Currently, transitioning from fossil fuels to renewable sources of energy is needed, considering the impact of climate change on the globe. From this point of view, there is a need for development in several stages such as storage, transmission, and conversion of power. In this paper, we demonstrate a simulation of a hybrid energy storage system consisting of a battery and fuel cell in parallel operation. The novelty in the proposed system is the inclusion of an electrolyser along with a switching algorithm. The electrolyser consumes electricity to intrinsically produce hydrogen and store it in a tank. This implies that the system consumes electricity as input energy as opposed to hydrogen being the input fuel. The hydrogen produced by the electrolyser and stored in the tank is later utilised by the fuel cell to produce electricity to power the load when needed. Energy is, therefore, stored in the form of hydrogen. A battery of lower capacity is coupled with the fuel cell to handle transient loads. A parallel control algorithm is developed to switch on/off the charging and discharging cycle of the fuel cell and battery depending upon the connected load. Electrically equivalent circuits of a polymer electrolyte membrane electrolyser, polymer electrolyte membrane fuel cell, necessary hydrogen, oxygen, water tanks, and switching controller for the parallel operation were modelled with their respective mathematical equations in MATLAB^® Simulink^®. In this paper, we mainly focus on the modelling and simulation of the proposed system. The results showcase the simulated system’s mentioned advantages and compare its ability to handle loads to a battery-only system.