Frequency-Adaptive Fractional-Order Repetitive Control of Shunt Active Power Filters

Repetitive control (RC), which can achieve zero steady-state error tracking of any periodic signal with known integer period, offers active power filters (APFs) a promising accurate current control scheme to compensate the harmonic distortion caused by nonlinear loads. However, classical RC cannot exactly compensate periodic signals of variable frequency and would lead to significant performance degradation of APFs. In this paper, a fractional-order RC (FORC) strategy at a fixed sampling rate is proposed to deal with any periodic signal of variable frequency, where a Lagrange-interpolation-based fractional delay (FD) filter is used to approximate the factional delay items. The synthesis and analysis of FORC systems are also presented. The proposed FORC offers fast online tuning of the FD and the fast update of the coefficients, and then provides APFs with a simple but very accurate real-time frequency-adaptive control solution to the elimination of harmonic distortions under grid frequency variations. A case study on a single-phase shunt APF is conducted. Experimental results are provided to demonstrate the validity of the proposed FORC.