The electric energy storage system (EESS) is considered as an efficient and promising tool to alleviate the power imbalance of grid-connected microgrid with distributed generation (DG). This work develops a perturbation observer-based fractional-order control (POFOC) strategy for superconducting magnetic energy storage (SMES) system. Initially, a high-gain state and perturbation observer (HGSPO) is designed for reliable estimation of the combined impact of the nonlinearities, parameter uncertainties, unmodeled dynamics, and external disturbances of SMES. Then the storage function of an SMES system is designed, which takes favorable terms into serious consideration to sufficiently utilize the physical properties of the SMES system. Moreover, a fractional-order control framework is applied for complete compensation for the estimated perturbation and adopted as the attached input to boost its dynamical responses. Furthermore, a newly proposed jellyfish search algorithm (JSA) is utilized to realize optimization and tuning of control gains of the developed strategy, upon which high-quality global optimum can be obtained to ensure prominent controlling performance. Case studies, e.g., active power and reactive power supply and system restoration capability under power grid fault effectively validate the effectiveness and reliability of the POFOC strategy compared with traditional PID control and interconnection and damping assignment passivity-based controller (IDA-PBC). In particular, the overshoot of PID is 115.264% of the rated value, while POFOC has no overshoot.