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Lyapunov functions for multimachine power systems with dynamic loads

This paper develops Lyapunov functions for power systems which have dynamic reactive power loads. These functions are extensions of earlier Lyapunov functions derived for structure preserving power system models having static loads. In order to obtain strict Lyapunov functions, the transient response of the dynamic load must have a logarithmic dependence on voltage. A Lyapunov function is initially generated using a "first integral" analysis. A Popov criterion analysis is then undertaken for comparison. The developed Lyapunov functions enable the investigation of the interaction between generator (angle) and load dynamics in multimachine power systems.