Modeling of performance degradation of proton exchange membrane fuel cells under sodium ion contamination

Abstract

The application discloses a kind of sodium ion pollution under the performance degradation modeling method of proton exchange membrane fuel cell, it is related to the field of fuel cell system optimization control, comprising: establishing the reference model under pure state;Based on liquid phase pollution experimental data and gas phase salt fog pollution experimental data, the expression of sodium ion comprehensive accumulation mass under pollution state is constructed by least square method and the relative sodium ion occupancy rate is calculated;Under the change of relative sodium ion occupancy rate, the sensitivity analysis of candidate model parameters to fuel cell output performance is carried out, the average change amount of stack voltage and average normalized parameter sensitivity are calculated, and the key pollution parameters are selected from the candidate model parameters;According to the key pollution parameter, construct pollution correction coefficient and modify the reference model, and the stack polarization characteristic curve under different sodium ion pollution conditions can be obtained by dynamic simulation.The application solves the problem of lacking system modeling in the performance degradation process of fuel cell under sodium pollution condition.

Description

Technical Field

[0001] This invention relates to the field of fuel cell system optimization control, and specifically to a method for modeling the performance degradation of proton exchange membrane fuel cells under sodium ion contamination. Background Technology

[0002] With the application of proton exchange membrane fuel cells in coastal vehicles, island energy systems, and ship auxiliary power, their cathode air supply systems face the prominent problem of marine salt spray pollution. Sea salt particles can form salt-containing aerosols through wave breakage, bubble collapse, and wind action, and participate in the formation of cloud droplets and fog droplets under high humidity conditions. Since the cathode air supply system of fuel cells usually directly uses ambient air for oxygen supply, sea salt aerosols and fog droplets containing sodium and chloride ions may enter the fuel cell with the cathode air intake, potentially affecting the long-term operating performance of the membrane electrode assembly.

[0003] Existing research on salt spray pollution in proton exchange membrane fuel cells (PEMFCs) largely focuses on high-concentration accelerated testing, lacking systematic modeling of the diffusion, accumulation, and performance degradation processes of pollutants in the membrane electrode assembly (MEA) under long-term exposure to low concentrations of sodium chloride. Therefore, there is an urgent need to develop a modeling method for the performance degradation of PEMFCs under sodium ion pollution. This method would calculate the accumulated sodium ion levels to correct the state parameters during actual operation, enabling the calculation and prediction of stack output performance under different levels of sodium ion pollution. Summary of the Invention

[0004] The purpose of this application is to propose a modeling method for the performance degradation of proton exchange membrane fuel cells under sodium ion pollution, in order to solve the problem of lack of systematic modeling of the diffusion, accumulation and performance degradation process of pollutants in membrane electrodes under the long-term action of low concentration sodium chloride.

[0005] In a first aspect, the present invention provides a method for modeling the performance degradation of proton exchange membrane fuel cells under sodium ion contamination, comprising the following steps:

[0006] A proton exchange membrane fuel cell stack model, cathode flow channel model, anode flow channel model, and water transport model under pure conditions were established and used as the benchmark model.

[0007] Based on experimental data of liquid-phase pollution and gas-phase salt spray pollution, an expression for the comprehensive accumulation mass of sodium ions under pollution conditions was constructed using the least squares method. The relative sodium ion occupancy rate was calculated based on the expression for the comprehensive accumulation mass of sodium ions under pollution conditions. The relative sodium ion occupancy rate is used to characterize the relative proportion of sodium ions occupying sulfonic acid group sites on the proton exchange membrane.

[0008] Candidate model parameters that are related to the baseline model and change with sodium ion pollution are identified. Sensitivity analysis of the candidate model parameters to fuel cell output performance under changes in relative sodium ion occupancy is conducted, and the average change in stack voltage and the average normalized parameter sensitivity are calculated. Key pollution parameters are screened from the candidate model parameters based on the average change in stack voltage and the average normalized parameter sensitivity.

[0009] Pollution correction coefficients are constructed based on key pollution parameters. The baseline model is then corrected using these coefficients, and dynamic simulations are performed to obtain the stack polarization characteristic curves under different sodium ion pollution conditions.

[0010] As a preferred embodiment, based on experimental data from liquid-phase pollution and gas-phase salt spray pollution, an expression for the comprehensive accumulation mass of sodium ions under pollution conditions is established using the least squares method, specifically including:

[0011] Based on the experimental results of liquid-phase pollution and gas-phase salt spray pollution respectively, the least squares method was used for linear fitting to obtain the fitting expressions of sodium ion mass fraction at different times under the two types of sodium ion pollution conditions of liquid-phase pollution and gas-phase salt spray pollution, as shown in the following formula:

[0012] ;

[0013] in, An index indicating conditions of sodium ion contamination. , and These represent liquid-phase sodium ion contamination conditions and gas-phase salt spray sodium ion contamination conditions, respectively. This represents the mass fraction of sodium ions under the corresponding sodium ion contamination conditions. The fitting function obtained by linear fitting; This indicates the mass concentration of sodium ions. Indicates time;

[0014] Under both types of sodium ion pollution conditions, the mass fraction of sodium ions and the cumulative mass of sodium ions are converted using the following relationship:

[0015] ;

[0016] in, The cumulative mass of sodium ions under the corresponding sodium ion pollution conditions. The total mass of the fuel cell membrane electrode assembly;

[0017] right and Combining the two formulas, we obtain the expression for the cumulative mass of sodium ions under the corresponding sodium ion pollution conditions, relating to the sodium ion mass concentration and time, as shown in the following equation:

[0018] ;

[0019] The comprehensive accumulated mass of sodium ions under pollution conditions is calculated based on the cumulative mass of sodium ions under the corresponding sodium ion pollution conditions, as shown in the following formula:

[0020] ;

[0021] in, This represents the total accumulated mass of sodium ions under polluted conditions. and Let these represent the first weighting coefficient and the second weighting coefficient, respectively. ;

[0022] The objective function Z is constructed as shown in the following equation:

[0023] ;

[0024] in, This indicates the first weighting coefficient or the second weighting coefficient. The index representing the calculation condition, the first... The calculation conditions are based on the sodium ion mass concentration. and pollution time jointly determined, This indicates the total number of sets of calculation conditions; Indicates the first The accumulated mass of sodium ions under liquid-phase sodium ion pollution conditions or gas-phase salt spray sodium ion pollution conditions calculated by the first set of calculations. mass concentration under group calculation conditions and pollution time Simultaneously, substituting the expression for the cumulative mass of sodium ions under the corresponding sodium ion pollution conditions with respect to the mass concentration of sodium ions and time, we obtain the following: Indicates the first The weighted cumulative mass of sodium ions obtained under the group calculation conditions is obtained by calculating the first... Accumulation mass of sodium ions under liquid-phase sodium ion contamination conditions under set calculation conditions The accumulation mass of sodium ions under conditions of sodium ion pollution in gaseous salt spray or other forms of pollution. The result is obtained by substituting the formula for calculating the total accumulated mass of sodium ions under polluted conditions;

[0025] When using the least squares method to find the minimum value of the objective function Then, this expression, along with the expression for the cumulative mass of sodium ions under the corresponding sodium ion pollution conditions in terms of sodium ion mass concentration and time, is substituted into the formula for calculating the comprehensive accumulated mass of sodium ions under pollution conditions, thus obtaining the established expression for the comprehensive accumulated mass of sodium ions under pollution conditions.

[0026] Preferably, the expression for the relative sodium ion occupancy rate is as follows:

[0027] ;

[0028] in, Indicates the relative sodium ion occupancy rate; The amount of sodium is expressed as the total accumulated mass of sodium ions under polluted conditions, and is calculated using an expression. The amount of substance at sulfonic acid group sites in the proton exchange membrane is calculated using the following formula:

[0029] ;

[0030] in, This is the equivalent weight of the proton exchange membrane. This represents the actual weight of the proton exchange membrane.

[0031] As a preferred approach, a sensitivity analysis of the candidate model parameters on the fuel cell output performance under changes in relative sodium ion occupancy is conducted, calculating the average change in stack voltage and the average normalized parameter sensitivity, specifically including:

[0032] While keeping all parameters in the baseline model except for the candidate model parameters unchanged, each candidate model parameter is adjusted from a pollution-free value to a pollution value under the corresponding relative sodium ion occupancy condition. Under different analytical conditions, the change in fuel cell stack voltage and the average change in stack voltage caused by the change in the k-th candidate model parameter are calculated using the baseline model after adjusting the candidate model parameters. The relative change in fuel cell stack voltage caused by the change in the k-th candidate model parameter is calculated under different analytical conditions. Combined with the change in the k-th candidate model parameter, the normalized parameter sensitivity and the average normalized parameter sensitivity of the k-th candidate model parameter under different analytical conditions are calculated, as shown in the following formula:

[0033] ;

[0034] in, For the first The candidate model parameters at the th ... The change in stack voltage caused by each analytical operating condition; For the first The candidate model parameters at the th ... Sensitivity of normalized parameters under various analytical conditions; The stack voltage is calculated using pollution-free values ​​for all candidate model parameters. To only the first The stack voltage calculated when the parameters of each candidate model are adjusted to the corresponding pollution values; For the first Uncontaminated values ​​of the parameters of each candidate model; For the first Under the first analytical working condition, the first Contamination values ​​of candidate model parameters; For the first The average change in stack voltage of each candidate model parameter; For the first Average normalized parameter sensitivity of candidate model parameters; This is to analyze the total number of operating conditions.

[0035] As a preferred option, the analysis conditions include current densities of 0.4 A / cm², 0.8 A / cm², and 1.2 A / cm².

[0036] As a preferred option, the candidate model parameters include at least the mole fraction of hydrogen, the mole fraction of oxygen, the mole fraction of water vapor, temperature, liquid water saturation, membrane water content, and current density; the key contamination parameters are determined to be membrane water content and current density by combining the average change in stack voltage with the sensitivity analysis of the average normalized parameter.

[0037] As a preferred method, a pollution correction coefficient is constructed based on key pollution parameters. This coefficient is then used to correct the baseline model before dynamic simulation is performed to obtain the stack polarization characteristic curves under different sodium ion pollution conditions. Specifically, this includes:

[0038] The equivalent membrane water content under sodium ion pollution conditions is calculated by weighting the equivalent membrane water content of the hydrogen ion membrane and the equivalent membrane water content of the sodium ion membrane based on the relative sodium ion occupancy rate, as shown in the following formula:

[0039] ;

[0040] in, This represents the equivalent membrane water content under sodium ion contamination conditions. This represents the equivalent membrane water content in the form of hydrogen ions. This represents the equivalent membrane water content in sodium ion form. Indicates the relative sodium ion occupancy rate;

[0041] The equivalent membrane water content of the hydrogen ion membrane and the equivalent membrane water content of the sodium ion membrane are respectively:

[0042] ;

[0043] in, Water activity;

[0044] The fouling correction factor for membrane water content is constructed based on the equivalent membrane water content under fouling conditions, as shown in the following formula:

[0045] ;

[0046] in, This is the fouling correction factor for membrane water content;

[0047] The membrane water content output from the baseline model is corrected using a fouling correction factor to obtain the corrected membrane water content under fouled conditions, as shown in the following formula:

[0048] ;

[0049] in, The membrane water content output by the baseline model. This represents the corrected membrane water content under fouling conditions.

[0050] By selecting a first reference cell voltage and a second reference cell voltage, and establishing a functional relationship between different relative sodium ion occupancy rates and reference current densities at the corresponding reference cell voltages, as shown in the following equation:

[0051] ;

[0052] ;

[0053] in, and These are the first reference current density and the second reference current density under the first reference battery voltage and the second reference battery voltage, respectively. This is a functional relationship between the relative sodium ion occupancy rate and the reference current density, established using piecewise linear interpolation, monotonic interpolation, or curve fitting methods.

[0054] Based on the ratio of the reference current density under sodium ion contamination conditions to the reference current density under sodium ion-free conditions, the current carrying capacity attenuation coefficients corresponding to the first and second reference cell voltages are constructed as shown in the following formula:

[0055] ;

[0056] in, and These are the current carrying capacity attenuation coefficients corresponding to the first and second reference cell voltages under sodium ion contamination conditions, respectively. and These are the reference current densities corresponding to the first and second reference cell voltages under conditions free of sodium ion contamination, respectively.

[0057] The actual operating current density of the fuel cell is calculated based on the actual input current of the fuel cell and the effective reaction area of ​​a single fuel cell, as shown in the following formula:

[0058] ;

[0059] in, For fuel cells in The actual operating current density at any given time, For fuel cells in The actual input current at any given time. The effective reaction area of ​​a single fuel cell;

[0060] When the second reference current density is greater than the first reference current density, the unlimited normalized current position is calculated based on the actual operating current density of the fuel cell, the first reference current density, and the second reference current density, as shown in the following formula:

[0061] ;

[0062] in, for The position of the unlimited normalized current at time;

[0063] The unlimited normalized current position is restricted to the range of 0 to 1 to obtain the limited normalized current position. Based on the limited normalized current position, a cubic smoothing function is used to calculate the transition weight between the first reference battery voltage and the second reference battery voltage, as shown in the following formula:

[0064] ;

[0065] ;

[0066] in, express The position of the normalized current after the time limit. express The transition weight at each time step ranges from 0 to 1.

[0067] Based on the current carrying capacity attenuation coefficients and transition weights corresponding to the first and second reference cell voltages under sodium ion contamination conditions, the composite current carrying capacity attenuation coefficient, which varies with the relative sodium ion occupancy rate and the actual operating current density, is obtained as shown in the following formula:

[0068] ;

[0069] in, Indicates the attenuation coefficient of composite current carrying capacity;

[0070] Based on the composite current carrying capacity attenuation coefficient, the actual operating current density is mapped to the equivalent current density used for calculating fuel cell polarization losses under sodium ion contamination conditions, as shown in the following formula:

[0071] ;

[0072] in, This represents the equivalent current density used for calculating polarization losses in fuel cells under sodium ion contamination conditions.

[0073] The equivalent current density is input into the benchmark model to obtain the stack voltage output by the proton exchange membrane fuel cell stack model under sodium ion contamination conditions, which is used as the value of the vertical axis of the stack polarization characteristic curve. The value of the horizontal axis of the stack polarization characteristic curve is calculated using the actual operating current density, and the stack polarization characteristic curves under different sodium ion contamination conditions are plotted.

[0074] As a preferred option, the relative sodium ion occupancy rate is in the range of 0 to 1, and six sodium ion pollution conditions are defined with sodium ion pollution concentrations of 0 mg / L, 1.01 mg / L, 2.99 mg / L, 4.92 mg / L, 6.79 mg / L and 8.62 mg / L.

[0075] Compared with the prior art, the present invention has the following beneficial effects:

[0076] (1) The proton exchange membrane fuel cell performance degradation modeling method mentioned in this invention uses a benchmark model under pure conditions, and based on liquid phase pollution experimental data and gas phase salt spray pollution experimental data, the weight coefficients corresponding to liquid phase and gas phase salt spray pollution are determined by the least squares method to construct an expression for the comprehensive accumulation mass of sodium ions under pollution conditions, thereby realizing a unified characterization of experimental results in multiple pollution environments.

[0077] (2) The proton exchange membrane fuel cell performance degradation modeling method mentioned in this invention is based on the amount of sulfonic acid group sites in the proton exchange membrane. It establishes a method for quantifying the degree of pollution based on the relative sodium ion occupancy rate (RSO) and uses different RSO values ​​to characterize different degrees of sodium ion pollution.

[0078] (3) The proton exchange membrane fuel cell performance degradation modeling method mentioned in this invention proposes a key pollution parameter sensitivity screening method for stack voltage, avoiding indiscriminate correction of all model variables. Based on the RSO value, the pollution correction coefficient corresponding to membrane water content and the composite current carrying capacity decay coefficient corresponding to equivalent current density are constructed respectively, realizing the accurate calculation of stack polarization characteristic curve under operating conditions. Attached Figure Description

[0079] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0080] Figure 1 This is a flowchart illustrating the performance degradation modeling method for proton exchange membrane fuel cells under sodium ion contamination, as described in an embodiment of this application.

[0081] Figure 2 This is an architectural diagram of a proton exchange membrane fuel cell performance degradation modeling method under sodium ion contamination, as described in an embodiment of this application.

[0082] Figure 3 A single-cell polarization characteristic curve obtained by modeling the performance degradation of a proton exchange membrane fuel cell in a pure state according to an embodiment of this application.

[0083] Figure 4 The graph shows the results of the sensitivity analysis of the influence of candidate model parameters on the output voltage of a proton exchange membrane fuel cell according to embodiments of this application.

[0084] Figure 5 The single-cell polarization characteristic curves of the proton exchange membrane fuel cell performance degradation modeling method under sodium ion contamination according to embodiments of this application are shown. The sodium ion contamination concentrations are 0 mg / L, 1.01 mg / L, 2.99 mg / L, 4.92 mg / L, 6.79 mg / L and 8.62 mg / L. Detailed Implementation

[0085] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0086] Figure 1This application illustrates an embodiment of a method for modeling the performance degradation of a proton exchange membrane fuel cell under sodium ion contamination, comprising the following steps:

[0087] S1. Establish a proton exchange membrane fuel cell stack model, cathode flow channel model, anode flow channel model, and water transport model under pure conditions and use them as the benchmark model.

[0088] Specifically, in the embodiments of this application, Simulink modeling is first used to construct a proton exchange membrane fuel cell stack model, cathode flow channel model, anode flow channel model, and water transfer model in a pure state. These four models serve as the basic modeling for the proton exchange membrane fuel cell, and are subsequently used as benchmark models. The inputs to the proton exchange membrane fuel cell stack model are current, oxygen partial pressure, hydrogen partial pressure, temperature, membrane water content, cathode partial pressure, and RSO, with the output being the stack voltage. The inputs to the cathode flow channel model are current, temperature, excess oxygen ratio, cathode inlet air flow rate, cathode outlet flow rate, cathode humidity, inlet pressure, outlet pressure, and inlet relative humidity, with the outputs being oxygen partial pressure, cathode partial pressure, cathode humidity, and cathode outlet mass flow rate. The inputs to the anode flow channel model are hydrogen inlet flow rate, anode outlet flow rate, inlet pressure, outlet pressure, current, anode inlet humidity, temperature, and membrane water transfer rate, with the outputs being hydrogen partial pressure and anode humidity. The inputs to the water transfer model are temperature, current, anode humidity, cathode humidity, and RSO, with the output being membrane water content. In the simulation process, the partial pressure of oxygen, the partial pressure of cathode, the humidity of cathode, the partial pressure of hydrogen, and the humidity of anode are first simulated using cathode and anode flow channel models respectively. Then, the simulated humidity of anode and cathode, combined with temperature, current, and RSO, are input into the water transport model to simulate the membrane water content. Finally, the simulated partial pressure of oxygen, the partial pressure of hydrogen, the membrane water content, and the partial pressure of cathode, combined with current, temperature, and RSO, are input into the proton exchange membrane fuel cell stack model to obtain the stack voltage. The above process is repeated in subsequent simulation calculations.

[0089] S2. Based on experimental data of liquid-phase pollution and gas-phase salt spray pollution, an expression for the comprehensive accumulation mass of sodium ions under pollution conditions is constructed using the least squares method. The relative sodium ion occupancy rate is calculated based on the expression for the comprehensive accumulation mass of sodium ions under pollution conditions. The relative sodium ion occupancy rate is used to characterize the relative proportion of sodium ions occupying sulfonic acid group sites on the proton exchange membrane.

[0090] In a specific embodiment, based on experimental data from liquid-phase pollution and gas-phase salt spray pollution, an expression for the comprehensive accumulation mass of sodium ions under pollution conditions is established using the least squares method, specifically including:

[0091] Based on the experimental results of liquid-phase pollution and gas-phase salt spray pollution respectively, the least squares method was used for linear fitting to obtain the fitting expressions of sodium ion mass fraction at different times under the two types of sodium ion pollution conditions of liquid-phase pollution and gas-phase salt spray pollution, as shown in the following formula:

[0092] ;

[0093] in, An index indicating conditions of sodium ion contamination. , and These represent liquid-phase sodium ion contamination conditions and gas-phase salt spray sodium ion contamination conditions, respectively. This represents the mass fraction of sodium ions under the corresponding sodium ion contamination conditions. The fitting function obtained by linear fitting; This indicates the mass concentration of sodium ions. Indicates time;

[0094] Under both types of sodium ion pollution conditions, the mass fraction of sodium ions and the cumulative mass of sodium ions are converted using the following relationship:

[0095] ;

[0096] in, The cumulative mass of sodium ions under the corresponding sodium ion pollution conditions. The total mass of the fuel cell membrane electrode assembly;

[0097] right and Combining the two formulas, we obtain the expression for the cumulative mass of sodium ions under the corresponding sodium ion pollution conditions, relating to the sodium ion concentration and time, as shown in the following equation:

[0098] ;

[0099] The comprehensive accumulated mass of sodium ions under pollution conditions is calculated based on the cumulative mass of sodium ions under the corresponding sodium ion pollution conditions, as shown in the following formula:

[0100] ;

[0101] in, This represents the total accumulated mass of sodium ions under polluted conditions. and Let these represent the first weighting coefficient and the second weighting coefficient, respectively. ;

[0102] The objective function Z is constructed as shown in the following equation:

[0103] ;

[0104] in, This indicates the first weighting coefficient or the second weighting coefficient. The index representing the calculation condition, the first... The calculation conditions are based on the sodium ion mass concentration. and pollution time jointly determined, This indicates the total number of sets of calculation conditions; Indicates the first The accumulated mass of sodium ions under liquid-phase sodium ion pollution conditions or gas-phase salt spray sodium ion pollution conditions calculated by the first set of calculations. mass concentration under group calculation conditions and pollution time Simultaneously, substituting the expression for the cumulative mass of sodium ions under the corresponding sodium ion pollution conditions with respect to the mass concentration of sodium ions and time, we obtain the following: Indicates the first The weighted cumulative mass of sodium ions obtained under the group calculation conditions is obtained by calculating the first... Accumulation mass of sodium ions under liquid-phase sodium ion contamination conditions under set calculation conditions The accumulation mass of sodium ions under conditions of sodium ion pollution in gaseous salt spray or other forms of pollution. The result is obtained by substituting the formula for calculating the total accumulated mass of sodium ions under polluted conditions;

[0105] When using the least squares method to find the minimum value of the objective function Then, this expression, along with the expression for the cumulative mass of sodium ions under the corresponding sodium ion pollution conditions in terms of sodium ion mass concentration and time, is substituted into the formula for calculating the comprehensive accumulated mass of sodium ions under pollution conditions, thus obtaining the established expression for the comprehensive accumulated mass of sodium ions under pollution conditions.

[0106] Specifically, the embodiments of this application, based on the results of liquid-phase pollution experiments and gas-phase salt spray pollution experiments, establish an expression for the comprehensive accumulation mass of sodium ions under pollution conditions using the least squares method. The specific steps are as follows:

[0107] First, based on the experimental results of liquid-phase pollution and gas-phase salt spray pollution respectively, the least squares method is used to perform linear fitting to obtain the corresponding fitting functions. We constructed fitted expressions for the mass fraction of sodium ions at different times under two types of sodium ion pollution conditions, relating them to the mass concentration of sodium ions and time. .

[0108] Under both types of sodium ion pollution conditions, there is a conversion relationship between the mass fraction of sodium ions and the cumulative mass of sodium ions. Therefore, and By combining the two formulas, we can obtain an expression for the cumulative mass of sodium ions under the corresponding sodium ion pollution conditions, which is related to the mass concentration of sodium ions and time. This expression can then be used in the subsequent process of constructing an expression for the comprehensive cumulative mass of sodium ions under pollution conditions.

[0109] The cumulative mass of sodium ions under both liquid-phase and gaseous salt spray pollution conditions is expressed as a function of sodium ion concentration and time. A least squares method is then used to construct an expression for the comprehensive accumulated mass of sodium ions under pollution conditions. Specifically, the expressions for the cumulative mass of sodium ions under both liquid-phase and gaseous salt spray pollution conditions are weighted by preset first and second weighting coefficients, respectively. An objective function is then established, and the first and second weighting coefficients that minimize this objective function are solved using the least squares criterion. Finally, the expression for the comprehensive accumulated mass of sodium ions under pollution conditions is obtained.

[0110] In a specific embodiment, the expression for the relative sodium ion occupancy rate is as follows:

[0111] ;

[0112] in, Indicates the relative sodium ion occupancy rate; The amount of sodium is expressed as the total accumulated mass of sodium ions under polluted conditions, and is calculated using an expression. The amount of substance at sulfonic acid group sites in the proton exchange membrane is calculated using the following formula:

[0113] ;

[0114] in, This is the equivalent weight of the proton exchange membrane. This represents the actual weight of the proton exchange membrane.

[0115] Specifically, after constructing an expression for the total accumulated mass of sodium ions under polluted conditions, the relative sodium-ion occupancy (RSO) can be calculated. RSO characterizes the relative proportion of sodium ions occupying sulfonic acid group sites on the proton exchange membrane; in the formula for calculating RSO... and All are known terms. Given the expression for the total accumulated mass of sodium ions under polluted conditions, we can calculate *m* by combining the sodium ion mass concentration and time. Then, we can use *m / 23* to calculate... Therefore, the RSO (Residual Sodium ion contamination) can be used to reflect the degree of sodium ion contamination. By setting different RSOs, the impact of different degrees of sodium ion contamination on the performance degradation of proton exchange membrane fuel cells can be illustrated.

[0116] S3. Identify candidate model parameters that are related to the baseline model and change with sodium ion pollution. Conduct sensitivity analysis of the candidate model parameters on fuel cell output performance under changes in relative sodium ion occupancy. Calculate the average change in stack voltage and the average normalized parameter sensitivity. Based on the average change in stack voltage and the average normalized parameter sensitivity, select key pollution parameters from the candidate model parameters.

[0117] In a specific embodiment, a sensitivity analysis of the candidate model parameters on the fuel cell output performance under changes in relative sodium ion occupancy is conducted, and the average change in stack voltage and the average normalized parameter sensitivity are calculated, specifically including:

[0118] While keeping all parameters in the baseline model except for the candidate model parameters unchanged, each candidate model parameter is adjusted from a pollution-free value to a pollution value under the corresponding relative sodium ion occupancy condition. Under different analytical conditions, the change in fuel cell stack voltage and the average change in stack voltage caused by the change in the k-th candidate model parameter are calculated using the baseline model after adjusting the candidate model parameters. The relative change in fuel cell stack voltage caused by the change in the k-th candidate model parameter is calculated under different analytical conditions. Combined with the change in the k-th candidate model parameter, the normalized parameter sensitivity and the average normalized parameter sensitivity of the k-th candidate model parameter under different analytical conditions are calculated, as shown in the following formula:

[0119] ;

[0120] in, For the first The candidate model parameters are at the th . The change in stack voltage caused by each analytical operating condition; For the first The candidate model parameters are at the th . Sensitivity of normalized parameters under various analytical conditions; The stack voltage was calculated using pollution-free values ​​for all candidate model parameters. To only the first The stack voltage calculated when the parameters of each candidate model are adjusted to the corresponding pollution values; For the first Uncontaminated values ​​of the parameters of each candidate model; For the first Under the first analytical working condition, the first Contamination values ​​of candidate model parameters; For the first The average change in stack voltage of each candidate model parameter; For the first Average normalized parameter sensitivity of candidate model parameters; This is to analyze the total number of operating conditions.

[0121] In a specific embodiment, the candidate model parameters include at least the mole fraction of hydrogen, the mole fraction of oxygen, the mole fraction of water vapor, temperature, liquid water saturation, membrane water content, and current density; the key contamination parameters are determined to be membrane water content and current density by combining the average change in stack voltage with the sensitivity analysis of the average normalized parameter.

[0122] In specific embodiments, the analyzed operating conditions include current densities of 0.4 A / cm², 0.8 A / cm², and 1.2 A / cm².

[0123] Specifically, first, candidate model parameters for changes caused by sodium ion pollution are identified. These candidate model parameters are not only the input and output parameters of the baseline model, but also variables that affect the internal structure of the baseline model. Furthermore, by referring to literature, one candidate model parameter can be adjusted from its pollution-free value to its pollution value under the corresponding RSO condition. Then, under single-factor perturbation, a sensitivity analysis of the effects of each candidate model parameter on the fuel cell output performance under RSO changes is conducted. Candidate model parameters include at least hydrogen mole fraction, oxygen mole fraction, water vapor mole fraction, temperature, liquid water saturation, membrane water content, and current density.

[0124] To eliminate the influence of changes in different candidate model parameters on the sensitivity analysis results, under different analysis conditions, the ratio of the relative change in stack voltage caused by the change in the k-th candidate model parameter to the relative change in the candidate model parameter itself is calculated to obtain the average normalized parameter sensitivity of the k-th candidate model parameter.

[0125] In one example, sensitivity analysis was conducted under three current densities: 0.4 A / cm², 0.8 A / cm², and 1.2 A / cm². The average change in stack voltage and the average normalized parameter sensitivity caused by variations in candidate model parameters were calculated. In another example, the relative sodium ion occupancy (RSO) ranged from 0 to 1, and six sodium ion contamination conditions were defined: 0 mg / L, 1.01 mg / L, 2.99 mg / L, 4.92 mg / L, 6.79 mg / L, and 8.62 mg / L.

[0126] The embodiments of this application use the average change in stack voltage as the main screening index and the average normalized parameter sensitivity as an auxiliary evaluation index to screen key pollution parameters from candidate model parameters. The key pollution parameters are selected preferentially from the current density and membrane water content, which can be directly characterized in the benchmark model and have a significant impact on the stack voltage output of the benchmark model.

[0127] S4. Construct pollution correction coefficients based on key pollution parameters, use the pollution correction coefficients to correct the baseline model, and then perform dynamic simulation to obtain the stack polarization characteristic curves under different sodium ion pollution conditions.

[0128] In a specific embodiment, step S4 specifically includes:

[0129] The equivalent membrane water content under sodium ion pollution conditions is calculated by weighting the equivalent membrane water content of the hydrogen ion membrane and the equivalent membrane water content of the sodium ion membrane based on the relative sodium ion occupancy rate, as shown in the following formula:

[0130] ;

[0131] in, This represents the equivalent membrane water content under sodium ion contamination conditions. This represents the equivalent membrane water content in hydrogen ion form. This represents the equivalent membrane water content in sodium ion form. Indicates the relative sodium ion occupancy rate;

[0132] The equivalent membrane water content of the hydrogen ion membrane and the equivalent membrane water content of the sodium ion membrane are respectively:

[0133] ;

[0134] in, Water activity;

[0135] The fouling correction factor for membrane water content is constructed based on the equivalent membrane water content under fouling conditions, as shown in the following formula:

[0136] ;

[0137] in, This is the fouling correction factor for membrane water content;

[0138] The membrane water content output from the baseline model is corrected using a fouling correction factor to obtain the corrected membrane water content under fouled conditions, as shown in the following formula:

[0139] ;

[0140] in, The membrane water content output by the baseline model. This represents the corrected membrane water content under fouling conditions.

[0141] A first reference cell voltage and a second reference cell voltage are selected, with the second reference current density being greater than the first reference current density. Under the reference current densities corresponding to the first and second reference cell voltages, a functional relationship between different relative sodium ion occupancy rates and the reference current density is established, as shown in the following equation:

[0142] ;

[0143] ;

[0144] in, and These are the first reference current density and the second reference current density under the first reference battery voltage and the second reference battery voltage, respectively. This is a functional relationship between the relative sodium ion occupancy rate and the reference current density, established using piecewise linear interpolation, monotonic interpolation, or curve fitting methods.

[0145] Based on the ratio of the reference current density under sodium ion contamination conditions to the reference current density under sodium ion-free conditions, the current carrying capacity attenuation coefficients corresponding to the first and second reference cell voltages are constructed as shown in the following formula:

[0146] ;

[0147] in, and These are the current carrying capacity attenuation coefficients corresponding to the first and second reference cell voltages under sodium ion contamination conditions, respectively. and These are the reference current densities corresponding to the first and second reference cell voltages under conditions free of sodium ion contamination, respectively.

[0148] The actual operating current density of the fuel cell is calculated based on the actual input current of the fuel cell and the effective reaction area of ​​a single fuel cell, as shown in the following formula:

[0149] ;

[0150] in, For fuel cells in The actual operating current density at any given time, For fuel cells in The actual input current at any given time. The effective reaction area of ​​a single fuel cell;

[0151] The unlimited normalized current position is calculated based on the actual operating current density of the fuel cell, the first reference current density, and the second reference current density, as shown in the following formula:

[0152] ;

[0153] in, for The position of the unlimited normalized current at time;

[0154] The unlimited normalized current position is restricted to the range of 0 to 1 to obtain the limited normalized current position. Based on the limited normalized current position, a cubic smoothing function is used to calculate the transition weight between the first reference battery voltage and the second reference battery voltage, as shown in the following formula:

[0155] ;

[0156] ;

[0157] in, express The position of the normalized current after the time limit. express The transition weight at each time step ranges from 0 to 1.

[0158] Based on the current carrying capacity attenuation coefficients and transition weights corresponding to the first and second reference cell voltages under sodium ion contamination conditions, the composite current carrying capacity attenuation coefficient, which varies with the relative sodium ion occupancy rate and the actual operating current density, is obtained as shown in the following formula:

[0159] ;

[0160] in, Indicates the attenuation coefficient of composite current carrying capacity;

[0161] Based on the composite current carrying capacity attenuation coefficient, the actual operating current density is mapped to the equivalent current density used for calculating fuel cell polarization losses under sodium ion contamination conditions, as shown in the following formula:

[0162] ;

[0163] in, This represents the equivalent current density used for calculating polarization losses in fuel cells under sodium ion contamination conditions.

[0164] The equivalent current density is input into the benchmark model to obtain the stack voltage output by the proton exchange membrane fuel cell stack model under sodium ion contamination conditions, which is used as the value of the vertical axis of the stack polarization characteristic curve. The value of the horizontal axis of the stack polarization characteristic curve is calculated using the actual operating current density, and the stack polarization characteristic curves under different sodium ion contamination conditions are plotted.

[0165] In a specific embodiment, the relative sodium ion occupancy rate ranges from 0 to 1, and six sodium ion pollution conditions are defined with sodium ion pollution concentrations of 0 mg / L, 1.01 mg / L, 2.99 mg / L, 4.92 mg / L, 6.79 mg / L, and 8.62 mg / L.

[0166] Specifically, pollution correction coefficients are constructed based on the selected key pollution parameters. These coefficients are then embedded into a benchmark model, and dynamic simulation calculations are used to obtain the stack polarization characteristic curves under different sodium ion pollution conditions. The pollution correction coefficients include a pollution correction coefficient for membrane water content and a composite current carrying capacity attenuation coefficient corresponding to current density.

[0167] For membrane water content, the equivalent membrane water content of the hydrogen ion membrane and the equivalent membrane water content of the sodium ion membrane are first calculated using the water activity obtained from the empirical formula in the reference. Then, the equivalent membrane water content of the hydrogen ion membrane and the equivalent membrane water content of the sodium ion membrane are weighted and calculated using the RSO value to obtain the equivalent membrane water content under fouling conditions. Based on the equivalent membrane water content under fouling conditions and the equivalent membrane water content of the hydrogen ion membrane, a fouling correction coefficient for membrane water content is constructed. This fouling correction coefficient is then used to correct the membrane water content output by the baseline model.

[0168] For current density, an equivalent current density is constructed based on dual reference voltage feature points to map and correct the baseline model. The dual reference voltage feature points include a first reference cell voltage and a second reference cell voltage. In one example, the first and second reference cell voltages are 0.6V and 0.3V, respectively. Using 0.6V and 0.3V as the first and second reference cell voltages, and based on sodium ion contamination conditions corresponding to different RSOs, a functional relationship between RSO and reference current density is established at the reference current density corresponding to the preset reference cell voltage. This functional relationship can be obtained using piecewise linear interpolation, monotonic interpolation, or curve fitting methods. Based on the ratio of the reference current density under contaminated conditions to that under uncontaminated conditions, current carrying capacity attenuation coefficients for the first and second reference cell voltages are constructed. The actual operating current density is calculated based on the actual input current of the fuel cell and the effective reaction area of ​​a single fuel cell. To characterize the position of the actual operating current density between two reference current densities, when the second reference current density is greater than the first reference current density, an unlimited normalized current position is calculated. This unlimited normalized current position represents the interval position of the actual operating current density relative to the first and second reference current densities at the same moment. The unlimited normalized current position is restricted to the range of 0 to 1, and a cubic smoothing function is used to calculate the transition weight between the two characteristic points. When the actual operating current density is not higher than the first reference current density, the transition weight is 0; when the actual operating current density is not lower than the second reference current density, the transition weight is 1. Based on the current carrying capacity attenuation coefficients corresponding to the first and second reference battery voltages under sodium ion contamination conditions, and the transition weight, a composite current carrying capacity attenuation coefficient varying with relative sodium ion occupancy and actual operating current density is obtained. Below the first reference current density, the current carrying capacity attenuation coefficient corresponding to the first reference battery voltage is used; above the second reference current density, the current carrying capacity attenuation coefficient corresponding to the second reference battery voltage is used. A smooth transition is performed between the two reference current densities according to the transition weight. Based on the degradation coefficient of the composite current carrying capacity, the actual operating current density is mapped to an equivalent current density for calculating fuel cell polarization losses. This equivalent current density is input into the activation polarization, ohmic polarization, and concentration polarization calculation modules in the proton exchange membrane fuel cell stack model to obtain the stack voltage under sodium ion contamination conditions. This stack voltage can be used as the value of the ordinate of the stack polarization characteristic curve. The actual operating current density is then used to calculate the value of the abscissa of the stack polarization characteristic curve, thus obtaining the stack polarization characteristic curve. Therefore, the degradation law of the fuel cell stack polarization characteristic curve under different sodium ion contamination levels can be studied. This invention can provide a theoretical basis for fuel cell system reliability assessment and lifespan prediction.

[0169] The technical effects of the embodiments of this application are illustrated below through specific examples.

[0170] First, plot the stack polarization characteristic curves under pollution-free conditions, such as... Figure 3 As shown, the single-cell voltage continuously decreases with increasing current density, exhibiting a non-linear trend of initial rapid decrease, followed by a slow decrease, and then a renewed acceleration at the end. In the low current density range (approximately 0–0.2 A / cm²), the voltage drops rapidly from approximately 0.95 V to 0.66 V, with a relatively steep curve. In the medium current density range (approximately 0.2–1.0 A / cm²), the voltage decrease rate slows down, gradually decreasing from approximately 0.66 V to 0.46 V, with a relatively flat curve. When the current density further increases to 1.0–1.4 A / cm², the voltage decrease gradually accelerates, especially near 1.4 A / cm², where the curve bends significantly downward, and the voltage drops to approximately 0.20 V. The rapid decrease at the beginning of the low current density stage and the accelerated decrease at the end of the high current density stage are the most pronounced.

[0171] The overall trend of the experimental data and simulation curves is consistent, both showing an increase in current density and a decrease in voltage. Local comparisons show that in the range of approximately 0.2–0.5 A / cm², the simulated voltage is slightly lower than the experimental value; near approximately 0.6–0.7 A / cm², the two are quite close; and in the range of approximately 0.8–1.2 A / cm², the simulated voltage is slightly higher than the experimental value. As can be seen from the figure, the baseline model can effectively reflect the trend of the polarization curve under the pollution-free operating condition.

[0172] The candidate model parameters are selected as follows: hydrogen mole fraction, oxygen mole fraction, water vapor mole fraction, temperature, liquid water saturation, membrane water content, and current density, and are denoted as x. H2 x O2 x H2O 、T、s l , lamda and j, such as Figure 4As shown in (a), the average change in stack voltage caused by variations in the parameters of each candidate model differs significantly. Under the three current density analysis conditions, current density, as a candidate model parameter, causes the largest change in stack voltage, and this increase is most pronounced under the analysis condition with a current density of 1.4 A / cm². Membrane water content also causes a relatively large change in stack voltage, second only to current density under the analysis conditions of 0.4 A / cm² and 0.8 A / cm². The effect of liquid water saturation increases significantly with increasing operating current density; under the analysis condition with a current density of 1.4 A / cm², the change in stack voltage caused by liquid water saturation is slightly higher than that caused by membrane water content. In contrast, the changes in stack voltage caused by the mole fractions of the three gases and temperature are relatively small. The effect of oxygen mole fraction is greater than that of hydrogen and water vapor mole fractions, and the changes in stack voltage corresponding to the three mole fractions do not vary significantly across different operating conditions.

[0173] like Figure 4 As shown in (b), the relative ranking of the parameters of each candidate model changed after evaluation using normalized parameter sensitivity. Under analytical conditions with current densities of 0.4 A / cm² and 0.8 A / cm², temperature showed the highest sensitivity to the normalized parameter, followed by current density. When the operating current density increased to 1.4 A / cm², the sensitivity of the normalized parameter for current density increased significantly, surpassing temperature and becoming the most sensitive variable. The sensitivity of the normalized parameter for membrane water content increased with increasing operating current density, but remained lower than that for temperature and current density under all three analytical conditions. The sensitivity of the normalized parameter for liquid water saturation was low under low and medium current density analytical conditions, but significantly increased under high current density analytical conditions. The sensitivity of the normalized parameter for the mole fractions of the three gases was relatively low, with oxygen showing a slightly higher sensitivity, while hydrogen and water vapor mole fractions were relatively close.

[0174] comprehensive Figure 4 It can be seen that current density has the most significant impact on the stack voltage, while membrane water content also has a relatively significant voltage effect under the three analytical conditions. Therefore, using the average change in stack voltage as the main screening criterion and the sensitivity of normalized parameters as an auxiliary evaluation criterion, current density and membrane water content were selected as key contamination correction parameters.

[0175] Depend on Figure 5 It can be seen that, under both pollution-free and varying sodium ion pollution concentrations, the single-cell voltage decreases with increasing current density. At the same current density, the voltages of the curves, from highest to lowest, are as follows: pollution-free, ... =1.01mg / L =2.99mg / L =4.92mg / L =6.79 mg / L and =8.62mg / L, indicating that with As the voltage increases, the voltage drop calculated by the model gradually increases, and the polarization curve shifts downwards overall. Among these, The curve for 1.01 mg / L is quite similar to the curve for no pollution, and the voltage drop is relatively small. =6.79 mg / L and The curve for 8.62 mg / L deviates significantly from the uncontaminated curve, especially... The voltage drop was most pronounced when the concentration was 8.62 mg / L.

[0176] Within the common current density range of all polarization curves, the voltage difference under different levels of contamination generally widens with increasing current density. For example, at a current density of approximately 0.4 A / cm², the voltage of a single cell in the uncontaminated state is approximately 0.59 V, while... When the concentration was 8.62 mg / L, the voltage dropped to approximately 0.35 V, a difference of about 0.24 V. Furthermore, with... As the voltage increases at equal intervals, the voltage difference between adjacent curves is not equal. The difference is more pronounced under conditions of high sodium ion pollution concentration, demonstrating a nonlinear relationship between the degree of sodium ion pollution and voltage drop.

[0177] At the same output voltage, the higher the sodium ion contamination concentration, the larger the RSO, and the lower the corresponding current density, indicating that the current output capability gradually decreases while maintaining this voltage level. When the voltage approaches 0.3V, the current density corresponding to the uncontaminated polarization curve is approximately 1.33A / cm², while... The polarization curve at 8.62 mg / L corresponds to a current density of only about 0.50 A / cm². Therefore, under the illustrated model and operating conditions, increasing RSO not only reduces the output voltage at the same current density but also gradually shrinks the range of current densities required to maintain voltages of 0.3V and above. The performance degradation was most pronounced under sodium ion contamination conditions of 8.62 mg / L.

[0178] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for modeling the performance degradation of proton exchange membrane fuel cells under sodium ion contamination, characterized in that, Includes the following steps: A proton exchange membrane fuel cell stack model, cathode flow channel model, anode flow channel model, and water transport model under pure conditions were established and used as the benchmark model. Based on experimental data of liquid-phase pollution and gas-phase salt spray pollution, an expression for the comprehensive accumulation mass of sodium ions under pollution conditions was constructed using the least squares method. The relative sodium ion occupancy rate is calculated based on an expression for the total accumulated mass of sodium ions under polluted conditions. This relative sodium ion occupancy rate is used to characterize the relative proportion of sodium ions occupying sulfonic acid group sites on the proton exchange membrane. Candidate model parameters that are related to the baseline model and change with sodium ion pollution are identified. Sensitivity analysis of the candidate model parameters to fuel cell output performance is carried out under the change of the relative sodium ion occupancy rate. The average change of stack voltage and the average normalized parameter sensitivity are calculated. Key contamination parameters are selected from the candidate model parameters based on the average change in the stack voltage and the sensitivity of the average normalized parameter. Based on the key pollution parameters, a pollution correction coefficient is constructed. The baseline model is then corrected using the pollution correction coefficient, and dynamic simulation is performed to obtain the stack polarization characteristic curves under different sodium ion pollution conditions.

2. The method for modeling the performance degradation of proton exchange membrane fuel cells under sodium ion contamination according to claim 1, characterized in that, Based on experimental data from liquid-phase pollution and gas-phase salt spray pollution, an expression for the comprehensive accumulation mass of sodium ions under pollution conditions is established using the least squares method, specifically including: Based on the experimental results of liquid-phase pollution and gas-phase salt spray pollution respectively, the least squares method was used for linear fitting to obtain the fitting expressions of sodium ion mass fraction at different times under the two types of sodium ion pollution conditions of liquid-phase pollution and gas-phase salt spray pollution, as shown in the following formula: ； in, An index indicating conditions of sodium ion contamination. , and These represent liquid-phase sodium ion contamination conditions and gas-phase salt spray sodium ion contamination conditions, respectively. This represents the mass fraction of sodium ions under the corresponding sodium ion contamination conditions. The fitting function obtained by linear fitting; This indicates the mass concentration of sodium ions. Indicates time; Under both types of sodium ion pollution conditions, the mass fraction of sodium ions and the cumulative mass of sodium ions are converted using the following relationship: ； in, The cumulative mass of sodium ions under the corresponding sodium ion pollution conditions. The total mass of the fuel cell membrane electrode assembly; right and Combining the two formulas, we obtain the expression for the cumulative mass of sodium ions under the corresponding sodium ion pollution conditions, relating to the sodium ion concentration and time, as shown in the following equation: ； The comprehensive accumulated mass of sodium ions under pollution conditions is calculated based on the cumulative mass of sodium ions under the corresponding sodium ion pollution conditions, as shown in the following formula: ； in, This represents the total accumulated mass of sodium ions under polluted conditions. and Let these represent the first weighting coefficient and the second weighting coefficient, respectively. ; The objective function Z is constructed as shown in the following equation: ； in, This indicates the first weighting coefficient or the second weighting coefficient. The index representing the calculation condition, the first... The calculation conditions are based on the sodium ion mass concentration. and pollution time jointly determined, This indicates the total number of sets of calculation conditions; Indicates the first The accumulated mass of sodium ions under liquid-phase sodium ion pollution conditions or gas-phase salt spray sodium ion pollution conditions calculated by the first set of calculations. mass concentration under group calculation conditions and pollution time Simultaneously, substituting the expression for the cumulative mass of sodium ions under the corresponding sodium ion pollution conditions with respect to the mass concentration of sodium ions and time, we obtain the following: Indicates the first The weighted cumulative mass of sodium ions obtained under the group calculation conditions is obtained by calculating the first... Accumulation mass of sodium ions under liquid-phase sodium ion contamination conditions under set calculation conditions The accumulation mass of sodium ions under conditions of sodium ion pollution in gaseous salt spray or other forms of pollution. The result is obtained by substituting the formula for calculating the total accumulated mass of sodium ions under polluted conditions; When using the least squares method to find the minimum value of the objective function Then, this expression, along with the expression for the cumulative mass of sodium ions under the corresponding sodium ion pollution conditions in terms of sodium ion mass concentration and time, is substituted into the formula for calculating the comprehensive accumulated mass of sodium ions under pollution conditions, thus obtaining the established expression for the comprehensive accumulated mass of sodium ions under pollution conditions.

3. The method for modeling the performance degradation of proton exchange membrane fuel cells under sodium ion contamination according to claim 1, characterized in that, The expression for the relative sodium ion occupancy rate is as follows: ； in, Indicates the relative sodium ion occupancy rate; The amount of sodium is expressed as the total accumulated mass of sodium ions under polluted conditions, and is calculated using an expression. The amount of substance at sulfonic acid group sites in the proton exchange membrane is calculated using the following formula: ； in, This is the equivalent weight of the proton exchange membrane. This represents the actual weight of the proton exchange membrane.

4. The method for modeling the performance degradation of proton exchange membrane fuel cells under sodium ion contamination according to claim 1, characterized in that, Sensitivity analysis of the candidate model parameters to fuel cell output performance under changes in the relative sodium ion occupancy rate was conducted, and the average change in stack voltage and the average normalized parameter sensitivity were calculated, specifically including: While keeping all parameters in the baseline model except for the candidate model parameters unchanged, each candidate model parameter is adjusted from a pollution-free value to a pollution value under the corresponding relative sodium ion occupancy condition. Under different analytical conditions, the change in fuel cell stack voltage and the average change in stack voltage caused by the change in the k-th candidate model parameter are calculated using the baseline model after adjusting the candidate model parameters. The relative change in fuel cell stack voltage caused by the change in the k-th candidate model parameter is calculated under different analytical conditions. Combined with the change in the k-th candidate model parameter, the normalized parameter sensitivity and the average normalized parameter sensitivity of the k-th candidate model parameter under different analytical conditions are calculated, as shown in the following formula: ； in, For the first The candidate model parameters at the th ... The change in stack voltage caused by each analytical operating condition; For the first The candidate model parameters at the th ... Sensitivity of normalized parameters under various analytical conditions; The stack voltage was calculated using pollution-free values ​​for all candidate model parameters. To only the first The stack voltage calculated when the parameters of each candidate model are adjusted to the corresponding pollution values; For the first Uncontaminated values ​​of the parameters of each candidate model; For the first Under the first analytical working condition, the first Contamination values ​​of candidate model parameters; For the first The average change in stack voltage of each candidate model parameter; For the first Average normalized parameter sensitivity of candidate model parameters; This is to analyze the total number of operating conditions.

5. The method for modeling the performance degradation of proton exchange membrane fuel cells under sodium ion contamination according to claim 4, characterized in that, The analysis conditions include current densities of 0.4 A / cm², 0.8 A / cm², and 1.2 A / cm².

6. The method for modeling the performance degradation of proton exchange membrane fuel cells under sodium ion contamination according to claim 1, characterized in that, The candidate model parameters include at least the mole fraction of hydrogen, the mole fraction of oxygen, the mole fraction of water vapor, temperature, liquid water saturation, membrane water content, and current density; the key contamination parameters are determined to be membrane water content and current density by combining the average change in stack voltage with the sensitivity analysis of the average normalized parameter.

7. The method for modeling the performance degradation of proton exchange membrane fuel cells under sodium ion contamination according to claim 6, characterized in that, Based on the key pollution parameters, pollution correction coefficients are constructed. These coefficients are then used to correct the baseline model. Dynamic simulations are then performed to obtain the stack polarization characteristic curves under different sodium ion pollution conditions. Specifically, this includes: The equivalent membrane water content under sodium ion pollution conditions is calculated by weighting the equivalent membrane water content of the hydrogen ion membrane and the equivalent membrane water content of the sodium ion membrane based on the relative sodium ion occupancy rate, as shown in the following formula: ； in, This represents the equivalent membrane water content under sodium ion contamination conditions. This represents the equivalent membrane water content in the form of hydrogen ions. This represents the equivalent membrane water content in sodium ion form. Indicates the relative sodium ion occupancy rate; The equivalent membrane water content of the hydrogen ion membrane and the equivalent membrane water content of the sodium ion membrane are respectively: in, Water activity; The fouling correction factor for membrane water content is constructed based on the equivalent membrane water content under fouling conditions, as shown in the following formula: ； in, This is the fouling correction factor for membrane water content; The membrane water content output from the baseline model is corrected using the fouling correction coefficient, resulting in the corrected membrane water content under fouled conditions, as shown in the following formula: ； in, The membrane water content output by the baseline model. This represents the corrected membrane water content under fouling conditions. By selecting a first reference cell voltage and a second reference cell voltage, and establishing a functional relationship between different relative sodium ion occupancy rates and reference current densities at the corresponding reference cell voltages, as shown in the following equation: ； ； in, and These are the first reference current density and the second reference current density under the first reference battery voltage and the second reference battery voltage, respectively. This is a functional relationship between the relative sodium ion occupancy rate and the reference current density, established using piecewise linear interpolation, monotonic interpolation, or curve fitting methods. Based on the ratio of the reference current density under sodium ion contamination conditions to the reference current density under sodium ion-free conditions, the current carrying capacity attenuation coefficients corresponding to the first and second reference cell voltages are constructed as shown in the following formula: ； in, and These are the current carrying capacity attenuation coefficients corresponding to the first and second reference cell voltages under sodium ion contamination conditions, respectively. and These are the reference current densities corresponding to the first and second reference cell voltages under conditions free of sodium ion contamination, respectively. The actual operating current density of the fuel cell is calculated based on the actual input current of the fuel cell and the effective reaction area of ​​a single fuel cell, as shown in the following formula: ； in, For fuel cells in The actual operating current density at any given time, For fuel cells in The actual input current at any given time. The effective reaction area of ​​a single fuel cell; When the second reference current density is greater than the first reference current density, the unlimited normalized current position is calculated based on the actual operating current density of the fuel cell, the first reference current density, and the second reference current density, as shown in the following formula: ； in, for The position of the unlimited normalized current at time; The unlimited normalized current position is restricted to the range of 0 to 1 to obtain the limited normalized current position. Based on the limited normalized current position, a cubic smoothing function is used to calculate the transition weight between the first and second reference battery voltages, as shown in the following formula: ； ； in, express The position of the normalized current after the time limit. express The transition weight at each time step ranges from 0 to 1. Based on the current carrying capacity attenuation coefficient and transition weight corresponding to the first and second reference battery voltages under the sodium ion contamination conditions, the composite current carrying capacity attenuation coefficient, which varies with the relative sodium ion occupancy rate and the actual operating current density, is obtained as shown in the following formula: ； in, Indicates the attenuation coefficient of composite current carrying capacity; Based on the composite current carrying capacity attenuation coefficient, the actual operating current density is mapped to the equivalent current density used for calculating fuel cell polarization loss under sodium ion contamination conditions, as shown in the following formula: ； in, This represents the equivalent current density used for calculating polarization losses in fuel cells under sodium ion contamination conditions. The equivalent current density is input into the reference model to obtain the stack voltage output by the proton exchange membrane fuel cell stack model under sodium ion pollution conditions, which is used as the value of the vertical axis of the stack polarization characteristic curve. The value of the horizontal axis of the stack polarization characteristic curve is calculated using the actual operating current density, and the stack polarization characteristic curves under different sodium ion pollution conditions are plotted.

8. The method for modeling the performance degradation of proton exchange membrane fuel cells under sodium ion contamination according to claim 7, characterized in that, The relative sodium ion occupancy rate ranges from 0 to 1, and six sodium ion pollution conditions are defined, with sodium ion pollution concentrations of 0 mg / L, 1.01 mg / L, 2.99 mg / L, 4.92 mg / L, 6.79 mg / L, and 8.62 mg / L.

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