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This paper proposes a series of new control methods for single-phase Z-source inverters. A detailed description of the concept and principle of each method is first presented, then a comparison among them is conducted comprehensively. Afterwards, an optimized closed-loop control scheme with better harmonic elimination performance is derived. Experimental results obtained from a 1kW un-isolated Z-source inverter prototype have demonstrated the effectiveness of the proposed control method. Compared to the conventional boost control, the proposed scheme has better performance with reduced harmonics, more flexible voltage gain, and simple algorithm.