Determination of controller gains for frequency control

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Determination of controller gains for frequency control

  1. 1. INTERNATIONAL JOURNAL and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN & International Journal of Electrical Engineering OF ELECTRICAL ENGINEERING 0976 – 6553(Online) Volume 3, Issue 3, October – December (2012), © IAEME TECHNOLOGY (IJEET)ISSN 0976 – 6545(Print)ISSN 0976 – 6553(Online)Volume 3, Issue 3, October - December (2012), pp. 52-62 IJEET© IAEME: www.iaeme.com/ijeet.aspJournal Impact Factor (2012): 3.2031 (Calculated by GISI) ©IAEMEwww.jifactor.com DETERMINATION OF CONTROLLER GAINS FOR FREQUENCY CONTROL BASED ON MODIFIED BIG BANG-BIG CRUNCH TECHNIQUE ACCOUNTING THE EFFECT OF AVR Miss Cheshta Jain Department of electrical and electronics engg., MITM, Indore email:cheshta_jain194@yahoo.co.in Dr. H.K. Verma Department of electrical engg., S.G.S.I.T.S., Indore email:vermaharishgs@gmail.com Dr. L.D. Arya Department of electrical engg., S.G.S.I.T.S., Indore email:ldarya@rediffmail.com ABSTRACT 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,……). ∆Ptie (i,j) : change in tie line power. ∆PL : load change. D : ∆PL / ∆f R : governor Speed regulation parameter. Th : speed governor time constant. Tt : speed turbine time constant TP : power system time constant. 52
  2. 2. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN0976 – 6553(Online) Volume 3, Issue 3, October – December (2012), © IAEMETe : exciter time constant.TG : generator field time constant. Ts : sensor time constant. KP : power system gain.H : inertia constant.Us : undershootMp : overshootts : settling time.tr : rise time.ess : steady state error. 1. INTRODUCTIONAN interconnected power system is made up of several control areas with respect to megawatt-frequency control. In each area, an AGC observes the system frequency, tie-lines flow and computesthe net change in the generation required to control error and set position of generation within eacharea to keep the error (area control error) at a low value. Over the past decades, many researchershave applied different control strategies, such as classical control, variable structure control, optimalfeedback control and robust control to AGC problem in order to achieve better performance [1]. Yu etal. [2] have praised a linear quadratic regulation (LQR) method to tune PID gain, but it requiresmathematical 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 PSObased PID controller for AGC. Some deficiencies in performance of GA method are identified byabove paper. To stabilize the system for load disturbance comparative transient performance ofthyristor controlled phase shifter (TCPS) and superconducting magnetic energy system (SMES) areproposed 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 operatingcondition. Many investigations in the area of AGC of isolated and interconnected power system havebeen 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 onreduction of total load demand during period on peak demand to maintain security of system but notexplained the selection of optimum gain of controller. The Big Bang- Big Crunch (BB-BC) a new optimization method relied on one of the theoriesof the evaluation of the universe namely Big Bang theory and Big Crunch theory which is introducedby Erol and Eskin [6]. This method has a low computational time and high convergence speed. Theproposed method is similar to the Genetic Algorithm in respect to creating an initial population. TheBB-BC method eliminates the possibility of Medicare scalability; one of the disadvantages of GAbased learning method. In this paper a BB-BC based controllers is proposed as the supplementary controllers, whichshow 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 andscheduled loading availability model are developed. Section 3 describes BB-BC algorithm and theimplementation of BB-BC based controller is presented in section 4. Section 5 shows the result withdetailed discussion and conclusion is drawn in section 6. 2. AGC-AVR SYSTEM MODEL The system investigated consists of two control areas with reheat type thermal unit connectedby tie-lines that allows power exchange between areas. If the load on the system is increased the 53
  3. 3. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN0976 – 6553(Online) Volume 3, Issue 3, October – December (2012), © IAEMEspeed 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 tomaintain a constant speed in automatic generation control (AGC). On the other hand the generatorexcitation 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 offrequency to nominal value, (ii) supplementary control to provide precise control strategy for fineadjustment of the frequency. The main function of supplementary control is to maintain systemfrequency at predetermined set point after a load perturbation. The input to the supplementarycontroller of the ith area is the area control error (ACEi) which is given by: ௡ ‫ܧܥܣ‬௜ = ෍(∆ܲ௧௜௘(௜,௝ሻ + ‫ܤ‬௜ ∆݂௜ ሻ ௝ୀଵ (1) Where, Bi is frequency bias coefficient of ith area, ∆fi is frequency error, ∆Ptie is tie-line powerflow error and ‘n’ is number of interconnected areas [18]. The area bias Bi determines the amount ofinteraction during load perturbation in neighboring area. To obtain better performance, bias Bi isselected as: (2)2.2 AVR System: This paper studied on coupling effect by extending the linear AGC to include the excitationsystem. The real power transfer over the line is: |‫ܧ‬ଵ ||‫ܧ‬ଶ | ܲ= ‫ߜ݊݅ݏ‬ ܺ (3) This is the product of the synchronizing power coefficient (Ps) and the change in the powerangle (∆δ). Now include small effect of voltage on real power as: ∆ܲ௥௘௔௟ = ܲ ∆ߜ + ‫ܸ1ܭ‬ ௦ ௙ (4) Where, K1 is the change in electrical power for a small change in stator emf and Vf is outputof generator field. Also, including the small effect of rotor angle on generator terminal voltage as: ∆ܸ௧ = ‫ܸ3ܭ + ߜ∆2ܭ‬ ௙ (5) Where, K2 is the change in the terminal voltage for a small change in the rotor angle atconstant stator emf, and K3 is the change in the terminal voltage for a small change in stator emf at aconstant rotor angle. Now finally modified generator field output is: ௄ಸ ܸ௙ = (ଵା௦் ሻ (ܸ − ‫ߜ∆4ܭ‬ሻ ௘ ಸ (6)Where, Ve is exciter output voltage, KG is a generator gain constant, and TG 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. 4. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN0976 – 6553(Online) Volume 3, Issue 3, October – December (2012), © IAEME Fig.1: Linear model of two area AGC-AVR system .1: 3. OVERVIEW OF BIG BANG BANG-BIG CRUNCH ALGORITHM The Big Bang-Big Crunch algorithm has been introduced by Erol and Eskin. This algorithm is Bigbased on the formation of universe stated by Big Bang theory. According to this theory the universewas once a sphere with infinite radius and density. Due to several internal forces, the existed mass isexploded massively called Big-Ban and billions of particles moved outwards. Once particles start Bangspreading, a gravitational force arises which depends on masses of two bodies considered and distancebetween them. As expansion takes place the gravitational force on each particle decreases and kineticenergy of expansion dissipated rapidly [6 [6]. Because of expansion gravitational energy between particles overcomes the kinetic energyresulting particles start shrinking. At this stage all particles collapse in to a single particle called Big- BigCrunch. This algorithm work through a simple cycle of stages as: runch.Stage 1 (Big Bang phase): The initialization in this phase is similar to other evolutionary method. Aninitial population of candidate is generated randomly over the entire search space as: (௞ሻ (௞ሻ ‫ݔ‬௜ (௞ = ‫ݔ‬௜(௠௜௡ሻ (௞ሻ + ‫ݔ( .݀݊ܽݎ‬௜(୫ୟ୶ሻ − ‫ݔ‬௜(୫୧୬ሻ ሻ ௞ሻ (7)Where, k=1, 2, 3…….. no of paramete and i=1, 2,…..pop. parameters xi(min) and xi(max)are upper and lower limit of ith candidate. The working of Big Bang phase is explained as energy dissipation. Randomness in the nginitialization is same as the energy dissipation in nature but this dissipation creates disordered fromordered particles and use this randomness to create new solution candidate (disorder or chaos). The (disordernumber 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 T rageas [9]: 55
  5. 5. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 3, Issue 3, October – December (2012), © IAEME (ೖሻ ೛೚೛ ೣ ∑೔సభ ೔ ܺ௖௢௠ = ೑೔ ೛೚೛ భ ∑೔సభ ೑೔ (8) Where, Xcom is position of the center of mass. xik is position of ith candidate in N dimensional search space. fi is fitness function value of ith 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 ‫ݔ(ߙ .݀݊ܽݎ‬௜(୫ୟ୶ሻ − ‫ݔ‬௜(୫୧୬ሻ ሻ number as: ‫ݔ‬௜௡௘௪ = ߚ. ܺ௖௢௠ + (1 − ߚሻ‫ݔ‬௕௘௦௧ + ݅‫݌݁ݐݏ ݊݋݅ݐܽݎ݁ݐ‬ (9) Where, α is parameter limiting the size of search space. β is parameter controlling the influence of the global best solution xbest on the location of new candidate solution. The best solution xbest 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 (xinew)) is compared with the previous fitness function (f (xi)) 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: ୮୰୧୴୧୭୳ୱ ୮୰୧୴୧୭୳ୱ x if f(x୧ ሻ ≤ f(x୧ ሻ ୬ୣ୵ x୧ ୬ୣ୶୲ ୧୲ୣ୰ୟ୲୧୭୬ = ൝ ୧ ୬ୣ୵ ୮୰୧୴୧୭୳ୱ ൡ x୧ if f(x୧ ሻ < ݂(x୧ ୬ୣ୵ ሻ (10) 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: ଶ ‫ = ݊݋݅ݐܿ݉ݑ݂ ݏݏ݁݊ݐ݅ܨ‬ቀ൫‫ܯ‬௣ + ݁‫ݏݏ‬൯. 1000ቁ + (ܷ௦ . 100ሻଶ + (‫ݐ‬௦ ሻଶ (11) Multiplying factor associated with overshoot (1000) and undershoot (100) 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 (xi = x1, x1, ….xN) 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 Mp, Us, ess, ts, for ith 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. 6. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 3, Issue 3, October – December (2012), © IAEMEstep6 Calculate new candidate around center of mass (eq. 9).step7 Apply selection criterion (eq. 10) and set c=c+1.step8 If maximum number of iteration reached then stop otherwise go to step 3. 5. 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 0.01 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 Fitness Execution Gain of function time AGC KP KI KD KI PSO 1.1090 0.6737 0.9198 0.2649 114.8966 58.848052 DE 0.6291 1.512 0.9466 0.2736 113.9013 140.608386 BB-BC 0.2904 0.2709 0.2594 0.3971 102.7837 51.005986 Table-2 Comparison of performance parameters Algorithm System performance parameters Settling Overshoot Undershoot Steady state error time(Sec.) PSO 9.619 6.466*10-5 -0.0473 2.4437*10-6 DE 9.427 5.675*10-4 -0.0497 2.2691*10-6 BB-BC 8.9245 1.82*10-4 -0.0382 9.459*10-7 0.005 f1PSO f1DE 0 f1BBBC -0.005 -0.01 -0.015 -0.02 -0.025 -0.03 0 5 10 15 20 25 30 35 40 45 50 Fig2 Comparative response of frequency deviation in area 1 57
  7. 7. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN0976 – 6553(Online) Volume 3, Issue 3, October – December (2012), © IAEME 0.01 f2PSO 0.005 f2DE f2BBBC 0 -0.005 -0.01 -0.015 -0.02 -0.025 -0.03 -0.035 0 5 10 15 20 25 30 35 40 45 50 Fig3 Comparative response of frequency deviation in area 2 0.1 ACE1PSO ACE1DE 0 ACE1BBBC -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 0 5 10 15 20 25 30 35 40 45 50 Fig4 Comparative response of area control error of area 1. 0.05 ACE2PSO ACE2DE ACE2BBBC 0 -0.05 -0.1 -0.15 -0.2 0 5 10 15 20 25 30 35 40 45 50 Fig5 Comparative response of area control error of area 2. 58
  8. 8. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN0976 – 6553(Online) Volume 3, Issue 3, October – December (2012), © IAEME -3 x 10 3 PtiePSO PtieDE 2.5 PtieBBBC 2 1.5 1 0.5 0 0 50 100 150 200 250 300 350 400 450 500 Fig6 dynamic response of tie-line power deviation 1.4 vtPSO vtDE 1.2 vtBBBC 1 0.8 0.6 0.4 0.2 0 0 2 4 6 8 10 12 14 16 18 20 Fig7 response of terminal voltage of generator field 0.05 0 -0.05 ACE1 of without AVR ACE1 with AVR -0.1 -0.15 -0.2 -0.25 -0.3 -0.35 -0.4 -0.45 0 5 10 15 20 25 30 35 40 45 50Fig8 Dynamic response of area control error of AGC with AVR and without AVR of area1 59
  9. 9. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN0976 – 6553(Online) Volume 3, Issue 3, October – December (2012), © IAEME 0.05 ACE2 without AVR ACE2 with AVR 0 -0.05 -0.1 -0.15 -0.2 0 5 10 15 20 25 30 35 40 45 50 Fig9 Dynamic response of area control error of AGC with AVR and without AVR of area2 -3 x 10 5 delta f1 without AVR delta f1 with AVR 0 -5 -10 -15 -20 0 5 10 15 20 25 30 35 40 45 50 Fig10 effect of AVR on AGC system frequency deviation on area 1 0.01 delta f2 without AVR 0.005 delta f2 with AVR 0 -0.005 -0.01 -0.015 -0.02 -0.025 -0.03 0 5 10 15 20 25 30 35 40 45 50Fig11 Comparative response of frequency deviation on area 2 with and without AVR6. CONCLUSIONIn 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 convergencespeed of the BB-BC is better than the PSO and DE with the same design parameter. This paper alsodemonstrated that BB-BC algorithm has ability to search global optimum accurately compared to DEand PSO methods. 60
  10. 10. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN0976 – 6553(Online) Volume 3, Issue 3, October – December (2012), © IAEME AppendixNominal parameters of two area test system [5]:H1=5, H2= 4 secondsD1=0.62, D2= 0.91 P.U. MW/HzR1= 0.051, R2=0.065 Hz/P.U. MWTh1=0.2, Th2=0.3 sec.Tt1=0.5, Tt2=0.6 secondsKp1= Kp2=159 Hz P.U. MWPs=0.145P.U. MW/RadianKH=KT=Ke= 1.KA=10, TA=0.1.Te=0.4.KG=0.8, TG=1.4.Ks=1, Ts=0.05.K1=1, K2=-0.1, K3=0.5, K4=1.4.Parameters for BB-BC algorithm:Initial population= 20Maximum iteration= 100β=0.5, α=0.1.Parameters for DE algorithm:Initial population= 20Maximum iteration= 100Scaling factor F= 0.5Crossover probability (CR) = 0.98Parameters for PSO algorithm:Initial population= 20Maximum iteration= 100Wmax= 0.6, Wmin= 0.1C1= C2= 1.5REFERENCES [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 hydro- hydro system”,International journal of electrical power and energy, vol33 issue 10 DEC2011. [2] G. Yu, and R. Hwang, (2004) “Optimal PID speed control of brush less DC motors using LQR approach,” in Proc. IEEE Int. Conf. Systems, Maand Cybernetics, pp. 473-478. [3] Nindul Sinha, Loi Lei Lai, Venu Gopal Rao, (April 2008) ” 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. 1186-1191. [4] S.P.Ghoshal ,N.K.Roy, (Sept. 2004) ” A novel approach for optimization of proportional integral derivative gains in automatic generation control”, Australasian universities power engineering conference (AUPEC 2004), 26-29. [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 2011. [6] K. Erol Osman, Ibrahim Eksin, “New optimization method: Big Bang- Big Crunch”, Elsevier, Advances in Engineering Software 37 (2006), pp. 106-111. [7] Nasser Jaleeli, Donald N. Ewart, Lester H. Fink; “Understanding automatic generation control”, IEEE Transaction on power system, Vol. 7, No. 3, August 1992. Pages: 1106-1122. 61
  11. 11. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN0976 – 6553(Online) Volume 3, Issue 3, October – December (2012), © IAEME [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 2001. [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, 2011.[10] Engin Yesil, Leon Urbas, “Big Bang- Big Crunch Learning Method for Fuzzy Cognitive Maps”, world Academy of Science, Engg and Technology, 71, 2010.[11] Dr. L.D. Arya, Dr. H. K. Verma and Cheshta Jain, (April 2011) “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, 2011, pp. 293-317.[13] Moacir Kripka and Rosana Maria Luvezute Kripka, “Big Crunch Optimization Method”, International Conference on Engg. Optimization 01-05 June 2008.[14] Nindul Sinha, Loi Lei Lai, Venu Gopal Rao, (April 2008) ” 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. 1186-1191.[15] Swagatam Das and Ponnuthurai N.Suganhan (Feb. 2011) “ 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-95-012, March 1995,ftp.ICSI.Berkeley.edu/pub/techreports, tr-95-012.[17] Z.-L. Gaing, (June 2004) “A particle swarm optimization approach for optimum design of PID controller in AVR system,” IEEE Trans. Energy Conversion, vol. 19, pp. 384-391.[18] O.I. Elgerd, (2001) “Electric energy system theory an introduction”, McGraw Hill Co., 2001.[19] Hadi Saadat; “Power System Analysis”, Mc Graw- Hill, New Delhi, 2002. 62

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