Multi-objective thermal optimization of ternary lithium-ion battery

doi:10.19799/j.cnki.2095-4239.2020.0154

Abstract

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

CLC Number:

TM 912

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

Figures/Tables 14

Table 1

Table 2

Governing equations and boundary conditions"

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
$ρ c p ? T ? t + ? ? - λ ? T = Q r e a + Q a c t + Q o h m$ $Q r e a = S a j l o c T ? U ? T = S a j l o c T ? S F$ , $Q a c t = S a j l o c η$ $Q o h m = σ 1 e f f ? φ 1 ? ? φ 1 + σ 2 e f f ? φ 2 - 2 R T σ 2 e f f F 1 + ? l n f ± ? l n c 2 1 - t + ? l n ? c 2 ? ? φ 2$	$- λ ? T ? x x = 0 = - λ ? T ? x x = L n + L s + L p = h T - T a m b$

Table 2

Fig.1

Fig.2

Fig.3

Table 3

Fig.4

Fig.5

Fig.6

Table 4

Fig.7

Fig.8

Fig.9

Table 5

References 17

1	ARAI J, YAMAKI T, YAMAUCHI S, et al. Development of a high power lithium secondary battery for hybrid electric vehicles[J]. Journal of Power Sources, 2005, 146(1): 788-792.
2	SCROSATI B, GARCHE J. Lithium batteries: Status, prospects and future[J]. Journal of Power Sources, 2010, 195(9): 2419-2430.
3	WANG Jiajun, SUN Xueliang. Understanding and recent development of carbon coating on LiFePO₄ cathode materials for lithium-ion batteries[J]. Energy & Environmental Science, 2012, 5(1): 5163-5185.
4	LU Languang, HAN Xuebing, LI Jianqiu, et al. A review on the key issues for lithium-ion battery management in electric vehicles[J]. Journal of Power Sources, 2013, 226: 272-288.
5	KIM U S, SHIN C B, KIM C S. Modeling for the scale-up of a lithium-ion polymer battery[J]. Journal of Power Sources, 2009, 189(1): 841-846.
6	KIM U S, YI J, SHIN C B, et al. Modelling the thermal behaviour of a lithium-ion battery during charge[J]. Journal of Power Sources, 2011, 196(11): 5115-5121.
7	GUO M, KIM G H, WHITE R E. A three-dimensional multi-physics model for a Li-ion battery[J]. Journal of Power Sources, 2013, 240: 80-94.
8	LI Jie, CHENG Yun, AI Lihua, et al. 3D simulation on the internal distributed properties of lithium-ion battery with planar tabbed configuration[J]. Journal of Power Sources, 2015, 293: 993-1005.
9	WEI Zhongbao, LIM T M, SKYLLAS-KAZACOS M, et al. Online state of charge and model parameter co-estimation based on a novel multi-timescale estimator for vanadium redox flow battery[J]. Applied Energy, 2016, 172: 169-179.
10	史玉军. 车用锂离子电池热分析[D]. 昆明: 昆明理工大学, 2017.
	SHI Yujun. Thermal analysis of lithium ion battery for vehicle[D]. Kunming: Kunming University of Science and Technology, 2017.
11	张立军, 李文博, 程洪正. 三维锂离子单电池电化学-热耦合模型[J]. 电源技术, 2016, 40(7): 1362-1366.
	ZHANG Lijun, LI Wenbo, CHENG Hongzheng. Coupled thermal-electrochemical model of 3D lithium-ion battery[J]. Chinese Journal of Power Sources, 2016, 40(7): 1362-1366.
12	张志超, 郑莉莉, 杜光超, 等. 基于多尺度锂离子电池电化学及热行为仿真实验研究[J]. 储能科学与技术, 2020, 9(1): 124-130.
	ZHANG Zhichao, DENG Lili, DU Guangchao, et al. Electrochemical and thermal behavior simulation experiments based on multiscale lithium ion batteries[J]. Energy Storage Science and Technology, 2020, 9(1): 124-130.
13	张剑波, 吴彬, 李哲. 车用动力锂离子电池热模拟与热设计的研发状况与展望[J]. 集成技术, 2014(1): 18-26.
	ZHANG Jianbo, WU Bin, LI Zhe. Thermal modeling and thermal design of lithium-ion batteries for automotive application: status and prospects[J]. Journal of Integration Technology, 2014(1): 18-26.
14	LI Huanhuan, LIU Chengyang, SAINI A, et al. Coupling multi-physics simulation and response surface methodology for the thermal optimization of ternary prismatic lithium-ion battery[J]. Journal of Power Sources, 2019, 438: 226974.
15	鲁淑霞, 张罗幻, 蔡莲香, 等. 带有方差减小的加权零阶随机梯度下降算法[J]. 河北大学学报(自然科学版), 2019, 39(5): 536-546.
	LU Shuxia, ZHANG Luohuan, CAI Lianxiang, et al. Weighted zeroth-order stochastic gradient descent algorithm with variance reduction[J]. Journal of Hebei University (Natural Science Edition), 2019, 39(5): 536-546.
16	崔伟. 某重型汽车车架多目标拓扑优化设计及其有限元分析[D]. 长沙: 湖南大学, 2012.
	CUI Wei. Multi-objective topology optimization and finite element analysis to a heavy automobile frame [D]. Changsha: Hunan University, 2012.
17	ONDA K, OHSHIMA T, NAKAYAMA M, et al. Thermal behavior of small lithium-ion battery during rapid charge and discharge cycles[J]. Journal of Power Sources, 2006, 158(1): 535-542.

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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