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 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.Index Terms-Ac-ac converter, matrix converter, reduced switch count converter, sparse matrix.

A novel three-phase AC-DC-AC Sparse Matrix Converter (SMC) having no energy storage elements in the DC link and employing only 15 IGBTs as opposed to 18 IGBTs of a functionally equivalent conventional AC-AC matrix converter (CMC) is proposed. It is shown that the realization effort could be further reduced to only 9 IGBTs (Ultra Sparse Matrix Converter, USMC) in case the phase displacement of the fundamentals of voltage and current at the input and at the output is limited to ±π/6. The dependency of the voltage and current transfer ratios of the systems on the operating parameters is analyzed and a space vector modulation scheme is described in combination with a zero current commutation procedure. Furthermore, a safe multi-step current commutation concept is treated briefly. Conduction and switching losses of the SMC and USMC are calculated in analytically closed form. Finally, the theoretical results are verified in Part II of the paper by digital simulations and results of a first experimental investigation of a 10kW/400V SMC prototype are given. 5 b c c 0 1 0 0 0 1 0 0 1 u bc 0 -u bc 0 i A -i A 6 b a a 0 1 0 1 0 0 1 0 0 -u ab 0 u ab -i A i A 0 7 c a a 0 0 1 1 0 0 1 0 0 u ca 0 -u ca -i A 0 i A 8 c b b 0 0 1 0 1 0 0 1 0 -u bc 0 u bc 0 -i A i A 9 a b b 1 0 0 0 1 0 0 1 0 u ab 0 -u ab i A -i A 0 10 c a c 0 0 1 1 0 0 0 0 1 u ca -u ca 0 i B 0 -i B 11 c b c 0 0 1 0 1 0 0 0 1 -u bc u bc 0 0 i B -i B 12 a b a 1 0 0 0 1 0 1 0 0 u ab -u ab 0 -i B i B 0 13 a c a 1 0 0 0 0 1 1 0 0 -u ca u ca 0 -i B 0 i B 14 b c b 0 1 0 0 0 1 0 1 0 u bc -u bc 0 0 -i B i B 15 b a b 0 1 0 1 0 0 0 1 0 -u ab u ab 0 i B -i B 0 16 c c a 0 0 1 0 0 1 1 0 0 0 u ca -u ca i C 0 -i C 17 c c b 0 0 1 0 0 1 0 1 0 0 -u bc u bc 0 i C -i C 18 a a b 1 0 0 1 0 0 0 1 0 0 u ab -u ab -i C i C 0 19 a a c 1 0 0 1 0 0 0 0 1 0 -u ca u ca -i C 0 i C 20 b b c 0 1 0 0 1 0 0 0 1 0 u bc -u bc 0 -i C i C 21 b b a 0 1 0 0 1 0 1 0 0 0 -u ab u ab i C -i C 0 22 a b c 1 0 0 0 1 0 0 0 1 u ab u bc u ca i A i B i C 23 a c b 1 0 0 0 0 1 0 1 0 -u ca -u bc -u ab i A i C i B 24 b a c 0 1 0 1 0 0 0 0 1 -u ab -u ca -u bc i B i A i C 25 b c a 0 1 0 0 0 1 1 0 0 u bc u ca u ab i C i A i B 26 c a b 0 0 1 1 0 0 0 1 0 u ca u ab u bc i B i C i A 27 c b a 0 0 1 0 0 1 1 0 0 -u bc -u ab -u ca i C i B i A

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