Eigenvalue methods for calculating dominant poles of a transfer function and their applications in small-signal stability

Abstract

In this paper, we give a new short proof of the local quadratic convergence of the Dominant Pole Spectrum Eigensolver (DPSE). Also, we introduce here the Diagonal Dominant Pole Spectrum Eigensolver (DDPSE), another fixed-point method that computes several eigenvalues of a matrix A at a time, which also has local quadratic convergence. From results of some experiments with a large power system model, it is shown that DDPSE can also be used in small-signal stability studies to compute dominant poles of a transfer function of the type cT(A−sI)−1b, where s∈C,b and c are vectors, by its own or combined with DPSE. Besides DDPSE is also effective in finding low damped modes of a large scale power system model.