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Repetitive control (RC) is a high-performance control scheme for constant-voltage constant-frequency (CVCF) pulse-width modulated (PWM) inverter systems to cancel output total harmonic distortion (THD). This paper presents a new 6k±1 order harmonic RC (6k±1 RC) scheme for CVCF three-phase PWM inverter systems to further improve the control performance of RC. The proposed control scheme can achieve zero-error tracking or perfect disturbance rejection for 6k±1 order harmonics. Compared with conventional RC (CRC), 6k±1 RC requires less data memory and offers faster error convergence rate. It also yields very low THD and very high tracking accuracy. In the presence of nonlinear load disturbances, an application example of a 6k±1 RC controlled three-phase PWM inverter is provided to evaluate the proposed 6k±1 RC scheme. Experimental results show the validity and advantages of the proposed 6k±1 RC scheme.