The increase in penetration of wind farms operating with doubly fed induction generators (DFIG) results in stability issues such as voltage dips and high short circuit currents in the case of faults. To overcome these issues, and to achieve reliable and sustainable power from an uncertain wind source, fault current limiters (FCL) are incorporated. This work focuses on limiting the short circuit current level and fulfilling the reactive power compensation of a DFIG wind farm using a capacitive bridge fault current limiter (CBFCL). To deliver sustainable wind power to the grid, a fuzzy-based CBFCL is designed for generating optimal reactive power to suppress the instantaneous voltage drop during the fault and in the recovery state. The performance of the proposed fuzzy-based CBFCL is presented under a fault condition to account for real-time conditions. The results show that the proposed fuzzy-based CBFCL offers a more effective solution for overcoming the low voltage ride through (LVRT) problem than a traditional controller.