Virtual synchronous generator control is considered as an effective solution to optimize the frequency response characteristics of doubly fed induction generator. However, due to the insufficient control bandwidth of the original virtual synchronous generator, it has little control effect over the oscillating components of the power caused by the unbalanced grid voltage. Therefore, long-term unbalanced voltage will cause a series of problems, such as distortion of stator and rotor currents, as well as oscillations of power and electromagnetic torque, which seriously affect the power quality and the operating performance of the doubly fed induction generator. To solve these problems, the concept of extended power is introduced, and the second-order generalized integrator-based resonant controller is used to control the extended power and traditional power. Control targets of the extended power method are discussed and extended, so that the doubly fed induction generator system using extended power resonant control-based virtual synchronous generator control can realize three different control targets under the unbalanced grid condition. The three control targets are: balanced and sinusoidal stator current, sinusoidal stator current and constant active power, and sinusoidal stator current and constant reactive power and electromagnetic torque. The three control targets can also be flexibly switched according to the real-time requirements of the grid with unbalanced voltage. The simulation results verify the effectiveness of the control method.