Parallel Algorithm for Transient Stability Simulation Based on Sherman-Morrison Formula

Abstract

Parallel computing is an effective approach to transient stability real-time simulation of large-scale power system. In this paper, a new parallel algorithm for power system transient stability simulation is proposed by combining Gauss method and the Sherman-Morrison formula. The algorithm adopts the Gauss method to convert the differential-algebraic equations into a set of nonlinear algebraic equations by multi-stages discretization, while the algebraic system is solved using rigorous Newton method. On this basis, the whole Jacobian matrix involved in Newton method is split to a block diagonal matrix and a block constant coefficients matrix according to s time points, and then based on the block diagonal matrix, the computing tasks at s time points are fully decoupled through the extended Sherman-Morrison matrix inverse formula. The proposed algorithm preserves the good convergence of rigorous Newton method and meanwhile has a high degree of parallelism both in time and in space.