Analysis of robust transient stability of power systems using sum of squares programming

Abstract

This paper analyzes the transient stability of power systems with uncertain parameters. More precisely, we suppose that the inertia constants and damping coefficients of generators are uncertain, and consider the problem of checking the stability of an equilibrium state for all possible values of these uncertain parameters, and estimating the intersection of the region of attraction for those parameter values. By using a polytopic representation for the uncertain parameters and a concept from the field of robust control, we present a method for solving this problem. In the presented method, we solve a sum of squares programming problem with constraints imposed on systems where the values of the uncertain parameters correspond to the vertices of a polytope. We prove that, if the sum of squares programming problem is feasible, our method solves the analysis problem of robust transient stability. A numerical example demonstrates that our method correctly analyzes transient stability despite the parameter uncertainties, whereas an existing method gives an incorrect analysis result owing to the uncertainties.