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This paper proposes a new family of three-switch three-state single-phase Z-source inverters (TSTS-ZSIs) that can be classified into two groups, boost-based TSTS-ZSI and buck-boost-based TSTS-ZSI, according to the step-up circuit. All of the topologies have the merits of buck-boost capability and low voltage stress, and some of them have the feature of dual grounding. In addition, the step-up in dc side and inversion in ac side is completely decoupled in the proposed topologies. In terms of a linear voltage gain, the conventional linear control methods can be used, which makes the control system very simple. The operating principles of the two types of topologies are described, respectively, and the comprehensive comparison between them is provided. Finally, the theoretical analysis and comparison of the proposed topologies are verified by the simulation and experimental results.