Rotor Angle Stability Analysis by Using Lyapunov's Direct Method of a SMIB Power System

Rotor angle stability of a power system refers to the ability of the system to return to equilibrium points after significant disturbances like application to sudden increase in power input or removal of the load, line faults etc. This paper presents the importance of the rotor angle stability of power systems. The rotor angle stability is analyzed based on solving swing equation of a power system. The swing equation is a nonlinear equation. Therefore, a several non-linear methods (Runge-Kutta, Euler etc.) can be used to solve the swing equation. In this study, Lyapunov's direct method is proposed to solve the swing equation. The proposed method is tested on a single machine infinite bus test system. The maximum limit value at which the mechanical input power of the system can suddenly increase has been found. The obtained results show that Lyapunov's direct method successfully detects the operating point close to the instability region of the system.