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Voltage harmonics in the grid can introduce stator current harmonics in a doubly fed induction generator (DFIG) wind turbine system, which may potentially impact the generated power quality. Therefore, wind turbine current controllers need to be designed to eliminate the impact of grid voltage harmonics, especially low-order harmonics. This paper proposes a stator current harmonic suppression method using a sixth-order resonant controller to eliminate negative sequence fifth- and positive sequence seventh-order current harmonics. A stator current harmonic control loop is added to the conventional rotor current control loop for harmonic suppression. The overall control scheme is implemented in dq frame. Based on a mathematical model of the DFIG control system, the effects on system stability using the resonant controller, an analysis of the steady-state error, and the dynamic performance, are discussed in this paper. Taking these effects into account, the parameters of the resonant controller can be designed and effectively damp the influence from the grid voltage harmonics. As a result, the impacts of the negative sequence fifth- and positive sequence seventh-order voltage harmonics on the stator current as well as the electromagnetic torque are effectively removed. Simulations and experiments are presented to validate the theoretical analysis.