APPLICATION OF THE CONCEPT OF THE DISTANCE TO AN UNCONTROLLABLE PAIR TO THE PLACEMENT OF CONTROLLERS IN POWER-SYSTEMS

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 pl acing a controller in a multimachine power system. The results given b y Gahinet and Laub9 are adapted by allowing perturbations only in the B matrix keeping the A matrix fixed. As a result of this adaptation th e distance to uncontrollability depends on the controllability of the modes of the system yielding measures of modal controllability. Dual r esults on observability are also given. The resulting measures provide a tool for tackling the problem of controller placement in power syst ems, where local stabilization control is often needed to mitigate und esirable performance. The measures of modal observability are used to compare supplementary feedback signals, and the measures of modal cont rollability are used to compare the suitability of inputs to control a given mode. A three-machine power system is used to test the ideas. T he results agree reasonably well with previously used methods which ar e based on the linear internal dynamics of the system.