Passivity-Based Design of Frequency Adaptive Selective Harmonic Repetitive Control for Grid-Connected Inverters

The repetitive controller (RC), owing to the capability of zero-error tracking periodical signals, is widely used to compensate for harmonics in the grid. Compared with Conventional RC, by eliminating specific order harmonics for different application scenarios, selective harmonic repetitive controller (SHRC) can simultaneously achieve high control accuracy and less computation burden. As SHRC is sensitive to frequency variations, it is improved to frequency adaptive SHRC (FA-SHRC) via adding filters to approximately compensate fractional-order delays caused by frequency variations. However, the external stability of FA-SHRC remains a problem. In the article, a detailed passivity-based designed approach of FA-SHRC is proposed. The proposed method can tune the impedance of the inverter with FA-SHRC passive for the full frequency range, which ensures the system is stable, dynamic, and adaptive regardless of grid impedance and frequency variations. Finally, experiments are performed to validate the superiority of the approach for designing FA-SHRC.