In the existing power system with a large-scale hydrogen storage system, there are problems such as low efficiency of electric-hydrogen-electricity conversion and single modeling of the hydrogen storage system. In order to improve the hydrogen utilization rate of hydrogen storage system in the process of participating in the power grid operation, and speed up the process of electric-hydrogen-electricity conversion. This article provides a detailed introduction to the mathematical and electrical models of various components of the hydrogen storage unit, and also establishes a charging and discharging efficiency model that considers the temperature and internal gas partial pressure of the hydrogen storage unit. These models are of great significance for studying and optimizing gas storage technology. Through these models, the performance of gas storage units can be better understood and improved. These studies are very helpful for improving energy storage efficiency and sustainable development. The factors affecting the charge-discharge efficiency of hydrogen storage units are analyzed. By integrating the models of each unit and considering the capacity degradation of the hydrogen storage system, we can construct an efficiency model for a large hydrogen storage system and power conversion system. In addition, the simulation models of the hydrogen production system and hydrogen consumption system were established in MATLAB/Simulink. The accuracy and effectiveness of the simulation model were proved by comparing the output voltage variation curve of the simulation with the polarization curve of the typical hydrogen production system and hydrogen consumption system. The results show that the charge-discharge efficiency of the hydrogen storage unit increases with the increase of operating temperature, and H_{2} and O_{2} partial voltage have little influence on the charge-discharge efficiency. In the process of power conversion system converter rectification operation, its efficiency decreases with the increase of temperature, while in the process of inverter operation, power conversion system efficiency increases with the increase of temperature. Combined with the efficiency of each hydrogen storage unit and power conversion system converter, the upper limit of the capacity loss of different hydrogen storage units was set. The optimal charge-discharge efficiency of the hydrogen storage system was obtained by using the Cplex solver at 36.46% and 66.34%.
The Guiding Opinions on Accelerating the Development of New Energy Storage issued by the National Development and Reform Commission and the National Energy Administration in July 2021 [
The electrochemical reaction of the HSS during charging and discharging is a nonlinear process affected by many factors. In terms of electrical engineering applications, in order to facilitate research, common electrical components are used, and the external characteristics of the voltage and current of the hydrogen storage system during the charging and discharging process are connected, and an equivalent circuit model is constructed to clearly describe the charging and discharging characteristics of the HSS. In terms of battery characteristics analysis and modeling, Li et al. [
For the research on the characteristics of each part of the hydrogen storage system, Liu et al. [
For the existing research on hydrogen storage system, Amir et al. [
Research on System Capacity Decay Characteristics, Liu et al. [
Current research may not fully consider the factors of the entire hydrogen storage system when modeling hydrogen storage systems, and there are few literature describing the relationship between temperature and pressure on the charging and discharging efficiency of hydrogen storage systems. In addition, there is a lack of detailed description of the factors that affect the capacity decay characteristics of hydrogen storage systems. Therefore, future research can continue to explore the modeling of the entire hydrogen storage system, and delve into the effects of temperature and pressure on the charging and discharging efficiency of the hydrogen storage system, while analyzing and describing the factors that affect the capacity attenuation characteristics of the hydrogen storage system.
In this paper, the capacity attenuation characteristic equation applicable to the hydrogen storage system is constructed first considering the system capacity attenuation. On this basis, the simulation models of each part and the whole of the large-scale hydrogen storage system are established, and the mathematical models and electrical models of each unit of the hydrogen storage system are introduced. The physical meaning of each part is analyzed. The hydrogen storage system is systematically simulated and analyzed in MATLAB/Simulink using the electrical model. The validity of the simulation model is proved by comparing the polarization curves of typical hydrogen production and hydrogen consumption systems. Finally, the optimal charging and discharging efficiency of hydrogen storage system considering the capacity attenuation factor is obtained by synthesizing the unit model.
The simplified structure of the power system with hydrogen storage system is shown in
The hydrogen storage system consists of multiple electrolytic cell units, hydrogen storage tanks, and multiple fuel cell units. After the system is connected to the power grid, each electrolytic cell unit generates hydrogen gas and compresses it into a hydrogen storage tank. When electrical energy is needed, each fuel cell unit converts the hydrogen stored in the hydrogen storage tank into electrical energy.
Due to the different internal characteristics of each electrolyzer unit and fuel cell unit, and when the internal temperature and gas pressure of the hydrogen storage system are different, the charge and discharge efficiency will also change accordingly. Considering the series-parallel combination of the monomer model, the construction is composed of the large-scale hydrogen storage system is shown in
Assume that the temperature set and pressure set of each single cell in the series-parallel combination are
The temperature and pressure set for each single fuel cell are
m and n are the number of parallel and series connected large-scale hydrogen storage systems, respectively.
From this, the formulas for the charge and discharge efficiency of large-scale hydrogen storage systems are obtained as follows:
where
The energy conversion efficiency of PCS (Power Conversion System) in hydrogen storage systems during external charging and discharging processes will also have an impact on the efficiency of the entire large-scale hydrogen storage system. In addition to considering the impact of internal characteristics of large hydrogen storage systems on efficiency, it is also necessary to consider the impact of PCS energy conversion efficiency on the efficiency of the entire hydrogen storage system. The efficiency of PCS has a nonlinear relationship with the output power of the hydrogen storage system [
where
In summary, the total charge-discharge efficiency of the large-scale hydrogen storage system is:
In the actual production process, the capacity of the hydrogen storage system will gradually decrease due to a decrease in the number of cycles. The changes in working temperature and internal pressure within the system will have an impact on the absorption and release of hydrogen in the hydrogen storage system, and thus affect the capacity of the hydrogen storage system. In order to better fit the engineering practice, The capacity decay effect formula [
where
According to the above formula, the total life loss of the hydrogen storage system is:
where
1) Electrolyzer Model
The electrolytic cell voltage model is derived from the relationship between the electrolysis voltage and electrolytic current [
where
In an electrolytic cell, the open circuit voltage is related to temperature and the activity of each component involved in the reaction. The open circuit voltage of the electrolytic cell can be derived through the Nernst equation. This equation is used to calculate the equilibrium voltage of a specific redox pair on the electrode relative to the standard potential:
where
The standard electromotive force expression is:
where
where
The ohmic polarization overvoltage is:
where
The cell efficiency formula is equal to the ratio of the input voltage inside the cell to the voltage at the cell port.
2) Fuel cell model
The output voltage of a single fuel cell [
where
Thermodynamic electromotive force means that the work done to transfer electrons during the H_{2} combustion reaction is equal to the Gibbs free energy released during the reaction without considering the loss, expressed by the Nernst equation and the Gibbs free energy change.
where
The activation polarization overvoltage is mainly manifested as a slow rate phenomenon when the electrode surface is just about to activate the electrochemical reaction, which is generally expressed by a fixed parameter.
where
The ohmic overvoltage of the PEMFC module is mainly caused by the voltage drop generated by the membrane impedance corresponding to the proton membrane, which is equivalent to the voltage drop generated by the internal resistance of the fuel cell.
where
The concentration overvoltage of the PEMFC module mainly occurs in the working state of high current. At this time, the electrochemical reaction is too fast, which causes the slow diffusion of reactants or products and the restriction of mass transfer of reactants. The mathematical expression is as follows:
where
The current density is:
The fuel cell efficiency formula is equal to the ratio of the output voltage of the fuel cell port to the thermodynamic electromotive force of the internal reaction.
3) Hydrogen storage tank model
The hydrogen production flow rate of a single electrolyzer is [
The principle of hydrogen consumption molar flow rate is the same as above:
Hydrogen storage:
1) Equivalent circuit model of electrolyzer
The electrolytic cell model can be equivalent to the charging process, so the electrolytic cell can be considered as an equivalent power source. In an electrolytic cell, internal current flows from the positive pole of the power supply to the negative pole. However, the direction of overvoltage caused by activation polarization loss and ohmic overvoltage is opposite to the direction of open circuit voltage. That is to say, the effects of activated polarization and ohmic overvoltage will require a higher voltage than the open circuit voltage for the actual electrolysis process to proceed. Ohmic loss is mainly caused by the current passing through electrode materials, connecting components, liquid junction potential when in contact with different solutions, and the resistance of ions in the electrolyte. The relationship between Ohm voltage loss and current follows Ohm’s law, which means that voltage loss is equal to current multiplied by resistance. Polarization loss is mainly caused by the deviation of cell equilibrium potential caused by changes in concentration in the electrolytic cell. When the electrolyte concentration changes, polarization loss can lead to a difference between the working voltage and open circuit voltage of the electrolytic cell. In summary, ohmic loss and polarization loss are the two main factors causing voltage loss in the electrolysis process.
According to the above analysis, the equivalent circuit model of the electrolytic cell [
According to the equivalent circuit and mathematical model, a simulation model is built through MATLAB/Simulink [
2) Equivalent circuit model of fuel cell
Since a series of physical and chemical changes will occur on the positive and negative electrodes of the fuel cell during operation, each process will generate a certain resistance. In order to make the reaction on the electrodes continue to occur, it needs to consume its own energy to overcome the resistance. During this process, the electrode potential shift phenomenon will occur, and the losses generated during the reaction include activation polarization voltage, ohmic polarization voltage and concentration overvoltage. The corresponding fuel cell equivalent circuit model [
The fuel cell simulation model structure [
In order to verify the validity of the model established in this paper, some parameters are set as shown in
In order to analyze the influence of temperature and partial gas pressure of each part of the hydrogen storage unit on the charging and discharging efficiency of the hydrogen storage unit, the hydrogen storage unit is charged and discharged under the constant current of 10, 30, 50 and 70 A, that is, the current density is 0.04, 0.12, 0.2 and 0.28 A/cm^{2}.
It can be seen from
The PCS converter efficiency is strongly related to the output power of the large-scale hydrogen storage system. When considering the influence of the internal characteristics of the hydrogen storage system on the system charge and discharge efficiency, changes in the internal temperature and pressure of the system will also affect the power and lead to changes in the PCS efficiency.
In the rectification stage of the PCS converter, as the temperature increases, the efficiency of the PCS converter will decrease, while the pressure has little effect on it. This is because during the rectification operation, power flows to the PCS converter, causing high current and low voltage, resulting in poor heat dissipation conditions inside the converter. However, an increase in temperature will further reduce the heat dissipation effect, thus negatively affecting the rectification efficiency.
In the inverter operation of the PCS converter, the PCS efficiency increases with increasing temperature and slightly increases with increasing pressure. This is because during the operation of the inverter, power is output from the PCS, and at this time, the current is low and the voltage is high, making the requirements for heat dissipation relatively low. At the same time, a high-temperature environment is beneficial for improving the performance of certain components, thereby improving inverter efficiency. The reason why the impact of pressure on efficiency is relatively small may be due to the small impact of pressure changes on the working state of circuit components.
In this paper, it is assumed that the capacity of the hydrogen storage tank is infinite, and the upper limit of the capacity decay rate is set to limit the quality of hydrogen that the hydrogen storage tank can hold. Since the partial pressure of the gas has little effect on the hydrogen storage unit, it is assumed that the partial pressure of the gas and the pressure in the tank are constant at 3 atm, the number of cycles of the hydrogen storage system is 2000 times, and the working environment is set to a constant temperature of 25°C. At this time, the capacity loss of the electrolyzer and the fuel cell increases with the increase of the internal working temperature, and the change curve of the capacity loss with temperature is shown in
Theoretically, if the temperature is kept at a high level, higher charge-discharge efficiency can be obtained, but in the actual production process, the capacity of the electrolyzer and fuel cell will decrease with the increase of temperature and the number of cycles. In order to be more practical, different upper limits of capacity decay are set for the hydrogen storage unit, as shown in
Electrolyzer unit number | Capacity loss upper limit/% | Fuel cell unit number | Capacity loss upper limit/% |
---|---|---|---|
1–10 | 70 | 1–10 | 30 |
11–20 | 60 | 11–20 | 40 |
21–30 | 50 | 21–30 | 50 |
31–40 | 40 | 31–40 | 60 |
41–50 | 30 | 41–50 | 70 |
It can be seen from
In this paper, firstly, the attenuation characteristics of the battery are considered, and the simulation model of each part of the large-scale hydrogen storage system is systematically constructed in detail. Secondly, the steady-state simulation model of each component of the hydrogen storage unit is constructed, as well as the charge-discharge efficiency model and PCS efficiency model considering the temperature of the hydrogen storage system and the internal gas partial pressure. Through the simulation and modeling of the hydrogen storage system in MATLAB/Simulink, the efficiency characteristics of the hydrogen storage system and hydrogen storage unit are analyzed. With the goal of optimizing the efficiency of the large-scale hydrogen storage system, the results obtained by using the Cplex solver are as follows:
(1) The overall efficiency of a large-scale hydrogen storage system is affected by the internal characteristics of each hydrogen storage unit that makes up the system, including charging and discharging current, operating temperature, gas partial pressure and hydrogen storage tank capacity attenuation, as well as the efficiency of the PCS converter during AC/DC conversion with the outside world.
(2) Properly increasing the internal working temperature of the hydrogen storage unit can improve the charging and discharging efficiency of the system and the PCS efficiency during inverter operation, but will reduce the PCS efficiency during rectifier operation; Increasing H_{2} and O_{2} partial pressure can increase the efficiency of the hydrogen storage unit and PCS, but the increase is small, indicating that the pressure has little effect on the efficiency of the hydrogen storage system. The efficiency of the hydrogen storage unit will increase with the increase of charge-discharge current.
(3) The overall efficiency of the large-scale hydrogen storage system is linear with the system loss and working temperature. The capacity decay rate of the hydrogen storage tank increases with the temperature and changes fastest between 20°C and 30°C. Although the high working temperature will affect the capacity attenuation of the system, it will increase the charging and discharging efficiency. Under the above conditions, the optimal total charging efficiency of the system is 63.46%, and the total discharge efficiency is 66.34%.
To sum up the actual situation, in order to obtain appropriate charging and discharging efficiency and ensure that the system capacity loss is within a certain range, it is necessary to reasonably design the parameters.
The authors acknowledge the reviewers for providing valuable comments and helpful suggestions to improve the manuscript.
This work was supported by the Jilin Province Higher Education Teaching Reform Research Project Funding (Contract No. 2020285O73B005E).
The authors confirm their contribution to the paper as follows: study conception: Junhui Li; design, data collection: Haotian Zhang; analysis and interpretation of results: Cuiping Li and Xingxu Zhu; draft manuscript preparation: Ruitong Liu, Fangwei Duan and Yongming Peng. All authors reviewed the results and approved the final version of the manuscript.
All data generated or analysed during this study are included in this published article.
The authors declare that they have no conflicts of interest to report regarding the present study.
Parameter name | Parameter expression | Numerical value | Unit |
---|---|---|---|
The number of electrons transferred | z | 2 | – |
Faraday constant | F | 96.487 | kJ/(V·mol) |
Gibbs | 236.48 | kJ/mol | |
Water activity | aH_{2}O | 1 | – |
Electrolyzer module area | 0.25 | m^{2} | |
Electrolyzer temperature | 25 | °C | |
Number of serial modules of electrolyzers | 80 | – | |
Ohm parameter | r_{1} | 0.000 073 | Ωm^{2} |
Ohm parameter | r_{2} | −0.000 000111 | Ωm^{2}°C^{−1} |
Electrode overvoltage parameters | s_{1} | 0.16 | V |
Electrode overvoltage parameters | s_{2} | 0.001 38 | V/°C |
Electrode overvoltage parameters | s_{3} | −0.000 016 | V/°C^{2} |
Electrode overvoltage parameters | t_{1} | 0.016 | m^{2}A^{−1} |
Electrode overvoltage parameters | t_{2} | −1.3 | m^{2}A^{−1}°C |
Electrode overvoltage parameters | t_{3} | 421 | m^{2}A^{−1}°C^{−2} |
Faraday efficiency coefficient | 99.5 | % | |
Faraday efficiency coefficient | −9.578 8 | m^{2}/A | |
Faraday efficiency coefficient | −0.055 5 | m^{2}°C/A | |
Faraday efficiency coefficient | 1 502.71 | m^{4}/A | |
Faraday efficiency coefficient | −70.8 | m^{4}°C/A | |
H2 high calorific value | HHV_{H2} | 286 | kJ/mol |
Entropy change | 0.164 | kJ/(K·mol) | |
Reference temperature | T_{ref} | 298.15 | K |
Gas constant | R | 8.314 41 * 10^{−3} | kJ/(K·mol) |
Empirical parameters | 0.951 4 | V | |
Empirical parameters | −0.003 12 | V/K | |
Empirical parameters | −7.4 * 10^{−5} | V·cm^{3}/(K·mol) | |
Empirical parameters | 1.87 * 10^{−4} | V/A/K | |
Water content | 10 | – | |
Film resistivity | – | Ω·cm | |
Battery operating factor | B | 0.016 | – |
Maximum battery current density | 1.5 | A/cm^{2} | |
PEMFC thickness | l | 51 * 10^{−4} | cm |
Membrane effective area | A | 250 | cm^{2} |
Impeding protons through the membrane impedance | R_{c} | 0.000 3 | Ω |
PCS efficiency piecewise linearization coefficient | a (inversion process) | 0.01797 (P/PN = 0.4~1) | – |
0.07134 (P/PN = 0.2~0.4) | |||
0.299 (P/PN = 0.1~0.2) | |||
PCS efficiency piecewise linearization coefficient | a (rectification process) | 0.01592 (P/PN = 0.4~1) | – |
0.06107 (P/PN = 0.2~0.4) | |||
0.2797 (P/PN = 0.1~0.2) | |||
PCS efficiency piecewise linearization coefficient | b (inversion process) | 0.9533 (P/PN = 0.4~1) | – |
0.0.9316 (P/PN = 0.2~0.4) | |||
0.0.8855 (P/PN = 0.1~0.2) | |||
PCS efficiency piecewise linearization coefficient | b (rectification process) | 0.96 (P/PN = 0.4~1) | – |
0.9418 (P/PN = 0.2~0.4) | |||
0.8976 (P/PN = 0.1~0.2) |