Optimization of PI Controller Gains in Nonlinear Controller of STATCOM Using PSO and GA

Abstract

According to nonlinear operation of STATCOM, nonlinear controller has a better performance in comparison with linear controller. Regulating the DC capacitor voltage in STATCOM is a common task and can improve the system dynamic. The nonlinear control is based on exact linearization via feedback. A PI controller exists in this control system to regulate the capacitor voltage. In conventional scheme, the trial and error method has been used to determine PI controller coefficients. In this paper, the effect of PI gains on responses of Vdc, Id and Modulation Index (M) is presented. The exact calculation of optimized PI coefficients can be carried out to reduce disturbances and steady state error in DC link voltage. Therefore, in this paper, Particle Swarm Optimization (PSO) approach is used. It is shown that capacitor voltage tracks the reference value and vibrations are less than conventional status. Also, Genetic Algorithm (GA) has been used and compared with the results. I. SIMULATION RESULTS In this section, GA is employed and compared with PSO. The results of running GA and PSO are shown in table 1. Comparison between two methods with a same function shows that PSO results in fitness function with lower value. PSO response has more disturbances but faster convergence speed in the case of optimization of Vdc & Id. Generally, PSO responses have less fluctuation in comparison with GA responses in the case of optimization of Vdc. In the case of optimization of double-objective function for PSO, Vdc response reaches to steady state with higher speed and less fluctuation, Id response reaches to steady state with higher speed and more fluctuations and M response has not a good performance in comparison with GA responses. Figure 1 compares PSO and GA for Vdc response with two types of objective functions. TABLE 1. RESULTS OF PSO AND GA Method Type of Function KP & KI Fitness Function value PSO SingleObjective KP=610.9952 KI=700 0.0084 DoubleObjective KP=65 KI=150 4.9996 GA SingleObjective KP=617.9668 KI=39.1076 0.0089 DoubleObjective KP=1.7748 KI=150 5.1100 Trial & Error SingleObjective KP=1 KI=70 0.4030 DoubleObjective KP=1 KI=70 5.4095 Figure 1. Capacitor voltage response Traditional solution is the calculation of these coefficients by using trial and error method. In new method, the time of reaching to steady state value, settling time the fluctuations and overshoot have been decreased, too. 0 0.02 0.04 0.06 0.08 0.1 0.12 199.99 200 200.01 200.02 200.03 C ap ac ito r V ol ta ge ( V ) Optimizing Vdc with PSO & GA