The generalized form of Zubov's partial differential equation (Szego 1962) is written using the dynamical equations of a power system. Then a Lyapunov function which satisfies the partial differential equation is obtained by using a transformation of state variables. The V function obtained is used to describe the region of stability. The application of the method to the power system stability problem is illustrated by considering a synchronous generator connected to an infinite bus, Three examples, using three different models for the synchronous machine, are given.