Fractional-Order New Generation of $6k+1$-Order Repetitive Control for Three-phase Grid-connected Converters

This paper proposed a fractional-order new generation of $6k\pm 1$ -order repetitive control scheme (FO-NG- $6k\pm 1$ RC). FO-NG- $6k\pm 1$ RC is composed of NG- $6k\pm 1$ RC and a Farrow structure fractional delay filter based on Taylor series expansion. Since $6 k\pm 1$ RC/FO-NG $6k\pm 1$ RC occupies less digital memory space, it has better dynamic performance than CRC/FO-CRC, which is more suitable for the control of three-phase power systems dominated by the $6k\pm 1$ -order harmonics. By updating filter coefficients online in real time, FO-NG- $6k\pm 1$ RC can quickly and effectively deal with the frequency variations of grid-connected converters, and has good frequency adaptability. Through a simulation example applied to a three-phase grid-connected inverter, the effectiveness and superiority of the proposed FO-NG- $6k\pm 1$ RC control scheme are fully verified.