nature of network facilitates its representations in terms of a and p components. The a and p network configurations have been presented in[9]. The differential equations of the RLC network can be written and are to be transformed to synchronous reference frame D-Q. The linearized state equation and output equations of the network model can be derived as Xh=AN.XN+BN2.UN2+BN3 .UN3 YNl=CNl.XN+DN2.UN2+DN3.UN3 YN2=CN2.XN YN3=CN3.XN (10) Where XN = [AX, A%]' xD = [ iID i4D iD U xQ Fig.2 PSS linearized model used for eigenvalue analysis. In the literature generator speed deviation (conventional PSS) and modal speeds have been taken as input signals for the PSS. A small signal model is derived for the system and the Hephron-Philips constants will be found. From this the required gain and phase lead to make the speed signal to be in phase with the electric torque will be found. The output of the PSS has been added at the Vref summer of excitation model. Here the improved model for the PSS[12] has been used and is given in the Fig.2. The inputs to this model are generator speed deviation and the deviation in electrical power output of the synchronous machine. The equivaIent speed deviation is obtained from these input signals and is gain and phase adjusted. Parameters of the blocks G(s),Q(s) and K are given in appendix B. The state equation of the PSS can be given as follows XPSS = APSS. XPSS CBPSS.UPSS YPSS = CPSS. XPSS (8) where UPSS = [U,,, Upss21f= [ Am AP, 1' ,YPSS= [ypss] The state and output equation of the linearized excitation system can be derived as = [ iIQ iZQ i4Q '2D '3D '4D '5D '6D I' 6 V2QV3QV4QV5QV6Qlf UN2= [AIIDAb]', UN3= UN2, YN1= AV,, YN2= [Ai, AiQ]' YN3= [ A V ~AV,* ~ 1' The outputs of the networks are generator terminal voltage, currents at the generator end and the voltage at the mid point, which are the inputs to exciter and SVC system respectively. F. Static Var System The SVC system considered is a combination of Fixed Capacitor (FC) and Thyristor Controlled Reactor(TCR). TCR provides continuous control of reactive power and in conjunction with the parallel FC. Fig.3. shows the schematic of the SVC system with auxiliary feedback. The terminal voltage perturbation and SVC incremental current, weighted by a factor &, representing current droop, are fed to the Vref junction. The voltage regulator is assumed to be PI controller. Thyristor control action is represented by average dead time Td and firing angle time delay Ts. The output of the control block is susceptance(B) variation. Parameters of the above block diagram are given in appendix B. The a and p axis currents entering TCR from the Network are given by the equations XE =AE.XE +BE.UE YE =CE.UE Where XE = [ AV, AV, AV,1'. YE = [AV, 1, UE = [Avg ypss]' (9) E. Network Model. The network that is considered is shown in the Fig.1. and the transmission line is compensated by series capacitors. The SVC has been placed at the midpoint of the network, which is the concept of compensation by sectioning to improve the power transfer capability of the line. For the linearized analysis the whole of SVC is represented as a fixed capacitor giving reactive power support at the midpoint. The Fig.3 Linearized SVC control block diagram. 304 Authorized licensed use limited to: INDIAN INSTITUTE OF TECHNOLOGY BOMBAY. Downloaded on December 4, 2008 at 06:23 from IEEE Xplore. Restrictions apply. TABLE 1. Real parts of Eigenvalues related to torsional modes. I I I1 I ITT I A- without PSS and SVC, I1 A- with SVC at midpoint performing voltage control action, I1 B- with torsional filters in SVC voltage measurement loop, I1 C- with LC controller, I1 D- with CIF controller, I1 E- with SVC bus angle deviation control, 111 A- with generator speed based PSS acting simultaneously with SVC, 111 B- proposed scheme. where R and L, represent the resistance and inductance of the TCR respectively. The state and output equations of SVC model can be written as X'S = AS.XS + BSl.US1 + BS2.US2 + BS3.US3 YS = CS.XS + DS.US1 (12) where xs = [ Ai3D AijQ z1 22 23 AB]' US 1 = [ AV,, AV,, 1' ,US2 = [Av,~] u s 3 = [AV,], Y s = [A& A&Q]' G. Auxiliary Control of SVC. The auxiliary stabilizer signal Avf is added to the main input of SVC controller to damp the oscillations. Different auxiliary control signals have been considered in [9]. In[9] linearized analysis has been carried out and it was shown that auxiliary signals Computed Intemal Frequency (CIF), and Line Current (LC) work better to damp oscillations. But the performance of the controllers for disturbances was not shown with simulations. Here in this study it is found that auxiliary signal based on the deviation of the bus angle at the SVC bus. The angle of the voltage at the SVC bus is given by -I 9 (13) Y1=tan where D and Q refer to D-Q frame of reference. Equation 13 is linearized around the operating point and can be obtained as Ay3 = ?AVIQ VI0 - *AVID Second order transfer function is taken for the auxiliary signal path. The state and output equations of the auxiliary control can be given by XC = AC.XC + BC.UC YC = CC.XC + DC.UC (14) Now the control signal (U, ) will be Ay3.Again which can be expressed as U, = FCR.XR + FCM.XM + FCN.XN + FCS.XS (15) in terms of the total system state variables. The output of the control block will be AV,. H. Overall System The state and output equations of overall system can be w.ritten as follows: XT = AT.XT + BT.UT + B.US2 YT = CT.XT + DT.UT (16) where XT = [ XR XN XE XM XS XPSS XC]*, YT = [YRl YR2 YR3 YNl YN2 YN3 YN4 YE YMI Yh42 YSI YS2 YPSS YC]', UT = [URl UR2 UR3 UN1 UN2 UN3 UE UM1 UM2 US1 u s 3 UPSS ucy The ineterconnectivity between models can be expressed as UT=FT.YT (17) substituting equation (17) in equation (16) and setting US2 to zero, we get the system equations in a reduced form as follows: (18) f T = AA. XT where AA = [AT + BT[I-FT.DT]' FT.CT] AT,BT,CT,DT are combined A,B,C,D independent model matrices. v30 305 111. ANALYSIS METHODS AND RESULTS A. Eigenvalue analysis From the overall system transformation matrix AA obtained as above, the eigenvalues of the system can be found. The stability of the system can be estimated from the real parts of the eigenvalues. If they are positive they represent an unstable operating condition and the growth of oscillations. The resulting eigen values with the use of Line Current(LC)[9], as auxiliary control signal are given in I1 C. LC controller improves the damping of mode 1 but the zeroth mode gets destabilized. The Computed Internal Frequency(CIF)[S)],as auxiliary signal has resulted in (I1 D), where it can be seen that damping of mode 1 gets worse. I1 E gives the eigenvalues with bus angle deviation as auxiliary stabilizing signal. It can be seen that all the modes negative real parts, but the damping of few torsional modes is still less. Then PSS , with generator speed deviation signal as the input signal(conventionai PSS) has been operated simultaneously along with SVC. The result ,111 A, shows that a few modes have become unstable, which were oscillatory (I1 E)with SVC alone. This, once again shows that the generator speed based stabilizers actually undamp the system oscillations. The results of the proposed scheme are given in 111 B. Comparing IIE and I11 B shows that the simultaneous operation of SVC and PSS has improved the damping of all modes. 0.m I 3.0 2.0 :10 L 0.0 .LO 40 0.1 mn4r4 -0-0- : ; - withut any contm&rs. with proposed scheme in operation. 0.0 OS Fig. 4. Mode 1 Instability and damping with the proposed scheme. For brevity only the eigenvalues related to torsional frequencies are given in Table 1. The eigen values have been obtained for the system in Fig. 1, with generator generating 800 MW and the compensation level being 50%. From I A, it can be seen that few modes have positive real parts and this represents the case SSR being set in. In I1 A, SVC is incorporated at the midpoint of the transmission line, which performs only voltage control action. From I A and I1 A it can be seen that the damping of mode 0 has increased. Which confirms the fact that SVC can be used in the damping of mode 0. The measured signal (voltage) contains subsynchronous components and as it is fed at the summing point Vref, Fig. 3. ,the reference voltage oscillates with subsynchronous frequency leading to instability. This has resulted in a unstable eigenvalue(one of the SVC modes) of the system with oscillating frequency of 287.0radsec. This instability is eliminated by the insertion of a torsional filter in the measurement loop, and the result is presented in I1 B, from which the improvement in the damping of mode 1 &o can be seen. 306 0.N U.@ aa 4.15 420 Rz5 tbnelsel Fig. 5 . Damping effect of the proposed scheme for 10% change in mechanical torque. B. Time Domain Simulations Digital simulation studies have been carried out to check the validity of the results of eigenvalue studies and to test the efficacy of the proposed scheme with large disturbances. All the independent components of the system, as explained above have been modeled in PSCAD. The variables that have been plotted are: Aw is the change in generated speed in p.u, AT(LPB-GEN) the change in torque transmitted from the second Low pressure turbine to the Generator, P is the electric power generated by the generator in p.u, Qc - is the reactive power supplied by the SVC at the mid point of the transmission line. In PSCAD, simulation is started with generator as a voltage source and is ramped upto the required power and is switched to the generator-turbine setup. In the present simulations the ramping is done for 0.3 secs and switchover takes place at 1.1 seconds. Different compensation levels are considered in different cases so that the efficacy of the proposed scheme can be tested for different mode instabilities. Derivation of SVC bus angle in the PSCAD simulation is explained in appendix A. - - - oscillations being damped out with the proposed scheme in operation. From Fig.4, the time taken by the masses to settle (which is approximately 3 secs), when they are brought into operation can be seen, which is not present in the system without the proposed scheme in operation. This is because of the interaction of the controllers with the masses when they are initialized. Case 2: Fig.5, presents a the result of a case where 10% change in mechanical torque has been applied for 4 cycles at 7th second when masses have settled. The generator is generating 0.9 pu , and the compensation of the transmission line being 75%. It can be seen that the growth of oscillations is arrested though the complete damping is not achieved. Case 3: Here two, 3 phase faults have been considered. Fig. 6. presents the results with fault inductance being 0.2075H , and Fig. 7. with fault inductance 0.004H, which tune mode-3 and mode-2 respectively and make these modes unstable. The 3 phase fault has been created at 7th second. Fig. 7 presents the result for the test case I-T given in [I31 by IEEE Subsynchronous Resonance Task force. The results show that the scheme has positive damping affect on large disturbances though complete damping is not achieved. ,o 10 8 0.0 E --- ;4.m 451 ,025 4.05. nm ".W 6 t .;am :au. at54 Fig.6. Damping of 3phase fault-mode 3 instability. Case 1: In Fig. 4., the generator is generating 0.9 p.u. of power with the line compensation being 85% . This case has been selected to show the mode 1 instability. The figure shows the growth of oscillations without controllers and the * 520 42s 307 Authorized licensed use limited to: INDIAN INSTITUTE OF TECHNOLOGY BOMBAY. Downloaded on December 4, 2008 at 06:23 from IEEE Xplore. Restrictions apply. IV. CONCLUSIONS Loop Control of Static Var Sources on EHV Transmission lines,” Paper A 78 135-6 presented at the IEEE PES Winter Meeting, NewYork, 1978. R. Mathur, P. Dash and A. Hammad, “Transient and Small signal Stability of a Superconducting Turbogenerator Operating with Thyristor Controlled Static Compensator,“ IEEE Trans. Vol. PAS-98, pp. 1937-1946, 1979. 0. Wasynczuk, “Damping Subsynchronous Resonance Using Reactive Power Control,” IEEE Trans. Vol. PAS100, pp. 1096-1 104, 1981. A. E. Hammad and M. El-Sadek, “Application of a Thyristor controlled VAR Compensator for damping Subsynchronous Oscillations in Power Systems,” IEEE Trans., Vol. PAS-103, pp. 198-212, 1984. R. M. Hamouda, M. R. Irwani, and R. Hackam, “Coordinated Static Var Compensator and Power System Stabilizer for damping PS Oscillations,” IEEE Trans., Vol. PWRS -2, pp. 1059-1067, 1987. K. R. Padiyar and R. K Varma, “Static Var system auxiliary controllers for damping Torsional Oscillations,” Electric Power Energy Systems, Vol. 12, No.12, pp. 271-285, 1990 P. A. Larsen and D.A. Swann, “Applying Power System Stabilizers, Part I, General Concept,” IEEE Trans., Vol. PAS -100, pp. 3017-3024, 1981. A. A. Fouad and K. T . Khu, “Damping of Torsional Oscillations in Power Systems with series Compensated lines ,” IEEE Trans., Vol. PAS-97, No.3, pp. 744-752, 1978. D. C. Lee, R. E. Beaulieu and J. R. R. Service, “A Power System Stabilizer using Speed and Electrical Power inputs - design and field experience,” IEEE Trans., Vol. PAS -100, NO. 9, pp. 4151-4157, 1981. IEEE Subsynchronous Working Group, “First Bench Mark Model for Computer Simulation of Subsynchronous Resonance,” IEEE Trans., PAS-96, No. 5 , pp. 1565-1672, 1977. IEEE Committee Report, “Computer Representation of Excitation Systems,” IEEE Trans., Vol. PAS-87, pp. 14601464. 1968. In this study, unified operation of PSS and SVC at the midpoint of the transmission line for arresting the growth of SSR has been presented. The study has been carried out on modified IEEE FBM model, presented in [9], using the eigen value analysis and the analytical results have been verified by time domain simulations. The conclusions can be summarized as: 1. Deviation in voltage angle of SVC bus as the auxiliary stabilizing signal damps the SSR better than existing stabilizing signals. 2. Simultaneous operation of SVC(with proposed auxiliary control signal) and conventional PSS destabilizes the system. 3. The proposed scheme arrests the growth of oscillations at critical compensation levels at small as well as large disturbances. Further study has to be done to achieve complete damping and to improve the initial settling time that has been observed with the proposed scheme in operation. APPENDIX A Derivation of SVC bus voltage angle with the quantities that can be measured at the SVC bus (Fig. 1). VI = I+j.O IV31 = 1.O, angle of the SVC bus, w.r.t infmite bus ,say, 6, 1 (e3d where P, is power flow from bus 3 to bus 1. z3i,-e3,is impedance between bus 3 and bus 1. APPENDIX B Data for the PSS block parameters: BIOGRAPHIES S. A. Kbaparde: was bom at Amravati of Maharashtra state in India, received his B.E. in 1971, M.Tech. in 1973 and Ph.D. in 1980 from Indian Institute of Technology, Kharagpur. He is currently an associate professor of electrical engineering at IIT Bombay. He has several publications to his credit and his research interests include pattern recognition, Data for the SVC block parameters: K, = 1200, K, = 1.0, K,, =0.01, T, =5.0e-3 T, = 1.667e-3, T, = 0.02, G(s) = -5 ( l+s0.02)2 V. REFERENCES U1 E21 [31 141 power IEEE Power System Engineering Committee, “Analysis and Control of Subsynchronous Resonance,” IEEE Power Engineering Society Winter Meeting and Tesla Symposium, 1976. R. G . Farmer, A. L. Schwalb and E. Katz, “Navajo Project Report on Subsynchronous Analysis and Solution,” IEEE Trans., Vol. PAS-96, pp. 1226-1232, 1977. P. M. Anderson, B. L. Aganval and J. E. Van Ness, “Sub synchronous Resonance in Power Systems,” IEEE Press. H. Schweickardt, G. Romegialai and K. Reichert, “Closed 308 system security, Artificial Intelligence and applications, parallel processing and neural networks. He is senior member of IEEE and International Neural Network society. Email: eesakia@ee.iitb.ernet.in. V. Krishna: was born in Narsapur of Andhra Pradesh state in India on May 4, 1972. He is currently working towards his Ph.D degree in Power Systems at Illinois Institute of Technology, Chicago. Email: kvuppala@ece.iit.edu.