Transient Stability Analysis of Multi-machine Power System with Automatic Voltage Regulators via Lyapunov's Direct Method

Abstract

In this paper, Lyapunov's direct method is applied to a multi-machine power system where generators are installed with atuomatic voltage regulators. The automatic voltage regulator and the thyrister exciter are represented by a third order transfer function. The stability of the power system is checked according to a generalized Popov criterion. This criterion guarantees that the system is stable if the gains of the voltage regulators are lower than the limit values. A Lur'e type Lyapunov function is constructed by the systematic method established by J. L. Willems. The obtained Lyapunov function is used in a transient stability analysis of a 10-machine power system. The direct method yields results which are very close to those obtained by simulations. It is concluded that Lyapunov's direct method is applicable with sufficient accuracy to transient stability analyses of power systems, where automatic voltage regulators are installed in generators on the condition that the gains of the automatic voltage regulators must be enlarged to practically used values in the future.