Lagrange-Charpit method and stability problem of power systems

The paper applies the Lagrange-Charpit method to construct a Lyapunov function for stability studies of power systems. The Lyapunov function is given for the single-machine system taking into account saliency and the effect of variable damping. The stability boundary obtained is compared with those obtained by conventional Lyapunov functions and the true stability boundary. It is shown that the application of the Lagrange-Charpit method results in considerable improvement of stability-boundary estimates over those which have been currently available concerning this problem. Another model including the effects of constant damping and the velocity governor with one time constant is also studied. In this 3rd-order system, cross-sections of the stability surface for various planes are given, showing the superiority of the proposed Lyapunov function.