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Several strategies have been proposed for operating doubly-fed induction generator (DFIG)-based wind turbine under unbalanced grid voltage conditions. This study focuses on those strategies in which the rotor-side power converter aims at eliminating the oscillations affecting the electromagnetic torque and the stator reactive power. Given the limited size of the DFIG's power converters, and hence their tolerable current and voltage boundaries, this study analyzes which DFIG power generation capability is under unbalanced grid voltage, and therefrom derives rotor current and stator power controllable ranges. Besides, the feasibility regions of the DFIG are also deduced for different types of imbalance. Furthermore, and based on the outcome of previous analysis, a modified rotor current limiter, as also its equivalent stator power limiter, is proposed. In contrast to the conventional ones, the limiters proposed here take into account that imbalances may arise in the grid voltage. As a consequence, system's overall performance is considerably enhanced under unbalanced grid voltage conditions. Finally, simulation results establish the validity of the treated issues.