Novel approach for calculation and analysis of eigenvalues and eigenvectors in microgrids

The calculation of eigenvalues and eigenvectors plays an important role in the stability analysis and optimal design of microgrids with multiple distributed energy resources. Microgrid systems are usually operated in various uncertain conditions. In this paper, a novel approach based on matrix perturbation theory is proposed for the calculation and analysis of eigenvalues and eigenvectors in a microgrid system. Rigorous theoretical analysis to solve eigenvalues and the corresponding eigenvectors for a system under various perturbations caused by fluctuations of irradiance, wind speed, or loads is presented. A computational flowchart is then proposed for the unified solution of eigenvalues and eigenvectors in microgrids, aimed toward obtaining eigenvalues and eigenvectors intuitively under different perturbations, which makes repeatedly solving an eigenvalue problem unnecessary. Finally, the effectiveness of the matrix perturbation-based approach in microgrids is verified by numerical examples on a typical low-voltage microgrid network.