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A synchronous reference frame controller with a multi-resonant harmonic compensator for single-phase grid-connected inverters is proposed in this paper. The essence of the proposed control strategy is to use a synchronous reference frame PI controller (SRFPI) to regulate the output current with zero steady state error, together with a multi-resonant harmonic compensator to provide an efficient attenuation of the grid voltage background harmonic distortion, and an average power controller to regulate the active and reactive powers. A detailed design procedure for the proposed control strategy is presented based on a frequency response approach. Extensive simulations confirm the validity of the proposed strategy.