In this paper, designed and controlled a hybrid microgrid with proton exchange membrane fuel cell (PEMFC), lithium-ion battery, and supercapacitor to achieve a reliable and efficient power source under dynamic load changes. To enable this, a cascade proportional and integral (PI) control strategy is developed for managing the power allocation amongst different storage sources while simultaneously maintaining the state of charge (SoC) of  battery and stabilizing DC bus voltage. With this approach, fuel cell is primarily responsible for supplying the average power demand, while the battery and supercapacitor handle the transient and peak power requirements. A thorough system modelling is carried out using MATLAB/Simulink and simulations are performed to verify the proposed strategy under several load conditions with the real component parameters and various load profiles. The results show that the PI based controller properly allocates the power flow among the sources, which helps to maintain the DC bus voltage stable during sudden changes in load, and in faulty cases. Several performance metrics including voltage regulation, power allocation efficiency, and transient response of the system are evaluated. The comparison with the optimal power management algorithms shows that this simple PI control strategy has lower computation cost than the optimization methods.