In the five-phase induction machine (IM) it is possible to better use the electromagnetic circuit than in the threephase IM. This requires the use of an adequate converter system which will be supplied by an induction machine. The electric drive system described in this paper includes the five-phase induction machine supplied by the current source inverter (CSI). The proposed noveltynot presented previouslyare the control system structures for the five-phase IM which are supplied by CSI. The proposed control systems allow for independent control of IM state variables in the first and the second system plane to inject the 3 rd harmonic. However, the 3 rd harmonic must be suitably associated with the fundamental harmonic. In the proposed solution, the machine vector model is not transformed into the (dq)-coordinate system that is connected to the rotor flux vector but utilizes the stationary system (α-β). The nonlinear model linearization is based on demonstrated nonlinear variables transformation for i-orthogonal (α-β)(i) planes. Voltage control is applied in the control system structure. The control variables of the five-phase IM are the voltage in the DC-link and the angular speed of the output current vector. In the control strategy, the control variables are determined for both system planes. Therefore, the transformation of these control variables to the DClink of CSI is proposed. The proposed control structure allows for independent control of variables in the 1 st and the 2 nd system planes. It leads to the possibility to increase the value of electromagnetic torque up to 12% for the five-phase IM, which has not been used before in the case of the machine supplied by the CSI. All theoretical issues are confirmed by experimental tests in the 5.5 kW five-phase IM.