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A novel three-phase ac-ac sparse matrix converter having no energy storage elements and employing only 15 IGBTs, as opposed to 18 IGBTs of a functionally equivalent conventional ac-ac matrix converter, is proposed. It is shown that the realization effort could be further reduced to only nine IGBTs in an ultra sparse matrix converter (USMC) in the case where only unidirectional power flow is required and the fundamental phase displacement at the input and at the output is limited to plusmnpi/6. The dependency of the voltage and current transfer ratios of the sparse matrix converters on the operating parameters is analyzed and a space vector modulation scheme is described in combination with a zero current commutation method. Finally, the sparse matrix concept is verified by simulation and experimentally using a 6.8-kW/400-V very sparse matrix converter, which is implemented with 12 IGBT switches, and USMC prototypes.