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Unified calculation of eigen-solutions in power systems based on matrix perturbation theory |
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| Authors: | Yan Li WenZhong Gao JiuChun Jiang ChenShan Wang Eduard Muljadi |
| Affiliation: | 1. National Active Distribution Network Technology Research Center (NANTEC), Beijing Jiaotong University, Beijing, 100044, China 2. Department of Electrical and Computer Engineering, University of Denver, Denver, CO, 80210, USA 3. Key Laboratory of Smart Grid of Ministry of Education, Tianjin University, Tianjin, 300072, China 4. National Renewable Energy Laboratory (NREL), Golden, CO, 80401, USA |
| Abstract: | 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. |
| Keywords: | matrix perturbation matrix spectrum decomposition shift method unified solution approach eigen-solutions |
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