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In this paper, a Frequency Adaptive Selective Harmonic Control (FA-SHC) scheme is proposed. The FA-SHC method is developed from a hybrid SHC scheme based on the internal model principle, which can be designed for gridconnected inverters to optimally mitigate feed-in current harmonics. The hybrid SHC scheme consists of multiple parallel recursive (nk±m)-order (k = 0, 1, 2, . . ., and m ≤ n/2) harmonic control modules with independent control gains, which can be optimally weighted in accordance with the harmonic distribution. The hybrid SHC thus offers an optimal trade-off among cost, complexity and also performance in terms of high accuracy, fast response, easy implementation, and compatible design. The analysis and synthesis of the hybrid SHC are addressed. More important, in order to deal with the harmonics in the presence of grid frequency variations, the hybrid SHC is transformed into the FA-SHC, being the proposed fractional order controller, when it is implemented with a fixed sampling rate. The FASHC is implemented by substituting the fractional order elements with the Lagrange polynomial based interpolation filters. The proposed FA-SHC scheme provides fast on-line computation and frequency adaptability to compensate harmonics in gridconnected applications, where the grid frequency is usually varying within a certain range (e.g., 50±0.5 Hz). Experimental tests have demonstrated the effectiveness of the proposed FASHC scheme in terms of accurate frequency adaptability and also fast transient response.