Unified calculation of eigen-solutions in power systems based on matrix perturbation theory

Calculation of eigen-solutions plays an important role in the small signal stability analysis of power systems. In this paper, a novel approach based on matrix perturbation theory is proposed for the calculation of eigen-solutions in a perturbed system. Rigorous theoretical analysis is conducted on the solution of distinct, multiple, and close eigen-solutions, respectively, under perturbations of parameters. The computational flowchart of the unified solution of eigen-solutions is then proposed, aimed toward obtaining eigen-solutions of a perturbed system directly with algebraic formulas without solving an eigenvalue problem repeatedly. Finally, the effectiveness of the matrix perturbation based approach for eigen-solutions' calculation in power systems is verified by numerical examples on a two-area four-machine system.