Fault diagnosis of proton exchange membrane fuel cell based on nonlinear dynamic model

doi:10.11949/0438-1157.20220487

Abstract

Abstract:

In order to carry out fault diagnosis for proton exchange membrane fuel cell (PEMFC) system to improve the safety and reliability of the system, aiming at the strong nonlinearity of the PEMFC system, a sliding mode observer is proposed based on the ninth-order state space model to generate residuals in real time, and the fault threshold detection method is used to establish a fault feature matrix to detect faults. In order to isolate faults, a relative fault sensitivity function is introduced to establish a theoretical relative fault sensitivity matrix, and the relative faults of each fault are calculated in real time when the system is running. The Euclidean distance between the sensitivity and the theoretical relative fault sensitivity, the fault corresponding to the minimum Euclidean distance is the fault that occurs in the system. The results verify the effectiveness of the proposed model-based fault diagnosis method, and the constructed observer can estimate the state variables that are difficult to measure directly in the PEMFC system, the average relative error is within 6%.

Key words: proton exchange membrane fuel cell system, sliding mode observer, fault detection, fault isolation

摘要：

为了对质子交换膜燃料电池(proton exchange membrane fuel cell，PEMFC)系统进行故障诊断以提高系统的安全性和可靠性，针对PEMFC系统的强非线性，在九阶状态空间模型的基础上提出一种滑模观测器实时生成残差，利用故障阈值检测法建立故障特征矩阵检测故障，进而为了隔离故障，引入相对故障敏感度函数建立理论相对故障敏感度矩阵，在系统运行时实时计算各故障相对故障敏感度与理论相对故障敏感度的欧氏距离，最小欧氏距离对应的故障则为系统发生的故障，结果验证了所提出的基于模型的故障诊断方法的有效性，且所构建观测器可以估计PEMFC系统中难以直接测取的状态变量，平均相对误差在6%以内。

关键词: 质子交换膜燃料电池, 滑模观测器, 故障检测, 故障隔离

CLC Number:

TQ 028.8

Jiawang YONG, Qianqian ZHAO, Nenglian FENG. Fault diagnosis of proton exchange membrane fuel cell based on nonlinear dynamic model[J]. CIESC Journal, 2022, 73(9): 3983-3993.

雍加望, 赵倩倩, 冯能莲. 基于非线性动态模型的质子交换膜燃料电池故障诊断[J]. 化工学报, 2022, 73(9): 3983-3993.

Figures/Tables 19

Table 1 Definition of major variables of the model

变量	主要定义	变量	主要定义
$x 1 = m H 2$	阳极氢气质量/kg	$x 7 = m s m$	供应歧管质量/kg
$x 2 = m O 2$	阴极氧气质量/kg	$x 8 = ω c p$	空压机转速/(r/min)
$x 3 = m w, c a$	阴极水质量/kg	$x 9 = p r m$	回流管道压力/Pa
$x 4 = m w, a n$	阳极水质量/kg	V_fc	电堆电压/V
$x 5 = p s m$	供应歧管压力/Pa	v_cm	压缩机电机电压/V
$x 6 = m N 2$	阴极氮气质量/kg	I_st	负载电流/A

Table 1 Definition of major variables of the model

变量	主要定义	变量	主要定义
$x 1 = m H 2$	阳极氢气质量/kg	$x 7 = m s m$	供应歧管质量/kg
$x 2 = m O 2$	阴极氧气质量/kg	$x 8 = ω c p$	空压机转速/(r/min)
$x 3 = m w, c a$	阴极水质量/kg	$x 9 = p r m$	回流管道压力/Pa
$x 4 = m w, a n$	阳极水质量/kg	V_fc	电堆电压/V
$x 5 = p s m$	供应歧管压力/Pa	v_cm	压缩机电机电压/V
$x 6 = m N 2$	阴极氮气质量/kg	I_st	负载电流/A

Table 2 Operating parameter setting

环境温度	电堆工作温度	氢气供给压力	空气供给压力	过氧比
25℃	72℃	3 atm	3 atm	2

Fig.1 Comparison of model and experimental polarization curves

Fig.2 Load current curve

Fig.3 Compressor motor voltage curve

Fig.4 Comparison of actual and estimated values of state variables

Fig.5 Comparison of actual and estimated stack output voltage

Fig.6 Fault diagnosis flow chart

Fig.7 No fault diagnosis signal results

Fig.8 Compressor fault diagnosis signal results

Fig.9 Humidifier fault diagnosis signal results

Fig.10 Air supply manifold blocked diagnostic signal results

Fig.11 Flow channel blocked diagnostic signal results

Fig.12 Hydrogen supply lack diagnostic signal results

Table 3 Fault signature matrix

故障	S₁	S₂	S₃	S₄
f₁	1	1	1	1
f₂	0	0	0	1
f₃	1	0	1	1
f₄	1	0	1	1
f₅	0	0	0	1

Table 4 Theoretical relative fault sensitivity matrix

故障	r₂/r₁	r₃/r₁	…	r_n /r₁
f₁	$S r 2, r 1, f 1 r e l, t h e o$	$S r 3, r 1, f 1 r e l, t h e o$	…	$S r n, r 1, f 1 r e l, t h e o$
f₂	$S r 2, r 1, f 2 r e l, t h e o$	$S r 3, r 1, f 2 r e l, t h e o$	…	$S r n, r 1, f 2 r e l, t h e o$
f₃	$S r 2, r 1, f 3 r e l, t h e o$	$S r 3, r 1, f 3 r e l, t h e o$	…	$S r n, r 1, f 3 r e l, t h e o$
$⋮$	$⋮$	$⋮$	$⋮$	$⋮$
f_m	$S r 2, r 1, f m r e l, t h e o$	$S r 3, r 1, f m r e l, t h e o$	…	$S r n, r 1, f m r e l, t h e o$

Table 4 Theoretical relative fault sensitivity matrix

故障	r₂/r₁	r₃/r₁	…	r_n /r₁
f₁	$S r 2, r 1, f 1 r e l, t h e o$	$S r 3, r 1, f 1 r e l, t h e o$	…	$S r n, r 1, f 1 r e l, t h e o$
f₂	$S r 2, r 1, f 2 r e l, t h e o$	$S r 3, r 1, f 2 r e l, t h e o$	…	$S r n, r 1, f 2 r e l, t h e o$
f₃	$S r 2, r 1, f 3 r e l, t h e o$	$S r 3, r 1, f 3 r e l, t h e o$	…	$S r n, r 1, f 3 r e l, t h e o$
$⋮$	$⋮$	$⋮$	$⋮$	$⋮$
f_m	$S r 2, r 1, f m r e l, t h e o$	$S r 3, r 1, f m r e l, t h e o$	…	$S r n, r 1, f m r e l, t h e o$

Table 5 Theoretical relative fault sensitivity matrix results

故障	r₂/ r₁	r₃/ r₁	r₄/r₁
f₁	0.0147	0.3681	6.86×10^-7
f₂	0.3850	0.0736	2.43×10^-4
f₃	0.0071	0.1977	1.97×10^-7
f₄	0.0083	0.1895	1.81×10^-7
f₅	0.0402	0.1448	3.34×10^-8

Fig.13 Euclidean distance variation curve of each fault when f4 occurs

Fig.14 Euclidean distance variation curve of each fault when f5 occurs

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