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In this note, the transient stability of the single-machine system with the effect of the automatic voltage regulator is studied, using the direct method of Lyapunov. A new Lyapunov function for stability study of the power system is constructed by the Lagrange-Charpit method. The Lyapunov function is then used to estimate the critical reclosing times for power-system transient stability. The critical reclosing times given by the proposed Lyapunov function are compared to those obtained by numerical integration.