Nonlinear transient stability study of synchronous machine via second method of lyapunov

The author makes an analytical study of the application of Lyapunov´s second method to the transient stability problem of a synchronous machine connected to a large power system. With suitable assumptions, the swing equations become 3rd or 4th order nonlinear differential equations. The resulting differential equation is of third order with one time constant of the prime-mover governor and is of fourth order with two time constants of the prime-mover governor. Suitable Lyapunov functions are generated by adding quadratic terms of other variables to the energy integral of the second-order conservative model. A rational approach has been presented for the selection of optimum Lyapunov parameters A3 and A4 for higher-order systems by including an algorithm for the same. For 3rd-order model, the stability domain obtained by the present technique developed by the author is compared with that of El-Abiad and Nagappan. It is found that the present method generates larger stability domains. It is believed that the present work will be a valuable addition to the existing literature for solving challenging nonlinear transient stability problems of a synchronous machine connected to a large power system.