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A new family of Z-source ac-ac converters with buck-boost ability are proposed, including four switches single-phase structure and six switches three-phase structure. New commutation strategies for these converters are proposed and safe commutation can be achieved without snubber circuit. The commutation strategies are easily to realize by sampling only voltage signals, and two switches are always turned on, so switching loss can be reduced. Analysis based on state-space averaging reveals the relationship between Z-source inductor current and filter inductor current as well as voltage ratio. The design considerations of voltage-fed single-phase topology are given as an example. Simulation results on the voltage-fed topologies and experimental results on voltage-fed single-phase topology verified the unique features of Z-source ac-ac converters and the proposed commutation strategies. These converters have merits such as less conduction and switching loss, less devices, therefore high efficiency and reliability can be achieved.