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In this paper, a three-phase six-switch standard boost rectifier with unity-power-factor correction is investigated. A general equation is derived that relates the input phase voltages, output DC voltage, and duty ratios of the switches in continuous conduction mode. Based on one of the solutions and using one-cycle control, a unified constant-frequency integration controller for PFC is proposed. For the standard bridge boost rectifier, a unity power factor and low total harmonic distortion can be realized in all three phases with a simple circuit that is composed of one integrator with reset along with several flips-flops, comparators, and some logic and linear components. It does not require multipliers and three-phase voltage sensors, which are required in many other control approaches. In addition, it employs constant-switching-frequency modulation that is desirable for industrial applications. The proposed control approach is simple and reliable. All findings are supported by experiments.