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CN117669139A - Optimization method of proton exchange membrane fuel cell flow channel based on improved genetic algorithm - Google Patents

Optimization method of proton exchange membrane fuel cell flow channel based on improved genetic algorithm Download PDF

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CN117669139A
CN117669139A CN202311383438.8A CN202311383438A CN117669139A CN 117669139 A CN117669139 A CN 117669139A CN 202311383438 A CN202311383438 A CN 202311383438A CN 117669139 A CN117669139 A CN 117669139A
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袁伟
李欣泽
张少鹏
柯育智
林镇河
刘子昂
王延刚
李康
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South China University of Technology SCUT
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Abstract

本发明公开了基于改进遗传算法的质子交换膜燃料电池流道优化方法,包括步骤:建立单直流道PEMFC三维模型;针对遗传算法自身在优化求解过程中所存在的种群分布不均匀、容易陷入局部最优解等问题,基于三种改进策略提出了改进的遗传算法。然后,结合改进的遗传算法在综合考虑损耗功率和输出功率的前提下对PEMFC流道的进出口截面尺寸进行仿真优化,从而得到最佳的尺寸配置。本发明不仅能够根据目标函数确定流道的最佳尺寸配置,而且在一定程度上提高了遗传算法的寻优能力和收敛速度,有助于改进质子交换膜燃料电池的设计方式。

The invention discloses a proton exchange membrane fuel cell flow channel optimization method based on an improved genetic algorithm, which includes the steps of: establishing a three-dimensional model of a single straight flow channel PEMFC; aiming at the uneven population distribution and easy falling into localization in the optimization solution process of the genetic algorithm itself. For optimal solution problems, an improved genetic algorithm is proposed based on three improvement strategies. Then, combined with the improved genetic algorithm, the inlet and outlet cross-sectional dimensions of the PEMFC flow channel are simulated and optimized under the premise of comprehensively considering the loss power and output power, so as to obtain the optimal size configuration. The invention can not only determine the optimal size configuration of the flow channel according to the objective function, but also improve the optimization ability and convergence speed of the genetic algorithm to a certain extent, and help improve the design method of the proton exchange membrane fuel cell.

Description

基于改进遗传算法的质子交换膜燃料电池流道优化方法Optimization method of proton exchange membrane fuel cell flow channel based on improved genetic algorithm

技术领域Technical field

本发明涉及燃料电池领域,更具体地说,涉及一种基于改进遗传算法的质子交换膜燃料电池流道优化方法。The present invention relates to the field of fuel cells, and more specifically, to a proton exchange membrane fuel cell flow channel optimization method based on an improved genetic algorithm.

背景技术Background technique

近年来,质子交换膜燃料电池(PEMFC)作为燃料电池的一个重要组成部分,由于其比功率高、启动快、环境特性好等优点在汽车领域和便携式电子设备中具有广泛的应用前景。流道是组成质子交换膜燃料电池(PEMFC)的重要结构之一,在反应物的运输和分配中起着重要作用,是影响电池性能的关键因素。因此,改变流道的几何配置以获得最佳流道形式是提升PEMFC性能的一个重要方面。In recent years, proton exchange membrane fuel cells (PEMFC), as an important component of fuel cells, have broad application prospects in the automotive field and portable electronic devices due to their high specific power, fast startup, and good environmental characteristics. The flow channel is one of the important structures that make up the proton exchange membrane fuel cell (PEMFC). It plays an important role in the transportation and distribution of reactants and is a key factor affecting battery performance. Therefore, changing the geometric configuration of the flow channel to obtain the optimal flow channel form is an important aspect to improve the performance of PEMFC.

一般来说,常规的流道结构主要包括平行流道、蛇形流道、交指流道和点状流道,其中平行流道由于其加工方便,压力损失小,电流密度分布均匀等优势极受欢迎。众多研究人员对平行流道截面形状尺寸进行研究,以期获得最有利于燃料电池运行的最佳截面形状。然而,现阶段的研究方法仅限于对不同截面形状的简单流道进行定性分析,无法获得性能输出与截面几何尺寸精确的定量关系。因此,开发设计一种精确、高效的质子交换膜燃料电池流道优化方法十分必要。Generally speaking, conventional flow channel structures mainly include parallel flow channels, serpentine flow channels, interdigitated flow channels and point flow channels. Among them, parallel flow channels have great advantages due to their convenient processing, small pressure loss, and uniform current density distribution. popular. Many researchers have studied the cross-sectional shape and size of parallel flow channels in order to obtain the best cross-sectional shape that is most beneficial to fuel cell operation. However, current research methods are limited to qualitative analysis of simple flow channels with different cross-sectional shapes, and cannot obtain an accurate quantitative relationship between performance output and cross-sectional geometric dimensions. Therefore, it is necessary to develop and design an accurate and efficient flow channel optimization method for proton exchange membrane fuel cells.

中国专利文献CN112582635A提供了一种PEMFC双极板流道截面的优化方法及三维质子交换膜燃料电池,研究了对于同一种流道结构,不同的流道截面对PEMFC的性能的影响,并且通过优化PEMFC双极板流道结构能够有效提高气体在催化层的均匀性,从而减少冷点、热点和水淹的现象,最终达到降低成本和延长寿命的目的。但是该优化方法只停留在“恒截面”流道的定性研究之上,没有得到最佳截面的精确尺寸配置,且在优化时没有考虑到不同截面所造成的压力损失的影响。目前,仍旧缺少一种精确、高效、全面的质子交换膜燃料电池流道优化方法。Chinese patent document CN112582635A provides a method for optimizing the flow channel cross section of a PEMFC bipolar plate and a three-dimensional proton exchange membrane fuel cell. The impact of different flow channel cross sections on the performance of PEMFC for the same flow channel structure was studied, and through optimization The PEMFC bipolar plate flow channel structure can effectively improve the uniformity of gas in the catalytic layer, thereby reducing cold spots, hot spots and flooding, ultimately achieving the purpose of reducing costs and extending life. However, this optimization method only stays on the qualitative study of "constant cross-section" flow channels, does not obtain the precise size configuration of the optimal cross-section, and does not take into account the influence of pressure losses caused by different cross-sections during optimization. At present, there is still a lack of an accurate, efficient and comprehensive method to optimize the flow channel of proton exchange membrane fuel cells.

发明内容Contents of the invention

本发明提供了一种基于改进遗传算法的质子交换膜燃料电池流道优化方法,通过建立单直流道PEMFC三维模型,结合改进的遗传算法在综合考虑损耗功率和输出功率的前提下对PEMFC流道的进出口截面尺寸进行仿真优化,从而得到最佳的尺寸配置,以至少克服现有技术的不足之一。The present invention provides a proton exchange membrane fuel cell flow channel optimization method based on an improved genetic algorithm. By establishing a three-dimensional model of a single DC channel PEMFC, combined with the improved genetic algorithm, the PEMFC flow channel is optimized under the premise of comprehensively considering the loss power and output power. The inlet and outlet cross-sectional dimensions are simulated and optimized to obtain the best size configuration to overcome at least one of the shortcomings of the existing technology.

为实现上述的技术目的,本发明提供的一种基于改进遗传算法的质子交换膜燃料电池流道优化方法,包括以下步骤:In order to achieve the above technical objectives, the present invention provides a proton exchange membrane fuel cell flow channel optimization method based on an improved genetic algorithm, which includes the following steps:

通过仿真软件COMSOL Multiphysic建立包括阴、阳极流道、气体扩散层(GDL)、催化层(CL)以及质子交换膜(PEM)等计算域在内的单直流道PEMFC三维模型,每个计算域的尺寸参数可根据需要自行设定,该模型控制方程主要包括质量守恒方程、动量守恒方程、能量守恒方程、组分守恒方程、电荷守恒方程以及边界方程;The simulation software COMSOL Multiphysic is used to establish a single DC channel PEMFC three-dimensional model including cathode and anode flow channels, gas diffusion layer (GDL), catalytic layer (CL) and proton exchange membrane (PEM) and other computational domains. The size parameters can be set according to needs. The control equations of this model mainly include mass conservation equation, momentum conservation equation, energy conservation equation, component conservation equation, charge conservation equation and boundary equation;

对单直流道PEMFC三维模型进行网格划分。网格数量设置在70000-95000之间,当电池工作电压为固定值时,在所求解的电流密度差异小于0.05%的范围内,选择网格数量较小的网格;Mesh the single DC channel PEMFC three-dimensional model. The number of grids is set between 70000-95000. When the battery operating voltage is a fixed value, within the range where the difference in current density being solved is less than 0.05%, select a grid with a smaller number of grids;

将单直流道PEMFC三维模型的阴、阳极进、出口截面的尺寸参数设置为优化变量,由改进的遗传算法在MATLAB中按照一定的规律自动生成,并传输到COMSOL Multiphysics中,每组变量对应一种特定的流道结构,并经过模拟计算得出达到收敛条件后的所需参数;The size parameters of the cathode and anode inlet and outlet sections of the single DC channel PEMFC three-dimensional model are set as optimization variables, which are automatically generated in MATLAB according to certain rules by an improved genetic algorithm and transferred to COMSOL Multiphysics. Each set of variables corresponds to a A specific flow channel structure, and through simulation calculations, the required parameters after reaching convergence conditions are obtained;

在电池工作电压为某一固定值的条件下,将仿真计算得到的电流密度和压降输入到MATLAB中,以此计算得到目标函数f,如果目标函数值没有达到最小值,那么个体的基因就会通过遗传、交叉、变异等方式不断改变,流道相应的几何参数也会改变;Under the condition that the battery operating voltage is a certain fixed value, the current density and voltage drop calculated by the simulation are input into MATLAB to calculate the objective function f. If the objective function value does not reach the minimum value, then the individual gene will It will continue to change through inheritance, crossover, mutation, etc., and the corresponding geometric parameters of the flow channel will also change;

根据上述循环过程,在电池工作电压为某一固定值的条件下,改进遗传算法不断迭代寻优,模型结构不断重建再生,从而得到流道最佳的尺寸配置。According to the above cycle process, under the condition that the battery operating voltage is a certain fixed value, the improved genetic algorithm continuously iteratively searches for optimization, and the model structure is continuously reconstructed and regenerated, thereby obtaining the optimal size configuration of the flow channel.

进一步地,还包括步骤:在建立了模型后,将多组仿真计算得到的PEMFC电池极化曲线与真实实验数据进行对比,通过两者的相对误差大小验证该模型的有效性。Further, it also includes steps: after establishing the model, compare the PEMFC battery polarization curves calculated by multiple sets of simulations with real experimental data, and verify the effectiveness of the model through the relative error between the two.

进一步,所述改进的遗传算法,同传统遗传算法相比,做出以下三点改进:Furthermore, compared with the traditional genetic algorithm, the improved genetic algorithm makes the following three improvements:

改进1,所述的改进的遗传算法选择Circle混沌映射作为生成初始种群的方法,该方法具有很强的随机性,会更好游历整个搜索范围,使得初始种群分布地更加均匀,从而有效增加种群的多样性。具体数学表达式如下:Improvement 1. The improved genetic algorithm selects Circle chaos mapping as the method to generate the initial population. This method has strong randomness and will better travel the entire search range, making the initial population more evenly distributed, thereby effectively increasing the population. diversity. The specific mathematical expression is as follows:

其中,mod为取余函数。Among them, mod is the remainder function.

改进2,所述的改进的遗传算法在迭代计算时采用自适应交叉概率Pc和自适应变异概率Pm,以提高算法的寻优能,具体计算公式如下:Improvement 2. The improved genetic algorithm uses adaptive crossover probability P c and adaptive mutation probability P m during iterative calculation to improve the optimization performance of the algorithm. The specific calculation formula is as follows:

其中,fmax为群体中的最大适应度,f为需要交叉的两个体较大的适应度,favg为群体平均适应度,f′为要变异个体的适应度。Among them, f max is the maximum fitness in the group, f is the larger fitness of the two individuals that need to be crossed, f avg is the average fitness of the group, and f′ is the fitness of the individual to be mutated.

改进3,所述的改进的遗传算法采用柯西-高斯变异策略,以确保优化结果为全局最优解,具体数学表达式如下:Improvement 3. The improved genetic algorithm uses the Cauchy-Gaussian mutation strategy to ensure that the optimization result is the global optimal solution. The specific mathematical expression is as follows:

XCG=Xbest[1+λ1cauchy(0,σ2)+λ2Gauss(0,σ2)]X CG =X best [1+λ 1 cauchy(0, σ 2 )+λ 2 Gauss(0, σ 2 )]

其中,XCG为最优个体变异后的位置,σ2为柯西-高斯变异策略的标准差,cauchy(0,σ2)为满足柯西分布的随机变量,Gauss(0,σ2)为满足高斯分布的随机变量,λ1、λ2为随迭代次数自适应调整的动态参数。 Among them , Random variables satisfying Gaussian distribution, λ 1 and λ 2 are dynamic parameters that are adaptively adjusted with the number of iterations.

所述的改进的遗传算法的目标函数f可以根据需要自行设置,对于不同的目标函数f,都会产生一组与之对应的最佳尺寸配置。The objective function f of the improved genetic algorithm can be set as needed. For different objective functions f, a set of corresponding optimal size configurations will be generated.

本发明与现有技术相比的优点在于:The advantages of the present invention compared with the prior art are:

1、本发明针对遗传算法自身在优化过程中所存在的种群分布不均匀、容易陷入局部最优解等问题,基于三种改进策略提出了改进的遗传算法,在一定程度上提高了遗传算法的寻优能力和收敛速度;1. In view of the problems that the genetic algorithm itself has in the optimization process, such as uneven population distribution and easy falling into local optimal solutions, the present invention proposes an improved genetic algorithm based on three improvement strategies, which improves the performance of the genetic algorithm to a certain extent. Optimization ability and convergence speed;

2、本发明采用改进的遗传算法对质子交换膜燃料电池流道阴、阳极进、出口截面同时进行优化,使得优化不仅仅停留在“恒截面”优化的层面上,适应范围更宽,应用更加广泛;2. The present invention uses an improved genetic algorithm to simultaneously optimize the cross-sections of the cathode and anode inlet and outlet of the proton exchange membrane fuel cell flow channel, so that the optimization does not only stay at the level of "constant cross-section" optimization, but has a wider scope of application and more applications. widely;

3、本发明采用改进的遗传算法对质子交换膜燃料电池流道进行优化,可以根据不同的优化需要设置目标函数f,最终可以得到满足条件的精确的尺寸配置,优化过程更加精确、高效、全面。3. The present invention uses an improved genetic algorithm to optimize the proton exchange membrane fuel cell flow channel. The objective function f can be set according to different optimization needs. In the end, an accurate size configuration that meets the conditions can be obtained, and the optimization process is more accurate, efficient and comprehensive. .

附图说明Description of drawings

图1为本发明实施例提供的一种基于改进遗传算法的质子交换膜燃料电池流道优化方法的流程图;Figure 1 is a flow chart of a proton exchange membrane fuel cell flow channel optimization method based on an improved genetic algorithm provided by an embodiment of the present invention;

图2为本发明实施例中单直流道PEMFC三维模型示意图;Figure 2 is a schematic diagram of a three-dimensional model of a single DC channel PEMFC in an embodiment of the present invention;

图中:1-阴极流道;2-阴极气体扩散层;3-阴极催化层;4-质子交换膜;5-阳极催化层;6-阳极气体扩散层;7-阴极流道。In the figure: 1-cathode flow channel; 2-cathode gas diffusion layer; 3-cathode catalytic layer; 4-proton exchange membrane; 5-anode catalytic layer; 6-anode gas diffusion layer; 7-cathode flow channel.

图3为本发明实施例中单直流道PEMFC三维模型网格独立性验证图;Figure 3 is a grid independence verification diagram of the single DC channel PEMFC three-dimensional model in the embodiment of the present invention;

图4为本发明实施例中单直流道PEMFC三维模型准确性验证图;Figure 4 is a verification diagram of the accuracy of the single DC channel PEMFC three-dimensional model in the embodiment of the present invention;

图5为本发明实施例中单直流道PEMFC流道优化截面图;Figure 5 is a cross-sectional view of a single DC channel PEMFC flow channel optimization in an embodiment of the present invention;

图6为本发明实施例中单直流道PEMFC流道优化前后极化曲线对比图。Figure 6 is a comparison chart of polarization curves before and after optimization of the single DC channel PEMFC flow channel in the embodiment of the present invention.

具体实施方式Detailed ways

下面将结合本发明实施例中的附图,对本发明实施例中的技术方案进行清楚、完整地描述,显然,所描述的实施例仅仅是本发明的一个具体实施例,而不是全部的实施例。以下对至少一个示例性实施例的描述实际上仅仅是说明性的,决不作为对本发明及其应用或使用的任何限制。基于本发明中的实施例,本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例,都属于本发明保护的范围。除非另外具体说明,否则在这些实施例中阐述的部件和步骤的相对布置、表达式和数值不限制本发明的范围。同时,应当明白,为了便于描述,附图中所示出的各个部分的尺寸并不是按照实际的比例关系绘制的。对于相关领域普通技术人员已知的技术、方法和设备可能不作详细讨论,但在适当情况下,所述技术、方法和设备应当被视为授权说明书的一部分。在这里示出和讨论的所有示例中,任何具体值应被解释为仅仅是示例性的,而不是作为限制。因此,示例性实施例的其它示例可以具有不同的值。The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiment is only a specific embodiment of the present invention, not all embodiments. . The following description of at least one exemplary embodiment is merely illustrative in nature and is in no way intended to limit the invention, its application or uses. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the scope of protection of the present invention. The relative arrangement of components and steps, expressions, and numerical values set forth in these examples do not limit the scope of the invention unless otherwise specifically stated. At the same time, it should be understood that, for convenience of description, the dimensions of various parts shown in the drawings are not drawn according to actual proportional relationships. Techniques, methods and devices known to those of ordinary skill in the relevant art may not be discussed in detail, but where appropriate, such techniques, methods and devices should be considered part of the authorized specification. In all examples shown and discussed herein, any specific values are to be construed as illustrative only and not as limiting. Accordingly, other examples of the exemplary embodiments may have different values.

以下对本发明的实例进行具体说明。Examples of the present invention will be described in detail below.

请参阅图1,本发明提供的一种基于改进遗传算法的质子交换膜燃料电池流道优化方法,包括以下步骤:Please refer to Figure 1. The present invention provides a proton exchange membrane fuel cell flow channel optimization method based on an improved genetic algorithm, which includes the following steps:

步骤1:在仿真软件COMSOL Multiphysic建立单直流道PEMFC三维模型。Step 1: Establish a three-dimensional model of a single DC channel PEMFC in the simulation software COMSOL Multiphysic.

在本发明的其中一些实施例中,首先建立了单直流道PEMFC三维模型,该模型理论上可以模拟电池内部几乎所有可发生的传输情况,其模型结构示意图如图2所示,图中:1-阴极流道、2-阴极气体扩散层、3-阴极催化层、4-质子交换膜、5-阳极催化层、6-阳极气体扩散层、7-阳极流道。其计算区域要包括阴极流道、阳极流道、气体扩散层(GDL)、催化层(CL)和质子交换膜(PEM),其中气体扩散层、催化层以及质子交换膜合称为膜电极组件(MEA)。每个计算域的尺寸参数可根据需要自行设定,本实施例中,各计算区域所对应的几何尺寸如表1所示。In some embodiments of the present invention, a three-dimensional model of a single DC channel PEMFC is first established. This model can theoretically simulate almost all transmission conditions that can occur inside the battery. The schematic diagram of the model structure is shown in Figure 2, in which: 1 -Cathode flow channel, 2-cathode gas diffusion layer, 3-cathode catalytic layer, 4-proton exchange membrane, 5-anode catalytic layer, 6-anode gas diffusion layer, 7-anode flow channel. The calculation area includes the cathode flow channel, anode flow channel, gas diffusion layer (GDL), catalytic layer (CL) and proton exchange membrane (PEM). The gas diffusion layer, catalytic layer and proton exchange membrane are collectively called the membrane electrode assembly. (MEA). The size parameters of each calculation area can be set as needed. In this embodiment, the geometric sizes corresponding to each calculation area are as shown in Table 1.

表1 PEMFC三维模型各计算区域尺寸表Table 1 Dimensions of each calculation area of the PEMFC three-dimensional model

参数名称parameter name 数值numerical value 单位unit 流道长度Runner length 2020 mmmm 流道高度runner height 11 mmmm 流道宽度Channel width 11 mmmm 肋板宽度Floor width 11 mmmm GDL厚度GDL thickness 0.30.3 mmmm CL厚度CL thickness 0.01290.0129 mmmm PEM厚度PEM thickness 0.1080.108 mmmm

所述的单直流道PEMFC三维模型模型,其控制方程主要包括质量守恒方程、动量守恒方程、能量守恒方程、组分守恒方程、电荷守恒方程以及边界方程。The control equations of the single DC channel PEMFC three-dimensional model mainly include mass conservation equations, momentum conservation equations, energy conservation equations, component conservation equations, charge conservation equations and boundary equations.

在本发明的其中一些实施例中,为了对控制方程进行准确求解,还需要设置一些边界条件。其中,在阴极和阳极入口处通入的氧气和氢气的浓度和湿度可以根据不同需要进行设置,流道入口温度和四周壁面温度均等于工作温度。根据理想气体定律,各组分的质量分数可通过入口温度、入口压力及相对湿度计算得到。In some embodiments of the present invention, in order to accurately solve the control equations, some boundary conditions need to be set. Among them, the concentration and humidity of oxygen and hydrogen introduced at the entrances of the cathode and anode can be set according to different needs. The temperature of the flow channel inlet and the surrounding wall temperature are equal to the operating temperature. According to the ideal gas law, the mass fraction of each component can be calculated from the inlet temperature, inlet pressure and relative humidity.

还需要预设初始条件,所述初始条件包括工作压力、温度、阴阳极化学计量比、GDL孔隙率、GDL导电率、GDL渗透率,各参数均可根据不同需要进行设置。It is also necessary to preset initial conditions, which include working pressure, temperature, cathode and anode stoichiometric ratio, GDL porosity, GDL conductivity, and GDL permeability. Each parameter can be set according to different needs.

在本发明的其中一些实施例中,所使用的单直流道PEMFC三维模型所涉及的部分电化学参数如表2所示。In some embodiments of the present invention, some of the electrochemical parameters involved in the single DC channel PEMFC three-dimensional model used are shown in Table 2.

表2 PEMFC三维模型电化学参数表Table 2 PEMFC three-dimensional model electrochemical parameter table

步骤2:对单直流道PEMFC三维模型进行网格划分。Step 2: Mesh the single DC channel PEMFC three-dimensional model.

对所述的单直流道PEMFC三维模型进行网格划分以及网格独立性验证。在本发明的其中一些实施例中,采用33124、54912、72192、92976四种不同网数量的网格模型对所建立的模型进行网格的独立性验证。如图3所示,当电池工作电压为0.5V时,通过网格数量为72192和92976的两种网格模型所求解的电流密度差异小于0.05%,在完全可接受的误差范围内,因此为缩短求解时间,所选择的网格数量为72192。The single DC channel PEMFC three-dimensional model was meshed and the mesh independence was verified. In some embodiments of the present invention, four grid models with different net numbers, 33124, 54912, 72192, and 92976, are used to verify the grid independence of the established model. As shown in Figure 3, when the battery operating voltage is 0.5V, the difference in current density solved by the two grid models with grid numbers of 72192 and 92976 is less than 0.05%, which is within the completely acceptable error range, so To shorten the solution time, the number of grids selected is 72192.

步骤3:将仿真计算得到的PEMFC电池极化曲线与实验数据进行对比,以此验证该模型的有效性。Step 3: Compare the PEMFC battery polarization curve calculated by simulation with experimental data to verify the effectiveness of the model.

在本发明的其中一些实施例中,为了验证所述PEMFC单流道三模型的准确性,将通过模拟计算得到的PEMFC电池极化曲线与实验数据进行对比,对比结果如图4所示。通过仿真计算得到的模拟结果与实验数据拟合较好,在电流密度较低时,两者相差很小,且在电流密度较高时,两者间的相对误差在5%以内。因此,该模型可以作为原始流道模型进行应用。In some embodiments of the present invention, in order to verify the accuracy of the PEMFC single-channel three-model, the PEMFC battery polarization curve calculated through simulation is compared with the experimental data. The comparison results are shown in Figure 4. The simulation results obtained through simulation calculation fit well with the experimental data. When the current density is low, the difference between the two is very small, and when the current density is high, the relative error between the two is within 5%. Therefore, this model can be applied as a primitive flow channel model.

步骤4:将单直流道PEMFC三维模型的阴极进、出口截面和阳极进、出口截面的尺寸参数设置为优化变量,由改进的遗传算法在MATLAB中按照一定的规律自动生成,并传输到COMSOL Multiphysics中,每组变量对应一种特定的流道结构,并经过模拟计算得出达到收敛条件后的电流密度和压降。Step 4: Set the size parameters of the cathode inlet and outlet cross-sections and the anode inlet and outlet cross-sections of the single DC channel PEMFC three-dimensional model as optimization variables, which are automatically generated in MATLAB according to certain rules by the improved genetic algorithm and transferred to COMSOL Multiphysics In , each set of variables corresponds to a specific flow channel structure, and the current density and voltage drop after reaching the convergence condition are obtained through simulation calculations.

本实施例选择遗传算法作为流道形状尺寸的优化算法,并同仿真模拟相结合从而得到流道最佳的尺寸配置。具体实施过程是通过商业数学软件MATLAB2021和仿真软件COMSOL Multiphysics6.0来实现的,两者可以通过接口联结实现自动计算,可以大大效提高优化效率。In this embodiment, the genetic algorithm is selected as the optimization algorithm for the shape and size of the flow channel, and is combined with simulation to obtain the optimal size configuration of the flow channel. The specific implementation process is realized through the commercial mathematics software MATLAB2021 and the simulation software COMSOL Multiphysics6.0. The two can be connected through interfaces to achieve automatic calculation, which can greatly improve the optimization efficiency.

选取流道阴、阳极流道进出口截面的尺寸为优化目标,如图5所示,阴极流道进口宽度和高度、阴极流道出口宽度和高度、阳极流道进口宽度和高度、阳极流道出口宽度和高度,分别用a、b、c、d、e、f、g、h表示,阴、阳极流道进出口截面尺寸确定后,流道的形状即可确定。Select the size of the inlet and outlet sections of the cathode and anode flow channels as the optimization target, as shown in Figure 5, the width and height of the cathode flow channel inlet, the width and height of the cathode flow channel outlet, the width and height of the anode flow channel inlet, the anode flow channel The outlet width and height are represented by a, b, c, d, e, f, g, h respectively. After the inlet and outlet cross-section dimensions of the cathode and anode flow channels are determined, the shape of the flow channel can be determined.

在优化过程中为了确保流道进出口处边界条件的一致性,将改进的遗传算法的限制条件为流道进、出口截面的面积相等,在本发明的其中一些实施例中,将进出口通道横截面积固定为1mm2,横截面积可根据模型大小自动调整,且根据实验与仿真经验将各尺寸参数范围规定如下:In order to ensure the consistency of the boundary conditions at the inlet and outlet of the flow channel during the optimization process, the restriction condition of the improved genetic algorithm is that the areas of the inlet and outlet cross-sections of the flow channel are equal. In some embodiments of the present invention, the inlet and outlet channels are The cross-sectional area is fixed at 1mm 2 , and the cross-sectional area can be automatically adjusted according to the model size, and the range of each size parameter is specified as follows based on experimental and simulation experience:

0.3mm≤a、b、c、d、e、f、g、h≤1.7mm0.3mm≤a,b,c,d,e,f,g,h≤1.7mm

步骤5:在电池工作电压为某一固定值的条件下,将仿真计算得到的电流密度和压降输入到MATLAB中,以此计算得到目标函数f,如果目标函数值没有达到最小值,那么个体的基因就会通过遗传、交叉、变异等方式不断改变,流道相应的几何参数也会改变。Step 5: Under the condition that the battery operating voltage is a certain fixed value, input the current density and voltage drop calculated by the simulation into MATLAB to calculate the objective function f. If the objective function value does not reach the minimum value, then the individual The genes will continue to change through inheritance, crossover, mutation, etc., and the corresponding geometric parameters of the flow channel will also change.

在PEMFC工作的过程中,通常需要空气压缩机来提供所需的氧气,然而不同的流道结构会产生不同的压降,从而使得空气压缩机消耗的能量也不相同,这部分能量在优化过程中也是不可忽略的。因此,在综合考虑输出功率和损耗功率的前提下,将目标函数f定义如下:During the operation of PEMFC, an air compressor is usually required to provide the required oxygen. However, different flow channel structures will produce different pressure drops, so that the energy consumed by the air compressor is also different. This part of energy is used in the optimization process. cannot be ignored. Therefore, under the premise of comprehensively considering the output power and loss power, the objective function f is defined as follows:

Ecell=VcelliaveAm E cell = V cell i ave A m

其中,k为常数,设置为105,Ecell为电池输出功率,Econ为电池损耗功率,Vcell为电池工作电压,取0.4V,iave为电池平均电流密度,Am为电池活化面积,Δpc为电池阴极压降,为电池入口流速,/>为电池流入口截面积,。当电池输出功率Ecell越大,损耗功率Econ越小时,适应度值(即目标函数值f)越小,表明该个体适应度越高,PEMFC净功率越高,电池的性能也就越好。Among them, k is a constant, set to 10 5 , E cell is the battery output power, E con is the battery loss power, V cell is the battery operating voltage, taken as 0.4V, i ave is the battery average current density, and A m is the battery activation area. , Δp c is the battery cathode voltage drop, is the battery inlet flow rate,/> is the cross-sectional area of the battery inlet,. When the battery output power E cell is larger and the power loss E con is smaller, the fitness value (that is, the objective function value f) is smaller, indicating that the fitness of the individual is higher, the net power of the PEMFC is higher, and the performance of the battery is better. .

当遗传算法的优化变量、限制条件、目标函数相继确定后,优化工作就可以开始进行。When the optimization variables, constraints, and objective functions of the genetic algorithm are determined one after another, the optimization work can begin.

所述的优化变量在MATLAB中由遗传算法按照一定的规律自动生成,每组变量都是种群中一个携带基因的个体。The optimization variables described are automatically generated by genetic algorithms in MATLAB according to certain rules, and each set of variables is a gene-carrying individual in the population.

所述的优化变量输入到COMSOL Multiphysics中,每组优化变量对应一种特定的流道结构,并经过模拟计算得出达到收敛条件后的电流密度和压降,以此计算目标函数值。如果目标函数值没有达到最小值,那么个体的基因就会通过遗传、交叉、变异等方式不断改变,流道相应的几何参数也会改变。The above-mentioned optimization variables are input into COMSOL Multiphysics. Each set of optimization variables corresponds to a specific flow channel structure, and the current density and voltage drop after reaching the convergence condition are obtained through simulation calculation, and the objective function value is calculated based on this. If the objective function value does not reach the minimum value, then the individual genes will continue to change through inheritance, crossover, mutation, etc., and the corresponding geometric parameters of the flow channel will also change.

根据上述循环过程,在电池工作电压为0.4V的条件下,遗传算法不断迭代寻优,模型结构不断重建再生,从而得到流道最佳的尺寸配置。According to the above cycle process, under the condition that the battery operating voltage is 0.4V, the genetic algorithm continues to iterate and optimize, and the model structure is continuously reconstructed and regenerated, thereby obtaining the optimal size configuration of the flow channel.

针对遗传算法自身在优化求解过程中所存在的种群分布不均匀、容易陷入局部最优解等问题,基于三种改进策略提出了改进的遗传算法。In view of the problems that the genetic algorithm itself has in the optimization and solution process, such as uneven population distribution and easy falling into local optimal solutions, an improved genetic algorithm is proposed based on three improvement strategies.

改进1,所述的遗传算法选择Circle混沌映射作为生成初始种群的方法,该方法具有很强的随机性,会更好游历整个搜索范围,使得初始种群分布地更加均匀,从而有效增加种群的多样性。具体数学表达式如下:Improvement 1. The genetic algorithm selects Circle chaos mapping as the method to generate the initial population. This method has strong randomness and will better travel the entire search range, making the initial population more evenly distributed, thereby effectively increasing the diversity of the population. sex. The specific mathematical expression is as follows:

其中,mod为取余函数,a为生成的第a个个体。Among them, mod is the remainder function, and a is the generated a-th individual.

改进2,所述的改进的遗传算法在迭代计算时采用自适应交叉概率Pc和自适应变异概率Pm,以提高算法的寻优能,具体计算公式如下:Improvement 2. The improved genetic algorithm uses adaptive crossover probability P c and adaptive mutation probability P m during iterative calculation to improve the optimization performance of the algorithm. The specific calculation formula is as follows:

其中,fmax为群体中的最大适应度,f为需要交叉的两个体较大的适应,favg为群体平均适应度,f′为要变异个体的适应度。Among them, f max is the maximum fitness in the group, f is the larger adaptation of the two individuals that need to be crossed, f avg is the average fitness of the group, and f′ is the fitness of the individual to be mutated.

改进3,所述的改进的遗传算法采用柯西-高斯变异策略,以确保优化结果为全局最优解,具体数学表达式如下:Improvement 3. The improved genetic algorithm uses the Cauchy-Gaussian mutation strategy to ensure that the optimization result is the global optimal solution. The specific mathematical expression is as follows:

XCG=Xbest[1+λ1cauchy(0,σ2)+λ2Gauss(0,σ2)]X CG =X best [1+λ 1 cauchy(0, σ 2 )+λ 2 Gauss(0, σ 2 )]

其中,XCG表示最优个体变异后的位置,Xbest为最优个体变异前的位置,Xi为第i个个体所在的位置,σ2表示柯西-高斯变异策略的标准差,Tmax为最大迭代次数,t为当前迭代次数,cauchy(0,σ2)是满足柯西分布的随机变量,Gauss(0,σ2)是满足高斯分布的随机变量,λ1、λ2是随迭代次数自适应调整的动态参数。Among them, X CG represents the position of the optimal individual after mutation , X best is the position of the optimal individual before mutation , is the maximum number of iterations, t is the current number of iterations, cauchy(0, σ 2 ) is a random variable that satisfies the Cauchy distribution, Gauss(0, σ 2 ) is a random variable that satisfies the Gaussian distribution, λ 1 , λ 2 are random variables with iteration Dynamic parameters for adaptive adjustment of times.

在本发明的其中一些实施例中,通过遗传算法和改进遗传算法分别对原始流道模型进行优化,经过30次迭代计算之后,当平均适应度与最佳适应度相同时,迭代寻优工作完成,可以得到最优解。In some embodiments of the present invention, the original flow channel model is optimized through a genetic algorithm and an improved genetic algorithm respectively. After 30 iterative calculations, when the average fitness is the same as the best fitness, the iterative optimization work is completed. , the optimal solution can be obtained.

所述遗传算法优化迭代到18代后,计算结果开始收敛,收敛后的最佳适应度值为3.1169;所述改进遗传算法迭代到18代后,计算结果开始收敛,收敛后的最佳适应度值为2.9673。同遗传算法相比,改进遗传算法收敛速度更快,收敛时间节省约33.3%。After the optimization iteration of the genetic algorithm to 18 generations, the calculation results began to converge, and the best fitness value after convergence was 3.1169; after the improved genetic algorithm iteration to 18 generations, the calculation results began to converge, and the best fitness value after convergence The value is 2.9673. Compared with the genetic algorithm, the improved genetic algorithm converges faster and saves about 33.3% of the convergence time.

所述遗传算法和改进遗传算法收敛后得到的最佳适应度所对应的优化变量即为流道形状尺寸的最佳参数,如表3所示。The optimization variables corresponding to the best fitness obtained after the convergence of the genetic algorithm and the improved genetic algorithm are the optimal parameters for the shape and size of the flow channel, as shown in Table 3.

表3 遗传算法和改进遗传算法优化后流道最佳尺寸Table 3 Optimum size of flow channel after optimization by genetic algorithm and improved genetic algorithm

所述遗传算法和改进遗传算法优化后的阴、阳极流道形状均为变截面的锥形流道,且呈现出沿着反应气体运输方向深度不断减小、宽度不断增大的变化趋势。The shapes of the cathode and anode flow channels optimized by the genetic algorithm and the improved genetic algorithm are both tapered flow channels with variable cross-sections, and show a trend of decreasing depth and increasing width along the reaction gas transport direction.

对遗传算法和改进遗传算法优化后的流道极化曲线进行研究,并同原始模型进行对比。The flow channel polarization curve optimized by genetic algorithm and improved genetic algorithm was studied and compared with the original model.

如图6所示,将优化前后极化曲线进行对比,可以看出,通过本发明方法优化后的PEMFC性能有明显的提升,在电流密度较低时,极化曲线的差异很小,然而随着电流密度的不断升高,优化后流道的性能优势越来越明显。As shown in Figure 6, comparing the polarization curves before and after optimization, it can be seen that the performance of the PEMFC optimized by the method of the present invention has been significantly improved. When the current density is low, the difference in the polarization curves is very small. However, as the current density is lower, the difference in the polarization curves is very small. As the current density continues to increase, the performance advantages of optimized flow channels become more and more obvious.

在本发明的其中一些实施例中,在0.4V的工作电压下,相比于原始流道模型,经过遗传算法和改进遗传算法优化后的流道电流密度分别提升14.20%和19.01%,峰值功率密度提升12.58%和15.77%,且改进遗传算法的优化效果更加显著。In some embodiments of the present invention, at an operating voltage of 0.4V, compared with the original flow channel model, the flow channel current density optimized by the genetic algorithm and the improved genetic algorithm increased by 14.20% and 19.01% respectively, and the peak power The density is increased by 12.58% and 15.77%, and the optimization effect of the improved genetic algorithm is more significant.

本发明前述实施例提供的方法通过仿真软件COMSOL Multiphysic和商业数学软件MATLAB联合实现。结合改进的遗传算法在综合考虑损耗功率和输出功率的前提下对PEMFC流道的进出口截面尺寸进行仿真优化,从而得到最佳的尺寸配置。本发明不仅能够根据特定的目标函数确定流道的最佳尺寸配置,而且在一定程度上提高了遗传算法的寻优能力和收敛速度,有助于改进质子交换膜燃料电池的设计方式。The method provided by the foregoing embodiments of the present invention is jointly implemented by the simulation software COMSOL Multiphysic and the commercial mathematics software MATLAB. Combined with the improved genetic algorithm, the inlet and outlet cross-sectional dimensions of the PEMFC flow channel are simulated and optimized under the premise of comprehensively considering the loss power and output power, so as to obtain the optimal size configuration. The present invention can not only determine the optimal size configuration of the flow channel according to a specific objective function, but also improves the optimization ability and convergence speed of the genetic algorithm to a certain extent, helping to improve the design of proton exchange membrane fuel cells.

本发明的保护范围不限于上述的实施例。本领域的技术人员和科研人员可以对本发明进行各种改动而不脱离本发明的范围。如若这些改动属于本发明权利要求及其等同技术的范围内,则本发明的意图也包含这些改动。The scope of protection of the present invention is not limited to the above-mentioned embodiments. Those skilled in the art and scientific researchers can make various modifications to the present invention without departing from the scope of the present invention. If these modifications fall within the scope of the claims of the present invention and equivalent technologies, the present invention is intended to include these modifications.

Claims (10)

1. The proton exchange membrane fuel cell runner optimization method based on the improved genetic algorithm is characterized by comprising the following steps:
establishing a single direct current channel PEMFC three-dimensional model;
grid division is carried out on the single direct current channel PEMFC three-dimensional model;
setting size parameters of an inlet section and an outlet section of a cathode section and an anode section of a single direct current channel PEMFC three-dimensional model as optimized variables, automatically generating in mathematical software by an improved genetic algorithm, transmitting the optimized variables into simulation software, wherein each group of optimized variables corresponds to a channel structure, obtaining current density and voltage drop after reaching convergence conditions by simulation and analog calculation based on the improved genetic algorithm, wherein the improvement of the improved genetic algorithm comprises the steps of selecting Circle chaotic map as a method for generating an initial population, and adopting self-adaptive crossover probability P in iterative calculation c And adaptive mutation probability P m And using a cauchy-gaussian variation strategy;
under the condition that the working voltage of the battery is a certain fixed value, the current density and the voltage drop obtained by simulation calculation are input into the mathematical software, so that an objective function f is obtained by calculation, if the objective function value does not reach the minimum value, the genes of an individual are continuously changed in a genetic, cross, mutation and other modes, and the corresponding geometric parameters of a flow channel are also changed;
according to the above-mentioned circulation process, under the condition that the working voltage of the battery is a certain preset fixed value, the improved genetic algorithm is continuously iterated and optimized, the model structure is continuously rebuilt and regenerated, and the optimum size configuration of the flow channel is obtained.
2. The improved genetic algorithm-based proton exchange membrane fuel cell flow channel optimization method as claimed in claim 1, wherein the calculation region of the single direct flow channel PEMFC three-dimensional model comprises a cathode flow channel, an anode flow channel, a gas diffusion layer, a catalytic layer and a proton exchange membrane.
3. The improved genetic algorithm-based proton exchange membrane fuel cell runner optimization method as claimed in claim 1, wherein the single direct current runner PEMFC three-dimensional model performs simulation calculation based on preset initial conditions and boundary conditions, wherein the initial conditions comprise working pressure, temperature, positive-negative polarization stoichiometric ratio, GDL porosity, GDL conductivity and GDL permeability, and the boundary conditions comprise oxygen concentration and humidity at an inlet of a cathode runner and hydrogen concentration and humidity at an inlet of an anode runner.
4. The improved genetic algorithm-based proton exchange membrane fuel cell runner optimization method as claimed in claim 1, wherein the dimensional parameters of the inlet and outlet sections of the single-direct-runner PEMFC three-dimensional model are set as optimization variables.
5. The method for optimizing a proton exchange membrane fuel cell flow channel based on an improved genetic algorithm as claimed in claim 4, wherein the limitation of the improved genetic algorithm is that the areas of the inlet and outlet sections of the flow channel are equal.
6. The improved genetic algorithm-based proton exchange membrane fuel cell runner optimization method as claimed in claim 1, wherein the initial population is generated by adopting Circle chaotic mapping, and the mathematical expression is X a+1 The following are provided:
where mod is the remainder function and a is the generated a-th individual.
7. The method for optimizing a proton exchange membrane fuel cell flow channel based on an improved genetic algorithm according to claim 1, wherein the improved genetic algorithm adopts an adaptive crossover probability P in iterative calculation c The calculation formula of (2) is as follows:
wherein f max For maximum fitness in the population, f is the required crossoverIs large in adaptability of two bodies, f avg Is population average fitness.
8. The improved genetic algorithm-based proton exchange membrane fuel cell flow channel optimization method as claimed in claim 1, wherein the improved genetic algorithm adopts an adaptive variation probability P in iterative calculation m The calculation formula of (2) is as follows:
wherein f max For maximum fitness in the population, f avg For population average fitness, f' is the fitness of the individual to be mutated.
9. The improved genetic algorithm-based proton exchange membrane fuel cell flow channel optimization method as claimed in claim 1, wherein the improved genetic algorithm adopts the following mathematical expression of cauchy-gaussian variation strategy:
X CG =X best [1+λ 1 cauchy(0,σ 2 )+λ 2 Gauss(0,σ 2 )]
wherein X is CG Represents the position after the mutation of the optimal individual, X best For optimal position before individual variation, X i For the location where the i-th individual is located,σ 2 standard deviation, T, representing the cauchy-gaussian variation strategy max For the maximum number of iterations, t is the current number of iterations, cauchy (0, σ) 2 ) Is a random variable satisfying the Coxis distribution, gauss (0, σ 2 ) Is a random variable satisfying a Gaussian distribution, lambda 1 、λ 2 Is a dynamic parameter adaptively adjusted with the number of iterations.
10. A proton exchange membrane fuel cell flow channel optimization method based on an improved genetic algorithm as claimed in any one of claims 1-9, wherein said objective function f is
E cell =V cell i ave A m
Where k is a constant, E cell For battery output power E con For battery power loss, V cell For battery operating voltage, i ave For average current density of battery, A m Δp for battery activation area c For the cathode fall of a battery,for the battery inlet flow rate, ">Is the cross-sectional area of the inlet of the battery.
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN118690690A (en) * 2024-08-29 2024-09-24 上海重塑能源科技有限公司 Method, device, equipment and medium for optimizing flow field of proton exchange membrane fuel cell
CN120199344A (en) * 2025-05-27 2025-06-24 福州大学 PEM water electrolysis equivalent voltage model and modeling method

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN118690690A (en) * 2024-08-29 2024-09-24 上海重塑能源科技有限公司 Method, device, equipment and medium for optimizing flow field of proton exchange membrane fuel cell
CN118690690B (en) * 2024-08-29 2024-12-24 上海重塑能源科技有限公司 Method, device, equipment and medium for optimizing flow field of proton exchange membrane fuel cell
CN120199344A (en) * 2025-05-27 2025-06-24 福州大学 PEM water electrolysis equivalent voltage model and modeling method

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