This paper presents a mathematical model of a doubly fed induction generator (DFIG) in the positive synchronous reference frame under distorted grid voltage conditions. The oscillations of the DFIG's electromagnetic torque and the instantaneous stator active and reactive powers are fully described when the grid voltage is harmonically distorted. Four alternative control targets are proposed to improve the system responses during grid harmonic distortions. A new rotor current control scheme implemented in the positive synchronous reference frame is developed. The control scheme consists of a proportional-integral (PI) regulator and a harmonic resonant (R) compensator tuned at six times the grid frequency. Consequently, the fundamental and the fifth-and seventh-order components of rotor currents are directly regulated by the PI-R controller without sequential-component decompositions. The feasibility of the proposed control strategy is validated by simulation studies on a 2.0-MW wind-turbine-driven DFIG system. Compared with the conventional vector control scheme based on standard PI current controllers, the proposed control scheme leads to significant elimination of either DFIG power or torque oscillations under distorted grid voltage conditions.