On Linear Multivariable Control Theory and the Stability of AC Power Systems

摘要

This paper presents a complete survey on linear multivariable control theory applied to the study of ac power systems stability. The paper uses system matrices and state-space multivariable system representations to cover the main concepts and definitions of linear multivariable systems, providing a comprehensive review of the most predominant frequency-response stability criteria developed during the 1970's—the epoch for multivariable controls development, focusing on MacFarlane's, Postlethwaite's, and Rosenbrock's extensive work on complex variable methods. These methods are finally applied on an ac power system representative of stability conditions of interest, i.e., an ac source feeding power electronics loads with negative incremental input impedance. In this way a sound understanding of the applied theory is achieved, additionally supported with simulations which are used to complement examples and verify the validity of the stability criteria analyzed.