Research Status and Prospect of Lithium-Ion Battery Modelling

doi:10.12096/j.2096-4528.pgt.24112

Abstract

Abstract:

Objectives As one of the core technologies of battery management system (BMS), the research on lithium-ion battery model plays a vital role in optimizing battery performance and extending battery life. In order to facilitate the selection of appropriate models in different scenarios, different types of modeling methods for lithium-ion batteries are systematically summarized and compared. Methods Firstly, the working principle of lithium-ion battery is explained, and the importance of accurate modeling is emphasized. Then, the current widely used lithium-ion battery models is comprehensively summarized according to different application scenarios, and a series of novel machine learning battery models are analyzed and discussed. Finally, the challenges of lithium-ion battery modelling techniques and future research trends are discussed. Conclusions It is found that traditional battery models all have certain limitations, while data-driven models often have more unique advantages in dealing with complex systems. Future research needs to find a balance between model complexity and usability. The research results provide a reference for application and future development of lithium-ion batteries in energy storage systems.

Key words: lithium-ion batterie, energy storage, electric vehicle, battery management system (BMS), battery modeling, equivalent circuit model (ECM), electrochemical model (EM), machine learning model

CLC Number:

TK 02

Jianlin LI, Yuchen PENG, Qian WANG, Xiaoxia JIANG, Lei WANG. Research Status and Prospect of Lithium-Ion Battery Modelling[J]. Power Generation Technology, 2025, 46(5): 857-871.

Figures/Tables 10

Fig. 1 Working principle of rechargeable lithium-ion battery

Fig. 2 Typical equivalent circuit model

Tab. 1 Comparison of commonly used equivalent circuit models

名称	描述方程	优点	缺点	参考文献	参数含义
Rint	$U L = U O C - I L R 0$	结构简单，参数个数少，计算量小	未考虑极化反应的影响	[35]	R_p和C_p分别为极化电阻和极化电容；U_e为电化学极化电容两端电压；U_c为浓差极化电容两端电压；U_b为等效电容两端电压；C_b为等效电容
Thevenin	$U L = U L + R 0 I L + U e U p = - U p R p C p + I L C p$	考虑了欧姆极化和电化学极化。模型结构相对简单，计算量小，具有较好的实用价值	仿真精度会随着电池老化和温度发生较大变化而下降	[36-37]
DP	$U L = U O C - I L R 0 - U e - U c U e = - U e R e C e + I L C e U c = - U c R c C c + I L C c$	应对快速充放电时能表现出更好的高频特性，更接近电池的实际运行特性	结构较为复杂，计算量较大，且未考虑温度等因素的影响	[38-39]
PNGV	$U L = U O C - U b - U e - I L R 0 U b = I L / C b U e = - (U e / R e C e) + I L / C e$	串联电容C_b能够描述开路电压随积分的变化，反映了电池的容量，使得电池SOC、SOH预测更精确	难以准确模拟电池在快速充放电过程中的动态响应，不适用于预测电池长期性能	[35]
GNL	$U L = U O C - U b - U e - U c - I L R 0 U b = (U b + U e + U c) R s C b + I L C b + U O C R s C e U e, c = - (U b + U c, e) R s C e, c - (U e, c R s C e, c + U e, c R e, c C e, c) + 1 C e, c + U O C R s C c$	结合了上述4种等效电路模型的优点，同时考虑了欧姆极化、电化学极化、浓差极化及自放电因素对锂离子电池的内部特性	模型非常复杂，且参数较多，计算量大，不建议用于小范围的锂离子电池SOC估算的实验仿真和实际应用	[41]
高阶RC	$U L = U O C - U 1 - U 2 - ⋯ - U m - I L R 0 U m = - U m R m C m + I L C m$	仿真精度高，考虑了电阻电容的分布函数，能根据规律计算参数	当m达到一定数量时，仿真精度会呈现下降的趋势，且计算量大，未考虑其他因素的影响	[42]	R_m 和C_m 分别为第m个RC环节的电阻和电容

Tab. 1 Comparison of commonly used equivalent circuit models

名称	描述方程	优点	缺点	参考文献	参数含义
Rint	$U L = U O C - I L R 0$	结构简单，参数个数少，计算量小	未考虑极化反应的影响	[35]	R_p和C_p分别为极化电阻和极化电容；U_e为电化学极化电容两端电压；U_c为浓差极化电容两端电压；U_b为等效电容两端电压；C_b为等效电容
Thevenin	$U L = U L + R 0 I L + U e U p = - U p R p C p + I L C p$	考虑了欧姆极化和电化学极化。模型结构相对简单，计算量小，具有较好的实用价值	仿真精度会随着电池老化和温度发生较大变化而下降	[36-37]
DP	$U L = U O C - I L R 0 - U e - U c U e = - U e R e C e + I L C e U c = - U c R c C c + I L C c$	应对快速充放电时能表现出更好的高频特性，更接近电池的实际运行特性	结构较为复杂，计算量较大，且未考虑温度等因素的影响	[38-39]
PNGV	$U L = U O C - U b - U e - I L R 0 U b = I L / C b U e = - (U e / R e C e) + I L / C e$	串联电容C_b能够描述开路电压随积分的变化，反映了电池的容量，使得电池SOC、SOH预测更精确	难以准确模拟电池在快速充放电过程中的动态响应，不适用于预测电池长期性能	[35]
GNL	$U L = U O C - U b - U e - U c - I L R 0 U b = (U b + U e + U c) R s C b + I L C b + U O C R s C e U e, c = - (U b + U c, e) R s C e, c - (U e, c R s C e, c + U e, c R e, c C e, c) + 1 C e, c + U O C R s C c$	结合了上述4种等效电路模型的优点，同时考虑了欧姆极化、电化学极化、浓差极化及自放电因素对锂离子电池的内部特性	模型非常复杂，且参数较多，计算量大，不建议用于小范围的锂离子电池SOC估算的实验仿真和实际应用	[41]
高阶RC	$U L = U O C - U 1 - U 2 - ⋯ - U m - I L R 0 U m = - U m R m C m + I L C m$	仿真精度高，考虑了电阻电容的分布函数，能根据规律计算参数	当m达到一定数量时，仿真精度会呈现下降的趋势，且计算量大，未考虑其他因素的影响	[42]	R_m 和C_m 分别为第m个RC环节的电阻和电容

Fig. 3 Structure of the P2D model

Tab. 2 Governing equations for the P2D model of lithium-ion batteries

性质	状态方程	边界条件
液相锂浓度	$∂ (ε e, n c e, n) ∂ t = ∂ ∂ x (D e, n e f f ∂ c e, n ∂ x)$	$∂ c e, n ∂ x x = 0 = 0, ∂ c e, p ∂ x x = l = 0$
固相颗粒锂浓度	$∂ c s ∂ t = D s r 2 ∂ ∂ x (r 2 ∂ c s ∂ r)$	$∂ c s ∂ r r = 0 = 0, D s ∂ c s ∂ r r = R s = - j L i α s F$
液相电势	$∂ ∂ x (K e e f f ∂ ϕ e ∂ x) + ∂ ∂ x (K D e f f ∂ l n c e ∂ x) + j L i = 0$	$∂ ϕ e ∂ x x = 0 = 0$
固相电势	$∂ ∂ x (σ e f f ∂ ϕ s ∂ x) = j L i$	$- σ e f f ∂ ϕ s ∂ x x = 0 = I A$

Tab. 2 Governing equations for the P2D model of lithium-ion batteries

性质	状态方程	边界条件
液相锂浓度	$∂ (ε e, n c e, n) ∂ t = ∂ ∂ x (D e, n e f f ∂ c e, n ∂ x)$	$∂ c e, n ∂ x x = 0 = 0, ∂ c e, p ∂ x x = l = 0$
固相颗粒锂浓度	$∂ c s ∂ t = D s r 2 ∂ ∂ x (r 2 ∂ c s ∂ r)$	$∂ c s ∂ r r = 0 = 0, D s ∂ c s ∂ r r = R s = - j L i α s F$
液相电势	$∂ ∂ x (K e e f f ∂ ϕ e ∂ x) + ∂ ∂ x (K D e f f ∂ l n c e ∂ x) + j L i = 0$	$∂ ϕ e ∂ x x = 0 = 0$
固相电势	$∂ ∂ x (σ e f f ∂ ϕ s ∂ x) = j L i$	$- σ e f f ∂ ϕ s ∂ x x = 0 = I A$

Fig. 4 Structure of the SP model

Fig. 5 Fractional-order impedance circuit structure diagram

Fig. 6 Schematic diagram of the ANN

Fig. 7 Schematic diagram of the SVM model

Fig. 8 Overview of multi-scale design simulations of lithium-ion battery

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