The increased penetration of wind energy conversion systems (WECS) into the grid creates many challenges for maintaining grid stability, reliability and efficiency. This paper proposes an approach that integrates the robustness and fast convergence capability of non-singular fast terminal sliding mode control (NFTSMC) with the fast current support of static synchronous compensators (STATCOM) to improve the dynamic stability of wind energy systems during network disturbances. The NFTSMC control approach is designed for the inner current control loop of a STATCOM with voltage source inverter topology. Its main objective is to support both the active and reactive currents and thereby effectively regulate the system's frequency and bus voltage. The proposed approach was implemented to a WECS-based test microgrid subject to sudden load variations and mismatched disturbances. The obtained results confirmed its effectiveness in properly mitigating dynamic instabilities stemming from grid disturbances and maintaining the voltage and frequency within their rated values. Further comparison between the performance of the proposed NFTSMC and that of a standard SMC approach showed better performance and reduced chattering compared to the standard SMC.