PEM electrolyzed water equivalent voltage model and modeling method

Abstract

According to the PEM water electrolysis equivalent voltage model and the modeling method, according to electrochemical properties and circuit properties, the total voltage obtained when a PEM electrolytic cell is connected to a power supply is divided into a theoretical voltage threshold value, an ohmic voltage and an electrochemical polarization voltage which can be spontaneously carried out in an electrolytic reaction, and modeling is carried out respectively; constructing an open-circuit reversible voltage during theoretical voltage threshold modeling which can be spontaneously performed based on an electrolytic reaction; when modeling based on ohmic voltage, constructing a proton membrane ohmic resistor based on the proton membrane key parameters; when modeling is carried out based on electrochemical polarization voltage, modeling is carried out based on various key parameters of the proton membrane, a chaos theory algorithm related formula is fused, and the voltage of the PEM electrolyzed water electrolytic tank under the actual working condition is constructed; modeling is carried out based on various key parameters of the proton membrane, the voltage of the PEM electrolyzed water electrolytic cell under the actual working condition is constructed by integrating a chaos theory related algorithm, and the external voltage characteristics of the electrolytic cell under the actual condition can be reflected.

Description

Technical Field

[0001] The invention relates to the technical field of computer models and water electrolysis, in particular to a PEM water electrolysis equivalent voltage model and a modeling method. Background Art

[0002] At a time when global energy shortages and climate change issues are becoming increasingly urgent, exploring and developing clean renewable energy has become an important issue that human society needs to solve urgently. In recent years, with the strong promotion of a series of incentive policies issued by the state, hydrogen energy, a type of renewable energy with huge potential, has ushered in an opportunity for rapid development. Their vigorous rise has provided solid and strong support for my country to achieve a diversified energy structure.

[0003] PEM water electrolysis hydrogen production technology realizes water electrolysis reaction through proton exchange membrane (PEM), with advantages such as fast response speed (start and stop in seconds) and high hydrogen purity (≥99.999%), and is the mainstream direction of green hydrogen production in the future. The current important research direction is to build a comprehensive, accurate, easy to understand and use PEM electrolyzer model, which can more accurately reflect the properties of the electrolyzer under the complex actual working conditions of large-scale grid connection in the future.

[0004] Therefore, establishing a complete and effective PEM electrolyzer model that comprehensively considers multiple factors is of great significance for future research on new power systems, solving the problem of the impact of multiple electrolyzers on the power grid when connected to the grid, and verifying the effectiveness of control strategies.

[0005] Under different working conditions, such as different current density, temperature, pressure, etc., the performance and internal process of the PEM water electrolysis system will change dynamically. The parameters of the existing equivalent circuit model are usually regarded as constants, which makes it difficult to accurately reflect the dynamic changes of these parameters with working conditions, resulting in large errors in simulating the dynamic behavior of the PEM water electrolysis system. In addition, there is no direct connection with the actual device data of the actual process parameters such as the ion exchange capacity, water absorption rate, swelling rate, etc. of the proton membrane, and the current electrolyzer situation cannot be predicted by the changes in the process parameters, which breaks the relationship between the PEM water electrolysis electrolyzer modeling and the actual process parameters. More importantly, the proton membrane is usually simplified when constructing the PEM electrolyzer model, ignoring the complex characteristics of the membrane: the proton exchange membrane is a key component of the PEM water electrolysis system, and its performance has an important influence on the electrolysis efficiency and stability. The existing equivalent circuit model usually simplifies the role of the membrane into a resistor, ignoring the complex characteristics such as the capacitance characteristics of the membrane, the nonlinear behavior of proton transport, and the interaction between the membrane and the electrode, and cannot fully and accurately describe the influence of the membrane in the PEM water electrolysis system. When studying the nonlinearity of PEM water electrolysis cells and their changes under complex working conditions, they are usually simplified through simple assumptions, and fail to take into account the complex factors in the actual electrolysis process. Summary of the Invention

[0006] The present invention proposes a PEM electrolyzed water equivalent voltage model and a modeling method, which are modeled based on the key parameters of the proton exchange membrane, and incorporate relevant algorithms of chaos theory to construct the voltage of the PEM electrolyzed water electrolyzer under actual working conditions, and can reflect the external voltage characteristics of the electrolyzer under real conditions.

[0007] The present invention adopts the following technical solutions.

[0008] A modeling method for the PEM electrolyzed water equivalent voltage model. The method establishes a PEM electrolyzer model for simulation according to the electrochemical properties and circuit properties of the PEM electrolyzer when electrolyzing water. The total voltage divided when the PEM electrolyzer model is connected to the power supply is split into the theoretical voltage threshold at which the electrolysis reaction can proceed spontaneously, the ohmic voltage, and the electrochemical polarization voltage. The simulation equivalent voltage models for the above three voltages are respectively established; when modeling based on the theoretical voltage threshold at which the electrolysis reaction can proceed spontaneously, an open-circuit reversible voltage is constructed; when modeling based on the ohmic voltage, a proton exchange membrane ohmic resistance is constructed based on the key parameters of the proton exchange membrane; when modeling based on the electrochemical polarization voltage, modeling is carried out based on the key parameters of the proton exchange membrane and relevant formulas of chaos theory algorithms are incorporated to construct the voltage of the PEM electrolyzed water electrolyzer under actual working conditions.

[0009] When modeling based on the theoretical voltage threshold at which the electrolysis reaction can proceed spontaneously, in the established model, the electrolysis reaction is in an equilibrium state and no net current is generated; if the voltage is lower than this value, the reaction cannot proceed; if the voltage is higher than this value, the electrolysis reaction will release current. An open-circuit reversible voltage is constructed in the established model, and the influence of the penetration of hydrogen between the membranes under actual working conditions on the open-circuit reversible voltage is introduced; When modeling based on the ohmic voltage, the model is constructed through the parameters of the proton exchange membrane That is, a local relationship is established according to the actual parameter situation of the PEM proton exchange membrane, and a proton exchange membrane ohmic resistance is constructed based on the key parameters of the proton exchange membrane; Where is the proton exchange membrane conductivity; is the water absorption rate of the proton exchange membrane; is the swelling rate of the proton exchange membrane; is the temperature; is the ion exchange capacity; represents the local voltage, represents the local current, When modeling based on the electrochemical polarization voltage, the model assumes that the electrochemical polarization voltage is caused by the kinetic factors of the electrode reaction. In an electrochemical reaction, reactant particles must obtain sufficient energy to overcome the energy barrier of the reaction, i.e., the activation energy, and the activation energy is closely related to the catalyst. The Logistic mapping in chaos theory is used to reflect the activity decay of the catalyst and the uncertain change of temperature in the actual working conditions, so as to reflect the influence of complex factors on the concentration of active groups. Replace with a time-related chaotic function , rather than a fixed value, so as to dynamically change to affect the reaction energy barrier, and integrate chaos theory to construct a voltage model of the PEM electrolyzer under actual working conditions, which is used to reflect the external voltage characteristics of the electrolyzer in real situations.

[0010] PEM electrolysis equivalent voltage model. The equivalent voltage model is based on the simulated proton membrane parameters in the PEM electrolyzer model and the simulation process of the electrolysis chemical reaction. The simulation components in the PEM electrolyzer model include bipolar plates, porous titanium mesh groups, gas diffusion layers, anode catalyst layers, cathode catalyst layers, and proton exchange membranes; The bipolar plate is used to simulate the conduction of current and the mechanical support structure of the PEM electrolyzer model, and its simulated internal flow channel structure is used for the uniform transportation and distribution of liquid and gas phases; The gas diffusion layer serves as the interface between the electrode and the catalytic layer, and is used to provide a transmission channel for deionized water reactants and hydrogen and oxygen products; The catalyst layer is used to simulate the catalytic part of the core area of the electrochemical reaction in the PEM electrolyzer model, and accelerates the electrochemical reaction process by reducing the reaction activation energy; The proton exchange membrane is used to simulate the proton membrane part in the core components of the PEM electrolyzer model, and is responsible for conducting hydrogen ions generated at the anode to the cathode to construct an internal ion transmission channel; This proton exchange membrane (Proton Exchange Membrane) has the dual functions of a gas isolation layer and a proton conduction medium, and only allows protons to pass through while blocking electron transmission, so as to achieve the ion conduction and gas separation required for the water electrolysis reaction; When constructing a theoretical voltage threshold model based on the spontaneous progress of the electrolysis reaction, in the model established for the PEM electrolyzer, the electrolysis chemical reaction of the PEM electrolyzer is in an equilibrium state, and there is no net current generation at this time. When the voltage is lower than this theoretical voltage threshold, the reaction cannot proceed; while when the voltage is higher than this threshold, the electrolysis reaction will release current; The permeation of hydrogen between the membranes in the actual working conditions will cause a change in the anode oxygen partial pressure, thus affecting the voltage threshold at which the electrolysis reaction can proceed spontaneously. Introduce the influence of the permeation of hydrogen between the membranes in the electrolyzer on the voltage threshold to obtain the open-circuit reversible voltage ; The proton exchange membrane can be equivalently considered to have a resistance property in the PEM electrolytic water chemical reaction, resulting in ohmic losses. And considering the conductivity, water absorption rate, and swelling rate in the proton exchange membrane parameters, the ohmic loss voltage of the proton exchange membrane is constructed. ; The dynamic change of the ion exchange capacity of the proton exchange membrane affects the activation energy of the anode and cathode chemical reactions, thereby affecting the electrochemical polarization voltage. ; The construction of each voltage in the PEM electrolytic water equivalent voltage model is divided into two steps. The first step is to incorporate the key parameters that affect the electrochemical properties of PEM electrolytic water in actual production into the model; the second step is to incorporate the relevant algorithm formulas of chaos theory into the constructed model in the construction of individual voltage components to reflect the determinacy of the electrochemical reaction in the operation process of PEM electrolytic water hydrogen production under actual working conditions and to simulate the uncertainty of the random process in actual production.

[0011] The PEM electrolyzer model, that is, the PEM electrolytic water electrolyzer model, and the single-cell port voltage is represented by the sum of the open-circuit reversible voltage, the ohmic loss voltage of the proton exchange membrane, and the electrochemical polarization voltage; In the PEM electrolytic water electrolyzer model, the single-cell port voltage is: Equation 1; In Equation 1: is the open-circuit reversible voltage; is the ohmic loss voltage of the proton exchange membrane; is the electrode polarization chaos voltage, that is, the electrochemical polarization voltage.

[0012] The derivation method of the open-circuit reversible voltage is as follows: In the electrical model of the electrolyzer, the open-circuit reversible voltage corresponds to the independent voltage source of the equivalent circuit. When the total voltage , other losses such as ohmic losses and electrochemical polarization voltages are only generated when the current flows through. This part of the voltage is obtained from the Nernst equation: Equation 2; In Equation 2: The universal gas constant R ; The Faraday constant F , the open-circuit reversible equilibrium voltage ; It is known from the literature that it is usually taken as 1.23V; T is the temperature; n is the number of electron transfers. In electrolytic water n =2, the water activity , in this model, the influence of impurities in the electrolysis process is ignored in PEM electrolytic water, that is, it is considered that ; respectively represent H 2 andO The gas activity of 2; in actual production, as the electrolytic cell is used, the permeation of gas on both sides of the membrane under real conditions needs to be considered, that is, the back permeation of hydrogen is considered. The back permeation of hydrogen will cause the oxygen partial pressure on the anode side to decrease, thereby affecting the reversible voltage. Therefore, the activity term needs to be corrected, and we get: In Formula 3: is the reference pressure, usually taken as 1 atm; is the oxygen partial pressure; is the energy barrier of the gas permeation reaction; The expression of the open-circuit reversible voltage after correction is: In Formula 4: is the hydrogen partial pressure.

[0013] In the PEM electrolyzed water equivalent voltage model, the proton exchange membrane conductivity is affected by the membrane thickness , water absorption rate , swelling ratio and temperature ; the effective thickness of the membrane increases with the increase of the swelling ratio, and the conductivity increases with the increase of temperature; according to Ohm's law, we get: Formula 5; In Formula 5: is the potential difference between both sides of the proton exchange membrane; is the effective thickness. The membrane thickness of the proton exchange membrane itself is affected by the swelling ratio in the actual electrolyzed water process. The swelling ratio is used as a correction term to obtain the membrane thickness that conforms to the actual working conditions, that is , in order to obtain a more accurate model, where is the correction coefficient of the swelling ratio to the thickness.

[0014] In the PEM electrolyzed water equivalent voltage model, considering the influence of the water absorption rate, that is, considering that the water absorption rate causes the change of the membrane porosity; in the PEM electrolyzed water equivalent voltage model, the moving electrons and protons in the electrolytic cell are regarded as physical particles. Then, based on the existing theory, the change of the membrane porosity will have a linear influence on the transmission of particles. The electrolytic cell equivalent conductivity correction factor is introduced, where is the experimental fitting coefficient; considering the temperature dependence, the conductivity changes with temperature following the Arrhenius relationship: Formula 6. In Formula 6: is the standard conductivity of the proton exchange membrane; is the reaction activation energy; is the Boltzmann constant; For the simplified model, a linear correction factor is directly introduced For the simplified model, the ohmic resistance constructed based on the actual key parameters of the proton membrane is as follows: Formula 7; In Equation 7: is the potential difference across the proton membrane; A is the cross-sectional area of the proton membrane, and the correction coefficient 、 is measured through experimental data, where is the water absorption correction coefficient; is the temperature linear correction coefficient measured through a controlled variable experiment by changing the temperature; the formula for the ohmic voltage is as follows: Formula 8.

[0015] is the current flowing through the proton membrane; In the PEM electrolyzed water equivalent voltage model, the electrochemical polarization chaotic voltage is derived as follows: Assume that the electrode reaction rate is controlled by the activation energy . According to the Arrhenius equation, we have: Formula 9; In Formula 9: is the pre-exponential factor; is the Boltzmann constant ; Assume that the ion exchange capacity IEC in the proton membrane parameters affects the reaction site density, IEC and the dynamic change in the actual situation affects the reaction rate. Then the relationship between the current density and IEC is expressed as: Formula 10; In Formula 10: is the reference ion exchange capacity , F is the Faraday constant ; n is the amount of substance undergoing the reaction, with the unit of mol. The Logistic map in chaos theory is used to describe the nonlinear perturbation under the actual working conditions, and the formula is obtained: Formula 11; In Formula 11: , and the specific value of the critical chaos parameter is related to the actual working conditions; ; The PEM electrolyzed water equivalent voltage model is to more realistically describeIEC The dynamic changes, such as the aging of the membrane and the poisoning of the catalyst in the actual large-scale electrolysis process, which are caused by complex actual factors, will change the concentration of active groups. IEC Replace a parameter constant of a proton membrane with a time-dependent chaotic function IEC(t) , rather than a fixed value; through linear scaling and translation, the chaotic variable is converted into the actual IEC value, and through normalization, we get as follows: Formula 12; In Equation (12): and are the actual physical maximum and minimum values of IEC determined by experiments; is the reference value of the ion exchange capacity; substituting Equation 12 into Equation 10, we get the chaotic current density as follows: Formula 13; In Formula 13: is the chaotic current density, that is, the current density obtained by describing the IEC dynamic changes using chaos theory; and the electrochemical polarization voltage in the electrolyzer is obtained from the Butler-Volmer kinetic equation as: Formula 14; In Formula 14: is the anodic charge transfer coefficient; is the cathodic charge transfer coefficient; is the anodic exchange current density; is the cathodic exchange current density.

[0016] The PEM electrolyzed water equivalent voltage model is a computer model used to simulate the PEM electrolyzed water working conditions. The input quantity of this computer model is ; in the model, is a parameter to be determined. It can be determined by parameter identification algorithms such as the least squares method, genetic algorithm, and particle swarm algorithm. Using the above measured data as input and the simulated electrolyzer voltage as output, the simulated voltage is compared with the measured voltage.

[0017] The present invention proposes a PEM electrolyzed water equivalent voltage model and a modeling method, which belongs to a modeling method of a PEM electrolyzed water equivalent circuit model that considers the key parameters of the proton membrane and integrates the chaos theory for the research of future grid-connected power grids and the actual hydrogen electrolysis process. Based on the electrochemical thermodynamics Nernst equation, the electrochemical kinetics Butler-Volmer equation, and Ohm's law, an actual working condition model of the PEM electrolyzer is constructed. The new model proposed by the present invention fully considers the gas penetration phenomenon inside the electrolyzer under actual working conditions, connects the key process parameters of the proton membrane in the PEM electrolyzed water electrolyzer with the modeling of the PEM electrolyzer, and effectively simulates the dynamic influence of various complex factors on the internal reaction of the electrolyzer in actual production through the cross-integration of chaos dynamics and the electrochemical process, enabling the model to capture the complex law of the electrochemical polarization voltage changing with the working conditions, and is expected to provide a key modeling tool for the dynamic control when the electrolyzer is connected to the grid in the future and the grid stability control. At the same time, it also provides a theoretical guidance basis for engineering practices such as the development of new membrane materials and the optimization of the flow channel structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] The present invention will be further described in detail below in conjunction with the drawings and specific embodiments: FIG Figure 1 is a schematic flow chart of the method of the present invention; FIG Figure 2 is a schematic structural principle diagram of the electrolyzer; FIG Figure 3 is a schematic proton membrane principle diagram of the electrolyzer. SPECIFIC EMBODIMENTS

[0019] As shown in the figure, for the modeling method of the PEM electrolyzed water equivalent voltage model, the method establishes a PEM electrolyzer model for simulation according to the electrochemical properties and circuit properties of the PEM electrolyzer when electrolyzing water, and splits the total voltage obtained when the PEM electrolyzer model is connected to the power supply into the theoretical voltage threshold at which the electrolysis reaction can proceed spontaneously, the Ohm voltage, and the electrochemical polarization voltage, and respectively conducts simulation equivalent voltage model modeling on the above three voltages; when modeling based on the theoretical voltage threshold at which the electrolysis reaction can proceed spontaneously, a break reversible voltage is constructed; when modeling based on the Ohm voltage, a proton membrane Ohm resistance is constructed based on the key parameters of the proton membrane; when modeling based on the electrochemical polarization voltage, modeling is carried out based on the key parameters of the proton membrane and the relevant formulas of the chaos theory algorithm are incorporated to construct the voltage of the PEM electrolyzed water electrolyzer under actual working conditions.

[0020] When modeling based on the theoretical voltage threshold at which the electrolysis reaction can proceed spontaneously, in the established model, the electrolysis reaction is in an equilibrium state and no net current is generated; if the voltage is lower than this value, the reaction cannot proceed; if the voltage is higher than this value, the electrolysis reaction will release current. In the established model, the open-circuit reversible voltage is constructed, and the influence of the hydrogen permeation between the membranes under actual working conditions on the open-circuit reversible voltage is introduced; When modeling based on the Ohmic voltage, the parameters of the proton exchange membrane are used to construct the model, that is, a local relationship is established according to the actual parameter situation of the PEM proton exchange membrane, and the Ohmic resistance of the proton exchange membrane is constructed based on the key parameters of the proton exchange membrane; where is the proton exchange membrane conductivity; is the water absorption rate of the proton exchange membrane; is the swelling rate of the proton exchange membrane; is the temperature; is the ion exchange capacity; represents the local voltage, represents the local current, When modeling based on the electrochemical polarization voltage, the model assumes that the electrochemical polarization voltage is caused by the kinetic factors of the electrode reaction. In the electrochemical reaction, the reactant particles must obtain sufficient energy to overcome the reaction energy barrier, that is, the activation energy, and the activation energy is closely related to the catalyst. The Logistic mapping in chaos theory is used to reflect the activity decay of the catalyst and the uncertain change of temperature in the actual working conditions, so as to reflect the influence of complex factors on the concentration of active groups. Replace with a time-related chaotic function , rather than a fixed value, and use IEC to dynamically change to affect the reaction energy barrier, and integrate chaos theory to construct the voltage model of the PEM electrolyzer under actual working conditions, which is used to reflect the external voltage characteristics of the electrolyzer under real conditions.

[0021] A PEM electrolysis equivalent voltage model, the equivalent voltage model is based on the simulated proton exchange membrane parameters in the PEM electrolyzer model and the electrolysis water chemical reaction simulation process. The simulation components in the PEM electrolyzer model include bipolar plates, porous titanium mesh groups, gas diffusion layers, anode catalyst layers, cathode catalyst layers and proton exchange membranes; The bipolar plates are used to simulate the conduction of the current and the mechanical support structure of the PEM electrolyzer model, and the simulated internal flow channel structure is used for the uniform transportation and distribution of liquid and gas phases; the gas diffusion layer, as the interface connecting the electrode and the catalytic layer, is used to provide a transmission channel for deionized water reactants and hydrogen and oxygen products; The catalyst layer is used to simulate the catalytic part of the core area of the electrochemical reaction in the PEM electrolyzer model, and accelerates the electrochemical reaction process by reducing the reaction activation energy; The proton exchange membrane is used in the proton membrane part of the core components for simulating the PEM electrolyzer model. It is responsible for conducting the hydrogen ions generated at the anode to the cathode and constructing an internal ion transport channel. This proton exchange membrane (Proton Exchange Membrane) has the dual functions of a gas isolation layer and a proton conduction medium, allowing only protons to pass through while blocking electron transport, thus achieving the ion conduction and gas separation required for the water electrolysis reaction. When constructing a theoretical voltage threshold model based on the spontaneous progress of the electrolysis reaction, in the model established for the PEM electrolyzer, the water electrolysis reaction in the PEM electrolyzer is in an equilibrium state, and no net current is generated at this time. When the voltage is lower than this theoretical voltage threshold, the reaction cannot proceed; while when the voltage is higher than this threshold, the electrolysis reaction will release current. The permeation of hydrogen between the membranes under actual working conditions will cause a change in the oxygen partial pressure at the anode, thereby affecting the voltage threshold at which the electrolysis reaction can proceed spontaneously. By introducing the influence of the permeation of hydrogen between the membranes in the electrolyzer on the voltage threshold, the open-circuit reversible voltage is obtained. ; The proton membrane can equivalently have a resistance property in the PEM water electrolysis reaction, generating ohmic losses. And considering the conductivity, water absorption rate, and swelling rate in the proton membrane parameters, the ohmic loss voltage of the proton membrane is constructed. ; The dynamic change of the ion exchange capacity of the proton membrane affects the activation energy of the chemical reactions at the anode and cathode, thus affecting the electrochemical polarization voltage. ; The construction of each voltage in the PEM water electrolysis equivalent voltage model is divided into two steps. The first step is to incorporate the key parameters that affect the electrochemical properties of PEM water electrolysis in actual production into the model. The second step is to incorporate the relevant algorithm formulas of chaos theory into the constructed model in the construction of individual voltage components to reflect the certainty of the electrochemical reaction in the operation process of PEM water electrolysis for hydrogen production under actual working conditions and to simulate the uncertainty of the random process in actual production.

[0022] The PEM electrolyzer model, that is, the PEM water electrolysis cell model, and its single-cell port voltage is represented by the sum of the open-circuit reversible voltage, the ohmic loss voltage of the proton membrane, and the electrochemical polarization voltage. In the PEM water electrolysis cell model, the single-cell port voltage is: Equation 1; In Equation 1: is the open-circuit reversible voltage; is the ohmic loss voltage of the proton membrane; is the electrode polarization chaos voltage, that is, the electrochemical polarization voltage.

[0023] The derivation method of the open-circuit reversible voltage is as follows: In the electrical model of the electrolytic cell, the open-circuit reversible voltage corresponds to the independent voltage source of the equivalent circuit. When the total voltage , other losses such as ohmic loss and electrochemical polarization voltage are only generated when the current flows through. This part of the voltage is obtained from the Nernst equation: Formula 2; In Formula 2: The universal gas constant R ; The Faraday constant F , the open-circuit reversible equilibrium voltage ; It is known from the literature that it is usually taken as 1.23V; T is the temperature; n is the number of electron transfers. In the electrolysis of water n =2, the water activity . In this model, the influence of impurities during the electrolysis process is ignored in PEM electrolyzed water, that is, it is considered that ; respectively represent H 2 and O 2 gas activities; In actual production, with the use of the electrolytic cell, the gas permeation on both sides of the membrane needs to be considered in the real situation, that is, the reverse permeation of hydrogen is considered. The reverse permeation of hydrogen will cause the oxygen partial pressure on the anode side to decrease, thereby affecting the reversible voltage. Therefore, the activity term needs to be corrected, and we get: In Formula 3: is the reference pressure, usually taken as 1 atm; is the oxygen partial pressure; is the gas permeation reaction energy barrier; After correction, the expression of the open-circuit reversible voltage is obtained: In Formula 4: is the hydrogen partial pressure.

[0024] In the PEM electrolyzed water equivalent voltage model, the proton membrane conductivity is affected by the membrane thickness , the water absorption rate , the swelling rate and the temperature ; The effective thickness of the membrane increases with the increase of the swelling rate, and the conductivity increases with the increase of the temperature. According to Ohm's law: Formula 5; In Formula 5: is the potential difference between both sides of the proton membrane; is the effective thickness. The thickness of the proton membrane itself In the actual electrolytic water process, affected by the swelling rate , the swelling rate is used as a correction term to obtain the membrane thickness that conforms to the actual working conditions, that is , in order to obtain a more accurate model, where is the correction coefficient of the swelling rate to the thickness.

[0025] In the PEM electrolytic water equivalent voltage model, the influence of the water absorption rate is considered, that is, considering that the water absorption rate causes changes in the membrane porosity; in the PEM electrolytic water equivalent voltage model, the moving electrons and protons in the electrolytic cell are regarded as physical particles. Then, based on the existing theory, the change in the membrane porosity will have a linear effect on the transmission of particles, and the equivalent conductivity correction factor of the electrolytic cell is introduced, where is the experimental fitting coefficient; considering the temperature dependence, the conductivity changes with temperature following the Arrhenius relationship: Equation 6. In Equation 6: is the standard conductivity of the proton membrane; is the reaction activation energy; is the Boltzmann constant; Simplify the model and directly introduce the linear correction factor Simplify the model to obtain the following Ohmic resistance constructed based on the actual key parameters of the proton membrane: Equation 7; In Equation 7: is the potential difference across the proton membrane; A is the cross-sectional area of the proton membrane, and the correction coefficients , are measured through experimental data, where is the water absorption rate correction coefficient; is the temperature linear correction coefficient measured through a controlled variable experiment of changing the temperature; the formula for the Ohmic voltage is as follows: Equation 8.

[0026] is the current flowing through the proton membrane; In the PEM electrolytic water equivalent voltage model, the derivation method of the electrochemical polarization chaos voltage is specifically as follows: Assume that the electrode reaction rate is controlled by the activation energy , and from the Arrhenius equation, we get: Equation 9; In Equation 9: is the pre-exponential factor; is the Boltzmann constant ; Let the ion exchange capacity in the proton membrane parameters IEC affect the reaction site density, IEC and its dynamic change in actual conditions affects the reaction rate. Then the relationship between the current density and IEC is expressed as: Formula 10; In Formula 10: is the reference ion exchange capacity , F is the Faraday constant ; n is the amount of substance undergoing the reaction, with the unit of mol. The Logistic map in chaos theory is used to describe the non-linear perturbation under actual working conditions, and the formula is obtained: Formula 11; In Formula 11: , where the specific value of the critical chaos parameter is related to the actual working conditions; ; The PEM electrolyzed water equivalent voltage model is to more realistically describe IEC its dynamic changes, such as the membrane aging and catalyst poisoning in the actual large-scale electrolysis process, which are caused by complex actual factors and result in the change of the concentration of active groups. IEC is replaced from a parameter constant of a proton membrane to a time-dependent chaotic function IEC(t) , rather than a fixed value; through linear scaling and translation, the chaotic variable is converted into the actual IEC value, and through normalization, the is obtained as follows: Formula 12; In Equation (12): and are the actual physical maximum and minimum values of IEC determined by experiments; is the reference value of the ion exchange capacity; Substituting Equation 12 into Equation 10, the chaotic current density is obtained as follows: Formula 13; In Formula 13: is the chaotic current density, that is, the current density obtained by describing IEC dynamic changes using chaos theory; And the electrochemical polarization voltage in the electrolytic cell is obtained from the Butler-Volmer kinetic equation as: Formula 14; In Formula 14: is the anodic charge transfer coefficient; is the cathode charge transfer coefficient; is the anodic exchange current density; is the cathodic exchange current density.

[0027] The PEM electrolyzed water equivalent voltage model is a computer model used to simulate the PEM electrolyzed water working conditions. The input variables of this computer model are ; in the model, are the parameters to be determined. They can be determined by parameter identification algorithms such as the least squares method, genetic algorithm, particle swarm algorithm, etc. Using the above measured data as the input and the simulated electrolytic cell voltage as the output, the simulated voltage is compared with the measured voltage to determine.

[0028] Example: This example proposes a new PEM electrolyzed water equivalent voltage model, providing a new method for studying various electrical property problems presented in the future grid connection and the actual hydrogen production electrolysis process. This model is based on the key parameters of the proton exchange membrane of the PEM electrolytic cell and other factors affecting the hydrogen production reaction. Through a multi-parameter coupling mechanism: integrating electrochemistry, various factors affecting the reaction, and chaotic dynamics [8] cross-integrated. The model is based on existing physical laws and mathematical theories. By splitting the total voltage divided by the electrolytic cell when the entire PEM electrolytic cell is connected to the power supply into three partial voltages according to electrochemical properties and circuit properties, and modeling them separately. First, based on the theoretical voltage threshold at which the electrolytic reaction can proceed spontaneously, that is, when the applied voltage is equal to this value, the electrolytic reaction is in equilibrium and no net current is generated. If the voltage is lower than this value, the reaction cannot proceed; if the voltage is higher than this value, the electrolytic reaction will release current. The open-circuit reversible voltage is constructed, and the influence of the hydrogen permeation between the membranes on the open-circuit reversible voltage in the real situation is considered based on the traditional modeling. The second part is the ohmic voltage, which is constructed through the actual key parameters of the proton membrane, that is, a local relationship is established according to the actual parameter situation of the PEM proton membrane, that is, the ohmic resistance of the proton membrane based on the key parameters of the proton membrane is constructed. The third part is the electrochemical polarization voltage, which is caused by the kinetic factors of the electrode reaction. In the electrochemical reaction, the reactant particles must obtain sufficient energy to overcome the energy barrier of the reaction, that is, the activation energy. And the activation energy is closely related to the catalyst. The Logistic mapping in chaos theory is used to reflect the influence of complex factors such as the activity decay of the catalyst and the uncertain change of temperature on the concentration of active groups in the actual working conditions. Therefore, IEC is replaced by a time-dependent chaotic function , rather than a fixed value. IECDynamic changes thus affect the reaction energy barrier. That is, this model is based on the key parameters of the proton membrane for modeling and incorporates chaos theory to construct the voltage of the PEM electrolyzer under actual working conditions [9] , reflecting the external voltage characteristics of the electrolyzer under real conditions.

Claims

1. A method for modeling the equivalent voltage of PEM electrolyzed water, characterized in that: The method establishes a PEM electrolyzer model for simulation according to the electrochemical properties and circuit properties of the PEM electrolyzer during water electrolysis. When the PEM electrolyzer model is connected to a power supply, the total voltage divided is split into the theoretical voltage threshold at which the electrolysis reaction can proceed spontaneously, the ohmic voltage, and the electrochemical polarization voltage. Equivalent voltage models are respectively built for the above three voltages. When modeling based on the theoretical voltage threshold at which the electrolysis reaction can proceed spontaneously, an open-circuit reversible voltage is constructed. When modeling based on the ohmic voltage, an ohmic resistance of the proton exchange membrane is constructed based on the key parameters of the proton exchange membrane. When modeling based on the electrochemical polarization voltage, modeling is carried out based on the key parameters of the proton exchange membrane and relevant formulas of the chaos theory algorithm are incorporated to obtain the voltage of the PEM electrolyzer under actual working conditions. The equivalent voltage model is based on the simulated proton exchange membrane parameters in the PEM electrolyzer model and the simulation process of the water electrolysis chemical reaction. The simulated components in the PEM electrolyzer model include bipolar plates, porous titanium mesh groups, gas diffusion layers, anode catalyst layers, cathode catalyst layers, and proton exchange membranes. The bipolar plates are used to simulate the conduction of current and the mechanical support structure of the PEM electrolyzer model, and the simulated internal flow channel structure is used for the uniform distribution of liquid and gas phases. The gas diffusion layer serves as the interface between the electrode and the catalyst layer and is used to provide a transmission channel for deionized water reactants and hydrogen and oxygen products. The catalyst layer is used to simulate the catalytic part of the core area of the electrochemical reaction in the PEM electrolyzer model and accelerates the electrochemical reaction process by reducing the reaction activation energy. The proton exchange membrane is used to simulate the proton exchange membrane part in the core components of the PEM electrolyzer model and is responsible for conducting hydrogen ions generated at the anode to the cathode to build an internal ion transmission channel. The proton exchange membrane has the dual functions of a gas isolation layer and a proton conduction medium, allowing protons to pass through while blocking electron transmission, thereby realizing the ion conduction and gas separation required for the water electrolysis reaction. The construction of each voltage in the PEM electrolysis equivalent voltage model is divided into two steps. The first step is to incorporate the key parameters that affect the electrochemical properties of PEM electrolysis in actual production into the model. The second step is to incorporate relevant algorithm formulas of the chaos theory into the constructed model during the construction of individual voltage components.

2. The modeling method of the PEM electrolyzed water equivalent voltage model according to claim 1, characterized in that: When modeling based on the theoretical voltage threshold at which the electrolysis reaction can proceed spontaneously, in the established PEM electrolyzer model, the electrolysis reaction is in an equilibrium state and no net current is generated. If the voltage is lower than this value, the reaction cannot proceed. If the voltage is higher than this value, the electrolysis reaction will release current. An open-circuit reversible voltage is constructed in the established model, and the influence of hydrogen permeation between the membranes under real working conditions on the open-circuit reversible voltage is introduced. Specifically: When constructing a model based on the theoretical voltage threshold at which the electrolysis reaction can proceed spontaneously, in the model established for the PEM electrolyzer, the electrolysis reaction of the PEM electrolyzer is in an equilibrium state and no net current is generated at this time. When the voltage is lower than the theoretical voltage threshold, the reaction cannot proceed; while when the voltage is higher than this threshold, the electrolysis reaction will release current; under real working conditions, the permeation of hydrogen between the membranes will cause a change in the anode oxygen partial pressure, thereby affecting the voltage threshold at which the electrolysis reaction can proceed spontaneously. By introducing the influence of the permeation of hydrogen between the membranes in the electrolyzer on the voltage threshold, the open-circuit reversible voltage is obtained. ; The proton exchange membrane can equivalently have a resistive property in the PEM electrolytic water chemical reaction to generate ohmic losses, and the ohmic loss voltage of the proton exchange membrane is constructed by considering the conductivity, water absorption rate, and swelling rate in the proton exchange membrane parameters ; The dynamic change of the ion exchange capacity of the proton membrane affects the activation energy of the chemical reactions at the anode and cathode, thus affecting the electrochemical polarization voltage ; When modeling based on the Ohmic voltage, the parameters of the proton exchange membrane are used to build the model, that is, to establish a local relationship according to the actual parameter situation of the PEM proton exchange membrane, and construct the Ohmic resistance of the proton exchange membrane based on the key parameters of the proton exchange membrane; wherein is the proton membrane conductivity; is the water absorption rate of the proton membrane; is the swelling ratio of the proton membrane; is the temperature; is the ion exchange capacity; represents the local voltage, represents the local current, When modeling based on the electrochemical polarization voltage, the model assumes that the electrochemical polarization voltage is caused by the kinetic factors of the electrode reaction. In an electrochemical reaction, reactant particles must obtain sufficient energy to overcome the energy barrier of the reaction, i.e., the activation energy, and the activation energy is closely related to the catalyst. The Logistic mapping in chaos theory is used to reflect the activity decay of the catalyst and the uncertain change of temperature in the actual working condition, so as to reflect the influence of complex factors on the concentration of active groups. Replace it with a time-related chaotic function , rather than a fixed value, so as to Dynamically change to affect the reaction energy barrier, model based on the parameters of the proton membrane, and incorporate chaos theory to construct the voltage model of the PEM electrolyzer under actual working conditions, which is used to reflect the external voltage characteristics of the electrolyzer in real situations.

3. The PEM electrolytic water equivalent voltage model modeling method according to claim 1, wherein: The PEM electrolyzer model, that is, the PEM electrolyzer model, has its single-cell port voltage represented by the sum of the open-circuit reversible voltage, the ohmic loss voltage of the proton exchange membrane, and the electrochemical polarization voltage. In the PEM electrolyzer model, the single-cell port voltage is as follows: Formula 1; In Formula 1: is the open-circuit reversible voltage; is the proton membrane ohmic loss voltage; is the polarization chaos voltage, i.e., the electrochemical polarization voltage.

4. The PEM electrolyzed water equivalent voltage model modeling method according to claim 3, characterized in that: The derivation method of the open - circuit reversible voltage is as follows: In the electrical model of the electrolytic cell, the independent voltage source corresponding to the open - circuit reversible voltage in the equivalent circuit is when the total voltage , the ohmic loss and the electrochemical polarization voltage in other losses are only generated when the current flows through. The open - circuit reversible voltage is obtained from the Nernst equation as follows: Formula 2; In Equation 2: Universal gas constant R ; Faraday constant F , open-circuit reversible equilibrium voltage ; T is the temperature; n is the number of electron transfers. In water electrolysis n = 2, water activity , in this model, the influence of impurities in the electrolysis process is ignored in PEM water electrolysis, that is, it is considered that ; respectively represent H 2 and O the gas activities of 2; in actual production, as the electrolytic cell is used, the gas permeation on both sides of the membrane needs to be considered in the real situation, that is, the reverse permeation of hydrogen is considered. The reverse permeation of hydrogen will cause the oxygen partial pressure on the anode side to decrease, thus affecting the reversible voltage. Therefore, the activity term needs to be corrected to obtain: In Formula 3: is the reference pressure; is the partial pressure of oxygen; is the energy barrier of the gas permeation reaction; The expression for the open-circuit reversible voltage after correction is: In Formula 4: is the hydrogen partial pressure.

5. The PEM electrolyzed water equivalent voltage model modeling method according to claim 3, characterized in that: In the equivalent voltage model of PEM electrolyzed water, the proton exchange membrane conductivity is affected by the membrane thickness , water absorption rate , swelling ratio and temperature ; the effective membrane thickness increases with the increase of the swelling ratio, and the conductivity increases with the increase of temperature; according to the ideal Ohm's law: Formula 5; In Equation 5: is the potential difference across the proton membrane; is the effective thickness, which is the membrane thickness of the proton membrane itself During the actual electrolysis of water, it is affected by the swelling rate The swelling rate is used as a correction term to obtain the membrane thickness that conforms to the actual working conditions, that is to obtain a more accurate model, where is the correction coefficient of the swelling rate to the thickness.

6. The PEM electrolyzed water equivalent voltage model modeling method according to claim 5, characterized in that: In the PEM electrolyzed water equivalent voltage model, the influence of water absorption rate is considered, that is, the water absorption rate is considered which causes the change of membrane porosity; in the PEM electrolyzed water equivalent voltage model, the moving electrons and protons in the electrolytic cell are regarded as physical particles. Then, based on the existing theory, the change of membrane porosity will have a linear influence on the particle transport, and the equivalent conductivity correction factor of the electrolytic cell is introduced , where is the experimental fitting coefficient; considering the temperature dependence, the conductivity changes with temperature following the Arrhenius relationship: Formula 6. In Equation 6: is the standard conductivity of the proton membrane; is the reaction activation energy; is the Boltzmann constant; Simplified model, directly introducing a linear correction factor For the simplified model, the ohmic resistance constructed based on the actual key parameters of the proton membrane is as follows: Formula 7; In Equation 7: is the potential difference across both ends of the proton membrane; A is the cross-sectional area of the proton membrane, and the correction factor , is measured through experimental data, where is the water absorption correction factor; is the temperature linear correction factor measured through a controlled variable experiment of changing temperature; The formula for the Ohmic voltage is as follows: Formula 8; is the current flowing through the proton membrane.

7. The method for modeling the PEM electrolyzed water equivalent voltage model according to claim 3, characterized in that: In the PEM electrolyzed water equivalent voltage model, the chaotic voltage of electrochemical polarization The derivation method is specifically as follows: Assume that the electrode reaction rate is controlled by the activation energy According to the Arrhenius equation, we have: Formula 9; In Formula 9: is the pre-exponential factor; is the Boltzmann constant ; Let the ion exchange capacity in the proton membrane parameters IEC affect the reaction site density, IEC and its dynamic change in actual conditions affects the reaction rate. Then the relationship between the current density and IEC is expressed as: Formula 10; In Formula 10: is the reference ion exchange capacity , F is the Faraday constant ; n is the amount of substance undergoing the reaction, with the unit of mol. The Logistic map in chaos theory is used to describe the non-linear perturbation under actual working conditions, and the formula is obtained: Formula 11; In Formula 11: , is the critical chaos parameter; .

8. The method for modeling the PEM electrolyzed water equivalent voltage model according to claim 3, wherein: The equivalent voltage model of PEM electrolyzed water is to more realistically describe IEC the dynamic changes such as the membrane aging and catalyst poisoning in the actual large-scale electrolysis process, which cause the change of the concentration of active groups. IEC A parameter constant of a proton membrane is replaced by a time-dependent chaotic function IEC(t) , rather than a fixed value; through linear scaling and translation, the chaotic variable is converted into the actual IEC value, and the is obtained through normalization as follows: Formula 12; In Equation 12: and are the actual physical maximum and minimum values measured by experiments; IEC the actual physical maximum and minimum values; is the reference value of the ion exchange capacity; Substituting Equation 12 into Equation 10, the chaotic current density is obtained as follows: Formula 13; In Equation 13: is the chaotic current density, which is the current density obtained by describing the dynamic change using chaos theory; IEC the current density obtained after dynamic change; The electrochemical polarization voltage in the electrolytic cell is obtained from the Butler-Volmer kinetic equation as follows: Equation 14; In Equation 14: is the anodic charge transfer coefficient; is the cathodic charge transfer coefficient; is the anodic exchange current density; is the cathodic exchange current density.

9. The PEM electrolyzed water equivalent voltage model modeling method according to claim 6, characterized in that: The PEM electrolytic water equivalent voltage model is a computer model used to simulate the PEM electrolytic water working conditions. The input variables of this computer model are ; the in the model are parameters to be determined. Through parameter identification algorithms such as the least squares method, genetic algorithm, and particle swarm algorithm, with the measured data of the PEM electrolytic water process as the input, the simulated electrolytic cell voltage is taken as the output, and the simulated voltage is compared with the measured voltage to determine the parameters.

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