Mathematics-Driven Analysis of Offshore Green Hydrogen Stations
Abstract
:1. Introduction
2. Materials and Methods
2.1. Mathematics-Driven Analysis and Simulation Method
2.2. Generalization and Particularization: Mathematics-Based Technical Model Configuration
2.3. Localization
2.4. PHASE I: Timeframe Definition
2.5. PHASE II: Modeling of Solar Electricity Generation
2.5.1. Modeling the Sun’s Position Relative to the Location of the Photovoltaic Panels Powering the Green Hydrogen Station
2.5.2. Modeling of Perpendicular Solar Radiation Received on the Surface of Photovoltaic Panels
- ka: Attenuation due to aerosols.
- kg: Attenuation due to gases (carbon dioxide and oxygen).
- kNO2: Attenuation due to nitrogen dioxide.
- kw: Attenuation due to water vapor.
- kO3: Attenuation due to ozone layer.
2.6. PHASE III: Modeling of an Electrolyzer: Type ALK and PEM
2.7. PHASE IV: Modeling of an Adiabatic Compressor
2.8. PHASE V: Integration of All Components into a Cohesive System
3. Results
4. Discussion
4.1. Solar Trajectory
4.2. Solar Irradiation and Green Hydrogen Station Capacity
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
Abbreviation | Variable description |
W | Watts |
J | Joules |
K | Kelvin degrees |
Dec | Decimal |
Deg | Degrees |
Min | Minutes |
S | Seconds |
M | Meters |
Lat | Latitude |
Long | Longitude |
Earth’s declination | |
Solar angle | |
Local time | |
Solar elevation | |
Solar azimuth | |
Day length | |
Total number of days in a year | |
n | Day number |
Synchronization constant with equinoxes | |
Time increment | |
Corrected solar angle | |
sunrise | Sunrise |
sunset | Sunset |
X | Displacement in X |
Y | Displacement in Y |
Z | Displacement in Z |
Solar Irradiation at the Upper Boundary of the Atmosphere | |
Reflected solar irradiation | |
Atmospheric attenuation constant | |
Csolar | Solar constant |
Air mass | |
Ka | Attenuation Constant Due to Aerosols |
Kg | Attenuation Constant Due to Gases: Carbon Dioxide and Oxygen. |
Kno2 | Attenuation Constant Due to Nitrogen Dioxide |
Kw | Attenuation Constant Due to Water Vapor |
Ko3 | Attenuation Constant Due to Ozone |
Incident angle | |
Reflection angle | |
Air reflection coefficient | |
Water reflection coefficient | |
Rs | Fresnel S coefficient |
rp | Fresnel P coefficient |
Fresnel reflection coefficient | |
Marine loss coefficient | |
Diffuse solar irradiation | |
Total solar irradiation | |
Trigonometric Correction Coefficient for Direct Irradiation | |
Trigonometric Correction Coefficient for Reflected Irradiation | |
Photovoltaic panel inclination angle | |
Photovoltaic panel azimuth angle | |
Normal and Direct Solar Irradiation Received on the Panels | |
Normal and Reflected Solar Irradiation Received on the Panels | |
Total Normal Irradiation Received on the Panels | |
Electrical power generated by the panels | |
Conversion Efficiency Coefficient of the Panels | |
Panel surface area | |
HV | Hydrogen heating value constant |
HHV | Hydrogen higher heating value constant |
LHV | Hydrogen lower heating value constant |
Moles per Second | |
Electrolyzer efficiency constant | |
Electrical Power Consumed by ALK/PEM Electrolyzer | |
Electrical Power Consumed by Compressor | |
year | Year |
Efficiency Ratio Between Electrolyzers | |
Output Pressure of ALK Electrolyzer | |
Output Pressure of PEM Electrolyzer | |
R | Ideal gas constant |
Inlet Temperature | |
Outlet Temperature | |
Compressor efficiency constant | |
Y | Adiabatic constant of the compressor |
Inlet pressure | |
Outlet pressure | |
Inlet Volume | |
Outlet Volume | |
P | Pressure |
V | Volume |
C | Adiabatic Relation Constant |
Total Power | |
Hydrogen Molecular Mass | |
Water Molecular Mass | |
Water Density |
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Parameter | Definition |
---|---|
Localization: | Localization of solar panels and green hydrogen station. |
Time definition: | Total number of days in a year. Specific day of the year. Day under study. Local time, referenced to 12 p.m. |
Atmosphere and marine conditions: | Atmospheric state/quality. Coefficient of losses associated with ocean surface irregularities. Ambient temperature. |
Photovoltaic panels: | Photovoltaic panel inclination and azimuth. Energy conversion efficiency. |
Electrolyzer: | ALK type. PEM type. Hydrogen calorific power constant. ALK electrolyzer efficiency. PEM electrolyzer efficiency. |
Compressor: | Input pressure. Output pressure. Compression efficiency. |
Parameter | Value |
---|---|
GPS position of the installation: | Santoña, Spain |
Year under study (year): | 2025 |
): | 365 |
Day of the year under study (N): | All |
): | All |
Atmospheric state/quality: | Normal |
): | 0 |
Panel inclination and azimuth relative to the sun’s position () and (): | Perfect alignment with the estimated sun position |
): | 0.2 |
Parameter | Value |
---|---|
): | 1 |
Electrolyzer type (i): | ALK, PEM |
Selected heating value constant (HV): | LHV |
): | PEM = 0.7 (Equation (32)) |
): | 0.7 |
): | 12.5 °C |
): | According to electrolyzer type and year (Equations (33) and (34)) |
): | 200 bars |
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García-Ruiz, Á.; Fernández-Arias, P.; Vergara, D. Mathematics-Driven Analysis of Offshore Green Hydrogen Stations. Algorithms 2025, 18, 237. https://doi.org/10.3390/a18040237
García-Ruiz Á, Fernández-Arias P, Vergara D. Mathematics-Driven Analysis of Offshore Green Hydrogen Stations. Algorithms. 2025; 18(4):237. https://doi.org/10.3390/a18040237
Chicago/Turabian StyleGarcía-Ruiz, Álvaro, Pablo Fernández-Arias, and Diego Vergara. 2025. "Mathematics-Driven Analysis of Offshore Green Hydrogen Stations" Algorithms 18, no. 4: 237. https://doi.org/10.3390/a18040237
APA StyleGarcía-Ruiz, Á., Fernández-Arias, P., & Vergara, D. (2025). Mathematics-Driven Analysis of Offshore Green Hydrogen Stations. Algorithms, 18(4), 237. https://doi.org/10.3390/a18040237