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A unified constant-frequency integration (UCI) controller for a three-phase star-connected switch three-level rectifier (VIENNA) with unity-power-factor-correction is proposed. One of advantages of this rectifier is that the switch voltage stress is one half of the total output voltage. The proposed control approach is based on one-cycle control and features great simplicity and reliability: all three phases will be power factor corrected using one or two integrators with reset along with several flips-flops, comparators and logic and linear components. It does not require multipliers to scale the current reference according to the output power level as used in many other control approaches. In addition, the input voltage sensor is eliminated. It employs constant switching frequency modulation that is desirable for industrial applications. The proposed controller can operate by sensing either the inductor currents or the switching currents. If the switching currents are sensed, the cost is further reduced because switching currents are easier to sense comparing with inductor currents. The proposed approach is supported by experimental results.