An Application of the Mapping Theorem and Kharitonov Theorem to Dynamical Stability Analysis

Abstract

When analyzing dynamical stability in power systems, there exist variable parameters, for example, variable gains and time constants of controllers in its system matrix. In the conventional representative techniques, we have to analyze all patterns of the system matrix one by one using Routh-Hurwitz method and so on, which is a difficult task. However, studies of the robust control theory such as Kharitonov theorem has been performed, recently. And some works have been published in the section of power systems. The Kharitonov theorem can distinguish stability of the characteristic polynomial whose coefficients have variable ranges independently. Therefore, we have to obtain the characteristic polynomial from the system matrix. However, in the conventional representative techniques, the transformation from the system matrix with variable parameters to the characteristic polynomial is very difficult, because the system matrix is generally huge in power systems. In this paper, we employ a simple way to do that transformation using Danilevski method. Furthermore, we apply the mapping theorem and the Kharitonov theorem to a one machine to infinite bus system which has variable parameters in its AVR and governor, and propose an efficient way to analyze using those theorems.