For stabilizing the power grid during voltage dips, a doubly fed induction machines (DFIM)-based flywheel energy storage system is applied in this paper. The reactive power support during voltage dips requires well-coordinated control schemes to handle transient challenges for a grid-connected DFIM. These challenges are the high induced rotor voltages due to DC and negative sequence flux linkages, saturation of the machine and transient torque. For this purpose, the machine control collectively controls the symmetrical components of the currents referred to the same reference frame by means of resonant controllers. In this context, a flux observer is required to robustly decrease the natural flux linkage by using the demagnetization current approach. Based on simulations and measurements, the effectiveness of the presented control to ensure a dynamic reactive power contribution during a voltage dip is emphasized. Simultaneously with the reduction of the induced rotor voltage, reactive power injection is present almost instantly after the voltage dip started due to the high converter capability of the system.