Iterative solver techniques in fast dynamic calculations of power systems

In this paper, iterative solver techniques belonging to the family of conjugate-gradient methods for solving the system of linear equations, Ax = b, are discussed. Specifically, we consider the Bi-Conjugate Gradient (BCG) Method, CGS Method, CGSTAB Method and the Generalized Minimal Residual Method (GMRES), which can handle unsymmetric matrices. In transient stability simulations, sparse matrices occur during the solution process of the differential-algebraic equations (DAEs) by the simultaneous implicit (SI) method. This paper investigates the effects of a new preconditioning technique, the dishonest preconditioner, on these methods. All of these methods are inherently vectorizable/parallelizable.