A Novel Approach to Small Signal Stability Enhancement using Fuzzy Thyristor Susceptance control of SVC using Lyapunov Stability

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1 16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, A Novel Approach to Small Signal Stability Enhancement using Fuzzy Thyristor Susceptance control of SVC using Lyapunov Stability D.Harikrishna, R.S.Dhekekar, * N.V.Srikanth Department of Electrical Engineering, National Institute of Technology, Warangal, India durgamharikrishna@ieee.org Abstract This paper presents a novel approach to small signal stability enhancement using fuzzy thyristor susceptance control of static VAR compensator (SVC). Static VAR compensator is proven the fact that it improves the dynamic stability of power systems apart from reactive power compensation; it has multiple roles in the operation of power systems. The additional auxiliary control signals to SVC play a very important role in mitigating the rotor electro-mechanical low frequency oscillations. A proportional-integral-derivative (PID) type controller is designed using the generator speed deviation, as a modulated signal to SVC, to generate the desired damping, is proposed in this paper. The fuzzy logic controller is considered to generate the required incremental firing angle delays for SVC. Fuzzy rules are designed based on Lyapunov s stability criteria. The simulations are carried out for multi-machine power system at different operating conditions. Keywords: Static VAR compensator, Fuzzy logic, Small signal stability, Thyristor susceptance control and FACTS I. INTRODUCTION The ability of power system to maintain synchronism under small disturbances is known as dynamic stability. In power system such small disturbances continuously occur due to small variations in loads and generation. The disturbances are considered sufficiently small for linearization of system equations to be permissible. Instability may result in two forms. (i) Steady increase in rotor angle due to lack of sufficient synchronizing torque. (ii) Rotor oscillations of increasing amplitude due to lack of sufficient damping torque. The nature of system response to small disturbances depends on a number of factors including initial operating conditions, transmission system and the type of generator excitation controls used. In today s practical power systems, small signal stability is largely a problem of insufficient damping of oscillations. Modern Power Systems are equipped with fast acting static excitation systems. As these units become a large percentage of the generating capacity, they have a large impact upon the small signal stability of power systems. They introduce negative damping at the electromechanical oscillation frequencies of the machines in the range of 0.1Hz to 2.5 Hz. They make the system unstable under local and inter-area modes of oscillations. In particular, when the system is weak and with weak tie lines, even a small disturbance will make the system unstable. The purpose of dynamic stability is to examine the dynamic behavior of a synchronous machine under small perturbations. Since the machine must remain in synchronism under small perturbations, it is essential to have positive damping for the machine. The damping torque of the synchronous machine is affected by a number of factors viz. machine loading, excitation controls, PSS parameters and loads etc. Hence, a detaillinearized model is required to examine the dynamic stability. Power System Stabilizers were developed to damp out these oscillations by modulating generator excitation and introducing positive damping to the system. Several attempts are made to replace the conventional power system stabilizers with Fuzzy Logic Based, Flexible AC Transmission Systems (FACTS) controllers based and Artificial Neural Network based stabilizers are proposed in the literature. This is because of the fact that the above novel approaches are superior to algorithmic methods and are adaptive in nature. They also possess fast response with reduced transients and can also adapt themselves to the non-linearity in the system. The limitation of the fuzzy based and adaptive fuzzy based stabilizers is in the development of rule base. This rule base may vary from system to system. The limitations of ANN based stabilizers are in its learning ability and suitable learning algorithms are required and this may even system dependent. Flexible AC transmission system (FACTS) is a concept of promoting thyristor-controlled devices in power systems with the objective of optimally using the existing transmission facilities. FACTS are to enhance the transmission system to be more flexible by enhancing the power transfer capabilities of transmission system and also improving the stability of power system. The FACTS devices play multiple roles viz. improving the power transfer capabilities, improving the dynamic stability of power system etc. Static var compensator (SVC) is one of the FACTS devices that are used widely by several utilities to support the voltage of power transmission systems. The SVCs with supplementary control signals in their voltage control loops can successfully improve the damping of power system oscillations and enhance power systems stability. In literature researchers have proposed techniques for tuning SVC stabilizers to enhance the damping of electro-mechanical oscillations of power systems and detailed simulations of SVC has taken place for the past decade to overcome the problem of dynamic * N.V. Srikanth is Associate Professor, Department of Electrical Engineering, NIT Warangal. D.Harikrishna and R.S.Dhekekar are Ph.D. Research Scholars at Department of Electrical Engineering, NIT Warangal..mail ID durgamharikrishna@ieee.org

2 16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, stability. E.Z.Zhou et al [1] begins with an investigation of the SVC effect on a simple single-machine power system. It is found that SVC can dynamically alter the system transfer characteristics by changing its reactive output. The basic control actions to change machine electrical power and to alter the characteristics of a power system, to increase power system damping are discussed based on the equal area criterion. Yousin Tang et al [2] proposed a comprehensive methodology, which includes (i) accurate modeling of FACTS elements, generators, etc. (ii) system steady state periodic analysis (iii) formulation of system steady state equations, and (iv) system eigen value analysis. Kitti phorang et al [4] presented the capability of fuzzy logic based stabilizer used for generating the supplementary control signal to voltage regulator of SVC for improving the damping of inter area modes of oscillations in power system. Fuzzy based SVC stabilizer used for generating the supplementary signal to voltage regulator control loop of SVC is proposed. Effective rule base development for fuzzy thyristor susceptence control of SVC is not reported. This paper attempts to replace the existing conventional power system stabilizers with fuzzy SVC based stabilizers. The fuzzy logic control is used to generate the required incremental firing angles of SVC controller, which is fast and adaptive and will not increase the order of the system. Additional PID damping controllers are placed in the supplementary control signals of SVC in order to achieve better dynamic performance. The rule base of fuzzy logic controller is developed using phaseplane plots and by means of limit cycle analysis, based on Lyapunov s stability for the input variables that are given to fuzzy logic controller. The method is tested on multimachine power systems. II. MATHEMATICAL MODELING The linearised mathematical modeling of the multimachine power system is carried out by linearising the equations around the operating point and hence obtained the required state equations [11]. A three-machine ninebus system is taken for the linearised modeling of multimachine power system [11], and hence its state equations are obtained. The order of multimachine power system (three-machine nine-bus system) is eleventh order with out power system stabilizers. A. Basic stability models of SVC The basic stability model of SVC [12] shown in Fig. 1(a), is used for the simulations and tested multi-machine power systems. The basic model of SVC consists of a voltage regulator block, which estimates the susceptance value from the measurement block, which measures the current through SVC controller. The thyristor susceptance block yields the incremental change in the susceptance value when a firing angle delay is given to it. The Z th is the thevinins impedance of SVC controller, which is generally specified as a constant. Fuzzy logic controller replaces the thyristor susceptance controller in this paper shown in Fig. 1(b). Fuzzy logic controller is fast, adaptive and reduces the order of the SVC controller. Fuzzy thyristor susceptance control of SVC with supplementary PID damping controller shown in Fig. 2 is used, as this introduces additional damping in the system and damps the rotor mechanical low frequency oscillations quickly. They are placed in the supplementary control signal of SVC. Additional PID damping controllers are used to obtain Vref3 signal from the generator speed deviation ω. Fig. 1(a). Static VAR compensator model Fig. 1(b). Fuzzy Thyristor susceptance control of SVC model Fig. 2. Fuzzy Thyristor susceptance control of SVC with supplementary PID damping controller. B. Modeling of multimachine power system with fuzzy SVC based PSS Modeling of multimachine power system is obtained by considering the three-machine nine-bus system [11]. Generator 1 is taken as reference and hence is modeled as classical model, Generators 2 & 3 are modeled as twoaxis models [11]. The excitation system on machines 2 & 3 are modeled as one time lag transfer function. The rotor dynamics of machines 2 & 3 are studied with respect to machine 1 [13]. Thus the state equation of the form X & = AX + BU and Y = CX + DU are obtained for the three machine nine bus system along with the Fuzzy SVC which is shown in the Fig. 3. The state vector X and the input vector U are as follows: X T = [ ω 1 E q2 E d2 ω 2 E q3 E d3 ω 3 δ 12 δ 13 E FD2 E FD3 Z 1 Z 2 Vm 1 Vm 2 V ref2 V ref3 ] and U T = [ T m1 T m2 V ref4 T m3 V ref5 ]. Perturbations on change in d-axis stator voltages are negligible. So, eliminating E d2 and E d3 and

3 16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, rearranging the state equation, the Unified Philips Heffron model for the multimachine power system is obtained and the new state vector X and the input vector U are as follows: X T = [ ω 1 E q2 ω 2 E q3 ω 3 δ 12 δ 13 E FD2 E FD3 Z 1 Z 2 Vm 1 Vm 2 V ref2 V ref3 ] and U T = [ T m1 T m2 V ref4 T m3 V ref5 ]. C. Fuzzy thyristor susceptance control using lyapunov stability The fuzzy logic controller, which replaces the thyristor succeptance control block of SVC, is utilized as the change in incremental firing angles, to obtain the change in the succeptance ( B). The inputs given to the fuzzy logic controller are the succeptance B which is the estimated output of voltage regulator block and the error input given to the voltage regulator block of SVC model. These inputs are chosen because the estimated succeptance and the error signals are responsible for obtaining the change in the succeptance of SVC. The inputs and the output of fuzzy logic controller are fuzzified using the triangular fuzzifications for seven linguistic variables viz., Negative big (NB), Negative medium (NM), Negative small (NS), Zero (ZE), Positive small (PS), Positive medium (PM) and Positive big (PB). The inference rules are framed with the aid of phase-plane plots and limit cycles of input variables [10] that are given to the fuzzy controller. The Lyapunov s stability criterion is applied for obtaining the stabilized phase-plane plots by the rule base modifications, which actually reduces the cumbersome task of heuristic rule base formation [10]. The output of the fuzzy logic controller is compared with the output of thyristor succeptance controller of SVC block and the rules are modified until both the outputs are same. Hence, this method of replacement of thyristor succeptance control block with fuzzy logic controller achieves the desired succeptance change quickly. Fuzzy Logic Controller input1= Z 1 (estimated susceptance i.e. output of voltage regulator), Fuzzy Logic Controller input2 = V error ( V ref3 - V m ), Fuzzy Logic Controller output = B, ( B = Vout). The block diagram of Fuzzy logic controller used in SVC model is shown in Fig. 3. Fig. 3. Fuzzy Logic controlled Thyristor susceptance controller D. Fuzzy Thyristor controlled SVC with PID Damping Controller One of the most common controllers available commercially is the proportional integral derivative (PID) controller. Unified Philips Heffron model of MMPS with Fuzzy Thyristor controlled SVC along with PID damping controller is developed as shown in Fig. 4. Fuzzy Thyristor controlled SVC with PID damping controller is used to improve the dynamic response as well as to reduce or eliminate the steady-state error. The simulations are carried out for different cases with PID damping controlled SVC placed on the terminal buses of machine 2 and machine 3 respectively, shown in Fig. 7. Fig. 4. Unified Philips Heffron model of MMPS with Fuzzy Thyristor controlled SVC along with PID damping controller III. SIMULATION AND RESULTS The linearized equations of multi-machine power system (3- machine nine-bus system) are solved using Runge Kutta forth order method. This system is simulated for the SVC, fuzzy thyristor susceptance controlled SVC and PID damping controlled fuzzy thyristor susceptance controlled SVC at different operating conditions. A. Multi-machine power system (MMPS) For machine 2 the settling times of δ 12 and ω 12 for operating condition 1 ( T m1 = 10%, T m2 = 0 and T m3 = 0) with SVC based power system stabilizers placed at the terminal voltages of machines 2 and 3 are 13 seconds. The peak over shoots in δ 12 and ω 12 are pu and 2.5e-4 pu respectively. The steady-state error in δ 12 is pu. The results are shown in Table I. whereas for machine 3 the settling times of δ 13 and ω 13 are 12 seconds. The peak over shoots in δ 13 and ω 13 are pu and 2.0e-4 pu respectively. The steady-state error in δ 13 is pu. The results are shown in Table II. The output plots for δ 12 and δ 13 are shown in Fig. 5 and Fig. 6 respectively. With fuzzy SVC based power system stabilizers placed at the terminal voltages of machines 2 and 3, for operating condition 1 the settling times of δ 12 and ω 12 for machine 2 are 12 seconds. The peak over shoots in δ 12 and ω 12 are pu and 2.8e-4 pu respectively. The steady-state error in δ 12 is pu. Whereas for machine 3 the settling times of δ 13 and ω 13 for operating condition 1 are 12 seconds. The peak over shoots in δ 13 and ω 13 are pu and 2.2e-4 pu respectively. The steady-state error in δ 13 is pu. The output plots for δ 12 and δ 13 are shown in Fig. 7 and Fig. 8 respectively. With PID damping controlled fuzzy SVC based power system stabilizers placed at the terminal voltages of machines 2 and 3 for operating condition 1, the settling times of δ 12 and ω 12 are 3 seconds. The peak over shoots in δ 12 and ω 12 are pu and 3e-4 pu respectively. The steady-state error in δ 12 is pu. For machine 3 the settling times of δ 13 and ω 13 for operating condition 1 are 4 seconds. The peak over shoots in δ 13 and ω 13 are pu and 3e-4 pu respectively.

4 16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, The steady-state error in δ 13 is pu. The output plots for δ 12 and δ 13 are shown in Fig. 9 and Fig. 10 respectively. The Terminal Voltage Fluctuations for machines 2 and 3 are shown in Fig. 11 and Fig. 12 respectively. The results for multi-machine power system for operating conditions 1 for machine 2 and 3 are shown in Table I and II respectively where as the results for operating condition 2 for machine 2 and 3 are shown in Tables III and IV respectively. Fig 8. MMPS with fuzzy SVC based PSS ( δ 13 Vs time) Fig 5. MMPS with SVC based PSS ( δ 12 Vs time) Fig. 9 MMPS with PID fuzzy SVC based PSS ( δ 12 Vs time) Fig 6. MMPS with SVC based PSS ( δ 13 Vs time). Fig. 10 MMPS with PID fuzzy SVC based PSS ( δ 13 Vs time) Fig 7. MMPS with fuzzy SVC based PSS ( δ 12 Vs time)

5 16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, Fig. 11 MMPS with PID fuzzy SVC based PSS ( V t2 Vs time) Fig. 12 MMPS with PID fuzzy SVC based PSS ( V t3 Vs time) TABLE I RESULTS OF MACHINE 2 FOR MULTI-MACHINE POWER SYSTEM OPERATING CONDITION 1 ( T m1 = 10%, T m2 = 0 and T m3 = 0) δ 12 ω 12 V t2 With SVC e-4-4e e-4 With Fuzzy SVC e-4-4.2e e-4 With PID Fuzzy SVC e-4-0.5e e-3 TABLE II RESULTS OF MACHINE 3 FOR MULTI-MACHINE POWER SYSTEM OPERATING CONDITION 1 ( T m1 = 10%, T m2 = 0 and T m3 = 0) δ 13 ω 13 V t3 With SVC e-4-3e e-4 With Fuzzy SVC e-4-3e e-4 With PID Fuzzy SVC e-4 1.5e e-4 TABLE III RESULTS OF MACHINE 2 FOR MULTI-MACHINE POWER SYSTEM OPERATING CONDITION 2 ( T M1 = 0, T M2 = 10% AND T M3 = 0) δ 12 ω 12 V t2 With SVC e-4-4.4e e-4 With Fuzzy SVC e-4-4.6e e-4 With PID Fuzzy SVC e-4-5e e-3 TABLE IV RESULTS OF MACHINE 3 FOR MULTI-MACHINE POWER SYSTEM OPERATING CONDITION 2 ( T M1 = 0, T M2 = 10% AND T M3 = 0) δ 13 ω 13 V t3 With SVC e-4-3e e-4 With Fuzzy SVC e-4-4e e-4 With PID Fuzzy SVC e-4-2e e-4 IV. CONCLUSIONS In this paper a novel approach has been adopted to enhance the small signal stability of power system using fuzzy thyristor susceptance control of SVC. Lyapunov direct method is utilized to design the fuzzy rules. Apart from damping of electro-mechanical oscillations of the generator, terminal voltages of generators are also analyzed for different case studies and operating conditions, and tested on multi-machine power system. The conclusions are i) Using fuzzy thyristor susceptance control of SVC, order of the SVC model has been reduced. ii) Tedious fuzzy rule tuning has been avoided using Lyapunov stability. iii) For the multi-machine power system under operating condition 1, the settling times of the rotor oscillations of machine 2 has reduced from 13 seconds with SVC based stabilizers to 3 seconds with PID fuzzy SVC based stabilizers. The settling times of the change in terminal voltages has reduced from 10 seconds to 3 seconds respectively. Whereas for machines 3, the rotor oscillations were damped out from 12 seconds with SVC based stabilizers to 4 seconds with PID fuzzy SVC based stabilizers. The settling times of the change in terminal voltages has reduced from 10 seconds to 4 seconds. Hence, it is evident that fuzzy SVC with sufficient supplementary damping controllers can improve the dynamic stability of power system; it is very fast as fuzzy controllers can achieve the incremental firing angles to enhance the succeptance of SVC. Hence, they can be utilized for the real-time control of power systems.

6 16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, REFERENCES [1] E.Z. Zhou, Application of static VAR compensators to increase power system damping, IEEE Trans. on Power Systems, Vol.8, No.2, PP May [2] Yousin. Tang & A.P Sakis Meliopoylos, Power Systems small signal stability analysis with FACTS elements, IEEE, on Power delivery, vol.12, no. 3, July [3] H.F.Wans, M.Li & F.J.Swift, FACTS based stabilizer designed by the phase compensation method PART I; Single machine infinite bus system, Proceedings of fourth International Conference on APSC, APS COM, pp , November [4] Kitty Phorang & Prof.Dr.Yoshibumi Mizutani, Damping improvement of oscillation in power system by fuzzy logic based SVC stabilizer, IEEE [5] B.Changaroom, S.C.Srivatsava, D.Tukaram & S.Chirarattanam, Neural network based power system damping controller for SVC, IEE proceedings Part-C, Vol.146, No.4, pp , July [6] Haifeng Wang, A Unified model for the analysis of FACTS Devices in damping power system oscillations Part III; Unified power flow controller, IEEE- Transactions- PD, Vol. 15, no. 3, pp , July [7] Farsangi, M.M. Song, Y.H. Lee, K.Y. Kerman Univ., Iran, Choice of FACTS device control inputs for damping inter-area oscillations, IEEE Transactions on Power Systems, pp , Vol. 19, May [8] K. Ellithy, A. Al-Naamany, A hybrid neuro-fuzzy static var compensator stabilizer for power system damping improvement in the presence of load parameters uncertainty, Electric Power Systems Research 56, pp , March 2000 [9] C.C. Lee, Fuzzy Logic in Control Systems, Fuzzy Logic controller Part I and II, IEEE Transactions on Systems Man and Cybernetics, Vol. 20, pp , March/April [10] D.Driankov, H.Hellendroon and M.Reinfrank, An Introduction to Fuzzy Control, Springer-Verlag Berlin Heidelberg 1993, USA. [11] P.M.Anderson and A.A. Fouad, Power System Control and Stability, The IOWA state university press, AMES, IOWA, USA. [12] IEEE special stability controls working group, Static VAR compensator models for power flow and Dynamic performance simulation, IEEE Transaction on power systems, Vol. 19, No. 1, pp , February [13] D. Harikrishna and N.V. Srikanth, Unified Philips-Heffron Model of Multi-Machine Power System equipped with PID damping controlled SVC for Power Oscillation Damping, INDICON 2009, IEEE India Council Conference, pp , Dec APPENDIX NOMENCLATURE: K 1 = Change in Electrical Power for a change in rotor angle with constant flux linkage. K 2 = Change in Electrical Power for a change in the direct axis flux linkage with constant rotor angle. τ do = Direct axis open circuit time constant of the machine. K 3 = An Impedance factor, and K 4 = Demagnetizing effect of a change in rotor angle (At steady state). K E = Exciter Gain, T E = Exciter Time constant. V t = Change in Synchronous machine terminal Voltage. K 5 = V t /δ = Change in the terminal Voltage with change in rotor angle for constant E q. K 6 =V t /E q =Change in the terminal voltage with change in E q for constant δ Tm is the mechanical torque disturbance. δ = change in the rotor angle of the generator w.r.t the infinite bus, ω is the change in the speed/angular velocity of the generator w.r.t the infinite bus and Vt is the change in the terminal voltage of the generator w.r.t the infinite bus voltage. where e ss is the steady-state error, t ss is the settling time and M p is the peak over shoot. Data for 3-machine 9-bus system: (All flows are in MW & MVAR) Generator 1 (G1): j27, Generator 2 (G2): j6.7 and Generator 3 (G3): - 85 j10.9. Load A: j50, Load B: j30 & Load C: j35. T m1, T m2, and T m3 are the torque disturbances on machine 1, 2 and 3 respectively. δ 12 and δ 13 are the rotor angles of machine 2 and 3 w.r.t machine 1 respectively. ω 12 and ω 13 are the angular velocities of machines 2 and 3 w.r.t machine 1 respectively. V t2 and V t3 are the change in the terminal voltages of machine 2 and machine 3 w.r.t machine 1 respectively. Data for basic SVC stability model: K R = Voltage regulator Gain = 80 T R = Voltage regulator time constant = seconds T d = Thyristor susceptance control firing angle delay = seconds T b = Thyristor susceptance control time constant = seconds. Z th = The thevinins impedance = 0.02 pu. T m = The measurement block time constant = seconds. BIOGRAPHIES D.Harikrishna Research Scholar at Electrical Engineering Department, National Institute of Technology, Warangal. His areas of interests are Power System Stability, application of FACTS Controller in power systems and Artificial Intelligent Techniques applications to Power Systems. R.S.Dhekeker from S.S.G.M.College of Engg Shegaon, India. He is working as senior lecturer in the Department of Electronics. His areas of interests are Power Electronics, Microprocessors, and Applications of Power Electronics to Power Systems. Presently he is Research Scholar at National Institute of Technology, Warangal, India in Electrical and Electronics Department. N.V. Srikanth has worked in the area of small signal stability using intelligent FACTS controllers. He is as an Associate Professor in the Department of Electrical and Electronics Engineering, National Institute of Technology, Warangal, India. His areas of interests are fuzzy logic Applications in Power Systems, Power System, Stability Control and Application of FACTS Controllers in Power Systems.

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