Iterative solver techniques in the dynamic simulation of power systems

Abstract

The time domain solution of power system models is generally done via the simultaneous implicit method. In the process, the trapezoidal integration formula is used to convert the differential algebraic system into a set of nonlinear algebraic equations. The algebraic system is then solved using Newton's method, which involves the solution of a set of linear equations at each time step of the integration. Instead of using the LU factorization, the authors use the GMRES method for the solution of the linear system. The reasons for the slow convergence of the GMRES when solving this system are examined, and methods to alleviate this problem are proposed. In addition, they use a modification of GMRES, which is shown to be more efficient for ill-conditioned systems. The methods are applied to the dynamic simulation of a 3-machine, 9-bus system and a 16-machine, 68-bus system.