A power system is a typical nonlinear dynamical system and voltage stability is an important subject of power system stability. This paper describes the use of the variable gradient method in a reduced order model of a single-machine infinite-bus power system. Additionally, the system's Lyapunov (energy) function is created and thus the system's energy level changes' effects on the system's stability are shown using the MACSYMA program. The Lyapunov function allows the determination of stability for nonlinear systems without the need to find exact solutions.

A power system is a typical nonlinear dynamical system and voltage stability is an important subject of power system stability. This paper describes the use of the variable gradient method in a reduced order model of a single-machine infinite-bus power system. Additionally, the system's Lyapunov (energy) function is created and thus the system's energy level changes' effects on the system's stability are shown using the MACSYMA program. The Lyapunov function allows the determination of stability for nonlinear systems without the need to find exact solutions.