# Mathematics-Driven Analysis of Offshore Green Hydrogen Stations
## 1 Introduction
Floating solar energy systems are estimated to exhibit higher efficiency than their land-based counterparts, reaching gains of up to 11-13% or more. This improvement is primarily attributed to the cooling effect provided by the water surface and the natural cleaning of the panels [20; 21]. It is also estimated that the natural cooling of solar panels by approximately 2.7-3.5 \({}^{\circ}\)C results in a daily efficiency increase of around 2.3-2.6% [19]. In terms of disadvantages, the main challenges are associated with the marine environment: saltwater-induced corrosion, difficulties in remote maintenance, high anchoring costs, and the need to ensure structural stability under extreme wind and wave conditions [19]. In terms of cost, offshore systems still present a higher Levelized Cost of Electricity (LCOE) compared to land-based systems--approximately 2.5% higher. However, this cost is ex pected to decrease as production scales up and technologies such as thin-film panels and flexible structures are increasingly adopted [19]. In parallel, hydrogen has emerged as a promising energy carrier in the transition toward a more sustainable and carbon-free future [22]. Unlike primary energy sources, hydrogen functions as an energy carrier, enabling the storage and transportation of energy produced by other sources. Its versatility lies in the fact that it can be obtained from various primary sources, and, when produced using renewable energy, it becomes green hydrogen--a clean and sustainable alternative [22; 23; 24]. Green hydrogen is primarily produced through the electrolysis process, driven by different electrolyzer technologies. In alkaline electrolyzers (ALK), an aqueous potassium hydroxide solution is used as the electrolyte, while, in proton exchange membrane (PEM) electrolyzers, the electrolyte is a thin, ion-conductive solid membrane that replaces the aqueous solution. Both technologies require electricity generated from renewable sources, such as solar or wind energy [25], to split the water molecule (H\({}_{2}\)O) into oxygen (O\({}_{2}\)) and hydrogen (H\({}_{2}\)) [26]. This production method ensures that no pollutant gases are emitted either during the production process (energy generation and storage) or during combustion (extraction and use of stored energy). Moreover, green hydrogen offers significant advantages, including its storage capacity--high energy density per kilogram--and its versatility to be converted into electricity or synthetic fuels, making it an attractive option for various industrial and mobility sectors [27]. The importance of green hydrogen in combating climate change lies in its potential to replace fossil fuels in hard to decarbonize sectors [24]. However, the development of green hydrogen faces challenges, primarily related to production costs and the need for expanded infrastructure. As progress is made in decarbonization and the cost of renewable energy generation decreases, these obstacles are expected to be overcome, allowing green hydrogen to play a crucial role in the global energy transition [26; 28]. In this context, the present article aims to promote the expansion and use of floating solar energy through the development of a mathematics-based technical model that enables the analysis of its integration with green hydrogen production stations [29], the assessment of energy efficiency gains resulting from increased solar irradiance in marine locations, as well as the impact of component efficiencies and key operating parameters in the green hydrogen production station (photovoltaic panels, electrolyzer, and compressor), on the total required surface area of photovoltaic panels. This reduction will not only simplify the support and anchoring structures of floating solar power stations but also reduce overall costs and improve structural stability under extreme wind and wave conditions.