TECHNOLOGY (IJEET) Miss Cheshta Jain Department of electrical and electronics engg., MITM, Indore

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1 INTERNATIONAL International Journal of Electrical JOURNAL Engineering and OF Technology ELECTRICAL (IJEET), ISSN 976 ENGINEERING 6545(Print), ISSN & TECHNOLOGY (IJEET) ISSN (Print) ISSN (Online) Volume 3, Issue 3, October - December (212), pp IAEME: Journal Impact Factor (212): (Calculated by GISI) IJEET I A E M E DETERMINATION OF CONTROLLER GAINS FOR FREQUENCY CONTROL BASED ON MODIFIED BIG BANG-BIG CRUNCH TECHNIQUE ACCOUNTING THE EFFECT OF AVR ABSTRACT Miss Cheshta Jain Department of electrical and electronics engg., MITM, Indore cheshta_jain194@yahoo.co.in Dr. H.K. Verma Department of electrical engg., S.G.S.I.T.S., Indore vermaharishgs@gmail.com Dr. L.D. Arya Department of electrical engg., S.G.S.I.T.S., Indore ldarya@rediffmail.com This paper presents a methodology for determining optimized controllers gains for frequency control of two area system. The optimized gains have been obtained using a fitness function which depends on peak overshoot, steady state error, settling time and undershoot. The AVR loop has been included in optimization and its effect on optimized PID controller has been investigated. The optimization has been achieved using Big Bang-Big Crunch (BB-BC) optimization. The performance of controllers as obtained by BB-BC technique have been compared on two area system with that obtained using modified particle swarm optimization (PSO) and differential evaluation (DE) technique. Keywords: AGC, AVR, Big Bang-Big Crunch, Differential evolution algorithm, Particle swarm optimization. NOMENCLATURE f : frequency deviation. i : subscript referring to area (i = 1, 2, ). P tie (i,j) : change in tie line power. P L : load change. D : P L / f R : governor Speed regulation parameter. T h : speed governor time constant. T t : speed turbine time constant : power system time constant. T P 52

2 International Journal of Electrical Engineering and Technology (IJEET), ISSN (Print), ISSN T e T G T s K P H U s M p ts tr e ss : exciter time constant. : generator field time constant. : sensor time constant. : power system gain. : inertia constant. : undershoot : overshoot : settling time. : rise time. : steady state error. 1. INTRODUCTION AN interconnected power system is made up of several control areas with respect to megawattfrequency control. In each area, an AGC observes the system frequency, tie-lines flow and computes the net change in the generation required to control error and set position of generation within each area to keep the error (area control error) at a low value. Over the past decades, many researchers have applied different control strategies, such as classical control, variable structure control, optimal feedback control and robust control to AGC problem in order to achieve better performance [1]. Yu et al. [2] have praised a linear quadratic regulation (LQR) method to tune PID gain, but it requires mathematical calculation and solving equations. Sinha et al. [3] introduced genetic algorithm (GA) based PID controller for AGC of two areas reheat thermal system. Ghoshal et al. [4] proposed PSO based PID controller for AGC. Some deficiencies in performance of GA method are identified by above paper. To stabilize the system for load disturbance comparative transient performance of thyristor controlled phase shifter (TCPS) and superconducting magnetic energy system (SMES) are proposed by Praghnesh Bhatt et.al with optimized gains by improved Particle swarm optimization (craziness based PSO) [1]. The controller of AGC and AVR are set for a particular operating condition. Many investigations in the area of AGC of isolated and interconnected power system have been reported in the past but they do not consider the effect of AVR. Dabur et al. [5] proposed AGC- AVR for multi-area power system with demand side management. The paper is mainly focused on reduction of total load demand during period on peak demand to maintain security of system but not explained the selection of optimum gain of controller. The Big Bang- Big Crunch (BB-BC) a new optimization method relied on one of the theories of the evaluation of the universe namely Big Bang theory and Big Crunch theory which is introduced by Erol and Eskin [6]. This method has a low computational time and high convergence speed. The proposed method is similar to the Genetic Algorithm in respect to creating an initial population. The BB-BC method eliminates the possibility of Medicare scalability; one of the disadvantages of GA based learning method. In this paper a BB-BC based controllers is proposed as the supplementary controllers, which show better dynamic response compared with DE and PSO based optimized controllers. In view of the above, the following are the main objectives of the proposed work to: 1. Obtain the optimize gain of integral controller of AGC and PID controller of AVR by Big Bang- Big Crunch algorithm for AGC-AVR of two area interconnected system. 2. Compare dynamic response of AGC system with and without AVR using MATLAB. 3. Compare the performance of the Big Bang- Big Crunch based controller to the DE and PSO based controller. The rest of the paper is organized as follows: In section 2 the two area system model and scheduled loading availability model are developed. Section 3 describes BB-BC algorithm and the implementation of BB-BC based controller is presented in section 4. Section 5 shows the result with detailed discussion and conclusion is drawn in section AGC-AVR SYSTEM MODEL The system investigated consists of two control areas with reheat type thermal unit connected by tie-lines that allows power exchange between areas. If the load on the system is increased the 53

3 International Journal of Electrical Engineering and Technology (IJEET), ISSN (Print), ISSN speed of turbine reduces before the governor can adjust the input of steam correspond to the new load. As the change in output of system become smaller, the position of governor move to set point to maintain a constant speed in automatic generation control (AGC). On the other hand the generator excitation system control generator voltage and reactive power flow using automatic voltage regulator (AVR) [19]. The proposed work investigates the effect of coupling between AGC and AVR. 2.1 AGC System: The AGC have two control actions (i) primary control which makes the initial readjustment of frequency to nominal value, (ii) supplementary control to provide precise control strategy for fine adjustment of the frequency. The main function of supplementary control is to maintain system frequency at predetermined set point after a load perturbation. The input to the supplementary controller of the i th area is the area control error (ACE i ) which is given by: = ( (, + (1) Where, B i is frequency bias coefficient of i th area, f i is frequency error, P tie is tie-line power flow error and n is number of interconnected areas [18]. The area bias B i determines the amount of interaction during load perturbation in neighboring area. To obtain better performance, bias B i is selected as: (2) 2.2 AVR System: This paper studied on coupling effect by extending the linear AGC to include the excitation system. The real power transfer over the line is: = (3) This is the product of the synchronizing power coefficient (Ps) and the change in the power angle ( δ). Now include small effect of voltage on real power as: = + 1 (4) Where, K1 is the change in electrical power for a small change in stator emf and V f is output of generator field. Also, including the small effect of rotor angle on generator terminal voltage as: = (5) Where, K2 is the change in the terminal voltage for a small change in the rotor angle at constant stator emf, and K3 is the change in the terminal voltage for a small change in stator emf at a constant rotor angle. Now finally modified generator field output is: = ( ( 4 (6) Where, V e is exciter output voltage, K G is a generator gain constant, and T G is generator time constant. The value of all the gains, time constants and constants are given in appendix. The complete transfer function model of AGC-AVR is shown in fig 1. 54

4 International Journal of Electrical Engineering and Technology (IJEET), ISSN (Print), ISSN Fig.1: Linear model of two area AGC-AVR system 3. OVERVIEW OF BIG BANG-BIG CRUNCH ALGORITHM The Big Bang-Big Crunch algorithm has been introduced by Erol and Eskin. This algorithm is based on the formation of universe e stated by Big Bang theory. According to this theory the universe was once a sphere with infinite radius and density. Due to several internal forces, the existed mass is exploded massively called Big-Bang and billions of particles moved outwards. Once particles start spreading, a gravitational force arises which depends on masses of two bodies considered and distance between them. As expansion takes place the gravitational force on each particle decreases and kinetic energy of expansion dissipated rapidly [6]. Because of expansion gravitational energy between particles overcomes the kinetic energy resulting particles start shrinking. At this stage all particles collapse in to a single particle called Big- method. An Crunch. This algorithm work through a simple cycle of stages as: Stage 1 (Big Bang phase): The initialization in this phase is similar to other evolutionary initial population of candidate is generated randomly over the entire search space as: ( ( = ( ( +.( ( ( ( (7) Where, k=1, 2, 3.. no of parameters and i=1, 2,..pop. x i(min) and x i(max) are upper and lower limit of i th candidate. The working of Big Bang phase is explained as energy dissipation. Randomness in the initialization is same as the energy dissipation in nature but this dissipation creates disordered from ordered particles and use this randomness to create new solution candidate (disorder or chaos). The number of individuals in the population must be big enough in order not to miss the global point. Stage 2 (Big Crunch phase): Big Crunch phase come as a convergence operator. This phase have only one output named as center of mass. The center of mass is the weighted average of candidate solution as [9]: 55

5 International Journal of Electrical Engineering and Technology (IJEET), ISSN (Print), ISSN = ( (8) Where, X com is position of the center of mass. x i k is position of i th candidate in N dimensional search space. f i is fitness function value of i th candidate. Pop is size of population. Stage 3 (Generate new population): Big Bang phase is normally distributed around center of mass. The new candidate around the center of mass is calculated by adding or subtracting a normal random number as: =. +(1 +. ( ( ( (9) Where, α is parameter limiting the size of search space. β is parameter controlling the influence of the global best solution x best on the location of new candidate solution. The best solution x best influences the direction of search [9]. Stage 4 (Selection or recombination): Now apply selection criterion. Selection determines that, whether the new candidate is suitable for next iteration or not. The value of fitness function of current generation (f (x i new )) is compared with the previous fitness function (f (x i )) of corresponding individual. If the fitness functions to newly generated candidate have lower value than previous one then former candidate replaced by new generated candidate as: x = x x if f(x f(x if f(x < (x (1) As the search space is contracted with new iteration, the algorithm arrives at the optimum point very fast. 4. BB-BC BASED OPTIMIZATION OF CONTROLLER GAINS This paper uses a fitness function based on overshoot, undershoot, steady state error and settling time proposed by Ghoshal et.al [4] as: = +.1 +(.1 +( (11) Multiplying factor associated with overshoot (1) and undershoot (1) are minimized its value to a greater extent. The optimum selection of these factors depends on the designer s requirement and characteristics of the system. High settling time does not require any amplification. 4.1 Implementation of algorithm: step1 Set system data (given in appendix), select value of α, β and number of population, number of maximum iteration. step2 Set iteration count c=1 and randomly initialize candidate solution (x i = x 1, x 1,.x N ) for gains of controller within limits using eq.7. step3 Run AGC-AVR model as given in fig.1 and calculate performance parameter such as M p, U s, ess, t s, for i th candidate solution. step4 Calculate fitness function using eq. 11 for all candidate solution and also find best fitness value. step5 Find the center of mass using eq. 8 (Big Bang phase). 56

6 International Journal of Electrical Engineering and Technology (IJEET), ISSN (Print), ISSN step6 Calculate new candidate around center of mass (eq. 9). step7 Apply selection criterion (eq. 1) and set c=c+1. step8 If maximum number of iteration reached then stop otherwise go to step RESULT AND DISCUSSION This section presents simulation results of Big Bang-Big Crunch optimized gains for two area automatic generation control with and without automatic voltage regulator. Figs 2-6 shown comparative performance of BB-BC algorithm of the frequency, area control error and tie-line power deviation in each area following a.1 pu load perturbation with particle swarm optimization and differential evaluation algorithm. These results illustrate the effectiveness of the presented BB-BC method over other evolutionary methods. Fig8 gives the better optimal performance using BB-BC based gains for terminal voltage of generator field. Table-1 and Table2 show that frequency response settling time is lower with BB-BC based controller compared to those of the other methods. It also depicts that the computational time with minimum fitness function is lowest. As seen from Figs 8-11, the responses of BB-BC optimized AGC system with AVR exhibits long-lasting oscillations with large overshoot and large steady state error compare to AGC without AVR. It shows the effect of coupling between AGC and AVR loop. Table-1 Optimal controller gains and best fitness function. Algorithm PID Controller Gains of AVR Integral Gain of AGC Fitness function Execution time K P K I K D K I PSO DE BB-BC Table-2 Comparison of performance parameters Algorithm System performance parameters Settling Overshoot Undershoot Steady state error time(sec.) PSO * *1-6 DE * *1-6 BB-BC * *1-7.5 f1pso f1de f1bbbc Fig2 Comparative response of frequency deviation in area 1 57

7 International Journal of Electrical Engineering and Technology (IJEET), ISSN (Print), ISSN.1.5 f2pso f2de f2bbbc Fig3 Comparative response of frequency deviation in area 2.1 ACE1PSO ACE1DE ACE1BBBC Fig4 Comparative response of area control error of area 1..5 ACE2PSO ACE2DE ACE2BBBC Fig5 Comparative response of area control error of area 2. 58

8 International Journal of Electrical Engineering and Technology (IJEET), ISSN (Print), ISSN x 1-3 PtiePSO PtieDE PtieBBBC Fig6 dynamic response of tie-line power deviation vtpso vtde vtbbbc Fig7 response of terminal voltage of generator field ACE1 of without AVR ACE1 with AVR Fig8 Dynamic response of area control error of AGC with AVR and without AVR of area1 59

9 International Journal of Electrical Engineering and Technology (IJEET), ISSN (Print), ISSN.5 ACE2 without AVR ACE2 with AVR Fig9 Dynamic response of area control error of AGC with AVR and without AVR of area2 5 x 1-3 delta f1 without AVR delta f1 with AVR Fig1 effect of AVR on AGC system frequency deviation on area delta f2 without AVR delta f2 with AVR Fig11 Comparative response of frequency deviation on area 2 with and without AVR 6. CONCLUSION In this paper a new but effective global optimization algorithm named Big Bang- Big Crunch (BB- BC) is used for optimizing gains of AGC-AVR system. Simulation results show the convergence speed of the BB-BC is better than the PSO and DE with the same design parameter. This paper also demonstrated that BB-BC algorithm has ability to search global optimum accurately compared to DE and PSO methods. 6

10 International Journal of Electrical Engineering and Technology (IJEET), ISSN (Print), ISSN Appendix Nominal parameters of two area test system [5]: H 1 =5, H 2 = 4 seconds D 1 =.62, D 2 =.91 P.U. MW/Hz R 1 =.51, R 2 =.65 Hz/P.U. MW Th 1 =.2, Th 2 =.3 sec. Tt 1 =.5, Tt 2 =.6 seconds Kp 1 = Kp 2 =159 Hz P.U. MW P s =.145P.U. MW/Radian K H =K T =K e = 1. K A =1, T A =.1. T e =.4. K G =.8, T G =1.4. K s =1, T s =.5. K1=1, K2=-.1, K3=.5, K4=1.4. Parameters for BB-BC algorithm: Initial population= 2 Maximum iteration= 1 β=.5, α=.1. Parameters for DE algorithm: Initial population= 2 Maximum iteration= 1 Scaling factor F=.5 Crossover probability (CR) =.98 Parameters for PSO algorithm: Initial population= 2 Maximum iteration= 1 W max =.6, W min =.1 C 1 = C 2 = 1.5 REFERENCES [1] Praghnesh Bhatt, S.P.Ghoshal Comparative performance evaluation of SMES-SMES, TCPS- SMES and SSSC-SMES controller in automatic generation control for a two area hydrohydro system,international journal of electrical power and energy, vol33 issue 1 DEC211. [2] G. Yu, and R. Hwang, (24) Optimal PID speed control of brush less DC motors using LQR approach, in Proc. IEEE Int. Conf. Systems, Maand Cybernetics, pp [3] Nindul Sinha, Loi Lei Lai, Venu Gopal Rao, (April 28) GA optimized PID controllers for automatic generation control of two area reheat thermal system under deregulated environment, proc. IEEE international conference on electric utilizes deregulation and restructuring and power technologies,6-9, pp [4] S.P.Ghoshal,N.K.Roy, (Sept. 24) A novel approach for optimization of proportional integral derivative gains in automatic generation control, Australasian universities power engineering conference (AUPEC 24), [5] Praveen Dabur, Naresh kumar Yadav, Vijay Kumar Tayel, MATLAB Design and Simulation of AGC and AVR Multi Area Power System and Demand Side Management, International journal of Computer Electrical Engg., vol. 3, no. 2, April 211. [6] K. Erol Osman, Ibrahim Eksin, New optimization method: Big Bang- Big Crunch, Elsevier, Advances in Engineering Software 37 (26), pp [7] Nasser Jaleeli, Donald N. Ewart, Lester H. Fink; Understanding automatic generation control, IEEE Transaction on power system, Vol. 7, No. 3, August Pages:

11 International Journal of Electrical Engineering and Technology (IJEET), ISSN (Print), ISSN [8] Vaibhav Donde, M.A.Pai, and Ian A.Hiskens; Simulation and Optimization in an AGC system after Deregulation, IEEE transactions on power systems, Vol.16, No -3, August 21. [9] Potuganti Prudhvi, A complete copper optimization technique using BB-BC in a smart home for a smarter grid and a comparision with GA, IEEE conferenceccece, 211. [1] Engin Yesil, Leon Urbas, Big Bang- Big Crunch Learning Method for Fuzzy Cognitive Maps, world Academy of Science, Engg and Technology, 71, 21. [11] Dr. L.D. Arya, Dr. H. K. Verma and Cheshta Jain, (April 211) Differential evolution for optimization of PID gains in automatic generation control, international journal of computer science and application. [12] A. Kaveh and H. Abbasgholiha, Optimization Design of Steel Sway Frames using Big Bang- Big Crunch Algorithm, Asia jornal of Civil Engg. Vol. 12, no. 3, 211, pp [13] Moacir Kripka and Rosana Maria Luvezute Kripka, Big Crunch Optimization Method, International Conference on Engg. Optimization 1-5 June 28. [14] Nindul Sinha, Loi Lei Lai, Venu Gopal Rao, (April 28) GA optimized PID controllers for automatic generation control of two area reheat thermal system under deregulated environment, proc. IEEE international conference on electric utilizes deregulation and restructuring and power technologies,6-9, pp [15] Swagatam Das and Ponnuthurai N.Suganhan (Feb. 211) Diffrential evolution: A survey of the state of the art, IEEE trans. On evolutionary computation, Vol. 15, No. 1. [16] R, Storn, K. Price, (1995) Differential evolution A simple and efficient adaptive scheme for globel optimization over continuous spaces, Technical report TR-95-12, March 1995,ftp.ICSI.Berkeley.edu/pub/techreports, tr [17] Z.-L. Gaing, (June 24) A particle swarm optimization approach for optimum design of PID controller in AVR system, IEEE Trans. Energy Conversion, vol. 19, pp [18] O.I. Elgerd, (21) Electric energy system theory an introduction, McGraw Hill Co., 21. [19] Hadi Saadat; Power System Analysis, Mc Graw- Hill, New Delhi,