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This study presents the auxiliary damping control with the reactive power loop on the rotor-side converter of doubly-fed induction generator (DFIG)-based wind farms to depress the sub-synchronous resonance oscillations in nearby turbogenerators. These generators are connected to a series capacitive compensation transmission system. First, the damping effect of the reactive power control of the DFIG-based wind farms was theoretically analyzed, and a transfer function between turbogenerator speed and the output reactive power of the wind farms was introduced to derive the analytical expression of the damping coefficient. The phase range to obtain positive damping was determined. Second, the PID phase compensation parameters of the auxiliary damping controller were optimized by a genetic algorithm to obtain the optimum damping in the entire subsynchronous frequency band. Finally, the validity and effectiveness of the proposed auxiliary damping control were demonstrated on a modified version of the IEEE first benchmark model by time domain simulation analysis with the use of DigSILENT/PowerFactory. Theoretical analysis and simulation results show that this derived damping factor expression and the condition of the positive damping can effectively analyze their impact on the system sub-synchronous oscillations, the proposed wind farms reactive power additional damping control strategy can provide the optimal damping effect over the whole sub-synchronous frequency band, and the control effect is better than the active power additional damping control strategy based on the power system stabilizator. [ABSTRACT FROM AUTHOR]