Heat generation analysis for lithium-ion battery components using electrochemical and thermal coupled model

doi:10.19799/j.cnki.2095-4239.2023.0082

Abstract

Abstract:

Understanding the thermal aspects of the battery electrochemical process is essential for managing the heat generated in lithium-ion batteries. Herein, an electrochemical-thermal coupled model was developed for an NMC lithium-ion battery. Experimental tests were conducted to validate the accuracy of the model in predicting voltage and temperature variations at different discharge rates and temperatures. Simulation studies were then conducted to estimate battery performance at different temperatures. At normal temperatures, regardless of the discharge rate, the NE heat generation was always smaller than the PE heat generation. While the NE polarization heat was higher than the PE polarization heat, the reversible heat absorption of NE was larger than that of PE. Consequently, the NE heat generation remained lower than that of PE. As the discharge rate increased, the proportion of PE heat generation decreased, whereas the proportion of NE heat generation increased first and then decreased. Simultaneously, the proportion of collector heat generation continued to rise. However, the heat generation characteristics differed when the battery discharge was discharged at subzero temperature compared to the normal temperature case. Firstly, subzero temperatures considerably increased the proportion of NE generation at low discharge rates. The reversible heat from NE became the primary contributor to the total reversible heat. Conversely, at high discharge rates, the NE heat generation rate decreased, while the PE heat generation rate exhibited the opposite trend. Secondly, the discharge time at subzero temperatures showed different trends with increasing discharge rates. At high discharge rates, the voltage rapidly decreased, leading to incomplete discharge and a phenomenon known as voltage rebound. At low discharge rates of 0.5—1 C discharge operation, the basic discharge process was completed, but the voltage rebound still occurred. The subzero temperature restricted the timely diffusion of lithium ions from the NE particles, leading to increased resistance and a rapid voltage drop. Meanwhile, a large amount of heat generation contributed to the temperature rise in the battery. Therefore, the battery exhibited the ability to rebound and maintain a continuous discharge at low rates.

Key words: lithium-ion battery, electrochemical-thermal coupled model, heat generation, subzero temperature characteristics, voltage rebound

CLC Number:

TM 911

Jiaxing YANG, Hengyun ZHANG, Yidong XU. Heat generation analysis for lithium-ion battery components using electrochemical and thermal coupled model[J]. Energy Storage Science and Technology, 2023, 12(8): 2615-2625.

Figures/Tables 19

Table 1

Fig. 1

Fig. 2

Table 2

P2D model control equations"

位置		控制方程		边界条件
正负电极颗粒	物质传输	$∂ c s ∂ t = 1 r 2 ∂ ∂ r D s r 2 ∂ c s ∂ r$	(1)	$∂ c s ∂ t r = 0 = 0$ , $- F D s ∂ c s ∂ r r = r p = j P$ , $c s t = 0 = c s, 0$
	物质传输	$i s = - σ e f f ∇ φ s$	(2)	$i s x = 0 = i s x = l n e + l S + l p e = I$ , $i s x = l n e = i s x = l n e + l S = 0$
	电荷守恒	$i l + i s = I$ ， $∇ ⋅ i l + ∇ ⋅ i s = 0$	(3)	$∇ ⋅ i l = α P j P$ ， $∇ ⋅ i s = - α P j P$
电解液	物质传输	$i l = - κ e f f ∇ φ l + 2 κ e f f R T F 1 - t + 1 + d l n f ± d l n c l ∇ l n c l$	(4)	$i l x = 0 = i l x = l n e + l S + l p e = 0$
电解液	物质守恒	$ε ∂ c l ∂ t = ∇ ⋅ (D e f f ∇ c l) + (1 - t +) ∇ ⋅ i l F$	(5)	$i l x = l n e = i l x = l n e + l S = I$

Table 2

Fig. 3

Table 3

Heat generation equation"

位置	方程
正负电极颗粒	$q p o l = α P j P η$	(12)
	$q O h m = σ e f f ∇ φ s ⋅ ∇ φ s + κ e f f ∇ φ l ⋅ ∇ φ l + 2 κ e f f R T F t + - 1 1 + d l n f ± d l n c l ∇ l n c l ⋅ ∇ φ l$	(13)
	$q r e v = α P j P T ∂ E ∂ T$	(14)
集流体	$q C = R C, C u + R C, A l I 2$	(15)
电解液	$q e l = κ e f f ∇ φ l ⋅ ∇ φ l + 2 κ e f f R T F t + - 1 1 + d l n f ± d l n c l ∇ l n c l ⋅ ∇ φ l$	(16)

Table 3

Table 4

Electrochemical model parameters at normal temperature"

参数	负极	隔膜	正极
厚度/μm	72.5	32	69.5
颗粒半径r/μm	7		5
固相体积分数 ε_s	0.5386		0.6348
电解液体积分数 ε_l	0.2807	0.43	0.3061
固相最大锂离子浓度c_{s, max}/(mol/m³)	28607		49388
固相初始锂离子浓度c_{s, 0}/(mol/m³)	0.84c_{s, max, ne}		0.279c_{s, max, pe}
电解液参考锂离子浓度c_{l, 0}=c_ref/(mol/m³)	1000	1000	1000
传递系数 α_ne, α_pe	0.5		0.5
Bruggeman因子Brug	1.5	1.5	1.5
锂离子固相扩散活化能E_aR/(J/mol)	68025.7		9976.8
锂离子固相参考扩散系数D_{s, ref}/(m²/s)	1.4523 $×$ 10^-13		5 $×$ 10^-13
等效固相电导率 σ /(S/m)	100		3.8
转移数t₊	0.363
电池径向热导率 λ_xy /[W/(m·K)]	1.63
电池轴向热导率 λ_z /[W/(m·K)]	36.96
电池密度 ρ /(kg/m³)	2510
比定压热容c_p /[J/(kg·K)]	1028

Table 4

Table 5

Variable temperature electrochemical dynamic parameters"

参数	动态表达式
等效电解液电导率 к /(S/m)	$κ c r e f, T = 10 - 4 c r e f - 8.2488 + 0.053248 T - 0.00002987 T 2 + 0.26235 × 10 - 3 c r e f - 0.0093063 × 10 - 3 c r e f T + 0.000008069 × 10 - 3 c r e f T 2 + 0.22002 × 10 - 6 c r e f 2 - 0.0001765 × 10 - 6 c r e f 2 T 2$
锂离子固相扩散系数D_s/(m²/s)	$D s = D s, r e f e x p E a R R 1 T r e f - 1 T$
锂离子液相扩散系数D_l/(m²/s)	$l g D l c r e f, T = - 4.43 - 54 T - 229 - 0.005 c r e f - 0.00022 c r e f - 4$
活性系数ν(f_±, t₊)	$ν (c r e f, T) = 1 - 0.363 1 - 0.399 0.601 - 0.24 × 10 - 2 c r e f 0.5 + 0.982 ⋅ 1 - 0.0052 T - 293.15 ⋅ (10 - 3 c r e f) 1.5$

Table 5

Fig. 4

Fig. 5

Fig. 6

Table 6

Fig. 7

Fig. 8

Fig. 9

Fig. 10

Fig. 11

Fig. 12

Fig. 13

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参数	数值
标准容量/mAh	2700
标称电压/V	3.60
充电截止电压/V	4.20
放电截止电压/V	2.50

电池组件	室温				低温
电池组件	0.5 C	1 C	2 C	3 C	0.5 C	1 C	2 C	3 C
负极	19.56%	29.02%	26.3%	23.73%	69.34%	65.13%	36.58%	29.96%
正极	59.26%	45.96%	34.08%	28.36%	20.98%	20.81%	38.73%	39.85%
电解液	0.95%	0.93%	0.52%	0.58%	0.27%	0.92%	0.78%	0.96%
集流体	20.23%	24.08%	39.11%	47.33%	9.41%	13.13%	23.91%	29.23%

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