A generalized non-affine nonlinear power system model is presented for a single machine bus power system with a Static Var Compensator (SVC) or State Var System (SVS) for hybrid Unmanned Aerial Vehicles (UAVs).The model is constructed by differential algebraic equations on the MATLAB-Simulink platform with the programming technique of its S-Function.Combining the inverse system method and the Linear Quadratic Regulation (LQR),an optimized SVC controller is designed.The simulations under three fault conditions show that the proposed controller can effectively improve the power system transient performance.