FACTS devices have been shown to be powerful in damping power system oscillations caused by faults; however, in the multi machine control using FACTS, the control problem involves solving differential-algebraic equations of a power network which renders the available control schemes ineffective due to heuristic design and lack of know how to incorporate FACTS into the network. A method to generate nonlinear dynamic representation of a power system consisting of differential equations alone with universal power flow controller (UPFC) is introduced since differential equations are typically preferred for controller development. Subsequently, backstepping methodology is utilized to reduce the generator oscillations by using a FACTS device after a fault has occurred. Finally, we use neural networks to approximate the nonlinear network dynamics for controller design. The net result is a representation that could be potentially utilized for studying the placement and number of FACTS devices as well as to design a better control scheme for FACTS given a power network. Simulation results justify theoretical conjectures.