When doubly-fed wind turbine units operate under unbalanced power grid, the system has positive and negative sequence paths. With the weakening of power grid strength, the coupling between the turbine and the grid intensifies, and disturbances in unbalanced stator voltage will affect the normal operation of the system. In order to study the unbalanced operation and stability mechanism of doubly-fed wind turbine units under weak grid, firstly, a small-signal state-space model of doubly-fed wind turbine unit is constructed, and the stability and unbalance degree of positive and negative sequence rotor current control are analyzed based on the system model. Then, the optimal control strategy based on adaptive virtual impedance is proposed to realize the cooperative compensation of the unbalanced stator voltage and current under the weak grid. The theoretical analysis proves that the proposed strategy effectively improves the stability of the doubly-fed wind turbine units under the unbalanced weak grid. Finally, through the hardware-in-the-loop experiment platform, the effectiveness of the proposed optimization strategy is verified.