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A simple near-unity power factor converter using two current control methods- the Average Current Control method (ACC) and Hysteresis Current Control method (HCC)-has been employed in this paper for a wind energy conversion system feeding simple loads. A simple stepped wind speed profile, comprising the rated wind speed and a higher wind speed, has been considered and the performance parameters of the unity power factor converter compared for these two current control methods. The wind turbine drives a Permanent Magnet Synchronous Generator (PMSG), which is interfaced with the near UPF converter feeding a resistive load. The performance parameters under study are the Total Harmonic Distortion (THD) of the input currents to the converter and the input Power Factor (PF) to the converter. Simulation has been performed in PSIM and Simulink employing SimCoupler for co-simulation and the results verify the efficacy of the converter in delivering satisfactory performance.