A Static VAR Compensator (SVC) plays a crucial role within a wind farm power system by ensuring stable and efficient grid interface and power generation. This paper delves into the intricate design Induction Generator (IG) system of wind turbines, incorporating an SVC guided by fuzzy logic control. This paper's primary objective is to examine the effect of using fuzzy logic controller on the overall stability of the system, providing a comprehensive analysis of the system's efficiency with an SVC connected to the system. The effects of fault have been tested to determine the most efficient and reliable type of controller as well as to prove the system's stability. This research study explores the distinctions and advantages between using Proportional Integral (PI) controller-based SVCs and fuzzy logic controller-based SVCs to an IG. Through this investigation, this paper aims to uncover the best approach for enhancing wind farm performance, ultimately contributing to more reliable and sustainable energy generation. Simulation results show that the fuzzy logic controlled SVC slightly outperforms in voltage stability, reactive power stabilization, and voltage overshoot compared to PI controllers.