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In this paper we study the closest unstable equilibrium point (closest u.e.p.) method from both the theoretical and computational points of view. The issues concerning the existence and uniqueness of the closest u.e.p. are investigated. The dynamical characterization of the closest u.e.p. is derived. The problem concerning the robustness of closest u.e.p. with respect to the changes in different parameters of power system is studied. The closest u.e.p. is shown to be independent of both the machine inertia matrix and damping matrix in power system model. An improved closest u.e.p. method is then proposed based on some theoretical result. This improved closest u.e.p. method possesses the spirit of model-reduction approach and is shown to be optimal in the sense that the estimated stability region characterized by the corresponding energy function is the largest one within the true stability region.