Renewable energy systems play an important role in alleviating environmental pollution, and their characteristics, including low emissions and recyclability, are highly favourable. At present renewable energy can be costly and renewable energy systems have room for optimization, particularly systems which cater to remote and island areas. This paper develops a P-graph-based multi-period energy model, using hydrogen for energy storage to satisfy the fluctuating electrical and thermal energy demand of an island. Hydrogen can be generated from renewable energy sources during off-peak periods and can be used to serve as an energy carrier. An economic and carbon footprint analysis of the system is performed, which compares a pure renewable energy system, with hydrogen storage, and with battery storage. Within the same scenario, the results show that the renewable energy systems with hydrogen storage and battery storage are 21.5 % and 5.3 % cheaper than the renewable energy system without energy storage, with CO2eq emissions of 1,717 t/y and 1,680 t/y. These findings show that the inclusion of energy storage systems has great potential to reduce costs within renewable energy systems. Changes in the supply of biomass were investigated (which had the greatest impact in the study area), as well as changes in the cost of hydrogen storage. In addition to the optimal solution, near-optimal solutions were also suggested to provide well-rounded guidance for implementation.