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In this paper a tracking problem for a single-phase PFC rectifier exploiting the Boost converter as nonlinear system using model predictive control (MPC) is discussed. 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 presented. The main advantage of the proposed digital control PFC method is that unity power factor can be achieved over wide input voltage and load current range. Boost PFC topology with NMPC shows better and more accurate performance in both steady state and transient state than linear control methods. Simulation results demonstrate the effectiveness of the proposed NMPC.