Parallel Simulation of Power Systems Transient Stability Based on Implicit Runge–Kutta Methods and W-transformation

Abstract

This paper presents a novel parallel algorithm for power systems transient stability simulation based on fully implicit Runge–Kutta (IRK) method. The s-stage IRK method is used to convert the differential-algebraic system simultaneously at s different time points into a set of non-linear algebraic equations, and the algebraic system is then solved by Newton's method. By the use of the matrix factorization technique, the solution of the linear equations involved in Newton's process is divided into two parts: the first part is decoupled at s different time points, thus it is fully parallelizable in time, and the second part is solved by preconditioned generalized minimal residual method (GMRES) method, while a new preconditioning method has been proposed by using the W-transformation and double-parameters method. For test, the proposed algorithm is implemented on multiple-graphics processing units (GPUs) computing platform. The results show that the proposed algorithm is accurate and has good convergence. Moreover, the parallel algorithm implemented on multiple-GPUs computing platform achieves high parallel efficiency.