An Improved IRA Algorithm and Its Application in Critical Eigenvalues Searching for Low Frequency Oscillation Analysis

Abstract

On the basis of implicitly restarted Arnoldi (IRA) method, an improved algorithm is proposed, in which the dimension of Krylov subspace is dynamically increased to compute eigenvalues in specified circle. First, the radius of searching circles is dynamically expanded through automatically increasing the number of eigenvalues and the dimension of Krylov subspace, based on the locking mechanism. Second, the region where the low frequency oscillation modes located is divided into small independent computing units, which are covered by specified searching circles. Third, the independent computing units can be calculated simultaneously with no effects on each other. The proposed method can avoid eigenvalues missing caused by inappropriate resetting of search number in equidistant-searching IRA method. Furthermore, no manual intervention is needed in the proposed method. Two systems with 570 and 5272 state variables are tested in this paper, and the results indicate that the proposed method is efficient, reliable, and practical.