Optimal H∞ control without reaching phase with the differential evolution PID based on PSS for multi-machine power system

The objective of this paper is to design a nonlinear robust controller for the multi-machine power systems. We present in this study an optimal H_∞ tracking control without reaching phase combined with the Proportional Integral Derivative based on Power System Stabilizer (PID-PSS) optimized by Differential Evolution algorithm. To eliminate the tradeoffs between the H_∞ tracking performance and the high gain at the control input, we have defined a new method based on the modified output tracking error by using the exponential function. The Differential Evolution algorithm is used in this study to find the optimal values of the three parameters (Kp, Ki, Kd) of (PID-PSS) and also used to tune the exponential function of the tracking error. The proposed approach is designed to eliminate completely the reaching phase and to enhance the stability and the dynamic response of the multi-machine power system. In order to test the effectiveness of the proposed method, the simulation results show the damping of the oscillations of the angle and angular speed with reduced overshoots and quick settling time.