Due to its high energy storage efficiency, rapid response, and unlimited discharging cycle, superconducting magnetic energy storage (SMES) can solve the voltage disturbances of the grid-integrated wind power system. Doubly-fed induction generator (DFIG) wind turbines are critically affected by voltage dips because of the direct interconnection of the stator with the grid. In this paper, SMES is integrated with the DC link of DFIG back-to-back converters to overcome this issue. This study investigated balanced voltage dips with 30% and 50% depths and unbalanced voltage dips of types G and I. The critical state model is analysed using the finite element method to avoid the thermal breakdown of the temperature distribution of 1 cm of 2 G Yttrium barium copper oxide (YBCO) based high-temperature superconducting (HTS) tape. Simulation results indicate a significant reduction in DC link voltage oscillations with the inclusion of SMES.