Frequency domain relaxation of power system dynamics

A highly parallel approach for solving nonlinear differential equations in the frequency domain is presented. Solutions of the frequency-domain equations involving polynomial approximations to the nonlinearities involved is handled using a relaxation technique to exploit parallelism. Identities involving frequency-domain matrix polynomials of dimension N and order n are developed to allow evaluation in O(log₂ N×log ₂ n) time. Results of applying the method to models involving hard limiters and sine nonlinearities are presented. Savings of the number of parallel computations is achieved through the elimination of the hard precedence relationships involved in the classical time-march methods