Application of the concept of the distance to an uncontrollable pair to the placement of controllers in power systems

Abstract

This paper reports on an application of the concept of the distance of a pair (A, B) to the nearest uncontrollable pair to the problem of placing a controller in a multimachine power system. The results given by Gahinet and Laub 9 are adapted by allowing perturbations only in the B matrix keeping the A matrix fixed. As a result of this adaptation the distance to uncontrollability depends on the controllability of the modes of the system yielding measures of odal contrallability. Dual results on observability are also given. The resulting measures provide a tool for tackling the problem of controller placement in power systems, where local stabilization control is often needed to mitigate undesirable performance. The measures of modal observability are used to compare supplementary feedback signals, and the measures of modal controllability are used to compare the suitability of inputs to control a given mode. A three-machine power system is used to test the ideas. The results agree reasonably well with previously used methods which are based on the linear internal dynamics of the system.