Construction of Lyapunov function for power systems

A systematic procedure of constructing Lyapunov functions for power systems is considered. A new approach is presented, which uses a construction technique of the Lagrange´s function resulting from 2nd-order ordinary differential equations. The application of this new method to power-system transient-stability problems is illustrated by considering a single-machine system, taking into account the effect of the velocity governor, which is represented by 1st-order or 2nd-order response. The Lyapunov functions may then be used to estimate the critical reclosing time for power-system transient stability. The critical reclosing times given by these Lyapunov functions are compared with those obtained by numerical integration, and numerical results are shown. Further-more, it is discussed how a Lyapunov function indicates the relative effects of control-system parameters on the stability characteristic of a generator.