Lyapunov analysis of two imbalanced power system areas

Transient stability refers to the system’s capability to preserve synchronism while affected by large disturbances. It is a nonlinear problem that requires the simultaneous solution of many differential equations. Therefore, a thorough analysis is needed to resolve it. In this paper, we present an analysis of multimachine transient stability under different fault cases using the Lyapunov function. It serves as an analytical tool to determine the condition necessary for stability. The system remains stable as long as it is contained in the region of attraction. Meanwhile, the swing equation and reduced admittance matrix are used to model the system in three conditions: Pre-fault, during the fault, and post-fault. Numerical simulations are conducted to verify the preservation of synchronism under fault on the transmission lines by achieving the critical clearing time. © 2021 Author(s).