Lyapunov function for power systems with transfer conductances: extension of the Invariance principle

In many engineering and physical problems, it is very difficult to find a Lyapunov Function satisfying the classical version of the LaSalle´s invariance principle. This difficulty has been a big drawback in the application of energetic methods to stability analysis of power systems with more realistic models. In this work, an extension of the invariance principle is used to support the proposal of a new function which is an extended Lyapunov function for power systems incorporating the transfer conductances. This function was tested in a single-machine-infinite-bus system and also in some multimachine systems. The results show that the proposed function can be used to obtain good estimates of the critical clearing time.