Network-Based Analysis of Small-Disturbance Angle Stability of Power Systems

This paper investigates small-disturbance angle stability of power systems with emphasis on the role of power network topology, which sheds new light on the instability mechanism. We introduce the concepts of active power flow graph and critical lines. It is shown that the inertia of the Laplacian matrix of this graph provides information on the stability and type of an equilibrium point. Then, the instability mechanism is elaborated from the impact of critical lines on the inertia of the Laplacian matrix. A stability criterion in terms of a critical line-based matrix is established. This criterion is a necessary and sufficient condition to judge the stability and type of an equilibrium point. It includes the existing results in the literature and applies to the unsolved cases where the critical lines exist but do not form cutsets. Moreover, we introduce the concept of equivalent weight between a pair of buses. Another stability criterion in terms of the equivalent weight is developed, from which the small-disturbance instability can be interpreted as the “electrical antagonism” between some buses in the power network resulting from the critical lines. The equivalent weight can also be used as a stability index and provides guidance for system operation. The obtained results are illustrated by numerical simulations.