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FACTS devices have been shown to be useful in damping power system oscillations. However, in large power systems, the FACTS control design is complex due to the combination of differential and algebraic equations required to model the power system. 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 back stepping methodology for the UPFC is utilized to mitigate the generator oscillations. Finally, the neural network approximation property is utilized to relax the need for knowledge of the power system topology and to approximate the nonlinear uncertainties. The net result is a power system representation that can be used for the design of an enhanced FACTS control scheme. Simulation results are given to validate the theoretical conjectures.