The paper deals with the direct AC-AC propulsion system and compares two matrix converter concepts with fivephase traction induction motors (IM) for the hybrid electric vehicle (HEV) including electronic differential. The first one consists of [3x5] matrix converter and [3x1] active PWM rectifier (4Q-converter) for full power performance. The second one comprises one [3x5] matrix converter for full power and auxiliary [0x5] matrix converter for partial output power. Configurations of [3x5] +

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... 5] MxC converters with five-phase motor(s) are not analyzed in available literature so far. The advantage of the proposed connection is in supposed higher efficiency of matrix converter then clasiccal VSI one. Part I deals with a theoretical study of converter concepts for hybrid electric vehicle. Based on simulation results the comparison and evaluation of the property and quality of the quantities of different type of the matrix powertrain are discussed in Part II.