PEM electrolytic cell efficiency optimization method based on PSO optimization algorithm

Abstract

The invention discloses a PEM electrolytic cell efficiency optimization method based on a PSO optimization algorithm. The method specifically comprises the steps that electrolytic cell system simulation results under multiple working conditions are calculated through a three-dimensional proton exchange membrane electrolytic cell multi-physical field model, and a data set is constructed; an ANN (artificial neural network) proxy model and a PSO (particle swarm optimization) algorithm are combined, and the operation variables are optimized in the full-power interval of the electrolytic cell; under the condition of ensuring that the maximum temperature of the membrane does not exceed 80 DEG C, determining the optimal working state of the electrolytic cell; and finally, determining a plurality of working condition points and drawing an efficiency contour line, and verifying whether the optimal operation variable combination realizes efficiency maximization under the power so as to verify the accuracy of a result. The method can reasonably balance improvement of hydrogen production efficiency, reduction of energy consumption of an auxiliary system and thermal safety guarantee in a full-power interval, and has certain effectiveness and practicability.

Description

Technical Field

[0001] The present invention belongs to the technical field of energy system optimization, and particularly relates to a method for optimizing the efficiency of a PEM electrolyzer based on a PSO optimization algorithm. Background Art

[0002] With the development of the low-carbon economy and the severe situation of global emission reduction and energy consumption reduction, as a clean energy storage medium, hydrogen energy has gradually become a key choice to replace traditional energy due to its high energy density, zero emissions, and renewable characteristics. Proton exchange membrane water electrolysis hydrogen production technology has become the most promising green hydrogen production technology at present due to its fast response ability, high current density tolerance, and adaptability to the intermittency and volatility of renewable energy. The performance of a PEM electrolyzer is mainly reflected in the electrolysis efficiency, and its comprehensive evaluation also includes key factors such as the energy consumption of auxiliary systems such as water pumps and radiators, and the thermal safety of the electrolyzer. Therefore, when evaluating the overall efficiency of a PEM electrolyzer, the comprehensive influence of these factors must be considered comprehensively.

[0003] In the existing research on optimizing the performance of electrolyzers, the operating variables mostly focus on increasing hydrogen production and electrolysis efficiency. It has been found that high temperature and low flow rate conditions help to reduce activation and ohmic polarization and reduce the bubble coverage on the catalyst surface. However, high temperature is likely to cause membrane drying effect and degradation of ion exchange resin, resulting in thinner membranes, reduced impedance, and increased risk of hydrogen permeation. And most of the existing research is based on low-latitude simplified models (such as lumped, one-dimensional models) or simplified three-dimensional models (such as single-channel, small-size direct channels without manifolds), which are difficult to accurately reflect the influence of operating parameters (such as inlet flow rate, temperature) on the performance of the electrolyzer, especially limited in simulating uneven temperature distribution. In addition, the energy consumption of auxiliary systems is often ignored. For example, the energy consumption of heat exchangers and circulating water pumps increases significantly at high operating temperatures and high current densities, affecting the overall efficiency of the system.

[0004] Therefore, when optimizing the performance of the electrolyzer, it is necessary to consider both efficiency and the safety of the membrane material, and the temperature constraint is a key factor. And constructing a full-size multi-physics field model with a manifold can accurately reflect the temperature distribution caused by uneven internal reactions and can reveal the influence of key operating variables on the performance. Therefore, comprehensively considering the energy consumption of the auxiliary system and the membrane safety temperature constraint to determine the optimal combination of operating parameters under different working conditions can achieve the balance between maximizing efficiency and safe operation. While improving the efficiency of the electrolyzer, it is also necessary to consider how to balance the increased energy consumption of auxiliary equipment.

[0005] In the current optimization methods, it is difficult to significantly shorten the simulation calculation time and reduce the economic cost while ensuring the accuracy when considering a full-size multi-physics field model. Therefore, the existing research lacks an optimization method that can provide an efficient solution for large-scale electrolyzer optimization. Summary of the Invention

[0007] In view of the above problems, the present invention provides a method for optimizing the efficiency of a PEM electrolyzer based on a PSO optimization algorithm.

[0008] The present invention combines a multi-physics electrolyzer model at a scale of 5 cm × 5 cm, an ANN surrogate model, and a PSO optimization algorithm. By modeling the key operating parameters of the electrolyzer (such as inlet water temperature and flow rate), the operating parameters are optimized under different power conditions, thereby improving the overall efficiency of the electrolyzer, forming an efficient optimization framework, aiming to reduce the computational burden and ensure accurate optimization. This method not only considers thermal safety constraints but also optimizes the BOP energy consumption.

[0009] A method for optimizing the efficiency of a PEM electrolyzer based on a PSO optimization algorithm according to the present invention calculates the simulation results of the electrolyzer system under multiple conditions through a three-dimensional proton exchange membrane electrolyzer multi-physics model and constructs a data set; combines an artificial neural network ANN surrogate model with a particle swarm optimization algorithm PSO to optimize the operating variables within the full power range of the electrolyzer; determines the optimal operating state of the electrolyzer under the condition that the maximum membrane temperature does not exceed 80°C; finally, by determining multiple operating points and drawing efficiency contour lines, it is verified whether the optimal operating variable combination at this power achieves efficiency maximization, thereby verifying the accuracy of the results. The specific steps are as follows:

[0010] Step 1: Multi-physics modeling of the PEM electrolyzer.

[0011] Step 1.1: Determination of the multi-physics model, including electrochemical equations and charge conservation, mass conservation, momentum conservation, and energy conservation.

[0012] Step 1.2: Hydrogen production amount of the electrolyzer, the corresponding hydrogen enthalpy value, and the energy consumption model of the entire system.

[0013] Step 2: Establishment of the electrolyzer system efficiency optimization problem.

[0014] Step 2.1: Define the decision variables as: inlet flow rate Q in , inlet temperature T in , operating voltage V cell .

[0015] Step 2.2: Define the system efficiency η sys as the ratio of the hydrogen calorific value corresponding to the hydrogen production amount to the sum of the electric power and the auxiliary system energy consumption, and at the same time consider the maximum temperature T mem,max on the membrane.

[0016] Step 2.3: Define the optimization objective as maximizing the system efficiency η in under the given electrolysis power input P sys , while ensuring that the maximum temperature on the membrane does not exceed the constraint temperature of 80°C.

[0017] Step 3: Based on the multi-physics field model and related formulas, calculate the efficiency and the maximum membrane temperature of the electrolyzer system under multiple working conditions, establish a dataset, and further construct an ANN surrogate model.

[0018] Step 3.1: Determine the input variables as the inlet flow rate Q in , the inlet temperature T in , the operating voltage V cell ; the output variables are the system efficiency η sys , the electrolyzer current I cell , the maximum membrane temperature T mem,max .

[0019] Step 3.2: Design the range and step size of the input variables, simulate the output variables of all working condition points using COMSOL to obtain the results, and divide the obtained input-output results into three parts, namely the training set, the test set, and the validation set, for surrogate model training.

[0020] Step 3.3: Given that the scales and units of the input variables are not unified, normalize the input variables.

[0021] Step 3.4: Adopt the Levenberg-Marquardt algorithm for optimization to minimize the combined squared error and weight parameters; at the same time, use the grid search method to determine the optimal number of hidden layers and the number of neurons in each layer; finally, select two hidden layers, where the number of neurons in each hidden layer is 20 and 30 respectively.

[0022] Step 3.5: After the model training is completed, evaluate the performance of the ANN surrogate model through regression metrics, using the coefficient of determination R 2 and the root mean square error RMSE.

[0023] Step 4: Based on the ANN surrogate model, combined with the particle swarm optimization PSO algorithm, search for the optimal combination of operating variables within the full power range, so as to optimize the performance of the electrolyzer system.

[0024] Step 5: Based on the optimal operating variables in the full power range obtained by the particle swarm optimization algorithm search, select three power points for verification, and draw the efficiency contour lines of these three working condition points to determine whether the optimal combination of operating variables obtained by the PSO search achieves the optimal efficiency under the premise of meeting the safety constraints.

[0025] Furthermore, the multi-physics field model is specifically:

[0026] Charge conservation:

[0027]

[0028] Among them, σ s and σm represent the electronic conductivity and the ionic conductivity respectively, and are the electronic conducting phase and the ionic conducting phase; i v is the volume current source term, obtained from the B-V equation;

[0029]

[0030] wherein, a v is the specific surface area of the catalyst layer, i ref is the reference exchange current density, α is the charge transfer coefficient, F is the Faraday constant, η act is the activation overvoltage, R is the gas constant, T is the temperature distribution.

[0031] Mass conservation:

[0032]

[0033] wherein, S l and S g represent the consumption of liquid water and the generation amount of hydrogen / oxygen respectively; ρ g , u g are the gas density and the gas flow rate respectively, ρ l , u l are the liquid density and the liquid flow rate respectively.

[0034] Momentum conservation:

[0035]

[0036] wherein, S u represents the momentum source term; p g , p l represent the gas and liquid partial pressures respectively, ε eff is the effective porosity, I is the mathematical transfer symbol, μ g , μ l are the gas and liquid dynamic viscosities respectively.

[0037] Energy conservation:

[0038]

[0039] wherein, S T represents the energy source term, ε is the porosity, C p,g , C p,l are the specific heat capacities of the gas and liquid respectively, T is the temperature distribution, k eff is the effective thermal conductivity.

[0040] Furthermore, the hydrogen production amount of the electrolyzer is:

[0041]

[0042] In the formula, F is the Faraday constant.

[0043] The corresponding enthalpy value of hydrogen:

[0044]

[0045] In the formula, is the low hydrogen calorific value.

[0046] The system energy consumption includes two parts. One part is the electric power of the electrolyzer, and the other part is the auxiliary system, including the circulation water pump and the radiator.

[0047] Among them, the electric power of the electrolyzer is expressed as:

[0048] P in =I cell V cell (8)

[0049] The energy consumption of the circulation water pump is expressed as:

[0050]

[0051] In the formula, H pump and ζ pump are the water head and the pump efficiency respectively; ρ w is the density of liquid water.

[0052] The energy consumption of the radiator is expressed as:

[0053]

[0054] In the formula, COP is the performance coefficient of the radiator, C P is the specific heat capacity of liquid water, is the average outlet temperature.

[0055] Therefore, the system efficiency of the electrolyzer is expressed as:

[0056]

[0057] Furthermore, the specific optimization model of the electrolyzer system efficiency is:

[0058]

[0059] x=[T in Q in V cell T (13)

[0060] The constraints are:

[0061] ​

[0062] Among them, x3 is the operating voltage, ∈ pem,T is the constrained temperature of the membrane, x i,min , x i,max are respectively the lower and upper boundaries of the operating variable.

[0063] Furthermore, the normalization formula in step 3 is:

[0064]

[0065] Furthermore, the ratios of the training set, test set, and validation set in step 3 are: 70%, 15%, and 15%.

[0066] Furthermore, the metrics for evaluating the ANN surrogate model in step 3 are:

[0067]

[0068] Furthermore, step 4 is specifically as follows:

[0069] Step 4.1: Particle position initialization:

[0070]

[0071] Step 4.2: Particle velocity initialization:

[0072]

[0073] Step 4.3: Objective function calculation:

[0074] f(x i )(20)

[0075] Step 4.4: Update the particle best position:

[0076] p best,i = x i (21)

[0077] Step 4.5: Update the global best position:

[0078] g best = p best,i (22)

[0079] Step 4.6: Velocity update:

[0080]

[0081] Step 4.7: Position update:

[0082]

[0083] The beneficial technical effects of the present invention are as follows:

[0084] On the premise of ensuring the thermal safety of the electrolyzer system, the present invention improves the overall efficiency. A high-precision and low-cost surrogate model based on artificial neural network (ANN) is proposed to replace the traditional multi-physics model to solve the optimization problem. Taking the maximum membrane temperature as a constraint condition and the overall efficiency as the objective function, the particle swarm optimization (PSO) algorithm is used to determine the optimal combination of inlet air temperature and flow rate at different input powers. By verifying the optimization results, it is proved that this method can reasonably balance the improvement of hydrogen production efficiency, the reduction of auxiliary system energy consumption, and the guarantee of thermal safety in the full power range, showing the effectiveness and practicality of the optimization results. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] Figure 1 It is a system diagram of a proton exchange membrane electrolyzer.

[0086] Figure 2 It is a three-dimensional simulation model diagram of a proton exchange membrane electrolyzer.

[0087] Figure 3 It is a schematic diagram of the ANN surrogate model.

[0088] Figure 4 It is a schematic diagram for verifying the accuracy of the ANN surrogate model.

[0089] Figure 5 It is a curve diagram of the optimal operating variables in the full operating condition range.

[0090] Figure 6 It is a schematic diagram for verifying the accuracy of the operating variables at some operating condition points.

[0091] Figure 7 It is a flow chart of the overall solution of the invention. DETAILED DESCRIPTION OF THE INVENTION

[0092] The present invention will be further described in detail below with reference to the drawings and specific implementation methods.

[0093] A method for optimizing the efficiency of a PEM electrolyzer based on the PSO optimization algorithm of the present invention is as Figure 7 shown. The simulation results of the electrolyzer system under multiple operating conditions are calculated through a three-dimensional multi-physics model of a proton exchange membrane electrolyzer, and a data set is constructed; combined with an artificial neural network ANN surrogate model and a particle swarm optimization algorithm PSO, the operating variables are optimized within the full power range of the electrolyzer; under the condition that the maximum membrane temperature does not exceed 80 °C, the optimal operating state of the electrolyzer is determined; finally, by determining multiple operating condition points and drawing efficiency contour lines, it is verified whether the optimal combination of operating variables at this power achieves the maximum efficiency, so as to verify the accuracy of the results. The specific steps are as follows:

[0094] Step 1: Multi-physics modeling of PEM electrolyzer.

[0095] The proton exchange membrane electrolyzer system as a whole includes a proton exchange membrane electrolyzer, a circulation water pump, and a heat exchanger. The circulation water pump and the heat exchanger belong to the auxiliary system, and the auxiliary system must be considered when considering the energy consumption of the overall system.

[0096] Figure 1 The structural schematic diagram of the proton exchange membrane electrolyzer system is shown. The working principle of the system is that the circulation water pump supplies water to the anode and cathode of the proton exchange membrane electrolyzer at a certain flow rate. Oxygen is generated at the anode and hydrogen is generated at the cathode. The anode outlet is a mixture of oxygen and liquid water, and the cathode outlet is a mixture of hydrogen and liquid water. Oxygen and hydrogen are respectively transported to the hydrogen storage tank and the oxygen storage tank, and the liquid water not only participates in the electrolysis reaction as a reactant, but also plays a role in taking away the heat inside the electrolyzer. Therefore, the liquid water at the electrolyzer outlet is collected, cooled to the inlet water temperature through the heat exchanger, and then continues to flow back to the electrolyzer.

[0097] Figure 2 The three-dimensional simulation model of the proton exchange membrane electrolyzer is shown. The model consists of a proton exchange membrane, an anode and cathode catalyst layer, an anode and cathode diffusion layer, and a flow channel with a manifold. Liquid water flows into the anode and cathode flow channel inlets at a certain flow rate. However, due to geometric constraints, the liquid water flow rates in each flow channel are inconsistent, resulting in differences in the liquid water content entering the diffusion layer, thus causing non-uniformity of the electrochemical reaction. The entire reaction process includes charge conservation, mass conservation, momentum conservation, and energy conservation.

[0098] Therefore, a multi-physics model is established, including electrochemical equations and charge conservation, mass conservation, momentum conservation, and energy conservation.

[0099] Charge conservation:

[0100]

[0101] Among them, σ s and σ m represent the electronic conductivity and ionic conductivity respectively, and are the electronic conducting phase and ionic conducting phase; i v is the volume current source term, obtained from the B-V equation;

[0102]

[0103] Among them, α is the charge transfer coefficient, F is the Faraday constant, η act is the activation overvoltage, R is the gas constant, and T is the temperature distribution.

[0104] Mass conservation:

[0105]

[0106] Among them, S l and S g respectively represent the consumption of liquid water and the production of hydrogen / oxygen; ρ g and u g are the gas density and gas flow rate respectively, and ρ l and u l are the liquid density and liquid flow rate respectively.

[0107] Conservation of momentum:

[0108]

[0109] Among them, S u represents the momentum source term; p g and p l represent the gas and liquid partial pressures respectively, ε eff is the effective porosity, I is the mathematical transfer symbol, and μ g and μ l are the gas and liquid dynamic viscosities respectively.

[0110] Conservation of energy:

[0111]

[0112] Among them, S T represents the energy source term, including the reversible heat, irreversible heat, and ohmic heat of the electrochemical reaction, ε is the porosity, C p,g and C p,l are the specific heat capacities of the gas and liquid respectively, T is the temperature distribution, and k eff is the effective thermal conductivity.

[0113] Furthermore, the hydrogen production of the electrolyzer is:

[0114]

[0115] In the formula, F is the Faraday constant.

[0116] The corresponding hydrogen enthalpy value:

[0117]

[0118] In the formula, is the low hydrogen calorific value.

[0119] The system energy consumption includes two parts. One part is the electric power of the electrolyzer, and the other part is the auxiliary system, including the circulation pump and radiator.

[0120] Among them, the electric power of the electrolyzer is expressed as:

[0121] Pin = I cell V cell (8)

[0122] The energy consumption of the circulating water pump is expressed as:

[0123]

[0124] Wherein, H pump and ζ pump are the head and the pump efficiency respectively; ρ w is the density of liquid water.

[0125] The energy consumption of the radiator is expressed as:

[0126]

[0127] Wherein, COP is the performance coefficient of the radiator, C P is the specific heat capacity of liquid water, is the average outlet temperature.

[0128] Therefore, the system efficiency of the electrolyzer is expressed as:

[0129]

[0130] Step 2: Establish the optimization problem of the electrolyzer system efficiency.

[0131] Step 2.1: Define the decision variables as: the inlet flow rate Q in , the inlet temperature T in , and the operating voltage V cell .

[0132] Step 2.2: Define the system efficiency η sys as the ratio of the hydrogen calorific value corresponding to the hydrogen production amount to the sum of the electric power and the energy consumption of the auxiliary system, and at the same time consider the maximum temperature T mem,max on the membrane.

[0133] Step 2.3: Define the optimization objective as to maximize the system efficiency η in under the given electrolysis power input P sys , while ensuring that the maximum temperature on the membrane does not exceed the constraint temperature of 80 °C.

[0134] The optimization model of the electrolyzer system efficiency is specifically:

[0135]

[0136] x = [T in Q in V cell T (13) ​

[0137] The constraints are as follows:

[0138]

[0139] Among them, x3 is the operating voltage, ∈ pem,T is the constraint temperature of the membrane, x i,min , x i,max are the lower and upper boundaries of the operating variables respectively.

[0140] Step 3: Based on the multi-physics field model and related formulas, calculate the efficiency and the maximum membrane temperature of the electrolytic cell system under multiple working conditions, establish a data set, and further construct an ANN surrogate model (the ANN surrogate model of the present invention is modeled as Figure 3 shown).

[0141] Step 3.1: Determine that the input variables are the inlet flow rate Q in , the inlet temperature T in , the operating voltage V cell ; the output variables are the system efficiency η sy , the electrolytic cell current I cell , the maximum membrane temperature T mem,max .

[0142] Step 3.2: Design the range and step size of the input variables, simulate the output variables of all working condition points using COMSOL and obtain the results, and divide the obtained input-output results into three parts, namely the training set, the test set and the validation set for surrogate model training.

[0143] The range of the designed input variables is as follows: the inlet temperature T in , the lower bound is 60 °C, the upper bound is 80 °C, and the step size is 2 °C; the inlet flow rate Q in , the lower bound is 6 mL / min, the upper bound is 40 mL / min, and the step size is 2 mL / min; the operating voltage V cell The lower bound is 1.4 V, the upper bound is 2.1 V, and the step size is 0.1 V. There are a total of 1496 groups of working conditions. Divide them into three parts for surrogate model training: the training set (70%), the test set (15%) and the validation set (15%).

[0144] Step 3.3: In view of the non-uniform scale and unit of the input variables, normalize the input variables.

[0145] The normalization formula is:

[0146]

[0147] Among them, X is the normalized data, and n is the total number of samples.

[0148] Step 3.4: Optimize using the Levenberg-Marquardt algorithm to minimize the combined squared error and weight parameters; meanwhile, use the grid search method to determine the optimal number of hidden layers and the number of neurons in each layer; finally, select two hidden layers, with the number of neurons in each hidden layer being 20 and 30 respectively.

[0149] is the output of the j-th neuron in the first layer, is the output of the j-th neuron in the l-th layer. f is a non-linear activation function, ω j,k represents the weight between the j-th neuron in the current layer and the k-th neuron in the previous layer, x represents the neuron input variable, and b represents the bias.

[0150] Step 3.5: After the model training is completed, evaluate the performance of the ANN surrogate model through regression metrics, using the coefficient of determination R 2 and the root mean square error RMSE.

[0151]

[0152] where, y k (i) represents the value of the three-dimensional simulation model, represents the predicted value of the ANN model, is the average output of the surrogate model. As Figure 4 shown, the verification results of the ANN surrogate model show that by calculating the coefficient of determination and the root mean square error of the three output variables, the accuracy of the surrogate model is verified and it has a high credibility.

[0153] Step 4: Based on the ANN surrogate model combined with the particle swarm optimization PSO algorithm, search for the optimal combination of operating variables within the full power range to optimize the performance of the electrolyzer system.

[0154] Step 4.1: Initialize the particle position:

[0155]

[0156] Step 4.2: Initialize the particle velocity:

[0157]

[0158] Step 4.3: Calculate the objective function:

[0159] f(x i )(20)

[0160] Step 4.4: Update the best position of the particle:

[0161] p best,i = xi (21)

[0162] Step 4.5: Update the global best position:

[0163] g best = p best,i (22)

[0164] Step 4.6: Velocity update:

[0165]

[0166] Step 4.7: Position update:

[0167]

[0168] Step 5: Based on the optimal operating variables obtained by the particle swarm optimization algorithm in the full power range, select three power points for verification and draw the efficiency contour lines of these three operating conditions to determine whether the optimal operating variable combination obtained by PSO achieves the optimal efficiency while satisfying the safety constraints.

[0169] As Figure 5 shown, the optimization results show that as the power increases, the inlet flow rate gradually rises, the inlet temperature gradually decreases, and the inlet voltage also increases with the increase of power. At the same time, the system efficiency decreases with the increase of the electric power.

[0170] Based on the optimal operating variables obtained by the particle swarm optimization algorithm in the full power range, three power points were selected for verification and the efficiency contour lines of these three operating conditions were drawn to determine whether the optimal operating variable combination obtained by PSO achieves the optimal efficiency while satisfying the safety constraints. As Figure 6 shown, the positions of the optimal operating points corresponding to 11W, 25W, and 35W are all located at the highest efficiency, and the values are consistent with the results in Figure 5 , verifying the rationality of the optimization results.

[0171] The present invention proposes a particle swarm algorithm parameter optimization method based on the combination of a three-dimensional physical field model of a proton exchange membrane electrolyzer and an ANN surrogate model, aiming to maximize the hydrogen production efficiency of the electrolyzer system during service operation, ensure safe operation, prevent membrane degradation, and reduce the energy consumption of the auxiliary system. In view of the high cost of multi-physical field simulation calculations, the proposed joint simulation of the three-dimensional model and the surrogate model provides an effective alternative to shorten the calculation time, and the optimization results based on the surrogate model have been verified and meet the expected requirements. This method is of great significance for improving the optimization efficiency and ensuring the safe operation of PEM electrolyzer single cell or stack systems in commercial applications.

Claims

1. A method for optimizing the efficiency of a PEM electrolyzer based on the PSO optimization algorithm, characterized in that: Calculate the simulation results of the electrolyzer system under multiple working conditions through a three-dimensional proton exchange membrane electrolyzer multi-physics field model and construct a dataset; combine the artificial neural network ANN surrogate model and the particle swarm optimization algorithm PSO to optimize the operating variables within the full power range of the electrolyzer; Under the condition of ensuring that the maximum membrane temperature does not exceed 80 °C, determine the optimal working state of the electrolyzer; finally, by determining multiple working condition points and drawing efficiency contour lines, verify whether the optimal operating variable combination at this power achieves maximum efficiency, so as to verify the accuracy of the results; the specific steps are as follows: Step 1: Multi-physics field modeling of the PEM electrolyzer; Step 1.1: Determine the multi-physics field model, including electrochemical equations and charge conservation, mass conservation, momentum conservation, and energy conservation; Step 1.2: Hydrogen production of the electrolyzer, the corresponding hydrogen enthalpy value, and the energy consumption model of the entire system; Step 2: Establish the electrolyzer system efficiency optimization problem; Step 2.1: Define the decision variables as: inlet flow rate Q in , inlet temperature T in , operating voltage V cell ; Step 2.2: Define the system efficiency η sys which is the ratio of the hydrogen calorific value corresponding to the hydrogen production amount to the sum of the electric power and the energy consumption of the auxiliary system, while considering the maximum temperature T on the membrane mem,max ; Step 2.3: Define the optimization objective as maximizing the system efficiency η in under the given electrolysis power input P sys , while ensuring that the maximum temperature on the membrane does not exceed the constraint temperature of 80 °C; Step 3: Based on the multi-physics field model and relevant formulas, calculate the efficiency and the maximum membrane temperature of the electrolyzer system under multiple working conditions, establish a dataset, and further construct an ANN surrogate model; Step 3.1: Determine that the input variables are the inlet flow rate Q in , the inlet temperature T in , the operating voltage V cell ; The output variable is the system efficiency η sys , the electrolyzer current I cell , the maximum membrane temperature T mem,max ; Step 3.2: Design the input variable range and step size, simulate the output variables of all working condition points using COMSOL and obtain the results, and divide the obtained input and output results into three parts, the training set, the test set, and the validation set for surrogate model training; Step 3.3: In view of the non-uniform scale and unit of the input variables, normalize the input variables; Step 3.4: Use the Levenberg-Marquardt algorithm for optimization to minimize the combined square error and weight parameters; at the same time, use the grid search method to determine the optimal number of hidden layers and the number of neurons in each layer; finally, select two hidden layers, where the number of neurons in each hidden layer is 20 and 30 respectively; Step 3.5: After the model training is completed, evaluate the performance of the ANN surrogate model through regression metrics, and adopt the coefficient of determination R 2 and the root mean square error RMSE; Step 4: Based on the ANN surrogate model, combine the particle swarm optimization PSO algorithm to search for the optimal operating variable combination within the full power range, so as to optimize the performance of the electrolyzer system; Step 5: Based on the optimal operating variables in the full power range obtained by the particle swarm optimization algorithm search, select three power points for verification and draw the efficiency contour lines of these three working condition points to determine whether the optimal operating variable combination obtained by PSO search achieves optimal efficiency under the premise of meeting safety constraints.

2. A PEM electrolyzer efficiency optimization method based on the PSO optimization algorithm according to claim 1, characterized in that: The multi-physics field model is specifically: Charge conservation: Among them, σ s and σ m represent the electronic conductivity and the ionic conductivity respectively, and are the electronic conducting phase and the ionic conducting phase; i v is the volume current source term, which is obtained from the B-V equation; Among them, a v is the specific surface area of the catalytic layer, i ref is the reference exchange current density, α is the charge transfer coefficient, F is the Faraday constant, η act is the activation overvoltage, R is the gas constant, and T is the temperature distribution; Mass conservation: Among them, S l and S g represent the consumption of liquid water and the generation of hydrogen / oxygen respectively; ρ g , u g are the gas density and gas flow rate respectively, and ρ l , u l are the liquid density and liquid flow rate respectively; Momentum conservation: Among them, S u represents the momentum source term; p g , p l represent the gas and liquid partial pressures respectively, ε eff is the effective porosity, I is the mathematical transfer symbol, μ g , μ l are the gas and liquid dynamic viscosities respectively; Energy conservation: Among them, S T represents the energy source term, ε is the porosity, C p,g , C p,l are the specific heat capacities of the gas and the liquid respectively, T is the temperature distribution, k eff is the effective thermal conductivity.

3. A PEM electrolyzer efficiency optimization method based on the PSO optimization algorithm according to claim 1, characterized in that: The hydrogen production of the electrolyzer is: In the formula, F is the Faraday constant; The corresponding hydrogen enthalpy value: In the formula, is the low hydrogen calorific value; The system energy consumption includes two parts, one is the electric power of the electrolyzer, and the other is the auxiliary system, including a circulation water pump and a radiator; Among them, the electric power of the electrolyzer is expressed as: P in = I cell V cell (8) The energy consumption of the circulation water pump is expressed as: where, H pump and ζ pump are the head and the pump efficiency respectively; ρ w is the density of liquid water; The energy consumption of the radiator is expressed as: where COP is the performance coefficient of the radiator, C P is the specific heat capacity of liquid water, is the average outlet temperature; Therefore, the system efficiency of the electrolyzer is expressed as:

4. A method for optimizing the efficiency of a PEM electrolyzer based on a PSO optimization algorithm according to claim 3, characterized in that: The electrolyzer system efficiency optimization model is specifically: x = [T in Q in V cell T (13)​ Constraints are: Among them, x3 is the operating voltage, ∈ pem,T is the constrained temperature of the membrane, x i,min , x i,max and x are the lower and upper boundaries of the operating variable respectively.

5. A PEM electrolyzer efficiency optimization method based on the PSO optimization algorithm according to claim 1, characterized in that: The normalization formula in Step 3 is:

6. The PEM electrolyzer efficiency optimization method based on the PSO optimization algorithm according to claim 1, wherein: The ratio of the training set, test set, and validation set in Step 3 is: 70%, 15%, and 15%.

7. A method for optimizing the efficiency of a PEM electrolyzer based on the PSO optimization algorithm according to claim 1, characterized in that: The indicators for evaluating the ANN surrogate model in Step 3 are:

8. A method for optimizing the efficiency of a PEM electrolyzer based on a PSO optimization algorithm according to claim 1, characterized in that: Step 4 is specifically: Step 4.1: Initialization of particle positions: Step 4.2: Initialization of particle velocities: Step 4.3: Calculation of the objective function: f(x i )(20) Step 4.4: Update of the best particle position: p best,i = x i (21) Step 4.5: Update of the global best position: g best = p best,i (22) Step 4.6: Velocity update: Step 4.7: Position update:

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