The authors present two sparsity-based eigenvalue techniques: simultaneous iterations and the modified Arnoldi method. It is shown that these two methods can 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. 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.
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