Solid oxide electrolytic cell electrolyte thickness optimization method considering current leakage
By optimizing the SOEC electrolyte thickness and combining current leakage and oxygen partial pressure safety models, an optimization algorithm was used to solve the problems of current leakage and oxygen partial pressure safety failure in SOEC, improving hydrogen production efficiency and equipment safety, and forming an efficient optimization framework.
Patent Information
- Application Number
- CN202511705417.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-20
- Publication Date
- 2026-02-24
AI Technical Summary
Existing technologies lack effective solutions to the oxygen partial pressure safety failure problem caused by current leakage and anode-electrolyte interface stratification in solid oxide electrolyzers (SOECs), especially the contradiction between ensuring efficient hydrogen production and interface safety has not been effectively resolved.
By establishing an optimization method for SOEC electrolyte thickness, and combining current leakage model, electrochemical model and optimization algorithm, the electrolyte thickness is optimized to balance current leakage and oxygen partial pressure safety. Nonlinear quadratic programming (SQP) and particle swarm optimization (PSO) algorithms are used to select an appropriate electrolyte thickness to maximize hydrogen production rate and ensure safety.
It achieves a reasonable balance between hydrogen production enhancement and the safety of the oxygen electrode/electrolyte interface under different application scenarios and input power, thereby improving the energy efficiency and hydrogen production performance of SOEC.
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Figure CN121562384A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of hydrogen production equipment design optimization technology, and particularly relates to a method for optimizing the electrolyte thickness of a solid oxide electrolyzer considering current leakage. Background Technology
[0002] As an ideal energy carrier and a promising fuel, hydrogen energy is considered globally as a practical way to effectively alleviate carbon emissions and environmental pollution, providing a significant opportunity to solve major energy crises and achieve sustainable development. To meet the growing demand for hydrogen energy, water electrolysis technology, through environmentally friendly hydrogen production, has become one of the most important sources of green hydrogen energy. Meanwhile, water electrolysis hydrogen production technology is receiving increasing attention in the field of large-scale hydrogen production from renewable energy sources. More details on hydrogen production technologies can be found in the following authoritative research. Compared to the performance characteristics of proton exchange membrane electrolyzers (PEM) and alkaline electrolyzers (AE), solid oxide electrolyzers (SOEC) can achieve high electrochemical reaction rates for hydrogen production with low energy consumption. Furthermore, SOEC can circumvent the high-temperature operating limitations of PEM and alkaline electrolyzers. Therefore, current research focuses on optimizing the system design and operating parameters of SOEC to maximize the utilization of renewable energy.
[0003] Current research on modeling current leakage in solid oxide electrolyzers (SOECs) and the safety failure of oxygen partial pressure caused by anode-electrolyte interface stratification is limited. Considering the randomness and volatility of renewable energy supply, these issues need to be addressed to ensure efficient hydrogen production and the safety of the anode-electrolyte interface. This is because the optimal electrolyte thickness should maximize the hydrogen production rate while ensuring the maximum oxygen partial pressure at the anode-electrolyte interface remains at a desired safe level. Therefore, based on the above mechanism, electrolyte thickness is the most critical decision variable in electrolyte thickness design to resolve the conflict between ensuring the safety of the maximum oxygen partial pressure at the anode-electrolyte interface and efficient hydrogen production. By selecting an appropriate electrolyte layer thickness, the oxygen partial pressure can be reduced to avoid anode-electrolyte interface stratification, and current leakage can be minimized to increase the hydrogen production rate. This is the starting point and core of this invention. Existing research lacks an optimization method that can provide an efficient solution for optimizing the electrolyte in SOEC electrolyzers. Summary of the Invention
[0004] To address the above problems, this invention provides a method for optimizing the electrolyte thickness in a solid oxide electrolyzer, taking into account current leakage.
[0005] The present invention provides a method for optimizing electrolyte thickness in a solid oxide electrolyzer considering current leakage, comprising the following steps:
[0006] Step 1: Geometry modeling of SOEC electrolyzer.
[0007] The solid oxide electrolyzer (SOEC) consists of three components: a porous anode electrode, a porous cathode electrode, and a dense ceramic electrolyte. Vapor is introduced into the porous cathode; the generated hydrogen is collected from the cathode channel, and the oxygen formed at the anode is collected from the anode channel. The gas inlet and outlet are located at the corners of the gas channels.
[0008] Step 2: Modeling the leakage current of the SOEC electrolyzer.
[0009] Step 2.1: SOEC current leakage principle.
[0010] The electrolyte material in SOEC is a hybrid conductor that, in addition to conducting oxygen ions, also conducts electrons and holes. It has a certain electrical conductivity; at the anode-electrolyte interface, there is a stable oxygen lattice. Activated under the action of electrolysis voltage, oxygen vacancies are generated. Oxygen and electrons are generated; then, under high oxygen partial pressure, oxygen molecules combine with oxygen vacancies in the electrolyte to reform an oxygen lattice and generate electron holes; next, electron holes diffuse from the anode electrode to the cathode electrode through the electrolyte; at the same time, electrons flow from the anode to the cathode through an external circuit driven by the potential difference; finally, at the cathode-electrolyte interface, electron holes recombine with electrons, and the portion of electrons that have combined with electron holes forms a leakage current.
[0011] Step 2.2: Describe the motion of charged matter in SOEC electrolyte based on the Nernst-Planck equation, including particles. The general transport equation is expressed as:
[0012] (1)
[0013] in, For particles conductivity, For current density, Valence, For electrochemical potential, It is Faraday's constant. It represents a change in chemical potential.
[0014] Step 2.3: The general transport equation for oxygen ions and electron-hole pairs, calculated according to equation (1), is expressed as follows:
[0015] (2)
[0016] in, and These represent the ion current density and the leakage current density, respectively. Let be the total current density flowing in the external circuit, and let them satisfy the following relationship with the total input current density:
[0017] (3)
[0018] For electrochemical reactions , as well as Based on the local equilibrium condition, the following calculations are performed:
[0019] (4)
[0020] (5)
[0021] in, and These are the chemical potential and the electrochemical potential, respectively.
[0022] Step 2.4: Based on and Further calculations were performed to determine the relationship between chemical potential and electrochemical potential, and between electrical potential. Let be the total current density flowing in the external circuit; they satisfy the following relationship with the total input current density:
[0023] (6)
[0024] (7)
[0025] in, For electric potential, The gas constant is For temperature, This refers to the local oxygen partial pressure.
[0026] Step 2.5: Based on formulas (6) and (7), further calculate the ion current density. With leakage current density :
[0027] (8)
[0028] (9)
[0029] Step 2.6: Based on formulas (8) and (9), further calculate the ion current density. With leakage current density And the relationship between oxygen partial pressure and conductivity:
[0030] (10)
[0031] in, The conductivity of electrons and holes is expressed as:
[0032] (11)
[0033] in, For the former exponential factor, To activate energy. It is the Boltzmann constant (1.380649 × 10⁻²³ J / K).
[0034] Step 2.7: Based on formulas (10) and (11), the ion current density along the electrolyte thickness direction is further calculated by integration. With leakage current density And the relationship between oxygen partial pressure and conductivity:
[0035] (12)
[0036] Then, the two sides are integrated along the electrolyte thickness direction:
[0037] (13)
[0038] in, For electrolyte thickness, and These represent the oxygen partial pressures at the anode-electrolyte interface and the cathode-electrolyte interface, respectively.
[0039] Step 2.8: Leakage current model construction.
[0040] Based on formula (13), a numerical model is established for the leakage current based on the transport mechanism of electrons and oxygen vacancies in the electrolyte; the leakage current density along the electrolyte thickness direction is expressed as follows. expression:
[0041] (14)
[0042] in, For the former exponential factor, and These represent the oxygen partial pressures at the anode-electrolyte interface and the cathode-electrolyte interface, respectively. Furthermore...
[0043] (15)
[0044] Step 3: SOEC electrochemical modeling.
[0045] Step 3.1: Based on electrochemical theory and charge conservation, an electrochemical model is used to predict the operating potential required for SOEC during operation:
[0046] (16)
[0047] in, , , and These represent the equilibrium voltage, activation overpotential, concentration overpotential, and ohmic overpotential, respectively.
[0048] Step 3.2: Ohmic overpotential With electrolyte thickness Related, defined as:
[0049] (17)
[0050] in, For the electrolyte surface area, The conductivity is the oxygen ion conductivity.
[0051] Step 3.3: Optimize the target hydrogen production rate model.
[0052] The expression for hydrogen production rate is defined as follows:
[0053] (18)
[0054] Step 3.4: Define the relationship between external current density and input power, corresponding to the input power. external current density Represented as:
[0055] (19)
[0056] Step 4: Construction of the oxygen partial pressure safety model.
[0057] Step 4.1: The oxygen partial pressure is highest at the anode-electrolyte interface, expressed as:
[0058] (20)
[0059] in, This represents the oxygen pressure at the anode. The chemical potential of oxygen at the anode; This represents the chemical potential of oxygen at the anode / electrolyte interface.
[0060] Step 4.2: Chemical potential of oxygen at the anode / electrolyte interface for The function is calculated by the following formula:
[0061] (twenty one)
[0062] Where r represents the polarization resistance of oxygen ions or electrons at the anode or cathode.
[0063] Step 4.3: To prevent stratification between the anode electrode and the electrolyte, the maximum oxygen partial pressure must meet the following requirements:
[0064] (twenty two)
[0065] in, This indicates the safe threshold for oxygen partial pressure.
[0066] Step 5: Mathematical modeling of the electrolyte thickness optimization problem for solid oxide electrolyzers, considering current leakage and oxygen partial pressure inside the oxygen electrode / electrolyte interface.
[0067] External current density With electrolyte thickness Inversely proportional to the total current, reducing the electrolyte thickness helps increase the hydrogen production rate; at the same time, a balance needs to be struck between leakage current and total current to select an appropriate electrolyte thickness. .
[0068] Based on different working conditions, the optimization objectives are divided into the following two cases:
[0069] (1) Input power Maximizing hydrogen production while keeping the yield constant:
[0070] (twenty three)
[0071] (2) Input power Maximizing hydrogen yield over time:
[0072] set up Numbering the sampling points on the discrete time axis. This represents the total number of sampling points; in electrolysis mode, The optimization problem is expressed as:
[0073] (twenty four)
[0074] in, and They represent the first time. Each sampling time and corresponding input power The hydrogen generation rate and oxygen partial pressure threshold under these conditions; The sampling interval represents the time difference between adjacent sampling points, i.e. ; This represents the total hydrogen production over the entire time series.
[0075] Step 6: Based on the SOEC electrochemical model and the oxygen partial pressure safety model, combined with the nonlinear quadratic programming (SQP) and particle swarm optimization (PSO) algorithms, solve the optimization problem to obtain the optimal electrolyte thickness and the optimal hydrogen production rate of the electrolyzer.
[0076] For stable grid constant power input, the nonlinear quadratic programming SQP optimization algorithm is used to select from low to high power points for verification, and the optimal electrolyte thickness combination is given when the power input is from low to high. At the same time, for variable power renewable photovoltaic power input, the optimal energy efficiency for the whole year is obtained with the annual photovoltaic input of six typical regions in China, and the optimal electrolyte thickness combination obtained by PSO search is verified to ensure that the result achieves the optimal energy efficiency of SOEC under the premise of satisfying stress safety constraints.
[0077] The beneficial technical effects of this invention are as follows:
[0078] This invention uses the safety of the oxygen partial pressure within the oxygen electrode / electrolyte interface of an SOEC as a constraint, and the hydrogen production rate of the SOEC as the objective function. An optimization algorithm is employed to determine the optimal electrolyte thickness under different application scenarios and input power conditions. Validation of the WYSIWYG model and optimization results demonstrates that this method can reasonably balance the improvement of hydrogen production while ensuring the safety of the oxygen electrode and electrolyte, indicating that the optimization results of this framework have promising engineering application prospects. Attached Figure Description
[0079] Figure 1 This is a diagram illustrating the current leakage mechanism in an SOEC solid oxide electrolyzer.
[0080] Figure 2 This is a diagram for verifying the electrochemical model of an SOEC solid oxide electrolyzer.
[0081] Figure 3 The figure shows the influence of leakage current density, total current density, hydrogen production, and oxygen partial pressure safety constraints on the anode side of SOEC under different YSZ electrolyte thicknesses at a power of 200W.
[0082] Figure 4 The figure shows the influence of leakage current density, total current density, hydrogen production, and oxygen partial pressure safety constraints on the anode side of SOEC under different YSZ electrolyte thicknesses at a power of 600W.
[0083] Figure 5 The figure shows the influence of leakage current density, total current density, hydrogen production, and oxygen partial pressure safety constraints on the anode side of SOEC under different GDC electrolyte thicknesses at a power of 200W.
[0084] Figure 6 The figure shows the influence of leakage current density, total current density, hydrogen production, and oxygen partial pressure safety constraints on the anode side of SOEC under different GDC electrolyte thicknesses at 600W power.
[0085] Figure 7The figure shows the influence of leakage current density, total current density, hydrogen production, and oxygen partial pressure safety constraints on the anode side of SOEC under different ESB electrolyte thicknesses at a power of 200W.
[0086] Figure 8 The figure shows the influence of leakage current density, total current density, hydrogen production, and oxygen partial pressure safety constraints on the anode side of SOEC under different ESB electrolyte thicknesses at 600W power.
[0087] Figure 9 The optimization results of electrolytes YSZ, GDC, and ESB under different constant power densities, as well as the optimal hydrogen production rate after optimization, are shown in the figure.
[0088] Figure 10 The optimal values for YSZ electrolyte thickness and annual optimal hydrogen production are shown in the diagrams for different regions.
[0089] Figure 11 The graph shows the optimal GDC electrolyte thickness and the optimal annual hydrogen production in different regions.
[0090] Figure 12 The diagram shows the optimal ESB electrolyte thickness and the optimal annual hydrogen production in different regions.
[0091] Figure 13 A comparison chart showing the optimal hydrogen production of the best YSZ, GDC, and ESB electrolytes in different regions. Detailed Implementation
[0092] The present invention will be further described in detail below with reference to the accompanying drawings and specific implementation methods.
[0093] Based on the optimal electrolyte thickness, current leakage can be reduced, but the maximum oxygen partial pressure required at the anode-electrolyte interface should be maintained while maximizing hydrogen production. Therefore, electrolyte thickness is the core variable for resolving the design contradiction—ensuring both maximum oxygen partial pressure safety and efficient hydrogen production. By selecting an appropriate electrolyte layer thickness to reduce oxygen partial pressure, both anode-electrolyte interface stripping can be avoided, and current leakage can be minimized, thereby increasing the hydrogen production rate. This invention not only optimizes the current leakage model but also introduces an oxygen partial pressure safety model. From a safety perspective, this model solves the contradiction that increasing the electrolyte layer thickness leads to a decrease in hydrogen production rate, while thinning it leads to anode-electrolyte interface stripping and high oxygen partial pressure. Specifically, it includes: (1) Based on the current leakage phenomenon inside the electrolyte layer, an updated theoretical leakage current model applicable to SOEC containing electrolyte is proposed, the analytical expression of leakage current corresponding to the SOEC electrolyte thickness is derived, and the safety constraint condition of maximum oxygen partial pressure at the SOEC anode-electrolyte interface is established. (2) To achieve efficient hydrogen production, this invention specifically addresses the aforementioned contradictions by implementing two optimizations: First, based on oxygen partial pressure safety requirements, the electrolyte thickness is optimized to simultaneously ensure leakage current control and efficient hydrogen production. Second, considering the randomness and volatility of renewable energy supply in practical applications, this invention proposes a comprehensive solution: prioritizing hydrogen production rate while using maximum oxygen partial pressure as a safety constraint. Furthermore, optimization designs were implemented for both constant and variable input power conditions, and the performance of the YSZ / GDC / ESB electrolyte material was compared. The results show that using the optimal electrolyte thickness significantly improves hydrogen production efficiency, outperforming empirical values. This optimization method, by optimizing electrolyte design and selecting a reasonable thickness, effectively improves the hydrogen production rate and yield in engineering applications, providing important guidance for advancing the development of solid oxygen electrolyzer technology.
[0094] This invention discloses a method for optimizing electrolyte thickness in a solid oxide electrolyzer (SOEC) considering current leakage. It combines an SOEC electrochemical model, an SOEC current leakage model, and an optimization algorithm. By analyzing the impact of electrolyte thickness on hydrogen production rate and current leakage, it optimizes operating parameters under stable input power (grid input) and variable power (renewable energy power input), thereby improving the energy efficiency of the electrolyzer. This forms a highly efficient optimization framework that considers stress failure safety, enhancing SOEC energy efficiency and hydrogen production performance. Specifically, it includes the following steps:
[0095] Step 1: Geometry modeling of SOEC electrolyzer.
[0096] The solid oxide electrolyzer (SOEC) consists of three components: a porous anode electrode, a porous cathode electrode, and a dense ceramic electrolyte. Vapor is introduced into the porous cathode; the generated hydrogen is collected from the cathode channel, and the oxygen formed at the anode is collected from the anode channel. The gas inlet and outlet are located at the corners of the gas channels.
[0097] First, the working principle and planar structure of SOEC are as follows: Figure 1 As shown. When an input power is applied to the SOEC via an external circuit, the high-temperature steam / hydrogen mixture (600–1000) ◦ C) It enters the SOEC through the gas channel and diffuses through the porous cathode electrode layer. The electrolyte material of the SOEC is usually a hybrid conductor that, in addition to conducting oxygen ions, also conducts electrons and holes (…). It has a certain electrical conductivity. At the anode-electrolyte interface, a stable oxygen lattice ( ) are activated under the action of electrolysis voltage, generating oxygen vacancies ( Oxygen and electrons are initially generated in the electrolyte. Oxygen molecules, under high oxygen partial pressure, combine with oxygen vacancies in the electrolyte to reform the oxygen lattice and generate electron holes. These electron holes then diffuse from the anode electrode through the electrolyte to the cathode electrode; simultaneously, electrons flow from the anode to the cathode through an external circuit driven by the potential difference. Finally, at the cathode-electrolyte interface, electron holes recombine with electrons. These electrons, combined with electron holes, form a leakage current. The complete current leakage mechanism of SOEC water electrolysis can be described as follows:
[0098] RI:
[0099]
[0100] RII:
[0101]
[0102] RIII:
[0103]
[0104] Step 2: Modeling the leakage current of the SOEC electrolyzer.
[0105] Step 2.1: Describe the motion of charged substances in SOEC electrolyte based on the Nernst-Planck equation, including particles. The general transport equation is expressed as:
[0106] (1)
[0107] in, For particles conductivity, For current density, Valence, is Faraday's constant.
[0108] Step 2.2: The general transport equation for oxygen ions and electron-hole pairs, calculated according to equation (1), is expressed as follows:
[0109] (2)
[0110] in, and These represent the ion current density and the leakage current density, respectively. Let be the total current density flowing in the external circuit, and let them satisfy the following relationship with the total input current density:
[0111] (3)
[0112] For electrochemical reactions , as well as Based on the local equilibrium condition, the following calculations are performed:
[0113] (4)
[0114] (5)
[0115] in, and These are the chemical potential and the electrochemical potential, respectively.
[0116] Step 2.3: Based on and Further calculations were performed to determine the relationship between chemical potential and electrochemical potential, and between electrical potential. Let be the total current density flowing in the external circuit; they satisfy the following relationship with the total input current density:
[0117] (6)
[0118] (7)
[0119] in, For electric potential, The gas constant is For temperature, This refers to the local oxygen partial pressure.
[0120] Step 2.4: Based on formulas (6) and (7), further calculate the ion current density. With leakage current density :
[0121] (8)
[0122] (9)
[0123] Step 2.5: Based on formulas (8) and (9), further calculate the ion current density. With leakage current density And the relationship between oxygen partial pressure and conductivity:
[0124] (10)
[0125] in, The conductivity of electrons and holes is expressed as:
[0126] (11)
[0127] in, For the former exponential factor, To activate energy.
[0128] Step 2.6: Based on formulas (10) and (11), the ion current density along the electrolyte thickness direction is further calculated by integration. With leakage current density And the relationship between oxygen partial pressure and conductivity:
[0129] (12)
[0130] Then, the two sides are integrated along the electrolyte thickness direction:
[0131] (13)
[0132] in, For electrolyte thickness, and These represent the oxygen partial pressures at the anode-electrolyte interface and the cathode-electrolyte interface, respectively.
[0133] Step 2.7: Leakage current model construction.
[0134] Based on formula (13), a numerical model is established for the leakage current based on the transport mechanism of electrons and oxygen vacancies in the electrolyte; the leakage current density along the electrolyte thickness direction is expressed as follows. expression:
[0135] (14)
[0136] in, For the former exponential factor, and These represent the oxygen partial pressures at the anode-electrolyte interface and the cathode-electrolyte interface, respectively. Furthermore,
[0137] (15)
[0138] Step 3: SOEC electrochemical modeling.
[0139] Step 3.1: Based on electrochemical theory and charge conservation, an electrochemical model is used to predict the operating potential required for SOEC during operation:
[0140] (16)
[0141] in, , , and These represent the equilibrium voltage, activation overpotential, concentration overpotential, and ohmic overpotential, respectively.
[0142] Step 3.2: Ohmic overpotential With electrolyte thickness Related, defined as:
[0143] (17)
[0144] in, For the electrolyte surface area, The conductivity is the oxygen ion conductivity.
[0145] Step 3.3: Optimize the target hydrogen production rate model.
[0146] The expression for hydrogen production rate is defined as follows:
[0147] (18)
[0148] Step 3.4: Define the relationship between external current density and input power, corresponding to the input power. external current density Represented as:
[0149] (19)
[0150] Step 4: Construction of the oxygen partial pressure safety model.
[0151] Step 4.1: The oxygen partial pressure is highest at the anode-electrolyte interface, expressed as:
[0152] (20)
[0153] in, This represents the oxygen pressure at the anode. The chemical potential of oxygen at the anode; This represents the chemical potential of oxygen at the anode / electrolyte interface.
[0154] Step 4.2: Chemical potential of oxygen at the anode / electrolyte interface for The function is calculated by the following formula:
[0155] (twenty one)
[0156] Where r represents the polarization resistance of oxygen ions or electrons at the anode or cathode.
[0157] Step 4.3: To prevent stratification between the anode electrode and the electrolyte, the maximum oxygen partial pressure must meet the following requirements:
[0158] (twenty two)
[0159] in, This indicates the safe threshold for oxygen partial pressure.
[0160] Step 5: Mathematical modeling of the electrolyte thickness optimization problem for solid oxide electrolyzers, considering current leakage and oxygen partial pressure inside the oxygen electrode / electrolyte interface.
[0161] External current density With electrolyte thickness Inversely proportional to the electrolyte thickness, reducing the electrolyte thickness helps increase the hydrogen production rate. However, when the electrolyte thickness approaches zero, the leakage current... The leakage current will tend towards infinity. Therefore, increasing hydrogen production by infinitely reducing the electrolyte thickness is impractical. Furthermore, the leakage current does not change monotonically with thickness. Therefore, a balance needs to be struck between the leakage current and the total current to select an appropriate electrolyte thickness. .
[0162] Based on different working conditions, the optimization objectives are divided into the following two cases:
[0163] (1) Input power Maximizing hydrogen production while keeping the yield constant:
[0164] (twenty three)
[0165] (2) Input power Maximizing hydrogen yield over time:
[0166] set up Numbering the sampling points on the discrete time axis. This represents the total number of sampling points; in electrolysis mode, The optimization problem is expressed as:
[0167] (twenty four)
[0168] in, and They represent the first time. Each sampling time and corresponding input power The hydrogen generation rate and oxygen partial pressure threshold under these conditions; The sampling interval represents the time difference between adjacent sampling points, i.e. ; This represents the total hydrogen production over the entire time series.
[0169] Step 6: Based on the SOEC electrochemical model and the oxygen partial pressure safety model, combined with the nonlinear quadratic programming (SQP) and particle swarm optimization (PSO) algorithms, solve the optimization problem to obtain the optimal electrolyte thickness and the optimal hydrogen production rate of the electrolyzer.
[0170] For stable grid constant power input, the nonlinear quadratic programming SQP optimization algorithm is used to select from low to high power points for verification, and the optimal electrolyte thickness combination is given when the power input is from low to high. At the same time, for variable power renewable photovoltaic power input, the optimal energy efficiency for the whole year is obtained with the annual photovoltaic input of six typical regions in China, and the optimal electrolyte thickness combination obtained by PSO search is verified to ensure that the result achieves the optimal energy efficiency of SOEC under the premise of satisfying stress safety constraints.
[0171] Example:
[0172] Based on the electrochemical theory of SOEC, the calculation steps are as follows:
[0173] Based on steps 1 and 2: constructing a mathematical model of leakage current according to the SOEC current leakage mechanism. And step 3: building an electrochemical model of SOEC: predicting the operating potential required for SOEC operation and building a model of hydrogen production rate of the electrolyzer.
[0174] The polarization curves obtained based on the established SOEC model were compared with experimental data at temperatures of 900℃, 950℃, and 1000℃. Figure 2 As shown, the model results agree well with the experimental data. The high degree of agreement between the model predictions and the experimental results confirms that the theoretical model established in this study has high accuracy and effectively verifies its ability to characterize SOEC behavior.
[0175] Consider using respectively , and The impact of using it as an electrolyte on leakage current density, total current density, hydrogen production, and oxygen partial pressure safety constraints in SOEC electrolyzers. Specifically, this includes:
[0176] Figure 3 and Figure 4The study demonstrates the effects of leakage current density, total current density, hydrogen production, and oxygen partial pressure safety constraints on the anode side of SOEC at power levels of 200 W and 600 W under different YSZ electrolyte thicknesses.
[0177] Figure 5 and Figure 6 The study demonstrates the effects of leakage current density, total current density, hydrogen production, and oxygen partial pressure safety constraints on the anode side of SOEC at power levels of 200 W and 600 W under different GDC electrolyte thicknesses.
[0178] Figure 7 and Figure 8 The study demonstrates the effects of leakage current density, total current density, hydrogen production, and oxygen partial pressure safety constraints on the anode side of SOEC at power levels of 200 W and 600 W under different ESB electrolyte thicknesses.
[0179] Meanwhile, for different constant power input scenarios of the power grid, the optimization framework and joint optimization algorithm are used to solve for the maximum hydrogen yield and the optimal electrolyte. Figure 9 The results show the maximum hydrogen yield and optimal electrolyte under a constant power input grid scenario.
[0180] Finally, for the variable power input scenario based on photovoltaic renewable energy, the optimal hydrogen yield and the optimal electrolyte are obtained by solving the joint optimization algorithm based on the optimization framework. Figure 10-13 The results show the maximum hydrogen production and optimal electrolyte for three electrolytes—YSZ, GDC, and ESB—under variable power input scenarios based on photovoltaic renewable energy.
[0181] This invention presents a method for optimizing electrolyte thickness in solid oxide electrolyzers (SOECs) considering current leakage and oxygen partial pressure at the oxygen electrode / electrolyte interface. The aim is to maximize hydrogen production rate, ensure safe operation, and prevent stratification caused by high oxygen partial pressure. The current leakage mechanism and the mechanism by which oxygen partial pressure leads to electrolyte crack propagation and even stratification in SOECs are analyzed in detail. Based on two application scenarios—constant input power and photovoltaic power conversion input—a leakage current model, an electrochemical model, and a maximum oxygen partial pressure safety constraint model at the oxygen electrode / electrolyte interface are introduced. Results show that the optimal electrolyte thickness for different materials and the maximum hydrogen production rate of SOECs are optimized using the SQP and PSO algorithms, respectively. This invention provides an important optimization strategy for balancing hydrogen production efficiency with electrolyte current leakage and stratification cracking. The results not only improve the rational design and optimization of SOEC electrolytes but also provide theoretical and practical guidance for subsequent academic research and engineering applications. Future work can further optimize electrolyte material selection and electrolyte thickness based on this method to further improve hydrogen production efficiency. Furthermore, by precisely adjusting the electrolyte thickness and electrode design to alleviate stress caused by oxygen partial pressure, the stability and lifespan of the device can be significantly enhanced. Further research into YSZ / GDC bilayer structures or multilayer electrolyte designs is a promising approach, simultaneously utilizing the electron blocking properties of YSZ and the high ionic conductivity of GDC to reduce interfacial stress and improve overall efficiency. However, it is important to consider that while balanced bilayer electrolytes reduce current leakage, they also significantly increase the ohmic resistance of the battery, and the relative complexity of the fabrication technology leads to increased costs. Additionally, further research is needed on methods to effectively prevent internal short circuits by doping cerium-based electrolyte materials with elements such as Pr, thereby reducing their electronic conductivity. These strategies provide pathways for optimizing SOEC performance under different environmental conditions.
Claims
1. A method for optimizing electrolyte thickness in a solid oxide electrolyzer considering current leakage, characterized in that, Includes the following steps: Step 1: Geometry modeling of SOEC electrolyzer; The solid oxide electrolyzer (SOEC) consists of three components: a porous anode electrode, a porous cathode electrode, and a dense ceramic electrolyte. Vapor is introduced into the porous cathode; the generated hydrogen is collected from the cathode channel, and the oxygen formed at the anode is collected from the anode channel. The gas inlet and outlet are located at the corners of the gas channels. Step 2: Modeling the leakage current of the SOEC electrolyzer; Step 2.1: SOEC current leakage principle: The electrolyte material in SOEC is a hybrid conductor that, in addition to conducting oxygen ions, also conducts electrons and holes. It has a certain electrical conductivity; at the anode-electrolyte interface, there is a stable oxygen lattice. Activated under the action of electrolysis voltage, oxygen vacancies are generated. Oxygen and electrons are generated; then, under high oxygen partial pressure, oxygen molecules combine with oxygen vacancies in the electrolyte to reform an oxygen lattice and generate electron holes; next, electron holes diffuse from the anode electrode to the cathode electrode through the electrolyte; at the same time, electrons flow from the anode to the cathode through an external circuit driven by the potential difference; finally, at the cathode-electrolyte interface, electron holes recombine with electrons, and the portion of electrons that have combined with electron holes forms a leakage current. Step 2.2: Describe the motion of charged matter in SOEC electrolyte based on the Nernst-Planck equation, including particle motion. The general transport equation is expressed as: （1） in, For particles conductivity, For current density, Valence, For electrochemical potential, It is Faraday's constant. Indicates a change in chemical potential; Step 2.3: The general transport equation for oxygen ions and electron-hole pairs, calculated according to equation (1), is expressed as follows: （2） in, and These represent the ion current density and the leakage current density, respectively. Let be the total current density flowing in the external circuit, and let them satisfy the following relationship with the total input current density: （3） For electrochemical reactions , as well as Based on the local equilibrium condition, the following calculations are performed: （4） （5） in, and These are the chemical potential and the electrochemical potential, respectively. Step 2.4: Based on and Further calculations were performed to determine the relationship between chemical potential and electrochemical potential, and between electrical potential. Let be the total current density flowing in the external circuit; they satisfy the following relationship with the total input current density: （6） （7） in, For electric potential, The gas constant is... For temperature, This refers to the local oxygen partial pressure. Step 2.5: Based on formulas (6) and (7), further calculate the ion current density. With leakage current density : （8） （9） Step 2.6: Based on formulas (8) and (9), further calculate the ion current density. With leakage current density And the relationship between oxygen partial pressure and conductivity: （10） in, The conductivity of electrons and holes is expressed as: （11） in, For the former exponential factor, To activate energy; Boltzmann's constant; Step 2.7: Based on formulas (10) and (11), the ion current density along the electrolyte thickness direction is further calculated by integration. With leakage current density And the relationship between oxygen partial pressure and conductivity: （12） Then, the two sides are integrated along the electrolyte thickness direction: （13） in, For electrolyte thickness, and These are the oxygen partial pressures at the anode-electrolyte interface and the cathode-electrolyte interface, respectively. Step 2.8: Leakage current model construction; Based on formula (13), a numerical model is established for the leakage current based on the transport mechanism of electrons and oxygen vacancies in the electrolyte; the leakage current density along the electrolyte thickness direction is expressed as follows. expression: （14） in, For the former exponential factor, and These are the oxygen partial pressures at the anode-electrolyte interface and the cathode-electrolyte interface, respectively; furthermore... （15） Step 3: SOEC electrochemical modeling; Step 3.1: Based on electrochemical theory and charge conservation, an electrochemical model is used to predict the operating potential required for SOEC during operation: （16） in, , , and These represent the equilibrium voltage, activation overpotential, concentration overpotential, and ohmic overpotential, respectively. Step 3.2: Ohmic overpotential With electrolyte thickness Related, defined as: （17） in, For the electrolyte surface area, The conductivity of oxygen ions; Step 3.3: Optimize the target hydrogen production rate model; The expression for hydrogen production rate is defined as follows: （18） Step 3.4: Define the relationship between external current density and input power, corresponding to the input power. external current density Represented as: （19） Step 4: Construction of the oxygen partial pressure safety model; Step 4.1: The oxygen partial pressure is highest at the anode-electrolyte interface, expressed as: （20） in, This represents the oxygen pressure at the anode. The chemical potential of oxygen at the anode; The chemical potential of oxygen at the anode / electrolyte interface; Step 4.2: Chemical potential of oxygen at the anode / electrolyte interface for The function is calculated by the following formula: （21） Where r represents the polarization resistance of oxygen ions or electrons at the anode or cathode; Step 4.3: To prevent stratification between the anode electrode and the electrolyte, the maximum oxygen partial pressure must meet the following requirements: （22） in, This indicates the safe threshold for oxygen partial pressure; Step 5: Mathematical modeling of the electrolyte thickness optimization problem for solid oxide electrolyzers, considering current leakage and oxygen partial pressure inside the oxygen electrode / electrolyte interface; External current density With electrolyte thickness Inversely proportional to the total current, reducing the electrolyte thickness helps increase the hydrogen production rate; at the same time, a balance needs to be struck between leakage current and total current to select an appropriate electrolyte thickness. ; Based on different working conditions, the optimization objectives are divided into the following two cases: (1) Input power Maximizing hydrogen production while keeping the yield constant: （23） (2) Input power Maximizing hydrogen yield over time: set up Numbering the sampling points on the discrete time axis. This represents the total number of sampling points; in electrolysis mode, The optimization problem is expressed as: （24） in, and They represent the first time. Each sampling time and corresponding input power The hydrogen generation rate and oxygen partial pressure threshold under these conditions; The sampling interval represents the time difference between adjacent sampling points, i.e. ; This represents the total hydrogen production over the entire time series. Step 6: Based on the SOEC electrochemical model and the oxygen partial pressure safety model, combined with the nonlinear quadratic programming (SQP) and particle swarm optimization (PSO) algorithms, solve the optimization problem to obtain the optimal electrolyte thickness and the optimal hydrogen production rate of the electrolyzer. For stable grid constant power input, the nonlinear quadratic programming SQP optimization algorithm is used to select from low to high power points for verification, and the optimal electrolyte thickness combination is given when the power input is from low to high. At the same time, for variable power renewable photovoltaic power input, the optimal energy efficiency for the whole year is obtained with the annual photovoltaic input of six typical regions in China, and the optimal electrolyte thickness obtained by PSO search is verified to ensure that the result achieves the optimal energy efficiency of SOEC under the premise of satisfying stress safety constraints.