Active power filter(APF)is an important equipment for controlling harmonic pollution in power grids. There exists a deviation between the resonant frequency of the conventional repetitive control and the actual frequency of the grid when the grid is operating outside the nominal frequency

leading to a reduction in the APF's ability to track and compensate for harmonics. To address the issue of insufficient tracking and compensation capability of repetitive control under non-nominal frequency conditions

a mathematical model of the active power filter was developed

analyzing the impact of the grid frequency deviations on traditional repetitive control. A novel fractional-order repetitive control method was proposed

incorporating an all-pass filter into the internal model of the repetitive control to construct a fractional delay element. The grid frequency was obtained via a phase-locked loop to adjust the counting parameters and filter settings of the repetitive control. The stability of the system was examined

enabling accurate tracking and compensation of harmonics by the repetitive control. Experiments demonstrate that the proposed control method effectively eliminates the deviation between the resonant frequency of the repetitive control and the grid frequency

enhancing the system's tracking and compensation capacity for periodic harmonics at non-nominal grid frequencies

and reducing the total harmonic distortion of the grid-side current.