Can a DFIG operate in a synchronous speed?
The machine-side converter regulates the torque of the DFIG and thus the rotational speed with a double loop structure, where the outer speed loop generates the reference signal for the inner current loop. The current control is carried out in rotational framework with stator flux orientation. In addition, the machine-side converter also regulates the reactive power injection of the DFIG.

The  grid-side converter transfers the active power from the machine-side converter into the grid through an LCL filter, and maintains the DC-link voltage.

Thus the DGIF is always supposed be synchronous to the grid to ensure stable power transfer of a fixed current peak sine that never exceeds supply or demand and phase as controlled by setpoint, normally 0 deg for pf=1.