Modeling and simulation experiments of temperature-coupled mechanism model for lithium-ion battery

doi:10.19799/j.cnki.2095-4239.2020.0198

Abstract

Abstract:

The mechanism model of a lithium-ion battery has high precision and can reveal the internal information that cannot be described in an experiment. Moreover, this model is greatly significant to aging research, fault diagnosis, and design of a battery management system. This study proposes a simplified method coupled with temperature to tackle the high computational complexity and temperature-coupled influence of the battery model. The proposed model is based on the single particle (SP) model. First, a two-parameter parabolic profile method is used to simplify the solid diffusion equations. Parabolic profile approximation and the finite difference method are then used to solve the liquid diffusion. Second, a whole model, called the simplified pseudo two-dimensional (SP2D) model, is built considering Ohm's law and solid electrolyte interface film polarization. The average temperature of the battery is calculated through the lumped model simplification method or the central difference method. The thermal model is related to the heat production calculated by the mechanism model. The electrochemical parameters in the mechanism model are influenced by the temperature from the thermal model. The mechanism and thermal models are finally coupled. The results show that when current is constant, the simplified coupled model is more accurate than the SP and SP2D models in terms of the battery temperature and battery voltage, respectively. The model also shows a good performance in complex conditions. The root mean square error of the battery terminal voltage and the temperature are less than 0.041 and 0.66, respectively, for the constant current test. In addition, the absolute percentage error is less than 1% and 0.15% for the urban dynamometer driving schedule test.

Key words: lithium-ion battery, electrochemical simplification, temperature-coupled, simulation experiment, dynamic parameters

CLC Number:

TM 912.9

Xuhao LI, Yu ZHOU, Bingchuan WANG. Modeling and simulation experiments of temperature-coupled mechanism model for lithium-ion battery[J]. Energy Storage Science and Technology, 2020, 9(6): 1991-1999.

Figures/Tables 15

Fig.1

Table 1

Mechanism and governing equations of P2D model"

方程原理	控制方程
固相扩散	$? c s ? t = D s r 2 ? ? r r 2 ? c s ? r = D s ? 2 c s ? r 2 + 2 r ? c s ? r$ (1)
液相扩散	$ε e ? c e ? t = ? ? x D e e f f ? c e ? x + 1 - ?? t + F j L i$ (2)
固相电势	$? ? x σ s e f f ? φ s ? x = j L i$ (3)
液相电势	$? ? x κ e e f f ? φ e ? x = - ?? j L i - ?? ? ? x 2 R T κ e e f f F t + - ?? 1 ? l n c e ? l n x$ (4)
Butler-Volmer方程	$j L i = 2 a s i 0 e x p α a F η R T - ?? e x p - ? α c F η R T$ (5)
法拉第定律	$? j i L i ? x = ± a s F J$ (6)
端电压	$V t = φ s L, t - ? φ s 0, t$ (7)

Table 1

Table 2

Table 3

Dynamic parameters used in electrochemical model"

参数	表达式
D_s,ca	$1.18 × 10 - 12 1 + y 1.6 e x p - ?? 35000 R 1 T - ?? 1 298.1 . 5$ (8)
D_s,an	$3.9 × 10 - 14 e x p - ?? 35000 R 1 T - ?? 1 298.1 . 5$ (9)
k_s,ca	$1.4 × 10 - 12 e x p - ?? y e x p - ?? 30000 R 1 T - ?? 1 298.1 . 5$ (10)
k_s,an	$3 × 10 - 11 e x p - ?? 20000 R 1 T - ?? 1 298.1 . 5$ (11)
U_ca,ref	3.4323-0.4828exp[-80.2493(1-y)^1.3198]-3.2474×10^-6exp[20.2645(1-y)^3.8003]+3.2482×10^-6exp[20.2646(1-y)^3.7995](12)
U_an,ref	$0.6379 + 0.5416 e x p - ?? 305.5309 x + 0.044 t a n h - ?? x - ?? 0.1958 0.1088 - ?? 0.1978 t a n h x - ?? 1.0571 0.0854 - ?? 0.6875 t a n h x + 0.0117 0.0529 - ?? 0.0175 t a n h x - ?? 0.5692 0.0875$ (13)
dU_ca/dT	-0.35376y⁸+1.3902y⁷-2.2585y⁶+1.9635y⁵-0.98716y⁴+0.28857y³-0.046272y²+0.0032158y-1.9186×10^-5 (14)
dU_an/dT	$344.1347148 × e x p - ?? 32.9633287 x + 8.316711484 1 + 749.0756003 e x p - ?? 34.79099646 x + 8.887143624 - ?? 0.8520278805 x + 0.362299229 x 2 + 0.2698001697$ (15)

Table 3

Table 4

Parameters used in thermal model"

参数	平均值
$p ˉ$ /kg·m^-3	1996.7
$c ˉ$ _p/J·(kg·K)^-1	938.67
k_T/W·(m·K)^-1	34.251

Table 4

Fig.2

Fig.3

Fig.4

Fig.5

Table 5

Fig.6

Table 6

Table 7

Fig.7

Fig.8

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参数	负极	正极	隔膜	电解质
ε_s	0.55	0.43
ε_e	0.33	0.332	0.54
L_i/μm	34	70	25
R_i/μm	0.0365	3.5
c_e,init/mol·m^-3				1200
c_s,max/mol·m^-3	31370	22806
c_s,init/mol·m^-3	26978.2	501.732
α_a,c	0.5	0.5
σ_s/S·m^-1	100	0.5
κ_e/S·m^-1				0.92
R_f/Ω	0.005	0.001
T_init/K	293.15	293.15	293.15	293.15
t₀				0.363
D_e/m²·s ^-1				7.5×10^-11

模型	放电倍率
模型	1 C	2 C	4 C
SP2D模型	0.062	0.0683	0.066
TCSP2D模型	0.0405	0.0333	0.0315

模型	温度/℃
模型	10	15	20
SP模型	1.5972	1.3906	1.0796
TCSP2D模型	0.6573	0.5539	0.4499

模型	运算时间/s
SP模型	0.2740
TCSP2D模型	0.6400
P2D模型	329

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