This paper describes the development of a semi-empirical numerical model for a solar hydrogen system consisting of a Proton Exchange Membrane Electrolyser (PEM) powered by photovoltaic panels to produce hydrogen as fuel for cooking applications, focussing on Jamaica as a suitable case-study. The model was developed in TRNSYS and includes a novel numerical component based on FORTRAN to model the operation of the PEM electrolyser. The numerical component was developed based on operational data from a purpose constructed small-scale experimental rig. The numerical model was calibrated using data from the experimental rig powered by operational data from a photovoltaic panel system in the UK and predicted photovoltaic panel power data from Jamaica. For the test conditions, experiments indicated an electrolysis maximum efficiency of 63.6%. The calibrated model was used to develop a case study analysis for a small community in Jamaica with a daily cooking demand of 39.6 kWh or 1.7 kg of H2 gas. Simulations indicate that the H2 production plan is sufficient for the cooking needs of the case-study.