DFIGs are almost classical induction machines that two typical operation modes: the subsynchronous mode (during this mode the rotor absorb power) and the supersynchronous mode (during this mode the rotor generate power). This is mainly due to the slip sign. the attached file is a copy extracted from course (in French) illustrating these two modes. I hope it will be helpful.
@Mohamed Benbouzid, your answer is useful, but i want to know why does it reabsorp the power in the subsynchronous mode for example and not the reverse, i've done a presenation about DFIG and someone asked me this question unfortunately i didn't find the answer.
The term ‘doubly fed’ refers that the generated power comes both from rotor and stator and during power demand; the rotor is fed from the utility grid.
Also it is able to equally import power from utility grid and export the reactive power to grid by means of this power electronic interface.