Application of sparse eigenvalue techniques to the small signal stability analysis of large power systems

Two sparsity-based eigenvalue simultaneous iterations and the modified Arnoldi method are presented and their application to the small signal stability analysis of large power systems is discussed. 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. Comparisons are made for the two eigenvalue methods with other techniques