EFFECT OF CUCKOO SEARCH OPTIMIZED INTEGRAL - DOUBLE DERIVATIVE CONTROLLER WITH TCPS FOR CONTAINING OSCILLATIONS IN AUTOMATIC GENERATION CONTROL (AGC)

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1 EFFECT OF CUCKOO SEARCH OPTIMIZED INTEGRAL - DOUBLE DERIVATIVE CONTROLLER WITH TCPS FOR CONTAINING OSCILLATIONS IN AUTOMATIC GENERATION CONTROL (AGC) 1 S.Sanajaoba Singh, 2 Nidul Sinha NIT Silchar, Assam 1 sanajaoba88@gmail.com, 2 nidulsingha@gmail.com Abstract In this paper, integral plus double derivative (IDD) in coordination with Thyristor Controlled Phase Shifter (TCPS) is applied for the first time in automatic generation control (AGC) system. Comparative studies on the performance of different classical controllers viz. integral (I), proportional plus integral (PI), proportional plus integral plus derivative (PID) and integral plus double derivative (IDD) in automatic generation control of two equal area reheat thermal system without and with TCPS is presented. The study is carried out considering appropriate generation rate constraints (GRC). The controller gains are optimized using a new meta-heuristic search algorithm called Cuckoo Search (CS). Comparison of convergence characteristics of Genetic Algorithm (GA), Particle swarm optimization (PSO) and CS algorithms reveal faster convergence in case of CS algorithm, which is an obvious choice of reducing computational burden. Further, comparison of dynamic responses reveals that responses for I, PI, PID controllers without and with TCPS are practically more or less same whereas those of IDD without and with TCPS are much better. The improved dynamic responses using IDD controller with TCPS, in terms of peak deviations and settling time as compared to the output responses of the system obtained without TCPS is also presented. Finally, sensitivity analysis is carried out to verify the robustness of the optimum gains of the IDD controllers to wide changes in system loading condition, several system parameters and size of step load perturbation(slp). Index Terms- Automatic Generation control, Cuckoo Search Algorithm, Integral Squared Error Technique, Integral Double Derivative, Thyristor Controlled Phase Shifter. I. INTRODUCTION Automatic generation control has evolved rapidly with the present application of sophisticated digital control schemes. Its principal aspects in an interconnected power system are maintenance of frequency and interchange tie-line power at scheduled values. In the past years, many control strategies [1-4] have been developed for the AGC of interconnected power systems. In the literature [3-6] attempts were made to design different types of AGC controllers. A comparative study on the performance of different controllers for AGC of interconnected hydro thermal system with GRC is reported in [7]. Performance comparison of several classical controllers in multiarea interconnected thermal system is carried out in [8]. The effect of TCPS in a tie-line on the AGC dynamics of a hydro-thermal system is reported in the literature [9]. Further, application of FACTS devices for oscillation damping in AGC is found in the literatures [10-12]. But, no analysis has been carried out to check the robustness of the optimum controller gains to wide changes in system loading conditions and system parameters in all the available literatures relating to application of FACTS devices for oscillation damping in AGC. Pragnesh Bhatt, S.P Goshal and Ranjit Roy have proposed a load frequency stabilization by coordinated control of TCPS and superconducting magnetic energy storage (SMES) and made a comparative performance evaluation of SMES-SMES, TCPS-SMES, SSSC-SMES controllers in AGC [13].However, no author has attempted to compare the performance of classical controllers in the process of AGC with TCPS in the tie-line in damping oscillations in tie-power and area frequency. In this work several classical controllers such as integral (I), proportional plus integral (PI), proportional plus integral plus derivative and integral plus double derivative are made use and their performances are investigated to reveal the best performed controller both in case of without and with TCPS in the tie-line. To determine the optimal designing parameters of the controllers, Cuckoo Search (CS) algorithm is used. It is a new meta-heuristic search algorithm proposed by Yang and Deb [14]. The CS algorithm is developed imitating the brood parasitism of some cuckoo species which lay and abandon their eggs in the nest of birds of other species. It is based on two major concepts, which are the breeding behavior of cuckoos and the characteristics of Levy flight. In CS, the number of parameters to be fine tuned is less compared to those of GA and PSO, and thus it is more potential and generic one to adapt to wider class of optimization problems. Its effectiveness and superiority over other well-known optimization techniques like GA, PSO, ant colony 132

2 algorithm etc. has been reported in the literature [14, 15]. Finally, the best controller optimum gains are subjected to sensitivity analysis to verify the robustness of the optimized parameters to wide changes in system loading condition several system parameters and size of SLP. II. SYSTEM INVESTIGATED The test system consists of a two equal area system of area1:2000mw; area2:2000mw provided with single reheat turbine and generation rate constraints of 3% per minute in each area. The nominal system parameters are taken from [16] and shown in Appendix. Integral (I), proportional plus integral (PI), proportional plus integral plus derivative (PID) and integral plus double derivative (IDD) controllers are considered for investigation. In this study the power system performance is examined by installing the active power model of TCPS in the tie-line. The transfer function model of two-area reheat thermal power system considering GRC along with Thyristor Controlled Phase Shifter (TCPS) in the tie-line is shown in fig.1. The system transfer function model has been shown using PID controller only, though the analysis has been carried out with Integral, PI, PID and IDD independently. The objective function used is given by eqn. (1). MATLAB version 7.08 has been used to obtain dynamic responses following a step load perturbation of 1% in area1 T J = {( f i ) 2 + P 2 tie 12 } dt, i=1, 2. (1) 0 Figure-1 : Transfer function model of two equal area reheat thermal power system with TCPS. III. FACTS CONTROLLER APPLICATION TO AGC A Thyristor Controlled Phase shifter is one of the FACTS devices which is capable of effective control of tie-line power flow in an interconnected power system. The control action is achieved by regulating the relative phase angle between the system voltages. The phase angle control affects the real line power flow to attenuate the frequency oscillations and enhance power system stability [9-10]. A TCPS connected in series with tie-line near area1 of a two area interconnected thermal reheat power system is shown in fig. 2. Figure-2 : Schematic of Two Area Interconnected Thermal Reheat Power System with TCPS in series with Tie-line In fig.2 the current I flowing from area1 to area2 is given by I = V 1 (δ 1 +φ) V 2 δ 2 jx 12 (2) Where x 12 is the line reactance, V 1 and V 2 are terminal bus voltages. The active and reactive power flows at bus1 are P tie 12 jq tie 12 = V 1 I = V 1 (δ 1 + φ) [ V 1 (δ 1 +φ) V 2 δ 2 ] jx 12 (3) The real part of (3) gives P tie 12= V₁ V₂ x 12 sin(δ₁ δ₂ + φ) (4) For small deviations in the angles δ₁, δ₂ and φ from their nominal values δ₁⁰, δ₂⁰ and φ⁰ respectively, the tie-line power changes with the amount P tie 12 = V₁ V₂ x 12 cos δ 1 0 δ φ 0 sin( δ 1 δ 2 + φ )Since δ1 δ2+ φis very small and hence sin δ 1 δ 2 + φ = ( δ 1 δ 2 + φ) Let the synchronizing power co-efficient T 12 = V 1 V 2 x 12 cos(δ 1 0 δ φ 0 ) Thus, P tie 12 = T 12 ( δ 1 δ 2 + φ) P tie 12 = 2πT 12 f 1 dt f 2 + T 12 φ (5) Taking Laplace Transform of (5) we get, P tie 12 s = 2πT 12 s F 1 s F 2 s + T 12 φ(s) (6) In the above expression φ(s) can be written as φ s = K φ 1+T φ Error(s) (7) Where Kφ and Tφ are the gain and time constant of TCPS. Considering TCPS input signal as the frequency deviation of area1 ( f 1 ), (6) can be written as 133

3 P tie 12 s = 2πT 12 s F 1 s F 2 s + T 12 K φ 1 + st φ F 1 (s) IV. OVERVIEW OF CUCKOO SEARCH Cuckoo Search (CS) is a new meta-heuristic optimization algorithm developed by Yang and Deb. It is developed based on the interesting breeding behaviour such as brood parasitism of some species of cuckoos and the characteristics of Levy flights. It is a population based search algorithm and contains a population of nests or eggs. Female cuckoos lay eggs that mimic the eggs of their host nest in colour and pattern. As an idealized rule each cuckoo lays one egg at a time and dumps it in a randomly chosen nest. The best nests with high quality of eggs (solutions) will carry over to the next generations, and the number of available host nests is fixed. On the other hand, some host birds can engage direct conflict with the intruding cuckoos and they discovered the alien eggs with a probability ofpa [0,1]1]. Once the eggs are discovered, they are either thrown away or the nest is abandoned and a completely new nest is built in a new location by host birds. The pseudo code of the Cuckoo Search (CS) can be summarized as follows begin Objective function f(x), x = (x1,...,xd) T, d is the number of variables Generate initial population of n host nests xi (i =1,2,.., n) while (t <MaxGeneration) or (stop criterion) Get a cuckoo randomly by L evy flights Evaluate its quality/fitness Fi Choose a nest among n (say, j) randomly if (Fi >Fj ), replace j by the new solution; end A fraction (pa) of worse nests is abandoned and new ones are built; Keep the best solutions Rank the solutions and find the current best end while End Post process results and visualization Starting with a randomly distributed initial population of host nest, cuckoo birds undergo repeated search process to lay an egg. The random host nest position for laying egg is decided by performing Levy flights and is given as x i (t+1) = x i t + α Levy(λ) (8) Where t is the current generation number and α>0 is the step size, which should be related to the scale of the problem of interest. The product means entry-wise multiplication (Yang 2010). Basically, random steps in Levy flight are drawn from a Levy distribution for large steps as Levy~u = t λ, (-1<λ 3) (9) This has an infinite variance with an infinite mean. In the real world, if a cuckoo s egg is very similar to a host s egg, then this cuckoo s egg is less likely to be discovered, thus the fitness should be related to the difference in solutions. Therefore, it is wise to do a random walk in a biased way with some random step sizes. V. RESULT AND ANALYSIS A. Comparison of dynamic responses obtained using integral, PI, PID and IDD controllers: Simulation studies have been carried out in two-area interconnected thermal reheat power system without and with TCPS in the tie-line following a SLP of 1% in area1. Different types of classical controllers, such as integral (I), proportional plus integral (PI), proportional plus integral plus derivative (PID) and integral plus double derivative (IDD) are examined separately and Cuckoo Search algorithm is used to optimize their gains. Convergence characteristics of GA, PSO and CS algorithms are shown in fig.3 which reveals that the convergence of the CS is the fastest among the three algorithms. Dynamic responses comparison of the aforesaid controllers for area frequency and tie power deviations without TCPS are shown in fig.4a-c and with TCPS in series with tie-line are shown in fig.5a-c. After critical examination of the dynamic responses shown in Fig. 4 and 5, the settling time, peak overshoot and peak undershoot of the responses for I, PI, PID and IDD are noted and shown in tables 1 and 2 for the system without and with TCPS respectively. Examining the columns for settling time and peak overshoot of the tables 1 and 2, it is clearly seen that in all the dynamic responses of frequency ( f i ) and tie power ( P tiei-j ), the settling time and peak overshoot for I, PI, PID controllers are more or less equal while that of IDD controller is significantly less. Looking into the magnitude of oscillations of the dynamic responses, it is seen that it is less for IDD controllers as compared to I, PI and PID controllers in all the responses for frequency and tie power. 134

4 B. Comparison of dynamic responses obtained using IDD controllers of the system without and with TCPS: Considering the better performed controller i.e. the IDD controller, a dynamic response comparison for area frequency and tie power deviations is presented in fig.6a-c for the system without TCPS and the system with TCPS in series with tie-line. Comparison shows that the system equipped with TCPS gives lesser values of settling time, peak overshoot, peak undershoot of the responses and magnitude of oscillations is much less. Hence, its control action can be effectively utilized for stabilizing area frequencies and tie power oscillations. C. Sensitivity analysis: Sensitivity analysis has been carried out to study the robustness of the optimum IDD controller gains for the system with TCPS to wide changes in system loading condition by ±25% from its nominal loading of 50%, wide changes in system parameters such as H, Kr and Tr by ±25% from their nominal values given in the appendix and change in size of the SLP. The optimum values of IDD controller gains for the system with TCPS at changed loading conditions, changed system parameters and different size of SLP are provided in table 3. Dynamic responses are depicted in fig.7a-h for each change condition with their corresponding optimum values and compared to the responses corresponding to the optimized values at nominal condition. The responses are reasonably more or less similar and hence optimized parameters at nominal loading and nominal parameters need not be reset for wide changes in system loading or system parameters. D. Optimum values The optimum values of integral controller gains are (i) without TCPS: KI1= and KI2= (ii) with TCPS: KI1= and KI2=1600.The optimum values of PI controller gains are (i) without TCPS: KP1=0.0066, KI1=0.1126, KP2= and KI2= (ii) with TCPS: KP1=0.0323, KI1=0.1291, KP2= and KI2= The optimum values of PID controller gains are (i) without TCPS: KP1=0.0378, KI1=0.1270, KD1=0.0436, KP2=0.0026, KI2= and KD2= (ii) with TCPS: KP1=0.0363, KI1=0.1204, KD1=0.0692, KP2=0.0308, KI2= and KD2= The optimum values of IDD controller gains are (i) without TCPS: KI1=0.1000, KDD1=0.0065, KI2= and KDD2= (ii) with TCPS: KI1=0.0899, KDD1=0.0040, KI2= and KDD2= Figure-3 : Convergence characteristics of GA, PSO and CS (a) (b) (c) 135

5 Figure-4 : Comparison of integral, PI, PID and IDD controller performance in two equal area system for 1% SLP in area1 without TCPS (c) Figure-5 : Comparison of integral, PI, PID and IDD controller performance in two equal area system for 1% SLP in area1 with TCPS. (a) (a) (b) (b) (c) Figure-6 : Comparison of dynamic responses of frequency and tie-power deviations without and with TCPS for 1% SLP in area1 using IDD controller. 136

6 (e) (a) (b) (f) (c) (g) (d) Figure 7: Dynamic responses of the system for changed loading and changed system parameters with corresponding optimized values compare with those for 50% nominal loading and nominal system parameters with TCPS for 1% SLP in area1. (h) 137

7 Table1: Comparative performance of different dynamic responses for I, PI, PID and IDD controllers in two area thermal system without TCPS. Controller Settling time (s) Peak overshoot Peak undershoot f 1 f 2 P tie12 f 1 f 2 P tie12 f 1 f 2 P tie12 1.I PI PID IDD Table3: Comparative performance of different dynamic responses for I, PI, PID and IDD controllers in two area thermal system with TCPS. Controller Settling time (s) Peak overshoot Peak undershoot f 1 f 2 P tie12 f 1 f 2 P tie12 f 1 f 2 P tie12 1.I PI PID IDD Table3: Optimum values of the IDD controller gains for the system with TCPS at changed loading condition, system parameters and at different size of the SLP. LOADING LOADING H H KR KR TR TR 2% 3% +25% -25% +25% -25% +25% -25% +25% -25% SLP SLP K I OPTIMUM VALUES K DD K I K DD VI. CONCLUSION In this paper, a comparative study on the performance of several classical controllers such as integral, PI, PID and IDD is carried out on two equal areas reheat thermal power system for two cases (i) system without any FACTS device and (ii) system equipped with TCPS. Critical examination of the simulation results shows that the performances for integral, PI and PID controllers are practically the same while those of IDD controllers are much better in terms of settling time, peak overshoot and magnitude of oscillations is also very less for both the cases. Hence, the system equipped with TCPS and IDD controller can be an effective measure for stabilizing area frequencies and tie power oscillations in AGC operation. Further, sensitivity analysis reveals the robustness of the optimum gains of the IDD controllers to wide changes in system loading condition, system parameters and different size of SLP. APPENDIX Nominal parameters of the system investigated f=60hz, Tgi=0.08s, Tti=0.3s, Tri=10s, Kr=0.5, Ptie max=200mw, Tpi=20s, Kpi= 120Hz/p.uMW, loading=50%, Pr1= Pr2= 2000MW, 2πT 12 = 0.545p.u. MW/Hz, a 12 =-1, R1=R2=2.4Hz/p.u.MW, Bi=βi= 0.425p.u.MW/Hz, i=1,2. Data for TCPS: Kφ=1.5rad/Hz, Tφ=0.1s, φmin=-13⁰, φmax=13⁰ 138

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