# Mathematics-Driven Analysis of Offshore Green Hydrogen Stations
## 1 Introduction  
Renewable energies are those obtained from virtually inexhaustible natural sources, either due to the immense amount of energy they contain or because they can regenerate naturally [1, 2]. Among the main sources of renewable energy are solar energy, wind energy, hydroelectric energy, geothermal energy, biomass, tidal, and wave energy [3, 4]. Interest and investment in renewable energies have experienced exponential growth in recent decades [5], driven by increasing concerns about climate change and the need to reduce greenhouse gas emissions [6, 7]. According to the International Renewable Energy Agency (IRENA) [8], global renewable energy generation capacity reached 3.86 TW by theend of 2023, representing a cumulative growth of 127.55% since 2014, when it stood at 1.7 TW. Over this period, the average annual growth rate was 9.58%. Notably, between 2022 and 2023 alone, the annual growth rate reached 13.95%. These energy sources offer a clean and sustainable alternative to traditional fossil fuels such as oil, coal, and natural gas, which, in addition to being finite, contribute negatively to global warming when burned [9; 10]. Moreover, renewable energies provide countries that adopt them with greater energy security by strategically and systematically reducing their dependence on imported and volatile resources [11]. The installation of offshore renewable energy systems presents enormous potential for a sustainable energy future [12; 13]. Offshore renewable technologies represent a promising frontier in the development of clean energy, harnessing the vast energy resources available in the world's oceans and seas [14; 15]. These technologies not only offer significant potential for clean energy generation but also provide unique advantages compared to their onshore counterparts [16; 17]. The potential of marine energy is estimated to range between 45.000 TWh and 130.000 TWh of electricity per year. However, as of now, only 508 MW of the total global capacity is being supplied by marine energy generators [18]. As of today, photovoltaic energy (1.42 TW) and wind energy (1.01 TW) are the two renewable sources contributing most significantly to global renewable energy capacity. Over the past decade, their cumulative growth has been approximately 706% and 191%, respectively. At the end of 2023, onshore wind energy capacity reached 944.2 GW, while offshore wind capacity amounted to 73.18 GW. Nonetheless, despite the substantial difference in their current capacities, onshore wind energy has exhibited a cumulative growth rate of 176.93%, while offshore wind has experienced a remarkable increase of 760.80% [8]. This significant trend underscores the growing influence that ocean-based solutions are expected to have on the near-term future of renewable energy. Floating solar energy is emerging as a strategic and innovative solution to address the global energy crisis and the increasing scarcity of land available for renewable energy deployment. Its development is particularly crucial for countries facing territorial constraints, high energy demand, or densely populated coastal areas [19; 20; 21]. Although most floating energy systems currently operate in freshwater environments such as lakes and reservoirs, the technical and geographical potential of the marine environment is driving the development of offshore projects, including Swimsol (Maldives), Ocean Sun (Norway/China), and SolarDuck (Europe). These projects also serve as platforms for exploring various structural configurations, such as rigid and flexible designs [19]. Among the most notable advantages of floating solar energy are the preservation of arable land, the reduction in water evaporation, and the improvement of water quality by limiting algal growth. Additionally, co-location with other types of infrastructure--such as onshore or offshore wind farms--can optimize space usage and enable the sharing of electrical equipment, thereby enhancing the overall stability and efficiency of the energy system [19].