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This paper provides a new tool to study transient stability of power systems. It consists of a direct method that provides critical clearing time estimates without resorting to numerical energy functions. The methodology consists of studying stability of relevant variables of a nonlinear dynamical system uniformly with respect to the non-relevant variables, which are treated as uncertainties. The methodology is successfully applied to the transient stability analysis of a small power system leading to much improved estimates of stability region and critical clearing times as compared to traditional energy functions, numerical energy functions and two-time-scale energy functions.