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 mi-crogrids, 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.