APPLICATION OF SPARSE EIGENVALUE TECHNIQUES TO THE SMALL-SIGNAL STABILITY ANALYSIS OF LARGE POWER-SYSTEMS

This paper presents two sparsity-based eigenvalue techniques — simultaneous iterations and the modified Arnoldi method — and their application to the small signal stability analysis of large power systems. Simultaneous iterations and the modified Arnoldi method are two recently developed methods for large, sparse unsymmetrical eigenvalue problems, and have been reported as very efficient in computing the partial eigensolution of several types of matrices, such as stochastic ones. It is shown in this paper that they can also be applied successfully to the matrices derived for small signal stability studies of power systems. An algorithm utilizing these two methods is proposed for calculating the eigenvalues around a fixed point which can be placed at will in various parts of the complex plane. The sparsity is fully preserved in the algorithm by using the augmented system state equations as the linearized power system small signal model and performing the corresponding sparsity-oriented calculations. Several applications of the algorithm are discussed and illustrated by numerical examples. The proposed methods and algorithm have been tested on two test systems with 20 and 50 machines respectively. The results show that they are suitable for the eigenanalysis of large power systems. © 1990 IEEE