Iterative solver techniques in fast dynamic calculations of power systems

In this paper, iterative solver techniques belonging to the family of conju gate-gradient methods for solving the system of Linear equations, Ax = b, a re discussed. Specifically, we consider the Bi-Conjugate Gradient (BCG) Met hod, CGS Method, CGSTAB Method and the Generalized Minimal Residual Method (GMRES), which can handle unsymmetric matrices. In transient stability simu lations, sparse matrices occur during the solution process of the different ial-algebraic equations (DAEs) by the simultaneous implicit (SI) method. Th is paper investigates the effects of a new preconditioning technique, the d ishonest preconditioner, on these methods. All of these methods are inheren tly vectorizable/parallelizable. (C) 2001 Elsevier Science Ltd. All rights reserved.