Computing Critical Eigenvalues of Power Systems Using Inexact Two-Sided Jacobi-Davidson

Abstract

This paper describes inexact two-sided Jacobi- Davidson (ITSJD) method to compute the critical (least damping ratio) eigenvalues and corresponding left and right eigenvectors of power systems. Using approximation correction vectors to expand search spaces of two-sided Jacobi-Davidson method leads to ITSJD, which is used to compute eigenvalues closest to the target. Only one LU factorization is needed in whole iteration to improve the computing efficiency. The critical eigenvalues are mapped to extreme eigenvalues of Cayley transformation matrix which can be calculated by using ITSJD. The proposed method has been tested on systems with orders of 493, 1461, and 3781. The results show that ITSJD is effective and able to compute the critical eigenvalues and eigenvectors.