This paper presents a multi-rate fractional-order repetitive control (MRFORC) scheme for three-phase shunt active power filter (APF). The proposed APF control scheme includes an inner proportional-integral (PI) control loop with a sampling rate identical to switching frequency and an external plug-in RC loop with a reduced sampling rate. The MRFORC loop is implemented in dq-frame with interleaving for the reduction of computational burden in each control cycle. Moreover, in order to deal with the harmonics in the presence of wide grid frequency variations, FORC, which replaces the fractional-order elements with the Lagrange-interpolation based finite impulse response (FIR) filter, is adopted instead of the conventional RC. The synthesis, stability analysis and parameters tuning criteria of the MRFORC system are derived in detail. A step by step design example of the proposed controller is also given in the paper. Finally, experiments are performed to validate the feasibility and effectiveness of the proposed scheme.
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