Simultaneous Implicit Research Articles

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.

FAST ACCURATE TRANSIENT STABILITY SIMULATIONS

ABSTRACT The paper describes a Simultaneous Implicit (SI) approach for transient stability simulations based on an iterative technique using traingularised admittance matrix [1]. The reduced saliency of generator in the subtransient state is taken advantage of to speed up the algorithm. Accordingly, generator differential equations, except rotor swing, contain voltage proportional to fluxes in the main field, dampers and a hypothetical winding representing deep flowing eddy currents, as state variables. The simulation results are validated by comparison with two independent methods viz. Runge-Kutta simulation for a simplified system and a method based on modelling damper windings using conventional induction motor theory[2].