A sparsity-oriented technique for power system small signal stability analysis with a precondition conjugate residual method

An efficient method for small-signal stability assessment in real-size power systems is presented. Eigenvalue-analysis-based approaches have been studied to evaluate the stability problem. The conventional methods require calculating all the eigenvalues in evaluating small-signal stability. Among them, the QR method is widely used due to its robustness and high accuracy. However, the method is not applicable to real-life systems with respect to computational time and storage. Recently, the S-matrix method has been developed to overcome the problem. The method is based on mapping the most critical eigenvalue from the s-plane to the z-plane. As a result, it requires calculating only the most critical eigenvalue rather than all the eigenvalues. Although the method is theoretically elegant, it generates unnecessary fill-in elements which result in increasing computational time since the direct method is used in solving a set of linear equations. That becomes more significant with system size. An efficient indirect method is developed using a precondition technique. The proposed method has been successfully applied to several systems. The simulation results indicated that the proposed method is 30 times and five times faster than the QR and the S-matrix methods, respectively, for a 46-unit, 191-bus system