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This paper develops a dynamic model and control scheme for DFIG systems to improve the performance and stability under unbalanced grid conditions. A dynamic DFIG model containing the positive and negative sequence components is presented using stator voltage orientation. The proposed model accurately illustrates the active power, reactive power and torque oscillations, and provides a basis for DFIG control system design during unbalanced network supply. Various control targets such as eliminating the oscillations of the torque, active/reactive power are discussed and the required rotor negative sequence current for fulfilling different control targets are described. Performance of a DFIG-based wind turbine under unbalanced condition using the proposed control method is evaluated by simulation studies using Matlab/Simulink. The proposed control scheme significantly attenuates the DFIG torque or active power oscillations during network unbalance whereas significant torque/power oscillations exist with the conventional control schemes.