Based on the detailed analysis on the control of rotor side convertor for the doubly-fed induction generator（DFIG） under harmonic grid voltage conditions， this paper presents a precise mathematical model of the DFIG in the stator-flux-oriented fundamental positive reference frame（dq）+ ， negative 5-order（dq）5-， and positive 7-order reference frames（dq）7+. The reasons of the oscillations in the instantaneous active power， reactive power and electromagnetic torque of the DFIG are analyzed and explained through redefining the powers and torque under this special operation condition. Four alternative control targets and the computation algorithm of their corresponding rotor current references for the fundamental and harmonic components are proposed. A novel current controller， consisting of a traditional PI regulator and a resonant（R） controller tuned at the 6 times of grid frequency and referred into the positive（dq）+reference frame， is designed. It can efficiently suppress the 5th and 7th order components of rotor current without the complex sequential-component decomposition and corresponding time delay involved. Simulation studies on a 2 MW commercial wind-turbine driven DFIG system proves that the suggested control scheme can efficiently smooth the instantaneous active and reactive power fluctuation and electromagnetic torque pulsation， which verifies the correctness of the proposed mathematical model of DFIG and the effectiveness of the suggested control strategy.