A drive train comprising an electric machine including a rotor and a stator, the stator being connected to an alternating grid and having a stator frequency, and a bidirectional system for converting an alternating current into another alternating current. The conversion system is connected between the grid and the rotor, and comprises an AC-DC converter connected to the grid, an inverter connected between the AC-DC converter and the rotor, and a device for controlling switches of the inverter according to a control law. The control law is such that the active power exchanged by the inverter with the rotor is essentially always lower than 0.3 times the nominal power of the direct current specifically circulating between the AC-DC converter and the inverter, for the frequencies of a target interval of between 0.6 times the stator frequency and 1.4 times the stator frequency.