Keywords

1 Introduction

As a green energy source with high calorific value, diverse sources, clean and environmental protection, and high conversion efficiency, hydrogen energy has been recognized as a clean energy carrier with zero emission and zero pollution. Hydrogen energy, which is called the ultimate energy in the 21st century, has received attention and research from scholars all over the world, and more and more countries are putting the development of hydrogen energy in the forefront of energy development [1, 2].

Electrolytic water to hydrogen technology is widely used in the hydrogen production industry for its simple preparation process, clean product and high purity. To achieve large-scale hydrogen production from renewable energy sources, the input energy for hydrogen production from electrolytic water is usually generated from renewable energy sources such as wind and light energy, whose input power is volatile and uncertain [3]. The electrolyzer is the core part of the electrolytic water hydrogen production process, and its performance has a great influence on the electrolytic hydrogen production system. Frequent fluctuations in the input power of the electrolyzer will cause the input current to fluctuate as well, resulting in frequent starts and stops of the electrolyzer, which will not only reduce the service life of the electrolyzer itself, but also lead to a decrease in its hydrogen production, and even affect the purity of the product and the concentration of hydrogen in oxygen, thus affecting the safety of the whole electrolytic water hydrogen production system [4]. Therefore, the mathematical model and simulation of hydrogen production from electrolytic water plays an important role in the safety of electrolytic water system. Ulleberg proposed an advanced mathematical model for alkaline electrolyzers based on basic thermodynamics, heat transfer theory and electrochemical relationships, which can be used to predict the voltage, hydrogen production, efficiency and operating temperature of electrolytic cells in electrolytic water systems [5]. Tijani et al. investigated the main parameters affecting the performance of the electrolyzer by means of basic thermodynamic and electrochemical reaction-related models [6]. Shen X. et al. developed a mathematical model of the equivalent impedance characteristics, electrothermal characteristics and power regulation characteristics of an alkaline electrolyzer [7]. Górecki et al. described the voltammetric characteristics of the electrolyzer and considered the effect of the concentration of potassium hydroxide solution on the hydrogen production, and verified the correctness of their model experimentally by varying the electrolyte concentration [8]. The electrolyzer model developed in the above literature provides a valuable reference for modeling and simulation of hydrogen production from alkaline electrolytic water, but does not take into account the effect of fluctuations in input power on the electrolyzer.

Since the operating condition of the electrolyzer is limited by the fluctuation of renewable energy input power, the lower power limit of the electrolyzer is generally set at 20–25% of the rated power to utilize as much renewable energy as possible. To improve the ability of electrolyzer to resist the fluctuation of renewable energy input power and to improve the hydrogen production rate of electrolytic water hydrogen production system, one can consider changing the electrode material of electrolyzer, increasing the surface area of electrode, optimizing the diaphragm material, using advanced electrolyte or adding new catalyst, etc. However, the research on the electrolyzer material is a long and complicated process, which cannot meet the demand of electrolyzer to adapt to wide power in the short term. Secondly, the feasibility of changing the structure of the electrolytic water hydrogen production system and optimizing the control strategy of the electrolytic system has been proved and more and more scholars have studied it. Fang R et al. proposed the combination of supercapacitor and modular control strategy to optimize the operation mode of the electrolyzer considering the effect of wind power fluctuation on the electrolyzer, thus extending the life of the electrolyzer and improving the hydrogen production [9]. Hong Z. et al. controlled the electrolyzer array by a segmented fuzzy control method as a way to improve the hydrogen yield of the electrolytic water hydrogen production system considering the efficiency of hydrogen production from wind power [10]. Shen et al. proposed a control strategy for the rotation of alkaline electrolytic water hydrogen production electrolyzer arrays, which enables the electrolyzer arrays to operate or shut down in different operating states sequentially according to the rotation cycle, improving the safety of the electrolytic water hydrogen production system and extending the service life of the electrolyzer [11]. Liu et al. developed a wide power adaptation model for alkaline electrolyzers to improve the adaptability of electrolyzers to input power fluctuations and to improve the level of wind power consumption [12]. The above literature does not provide a clearer description of the power settings for the wide power model of the electrolyzer.

Based on the above research, this paper proposes a digital twin-based alkaline electrolytic water hydrogen production model and a multi-electrolyzer adaptive wide power model, which combines the working mechanism of alkaline electrolytic water hydrogen production and digital twin technology to construct a digital twin framework for alkaline electrolytic water hydrogen production. And it is verified by simulation that the wide power model proposed in the paper can improve the ability of the electrolyzer module to adapt to wind power fluctuations.

2 Alkaline Electrolytic Water Digital Twin Framework

Digital twin technology has attracted much attention in the fields of intelligent manufacturing and energy monitoring and analysis, and realizing information, digitalization and intelligence in the new energy field is a hot research topic in the energy field [13, 14]. Applying digital twin technology to the field of alkaline electrolytic water hydrogen production, which is a data visualization presentation of electrolytic water hydrogen production system, this paper gives the framework of renewable energy electrolytic water hydrogen production digital twin by combining the framework of digital twin and the working mechanism of electrolytic water hydrogen production.

As shown in Fig. 1, the renewable energy electrolytic water to hydrogen digital twin framework consists of four layers: the physical device layer, the data interaction layer, the model layer and the application layer. The physical equipment layer includes scenery power generation equipment, electrolytic water hydrogen production equipment and sensors, which realize data sensing through communication and IOT technologies. The data interaction layer consists of data transmission, data processing and data storage, which provides powerful data support for electrolytic water to hydrogen digital twin technology, involving transmission communication protocols and methods, processing of data and database storage and management, interconnecting the physical device layer, model layer and application layer. The model layer is divided into a mathematical model of electrolytic hydrogen production and a twin model. The mathematical model is a semi-empirical formula or equation fitted by data processing of historical data according to the working mechanism of electrolytic hydrogen production, and the twin model is a virtual three-dimensional model based on electrolytic hydrogen production equipment, which can simulate the process of electrolytic hydrogen production. The application layer includes production monitoring, report generation, intelligent warning and production forecasting, which presents the production status of electrolytic water hydrogen production in real time and is a visual representation of the digital twin of electrolytic water hydrogen production.

Fig. 1.
figure 1

Digital twin framework for hydrogen production from electrolytic water.

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3 Model Construction

3.1 Mathematical Model of Alkaline Electrolyzer

The electrolyzer is the core component of the electrolytic water hydrogen production system. In the whole hydrogen production system, the electrolyzer is equivalent to a voltage sensitive non-linear DC load, so the I-U curve describing its voltage variation with current is one of the most important characteristics of the electrolyzer. To describe this characteristic of the electrolyzer, Ulleberg proposed a mathematical model of the electrolyzer voltage with respect to current and temperature to show the relationship between the electrolyzer voltage and its current and tank temperature. The electrical characteristics of the electrolyzer are also influenced by the pressure inside the electrolyzer, and the mathematical model proposed by Ulleberg was modified by Sánchez et al. to give the following Eq. (1) for its characteristics [15].

$$ U_{el} = U_{rev} + \left[ {\left( {r_{1} + d_{1} } \right) + r_{2} \cdot T + d_{2} \cdot P\left] { \cdot \frac{I}{{\text{A}}} + s \cdot \log } \right[\left( {t_{1} + \frac{{t_{2} }}{T} + \frac{{t_{3} }}{{T^{2} }}} \right) \cdot \frac{I}{{\text{A}}} + 1} \right] $$
(1)

where \(U_{el}\) represents the voltage of a single electrolyzer cell, \(U_{rev}\) is the reversible voltage of the electrolyzer, \(r_{1}\), \(r_{2}\), \(d_{1}\), \(d_{2}\), s, \(t_{1}\), \(t_{2}\), \(t_{3}\) are its coefficients, I is the input current, and A is the electrolytic cell electrode surface area. When the electrolyzer is at a temperature of 25 °C and a pressure of 0.1 MPa, the reversible voltage can be found by the ratio of the Gibbs free energy ∆G to the product of the Faraday constant F and the number of electrons transferred z. The expression is shown in Eq. (2).

$$ U_{rev} = \frac{{\Delta {\text{G}}}}{{{\text{zF}}}} $$
(2)

Considering that the reversible voltage \((U_{rev} )\) has a tendency to decrease as the tank temperature increases, it can be derived from Eq. (3).

$$ U_{rev} = - 7.3 \times 10^{ - 4} \cdot T + 1.248 $$
(3)

3.2 Electrolytic Tank Wide Power Adaptation Model

Wind power is used directly as the input energy for alkaline electrolysis of water for hydrogen production, whose input power is stochastic and fluctuating. Frequent fluctuations of natural wind can lead to unstable operation of the cell, which not only directly affects the hydrogen production and purity, but also the safety of the hydrogen production system. Moreover, the technology of direct integration of large-scale wind power generation into electrolytic water for hydrogen production is gradually maturing, while large-scale hydrogen production equipment is gradually developing towards the many-to-one mode [16]. Thus, improving the wide power adaptability of electrolytic water hydrogen production systems is essential. In response to this problem, a "4-to-1" model of alkaline electrolytic hydrogen production is established based on four alkaline electrolytic cells sharing one gas-liquid unit in the hydrogen production system, shown in Fig. 2.

Power of the electrolyzer operation is limited by the purity of the product gas. To ensure the safety of the system, its minimum operating power is 20% of the rated power, and it cannot guarantee long-time operation. Meanwhile, the maximum operating power of the electrolytic cell can reach 110–130% of the rated power in a short period of time due to its overload characteristics. In this paper, we only study the case where the upper power limit of the electrolyzer is the rated power, and consider the operating power range of a single electrolyzer from 20 to 100% of the rated power, without considering its start-stop characteristics. As shown in Fig. 2, where 4 electrolytic cells of the same size share one set of gas-liquid unit, the power range that this electrolytic cell module can accommodate is extended from its full 20–100% of its capacity to 5–100%.

Fig. 2.
figure 2

Simple diagram of “4-to-1” hydrogen production plant in alkaline electrolyzer.

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Based on the operation of the electrolyzer module and the renewable energy power, it is possible to express the relationship between the power required to operate the electrolyzer module and the power generated by renewable energy as well as the renewable energy power not absorbed by the electrolyzer module.

$$ P_{w} = k \cdot P_{E} + P_{waste} \quad k = 0,1,2,3,4 $$
(4)

where \(P_{w}\) is the input power of renewable energy to the electrolyzer module, k indicates the number of electrolyzers operating at rated power, \(P_{E}\) is the rated power of a single electrolyzer, and \(P_{waste}\) is the power not absorbed by the electrolyzer module.

Electrolyzer operating power is limited by the purity of the product air, whose minimum operating power is 20% of the nominal power. The lower limit of operating power of the proposed electrolyzer module consisting of four electrolytic cells is 20% of the rated power of a single electrolyzer, which is 5% of the full power of the electrolyzer module. In case the full operating power of the electrolyzer module is \(\sum P_{E}\), the lower limit of its operating power can be expressed as Eq. (5).

$$ P_{min} = 5\% \sum P_{E} = 20\% P_{E} $$
(5)

In Eq. (4), when all four cells in the electrolyzer module are operating at full power and the renewable energy power is greater than the power required by the electrolyzer module, the power is overloaded. The renewable energy power not absorbed by the electrolyzer at this point is Eq. (6).

$$ P_{waste} = P_{w} - \sum P_{E} $$
(6)

While the power is not overloaded, according to the power dissipation of the electrolyzer module, it is classified into 3 operating conditions: low power, high power and full power. Expressing the number of electrolytic cells of the same size as i (i = 1, 2, 3, 4), the power operation condition of the cell module is Eq. (7).

$$ \left\{ {\begin{array}{*{20}l} {P_{el} = P_{wave} } \hfill & {i = 1} \hfill \\ {P_{el} = k \cdot P_{E} + P_{wave} } \hfill & {i = 2,3,4,k = 1,2,3} \hfill \\ {P_{el} = k \cdot P_{E} } \hfill & {i = 4,k = 4} \hfill \\ \end{array} } \right. $$
(7)

where \(P_{el}\) is the operating power of the electrolyzer module, k indicates the number of electrolyzers operating at rated power, and \(P_{E}\) is the rated power of one electrolyzer. \(P_{wave}\) is the fluctuating power at which an electrolyzer can operate and the fluctuating power is greater than the minimum operating power of the electrolyzer and less than the rated power of the electrolyzer, \(P_{min} \le P_{wave} \le P_{E}\).

Equation (7) indicates that the electrolyzer module is in a low power operation state, when the input power of renewable energy to the electrolyzer module is less than the rated power of the electrolyzer, and only one electrolyzer module works in this state. If the fluctuating power is equal to the lower limit of the operating power of a single electrolyzer, \(P_{wave} = P_{min}\), which is 5% of the rated power, and 5% \(\sum P_{E}\) is the minimum running power of the electrolyzer module. When the renewable energy power is less than the electrolyzer operating power, \(P_{w} < P_{wave}\), \(P_{w}\) is the power not absorbed by the electrolyzer module, \(P_{waste} = P_{w}\).

Equation (7) represents the electrolyzer module in high power operation, where the renewable energy input power to the electrolyzer module is less than the full power value of the electrolyzer module. The operating state of the electrolyzer module under high power includes two electrolyzers, three electrolyzers and four electrolyzers, and only one electrolyzer in each case is operating at less than its rated power, while the rest of the operating electrolyzers are operating at rated power. If the electrolyzer module has k cells at rated power and \((P_{w} - k \cdot P_{E} )\) is less than the minimum running power of cell, the power not absorbed by the cell module can be expressed as Eq. (8).

$$ P_{waste} = P_{w} - k \cdot P_{E} \quad k = 1,2,3 $$
(8)

Equation (7) means that the electrolyzer module is in full power operation, at this time, all four electrolyzers are working at rated power, all renewable energy power is consumed by the electrolyzer module, and the operating power of the electrolyzer module reaches 100%.

4 Simulation and Analysis

To verify the adaptability of the above models, the electrical model and wide power adaptation model are experimented and analyzed based on the mathematical models developed in Sect. 3.

4.1 Electrical Model Analysis

The relationship between electrolyzer cell voltage \((U_{el} )\) and current density is analyzed according to Eqs. (1–3), and Fig. 3(a) and (b) show the curves of electrolyzer cell voltage with current density under different temperatures and different pressures, respectively. The temperature is set to 45–75 °C and the pressure is fixed at 0.5 MPa, as shown in Fig. 3(a) the voltage of the cell increases with the increase of current density and decreases with the increase of temperature. The chemical reaction of electrolytic water is affected by temperature, and the redox reaction of electrolytic water is easier to achieve at high temperature, so the electrolytic voltage required is slightly lower than at low temperature. The pressure in Fig. 3(b) is set to 0.5–2.0 MPa and the temperature is fixed at 75 °C. The variation of the cell voltage with current density has the same trend as its variation under the influence of temperature, but the convergence of applying different pressures on the cell voltage almost does not affect the electrical performance of the cell voltage.

Fig. 3.
figure 3

Small chamber voltage variation curve with current density (a: pressure 0.5 MPa, b: temperature 75 °C).

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4.2 Alkaline Electrolytic Water to Hydrogen Wide Power Model Analysis

According to the wide power model of alkaline electrolytic water hydrogen production described in Eqs. (4–8) and the output power of a certain 1.6 MW wind turbine, two different sets of electrolytic cells are selected for the hydrogen production system. The first group is one electrolyzer with a rated power of 1500 kW and the second group is an electrolyzer module with a total power of 1500 kW consisting of four electrolyzers with a rated power of 375 kW. The output power of a 1.6 MW wind turbine in a wind farm in Zhangbei area for a certain month is directly used as the input power of two sets of electrolyzer modules. The range of wind power that a single electrolyzer can withstand is 20–100% of its rated power, so the minimum operating power for a 1500 kW electrolyzer is 300 kW and for a 375 kW electrolyzer is 75 kW.

Figure 4 shows the power curves consumed by the two electrolyzer sets for operation. The power curves consumed by the two electrolyzer sets and the fan wind power curves basically overlap below 1500 kW, with a small deviation in the low power range. The reason for this is that the power consumption level of the electrolyzer depends on the output of wind power since the wind turbine power generation is directly supplied to the electrolyzer, so its power consumption curve goes in the same direction as the wind power basically. In the low power range, the power consumption curve of the electrolyzer set deviates from the wind power curve, and the wind power absorbed by the electrolyzer set for wide power hydrogen production is higher than the wind power absorbed by the electrolyzer set without wide power hydrogen production. Due to the limitation of the minimum operating power of the electrolytic cell, wind power below the minimum operating power of the electrolytic cell will not be absorbed by the cell. From the figure, the overlap between the power consumption curve and wind power curve of four 375 kW electrolyzer modules is higher than that between the power consumption curve and wind power curve of one 1500 kW electrolyzer, which also indicates that the level of wind power dissipation by the modules of the cells can be improved by using a wide power model.

Fig. 4.
figure 4

Electrolyzer power dissipation curve.

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5 Conclusion

This paper combines digital twin technology and the working mechanism of electrolytic water hydrogen production, constructs a digital twin framework for alkaline electrolytic water hydrogen production, and describes the technical method of digital twin of electrolytic water hydrogen production. A model of alkaline electrolytic water hydrogen production with multiple electrolyzers to adapt to wide power is established, and the analysis shows that the wide power adaptation of the multiple electrolyzer wide power model is better than that without the wide power model, and the power dissipation level is high. This paper has some reference value in the problems of digital twin application and wide power adaptation of electrolytic cells for hydrogen production from electrolytic water.