A nonlinear dynamic circuit model is proposed to represent the differential-algebraic equations arising from the analysis of power system transient stability. By using the circuit-theoretic model, the following results are obtained. (1) Conditions are derived for the existence of Hamiltonian formulation of power systems. (2) A formula for calculating the critical reclosing time is derived using the Hamiltonian. (3) Conditions are obtained for the power system to reach synchronism asymptotically.