Doubly-fed induction generators (DFIGs) are crucial in wind turbines due to their advanced control features and efficient power conversion, but they're vulnerable to grid issues like voltage dips and short circuits. This study explores enhancing DFIGs' low voltage ride-through (LVRT) capabilities using a superconducting fault current limiter (SFCL) system. The SFCL's superconducting coil plays a key role by limiting fault current to stabilize power output, reducing excessive currents during faults, and mitigating voltage fluctuations, protecting the rotor-side converter and gearbox. The research focuses on optimizing the coil's inductance to improve SFCL performance, showing through MATLAB/Simulink simulations that adjusting inductance can lessen rotor current oscillations during short circuits. The results indicate significant enhancements in LVRT capabilities, reducing electrical and mechanical stress on generators and converters, preventing severe voltage drops, and maintaining torque levels. Incorporating an SFCL into DFIG systems greatly increases stability, reliability, and fault tolerance, supporting more wind energy integration.