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Comparison of optimization technique of power system stabilizer by using gea

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  • 1. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 4, July-August (2013), © IAEME 225 COMPARISON OF OPTIMIZATION TECHNIQUE OF POWER SYSTEM STABILIZER BY USING GEA /PHASE COMPENSATION TECHNIQUE Mrs. Babita Nanda Associate Professor EEE Department, Malla Reddy College of Engineering for Women, Hyderabad, India ABSTRACT Power system stability is the ability of an electrical power system, for given operating conditions, to regain its state of operating equilibrium after being subjected to a physical disturbance, with the system variables bounded, so that the entire system remains intact and the service remains uninterrupted”. Traditionally the excitation system regulates the generated voltage and there by helps control the system voltage. The automatic voltage regulators (AVR) are found extremely suitable for the regulation of generated voltage through excitation control. But extensive use of AVR has detrimental effect on the dynamic stability or steady state stability of the power system as oscillations of low frequencies (typically in the range of 0.2 to 3 Hz) persist in the power system for a long period and sometimes affect the power transfer capabilities of the system. The power system stabilizers (PSS) were developed to aid in damping these oscillations by modulation of excitation system and by this supplement stability to the system .The PSS is designed by taking the consideration of gain block, signal washout and two identical phase lead compensators and the parameter are optimized by two alternative approach i.e. Phase compensation Technique & Genetic And Evolutionary Algorithm. Keywords-Power system stabilizer; Genetic algorithm; Matlab 1.INTRODUCTION The stabilizer parameters are selected in such a manner to damp the power system oscillation. In this paper optimization technique has been compared by using phase compensation and GEA algorithm. The objective function allows the selection of the stabilizer parameters to optimally place the closed-loop Eigen values in the left hand side of the complex s-plane. The single machine connected to infinite bus system is considered for this study. The effectiveness of the stabilizer tuned using the best technique; in enhancing the stability of power system. PSS is used to damp oscillations by controlling its excitation using auxiliary stabilizing signals. INTERNATIONAL JOURNAL OF ELECTRICAL ENGINEERING & TECHNOLOGY (IJEET) ISSN 0976 – 6545(Print) ISSN 0976 – 6553(Online) Volume 4, Issue 4, July-August (2013), pp. 225-231 © IAEME: www.iaeme.com/ijeet.asp Journal Impact Factor (2013): 5.5028 (Calculated by GISI) www.jifactor.com IJEET © I A E M E
  • 2. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 4, July-August (2013), © IAEME 226 up ∆ w Gain Signal washout Phase compensator Fig-1 Transfer function model of conventional PSS 2.SYSTEM INVESTIGATED The step-by-step procedure for optimizing PSS parameters by 2.1. Phase compensation technique is as follows: 2.1.1 Computation of natural frequency of oscillation (ωn) from the mechanical loop: Neglecting the effect of damping D, the characteristic equation of the mechanical loop is written as: 2 o 1M s + ω K = 0 The roots of equation are: 1 o 1 2 K ω s , s = ± j M Thus the natural frequency of oscillation is: 1 o n K ω ω = M 2.1.2. Computation of ∠GEP (Phase shift between stabilizing signal u and ∆Te) The transfer function relating stabilizing signal up and ∆Te, setting ∆δ = 0 is : e p ∆T GEP(s) = u Let γ be the phase angle of GEP(s) at ns = jω 2.1.3. Design of phase compensator Gc The phase compensator Gc is designed to provide required degree of phase compensation. For 100 % phase compensation: ∠Gc(j ωn ) + ∠GEP(j ωn ) = 0 The transfer function of phase compensator of the damping controller is given as: 1 2 1+sT Gc(s) = 1+sT 1 2T = a T Where, 1+sinγ a = 1-sinγ and 2 n 1 T = ω a Depending upon the phase shift one or two stages of the phase compensator are connected in cascade. Ks w w s T 1 + s T 1 3 2 4 (1 + s T )( 1 + s T ) (1 + s T )( 1 + s T )
  • 3. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 4, July-August (2013), © IAEME 227 2.1.4. Computation of optimum gain Ks of damping controller The required gain setting Ks for the desired value of damping ratio ξ, is obtained from: n s c 2 ξ ω M K = |GEP| |G | Where |GEP| and |Gc| are evaluated at ns = jω Damping ratio ξ = 0.5 is assumed for electromechanical mode. The washout time constant Tw = 10 seconds is chosen in present studies. Assuming two identical cascade connected lead blocks where T1=T3 and T2=T4. Only three parameters are to be optimized i.e. Kp, T1, T2.The optimum parameters of PSS obtained using Phase Compensation Technique are T1 = T3 = 0.2977 sec T2 = T4= 0.0972 sec Kp = 14.3 2.2. GEA (Genetic and Evolutionary Algorithm) The Genetic and Evolutionary Algorithm is as follows: 2.2.1. Creation of initial population: The initial population is created randomly within the upper and lower bounds of the variables specified. 2.2.2. Evaluation of individuals: A performance index J is defined to evaluate the individuals. For each chromosomes, the value of performance index is obtained ,which is assigned to it as its fitness value .The chromosomes are ranked in the descending order of the fitness value in the population. 2.2.3. If the optimization criteria (i.e. specified value of J and / maximum number of generations) is not satisfied ,the creation of new generation starts as following (step 2.2.4-2.2.8): 2.2.4. Selection: On the basis of the ranking, the chromosomes are selected for recombination .Each individual in the selection pool receives a reproduction probability depending on its own performance index and the performance indices of the other individuals in the selection pool. Different methods for selectionare,Roulette-wheel selection ,stochastic universal sampling ,local selection ,truncation selection and tournament selection . 2.2.5. Recombination: Recombination produces new individuals by combining the information contained in the parents (mating population).This is done, by combining the variables value of the parents. Depending on the representation (i, e, binary, real valued etc.) of the variables different methods are used .Discrete Recombination can be applied to all the variable representations. 2.2.6. Mutations: By Mutation the individuals are randomly altered. These variations (mutation step)are mostly small and applied to the variables of individuals with low probability specified by mutation rate. The mutation of real values means, that the randomly created values are added to the variables with a low probability. 2.2.7. Reinsertion: Reinsertion scheme determines which individuals are to exist in the new population. The selection of reinsertion scheme depends on the selection scheme used. The elitist reinsertion scheme produces less offspring than parented and replaces the worst parents. However, the fitness-based reinsertion scheme produces more offspring than needed for reinsertion and reinsert only the best offspring. The Elitist reinsertion combined with
  • 4. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 4, July-August (2013), © IAEME 228 fitness-based reinsertion, which prevents the loosing of information is the recommended method .At each generation, a given number of the least fit parents is replaced by the same number of most fit offspring. The best individuals can live for many generations. 2.2.8. Migration: The regional model divides the population into multiple subpopulations. These subpopulations evolve independently of each other for certain number of generations(isolation time ).After the isolation time is over a number of individuals is distributed between the subpopulations .The migration rate ,the selection method of the individuals for migration and the scheme of migration determines how much genetic diversity can occur in the subpopulation .The most general migration strategy is that of unrestricted migration .For each subpopulation, a pool of potential immigrants is constructed from the other subpopulation. The individual migrants are then uniformly at random determined from the pool. 2.2.9. Termination: A number of methods are available for termination of the optimization, like maximum number of generations, maximum computing time in minutes, minimal difference to defined optimum, running mean of best objective values, minimal standard deviation of all current objectives values etc. Once the predefined termination criterion is met, the optimization algorithm terminated. 2.3. Steps of Algorithm Using MATLAB Tool Box The optimization of controller parameters using GEA presented in this thesis is done using GEA toolbox along with MATLAB software package .While applying GEA, a number of parameters affects the speed of convergence of the algorithm. The typical parameters /options for applying GEA are defined as follows: 2.3.1. Number of individuals: An individual is string of variables (i.e. parameters to be optimized).The choice of number variables depends on the problem. The larger and more complex a problem is the higher the number of individuals ought to be. 2.3.2. Generation Gap: It is the fraction of the population to be reproduced every generation .If generation gap >1,more offspring than individuals in the population are produced. However, if generation gap <1, less offspring than the individuals in the population are produced, some parents survive in next generation. 2.3.3. Reinsertion rate: This options defines how much parents are replaced by the produced offspring. The reinsertion rate of 1 means all the parents may be replaced by offspring. 2.3.4. Mutation rate: It is the factor of how many variables per individuals are mutated. Mutation rate =1 means on an average 1 variable per individual is mutated. 2.3.5. Mutation range: This option defines the range of the mutation steps for every variable depending on the size of the domain of the respective variables. 2.3.6. Mutation Precision: This option defines the precision of the mutation steps depending on the mutation range. 2.3.7. Migration interval: This option defines the number of generations between successive migrations. It is also called as isolation time.
  • 5. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 4, July-August (2013), © IAEME 229 3. FLOW CHART OF GEA GEN=1 GEA (Genetic and Evolutionary Algorithm -- The optimum PSS parameters are obtained by using GEA, minimizing the following performance index, J 2 0 ( )w dt ∞ = ∆∫ The range of the parameters over which search is carried out are given below: 0.1 < T1< 0.5 0.1 < T2 < 0.5 5 <Kp< 20 T1 = T3 T2 = T4 J is evaluated considering step increase in Pm by 5%. Apply GA operators: selection,crossover and mutation NO YES Specify the parameters for GA Generate initial population Time-domain simulation Find the fitness of each individual in the current population Gen.>Max.G en? Gen.= Gen.+1 start STOP
  • 6. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 4, July-August (2013), © IAEME 230 Fig-2: shows the variation of value of objective function J corresponding to best individual in each generation with the generation number. The optimum parameters of PSS obtained using GEA are T1 = T3 = 0.367 sec T2 = T4 = 0.1863 sec Kp = 11.58 Dynamic responses for the system are obtained with PSS optimized by two alternative approaches considering a step increase in mechanical power Pm by 5%. (i.e. ∆ Pm = 5%) The values are taken for showing the comparison is shown in the below: Number individuals---------------10 Selection. Name-------------------selsus Selection. Generation Gap-------0.9 Selection. Reinsertionrate-------0.8 Selection. Reinsertion Method --2 Recombination. Name------------recdis Recombination. Rate--------------0.7 Mutation.Name--------------------mutreal Termination. Running Mean------0 Termination. Method---------------4 VLUB=[1 1 -20 -10.5;10 10 10] 4. CONCLUSION It is clear that the responses with GEA optimized PSS settles faster than the phase compensation Technique. Hence the optimum parameters obtained by GEA are considered. 5. ACKNOWLEDGMENT I would like to express sincere gratitude to my Guide Prof. M. L. Kothari. He is Emeritus Professor in Electrical Department from IIT DELHI .It has been my proud privilege to work under Prof. M. L. Kothari, a luminary in the field of power system engineering. I am very grateful for continued guidance, valuable advice and suggestion and the co-operation extended throughout the project work
  • 7. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 4, July-August (2013), © IAEME 231 6. REFERENCES [1] L. Gyugyi, "Reactive power generation and control by thyristor circuits", IEEE Transactions on Industrial Applications, Vol. IA-15, No. 5, Sep/Octo. 1979, pp. 521-532. [2] N.G. Hingorani, "FACTS - Flexible AC Transmission Systems", IEE fifth international conference on AC and DC Transmission, London, 1991, pp. 1-7. [3] C. Schauder and H. Mehta, “Vector Analysis and control of advanced static VAR compensators”, IEE Proceedings-C, Vol. 140, No. 4, July 1993. [4] H.F. Wang and F.J. Swift, “Capability of the static var compensator in damping power system oscillations.”IEE Proc.-Gener. Transm. Distib., Vol.143, No.4,July. 1996. [5] H.F. Wang and F.J. Swift, "A Unified Model for Analysis of FACTS Devices in Damping Power System Oscillations, Part I: Single-machine Infinite- bus Power Systems", IEEE Transactions on Power Delivery, Vol. 12, No. 2, April 1997, pp. 941-946. [6] C. Schauder and M. Gernhardt, E. Stacey, T. Lemak, L. Gyugyi, T. W. Cease and A. Edris, "Operation of ±100 MVA TVA STATCON," IEEE Trans. Power Delivery, vol. 12, pp. 1805-1811, Oct. 1997. [7] H.F. Wang, "Phillips - Heffron model of power systems installed with STATCOM and applications", IEE proc.-Gener. Transm. Distrib., Vol. 146, No. 5, September 1999, pp. 521-527. [8] H.F. Wang, "Applications of damping torque analysis to STATCOM control”, Electrical Power and Energy Systems 22 (2000) 197–204. [9] N. G. Hingorani and L. Gyugyi, “Understanding FACTS: concepts and technology of flexible ac transmission system”, IEEE Press, New York, 2000. [10] Pablo Garcia-Gonzalez, Aurelio Gracia-Cerrada, “Control system for a PWM based STATCOM”, IEEE Trans. Power Delivery, vol. 15, No. 4,pp. 1252-1257, Oct. 2000. [11] I Papic, “Mathematical analysis of FACTS devices based on a voltage source converter Part 1: mathematical models”, Electric Power Systems Research 56 (2000) 139–148. [12] M. Mohaddes, A. M. Gole, and SladjanaElez, “Steady State Frequency Response of STATCOM”, IEEE Transactions on Power Delivery, VOL. 16, NO. 1, Jan. 2001. [13] Z. Yang, C. Shen, L. Zhang, M.L. Crow and S. Atcitty, "Integration of a STATCOM and Battery energy storage", IEEE Transactions on Power Systems, Vol. 16, No. 2, May 2001, pp. 254-260. [14] Olimpo Anaya-Lara and E. Acha, “Modeling and Analysis of Custom Power Systems by PSCAD/EMTDC”, IEEE Transactions on Power Delivery, VOL. 17, NO.1 Jan. 2002. [15] A.H.M.A. Rahim, S.A. Al-Baiyat and H.M. Al-Maghrabi, "Robust damping controller design for static compensator", IEE Proc.-Gener. Transm. Distrib., Vol. 149, No. 4, July 2002, pp. 491-496. [16] N. Mithulananthan, C.A. Canizares, J. Reeve and G.J. Rogers, "Comparison of PSS, SVC and STATCOM controllers for damping power system oscillations", IEEE Transactions on Power Systems, Vol. 18, No. 2, May 2003, pp. 786-792. [17] A. Arulampalam, J.B. Ekanayake and N. Jenkins,” Application study of a STATCOM with energy storage” IEE Proc.-Gener. Transm. Distrib.,Vol 150, No. 3 May 2003. [18] Claudio A. Canizaresa, Massimo Pozzib, SandroCorsib, EdvinaUzunovic, “STATCOM modeling for voltage and angle stability studies”, Electrical Power and Energy Systems 25 (2003) 431–441. [19] Amir H. Norouzi and A. M. Sharaf, “Two Control Schemes to Enhance the Dynamic Performance of the STATCOM and SSSC”, IEEE Transactions on Power Delivery, Vol. 20, No. 1, Jan 2005. [20] I. Papic, P. Zunko, D. Povh and M. Weinhold, "Basic control of Unified Power Flow controller", IEEE Trans. on Power Systems, Vol. 12, N0. 4, November 1997, pp. 1734-1739. [21] Gowrishankar Kasilingam, “Effect of Genetic Pid Power System Stabilizer for a Synchronous Machine”, International Journal of Electrical Engineering & Technology (IJEET), Volume 4, Issue 4, 2013, pp. 8 - 21, ISSN Print : 0976-6545, ISSN Online: 0976-6553. [21] Tan Qian Yi, Gowrishankar Kasilingam and Mr.Raman Raghuraman, “Optimal-Tuning of Pid Power System Stabilizer in Simulink Environment for a Synchronous Machine”, International Journal of Electrical Engineering & Technology (IJEET), Volume 4, Issue 1, 2013, pp. 115 - 123, ISSN Print : 0976-6545, ISSN Online: 0976-6553.