Does the grid side converter in a DFIG absorb/provide reactive power or is it reactive neutral? Also, what can we say about reactive power exchange in the rotor side converter?
Both Grid Side Converter (GSC) and Rotor Side Converter (RSC) can work in all three modes, consume/generate/stay neutral, depending on the control mode you apply to them. You can actually assume that they are nothing but STATCOM. However, every one of them is controlled for different purposes.
Note that total reactive power supplied/consumed by DFIG = Reactive power supplied by GSC + reactive power supplied by DFIG stator.
GSC can be controlled to supply/consume a part of the required reactive power to control the terminal voltage of DFIG. While the other part of reactive power required to control DFIG terminal voltage is supplied by the stator which is actually controlled by RSC.
Practically, RSC is controlled based on the quantities measured on the stator side. So it may supply/consume reactive power to the rotor, however, what is actually the target is the quantities supplied by the stator as long as the rotor current/voltage are within the allowed limits.