Design of low sensitivity optimal regulators for synchronous machines

Abstract

The usual procedure for the optimal design of linear regulators for synchronous machines is to minimize a chosen quadratic performance index subject to the system dynamics constraint. However, the optimal control synthesized in such a straightforward fashion is unsatisfactory due to the departure of the system parameters from their nominal values or due to the divergence between the mathematical model and the physical system. In an attempt to resolve this difficulty, the paper presents a method of synthesizing optimal control in such a way as to minimize not only a certain cost function, but also the sensitivity of the cost function and trajectory sensitivity. It is shown that the optimal control so obtained will result in a system whose cost function and transient response are little sensitive to first-order variations in plant parameter values. A numerical example involving a synchronous machine swinging against an infinite bus is used to demonstrate the feasibility of incorporating sensitivity considerations into the design of optimal regulators. Considering the overall gain of the voltage regulator as a system parameter, prime mover optimal control signal of low sensitivity is obtained for combined optimum frequency and voltage control. The method can readily be generalized to the case of multi-machine power systems and the sensitivities minimized for any system parameter.