Small-Disturbance Angle Stability Analysis of Microgrids: A Graph Theory Viewpoint

This paper is concerned with small-disturbance angle stability of microgrids from a graph theory perspective. Firstly, we build up the structure preserving model for microgrids, and introduce the concept of the active power flow graph, the Laplacian matrix and the critical lines. We show that small-disturbance stability is equivalent to the positive semi-definiteness of the Laplacian matrix, and it is the critical lines that cause instability. Then, we elaborate the impact of the critical lines on small-disturbance stability. A stability criterion is proposed, which is a matrix inequality in terms of the critical lines. This criterion also indicates the type of unstable equilibrium point (UEP) and can be considered as a supplement to eigenvalue-based small-disturbance analysis. The obtained results are validated by using a modified IEEE 9-bus test system.