基于电化学-热耦合模型的电池低温脉冲加热

doi:10.19799/j.cnki.2095-4239.2022.0342

摘要/Abstract

摘要：

低温环境下，锂离子电池性能下降，充放电困难，严重影响了电动汽车的使用。采用脉冲加热方法是一种解决该问题的有效策略。本工作采用三元锂离子电池，通过对比放电电压曲线和温升曲线的实验值和模拟值建立电化学热耦合模型，仿真分析脉冲加热下锂离子电池的电化学和热特性，研究不同脉冲振幅和环境温度下的产热分布。结果表明，在环境温度为-8 ℃时，4 C脉冲加热电池的温升是2 C脉冲加热的2.25倍。欧姆热和极化热决定着总产热量的大小。环境温度越低，锂离子电池的极化越严重，但随着脉冲的进行，极化有所平缓。大脉冲电流和较低温度下的脉冲加热有更大的温升速率。脉冲加热后电池表面最高温度在几何中心偏下的位置，且最大温差不超过2 ℃，具有良好的温度均匀性。

关键词: 锂离子电池, 低温性能, 脉冲加热, 电化学-热耦合模型, 温度分布

Abstract:

In low-temperature environments, the performance of lithium-ion batteries is degraded, making charging and discharging difficult, which seriously affects the use of electric vehicles. The use of pulse heating is an effective strategy to solve this problem. Therefore, in this paper, a ternary lithium-ion battery was used, after which we established an electrochemical-thermal coupling model by comparing the experimental and simulated values from the discharge voltage and temperature rise curves, including those of the electrochemical and thermal characteristics of the lithium-ion battery. Then, a simulation analysis of an ion battery under pulsed heating was conducted, followed by heat production distribution at ambient temperature. The results showed that the temperature rise of the 4 C pulse-heated battery was 2.25 times higher than that of the 2 C-pulse-heated battery at -8 ℃ ambient temperature, with ohmic heat and polarization heat determining the size of the total heat production. We also observed that although the lower the ambient temperature, the more severe the polarization of the lithium-ion battery, the polarization moderated as the pulse progressed. Pulse heating at a high pulse current and a lower temperature also had a larger temperature rise rate. Hence, after pulse heating, the battery surface's maximum temperature was at the geometric centre's lower position, the maximum temperature difference did not exceed 2 ℃, and the temperature uniformity was good.

Key words: lithium-ion battery, low temperature performance, pulse heating, electrochemical-thermal coupled model, temperature distribution

中图分类号:

TM 911

张冬冬, 文华, 欧阳宏伟. 基于电化学-热耦合模型的电池低温脉冲加热[J]. 储能科学与技术, 2022, 11(12): 3957-3964.

Dongdong ZHANG, Hua WEN, Hongwei OUYANG. Research on low-temperature pulse heating of a battery based on an electrochemical-thermal coupled model[J]. Energy Storage Science and Technology, 2022, 11(12): 3957-3964.

图/表 14

图1

表1

电化学模型基本方程和边界条件"

方程名称	控制方程和边界条件
固相质量守恒	$∂ c 1 ∂ t + 1 r 2 ∂ ∂ r (- r 2 D 1 ∂ c 1 ∂ r) = 0$ ; $∂ c 1 ∂ t \| r = 0 = 0$ ; $- D 1 ∂ c 1 ∂ r \| r = R p = j l o c F$
液相质量守恒	$ε 2 ∂ c 2 ∂ t = ∂ ∂ x (D 2 e f f ∂ c 2 ∂ x) + (1 - t +) S a j l o c F$ ; $S a = 3 ε 1 R p$ ; $D 2 e f f = D 2 ε 2 1.5$ ; $∂ c 2 ∂ x \| x = 0 = ∂ c 2 ∂ x \| x = L = 0$
固相电荷守恒	$∂ ∂ x (- σ 1 e f f ∂ φ 1 ∂ x) = - S a j l o c$ ; $σ 1 e f f = σ 1 ε 1 1.5$ ; $φ 1 \| x = 0 = 0$ ; $- σ 1 e f f ∂ φ 1 ∂ x \| x = L n + L s + L p = - I a p p$ ; $- σ 1, n e f f ∂ φ 1 ∂ x \| x = L n = - σ 1, p e f f ∂ φ 1 ∂ x \| x = L n + L s = 0$
液相质量守恒	$∇ [- σ 2 e f f ∇ φ 2 + 2 R T σ 2 e f f F (1 + ∂ l n f ± ∂ l n c 2) (1 - t +) ∇ (l n c 2)] = S a j l o c$ ; $σ 2 e f f = σ 2 ε 2 1.5$ ; $K j u n c = 2 R T F (1 + ∂ l n f ± ∂ l n c 2) (1 - t +) = 2 R T F υ$ ; $∂ φ 2 ∂ x \| x = 0 = ∂ φ 2 ∂ x \| x = L n + L s + L p = 0$
电极过程动力学	$j l o c = i 0 e x p (α a F R T η) - e x p (α c F R T η)$ ; $η = φ 1 - φ 2 - U$ ; $i 0 = F k 0 c 2 α a (c 1, m a x - c 1, s u r f) α a c 1, s u r f α c$ ; $U = U r e f + (T - T r e f) d U d T$
能量守恒	$ρ C p ∂ T ∂ t + ∇ ⋅ (- λ ∇ T) = Q r e a + Q a c t + Q o h m$ ; $Q r e a = S a j l o c T ∂ U ∂ T = S a j l o c T Δ S F$ ; $Q a c t = S a j l o c η$ ; $Q o h m = σ 1 e f f ∇ φ 1 ⋅ ∇ φ 1 + [σ 2 e f f ∇ φ 2 - 2 R T σ 2 e f f F (1 + ∂ l n f ± ∂ l n c 2) (1 - t +) ∇ (l n c 2)] ⋅ ∇ φ 2$ ; $- λ ∂ T ∂ x \| x = 0 = - λ ∂ T ∂ x \| x = L n + L s + L p = h (T - T a m b)$

表1

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表3

图2

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图8

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图11

参考文献 17

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描述	参数	阴极	隔膜	阳极
颗粒半径	r_p/μm	8.5	—	12.5
电极体积分数	ε₁	0.435	—	0.56
电解液体积分数	ε₂	0.28	0.4	0.3
厚度	L/μm	99	32	72
最大固相锂离子浓度	c_1,max/(mol/m³)	36100	—	30100
初始电解液锂离子浓度	c_2,0/(mol/m³)	1200	1200	1200
阳极/阴极电荷交换系数	α_a/α_c	0.5	—	0.5
电极参考速率常数	k_{0, ref} /[m^2.5/(mol^0.5·s)]	4.38×10^-11	—	1.63×10^-11
固相电导率	σ₁/(S/m)	3.8	—	100
电极参考电导率	D_1,ref/(m²/s)	1×10^-13	—	3.9×10^-14
电极扩散系数	D₁/(m²/s)	—
传递系数	t₊	—	0.363	—
扩散活化能	E_aD/(J/mol)	20000	—	35000
反应活化能	E_aR/(J/mol)	4000	—	4000
液相锂离子扩散系数	D₂/(m²/s)	—
参考温度	T_ref/K	298.15
通用气体常数	R	8.314
法拉第常数	F/(C/mol)	96487

参数	值
尺寸(高×宽×厚)/mm	225×160×9
正极极耳宽度/mm	50
负极极耳宽度/mm	45
极耳长度/mm	15
重量/g	609
额定电压/V	3.7
充电截止电压/V	4.2
放电截止电压/V	2.75
额定容量/Ah	36

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