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This work proposes a space vector modulation (SVM) scheme applied to an interphase transformers-based five-level current source inverter (IT-MCSI) in order to fulfill the following requirements: the reduction of the number of switching transitions during a switching period, the doubling of the ripple frequency with respect to the switching frequency at the input and output terminals, the balance of the interphase transformers magnetizing voltages leading to zero average flux in the cores at each switching period, and the use of the full linear modulation range. The proposed modulation is compared to a conventional phase-shifted modulation. The proposal is experimentally tested in a 2.2 kW lab-prototype employing state-of-the-art power components. The results verify the theoretical analysis and show that the SVM is able to improve the electrical performance of an IT-MCSI.