Review of parameter identification for physics-based lithium-ion battery models

doi:10.11949/0438-1157.20250063

Abstract

Abstract:

Lithium-ion batteries have gained widespread application in recent years due to their high energy density, low cost, and long cycle life, spurring rapid advancements in battery modeling. Compared to equivalent circuit models, physics-based models can provide high-precision predictions of battery performance under varying temperatures and operating conditions. However, the accuracy of these models is highly dependent on the precision of their parameters. Traditional invasive measurement methods are cumbersome and often fail to ensure sufficient accuracy. Consequently, parameter identification based on data such as voltage and current has emerged as a prominent research focus. This paper reviews the key steps of parameter identification of lithium-ion battery mechanism models, including model establishment, parameter sensitivity analysis and final parameter optimization.

Key words: lithium-ion battery, electrochemistry, physics-based model, parameter identification, sensitivity analysis, algorithm

摘要：

锂离子电池因其高能量密度、低成本与长循环寿命在近年来得到广泛应用，电池模型的研究也迅速发展。与等效电路模型相比，机理模型能够对不同温度、不同工况下电池的性能表现进行高精度预测，然而模型的精度高度依赖参数的精度，传统侵入式测量方法烦琐且精度无法保证，基于电压、电流等数据对电池模型的参数进行辨识成为研究的热门。综述了锂离子电池机理模型参数辨识的关键步骤，包括模型建立、参数敏感性分析以及最终的参数寻优。

关键词: 锂离子电池, 电化学, 机理模型, 参数识别, 敏感性分析, 算法

CLC Number:

TM 912

Lanhao LOU, Lipeng YANG, Xiaoguang YANG. Review of parameter identification for physics-based lithium-ion battery models[J]. CIESC Journal, 2025, 76(9): 4369-4382.

娄岚浩, 杨立鹏, 杨晓光. 锂离子电池电化学机理模型参数辨识研究综述[J]. 化工学报, 2025, 76(9): 4369-4382.

Figures/Tables 10

Fig.1 Workflow of parameter identification

Fig.2 Schematic of DFN model

Table 1 Equations of DFN model

机理	控制方程	边界条件
输出电压	$V (t) = ϕ s (L, t) - ϕ s (0, t) - R c c A i a p p (t)$
固相传质	$∂ c s r, x, t ∂ t = 1 r 2 ∂ ∂ r D s r 2 ∂ c s r, x, t ∂ r$	$D s i ∂ c s i r, x, t ∂ r r = 0 = 0$ $D s i ∂ c s i r, x, t ∂ r r = R p i = - j (x, t)$
液相传质	$∂ c e x, t ∂ t = ∂ ∂ x D e, e f f ∂ c e x, t ∂ x + a 1 - t + 0 ε e j x, t$	$∂ c e x, t ∂ x x = 0 = 0$ $∂ c e x, t ∂ x x = L = 0$
固相电荷守恒	$∂ ∂ x σ s, e f f ∂ ϕ s (x, t) ∂ x = a F j (x, t)$	$σ s, e f f ∂ ϕ s (x, t) ∂ x x = L n, L n + L s = 0$ $σ s, e f f ∂ ϕ s (x, t) ∂ x x = 0, L = i a p p (t) A$
液相电荷守恒	$∂ ∂ x σ e, e f f ∂ ϕ e (x, t) ∂ x - σ e, e f f 2 R T (1 - t + 0) F ∂ l n c e (x, t) ∂ x = - a F j (x, t)$	$σ e, e f f ∂ ϕ e (x, t) ∂ x x = L n, L n + L s =$ $i a p p (t) A σ e, e f f ∂ ϕ e (x, t) ∂ x x = 0, L = 0$
反应动力学	$j x, t = i 0 (x, t) F e x p α a F R T η (x, t) - e x p - α c F R T η (x, t)$ $η x, t = ϕ s x, t - ϕ e x, t - U c s s x, t c s, m a x - F R f j x, t$ $i 0 x, t = κ e f f F c e (x, t) α a c s, m a x - c s s x, t α a c s s x, t α c$

Table 1 Equations of DFN model

机理	控制方程	边界条件
输出电压	$V (t) = ϕ s (L, t) - ϕ s (0, t) - R c c A i a p p (t)$
固相传质	$∂ c s r, x, t ∂ t = 1 r 2 ∂ ∂ r D s r 2 ∂ c s r, x, t ∂ r$	$D s i ∂ c s i r, x, t ∂ r r = 0 = 0$ $D s i ∂ c s i r, x, t ∂ r r = R p i = - j (x, t)$
液相传质	$∂ c e x, t ∂ t = ∂ ∂ x D e, e f f ∂ c e x, t ∂ x + a 1 - t + 0 ε e j x, t$	$∂ c e x, t ∂ x x = 0 = 0$ $∂ c e x, t ∂ x x = L = 0$
固相电荷守恒	$∂ ∂ x σ s, e f f ∂ ϕ s (x, t) ∂ x = a F j (x, t)$	$σ s, e f f ∂ ϕ s (x, t) ∂ x x = L n, L n + L s = 0$ $σ s, e f f ∂ ϕ s (x, t) ∂ x x = 0, L = i a p p (t) A$
液相电荷守恒	$∂ ∂ x σ e, e f f ∂ ϕ e (x, t) ∂ x - σ e, e f f 2 R T (1 - t + 0) F ∂ l n c e (x, t) ∂ x = - a F j (x, t)$	$σ e, e f f ∂ ϕ e (x, t) ∂ x x = L n, L n + L s =$ $i a p p (t) A σ e, e f f ∂ ϕ e (x, t) ∂ x x = 0, L = 0$
反应动力学	$j x, t = i 0 (x, t) F e x p α a F R T η (x, t) - e x p - α c F R T η (x, t)$ $η x, t = ϕ s x, t - ϕ e x, t - U c s s x, t c s, m a x - F R f j x, t$ $i 0 x, t = κ e f f F c e (x, t) α a c s, m a x - c s s x, t α a c s s x, t α c$

Table 2 Parameters of DFN model

分类	符号	意义	相关性	单位	测试方法
几何参数	$L p$	正极厚度	SoH	$m$
	$L s$	隔膜厚度	SoH	$m$
	$L n$	负极厚度	SoH	$m$
	$A$	活性电极面积		$m 2$	BET^[35]
	$ε s +$	正极活性材料体积分数	X，SoH
	$ε s -$	负极活性材料体积分数	X，SoH
	$ε e +$	正极孔隙率	X，SoH		压汞法^[36]
	$ε e s$	隔膜孔隙率			真密度，SEM
	$ε e -$	负极孔隙率	X，SoH		压汞法
	$R p +$	正极材料颗粒半径		$m$	激光粒度（DLS）^[37]、SEM、压汞法激光粒度（DLS）^[37]、SEM、压汞法^[38]
	$R p -$	负极材料颗粒半径		$m$	激光粒度（DLS）^[37]、SEM、压汞法激光粒度（DLS）^[37]、SEM、压汞法^[38]
传质参数	$D s +$	正极材料固相扩散系数	SoC，T	$m 2 / s$	GITT^[39]、EIS^[40]、恒电位间歇滴定（PITT）^[41]
	$D s -$	负极材料固相扩散系数	SoC，T	$m 2 / s$	GITT^[39]、EIS^[40]、恒电位间歇滴定（PITT）^[41]
	$D e$	电解液液相扩散系数	Ce，T	$m 2 / s$	脉冲弛豫^[42]
	$t 0 +$	电解液阳离子迁移数	Ce，T		浓差电池^[42]
	$σ s +$	正极电导率		$S / m$	四探针法四探针法
	$σ s -$	负极电导率		$S / m$	四探针法四探针法
	$σ e$	电解液离子电导率	Ce，T	$S / m$	电导率测试仪
反应动力学参数	$k +$	正极反应速率常数	SoC，T	$m 2.5 / (m o l 0.5 · s)$	EIS^[43] EIS^[43]
	$k -$	负极反应速率常数	SoC，T	$m 2.5 / (m o l 0.5 · s)$	EIS^[43] EIS^[43]
	$R f$	SEI膜电阻率	SoH，T	$Ω · m 2$
	$U O C P +$	正极开路电势	SoC，T	$V$	GITT、PITT GITT、PITT
	$U O C P -$	负极开路电势	SoC，T	$V$	GITT、PITT GITT、PITT
参考浓度参数	$c s, m a x +$	正极最大嵌锂浓度		$m o l / m 3$
	$c s, m a x -$	负极最大嵌锂浓度		$m o l / m 3$
	$c e, 0$	电解液初始浓度		$m o l / m 3$
外电路参数	$i a p p$	输出/输入电流		$A$
	$R c c$	集流体电阻率		$Ω · m 2$

Table 2 Parameters of DFN model

分类	符号	意义	相关性	单位	测试方法
几何参数	$L p$	正极厚度	SoH	$m$
	$L s$	隔膜厚度	SoH	$m$
	$L n$	负极厚度	SoH	$m$
	$A$	活性电极面积		$m 2$	BET^[35]
	$ε s +$	正极活性材料体积分数	X，SoH
	$ε s -$	负极活性材料体积分数	X，SoH
	$ε e +$	正极孔隙率	X，SoH		压汞法^[36]
	$ε e s$	隔膜孔隙率			真密度，SEM
	$ε e -$	负极孔隙率	X，SoH		压汞法
	$R p +$	正极材料颗粒半径		$m$	激光粒度（DLS）^[37]、SEM、压汞法激光粒度（DLS）^[37]、SEM、压汞法^[38]
	$R p -$	负极材料颗粒半径		$m$	激光粒度（DLS）^[37]、SEM、压汞法激光粒度（DLS）^[37]、SEM、压汞法^[38]
传质参数	$D s +$	正极材料固相扩散系数	SoC，T	$m 2 / s$	GITT^[39]、EIS^[40]、恒电位间歇滴定（PITT）^[41]
	$D s -$	负极材料固相扩散系数	SoC，T	$m 2 / s$	GITT^[39]、EIS^[40]、恒电位间歇滴定（PITT）^[41]
	$D e$	电解液液相扩散系数	Ce，T	$m 2 / s$	脉冲弛豫^[42]
	$t 0 +$	电解液阳离子迁移数	Ce，T		浓差电池^[42]
	$σ s +$	正极电导率		$S / m$	四探针法四探针法
	$σ s -$	负极电导率		$S / m$	四探针法四探针法
	$σ e$	电解液离子电导率	Ce，T	$S / m$	电导率测试仪
反应动力学参数	$k +$	正极反应速率常数	SoC，T	$m 2.5 / (m o l 0.5 · s)$	EIS^[43] EIS^[43]
	$k -$	负极反应速率常数	SoC，T	$m 2.5 / (m o l 0.5 · s)$	EIS^[43] EIS^[43]
	$R f$	SEI膜电阻率	SoH，T	$Ω · m 2$
	$U O C P +$	正极开路电势	SoC，T	$V$	GITT、PITT GITT、PITT
	$U O C P -$	负极开路电势	SoC，T	$V$	GITT、PITT GITT、PITT
参考浓度参数	$c s, m a x +$	正极最大嵌锂浓度		$m o l / m 3$
	$c s, m a x -$	负极最大嵌锂浓度		$m o l / m 3$
	$c e, 0$	电解液初始浓度		$m o l / m 3$
外电路参数	$i a p p$	输出/输入电流		$A$
	$R c c$	集流体电阻率		$Ω · m 2$

Table 3 Related literature on sensitivity analysis for physics-based lithium-ion battery models

类型	方法	模型	工况	分析目标	优缺点	文献
局部	方差	DFN	恒流恒压充电、WLTP	电压、 $ϕ s - ϕ e$	考虑多种工况以及对负极点位的敏感性，但计算量大且OAT存在局限性	[51]
局部	方差	DFN+热阻网络	恒流放电	电压、温度	模型能够预测电压及温度，但实验复杂	[52]
局部	方差	SPMe	恒流放电	电压	有效简化模型，减少计算量，但适用工况少，存在局限性	[53]
全局	Morris	SPM	恒流恒压充电、恒流放电、FUDS	电压	采样方法高效，但简化模型存在局限性	[54]
全局	偏相关性	DFN	恒流充电、FUDS	电压误差	全面分析老化参数，并进行收敛性分析，确保可靠性，但模型复杂，计算量大	[55]

Table 3 Related literature on sensitivity analysis for physics-based lithium-ion battery models

类型	方法	模型	工况	分析目标	优缺点	文献
局部	方差	DFN	恒流恒压充电、WLTP	电压、 $ϕ s - ϕ e$	考虑多种工况以及对负极点位的敏感性，但计算量大且OAT存在局限性	[51]
局部	方差	DFN+热阻网络	恒流放电	电压、温度	模型能够预测电压及温度，但实验复杂	[52]
局部	方差	SPMe	恒流放电	电压	有效简化模型，减少计算量，但适用工况少，存在局限性	[53]
全局	Morris	SPM	恒流恒压充电、恒流放电、FUDS	电压	采样方法高效，但简化模型存在局限性	[54]
全局	偏相关性	DFN	恒流充电、FUDS	电压误差	全面分析老化参数，并进行收敛性分析，确保可靠性，但模型复杂，计算量大	[55]

Fig.3 Parameter sensitivity analysis results in literature

Fig.4 Schematic diagram of principles of different optimization algorithms

Fig.5 Workflow of different metaheuristic optimization algorithms

Table 4 Related literature on metaheuristic optimization algorithms

模型	算法	优化参数	辨识结果	优缺点	文献
DFN	GA	17个标量参数、71函数参数	误差<5%	研究框架全面，实验数据丰富，但参数设置较多,计算成本高	[81]
DFN	GA	$ε s +, ε s -, L +, L -, D s +, D s -, R p +, R p -,$ $C s, m a x +, C s, m a x -$	恒流工况MAE< 25 mV 动态工况MAE<80 mV	平均电极模型简化合理，实验验证全面，但简化模型适用有限	[82]
DFN	PSO	$D s +, D s -, k +, k -$	仅图示	优化算法简单高效，但辨识参数范围有限	[85]
SPMe	自适应PSO	$C s, 0 +, C s, 0 -, D s +, D s -, k +, k -$	恒流工况RMSE<30 mV；脉冲工况RMSE<30 mV	模型简化合理，算法高效，但验证工况较少	[53]
DFN	CSA	$L +, L -, C s, m a x +, C s, m a x -, ε s +, ε s -, A,$ $k +, k -, R p +, R p -, ε e +, ε e -, D s +, D s -, D e$	恒流工况RMSE 9 mV； WLTP工况RMSE 12.7 mV	多目标优化框架提升精度，但数据需求量大	[50]

Table 4 Related literature on metaheuristic optimization algorithms

模型	算法	优化参数	辨识结果	优缺点	文献
DFN	GA	17个标量参数、71函数参数	误差<5%	研究框架全面，实验数据丰富，但参数设置较多,计算成本高	[81]
DFN	GA	$ε s +, ε s -, L +, L -, D s +, D s -, R p +, R p -,$ $C s, m a x +, C s, m a x -$	恒流工况MAE< 25 mV 动态工况MAE<80 mV	平均电极模型简化合理，实验验证全面，但简化模型适用有限	[82]
DFN	PSO	$D s +, D s -, k +, k -$	仅图示	优化算法简单高效，但辨识参数范围有限	[85]
SPMe	自适应PSO	$C s, 0 +, C s, 0 -, D s +, D s -, k +, k -$	恒流工况RMSE<30 mV；脉冲工况RMSE<30 mV	模型简化合理，算法高效，但验证工况较少	[53]
DFN	CSA	$L +, L -, C s, m a x +, C s, m a x -, ε s +, ε s -, A,$ $k +, k -, R p +, R p -, ε e +, ε e -, D s +, D s -, D e$	恒流工况RMSE 9 mV； WLTP工况RMSE 12.7 mV	多目标优化框架提升精度，但数据需求量大	[50]

Table 5 Comparison of different metaheuristic optimization algorithms

特性	GA	PSO	CSA
全局搜索能力	强	中等	强
收敛速度	慢	快	中等
计算开销	高	低	中等
参数依赖性	高	中等	低
实现难度	高	低	低
理论基础	强	强	弱
适用问题	连续、离散、组合优化	连续优化	连续、离散、组合优化

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