基于电化学-热耦合模型的锂离子电池组件产热分析

doi:10.19799/j.cnki.2095-4239.2023.0082

摘要/Abstract

摘要：

研究电池电化学过程产热对锂离子电池的热管理至关重要。本工作建立了三元NMC锂离子电池的电化学-热耦合模型，首先通过对该电池进行不同倍率的放电与温度实验测试，验证了该模型在电压和温度变化预测准确性。然后针对不同温度下的表现进行模拟仿真研究。在室温下，无论倍率大小，负极产热总是小于正极产热，虽然负极的极化热高于正极，但其可逆吸热较大，导致产热水平低于正极。而随着放电倍率的增加，正极产热所占比例减小，负极所占比例先增加后减小，而集流体产热所占比例持续增加。然而，低温条件下的电池放电表现出与室温情况不同的产热特性，首先，低温导致低倍率负极产热率比例大大增加，负极可逆热为总可逆热的主要贡献热。而高倍率负极产热率减少，正极则呈相反趋势。其次在低温下放电时间随倍率增加呈现不同趋势，高倍率下放电电压快速降低导致放电不完全，在低倍率0.5～1 C放电运行时出现了电压反弹现象但基本放电完全，这是由于低温限制了负极颗粒内部锂离子及时向外扩散，造成电阻增加与电压快速降低，同时大量产热导致自身温升，从而在低倍率下获得电压反弹并保持持续放电的能力。

关键词: 锂离子电池, 电化学热耦合模型, 产热, 低温特性, 电压反弹

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

中图分类号:

TM 911

杨佳兴, 张恒运, 徐屹东. 基于电化学-热耦合模型的锂离子电池组件产热分析[J]. 储能科学与技术, 2023, 12(8): 2615-2625.

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.

图/表 19

表1

图1

图2

表2

P2D模型控制方程"

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)	$i l x = l n e = i l x = l n e + l S = I$

表2

图3

表3

产热方程"

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)

表3

表4

室温下电化学模型参数"

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

表4

表5

变温电化学动态参数"

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₊)	$ν (c r e f, T) = 1 - 0.363 1 - 0.399 0.601 - 0.24 × 10 - 2 c r e f 0.5 + 0.982 ⋅ 1 - 0.0052 T - 293.15 ⋅ (10 - 3 c r e f) 1.5$

表5

图4

图5

图6

表6

图7

图8

图9

图10

图11

图12

图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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