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A Novel approach for tuning Power System Stabilizer (SMIB system) using Genetic Local Search technique J.SATHEESHKUMAR JEGADEESAN Dr.A.EBENEZER JEYAKUMAR Department of Electrical Engineering Department of Electrical Engineering Government College of Technology Government College of Technology Coimbatore, INDIA Coimbatore, INDIA Abstract: - The genetic local search technique (GLS) hybridizes the genetic algorithm (GA) and the local search (such as hill climbing) in order to eliminate the disadvantages in GA. The parameters of the PSS (gain, phase lead time constant) are tuned by considering the single machine connected to infinite bus system (SMIB). Here PSS are used for damping low frequency local mode of oscillations. Eigen value analysis shows that the proposed GLSPSS based PSS have better performance compared with conventional and the Genetic algorithm based PSS (GAPSS). Integral of time multiplied absolute value of error (ITAE) is taken as the performance index of the selected system. Genetic and Evolutionary algorithm (GEA) toolbox is used along with MATLAB/SIMULINK for simulation. Key-words: - Genetic local search, Power system oscillations, Power system stabilizer, Genetic algorithms, SMIB, K-constants power system utilities still prefer the 1. Introduction conventional lead-lag PSS structure. The Power systems experience low- reasons behind that might be the ease of on- frequency oscillations due to disturbances. line tuning and the lack of assurance of the These low frequency oscillations are stability related to some adaptive or variable related to the small signal stability of a structure techniques. power system. The phenomenon of stability Unlike other optimization of synchronous machine under small techniques, Genetic Algorithm (GA) works perturbations is explored by examining the with a population of strings that represent case of a single machine connected to an different potential solutions therefore, GA infinite bus system (SMIB). The analysis of has implicit parallelism that enables it to SMIB [4] gives physical insight into the search the problem space globally and the problem of low frequency oscillations. optima can be located more quickly when These low frequency oscillations are applied to complex optimization problem. classified into local mode, inter area mode Unfortunately, recent research has identified and torsional mode of oscillations. The some deficiencies in GA performance. This SMIB system is predominant in local mode degradation in efficiency is apparent in low frequency oscillations. These applications with highly epistatic objective oscillations may sustain and grow to cause functions, i.e. where parameters being system separation if no adequate damping optimized are highly correlated. In addition, is available. In recent years, modern control the premature convergence of GA represents theory have been applied to power system a major problem. stabilizer (PSS) design problems. These In this proposed genetic local search (GLS) include optimal control, adaptive control, [7] approach, GA is hybridized with a local variable structure control, and intelligent search algorithm to enhance its capability of control. exploring the search space and overcome the Despite the potential of modern premature convergence. The design problem control techniques with different structures, with mild constraints and an eigenvalue- K3 K3 K 4 Eq = ' E fd (3) based objective function. 1 sTd 0 K 3 ' 1 sTd' 0 K 3 The GLS algorithm is employed to solve this optimization problem and Vt K5 K 6 Eq ' (4) search for the optimal settings of PSS The K-constants are given in appendix. parameters. The proposed design approach The system data are as follows [8]: has been applied to SMIB system. Eigen Machine (p.u): value analysis and simulation results have ' xd = 0.973 xd = 0.19 been carried out to assess the effectiveness and robustness of the proposed GLSPSS to x q = 0.55 Td' 0 = 7.765 s (5) damp out the electromechanical modes of oscillations and enhance the dynamic D = 0.0 H = 4.63 stability of power systems. Transmission line (p.u): re = 0.0 xe = 0.997 (6) 2. System investigated Exciter : A single machine-infinite bus (SMIB) system is considered for the KA = 50.00 TA= 0.05 s (7) present investigations. A machine Operating point : connected to a large system through a transmission line may be reduced to a Vt 0 = 1.0 P0 = 0.9 (8) SMIB system, by using Thevenin’s equivalent of the transmission network Q0 = 0.1 δ0 = 65 0 external to the machine. Because of the The interaction between the speed and relative size of the system to which the voltage control equations of the machine is machine is supplying power, the dynamics expressed in terms of six constants k1-k6. associated with machine will cause These constants with the exception of k3, virtually no change in the voltage and which is only a function of the ratio of frequency of the Thevenin’s voltage impedance, are dependent upon the actual (infinite bus voltage). The Thevenin real and reactive power loading as well as the equivalent impedance shall henceforth be excitation levels in the machine. referred to as equivalent impedance (i.e. Conventional PSS comprising cascade Re+jXe). connected lead networks with generator The synchronous machine is angular speed deviation () as input signal described as the fourth order model. The has been considered. Fig.1 shows the two-axis synchronous machine linearized model of the single machine representation with a field circuit in the connected to large system (SMIB) around the direct axis but with out damper windings is operating point. considered for the analysis. The equations describing the steady state operation of a synchronous generator connected to an infinite bus through an external reactance can be linearized about any particular operating point as follows(eq:1-4): d 2 Tm P M (1) dt 2 P K1 K2Eq ' (2) Fig.1 Linearized model of SMIB system contribute to the negative synchronizing From the transfer function block diagram, torque component. the following state variables are chosen for Wash out function (Tw) has the single machine system. The linearized value of anywhere in the range of 1 to 20 differential equations can be written in the seconds. The main considerations are that it form state space form as should be long enough to pass stabilizing 0 signals at the frequencies of interest relatively X(t) A.x(t) BU(t) (9) unchanged, but not so long that it leads to undesirable generator voltage excursions as a Where result of stabilizer action during system- islanding conditions. For local mode of X(t) = [ Δδ Δω ΔEq’ ΔEfd]T (10) oscillations in the range of 0.8 to 2 Hz, a 0 314 0 0 wash out of 1.5 sec is satisfactory. From the A= 0 view point of low-frequency interarea D M K1 M K2 M K4 0 1 K 3T 'do 1 T 'do oscillations, a wash out time constant of 10 K A TA K 5 K A TA K 6 0 1 TA seconds or higher is desirable, since low- time constants result in significant phase lead (11) at low frequencies. . T The stabilizer gain K has an important effect on damping of rotor KA (12) B 0 0 0 oscillations. The value of the gain is chosen TA by examining the effect for a wide range of values. The damping increases with an System state matrix A is a increase in stabilizer gain upto a certain point function of the system parameters, beyond which further increase in gain results which depend on operating conditions. in a decrease in damping. Ideally, the Control matrix B depends on system stabilizer gain should be set at a value parameters only. Control signal U is the corresponding to maximum damping. PSS output. From the operating However the gain is often limited by other conditions and the corresponding considerations. The transfer function model parameters of the system considered, of the SMIB system with the PSS is given in the system eigenvalues are obtained. Fig.2. The transfer function of Power System Stabilizer is given by, 10s 1 sT1 2 3. Transfer function model of H1(s) K * *( ) (13) (1 10s) 1 0.05 s PSS and design considerations The exciter considered here is Where, only having the gain of KA and the time K—PSS gain constant of TA. The typical PSS consists of Tw—washout time constant a washout function, a phase compensator T1-T4---phase lead time constants (lead/lag functions),and a gain. It is well A low value of T2=T4=0.05 sec is chosen known that the performance of the PSS is from the consideration of physical mostly affected by the phase compensator realization. Tw=10 sec is chosen in order to and the gain. Therefore, these are the main ensure that the phase shift and gain focus of the tuning process. Two first order contributed by the wash out block for the phase compensation blocks are considered. range of oscillation frequencies normally If the degree of compensation required is encountered is negligible. The wash out time small, a single first-order block may be constant (Tw) is to prevent steady state used. Generally slight under compensation voltage off sets as system frequency changes. is preferable so that the PSS does not Considering two identical cascade connected Fig.2 SMIB system with power system stabilizer lead-lag networks for the PSS T1=T3 . Where Hence now the problem reduces to the n is the undamped natural frequency of tuning of gain (K) and T1 only. the corresponding root. The parameters of the PSS For the determination of PSS parameters obtained for the damping ratio of 0.3. The a damping factor of =0.3 is chosen oscillation frequency is generally about (maximum damping). Corresponding to 0.8-2 Hz for the local mode of oscillations. this damping factor the desired In this SMIB system only local mode of eigenvalues are obtained as. oscillations are considered for the tuning of PSS. The local mode of oscillation occurs 1= -n+ n 1 2 when a machine supplies power to a load 2= -n- n 1 2 center over long, weak transmission lines. Pole placement technique is used for the It is to be noted here that the some of the tuning of CPSS design [6]. eigenvalues need not be shifted since they are placed for off in LHP. If any 3.1. Conventional PSS design electromechanical modes of oscillations The eigenvalues of the above are present then PSS needs to be added to A matrix are obtained using Matlab. It is enhance the dynamic stability of the evident from the open loop eigenvalues, the system. By using Decentralized modal system without PSS is unstable and therefore control (DMC) algorithm the parameters it is necessary to stabilize the system by of the conventional power system shifting these eigenvalues to the LHP and far stabilizer are found. off from the imaginary axis. The location of the desired eigenvalues is calculated by choosing a damping factor for the dominant 3.2. GA based design of PSS Minimizing the following error root. The real part is -n and the criteria the controller generates the imaginary part is parameters of the gain and the phase lead n 1 2 time constant. In this paper Integral of time Lead-Lag compensator was achieved using multiplied absolute value of error (ITAE) the MATLAB/Simulink environment. [4] will be minimized through the application of a genetic algorithm, as will 3.3. GLS Algorithm presently be elucidated. The GA works on Step 1: set the generation counter k=0 and a coding of the parameters (K, T) to be generate randomly n initial solutions, X0 = optimized rather than the parameters {xi, i=1……….n}. The ith initial solution xi themselves. In this study Gray coding was can be written as xi =[p1 p2…pj…pm], used where each parameter was represented where the jth optimized parameter pj is by 16 bits and a single individual or generated by randomly selecting a value chromosome was generated by with uniform probability over its search concatenating the coded parameter strings. space [pimin ,pjmax]. These initial solutions In contrast to traditional stochastic search constitute the parent population at the techniques the GA requires a population of initial generation x0. Each individual of x0 initial approximations to the solution. Here is evaluated using objective function J. set 30 randomly selected individuals were used x=x0; to initialize the algorithm. The GA then Step 2: optimize locally each individual in proceeds as follows: x. replace each individual in x by its locally optimized version. Update the objective 3.2.1. Fitness determination function values accordingly. The first step of the GA Step 3: search for the optimum value of the procedure is to evaluate each of the objective function, Jmin. set the solution chromosomes and subsequently grade associated with J min as the best solution, them. Each individual was evaluated by xbest with an objective function of Jbest. decoding the string to obtain the Lead-lag Step 4: check the stopping criteria. If one compensator parameters which were then of them is satisfied then stop, else set applied in a Simulink representation of the k=k+1 and go to step 5. closed-loop system. Step 5: set the population counter i=0; 1. The five fittest individuals were Step 6: draw randomly, with uniform automatically selected while the remainders probability, two solutions x1 and x2 from x. were selected probabilistically, according to apply the genetic crossover and mutation their fitness. This is an elitist strategy that operators obtaining x3; ensures that the next generation's best will Step 7 : optimize locally the solution x3 and never degenerate and hence guarantees the obtain x3; asymptotic convergence of the GA. Step 8 : check if x3 is better than the worst 2. Using the individuals selected above the solution in x and different from all next population is generated through a solutions in x then replace the worst process of single-point cross-over and solution in x by x3 and the value of mutation. Mutation was applied with a very objective by that of x3; low probability of 0.001 per bit. Step 9: if i=n go to step 3, else set i=i+1 Reproduction through the use of crossover and go back to step 6; and mutation ensures against total loss of any To demonstrate the effectiveness and genes in the population by its ability to robustness of the proposed GLSPSS over a introduce any gene which may not have wide range of loading conditions are existed initially, or, may subsequently have verified. been lost. 3. This sequence was repeated until the algorithm was deemed to have converged (50 iterations). As was indicated previously the simulation and evaluation of the GA tuned 4. Comparision of various Table 1 design techniques The linearized incremental state PSS parameters of various pss for space model for a single machine system single machine system. with its voltage regulator with four state variables has been developed. The single PSS type PSS parameters machine system without PSS is found unstable with roots in RHP. The system CONVENTIONAL K = 7.6921 dynamic response without PSS is simulated LEAD-LAG PSS T =0.2287 using Simulink for 0.05 p.u disturbance in GA BASED PSS K =26.5887 mechanical torque. MATLAB coding is T=0.2186 used for conventional PSS, Genetic PSS, GLS BASED PSS K=35.1469 and Genetic local search (GLS) PSS design T=0.2078 techniques. The final values of gain (K), and phase lead time constant (T) obtained from all the techniques are given to the 4.1. Simulation results simulink block. The dynamic response 1. Performance of fixed-gain CPSS is better curves for the variables Δω, Δδ and ΔVt are for particular operating conditions. It may taken from the simulink. The system not yield satisfactory results when there is a responses curves of the conventional PSS drastic change in the operating point. (CPSS), GA based PSS as well as GLS 2. Dynamic response shows that the GA based PSS are compared. based PSS has optimum response and the Shaft speed deviation is taken as the input response is smooth and it has less over to the all the Power system stabilizers. So shoot and settling as compared to the PSS is also called as delta-omega PSS. conventional PSS. The system dynamic response with PSS is 3. As compared to the conventional PSS simulated using these Simulink diagrams & GA based PSS the proposed genetic for 0.05 p.u step change in mechanical local search (GLS) based design of PSS torque ΔTm. The dynamic response curves gives the optimum response and the for the variables change in speed deviation response is smooth and it has reduced (Δω), change in rotor angle deviation (Δδ) settling time. and change in terminal voltage deviation 4. The time multiplied absolute value of (ΔVt) of the single machine system with the error (ITAE) performance index is PSS are plotted for three different types of considered. The simulation results show the power system stabilizers (PSS) are shown proposed Genetic local search based PSS in Figs. 3– 5. It is observed that the can work effectively and robustly over a oscillations in the system output variables wide range of loading conditions over the with PSS are well suppressed. The Table I conventional and GA based design of PSS. shows various types of PSS and its 5. The response curves shows that GLS parameters after tuned by conventional, PSS has less over shoot and settling time as genetic and genetic local search technique. compared to the GA PSS and the traditional Lead-lag PSS. Figure.3 Δ Vs time for normal load condition of the SMIB system Fig.4 Δδ Vs time for normal load condition of the SMIB system Fig .5 ΔVt Vs time for normal load condition of the SMIB system and robustly over wide range of loading Conclusion conditions and system configurations. In this study, a genetic local search algorithm is proposed to the PSS design problem. The proposed design Appendix approach hybridizes Genetic Algorithm Derivation of k-constants with a local search to combine their All the variables with subscript 0 different strengths and overcome their are values of variables evaluated at their pre- drawbacks (i.e.) GA explores the search disturbance steady-state operating point from space (spectrum of optimum location the known values of P0 , Q0 and Vt0. points either maxima or minima) before it P0Vto gives data to the local search technique. iq 0 = (14) Then local search technique is the best ( P0 x q ) 2 (Vt 2 Q0 x q ) 2 0 technique than GA to find the optima (either maxima or minima). The potential vd 0 = iq 0 xq (15) of the proposed design approach has been demonstrated by comparing the response vqo = Vt 2 vt20 (16) 0 curves of various power system stabilizer (PSS) design techniques. Optimization results show that the Q0 xqiq 0 2 proposed approach solution quality is id 0 = (17) vq 0 independent of the initialization step. Eigen value analysis reveals the effectiveness and robustness of the proposed GLSPSS to Eq 0 = vq0 id 0 xq (18) damp out local mode of oscillations. In addition, the simulation results show that E0 = (vd 0 xeiq 0 ) 2 (vq 0 xe id 0 ) 2 (19) the proposed GLSPSS can work effectively (vd 0 xeiq 0 ) K4 Demagnetising effect of a change in 0 = tan 1 (20) rotor angle (vq 0 xeid 0 ) K5 Change in Vt with change in rotor xq xd ' Eq 0 E0 cos 0 angle for constant Eq’ K1 = iq 0 E0 sin 0 K6 Change in Vt with change in Eq’ xe x ' d xe xq constant rotor angle (21) E0 sin 0 References K2 = (22) xe xd ' [1] Hu Guo-qiang, Xu Dong-jie and He Ren-mu, ―Genetic algorithm based design of xd xe ' power system stabilizers‖, IEEE K3 = (23) xd xe International conference on electric utility deregulation, restructuring and power xq xd ' technologies‖, pp. 167-171, Apr.2004. 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