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This paper addresses a nonlinear model predictive controller design for a single-phase PFC rectifier exploiting the Sheppard-Taylor converter. After approximation of the tracking error in the receding horizon by its Taylor-series expansion to any specified order, an analytic solution to the MPC is developed and a closed-form nonlinear predictive controller is introduced. The proposed nonlinear model predictive control (NMPC) derived using approximation can stabilize the original nonlinear systems if certain conditions, which can be met by properly choosing predictive times and the order for Taylor expansion, are satisfied. The main advantage of this digital control method is that unity power factor can be achieved over wide input voltage and load current range. Sheppard-Taylor PFC topology with NMPC shows better and more accurate performance in both steady state and transient state compared to linear control methods. Simulation results show the effectiveness of the proposed NMPC.