With the increasing integration of wind turbines, series capacitor compensation is widely used to improve transmission efficiency but raises the risk of sub-synchronous oscillations (SSO), especially in doubly fed induction generator (DFIG) systems. The slip-dependent rotor resistance can introduce a negative resistance effect on the stator side, potentially destabilizing the system. This study investigates the mechanisms of sub-synchronous resonance (SSR) in DFIG-based systems using mathematical modelling and impedance analysis. To enhance stability, a novel sub-synchronous stator flux injection method is proposed. This approach effectively reduces the equivalent mutual inductance, mitigating the stator-side influence of rotor-induced negative resistance and significantly improving damping performance. Impedance scanning and simulation results validate the theoretical findings, demonstrating that the proposed method provides a robust means to suppress SSR in series-compensated DFIG systems.