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The transient stability of an a.c. generator is analysed by utilizing Lyapunov's direct method. Lyapunov functions are developed, which include the effects of flux docay and simplified representations of speed governer and voltage regulator. It is shown that Lyapunov's method can be utilized to estimate reasonably accurately the critical fault clearing time with considerably fewer computations and in much shorter time than by conventional techniques. Furthermore, it is shown how a Lyapunov function can indicate the relative effects of various factors on the stability property of a generator. The Lyapunov functions have been developed essentially by trials based on physical considerations. Various existing methods of constructing the Lyapunov functions were also considered but were found to be of no help in the present study. more...