To address the stability issues caused by Doubly Fed Induction Generator (DFIG) during grid connection or operation, this paper proposes a coordinated reactive power compensation method utilizing Static Var Generator (SVG) in conjunction with DFIGs. Furthermore, the traditional PI control for converters is replaced with Linear Active Disturbance Rejection Control (LADRC), and supercapacitors are installed to optimize the DC-side control of DFIG converters. Finally, based on the actual conditions of wind farms, a grid-connected DFIG model integrated with supercapacitors and utilizing LADRC is established in MATLAB. A simulation analysis is conducted on the AC-DC fluctuations and reactive power transmission during grid connection. The experimental results verify that this control strategy can enhance the stable operation of DFIGs, resolve the issue of AC-DC side power imbalance in converters during power fluctuations, and the coordinated control strategy with SVG can improve the system's low-voltage ride-through capability, thereby enhancing the overall stability of the wind power generation system.