On the solution of small signal stability of power systems by a block-Krylov subspace algorithm

Abstract

Iterative methods built on Krylov subspaces for the computation of eigenvalues in small-signal stability problems of power systems have been little explored to date. This computation is one of the most challenging and time-consuming part of the simulation, especially for matrices with clustered eigenvalues and having multiplicity greater than one (named here as CME matrices). This paper proposes a block-Krylov algorithm built on the augmented block Householder Arnoldi method to compute eigenvalues in small-signal stability problems with CME matrices, exploring enlarged subspaces that normally result in less steps to achieve convergence. Both efficiency and robustness are examined through numerical experiments using two power systems and the conventional Arnoldi (unblock) and QR decomposition methods. The results indicate that the block-Krylov algorithm performs better for CME matrices than the other two. On the other hand, it is no longer as efficient on matrices with none or just few clustered and (or) multiple eigenvalues. The proposed block-Krylov algorithm has never been tested in the small-signal stability problem.