Big bang-big crunch based optimized controller for automatic generation control and automatic voltage regulator system

Transcription

1 MultiCraft International Journal of Engineering, Science and Technology Vol. 3, No. 10, 2011, pp INTERNATIONAL JOURNAL OF ENGINEERING, SCIENCE AND TECHNOLOGY MultiCraft Limited. All rights reserved Big bangbig crunch based optimized controller for automatic generation control and automatic voltage regulator system Cheshta Jain 1 *, H.K. Verma 2, L.D. Arya 3 1* Department of Electrical Engineering, MITM, Indore, INDIA 2 Department of Electrical Engineering, Shri G.S.I.T.S, Indore, INDIA 1* Department of Electrical Engineering, Shri G.S.I.T.S, Indore, INDIA * Corresponding Author: cheshta_jain194@yahoo.co.in, Abstract In modern power system one of the major problems is to control generator output frequency with excitation voltage at a specified level. Automatic generation control (AGC) maintains system frequency, where as automatic voltage regulator (AVR) controls the terminal voltage of synchronous generator when subjected to load perturbation. This paper presents a Big Bang Big Crunch based optimum gains of controllers to maintain both system frequency and voltage magnitude. The proposed method, have shown better performance over particle swarm optimization (PSO) and differential evaluation (DE) optimization method for AGCAVR system. Keywords: Automatic generation control, Automatic voltage regulator, Big BangBig Crunch optimization, particle swarm optimization, differential evolution.. DOI: 1. Introduction Automatic generation control mainly refers to real time frequency control loop to match the area generation changes corresponding to change in area load in order to meet tieline flows and to maintain frequency at nominal value. Another control loop, usually assumed to be decoupled from above control loop, of the generator excitation system maintains generators voltage and reactive power flow. To simplify the overall controller design, the interaction between the frequency and voltage control loop is usually neglected in most of the studies. In an interconnect power system load frequency control and automatic voltage regulator equipment are installed for each generator. This paper presents a study of interaction between exciter AVR with frequency control loop of AGC. 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 have not considered the effect of AVR. (Dabur et al. 2011) proposed AGCAVR for multiarea power system with demand side management. Their paper mainly focused on reduction of total load demand during period on peak demand to maintain security of system but the selection of optimum gains of controllers is not explained. A number of different approaches such as classical optimal, Genetic algorithm, fuzzy logic, artificial neural network etc. for selection of controller parameters have been (Nindul, 2008) applied on AGC without AVR. Some authors have applied particle swarm optimization (PSO) to optimize controller gains more effectively and efficiently than classical. Recent research papers identified some deficiency in PSO performance (Arya et al., 2011). Premature convergence of PSO is overcome by differential evaluation (DE) algorithm (Arya et al., 2011). A new computational technique Big BangBig Crunch (BBBC) is available and this has been successfully applied on some areas of engineering. This paper proposes optimization of proportional plus integral plus derivative controller for voltage regulator and integral controller for load frequency control by use of Big Bang Big Crunch (BBBC) optimization algorithm. Integral controller has ability to return a system to its set point and generation is

2 13 adjusted automatically to restore the system frequency to the nominal value. The PID controller of AVR improves the dynamic response with minimum steady state error. BBBC is a new algorithm relies on one of the evolutionary theories of universe namely the Big Bang theory and Big Crunch theory. According to these theories, if the gravitational energy is greater than the energy generated by Big Bang the expansion of universe stop (Kripka et al, 2008), which is followed by a contraction. This will reduce the universe to a single point. In view of the above, the following are the main objective of the proposed work. Obtain optimized gains of controller for both AGC and AVR system. Obtain dynamic response of AGCAVR system to show the effect of coupling between them by using MATLAB software. Compare the performance of BBBC algorithm to the PSO and DE algorithm. The rest of the paper is organized as follows: Section 2 describes BBBC algorithm. In section 3 the AGCAVR system model is developed and implement BBBC based controller in section 4. Section 5 shows the results with detailed discussions and conclusion is drawn in section Overview of Big Bang Big Crunch Optimization The Big Bang Big Crunch optimization is a heuristic population based evolutionary method. This method is developed by (Osman and Eskin, 2006) which can easily handle multidimensional problem with very fast convergence. This algorithm is based on the formation of Universe 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 BigBang and billions of particles moving 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 (Potuganti, 2011). Because of expansion gravitational energy between particles overcomes the kinetic energy resulting particles are shrinking. At this stage all particles collapse in to a single particle called BigCrunch. 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 method. An initial population of candidate is generated randomly over the entire search space as: ( ) = ( ) ( ) ( ).( ( ) ( ) ( ) ) (1) Where, k=1, 2, 3.. no of parameters and i=1, 2,..population size. 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 has only one output named as center of mass. The center of mass is the weighted average of candidate solution as (Yesil et al, 2010): = ( ) Where, X com is position of the center of mass. x k i is position of i th candidate in N dimensional search space. f i is fitness function value of i th candidate. Pop is number of candidate 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 ). ( ( ) ( ) ) 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 influence the direction of search (Yesil et al, 2010). (2) (3)

3 14 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: = ( ) ( ) ( )< ( (4) ) As the search space is contracted with new iteration the algorithm arrives at the optimum point very fast. 3. AGCAVR System Model Nowadays loads are continuously changing. If the load on the system is increased the speed of turbine is reduced before the governor can adjust the input of steam to the new load. As the change in output of system become smaller, the position of governor moves 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) (Hadi saadat, 2002). Modern excitation system uses ac generators with rectifiers. The interaction between AGC and AVR is weak but they affect both system frequency and generator voltage due to load change. However, the AVR loop is faster than AGC loop. Therefore, AVR dynamics settle before they make themselves in slower AGC 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: = (5) 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 (6) Where, K1 is the change in electrical voltage 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: = 2 3 (7) 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 modify the generator field output as: = ( ( ) 4 ) (8) 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 AGCAVR is shown in fig 1.

4 15 P L Governor Turbine system K4 P s K1 K2 δ V ref PID Amplifier Exciter V e Generator Field V f K3 V t Sensor Fig.1 transfer function model of AGCAVR system. 4. Big Bang Big Crunch Based Optimization of Controller Gains In tuning of controller gains, the common performance criterion are integral square error (ISE), integral weight square error (ITSE) etc. but minimizing using these criterion results in a small overshoot with long settling time. Because of these reasons, this paper proposed undershoot, steady state error and settling time based performance criterion as: 4.1 Implementation of Algorithm: =.1000 (.100) 2 ( ) 2 (9) 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.1. step3 Run AGCAVR model and calculate performance parameter for each i th candidate solution. step4 Calculate fitness function using eq. 9 for all candidate solution and best fitness value. step5 Find the center of mass using eq. 2 (Big Bang phase). step6 Calculate new candidate around center of mass (eq. 5). step7 Apply selection criterion (eq. 4) and set c=c1. step8 If maximum number of iteration reached then stop otherwise go to step 3. The flow chart of BBBC computational procedure is shown in fig.2.

5 16 start Read system data, set max. no. of iteration, population size etc. Generate initial population randomly using eq.1. Run AGCAVR system and calculate fitness function using eq.9 Calculate center of mass using eq.2. c=c1 Generate new candidate solution using eq.3. Apply selection criterion using eq. 4. Gen < max. iteration Obtain system dynamic response End Fig. 2 BBBC optimization power flow chart 5. Result and Discussion The proposed BBBC algorithm is tested on AGCAVR system for one percent step load perturbation and compared with other heuristic algorithm like particle swarm optimization and differential evaluation algorithm using MATLAB software. All methods are performed with five trials under the same performance criteria and number of individual to compare their efficiency. Fig.3 depicts the plot of fitness function value corresponding to best value against number of iteration. The BBBC algorithm based solution converged very fast with minimum value. Fig.4 and Table 1 shows that the computational time and fitness function of the BBBC algorithm is lowest in comparison to those of the other methods. Fig.5 and 6 shows the BBBC based controller gains give better optimal performance compared with other algorithms for change in system frequency and terminal voltage of generator field respectively. Table2 shows the proposed algorithm based optimal gains results in a minimum overshoot, steady state error and settling time.

6 17 best fitness by PSO best fitness by DE best fitness by BBBC Fig. 3 comparison of convergence characteristics Fig.4 characteristics of computation time 0.02 Step Response w bbbc w pso w DE Amplitude Time (sec) Fig.5 Comparative dynamic response of change in system frequency

7 18 2 Step Response vt_pso vt_de vt_bbbc 1.2 Amplitude Time (sec) Fig.6 response of change in voltage magnitude of generator field 6. Conclusion Table1 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 BBBC Table2 comparison of performance parameters Algorithm System performance parameters Settling time(sec.) Overshoot Undershoot Steady state error PSO DE BBBC In this paper a combined MATLAB model of AGC and AVR is used to study the interaction of AVR loop with AGC loop. Big BangBig Crunch algorithm is used to obtain the optimum design of controllers for AGC and AVR system. The relative merit of BBBC for search of global optimum point with many local optima over PSO and DE algorithm is established through efficient and reliable results obtained in this paper following a step load change in a control area. The proposed algorithm involved few control parameters compared to other heuristic methods shown the convergence speed better than PSO and DE with the same design parameter. Nomenclature w = Frequency deviation. P L = Load change. D= P L / w R = Governor Speed regulation parameter. T h = Speed governor time constant. T t = Speed turbine time constant T P = Power system time constant. T e = Exciter time constant. T G = Generator field time constant. T s = Sensor time constant. K P = Power system gain.

8 19 H = Inertia constant. U s = Undershoot M p = Overshoot ts = Settling time. tr = Rise time. e ss = Steady state error. Appendix Nominal parameters of AGCAVR system (Elgerd, 2001): H= 5 seconds D= P.U. MW/Hz R=2.4 Hz/P.U. MW Th=80 ms Tt=0.3 seconds Kp=120HzP.U. MW Tp=20 seconds P s =0.145P.U. MW/Radian K H =K T =K e = 1. K A =10, T A =0.1. T e =0.4. K G =0.8, T G =1.4. K s =1, T s =0.05. K1=1, K2=0.1, K3=0.5, K4=1.4. Parameters for BBBC algorithm: Initial population= 20 Maximum iteration= 100 β=0.5, α=0.1. Parameters for DE algorithm: Initial population= 20 Maximum iteration= 100 Scaling factor F= 0.5 Crossover probability (CR) = 0.98 Parameters for PSO algorithm: Initial population= 20 Maximum iteration= 100 W max = 0.6, W min = 0.1 C 1 = C 2 = 1.5 References Dabur P., Yadav N., Tayel V.K., MATLAB design and simulation of AGC and AVR multi area power system and demand side management, International Journal of Computer Electrical Engineering, Vol. 3, No. 2. Sinha N., Lai L.L., Rao V.G., GA optimized PID controllers for automatic generation control of twoarea reheat thermal system under deregulated environment, Proceedings of. IEEE International Conference on Electric Utilizes Deregulation and Restructuring and Power Technologies, pp Arya L.D., Verma H. K. and Jain C., April Differential evolution for optimization of PID gains in automatic generation control, International Journal of Computer Science and Application. Osman K.E., Ibrahim Eksin, New optimization method: Big BangBig Crunch, Elsevier, Advances in Engineering Software Vol. 37, pp Potuganti Prudhvi, 2011.A complete copper optimization technique using BBBC in a smart home for a smarter grid and a comparison with GA, IEEE ConferenceCCECE. Moacir Kripka and Rosana Maria Luvezute Kripka, (2008) Big Crunch Optimization Method, International Conference on Engg. Optimization 0105 June Engin Yesil, Leon Urbas, Big Bang Big Crunch Learning Method for Fuzzy Cognitive Maps, world Academy of Science, Engg and Technology, 7. Hadi Saadat; Power System Analysis, Mc Graw Hill, New Delhi. Nasser Jaleeli, Donald N. Ewart, Lester H. Fink; Understanding automatic generation control, IEEE Transaction on Power System, Vol. 7, No. 3, Pages: Vaibhav Donde, M.A.Pai, and Ian A.Hiskens; 2001.Simulation and optimization in an AGC system after deregulation, IEEE Transactions on Power Systems, Vol.16, No 3. Kaveh and H. Abbasgholiha, Optimization design of steel sway frames using big bang big crunch algorithm, Asia Journal of Civil Engg. Vol. 12, no. 3, pp Das S.and Suganhan P.N Difrential evolution: A survey of the state of the art, IEEE trans. on Evolutionary Computation, Vol. 15, No. 1. Storn R,, Price K., Differential evolution A simple and efficient adaptive scheme for global optimization over continuous spaces, Technical report TR95012, March 1995,ftp.ICSI.Berkeley.edu/pub/techreports, tr Gaing Z.L., A particle swarm optimization approach for optimum design of PID controller in AVR system, IEEE Trans. Energy Conversion, Vol. 19, pp Elgerd O.I., Electric energy system theory an introduction, McGraw Hill Co..

9 20 Biographical notes Cheshta Jain received M.E from Shri G.S.I.T.S, Indore India in She is a Asst. Professor in the Department of Electrical and Electronics, MITM, Indore, India. Presently she is pursing Phd from S.G.S.I.T.S Indore, India. Her research interests include power system restructuring, power system optimization & control. Dr. H. K. Verma is a professor in the Department of Electrical Engineering, shri G.S.I.T.S Indore, India. He has more than 20 years of experience in teaching and research. His current area of research includes Power system, control system, Drives, Optimization and Neural Networks. He has published more than fifteen papers in referred international journals. He has also presented more than fifty research articles in national and international conferences. He is a member of ISTE and IE (India). Dr.L.D Arya is a professor in the Department of Electrical Engineering, shri G.S.I.T.S Indore, India. He has more than 35 years of experience in teaching and research. His current area of research includes Power system stability, Voltage stability, Voltage Security, Optimization and Neural Networks. He has published more than seventy five papers in referred international journals. He has also presented more than hundred research articles in national and international conferences. He is a Fellow member of IE (India).. Received December 2011 Accepted May 2012 Final acceptance in revised form October 2012