三元锂离子电池多目标热优化

doi:10.19799/j.cnki.2095-4239.2020.0154

摘要/Abstract

摘要：

锂离子电池的产热对其安全性和寿命有很重要的影响。本文基于COMSOL Multiphysics平台，针对51 A·h三元软包层叠式锂离子电池，提出了其与电极对耦合的三维电化学-热耦合有限元分析模型，结合响应面法研究正极厚度、极板宽度、正极极耳厚度、正极极耳宽度、负极极耳厚度、负极极耳宽度6个设计参数对温度场的影响，通过线性加权组合法和随机梯度下降法，求得降低电池平均温升和最大温差的最优方案。结果表明，正极厚度对温度场影响较大，与温升正相关，但是厚度小到一定程度后影响减弱。极板宽度与极耳尺寸的增加能降低放电末期电池的温升；其数值在一定范围内时，电池的最大温差达到最小值。这套优化方案误差小于2.68%，平均温升降低2.93 ℃，最大温差降低0.596 ℃，有助于提高电池的安全性和寿命，为其他电池的多目标热优化提供了参考。

关键词: 锂离子电池, 电化学-热耦合模型, 响应面法, 热分析, 多目标优化

Abstract:

The heat production of the lithium-ion battery has a very important impact on its safety and life. Based on COMSOL Multiphysics, this study proposes a three-dimensional electrochemical thermal coupled finite element analysis model for a 51 A·h laminated lithium-ion pouch battery. The effects of six design parameters on the temperature field (i.e., positive electrode thickness, plate width, positive electrode tab thickness, positive electrode tab width, negative electrode tab thickness, and negative electrode tab width) are studied using the response surface method. The linear weighted sum and random gradient descent methods are used to obtain the optimal scheme to reduce the average temperature rise and the maximum temperature difference of the battery. The average temperature rise and the maximum temperature difference of the battery can be reduced by using the random gradient descent method. The results show that the positive electrode thickness greatly influences the temperature field positively related to the temperature rise; however, the influence is weakened when the thickness is reduced to a certain extent. The increase of the plate width and the tab size can reduce the temperature rise of the battery at the end of the discharge. In addition, the maximum temperature difference of the battery reaches the minimum value within a certain range. The error of the scheme is less than 2.68%. The temperature rise is reduced by 2.93 ℃. The temperature difference is reduced by 0.596 ℃, which is helpful in improving the safety and life of the battery, and provides a reference for the multi-objective thermal optimization of other batteries.

Key words: lithium-ion battery, electrochemical-thermal coupling model, response surface methodology, thermal analysis, multi-objective optimization

中图分类号:

TM 912

丁昌明, 文　华. 三元锂离子电池多目标热优化[J]. 储能科学与技术, 2020, 9(6): 1961-1968.

Changming DING, Hua WEN. Multi-objective thermal optimization of ternary lithium-ion battery[J]. Energy Storage Science and Technology, 2020, 9(6): 1961-1968.

图/表 14

表1

表2

控制方程和边界条件"

控制方程	边界条件
质量守恒
$? c 1 ? t + 1 r 2 ? ? r - r 2 D 1 ? c 1 ? r = 0$	$? c 1 ? t r = 0 = 0, - D 1 ? c 1 ? r r ? = ? R p = j l o c F$
$ε 2 ? c 2 ? t = ? ? x D 2 e f f ? c 2 ? r + 1 - t + S a j l o c F$	$? c 2 ? x x ? = ? 0 = ? c 2 ? x x ? = ? L = 0$
电荷守恒
$? ? x (- σ 1 e f f ? φ 1 ? x) = - S a j 1 o c$	$φ 1 x = 0 = 0, - σ 1 e f f ? φ 1 ? x x = L n + L s + L p = - I a p p, - σ 1, n e f f ? φ 1 ? x x = L n = - σ 1, p e f f ? φ 1 ? x x = L n + L s = 0$
$? - σ 2 e f f ? φ 2 + 2 R T σ 2 e f f F 1 + ? l n f ± ? l n c 2 1 - t + ? l n c 2 = S a j l o c$	$? φ 2 ? x x = 0 = ? φ 2 ? x x = L n + L s + L p = 0$
电化学反应速率
$j l o c = i 0 e x p α a F η R T - e x p α c F η R T$ , $η = φ 1 - φ 2 - U$ , $i 0 = F k 0 c 2 α a c 1, m a x - c 1, s u r f α a c 1, s u r f α c$
能量守恒
$ρ c p ? T ? t + ? ? - λ ? T = Q r e a + Q a c t + Q o h m$ $Q r e a = S a j l o c T ? U ? T = S a j l o c T ? S F$ , $Q a c t = S a j l o c η$ $Q o h m = σ 1 e f f ? φ 1 ? ? φ 1 + σ 2 e f f ? φ 2 - 2 R T σ 2 e f f F 1 + ? l n f ± ? l n c 2 1 - t + ? l n ? c 2 ? ? φ 2$	$- λ ? T ? x x = 0 = - λ ? T ? x x = L n + L s + L p = h T - T a m b$

表2

图1

图2

图3

表3

图4

图5

图6

表4

图7

图8

图9

表5

参考文献 17

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参数	单位	正极	隔膜	负极	其余	描述
L	μm	90^①	20^①	60^①		厚度
R_p	μm	3.5^①		6^①		活性颗粒粒子半径
ε₁		0.56^②		0.44^②		固相体积分数
ε₂		0.5556^②	0.4^②	0.4444^②		液相体积分数
c_1,max	mol/m³	19102^②		36100^②		最大可嵌锂浓度
c_2,0	mol/m³	1200^②	1200^②	1200^①		初始电解液锂浓度
k₀	m/s	4.38×10^-11③		1.63×10^-11③		反应速率常数
H×W×L	mm				342×109.5×9.5^①	电池长×宽×厚
TH_b	mm	0.3^①		0.2^①		极耳厚度
L_b	mm	16^①		16^①		极耳长度
W_b	mm	50^①		45^①		极耳宽度
c_p_a	J/(kg·K)				1299.4^①	电芯平均比热容
c_p_b	J/(kg·K)	900^①			385^①	极耳比热容
λ_a	W/(m·K)				1.2827^②	电芯平均热导率
λ_b	W/(m·K)	238^②		400^②		极耳热导率

因素	Level-1	Level 0	Level +1
正极厚度L_pos/μm	50	90	130
极板宽度W_p/mm	10.95	22.575	34.2
正极极耳厚度TH_pos/mm	0.1	0.4	0.7
正极极耳宽度W_pos/mm	30	60	90
负极极耳厚度TH_neg/mm	0.1	0.4	0.7
负极极耳宽度W_neg/mm	30	60	90

实验因素	温升p值	显著性	温差p值	显著性
A(正极厚度)	<0.0001	极其显著	<0.0001	极其显著
B(极板宽度)	<0.0001	极其显著	0.4326
C(正极极耳厚度)	<0.0001	极其显著	0.1331
D(正极极耳宽度)	0.0037	极其显著	0.4960
E(负极极耳厚度)	0.0021	极其显著	0.2772
F(负极极耳宽度)	<0.0001	极其显著	0.0623
AB	0.0031	极其显著	0.9684
AC	0.0009	极其显著	0.0292	显著
AD	0.4102		0.9823
AE	0.1055		0.3880
AF	<0.0001	极其显著	0.0088	极其显著
BC	0.9222		0.8661
BD	0.6964		0.9646
BE	0.8901		0.7789
BF	0.2878		0.8089
CD	0.0875		0.5649
CE	1.0000		0.3988
CF	<0.0001	极其显著	0.0100	极其显著
DE	0.9222		0.8547
DF	0.0592		0.4580
EF	0.0875		0.4200

项目	L_pos/μm	W_p/cm	TH_pos/mm	W_pos/mm	TH_neg/mm	W_neg/mm	T_ave/℃	ΔT_max/℃
优化前	90	10.95	0.3	50	0.2	45	9.49	1.771
优化后	50.521	33.203	0.653	58.352	0.694	73.009	6.452	1.126
验证值	50.521	33.203	0.653	58.352	0.694	73.009	6.53	1.157
圆整值	51	33	0.7	58	0.7	73	6.56	1.175

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