Transient Stability of Multimachine Power Systems via the Direct Method of Lyapunov

The direct method of Lyapunov applied to the problem of transient power system stability is developed to permit the practical study of n-machine systems. A simple physical interpretation and a proof are given for two Lyapunov functions. A new and better Lyapunov function is defined, and several possibilities for its evaluation are studied. Through an analysis of the singular points of the system the causes of the conservativeness of the results are established, and a further improvement on the Lyapunov function is made. A general structure for a computer program is proposed, and results of an example with a 10-machine system solved by the conventional and the new methods are presented; the computing time by the Lyapunov method was about 40-percent shorter. Finally, several ideas for a further generalization and optimization of the method and a possibility for the design and control of power systems are proposed.