A procedure to specify the weighting matrices for an optimal load-frequency controller

Authors: SILVIO JOSÉ PINTO SIMÕES MARIANO, JOSE ÁLVARO NUNES POMBO, MARIA DO ROSÁRIO ALVES CALADO, LUIS ANTÓNIO FIALHO MARCELINO FERREIRA

Abstract: The linear quadratic optimal regulator is one of the most powerful techniques for designing multivariable control systems. The performance of the system is specified in terms of a cost, which is the integral of a weighted quadratic function of the system state and control inputs, that is to be minimized by the optimal controller. The components of the state cost weighting matrix, Q, and the control cost weighting matrix, R, are ours to choose in mathematically specifying the way we wish the system to perform. Changing these matrices, we can modify the transient behavior of the closed-loop system. This paper addresses the stabilization and performance of the load-frequency controller by using the theory of the optimal control. A new technique, based on pole placement using optimal regulators, to overcome the difficulties of specifying weighting matrices Q and R is proposed. The design method employs successive shifting of either a real pole or a pair of complex conjugate poles at a time. The proposed technique builds Q and R in such a way that the system response also obeys conventional criteria for the system pole location. The effectiveness of the proposed method is illustrated by numerical examples.

Keywords: Power systems, load-frequency control, optimal control, weighting matrices

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