A matrix converter is a direct ac/ac power converter that can achieve sine wave in and out operation without the need of bulky passive components. With these features, it offers remarkable advantages over other similar solutions in applications requiring improved utility interaction and weight/volume reduction, but it has the disadvantage of a 0.866 Voltage Transfer Ratio (VTR) which means it cannot establish rated magnetic flux into standard AC motors. The performance is further affected when the voltage supply is unbalanced. This paper presents a new solution to increase the VTR and improve the system behaviour under unbalanced supply conditions by employing a new hybrid arrangement which is using an open winding induction motor fed by a Matrix Converter (MC) on one end and a Voltage Source Inverter (VSI) rated at only a small fraction of the supply voltage on the other end. Two control methods for this hybrid arrangement are proposed. Simulation results reveal the improved performance in terms of better VTR (equal to or potentially higher than one) under balanced and unbalanced supply voltage, higher power throughput relative to the overall power installed in the switches and improved efficiency.