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Power system is usually modeled using a combination of differential and algebraic equations. Advanced control design generally requires that a system be represented by purely differential equations. In this paper, a new method to generate a nonlinear dynamic representation of the power network is introduced to enable more sophisticated control design. Once the new representation is obtained, a new method for nonlinear control design for power system with UPFC is provided. The proposed approach is a complementary way of solving the differential-algebraic equations, in which the control design is difficult to achieve. In the proposed method damping of power system oscillation is achieved in a nonlinear sense by defining an appropriate Lyapunov function. A back stepping methodology for the UPFC is utilized to mitigate the generator oscillations resulting from a disturbance such as three-phase to ground fault. Simulations on a two area power system demonstrate the effectiveness of the suggested method.