To secure the voltage-dependent loads from voltage disturbances, a dynamic voltage restorer (DVR) has been examined for the smooth functioning of a three-phase distribution system. The investigation of DVR performance is accounted for various voltage disturbances. Firstly, the least-mean-square (LMS) method is designed with variable step-size capabilities then it is modified which results in a faster convergence rate of the weight of the source voltage active component in distorted grid conditions. Further, the fractional order approach is introduced in the LMS control algorithm to achieve an extended degree of control freedom. The resultant fractional-order modified adaptive variable step-size least-mean-square (FMAVLMS) algorithm uses two fractional-order proportional-integral (FOPI) controllers that are associated to operate DC-bus voltage control & load voltage control using reactive power individually. Further, the main attribute of this paper is the application of a recent black-widow optimization algorithm (BWOA) to determine optimal gains of the FOPI controllers in the proposed FMAVLMS algorithm. The control algorithm is developed in the Simulink environment and the performance is found satisfactory in various grid voltage disturbances. The proposed algorithm is validated for the DVR system experimentally through OPAL-RT real-time simulator with X11SSM-E-F-O super micro server motherboard that examines the real-time performance.