This study analyses the dynamic behaviour of the doubly fed induction generator exposed to unsymmetrical voltage sags, providing insights into wind turbine fault ride-through capability. The sags are assumed to be caused by faults. An analytical approach assuming that the rotor-side converter can keep constant the rotor current in the synchronous reference frame during the event is used. The voltage limit of the rotor-side converter is also considered in order to determine the situations where the rotor current can be controlled. The effects of sags on grid-connected equipments depend on the sag characteristics (duration and depth), but also on the fault clearing process. In this process, the fault is not cleared instantaneously, as in the case of abrupt sags (which is the usual approach in the literature), but in the successive natural fault-current zeros, leading to a voltage recovery in several steps known as discrete sags. The effects of both abrupt and discrete sags on the doubly fed induction generator behaviour are compared. This comparison reveals that the discrete clearing process smoothes the sag effects on the generator.