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A novel method to compute the stability region in power system transient stability analysis is presented. This method is based on the level set analysis. The key to this method is to construct the Hamilton-Jacobi-Isaacs (HJI) partial differential equation (PDE) of a nonlinear system, using which we can compute the backward reachable set by applying the level set methods. The backward reachable set of a stable equilibrium yields the stability region of the equilibrium point in power system transient stability assessment. The proposed method is applied to a single machine infinite bus system and a classical two-machine system yielding satisfactory results.