In the five-phase induction machine (IM), it is possible to better use the electromagnetic circuit than in the three-phase 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 article, includes the five-phase induction machine supplied by the current source inverter (CSI). The proposed novelty—not presented previously—is the control system structures for the five-phase IM, which is 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 third harmonic. However, the third harmonic must be suitably associated with the fundamental harmonic. In the proposed solution, the machine vector model is not transformed into the ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d–q</i> ) coordinate system that is connected to the rotor flux vector but utilizes the stationary system ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α–β</i> ). The nonlinear model linearization is based on the demonstrated nonlinear variables transformation for i-orthogonal ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α–β</i> ) (i) planes. Voltage control is applied to 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 dc link of CSI is proposed. The proposed control structure allows for independent control of variables in the first and second 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.