Yuan Kai

Matrix perturbation based approach for sensitivity analysis of eigen-solutions in a microgrid

Sensitivities of eigen-solutions to control variables play an important role in microgrid studies, such as coordinated optimal design of controllers and parameters, robust stability analysis on control variables, oscillation modes analysis on a system, etc. Considering the importance of sensitivities and the complexity of state matrix in a microgrid, parameter perturbations are utilized in this paper to analyze the construction characteristics of state matrix. Then, the sensitivities of eigenvalues and eigenvectors to control variables are obtained based on the first-order matrix perturbation theory, which makes the complex derivations of sensitivity formulas and repeated solutions of eigenvalue problem unnecessary. Finally, the effectiveness of the matrix perturbation based approach for sensitivity calculation in a microgrid is verified by a numerical example on a low-voltage microgrid prototype.