In the field of electricity generation, hybrid microgrids (HMGs) become crucial. A HMG has been taken in this paper which consists of renewables like solar, wind, and battery storage system along with ac and dc load. An HMG system needs a battery storage system to reduce power fluctuations from unreliable renewable energy sources (RESs). To connect a battery to the dc bus, a dc-dc bi-directional converter was employed. The control technique of the dc-dc bi-directional converter is consisting of two control loops which are the voltage-controlled loop and the current-controlled loop. A hybrid fuzzy integrated three-degrees-of-freedom fractional-order proportional-integral-derivative (HFI 3-DOF FOPID) controller is proposed in this study to stabilise the voltage on the dc bus and maintain a constant power supply in an HMG. A modified salp swarm algorithm (MSSA) is used here to optimise the controller parameters of the proposed HFI 3-DOF FOPID controller. This paper considers a HMG transfer function model.. The time-domain analysis, stability, and robustness tests are included in this work to confer the efficacy of the proposed MSSA optimized HFI 3-DOF FOPID controller. MATLAB/Simulink has been used to study the performance of the system using the aforementioned controllers. The real-time (Opal RT) studies are also performed on the power management between renewable resources like PV, wind, and battery energy storage to prove the efficacy of the proposed MSSA optimized HFI 3-DOF FOPID controller.