This paper introduces a novel power management strategy (PMS) that aims to facilitate power-sharing between battery and supercapacitor (SC) energy storage systems. The proposed technique is employed to resolve the discrepancy between power demand and generation, as well as to regulate the voltage of the dc bus. The implementation of a hybrid adaptive fuzzy integrated fractional order PD-PI controller (HAFI FPD-PI controller), in the hybrid energy storage system (HESS) results in enhanced regulation of the dc bus, while simultaneously minimising the levels of stress imposed on the battery. Moreover, the proposed PMS improves the lifespan of batteries by redirecting unwaged battery currents to SCs for rapid compensations. In addition, the stability study of dc microgrid is performed. The efficacy of the proposed PMS is evaluated by the utilisation of varying solar irradiation, wind speed, and load. The effectiveness of the proposed PMS was examined by simulations, which involved a comparison of peak deviations in the dc bus voltage with conventional PMS techniques used in literature. The real-time verification of the results has been conducted using OPAL-RT real-time simulator.