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Hydrogen has received increased attention in the last decades as a green energy carrier and a promising future fuel. The integration of hydrogen, as well as the development of cogeneration plants, makes the energy sector more eco-friendly, and sustainable. The aim of this paper is the investigation of a solar-fed cogeneration system that can produce power and compressed green hydrogen. The examined unit contains a parabolic trough collector solar field, a thermal energy storage tank, an organic Rankine cycle, and a proton exchange membrane water electrolyzer. The installation also includes a hydrogen storage tank and a hydrogen compressor. The unit is analyzed parametrically in terms of thermodynamic performance and economic viability in steady-state conditions with a developed and accurate model. Taking into account the final results, the overall energy efficiency is calculated at 14.03%, the exergy efficiency at 14.94%, and the hydrogen production rate at 0.205 kg/h. Finally, the payback period and the net present value are determined at 9 years and 122 k€, respectively.