Transient stability analysis of microgrids with a line-based model

Abstract

This paper investigates transient stability of microgrids with radial topology from the line-based perspective rather than the bus dynamics perspective. A line-based model is proposed to describe the dynamics of angle differences across transmission lines. Based on this model, the equilibrium points of the system are expressed in explicit form and the local stability is characterized. Then, a computationally efficient method to estimate the stability region is developed by using a topological Lyapunov function, where the critical energy for transient stability is evaluated by traversing the value of the topological Lyapunov function over a small and finite set of equilibrium points. This method also helps to identify the topological weakness in the system. Moreover, we build up easy-to-solve optimization problems to measure the impact of power variations of renewables and loads on the stability level. The results are validated by numerical studies on a 9-bus test system.