# Model for Hydrogen Production Scheduling Optimisation

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## Abstract

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## 1. Introduction

_{2}) emissions and is an important step towards energy sustainability. One of the scenarios for future energy sustainability is the production of “green” hydrogen (H

_{2}). Hydrogen is an energy carrier, and its “cleanness” directly reflects the energy source and methods that were used in its production [3]. To classify hydrogen as “green” its production must not involve any (or minimal) greenhouse gas emissions. One way to achieve this is to solely base the production on RE sources [4].

_{2}and oxygen (O

_{2}). One of the sustainable methods of water splitting is the use of a proton exchange membrane (PEM) water electrolyser, which is powered by RE sources [5]. To fully power a PEM electrolyser from renewable energy sources, however, introduces a lot of challenges related to the availability of RE affected by day–night cycles, seasonality and other factors (e.g., climate change). This directly impacts the operational stability of the electrolyser. Therefore, a combination of RE sources and electrical energy from the grid [6] can be a valid solution to power the electrolyser and avoid intermittency periods. However, in this case, the produced hydrogen may not be considered “truly green” due to the fact that the source of the produced energy in the grid is unknown.

_{2}electrolyser operation, considering the combination of various energy sources and varying electricity prices and to tackle the disadvantages of the previously developed MCTS model.

## 2. Materials and Methods

#### 2.1. Optimisation Problem Setup

_{2}and O

_{2}production subject to varying grid energy prices and availability of RE sources. In our particular case, various electrolyser states (offline, various levels of production, startup or shutdown sequences) with fixed duration and variable cost profiles are assigned to each timespan taking into account defined state transition constraints. An inherent trait of electrolysers is their process inertia, where the initiation and cessation of H

_{2}production do not occur immediately upon activating or deactivating the electrolyser. Electrolysers undergo distinct “StartUp” and “Shutdown” sequences, which may extend up to 1 h, as employed in our model. The duration of these sequences may differ among various electrolysers, influenced by factors such as the necessary electrolyte temperature for optimal efficiency and the types of membranes employed.

^{+}denotes sub-graph of states accessible from the previous state.

- An array of photovoltaic solar (PV) cells with a theoretical maximum capacity of 100 kW. This represents the source of RE with available excess power that can vary over the day. Other RE sources can be considered as well.
- Relative solar irradiation is simulated for daylight periods corresponding to the spring or fall equinoxes. Specific latitudes and the day of the year have further effects on solar declination angle and power output of PV cells.
- The power grid connection is considered a backup energy source. Its capacity is not limited, but it has fluctuating prices for each hour.
- The main income for the electrolysis process is modelled as sales of the output products (H
_{2}and O_{2}). While prices of products fluctuate depending on production methods, required post-processing and targeted applications, the model considers fixed prices of the products: PH_{2}for EUR 5.00/kg and PO_{2}for EUR 0.10/kg.

#### 2.2. Constraint Satisfaction Problem Optimisation Using OR-Tools

## 3. Results and Discussion

#### 3.1. CP-SAT and MCTS Model Comparison

_{0}at midnight with the electrolyser being switched off (thus the first valid states are either continued Off state or the beginning of StartUp sequence). Figure 1 shows the comparison between a manually created “full power” schedule, the results from a previously developed [14] MCTS algorithm and the best solution found by the CP-SAT model. The model outputs are as follows: total energy consumption E, hydrogen produced Q

_{H2}, oxygen produced Q

_{O2}and profit F.

#### 3.2. Input Parameter Analysis for the CP-SAT Model

## 4. Conclusions

_{2}production process. In our case, the model is defined using Python code, which opens additional advantages of OR-Tools, namely the ability to automate repetitive parts and raise development to the metaprogramming level.

_{2}production is not profitable from grid energy (especially from fossil fuels). Common practice is to use a surplus of the RE for H

_{2}production effectively transforming it into long-term energy storage, which is later used for various applications such as mobility or small-scale electricity production. Also, this industry in its current state heavily relies on support from regulatory bodies. There are more profitable uses for the excess of renewable energy as far as H

_{2}production via methane steam reforming is available and not suppressed by regulatory bodies.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

_{2}-Compression, No. 1.1.1.1/20/A/185), led by Ventspils University of Applied Sciences.

## Conflicts of Interest

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**Figure 1.**Electrolyser schedules compared (1 h resolution): (

**a**) “full power” production, (

**b**) the best schedule by MCTS and (

**c**) the best schedule by CP-SAT model.

**Figure 2.**Electrolyser schedules compared (15 min resolution): (

**a**) “full power” production, (

**b**) the best schedule by MCTS, (

**c**) the best schedule by CP-SAT model (fixed production levels) and (

**d**) the best schedule by CP-SAT model (variable production levels).

**Figure 3.**Electrolyser schedules depending on various amortisation costs per on–off cycle: (

**a**) EUR 6.00 (baseline), (

**b**) EUR 3.00 and (

**c**) EUR 1.50.

**Figure 4.**Electrolyser schedules depending on available renewable power (solar at peak): (

**a**) 100 kWp (baseline), (

**b**) 60 kWp, (

**c**) 30 kWp and (

**d**) 10 kWp.

**Figure 5.**Total profit of the optimal schedule depending on input parameters of the model: (

**a**) amortisation costs, (

**b**) H

_{2}price and (

**c**) available solar power.

Symbol | Property | Units |
---|---|---|

${Q}_{s}^{H2}$ | Quantity of H_{2} produced in a specific state | kg |

${Q}_{s}^{O2}$ | Quantity of O_{2} produced in a specific state | kg |

${P}^{H2}$ | Price of H_{2} | EUR/kg |

${P}^{O2}$ | Price of O_{2} | EUR/kg |

${P}_{t}^{E}$ | Price of electricity | EUR/kWh |

${E}_{s}$ | Energy consumed in a specific state | kWh |

${E}_{t}^{PV}$ | RE available in a specific time span | kWh |

${C}_{s}$ | Amortisation costs in a specific state | EUR |

F | Profit | EUR |

Constraint Formulation | Description |
---|---|

$n\left({s}_{t}\right)=1,\forall t\in T$ | Exactly one state assigned to each timestamp. |

${s}_{0}\in \left\{Off,StartUp\right\}$ | Initial state of the electrolyser is either Off or StartUp (similar to experiments with MCTS model). |

${s}_{t}\in \left\{s:s\in {G}^{+}\left({s}_{t-1}\right)\right\},\forall t\in T$ | For all timespans, the state is selected from a subset of states, which are reachable from the previous state. |

$max\left\{v\times F,\forall t\in T,\forall s\in S\right\}$ | The model variables are restricted to Boolean values indicating the state assignment to the timespan. The objective of the model is to maximise dot product between assignment variables and their corresponding revenue. |

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**MDPI and ACS Style**

Komasilovs, V.; Zacepins, A.; Kviesis, A.; Bezrukovs, V.
Model for Hydrogen Production Scheduling Optimisation. *Modelling* **2024**, *5*, 265-275.
https://doi.org/10.3390/modelling5010014

**AMA Style**

Komasilovs V, Zacepins A, Kviesis A, Bezrukovs V.
Model for Hydrogen Production Scheduling Optimisation. *Modelling*. 2024; 5(1):265-275.
https://doi.org/10.3390/modelling5010014

**Chicago/Turabian Style**

Komasilovs, Vitalijs, Aleksejs Zacepins, Armands Kviesis, and Vladislavs Bezrukovs.
2024. "Model for Hydrogen Production Scheduling Optimisation" *Modelling* 5, no. 1: 265-275.
https://doi.org/10.3390/modelling5010014