A general Liapunov function for multi-machine power systems with transfer conductances

This paper deals with a general Liapunov function for multi-machine power systems taking into account the effects of damping and transfer conductances. The n-machine power system is described by variables of order (2n—1) in the minimal state spaco. The derivation follows from the Liapunov theory and the generalized Popov criterion for multi-variable feedback systems due to Anderson. The criterion of Willems for the optimum Liapunov function is incorporated and hence it yields a large transient stability region. The same function is suitable with proper substitutions to study the cases of a power system with non-uniform or uniform damping either with or without the effect of transfer conductances.