Method and system of control of the converter of an electricity generation facility of the type which comprises at least one electric generator, such as a wind generator, connected to an electricity network, in the presence of voltage sags in said network, the electric generator being a double-fed asynchronous generator formed by two windings, a winding in the stator, directly connected to the network, and a winding in the rotor which is fed on normal regime by said converter which imposes on it a predetermined voltage current called setpoint current. In the event of a voltage sag occurring, the converter imposes a new setpoint current which is the result of adding to the previous setpoint current a demagnetizing current which generates a flow in the rotor winding opposed to the free flow, consequently reducing the voltage in converter connectors.