Simulation on lithium ion battery discharge process with large current

doi:10.11949/0438-1157.20200279

Abstract

Abstract:

With the widespread application of lithium-ion batteries, the demand for batteries to operate at higher power and higher rates is becoming more and more urgent. It is necessary to explore the electro-thermal behavior and internal key parameters of lithium-ion batteries at high current operation. In this paper, a combined model of the electrochemical- thermal (ECT) coupling model and the thermal model for abusive reaction of battery materials is established. The electrical-thermal behaviors of a prismatic single-layer LiCoO₂/C cell during discharge processes of various C-rates are simulated. The key electrochemical parameters and their dynamics for the cell during 1C and 14C discharge processed are analyzed and compared. The results show that with the increase of discharge current, heat accumulation in the battery will trigger the exothermic reactions of battery materials, making the battery vulnerable to thermal runaway. Besides, the concentration of Li-ion in the electrolyte, the transfer current density, the over potential, the electrolyte potential and the lithium concentration at the surface of solid particles fluctuate greatly during high C-rate discharge processes, leading to significant differences of species concentration, density and electric potential in the relevant regions inside the battery.

Key words: Li-ion battery, large current discharge, heat transfer, chemical reaction, transport processes, evolution of electrochemical parameters

摘要：

随着锂离子电池的广泛应用，电池以更大功率、更高倍率运行的需求日益迫切，探索锂离子电池大电流运行时的电-热行为及内部关键参数演化十分必要。建立了锂离子电池的电化学-热（ECT）模型和电池材料的热滥用模型，模拟了方形单层LiCoO₂/C电芯在不同放电电流下的电-热行为，对比分析了电池分别以1C和14C倍率放电时电池内部关键电化学参数的演化过程。结果表明：随着放电电流增加，电池内部积聚的热量会引发材料的放热反应，有引发电池热失控的可能性；大电流放电过程电解液中锂离子浓度、输运电流密度、过电势、电解质电势和固相颗粒表面的锂离子浓度波动较大，在电池内部相关区域形成了明显的浓度差、密度差和电势差。

关键词: 锂离子电池, 大电流放电, 传热, 化学反应, 传递过程, 电化学参数演化

CLC Number:

TK 02

Ti DONG, Peng PENG, Yiwei WANG, Wenjiong CAO, Yaodong ZHENG, Bo LEI, Fangming JIANG. Simulation on lithium ion battery discharge process with large current[J]. CIESC Journal, 2020, 71(8): 3710-3721.

董缇, 彭鹏, 王亦伟, 曹文炅, 郑耀东, 雷博, 蒋方明. 锂离子电池大电流放电过程模拟研究[J]. 化工学报, 2020, 71(8): 3710-3721.

Figures/Tables 13

Fig.1 Physical model of Li-ion single cell

Table 1 Model parameters of different regions from battery

参数	正极集流体	负电极	隔膜	正电极	负极集流体
厚度, L /μm	10	60	25	64	20
密度, ρ/(kg·m^-3)	8900	2660	492	2500	2700
比热容, c_p/(J·kg^-1·K^-1)	385	1437.4	1978	700	903
热导率^[25], λ/(W·m^-1·K^-1)	398	1.04	0.334	1.48	238
离子半径, r /μm		10	N/A	8
初始SOC		0.81		0.13
电极比面积, α_s/(m²·m^-3)		1.77×10⁵		2.40×10⁵
固相最大锂离子浓度^[26] /(mol·m^-3)		30555		51555
起始SOC^a		0.806		0.51
起始电解质浓度,c_e /(mol·m^-3)		1000	1200	1000
交换电流密度参考值/(A·m^-2)		36		26
固相离子电导率, σ/(S·m^-1)	6.0×10⁷	2.0	0	0.1	3.8×10⁷
固相锂离子扩散系数, D_s /(m²·s^-1)	0	式(15)	0	1×10^-13	0
电解质相锂离子扩散系数, D_e/(m²·s^-1)			式(17)
活化能 E_act_D_s(锂离子扩散)/(J·mol^-1)		4000	N/A	20000
活化能E_act_i₀(交换电流密度)/(J·mol^-1)		4000	N/A	4000
Bruggeman 指数		1.5	1.5	1.5
表观交换系数α_a,α_c		0.5		0.5
接触电阻, R_c/ (Ω·m²)			0.005
锂离子转移系数t₊⁰			0.363
法拉第常数, F/(C·mol^-1)			96487.0
参考温度, T_ref/K			298.15

Table 2 Battery physical parameters

参数	负极			隔膜 PP/PE/PP	正极			电解液 LiPF₆/EC+DMC+EMC
参数	铜箔	碳	黏结剂等	隔膜 PP/PE/PP	铝箔	LiCoO₂	黏结剂等	电解液 LiPF₆/EC+DMC+EMC
ρ /(kg·m^-3)	8900	2660	1750	492	1500	2500	1750	1290
c_p/(J·kg^-1·K^-1)	385	1437.4	1120	1978	903	700	1120	133.9
k/(W·m^-1·K^-1)	398	1.04	0.12	0.334	238	1.48	0.12	0.45

Table 3 Thermal abuse model of Li-ion battery

模型	方程
控制方程	$ρ c_{p} \frac{? T}{? t} = ? ? λ ? ? T + Q_{1} + Q_{2}$
能量方程	$Q_{2} = q_{s e i} + q_{n e} + q_{p e} + q_{e l e}$
SEI膜分解反应	$q_{s e i} = H_{s e i} W_{c} R_{s e i}$ , $R_{s e i} (T, c_{s e i}) = A_{s e i} e x p (- \frac{E_{a, s e i}}{R T}) c_{^{s e i}}^{m_{s e i}}$ , $\frac{d c_{s e i}}{d t} = - R_{s e i}$
负电极材料与电解质反应	$q_{n e} = H_{n e} W_{c} R_{n e}$ , $R_{n e} (T, c_{e}, c_{n e g}, t_{s e i}) = A_{n e} e x p (- \frac{t_{s e i}}{t_{s e i 0}}) c_{n e g}^{m_{n e, n}} e x p (- \frac{E_{a, n e}}{R T})$ ， $\frac{d t_{s e i}}{d t} = R_{n e}$ , $\frac{d c_{n e g}}{d t} = - R_{n e}$
正电极分解/ 正电极与电解质反应	$q_{p e} = H_{p e} W_{p} R_{p e}$ , $R_{p e} (T, α, c_{e l e}) = A_{p e} α^{m_{p e, p 1}} {(1 - α)}^{m_{p e, p 2}} e x p (- \frac{E_{a, p e}}{R T})$ , $\frac{d α}{d t} = R_{p e}$
电解液分解反应	$q_{e l e} = H_{e} W_{e} R_{e}$ , $R_{e} (T, c_{e l e}) = A_{e} e x p [- \frac{E_{a, e}}{R T}] c_{e l e}^{m_{e}}$ , $\frac{d c_{e l e}}{d t} = - R_{e}$

Table 3 Thermal abuse model of Li-ion battery

模型	方程
控制方程	$ρ c_{p} \frac{? T}{? t} = ? ? λ ? ? T + Q_{1} + Q_{2}$
能量方程	$Q_{2} = q_{s e i} + q_{n e} + q_{p e} + q_{e l e}$
SEI膜分解反应	$q_{s e i} = H_{s e i} W_{c} R_{s e i}$ , $R_{s e i} (T, c_{s e i}) = A_{s e i} e x p (- \frac{E_{a, s e i}}{R T}) c_{^{s e i}}^{m_{s e i}}$ , $\frac{d c_{s e i}}{d t} = - R_{s e i}$
负电极材料与电解质反应	$q_{n e} = H_{n e} W_{c} R_{n e}$ , $R_{n e} (T, c_{e}, c_{n e g}, t_{s e i}) = A_{n e} e x p (- \frac{t_{s e i}}{t_{s e i 0}}) c_{n e g}^{m_{n e, n}} e x p (- \frac{E_{a, n e}}{R T})$ ， $\frac{d t_{s e i}}{d t} = R_{n e}$ , $\frac{d c_{n e g}}{d t} = - R_{n e}$
正电极分解/ 正电极与电解质反应	$q_{p e} = H_{p e} W_{p} R_{p e}$ , $R_{p e} (T, α, c_{e l e}) = A_{p e} α^{m_{p e, p 1}} {(1 - α)}^{m_{p e, p 2}} e x p (- \frac{E_{a, p e}}{R T})$ , $\frac{d α}{d t} = R_{p e}$
电解液分解反应	$q_{e l e} = H_{e} W_{e} R_{e}$ , $R_{e} (T, c_{e l e}) = A_{e} e x p [- \frac{E_{a, e}}{R T}] c_{e l e}^{m_{e}}$ , $\frac{d c_{e l e}}{d t} = - R_{e}$

Table 4 Calculation parameters used in thermal abuse model

反应热/(J·kg^-1)					频率因子/s^-1					活化能/(J·mol^-1)
H_sei	H_ne		H_pe	H_ele	A_sei	A_ne	A_pe	A_e		E_a_,_sei	E_a_,_ne	E_a,pe	E_a,e
2.57×10⁵	1.714×10⁶		7.9×10⁵	1.55×10⁵	2.25×10¹⁵	2.5×10¹³	2.55×10¹⁴	5.14×10²⁵		1.3508×10⁵	1.3508×10⁵	1.5888×10⁵	2.74×10⁵
初始无量纲常数						反应级数					材料组分/(kg·m^-3)
c_sei0		c_neg0	α₀	c_ele0	t_sei0	m_sei	m_ne,n	m_pe,p1	m_pe,p2	m_e	W_c	W_p	W_e
0.15		0.75	0.04	1	0.033	1	1	1	1	1	1.39×10³	1.5×10³	5×10²

Fig.2 Voltage change and temperature change of single cell/single battery during discharge process

Fig.3 Thermal sources analysis of cell

Fig.4 Spatial and temporal distribution of Li+ concentration distribution in electrolyte during discharge process

Fig.5 Spatial and temporal distribution of the transfer current density during discharge process

Fig.6 Spatial and temporal distribution of the overpotential during discharge process

Fig.7 Spatial and temporal distribution of the solid phase potential during discharge process

Fig.8 Spatial and temporal distribution of the electrolyte phase potential during discharge process

Fig.9 Spatial and temporal distribution of SOC/DOD during discharge process

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