A control method implemented in a power converter, such as a variable speed drive, is disclosed. This control method is designed to make the power converter operate when the latter is connected to the network in single-phase mode. The power converter includes a controlled current source connected in series to its DC power supply bus. This controlled current source includes an electronic converter provided with two controlled switching arms. The switching arms are controlled by alternating a modulation phase with a saturation phase, the saturation phase being applied for a determined duration β in order to make the power converter operate in discontinuous mode.