基于弛豫时间的不同工况下直接甲醇燃料电池性能退化分析

doi:10.16183/j.cnki.jsjtu.2024.110

基于弛豫时间的不同工况下直接甲醇燃料电池性能退化分析

王阳达¹, 王建国², 连冠^,³, 张大骋¹

1 昆明理工大学信息工程与自动化学院,昆明 650500

2 中国铜业有限公司,昆明 650000

3 云南省建筑工程设计院有限公司,昆明 650000

Performance Degradation Analysis of DMFC Under Different Operating Conditions Based on Relaxation Times

WANG Yangda¹, WANG Jianguo², LIAN Guan^,³, ZHANG Dacheng¹

1 Faculty of Information Engineering and Automation, Kunming University of Science and Technology, Kunming 650500, China

2 China Copper Corporation Limited, Kunming 650000, China

3 Yunnan Architectural Engineering Design Corporation Limited, Kunming 650000, China

通讯作者: 连冠,高级工程师;E-mail:guan.lian@outlook.com.

收稿日期: 2024-04-2 修回日期: 2024-05-27 接受日期: 2024-07-11

基金资助:

国家自然科学基金(62103174)
云南省科技厅重大专项(202202AD080006)

Received: 2024-04-2 Revised: 2024-05-27 Accepted: 2024-07-11

作者简介 About authors

王阳达(1998—),硕士生,从事燃料电池系统可靠性研究.

摘要

为研究直接甲醇燃料电池(DMFC)在全球统一轻型车辆测试循环(WLTC)和中国轻型汽车测试循环(CLTC)两种不同工况下的性能退化特征,采用极化曲线、等效电路模型和弛豫时间分布(DRT)相结合的方法分析DMFC的退化特征.根据波形演变,利用电化学阻抗谱计算DRT,表征DMFC各极化过程中的退化.结果表明:在WLTC工况下性能的衰退要大于CLTC工况.两种工况下,传质过程阻碍都对DMFC性能退化起主导作用,传质过程阻碍变化率在WLTC工况下为2.39 mΩ/h,CLTC工况下为0.764 mΩ/h;氧还原反应阻碍不受工况影响.在CLTC工况下,其显著的动态波动性和丰富的瞬态工况对质子传输构成较大阻碍,有效降低膜结合水含量,但对传质阻碍的影响较小,促进了氧气扩散速率的提升.根据氧还原反应阻碍的弛豫时间分布,建立一个燃料电池退化模型用于表征DMFC的健康状态,为DMFC运行中的健康状态评估提供了参考.

关键词： 不同工况; 直接甲醇燃料电池; 等效电路模型; 弛豫时间分布; 性能退化特征

Abstract

To investigate the performance degradation characteristics of direct methanol fuel cell (DMFC) under two different operating conditions, the worldwide harmonized light vehicle test cycle (WLTC) and China light vehicle test cycle (CLTC), a combined method of polarization curves, equivalent circuit models, and the distribution of relaxation times (DRT) is adopted to analyze the performance degradation characteristics of DMFC. Using electrochemical impedance spectroscopy, the degradation behavior of DMFC is characterized during the polarization process by calculating the variation in DRT based on the evolution of the waveforms. The results show that the degradation in the WLTC condition is more severe than in the CLTC condition. The obstruction of the mass transfer process resistance plays a dominant role in the performance degradation of DMFC under both operating conditions. The rate of change of the mass transfer process resistance is 2.39 mΩ/h under WLTC and 0.764 mΩ/h under CLTC. Meanwhile, the oxygen reduction reaction resistance is not affected by the operating conditions. The significant dynamic fluctuations and abundant transient states of CLTC operating conditions pose greater hindrance to proton transport, thereby effectively reducing the membrane-bound water content. However, it exerts a minor impact on the mass transfer resistance and promotes an increase in the rate of oxygen diffusion. A fuel cell degradation model is developed to characterize the ageing state of DMFCs based on the distribution of relaxation times hindered by the oxygen reduction reaction, which provides a reference for the health state assessment and optimization in DMFC operation.

Keywords： different operating conditions; direct methanol fuel cell (DMFC); equivalent circuit model; distribution of relaxation times (DRT); performance degradation characteristics

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本文引用格式

王阳达, 王建国, 连冠, 张大骋. 基于弛豫时间的不同工况下直接甲醇燃料电池性能退化分析[J]. 上海交通大学学报, 2026, 60(2): 289-299 doi:10.16183/j.cnki.jsjtu.2024.110

WANG Yangda, WANG Jianguo, LIAN Guan, ZHANG Dacheng. Performance Degradation Analysis of DMFC Under Different Operating Conditions Based on Relaxation Times[J]. Journal of Shanghai Jiaotong University, 2026, 60(2): 289-299 doi:10.16183/j.cnki.jsjtu.2024.110

质子交换膜燃料电池(proton exchange membrane fuel cell, PEMFC)具有启动快速、质量小、污染小、排放低的优点,是极具前景的替代能源装置^[1].直接甲醇燃料电池(direct methanol fuel cell, DMFC)是PEMFC的一种,其系统结构简单、不需外部辅助设备和成本低廉的特点,促进了其在新能源汽车、便携式设备等方面的应用^[2-3].然而,DMFC耐久性仍制约其在新能源汽车领域的发展^[4-5].

燃料电池在不同工况下使用寿命不同.在稳态工况下,使用寿命通常在5 000 h以上,而在变工况环境中使用寿命将大幅缩短^[6].燃料电池新能源汽车的动态工况包括加速、减速、匀速、怠速等,动态工况下的负载变化,会导致局部热点等故障加速燃料电池的退化^[7].同时,新能源汽车在不同地区面临不同行驶环境,工况极大影响燃料电池使用寿命.因此,研究不同动态工况下DMFC的性能退化对延长其使用寿命具有一定指导意义.

常用DMFC性能参数的获取方法有电镜扫描、傅里叶变换红外光谱、极化曲线以及电化学阻抗谱(electrochemical impedance spectroscopy, EIS)^[8-11].其中EIS用来描述燃料电池的各极化过程,通过等效电路模型(equivalent circuit model, ECM)来表征DMFC的性能.Kim等^[12]利用等效电路模型拟合EIS数据,建立PEMFC的健康状态评估模型并实现寿命预测.Hsueh等^[13]分析DMFC的EIS曲线弧度并与具体的极化过程对应.Rezaei Niya等^[14]分别从高、中、低3个频段研究EIS,建立了一个完整的等效电路模型,并采用实验和传输方程相结合验证了ECM的准确性.然而,等效电路模型的建立很大程度上依赖先验知识,同一段EIS可能与多种等效电路相对应,难以在有限尝试下建立最准确的ECM.

弛豫时间分布(distribution of relaxation times, DRT)用于解析电化学反应的物理化学过程^[15],可直接将各极化过程直接表征为波峰,且同一段EIS只有唯一的弛豫时间分布函数与之对应,是一种不依赖先验假设的EIS解析技术.DRT直接将电化学过程等效为若干电阻和电容并联的电阻-电容(RC)电路,每个RC代表一个极化过程,并将EIS转化为具有不同波峰的时间常数分布函数^[16].张雪霞等^[17]采用ECM和DRT分析机车工况下PEMFC电堆中不同位置的性能退化,发现电堆性能退化率与运行时间的关系.Chen等^[18]分析DRT函数单个波峰,进而确定PEMFC的水淹、供气不足等故障.Yuan等^[19]利用DRT定量分析了PEMFC内部的极化动力学过程.相对于传统分析EIS工具,DRT可作为EIS和等效电路模型的补充分析方法.在燃料电池的退化分析领域,对于直接甲醇燃料电池而言,利用DRT技术进行退化分析的案例并不多见.此外,在变工况条件下进行退化分析的情况也较为罕见,尤其是对两种不同变工况条件进行退化分析的案例.

为解决直接甲醇燃料电池在运行过程中存在退化特征分析困难、不同变工况下退化特征不明确等问题,以不同工况下DMFC为研究对象,利用极化曲线定性分析两种工况下DMFC的性能退化特征;根据EIS建立等效电路模型定量分析不同工况下模型参数的时序变化;采用DRT解释两种工况下DMFC的内部极化过程变化,分析DMFC的性能退化特征.

1 实验设置

1.1 DMFC制备及测试平台

DMFC主要由阳极端板、阳极集流板、交换膜、阴极集流板、阴极端板及垫片构成,膜电极主要由催化层、扩散层以及质子交换膜构成,质子交换膜采用的是杜邦公司的Nafion^® 117膜.阳极端板有一容量为1 cm³的储液腔,用于存放甲醇,阴极集流板开有1 cm×1 cm方孔,用于提供反应所需要的空气.阳极集流板采用厚度为1.33 mm、开孔率为38.5%的不锈钢制作,为存储的甲醇提供流道,同时收集电子.阴极集流板采用厚度为1.33 mm、开孔率为38.5%的泡沫不锈钢制作,为阴极的空气参与反应提供流道并且实现水管理^[20].DMFC结构及测试平台如图1所示.按图1(a)所示顺序进行组装,图1(b)所制备的DMFC实物图.

图1

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图1 DMFC结构及测试平台

Fig.1 Structureof DMFC and test platform

储液腔中注满去离子水,在确认无渗漏后放入恒温箱,60 ℃处理3 h,以形成电联;之后向制得的直接甲醇燃料电池注入甲醇水溶液,静止30 min;在60 ℃下从10 mA开始,以5 mA为间隔递增放电至电压下降为0 V,以获得催化剂最佳活性^[21].测试平台由艾德克斯直流电子负载、上海辰华电化学工作站及天津赛得利斯恒温干燥箱组成,如图1(c)所示.其中,电子负载记录极化曲线,电化学工作站测试电化学阻抗谱.

1.2 DMFC动态运行工况

测试使用全球统一轻型车辆测试循环(worldwide harmonized light vehicles test cycle, WLTC)及中国轻型车测试循环(China light vehicle test cycle, CLTC)两种运行工况.

如表1所示,WLTC下运行状态为加速、匀速、低速.其平均运行速度为53.2 km/h,平均加速度为0.53 m/s²,平均减速度-0.58 m/s²,最大速度131.2 km/h^[22].由于单芯燃料电池的功率有限,所以依据WLTC工况产生的负载电流分别为0.093、0.030、0.011 A,电流占比与实际工况一致.在实验中采用马尔可夫随机过程对3个负载电流随机分配^[23].

表1 基于WLTC负载设置

Tab.1 WLTC-based loading profile

WLTC工况	工况占比/%	输出功率/kW	负载电流/A
加速	35.4	35	0.093
匀速	31.9	21	0.030
低速	32.7	10	0.011

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测试过程的负载电流通过马尔可夫过程产生.因此,在预测未来时段的负载电流情况时,假定每个特定的电流强度层级的发生概率相等,这一过程符合马尔可夫过程的定义.随机序列 ${X (c), c = 1, 2, \dots}$ 满足:

(1) 对于每一个c(c=1, 2, …),X(c)取整数或它的子集,记为I'.

(2) 对于任意w+1个非负整数c₁, c₂, …, c_w, m (0≤c₁<c₂<…<c_w<m)和任意正整数k,以及状态d₁, d₂, …, d_w, d, j∈I'有

(1)

\begin{array}{l} B {X (m + k) = j | X (c_{1}) = d_{1}, X (c_{2}) = \\ d_{2}, \dots, X (c_{w}) = d_{w}, X (m) = d} = \\ B {X (m + k) = j | X (m) = d} \end{array}

条件概率B{X(m+k)=j|X(m)=d}为m时刻从状态d到状态j的k步转移概率:

(2)

\begin{array}{l} B_{d j} (m, m + k) = \\ B {X (m + k) = j | X (m) = d} \end{array}

WLTC的工况有3种负载电流,对应状态空间为

(3)

\begin{array}{l} S_{W L T C} = [S_{1} S_{2} S_{3}] = \\ [0.011 A 0.030 A 0.093 A] \end{array}

3种负载电流对应的转移概率矩阵为

(4)

\begin{array}{l} B_{W L T C} = [B_{1} B_{2} B_{3}] = \\ [0.327 0.319 0.354] \end{array}

各状态及转移概率如图2所示.

图2

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图2 负载电流概率转移图

Fig.2 Probability transfer of loading current

CLTC测试工况如表2所示,其运行过程包括低速、中速、高速3个速度区间,平均运行速度为37.18 km/h,平均加速度为0.45 m/s²,平均减速度-0.49 m/s²,最大速度114 km/h,CLTC工况速度状态较多,为更复杂的工况.采用上述方法得出的负载电流分别为0.018、0.038、0.053、0.068、0.089、0.096、0.114、0.133和0.138 A^[24].

表2 基于CLTC负载设置

Tab.2 CLTC-based loading profile

CLTC工况	特征	工况占比/%	平均车速/ (km·h^-1)	负载电流/A
低速	减速	11.7	11.85	0.018
	匀速	10.6	24.91	0.038
	加速	11.0	35.02	0.053
中速	减速	10.8	44.52	0.068
	匀速	11.5	55.53	0.089
	加速	11.1	62.49	0.096
高速	减速	6.8	75.13	0.114
	匀速	19.7	87.71	0.133
	加速	6.8	90.92	0.138

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CLTC的运行工况有9个负载电流,对应马尔可夫链的状态空间为

(5)

\begin{array}{l} S_{C L T C} = [\begin{array}{l} S'_{1} & S'_{2} & S'_{3} \\ S_{4} & S_{5} & S_{6} \\ S_{7} & S_{8} & S_{9} \end{array}] = \\ [\begin{array}{l} 0.018 A & 0.038 A & 0.053 A \\ 0.068 A & 0.089 A & 0.096 A \\ 0.114 A & 0.133 A & 0.138 A \end{array}] \end{array}

对应的转移概率矩阵为

(6)

\begin{array}{l} B_{C L T C} = [\begin{array}{l} B'_{1} & B'_{2} & B'_{3} \\ B_{4} & B_{5} & B_{6} \\ B_{7} & B_{8} & B_{9} \end{array}] = \\ [\begin{array}{l} 0.117 & 0.106 & 0.110 \\ 0.108 & 0.115 & 0.111 \\ 0.068 & 0.197 & 0.068 \end{array}] \end{array}

根据各状态空间以及转移概率矩阵实现对负载电流的模拟.

1.3 数据描述

不同工况下运行的两块DMFC具有相同工艺参数.运行WLTC工况的DMFC的操作条件为:运行温度为70 ℃,在恒温干燥箱内进行恒温干燥.由于本实验选用的DMFC不能持续供给甲醇,所以每次储液腔中的甲醇溶液消耗完毕,均需及时更换新的甲醇溶液.两种工况一次放电周期如图3所示.图3(a)描述了一次完整的放电过程,持续时间约为3 h.图中: I为随机分配的负载电流;U为与之对应的输出电压;t为时间;最后阶段电压迅速下降是因为甲醇燃料耗尽.针对CLTC运行工况,DMFC的操作条件为:运行温度为70 ℃,在恒温干燥箱内进行恒温干燥.图3(b)展示了一次完整放电过程,持续时间约为2 h.

图3

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图3 两种工况一次放电周期

Fig.3 A discharge cycle under two operating conditions

本次实验间隔60 h对两种不同工况下DMFC的极化曲线和交流电化学阻抗谱进行测量,EIS检测范围是0.01 Hz~100 kHz.

2 DMFC等效电路模型

等效电路如图4所示.EIS主要分为高频区、中频区和低频区3个部分.高频区主要反映阴极侧质子的传输过程,中频区与阴极的活化作用(即催化剂层中的氧还原反应)相关,低频区则涉及传质过程,即氧气的扩散情况^[25],具体如图4(a)所示.图中: $R$ 为阻抗.

图4

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图4 等效电路

Fig.4 Equivalent circuit

考虑了以上高、中、低3个频段过程,采用电阻、常相位元件以及电感构建如图4(b)所示的等效电路图.图中:L₁为高频电感;R₁为极板与质子交换膜之间的欧姆阻抗^[26];R₂为膜和催化层之间的接触阻抗,即质子传输阻抗;C_CPE1表示膜和催化层之间的电容行为^[27];R₃为电荷转移阻抗,即活化阻抗;R₅为传质阻抗;C_CPE2、C_CPE3分别表示阳极和阴极双层电容的充放电过程^[28];R₄为修正相位延迟阻抗;L₂为低频电感^[27,29].C_CPE反映了电极表面分布不均所引发的EIS异常的问题^[30].根据Kim等^[12]的研究,电容和电感几乎不会随着老化而改变,而电阻对老化比较敏感,DMFC的内部总阻抗为

(7)

\begin{matrix} Z = R_{1} + R_{2} + \frac{R_{3} R_{4}}{R_{3} + R_{4}} + R_{5} \end{matrix}

3 DMFC弛豫时间分布

采用DRT法解析DMFC的电化学阻抗谱,EIS与DRT的关系^[31]可表示为

(8)

\begin{array}{l} Z (f) = R_{0} + Z_{p o l} (f) = \\ R_{0} + R_{p o l} \int_{0}^{\infty} \frac{g (τ)}{1 + i 2 π f τ} d τ \end{array}

式中:Z(f)为总阻抗;R₀为欧姆阻抗;Z_pol(f)、R_pol分别为极化阻抗和极化电阻;g(τ)为弛豫时间分布函数,其中τ为弛豫时间;f为电化学扫描频率.

若将DMFC电路等效为欧姆阻抗与无穷多个极化过程串联而成,可以近似为任意电化学系统的阻抗模型,从而避免阻抗模型难以确定的问题^[15].弛豫时间分布如图5所示.单个电化学极化过程可用电阻和电容并联表示,完整的电化学阻抗模型如图5(a)所示.图中: $R_{n} 、 C_{n}$ 分别为无穷个电阻和电容;γ为DRT峰宽度参数.

图5

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图5 弛豫时间分布

Fig.5 Distribution of relaxation times

频率数据通常以对数进行表示,工程上以每十倍频进行频率表示,式(8)可转化为

(9)

\begin{matrix} Z (f) = R_{0} + R_{p o l} \int_{0}^{\infty} \frac{γ (l n τ)}{1 + i 2 π f τ} d l n τ \end{matrix}

式中:γ(ln τ)=τ g(τ),γ(ln τ)对实验误差尤为敏感,无法求出精确的解析解,求解过程存在不适定问题,采用正则化的方法求解γ(ln τ)^[32].DMFC的典型DRT如图5(b)所示.

P₁、P₂、P₃、P₄这4个峰值主要对阴极极化反应敏感,对与阳极参数的改变不敏感^[33].高频段峰P₁与阴极侧质子传输过程中膜结合水含量有关.中频段P₂、P₃与阴极侧的催化剂层氧还原反应有关.当阴极过量系数增加时,P₄峰值和频率都减少,表明与传质过程,即氧气扩散过程有关.若采用纯氧代替空气通入阴极,P₄峰几乎消失^[34],同样表明P₄峰与氧气扩散有关.由图5(b)可知,DRT可以解析出电化学系统的不同极化过程在频域的分布,且不需要根据经验建立等效电路模型.同时,对EIS高频或低频处出现的弧重叠,可以实现分离解析.

4 实验结果

4.1 不同工况下DMFC极化曲线

固定间隔60 h,测量两种运行工况下0~840 h的极化曲线,图6展示了不同时刻的极化曲线及两种工况的电压衰减率,电压衰减率计算公式如下:

(10)

\begin{matrix} δ U_{h} = \frac{1}{l} \sum_{1}^{l} \frac{U_{h} - U_{t}}{h - t} \end{matrix}

图6

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图6 不同工况极化曲线及电压退化率

Fig.6 Polarization curves and voltage decay rate of DMFC under different operating conditions

式中:δU_h为h时刻电压衰减率,U_h为h时刻电压值;U_t为t时刻电压值;h、t为不同测量时刻;l为极化曲线中第l个值.

CLTC运行工况的极化曲线如图6(a)所示.由图可知,随着运行时间增加,DMFC输出电压不断下降.0~240 h时,电压退化趋势较大.同时,极化曲线的最大放电电流也逐渐下降,前期下降较快,后期下降减缓,最大放电电流在720 h为 100 mA.

WLTC运行工况的极化曲线如图6(b)所示.由图可见,WLTC运行工况下燃料电池的总体衰减情况与CLTC工况相似,最大放电电流在720 h为55 mA.

燃料电池的性能退化分为可逆和不可逆,可逆退化可以通过改变操作条件得到改善.在图6(c)中,可能是活化不充分导致电压衰减率出现负值.从图6(c)中计算得出WLTC工况的平均电压衰减率为0.402 mV/h而CLTC工况的平均电压衰减率为0.259 mV/h,表明WLTC工况下衰退要大于CLTC工况.

DMFC在WLTC和CLTC工况下都出现了前期性能波动较大的情况,是因为前期DMFC活化不够完全,燃料电池性能没有达到一个相对稳定的状态.从电压衰减率的角度观察,CLTC工况因其平均运行速度较低、加速度相对平缓且加减速过程频繁的特点,有效地减缓了燃料电池在该工况下的衰退速度.

4.2 不同工况下DMFC电化学阻抗谱

极化曲线只能定性分析DMFC退化性能,为更具体分析DMFC衰退,采用等效电路模型来定量分析DMFC性能退化.图7展示了DMFC分别运行在CLTC和WLTC工况下的EIS.由图可知,两种工况下阻抗谱的弧大体上都呈现出随时间而扩大的趋势.

图7

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图7 不同工况下EIS

Fig.7 EIS under different operating conditions

具体而言,在CLTC工况下,前期EIS弧增长最大,表明燃料电池在前期退化最为严重,后期弧变化减小,表明在后期退化减缓;在WLTC工况下呈现出相同的变化趋势,但CLTC工况下前期衰退要大于WLTC工况.对比两者发现,更为复杂工况主要影响燃料电池性能前期.由于EIS弧只能定性分析出DMFC的退化情况,所以利用EIS识别两种工况下的等效电路模型,如图8所示.

图8

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图8 不同工况下ECM参数

Fig.8 ECM parameters under different operating conditions

由图8(a)可知,在CLTC工况下R₁、R₂、R₅基本不随时间而变化,表明欧姆阻抗、质子传输和传质过程变化不大.R₃变化较大,说明CLTC工况主要影响氧还原阻碍.由图8(b)可知,在WLTC工况下R₁、R₅变化不大,表明欧姆阻抗和传质过程变化不大.R₂和R₃随时间变化较大.说明WLTC工况对质子传输阻碍和氧还原阻碍都有影响.

两种工况下氧还原反应的参数变化较为明显.CLTC工况下,氧还原反应的参数变化较大,WLTC工况下氧还原和质子传输的参数变化都较大,表明复杂工况对质子传输阻碍有影响.CLTC工况下的平均运行速度和平均加减速度均保持在较低水平,这反映出其速度变化相对平缓,从而主要对质子传输的阻碍作用有影响.

4.3 不同工况下DMFC弛豫时间分布

由于DRT的建立不依赖先验知识,同时可实现对EIS重叠弧完全解析,所以采用DRT解析EIS.图9展示了采用DRT分析EIS的结果.由图可知,DMFC的DRT主要由P₁、P₂、P₃、P₄这4个波峰构成,分别出现在100 kHz、1 kHz、100 Hz、1 Hz附近.P₁、P₃、P₄这3个峰的峰值较大,表明阴极质子传输、氧还原反应和传质过程的极化过程为主要极化过程.图中出现的波峰P₅,在实验后期才产生,发生在中频区域可能与膜后期出现针孔有关^[35].

图9

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图9 不同工况下DRT

Fig.9 DRT under different operating conditions

完整实验周期的DRT和不同工况下DRT峰值变化分别如图10和图11所示.对于CLTC工况,由图10(a)和图11(a)可知,P₁峰值呈现出先增大再减小的趋势,说明质子传输阻碍先呈现上升趋势再减小,这可能与交换膜退化导致膜结合水含量变化有关.P₃峰值总体上呈现出上升趋势,说明氧还原反应阻碍一直在增大,这可能与膜催化剂的退化有关.P₄峰值的变化趋势呈现先上升后下降,反映传质阻碍呈现先增大后减小的变化趋势,这可能与阴极侧的氧气扩散以及扩散层退化导致的孔隙率变化有关.

图10

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图10 DMFC全生命周期不同工况下的DRT

Fig.10 DRT of DMFC lifecycle under different operating conditions

图11

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图11 不同工况下DRT峰值变化

Fig.11 Changes of DRT peaks under different operating conditions

由图10(b)和图11(b)可知,对于WLTC工况,P₁峰值大致呈现一直增大的趋势,表征阴极侧质子传输阻碍一直在增大;交换膜结合水含量减小.P₃峰值总体上呈现出上升趋势,说明氧还原反应阻碍一直在增大,这可能与膜催化剂的退化有关.在WLTC工况下,P₄峰值变化趋势与CLTC工况一致.

不同运行工况下的极化过程阻碍如图11所示,其极化过程阻碍变化率为

(11)

\begin{matrix} δ γ_{h} = \frac{1}{Q} \sum_{1}^{Q} \frac{γ_{h} - γ_{t}}{h - t} \end{matrix}

式中:δγ_h为h时刻极化过程阻碍变化率,γ_h为h时刻极化过程阻碍值;γ_t为t时刻极化过程阻碍值;Q为弛豫时间分布曲线样本数.

分析不同工况下DRT可知,对于P₁峰,WLTC工况下阴极侧质子传输阻碍变化率为0.645 mΩ/h,CLTC工况下阴极侧质子传输阻碍变化率为1.516 mΩ/h.CLTC工况动态波动性较大,拥有更多瞬态工况,造成质子传输阻碍变化率较大,同时导致交换膜的结合水含量减少.对于P₃峰,WLTC工况下氧还原反应阻碍变化率为0.852 mΩ/h,CLTC工况下氧还原反应阻碍变化率为1.119 mΩ/h.两种不同工况下P₃峰值变化差距较小,表明氧还原反应极化过程与工况无关.对于P₄峰,WLTC工况下传质过程阻碍变化率为2.39 mΩ/h,CLTC工况下传质过程阻碍变化率为0.764 mΩ/h.P₄峰值较大,说明传质过程阻碍对燃料电池的退化起到主要作用.由于WLTC工况的最大速度、平均速度和平均加减速度较大,所以导致传质阻碍变化较大,造成阴极侧氧气扩散困难.

由图11(a)和11(b)可知,在全生命周期下,拟合两种运行工况下氧还原反应阻碍(P₃峰)退化数据,结果如表3所示.结合图11和表3可知DMFC的氧还原反应阻碍呈现出随运行时间增加而增大的趋势.对比常用电化学装置退化趋势模型的拟合结果,发现二次多项式更为符合.因此,可以认为DMFC的退化趋势满足:

(12)

\begin{matrix} γ_{3 - t} = a t^{2} + b t + e \end{matrix}

表3 氧还原反应阻碍数据拟合模型比较

Tab.3 Comparison of fitting models for oxygen reduction reaction resistance data

运行工况	模型	决定系数R²
CLTC	一阶多项式	0.913
	二阶多项式	0.937
	指数	0.872
	对数	0.652
WLTC	一阶多项式	0.929
	二阶多项式	0.945
	指数	0.898
	对数	0.594

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式中:γ_3-_t为t时刻P₃纵坐标;a、b、e为拟合参数.式(12)描述DMFC的氧还原反应阻碍随时间而增大,故可用其表征DMFC的健康状态.相较于等效电路模型,DRT方法可以更直观、准确地展示DMFC的每一个极化过程的变化.中频弧具体分解为P₂和P₃两个波峰,表明P₂和P₃两个波峰与氧还原反应有关,这将有助于更好地理解分析氧还原反应.

5 结论

针对DMFC在CLTC和WLTC两种不同工况下的运行,采用极化曲线、等效电路模型以及弛豫时间分布的方法,具体分析不同工况下DMFC的性能变化.结果表明DMFC的性能退化主要受到阴极极化过程的影响,不同工况下DMFC的性能退化不一致.

(1) 两种运行工况下,WLTC工况的衰退要大于CLTC工况,CLTC工况因其平均运行速度较低、加速度相对平缓且加减速过程频繁的特点,有效减缓燃料电池在该工况下的衰退速度.

(2) 在两种不同动态工况下,氧还原反应极化过程变化相近,表明氧还原反应阻碍与工况无关.氧还原反应阻碍呈现出随运行时间增加而增大的趋势,通过比较常用电化学装置退化趋势模型的拟合结果,选用二次多项式作为DMFC的退化趋势模型.

(3) 两种不同工况下,传质过程都对DMFC性能退化起主导作用,传质过程阻碍变化率在WLTC工况下为2.39 mΩ/h,在CLTC工况下为0.764 mΩ/h.因WLTC工况的最大速度、平均速度和平均加减速度较大,其对传质阻碍影响较大,导致氧气扩散困难.CLTC工况由于动态波动性较大、平均运行速度且平均加减速度均保持在较低水平、拥有更多瞬态工况,对质子传输阻碍影响较大,可以减小膜结合水含量,而对传质阻碍影响较小,提高了氧气扩散的速率.利用3种方法分析DMFC在不同工况下的性能,为DMFC运行中的健康状态评估提供了一定参考.

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The micro direct methanol fuel cell (μDMFC) has attracted more and more attention in the field of new energy due to its simple structure, easy operation, and eco-friendly byproducts. In a μDMFC’s structure, the current collector plays an essential role in collecting the conduction current, and the rational distribution of gas and water. The choice of its material and flow fields would significantly impact the μDMFC’s performance. To this end, four different types of cathode current collector were prepared in this study. The materials selected were stainless steel (SS) and foam stainless steel (FSS), with the flow fields of hole-type and grid-type. The performance of the μDMFC with different types of cathode current collector was investigated by using polarization curves, electrochemical impedance spectroscopy (EIS), and discharging. The experimental results show that the maximum power density of μDMFC of the hole-type FSS cathode current collector is 49.53 mW/cm2 at 70 °C in the methanol solution of 1 mol/L, which is 115.72% higher than that of the SS collector. The maximum power density of the μDMFC with the grid-type FSS collector is 22.60 mW/cm2, which is 27.39% higher than that of the SS collector. The total impedance of the μDMFC of the FSS collector is significantly lower than that of the μDMFC of the SS collector, and the total impedance of the μDMFC with the hole-type flow field collector is lower than that of the grid-type flow field. The discharging of μDMFC with the hole-type FSS collector reaches its optimal value at 70 °C in the methanol solution of 1 mol/L.

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薛瑞.

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Rui

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基于NEDC和WLTC工况循环的混合动力汽车排放特性研究

[J]. 河北工业大学学报, 2021, 50(4): 51-56.

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Chunsheng

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Tiechen

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Yilong

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等效电路模型法预测动态工况下微型直接甲醇燃料电池剩余使用寿命

[J]. 上海交通大学学报, 2024, 58(10): 1575-1584.

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Yulin

, LIAN

Guan

, ZHANG

Dacheng

Equivalent circuit model-based prognostics for micro direct methanol fuel cell under dynamic operating conditions

[J]. Journal of Shanghai Jiao Tong University, 2024, 58(10): 1575-1584.

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WIDANAGE W

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YUAN

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A novel button-type micro direct methanol fuel cell with graphene diffusion layer

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In order to solve the problem that bolts in traditional packaged direct methanol fuel cells (DMFCs) take up a large area and reduce the specific energy (energy per unit weight) and power density (power per unit area), a new button-type micro direct methanol fuel cell (B-μDMFC) is designed, assembled, and packaged. The cell with four different structures was tested before and after packaging. The results indicate that the button cell with three-dimensional graphene and springs has the best performance. The equivalent circuit and methanol diffusion model was applied to explain the experimental results. The peak volumetric specific power density of the cell is 11.85 mW cm−3. This is much higher than traditional packaged DMFC, because the novel B-μDMFC eliminates bolts in the structure and improves the effective area ratio of the cell.

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YUAN

, YANG

, WANG

Y L

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Anodic diffusion layer with graphene-carbon nanotubes composite material for passive direct methanol fuel cell

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[J]. 机械工程学报, 2020, 56(22): 120-130.

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Hao

, DAI

Haifeng

, DU

Runben

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Distribution of relaxation times analysis of high-temperature PEM fuel cell impedance spectra

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陈丽丽, 曾东荣, 刘锋.

质子交换膜燃料电池电堆故障研究

[J]. 广东化工, 2022, 49(21): 35-37.

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CHEN

Lili

, ZENG

Dongrong

, LIU

Feng

Failure research of proton exchange membrane fuel cell stack

[J]. Guangdong Chemical Industry, 2022, 49(21): 35-37.

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SPEEK and SPPO blended membranes for proton exchange membrane fuel cells

2022

... 质子交换膜燃料电池(proton exchange membrane fuel cell, PEMFC)具有启动快速、质量小、污染小、排放低的优点,是极具前景的替代能源装置^[1].直接甲醇燃料电池(direct methanol fuel cell, DMFC)是PEMFC的一种,其系统结构简单、不需外部辅助设备和成本低廉的特点,促进了其在新能源汽车、便携式设备等方面的应用^[2-3].然而,DMFC耐久性仍制约其在新能源汽车领域的发展^[4-5]. ...

A review of high-temperature proton exchange membrane fuel cell (HT-PEMFC) system

2017

A state-of-art on the development of nafion-based membrane for performance improvement in direct methanol fuel cells

2022

Direct hydrogen fuel cell electric vehicle cost analysis: System and high-volume manufacturing description, validation, and outlook

2018

Estimating the end-of-life of PEM fuel cells: Guidelines and metrics

2016

Investigation of dynamic driving cycle effect on performance degradation and micro-structure change of PEM fuel cell

2009

... 燃料电池在不同工况下使用寿命不同.在稳态工况下,使用寿命通常在5 000 h以上,而在变工况环境中使用寿命将大幅缩短^[6].燃料电池新能源汽车的动态工况包括加速、减速、匀速、怠速等,动态工况下的负载变化,会导致局部热点等故障加速燃料电池的退化^[7].同时,新能源汽车在不同地区面临不同行驶环境,工况极大影响燃料电池使用寿命.因此,研究不同动态工况下DMFC的性能退化对延长其使用寿命具有一定指导意义. ...

A review of the main parameters influencing long-termperformance and durability of PEM fuel cells

2008

Sandwich-structure PI/SPEEK/PI proton exchange membrane developed for achieving the high durability on excellent proton conductivity and stability

2022

... 常用DMFC性能参数的获取方法有电镜扫描、傅里叶变换红外光谱、极化曲线以及电化学阻抗谱(electrochemical impedance spectroscopy, EIS)^[8-11].其中EIS用来描述燃料电池的各极化过程,通过等效电路模型(equivalent circuit model, ECM)来表征DMFC的性能.Kim等^[12]利用等效电路模型拟合EIS数据,建立PEMFC的健康状态评估模型并实现寿命预测.Hsueh等^[13]分析DMFC的EIS曲线弧度并与具体的极化过程对应.Rezaei Niya等^[14]分别从高、中、低3个频段研究EIS,建立了一个完整的等效电路模型,并采用实验和传输方程相结合验证了ECM的准确性.然而,等效电路模型的建立很大程度上依赖先验知识,同一段EIS可能与多种等效电路相对应,难以在有限尝试下建立最准确的ECM. ...

Enhancing voltage reversal tolerance of proton exchange membrane fuel cells by tuning the microstructure of IrO_x catalysts

2022

Two parameters identification for polarization curve fitting of PEMFC based on genetic algorithm

2022

Electrochemical impedance spectroscopy as a diagnostic tool for passive direct methanol fuel cells

2022

A degenerated equivalent circuit model and hybrid prediction for state-of-health (SOH) of PEM fuel cell

2014

... 考虑了以上高、中、低3个频段过程,采用电阻、常相位元件以及电感构建如图4(b)所示的等效电路图.图中:L₁为高频电感;R₁为极板与质子交换膜之间的欧姆阻抗^[26];R₂为膜和催化层之间的接触阻抗,即质子传输阻抗;C_CPE1表示膜和催化层之间的电容行为^[27];R₃为电荷转移阻抗,即活化阻抗;R₅为传质阻抗;C_CPE2、C_CPE3分别表示阳极和阴极双层电容的充放电过程^[28];R₄为修正相位延迟阻抗;L₂为低频电感^[27,29].C_CPE反映了电极表面分布不均所引发的EIS异常的问题^[30].根据Kim等^[12]的研究,电容和电感几乎不会随着老化而改变,而电阻对老化比较敏感,DMFC的内部总阻抗为 ...

Electrochemical impedance spectroscopy of direct methanol fuel cell

2006

Process modeling of electrodes in proton exchange membrane fuel cells

2015

Distribution of relaxation times: A method for measuring air flow distribution in high-temperature proton exchange membrane fuel cell stacks

2022

... 弛豫时间分布(distribution of relaxation times, DRT)用于解析电化学反应的物理化学过程^[15],可直接将各极化过程直接表征为波峰,且同一段EIS只有唯一的弛豫时间分布函数与之对应,是一种不依赖先验假设的EIS解析技术.DRT直接将电化学过程等效为若干电阻和电容并联的电阻-电容(RC)电路,每个RC代表一个极化过程,并将EIS转化为具有不同波峰的时间常数分布函数^[16].张雪霞等^[17]采用ECM和DRT分析机车工况下PEMFC电堆中不同位置的性能退化,发现电堆性能退化率与运行时间的关系.Chen等^[18]分析DRT函数单个波峰,进而确定PEMFC的水淹、供气不足等故障.Yuan等^[19]利用DRT定量分析了PEMFC内部的极化动力学过程.相对于传统分析EIS工具,DRT可作为EIS和等效电路模型的补充分析方法.在燃料电池的退化分析领域,对于直接甲醇燃料电池而言,利用DRT技术进行退化分析的案例并不多见.此外,在变工况条件下进行退化分析的情况也较为罕见,尤其是对两种不同变工况条件进行退化分析的案例. ...

... 若将DMFC电路等效为欧姆阻抗与无穷多个极化过程串联而成,可以近似为任意电化学系统的阻抗模型,从而避免阻抗模型难以确定的问题^[15].弛豫时间分布如图5所示.单个电化学极化过程可用电阻和电容并联表示,完整的电化学阻抗模型如图5(a)所示.图中:

R_{n} 、 C_{n}

分别为无穷个电阻和电容;γ为DRT峰宽度参数. ...

电化学阻抗谱弛豫时间分布基础

2020

Fundamentals of distribution of relaxation times for electrochemical impedance spectroscopy

2020

动态机车工况下质子交换膜燃料电池电堆衰退性能分析

2022

Degradation performance analysis of proton exchange membrane fuel cell stack under dynamic locomotive conditions

2022

Multi-impedance distribution of relaxation times applied to predicting fuel cell stack operating state: A theoretical and experimental study

2022

Quantitative analysis of internal polarization dynamics for polymer electrolyte membrane fuel cell by distribution of relaxation times of impedance

2021

Performance optimization of μDMFC with foamed stainless steel cathode current collector

2021

... DMFC主要由阳极端板、阳极集流板、交换膜、阴极集流板、阴极端板及垫片构成,膜电极主要由催化层、扩散层以及质子交换膜构成,质子交换膜采用的是杜邦公司的Nafion^® 117膜.阳极端板有一容量为1 cm³的储液腔,用于存放甲醇,阴极集流板开有1 cm×1 cm方孔,用于提供反应所需要的空气.阳极集流板采用厚度为1.33 mm、开孔率为38.5%的不锈钢制作,为存储的甲醇提供流道,同时收集电子.阴极集流板采用厚度为1.33 mm、开孔率为38.5%的泡沫不锈钢制作,为阴极的空气参与反应提供流道并且实现水管理^[20].DMFC结构及测试平台如图1所示.按图1(a)所示顺序进行组装,图1(b)所制备的DMFC实物图. ...

2019

... 储液腔中注满去离子水,在确认无渗漏后放入恒温箱,60 ℃处理3 h,以形成电联;之后向制得的直接甲醇燃料电池注入甲醇水溶液,静止30 min;在60 ℃下从10 mA开始,以5 mA为间隔递增放电至电压下降为0 V,以获得催化剂最佳活性^[21].测试平台由艾德克斯直流电子负载、上海辰华电化学工作站及天津赛得利斯恒温干燥箱组成,如图1(c)所示.其中,电子负载记录极化曲线,电化学工作站测试电化学阻抗谱. ...

2019

基于NEDC和WLTC工况循环的混合动力汽车排放特性研究

2021

... 如表1所示,WLTC下运行状态为加速、匀速、低速.其平均运行速度为53.2 km/h,平均加速度为0.53 m/s²,平均减速度-0.58 m/s²,最大速度131.2 km/h^[22].由于单芯燃料电池的功率有限,所以依据WLTC工况产生的负载电流分别为0.093、0.030、0.011 A,电流占比与实际工况一致.在实验中采用马尔可夫随机过程对3个负载电流随机分配^[23]. ...

Study on emission characteristics of hybrid electric vehicle based on NEDC and WLTC working cycle

2021

等效电路模型法预测动态工况下微型直接甲醇燃料电池剩余使用寿命

2024

Equivalent circuit model-based prognostics for micro direct methanol fuel cell under dynamic operating conditions

2024

Development of China light-duty vehicle test cycle

2020

... CLTC测试工况如表2所示,其运行过程包括低速、中速、高速3个速度区间,平均运行速度为37.18 km/h,平均加速度为0.45 m/s²,平均减速度-0.49 m/s²,最大速度114 km/h,CLTC工况速度状态较多,为更复杂的工况.采用上述方法得出的负载电流分别为0.018、0.038、0.053、0.068、0.089、0.096、0.114、0.133和0.138 A^[24]. ...

Equivalent electric circuit modeling and performance analysis of a PEM fuel cell stack using impedance spectroscopy

2010

... 等效电路如图4所示.EIS主要分为高频区、中频区和低频区3个部分.高频区主要反映阴极侧质子的传输过程,中频区与阴极的活化作用(即催化剂层中的氧还原反应)相关,低频区则涉及传质过程,即氧气的扩散情况^[25],具体如图4(a)所示.图中:

R

为阻抗. ...

Identification and quantification of ageing mechanisms in lithium-ion batteries using the EIS technique

2016

New anodic diffusive layer for passive micro-direct methanol fuel cell

2009

... [27,29].C_CPE反映了电极表面分布不均所引发的EIS异常的问题^[30].根据Kim等^[12]的研究,电容和电感几乎不会随着老化而改变,而电阻对老化比较敏感,DMFC的内部总阻抗为 ...

A novel button-type micro direct methanol fuel cell with graphene diffusion layer

2019

Anodic diffusion layer with graphene-carbon nanotubes composite material for passive direct methanol fuel cell

2014

Studies on the electrochemical behavior of polymer electrolyte membrane fuel cell (PEMFC) by AC impedance method

2003

Optimization and application of the distribution of relaxation times based on characteristic frequency resolution and hyperparameters

2022

... 采用DRT法解析DMFC的电化学阻抗谱,EIS与DRT的关系^[31]可表示为 ...

Influence of the discretization methods on the distribution of relaxation times deconvolution: Implementing radial basis functions with DRT tools

2015

... 式中:γ(ln τ)=τ g(τ),γ(ln τ)对实验误差尤为敏感,无法求出精确的解析解,求解过程存在不适定问题,采用正则化的方法求解γ(ln τ)^[32].DMFC的典型DRT如图5(b)所示. ...

质子交换膜燃料电池电化学阻抗谱弛豫时间分布研究

2020

... P₁、P₂、P₃、P₄这4个峰值主要对阴极极化反应敏感,对与阳极参数的改变不敏感^[33].高频段峰P₁与阴极侧质子传输过程中膜结合水含量有关.中频段P₂、P₃与阴极侧的催化剂层氧还原反应有关.当阴极过量系数增加时,P₄峰值和频率都减少,表明与传质过程,即氧气扩散过程有关.若采用纯氧代替空气通入阴极,P₄峰几乎消失^[34],同样表明P₄峰与氧气扩散有关.由图5(b)可知,DRT可以解析出电化学系统的不同极化过程在频域的分布,且不需要根据经验建立等效电路模型.同时,对EIS高频或低频处出现的弧重叠,可以实现分离解析. ...

Distribution of relaxation times analysis of proton exchange membrane fuel cell electrochemical impedance spectra

2020

Distribution of relaxation times analysis of high-temperature PEM fuel cell impedance spectra

2017

质子交换膜燃料电池电堆故障研究

2022

... 由于DRT的建立不依赖先验知识,同时可实现对EIS重叠弧完全解析,所以采用DRT解析EIS.图9展示了采用DRT分析EIS的结果.由图可知,DMFC的DRT主要由P₁、P₂、P₃、P₄这4个波峰构成,分别出现在100 kHz、1 kHz、100 Hz、1 Hz附近.P₁、P₃、P₄这3个峰的峰值较大,表明阴极质子传输、氧还原反应和传质过程的极化过程为主要极化过程.图中出现的波峰P₅,在实验后期才产生,发生在中频区域可能与膜后期出现针孔有关^[35]. ...

Failure research of proton exchange membrane fuel cell stack

2022

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