The main drawback of the Cascaded-H Bridge converter based on three-phase/single-phase current-source inverters is the large DC inductors needed to limit the variation of the DC current caused by the single-phase inverter oscillating power. If the oscillating power is some-how compensated, then the DC inductor can be designed just as a function of the semiconductors’ switching frequency, reducing its value. This work explores the use of three-phase/single-phase cells magnetically coupled through their DC links to compensate for the oscillating power among them and, therefore, reduce the DC inductor value. At the same time, front ends controlled by a non-linear control strategy equalize the DC currents among coupled cells to avoid saturating the magnetic core. The effectiveness of the proposal is demonstrated using mathematical analysis and corroborated by computational simulation for a 110 kVA load per phase and experimental tests in a 2 kVA laboratory prototype. The outcomes show that for the tested cases, coupling the DC links by a 1:1 ratio transformer allows reducing the DC inductor value below 20% of the original DC inductor required. The above leads to reducing by 50% the amount of magnetic energy required in the DC link compared to the original topology without oscillating power compensation, keeping the quality of the cell input currents and the load voltage. © 2022 by the authors. Licensee MDPI, Basel, Switzerland.