# Mathematics-Driven Analysis of Offshore Green Hydrogen Stations
## 2 Materials and Methods  
### Mathematics-Driven Analysis and Simulation Method  
The following sections present the mathematics-based technical model proposed in this paper. A set of input parameters and mathematical expressions were used to describe the physical relationships among the different components of the system. To perform the simulation and subsequent analysis of the results, these expressions were implemented using Python 3.12 as programming language, which is widely adopted in both scientific and industrial communities. Python, as an open-source solution from the Python Software Foundation, provides a broad range of scientific and visualization libraries, making it ideal for performing complex calculations and processing the data required at each phase of the simulation. In addition, this Python-based approach not only enhances the model's accuracy and flexibility but also facilitates its adaptation to different scenarios and conditions, which is an essential feature for optimizing the design and operation of current and future offshore renewable energy systems. Due to Python's handling of trigonometric functions, all angles used as input parameters for these mathematical expressions are expressed in radians (rad). However, for ease of interpretation and visualization, all other angles are presented in degrees (\({}^{\circ}\)). All external and internal technical model variables introduced throughout this paper are listed and summarized in the Abbreviations Section. Figure 1: Block diagram of a green hydrogen production station powered by solar energy. The development of the mathematics-based technical model and its subsequent validation through the execution of a set of numerical simulations requires a logical and structured approach, consisting of distinct phases that simplify the original problem while preserving the sequential and/or parallel relationships among their components. Figure 2 presents the high-level flow diagram used for the development and simulation of the proposed technical model for a green hydrogen production station powered by solar energy. The main sets of parameters used for model configuration are shown in green (also see Section 2.2). In red, the main outputs of the proposed technical model are represented. As part of the methodology presented in this paper, five phases were defined and are represented in yellow, purple, blue, and orange. As part of each phase, the corresponding block diagram provides a high-level definition and illustrates the physical relationships among the various variables involved. As shown, in PHASE I, the simulation time frame was defined by setting the total duration and time intervals for the calculations. In PHASE II, the solar-based electricity generation process is modeled. This involves first determining the position of the sun relative to the photovoltaic panels and subsequently calculating the solar radiation received on their surface. To model the sun's position relative to the photovoltaic panels, it is necessary to determine the following variables: Earth's declination (\(\alpha_{declination}\)), corrected solar angle (\(\alpha_{corrected\_solar}\)), solar elevation angle (\(\alpha_{solar\_elevation}\)), solar azimuth angle (\(\alpha_{solar\_ azimuth}\)), photovoltaic panel inclination angle (\(\beta_{inclination}\)), and photovoltaic panel inclination angle (\(\beta_{azimuth}\)) (Figure 3). In PHASEs III and IV, the operation of the electrolyzer and compressor were modeled based on their specific operational parameters and efficiencies. Finally, in PHASE V, all component models of the green hydrogen station powered by solar energy were integrated. Figure 2: High-level flow diagram used for the development and simulation of the proposed mathematics-based technical model for a green hydrogen production station powered by solar energy. This phase involves synchronizing the various subsystems to ensure that the energy generated by the photovoltaic panels was appropriately balanced to power both the electrolyzer and the compressor.