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The electricity production from Renewable Energy (RE) in isolated locations requires long-term energy storage systems. To that end, Hybrid Energy Storage Systems (HESS), through a combination of hydrogen and batteries, can benefit from the different advantages of both technologies. This paper presents a hybrid Power-to-Power (PtP) Optimal Power Dispatch (OPD) model for isolated systems with no electric grid access. Currently, the electricity supply in such cases is usually based on a mix of RE as the primary energy source sustained by a diesel genset acting as a backup generator. In this context, the model delivers the hourly energy flows between renewable production sources, energy storage devices and the electrical load, which minimises costs and Green House Gases (GHG) emissions. For validation purposes, the model was tested through its application to a case study in an isolated area in the Canary Islands, Spain. The results show that the algorithm calculates the hourly OPD successfully for a given plant sizing, considering the defined operational states of the different assets. These operational constraints showed a decrease in the PtP round-trip efficiency of 5.4% and a reduction of the hydrogen production of 9.7%. Finally, the techno-economic analysis of the results proves that the combination of hydrogen and batteries with RE production is a feasible alternative to phasing out fossil fuels for the selected case study – reducing the diesel generator usage down to 1.2% of the yearly energy supply. • Novel multi-state optimal power dispatch model for power-to-power energy systems. • Multi-year techno-economic evaluation of an off-grid case study. • Phasing out fossil fuels with renewable energy-based hybrid energy storage systems. • Hydrogen technology contributes to a lower levelized cost of energy. • High initial investment cost was a significant entry barrier to deploying hydrogen. [ABSTRACT FROM AUTHOR]