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A carrier-rotation PWM technique to solve the voltage unbalancing problem of flying capacitors in the flying capacitor multilevel inverter (FCMI) is proposed. The PWM technique equalises the utilisation of phase leg voltage redundancies corresponding to the charging and the discharging state of individual flying capacitors during one switching period of all the switches. Therefore, the charging and the discharging quantities of the flying capacitors are equal, which causes the average variation of the flying capacitor voltages to become zero and keeps their voltage stable during a minimum specified period. The proposed PWM technique also has the same switch utilisation and the reduced harmonic content of the output voltage since the switching frequency of each switch is identical and all the carrier signals are in phase. Hence, it is more suitable for the FCMI than the phase-shift PWM method. The proposed PWM technique is analysed in a flying capacitor three-level inverter and is then expanded to an N-level FCMI (N>3). Simulation and experimental results on the laboratory prototype flying capacitor three-level inverter confirm the validity of the proposed PWM technique.