Minimal Realized Power Systems for Load Frequency Control Using Optimal Theory Based PID Controller

Abstract

The load-frequency control is a matter of interest in power system operation as it addresses the problem of controlling the system in response to the disturbances. A well-known solution to this problem is feedback stabilization through Linear Quadratic Regulator. The observability condition has to be satisfied for the implementation of LQR, but for certain cases of multi-source power systems this criteria fails. Also, to obtain the desired response, proper selection of the weighting matrices Q and R for LQR controller is inevitable. On a trial and error based choice of these matrices, the classical optimal controller may fail to achieve an optimum set point tracking, due to the absence of an integral control action. In this paper, a balanced reduction technique is proposed to obtain a minimal realization of the unobservable system, which makes the optimal control design possible for the control of change in frequency. Thus the paper also applies PID output feedback controller designed through LQR. The impact of reduction for minimal realization and the LQR based PID controller in the frequency stabilization of the considered systems are highlighted in this paper through pertinent cases.