Center manifold computations in bifurcation analysis of large systems such as the power system

Abstract

Methods for computing the center manifold in large systems are developed in this paper. Using results from nonlinear control theory, it is shown that the problem or formally computing a center manifold is equivalent to solving a sequence of Sylvester equations. These results prove that bifurcation analysis based on center manifold computations is practically feasible even in very large-scale systems such as the power system where the large dimensionality makes traditional symbolic computations almost impossible to implement. Algorithms are illustrated by center manifold based analysis of certain local and global bifurcations in an electrical power system model.