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This paper proposes a new single phase back-to-back PWM converter for the power supply of the single phase by using both a full-bridge PWM rectifier and a half-bridge PWM inverter. In addition, the balancing control algorithm of DC voltage for this topology is also proposed by controlling the current of the half-bridge inverter. With the full-bridge PWM rectifier and the half-bridge PWM inverter, AC/DC/AC operation can be carried out by using only a six-pack power module and two series DC capacitors. Since two series connected capacitors are installed at the DC link, each capacitor voltage must be balanced for the safe operation. Using a IP(Integral-Proportional) controller, the DC voltage can be balanced without the current distortion. The proposed algorithm can be easily implemented without much computation and additional hardware circuit. The validity of the proposed algorithm is verified through simulations.