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This paper investigates the use of adaptive repetitive and resonant control approaches for the control of a single-phase hybrid cascaded multilevel converter designed to interface with power grids of highly distorted voltage waveform. The proposed repetitive/resonant control (RPC/RSC) is used for the extraction of clean phase angle, frequency, and magnitude information of the fundamental grid voltage together with the control of the converter current and mitigation of current harmonics under distorted grid voltage and variable frequency. The RPC time period and the RSC resonant frequency are updated adaptively using the estimated grid frequency while interpolation is used to preserve the RPC rejection capability under noninteger number of time steps per period. Detailed modeling and experimental investigation of the proposed control scheme are carried out.