With the increase in doubly fed induction generator-based wind energy conversion systems (DFIG-WECS) worldwide, improving the fault ride-through (FRT) capability of the entire system has been given much attention. Enhancement of the FRT capability of a DFIG-WECS is conventionally realized by employing a flexible AC transmission system device with a proper control system. This paper presents a non-conventional method for the improvement of the FRT of DFIG-WECS, using a high-temperature superconducting coil interfaced with the DC-link of the rotor and stator side converters through a DC-chopper. A fractional-order proportional-integral (FOPI) controller is utilized to regulate the DC-chopper duty cycle in order to properly manage the power flow between the DC-link and the coil. Two optimization techniques, Harmony Search and Grey Wolf Optimizer, are employed to determine the optimum size of the superconducting coil along with the optimum parameters of the FOPI controller. The effectiveness of the two proposed optimization techniques is highlighted through comparing their performance with the well-known particle swarm optimization technique.