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Three-phase single-switch boost power factor correction (PFC) converter features zero-current turn-on for the switch, no reverse recovery in diode, constant frequency operation, simple control and low cost and it is suitable for low-to-medium power conversions. However, the input power factor (PF) is relatively low when the duty cycle is constant in the whole line cycle. This study analyses the operation principle of the three-phase single-switch boost PFC converter, and the expressions of the input current and PF are derived, based on which, a variable duty cycle control is proposed so as to improve the PF and reduce the input current harmonics. A method of fitting the duty cycle is further proposed for simplifying the circuit implementation. Besides a higher PF and lower input current harmonics, the proposed variable duty cycle control achieves a lower output voltage ripple and a higher efficiency over the constant duty cycle control. A 3 kW prototype has been built and tested in the laboratory, and the experimental results are presented to verify the effectiveness of the proposed method.