Application of linear stability via Lyapunov exponents in high dimensional electrical power systems

Abstract

Applications of linear stability via Lyapunov exponents in high dimensional test systems are presented. The stochastic disturbance model is given by a bounded Markov diffusion process, as it appears in the description of load or generation uncertainties of power systems, for example. For such systems, the Lyapunov exponents describe necessary and sufficient conditions for almost sure asymptotic stability. The present article reports results obtained by applying the proposed methodology to four-machine ten-bus, ten-machine thirty-nine-bus, and sixteen-machine sixty-eight-bus international test systems.