耦合温度的锂离子电池机理建模及仿真试验

doi:10.19799/j.cnki.2095-4239.2020.0198

摘要/Abstract

摘要：

锂离子电池机理模型精度高，可以揭示试验所无法描述的电池内部信息，对电池的老化研究、故障诊断和电池管理系统的设计具有重要意义。为解决模型计算复杂、易受温度影响的问题，提出一种耦合温度的建模方法。本文提出的模型以单粒子模型为基础：首先采用二参数抛物线法简化固相扩散方程，采用抛物线轮廓-有限差分结合法简化液相扩散方程，化偏微分方程为常微分方程；而后建立包含固、液相欧姆定律与固体电解质（SEI）膜极化作用的端电压表达式；针对恒流与复杂工况，采用集总模型法或中心差分法计算热模型中电池的平均温度；热模型与机理模型计算出的产热量相关，机理模型中的电化学参数受热模型得到的温度影响，热模型与机理模型耦合。结果表明：在恒流工况，耦合温度的简化模型比单粒子模型的温度值更准确，比不考虑温度的简化模型的电压值更准确；在高倍率复杂工况下，模型精度良好。在1C、2C、4C恒流放电工况下，电池端电压、温度的均方根误差不超过0.041、0.66；在城市道路循环工况下，电池的端电压、温度的绝对百分比误差不超过1%和0.15%。

关键词: 锂离子电池, 电化学简化, 温度影响, 仿真试验, 动态参数

Abstract:

The mechanism model of a lithium-ion battery has high precision and can reveal the internal information that cannot be described in an experiment. Moreover, this model is greatly significant to aging research, fault diagnosis, and design of a battery management system. This study proposes a simplified method coupled with temperature to tackle the high computational complexity and temperature-coupled influence of the battery model. The proposed model is based on the single particle (SP) model. First, a two-parameter parabolic profile method is used to simplify the solid diffusion equations. Parabolic profile approximation and the finite difference method are then used to solve the liquid diffusion. Second, a whole model, called the simplified pseudo two-dimensional (SP2D) model, is built considering Ohm's law and solid electrolyte interface film polarization. The average temperature of the battery is calculated through the lumped model simplification method or the central difference method. The thermal model is related to the heat production calculated by the mechanism model. The electrochemical parameters in the mechanism model are influenced by the temperature from the thermal model. The mechanism and thermal models are finally coupled. The results show that when current is constant, the simplified coupled model is more accurate than the SP and SP2D models in terms of the battery temperature and battery voltage, respectively. The model also shows a good performance in complex conditions. The root mean square error of the battery terminal voltage and the temperature are less than 0.041 and 0.66, respectively, for the constant current test. In addition, the absolute percentage error is less than 1% and 0.15% for the urban dynamometer driving schedule test.

Key words: lithium-ion battery, electrochemical simplification, temperature-coupled, simulation experiment, dynamic parameters

中图分类号:

TM 912.9

李旭昊, 周　宇, 王冰川. 耦合温度的锂离子电池机理建模及仿真试验[J]. 储能科学与技术, 2020, 9(6): 1991-1999.

Xuhao LI, Yu ZHOU, Bingchuan WANG. Modeling and simulation experiments of temperature-coupled mechanism model for lithium-ion battery[J]. Energy Storage Science and Technology, 2020, 9(6): 1991-1999.

图/表 15

图1

表1

伪二维模型控制方程及原理"

方程原理	控制方程
固相扩散	$? c s ? t = D s r 2 ? ? r r 2 ? c s ? r = D s ? 2 c s ? r 2 + 2 r ? c s ? r$ (1)
液相扩散	$ε e ? c e ? t = ? ? x D e e f f ? c e ? x + 1 - ?? t + F j L i$ (2)
固相电势	$? ? x σ s e f f ? φ s ? x = j L i$ (3)
液相电势	$? ? x κ e e f f ? φ e ? x = - ?? j L i - ?? ? ? x 2 R T κ e e f f F t + - ?? 1 ? l n c e ? l n x$ (4)
Butler-Volmer方程	$j L i = 2 a s i 0 e x p α a F η R T - ?? e x p - ? α c F η R T$ (5)
法拉第定律	$? j i L i ? x = ± a s F J$ (6)
端电压	$V t = φ s L, t - ? φ s 0, t$ (7)

表1

表2

表3

机理模型动态参数"

参数	表达式
D_s,ca	$1.18 × 10 - 12 1 + y 1.6 e x p - ?? 35000 R 1 T - ?? 1 298.1 . 5$ (8)
D_s,an	$3.9 × 10 - 14 e x p - ?? 35000 R 1 T - ?? 1 298.1 . 5$ (9)
k_s,ca	$1.4 × 10 - 12 e x p - ?? y e x p - ?? 30000 R 1 T - ?? 1 298.1 . 5$ (10)
k_s,an	$3 × 10 - 11 e x p - ?? 20000 R 1 T - ?? 1 298.1 . 5$ (11)
U_ca,ref	3.4323-0.4828exp[-80.2493(1-y)^1.3198]-3.2474×10^-6exp[20.2645(1-y)^3.8003]+3.2482×10^-6exp[20.2646(1-y)^3.7995](12)
U_an,ref	$0.6379 + 0.5416 e x p - ?? 305.5309 x + 0.044 t a n h - ?? x - ?? 0.1958 0.1088 - ?? 0.1978 t a n h x - ?? 1.0571 0.0854 - ?? 0.6875 t a n h x + 0.0117 0.0529 - ?? 0.0175 t a n h x - ?? 0.5692 0.0875$ (13)
dU_ca/dT	-0.35376y⁸+1.3902y⁷-2.2585y⁶+1.9635y⁵-0.98716y⁴+0.28857y³-0.046272y²+0.0032158y-1.9186×10^-5 (14)
dU_an/dT	$344.1347148 × e x p - ?? 32.9633287 x + 8.316711484 1 + 749.0756003 e x p - ?? 34.79099646 x + 8.887143624 - ?? 0.8520278805 x + 0.362299229 x 2 + 0.2698001697$ (15)

表3

表4

热模型参数"

参数	平均值
$p ˉ$ /kg·m^-3	1996.7
$c ˉ$ _p/J·(kg·K)^-1	938.67
k_T/W·(m·K)^-1	34.251

表4

图2

图3

图4

图5

表5

图6

表6

表7

图7

图8

参考文献 20

1	张书桥. 电动汽车发展现状及前景分析[J]. 电气时代, 2019(9): 12-15.
	ZHANG Shuqiao. Analysis on the development status and prospect of electric vehicles[J]. Electric Age, 2019(9): 12-15.
2	LI Junfu, LAI Qingzhi, WANG Lixin, et al. A method for SOC estimation based on simplified mechanistic model for LiFePO₄ battery[J]. Energy, 2016, 114: 1266-1276.
3	LAI Xin, Wang Shuyu, Ma Shangde, et al. Parameter sensitivity analysis and simplification of equivalent circuit model for the state of charge of lithium-ion batteries[J]. Electrochimica Acta, 2020, 330: doi: 10.1016/j.electacta.2019.135239.
4	LI Jie, ADEWUYI K, LOTFI N, et al. A single particle model with chemical/mechanical degradation physics for lithium ion battery state of health (SOH) estimation[J]. Applied Energy, 2018, 212: 1178-1190.
5	DOYLE M, FULLER T F, NEWMAN J. Modeling of galvanostatic charge and discharge of the lithium/polymer/insertion cell[J]. Journal of the Electrochemical Society, 1993, 140(6): doi: 10.1149/1.2221597.
6	DOYLE M, NEWMAN J, GOZDZ A S, et al. Comparison of modeling predictions with experimental data from plastic lithium ion cells[J]. Journal of the Electrochemical Society, 1996, 143(6): 1890-1903.
7	JOKAR A, RAJABLOO B, DÉSILETS M, et al. Review of simplified pseudo-two-dimensional models of lithium-ion batteries[J]. Journal of Power Sources, 2016, 327: 44-55.
8	ZHANG Dong, POPOV B N, WHITE R E. Modeling lithium intercalation of a single spinel particle under potentiodynamic control[J]. Journal of the Electrochemical Society, 2000, 147(3): doi: 10.1149/1.1393279.
9	SUBRAMANIAN V R, RITTER J A, WHITE R E. Approximate solutions for galvanostatic discharge of spherical particles i. constant diffusion coefficient[J]. Journal of The Electrochemical Society, 2001, 148(11): E444-E449.
10	GUO Meng, SIKHA G, WHITE R E. Single-particle model for a lithium-ion cell: thermal behavior[J]. Journal of the Electrochemical Society, 2011, 158(2): A122-A132.
11	TANIM T R, RAHN C D, WANG Chaoyang. A temperature dependent, single particle, lithium ion cell model including electrolyte diffusion[J]. Journal of Dynamic Systems, Measurement & Control, 2014, 137(1): doi: 10.1115/1.4028154.
12	吕超, 郑君, 罗伟林, 等. 锂离子电池热耦合SP+模型及其参数化简[J]. 电源学报, 2015, 13(3): 28-35.
	LÜ Chao, ZHENG Jun, LUO Weilin, et al. Thermal coupling SP+ model of lithium-ion battery and parameters simplification[J]. Journal of Power Supply, 2015, 13(3): 28-35.
13	刘征宇, 杨昆, 魏自红, 等. 包含液相扩散方程简化的锂离子电池电化学模型[J]. 物理学报, 2019, 68(9): 251-258.
	LIU Zhengyu, YANG Kun, WEI Zihong, et al. Electrochemical model of lithium ion battery with simplified liquid phase diffusion equation[J]. Acta Physica Sinica, 2019, 68(9): 251-258.
14	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.
15	LI Jie, CHENG Yun, JIA Ming, et al. An electrochemical-thermal model based on dynamic responses for lithium iron phosphate battery[J]. Journal of Power Sources, 2014, 255: 130-143.
16	TANG Yiwei, JIA Ming, LI Jie, et al. Numerical analysis of distribution and evolution of reaction current density in discharge process of lithium-ion power battery[J]. Journal of the electrochemical society, 2014, 161(8): E3021-E3027.
17	SUBRAMANIAN V R, DIWAKAR V D, TAPRIYAL D. Efficient macro-micro scale coupled modeling of batteries[J]. Journal of The Electrochemical Society, 2005, 152(10): A2002-A2008.
18	HAN Xuebing, OUYANG Minggao, LU Languang, et al. Simplification of physics-based electrochemical model for lithium ion battery on electric vehicle (Ⅰ): Diffusion simplification and single particle model[J]. Journal of Power Sources, 2015, 278: 802-813.
19	LUO Weilin, Chao LYU, WANG Lixin, et al. An approximate solution for electrolyte concentration distribution in physics-based lithium-ion cell models[J]. Microelectronics Reliability, 2013, 53(6): 797-804.
20	FOEGEZ C, DO D V, FRIEDRICH G, et al. Thermal modeling of a cylindrical LiFePO₄/graphite lithium-ion battery[J]. Journal of Power Sources, 2010, 195(9): 2961-2968.

参数	负极	正极	隔膜	电解质
ε_s	0.55	0.43
ε_e	0.33	0.332	0.54
L_i/μm	34	70	25
R_i/μm	0.0365	3.5
c_e,init/mol·m^-3				1200
c_s,max/mol·m^-3	31370	22806
c_s,init/mol·m^-3	26978.2	501.732
α_a,c	0.5	0.5
σ_s/S·m^-1	100	0.5
κ_e/S·m^-1				0.92
R_f/Ω	0.005	0.001
T_init/K	293.15	293.15	293.15	293.15
t₀				0.363
D_e/m²·s ^-1				7.5×10^-11

模型	放电倍率
模型	1 C	2 C	4 C
SP2D模型	0.062	0.0683	0.066
TCSP2D模型	0.0405	0.0333	0.0315

模型	温度/℃
模型	10	15	20
SP模型	1.5972	1.3906	1.0796
TCSP2D模型	0.6573	0.5539	0.4499

模型	运算时间/s
SP模型	0.2740
TCSP2D模型	0.6400
P2D模型	329

[1]	李海涛, 孔令丽, 张欣, 余传军, 王纪威, 徐琳. N/P设计对高镍NCM/Gr电芯性能的影响[J]. 储能科学与技术, 2022, 11(7): 2040-2045.
[2]	陈龙, 夏权, 任羿, 曹高萍, 邱景义, 张浩. 多物理场耦合下锂离子电池组可靠性研究现状与展望[J]. 储能科学与技术, 2022, 11(7): 2316-2323.
[3]	易顺民, 谢林柏, 彭力. 基于VF-DW-DFN的锂离子电池剩余寿命预测[J]. 储能科学与技术, 2022, 11(7): 2305-2315.
[4]	祝庆伟, 俞小莉, 吴启超, 徐一丹, 陈芬放, 黄瑞. 高能量密度锂离子电池老化半经验模型[J]. 储能科学与技术, 2022, 11(7): 2324-2331.
[5]	王宇作, 王瑨, 卢颖莉, 阮殿波. 孔结构对软碳负极储锂性能的影响[J]. 储能科学与技术, 2022, 11(7): 2023-2029.
[6]	刘显茜, 孙安梁, 田川. 基于仿生翅脉流道冷板的锂离子电池组液冷散热[J]. 储能科学与技术, 2022, 11(7): 2266-2273.
[7]	孔为, 金劲涛, 陆西坡, 孙洋. 对称蛇形流道锂离子电池冷却性能[J]. 储能科学与技术, 2022, 11(7): 2258-2265.
[8]	霍思达, 薛文东, 李新丽, 李勇. 基于CiteSpace知识图谱的锂电池复合电解质可视化分析[J]. 储能科学与技术, 2022, 11(7): 2103-2113.
[9]	邓健想, 赵金良, 黄成德. 高能量锂离子电池硅基负极黏结剂研究进展[J]. 储能科学与技术, 2022, 11(7): 2092-2102.
[10]	欧宇, 侯文会, 刘凯. 锂离子电池中的智能安全电解液研究进展[J]. 储能科学与技术, 2022, 11(6): 1772-1787.
[11]	韩俊伟, 肖菁, 陶莹, 孔德斌, 吕伟, 杨全红. 致密储能：基于石墨烯的方法学和应用实例[J]. 储能科学与技术, 2022, 11(6): 1865-1873.
[12]	辛耀达, 李娜, 杨乐, 宋维力, 孙磊, 陈浩森, 方岱宁. 锂离子电池植入传感技术[J]. 储能科学与技术, 2022, 11(6): 1834-1846.
[13]	燕乔一, 吴锋, 陈人杰, 李丽. 锂离子电池负极石墨回收处理及资源循环[J]. 储能科学与技术, 2022, 11(6): 1760-1771.
[14]	沈秀, 曾月劲, 李睿洋, 李佳霖, 李伟, 张鹏, 赵金保. γ射线辐照交联原位固态化阻燃锂离子电池[J]. 储能科学与技术, 2022, 11(6): 1816-1821.
[15]	于春辉, 何姿颖, 张晨曦, 林贤清, 肖哲熙, 魏飞. 硅基负极与电解液化学反应的分析与抑制策略[J]. 储能科学与技术, 2022, 11(6): 1749-1759.