GPU based parallel simulation of transient stability using symplectic Gauss algorithm and preconditioned GMRES method

This paper presents a parallel algorithm for power system transient stability computing. The proposed algorithm uses the s-stage 2s-order symplectic Gauss method to convert the differential-algebraic system simultaneously at s time points into a set of nonlinear algebraic equations, and the algebraic system is then solved by Newton method. By the use of the matrix factorization technique, the solution of the linear equations involved in Newton process is decomposed into two parts: the first is fully parallelizable-in-time, and the second is solved using a preconditioned GMRES method while an efficient preconditioner has been proposed for iterative method. For test, the convergence of the proposed algorithm has been examined on 3 example systems. Furthermore, the proposed algorithm has been implemented on a single GPU based computer, and the results show the proposed algorithm achieves great computational efficiency relative to the traditional CPU computing.