Conditions for existence of optimal solution in the synthesis of a multivariable control problem for power systems by using optimization problem

Abstract

This paper considers the synthesis of a multivariable control problem for power systems by using the optimization method. The power system dynamics based on the usual assumptions can be formulated as a class of nonlinear dynamic systems which contain the sinusoidal functions associated with the power torque-angle curve of the ac generator. Then, an optimal control law, which retains the principal nonlinearity of the power system, is derived by using the optimization techniques in the linear optimal control theory. The feedback gain matrices are obtained by solving matrix equations which appear in the optimization procedure. In this paper, the conditions for the existence of an optimal solution of these matrix equations are derived by using Anderson's theorem. The stability criterion for the control system is discussed from the viewpoint of a Lur'ye-type Lyapunov function. Thus, the optimal control law can be applied to a class of nonlinear dynamical systems represented by the ordinary differential equations divided into linear and nonlinear terms.