Electrochemical model of lithium ion battery with simplified liquid phase diffusion equation

Zheng-Yu Liu; Kun Yang; Zi-Hong Wei; Li-Yang Yao

doi:10.7498/aps.68.20190159

Journals >Acta Physica Sinica >Volume 68 >Issue 9 >Page 098801-1 > Article

Acta Physica Sinica
Vol. 68, Issue 9, 098801-1 (2019)

Electrochemical model of lithium ion battery with simplified liquid phase diffusion equation

Zheng-Yu Liu^1、2, Kun Yang^1、*, Zi-Hong Wei¹, and Li-Yang Yao¹

Author Affiliations

¹School of Mechanical Engineering, Hefei University of Technology, Hefei 230009, China

²Key Laboratory of Industrial Safety and Emergency Technology of Anhui Province, Hefei 230009 China

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DOI: 10.7498/aps.68.20190159 Cite this Article

Zheng-Yu Liu, Kun Yang, Zi-Hong Wei, Li-Yang Yao. Electrochemical model of lithium ion battery with simplified liquid phase diffusion equation[J]. Acta Physica Sinica, 2019, 68(9): 098801-1 Copy Citation Text

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Fig. 1. Lithium ion battery schematic.锂离子电池示意图

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Fig. 2. Simplified schematic diagram of the LSP2D model.LSP2D模型简化示意图

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Fig. 3. Comparison of liquid phase Li⁺ concentration obtained by SP, LSP2D and P2D model at 1C and 3C discharge rates. 1C和3C放电率下, SP, LSP2D和P2D模型得到的放电末期液相Li⁺浓度比较

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Fig. 4. Discharge curves of three models at 1C and 3C discharge rates.三种模型在放电率为1C和3C时的放电曲线

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${a_1}$	${b_1}$	${c_1}$	${a_2}$	${b_2}$	${a_3}$	${b_3}$	${c_3}$
$\displaystyle\frac{1}{8} + \alpha \tau $	$\displaystyle\frac{{15}}{4}$	$ - \displaystyle\frac{{15}}{8}$	$1$	0	1	$\displaystyle\frac{{30}}{7}\beta \tau $	$ - \displaystyle\frac{{15}}{7}\beta \tau $

Table 1.

Values of parameters.

各参数的值

Symbol	Anode	Cathode	Separator
$\sigma$/S·m^–1	100	100
${\varepsilon _{\rm s}}$	0.49	0.59
${\varepsilon _{\rm e}}$	0.485	0.365	0.724
Brug	4.0	4.0	4.0
${c_{{\rm{e,0}}}}$/mol·m^–3	1000	1000	1000
${c_{{\rm{s,0}}}}$/mol·m^–3	916.65	48977.25
${c_{{\rm{s,max}}}}$/mol·m^–3	30555	51555
A/m²	$6.03 \!\times\! {10^{ - 4}}$	$5.31 \!\times\! {10^{ - 4}}$
${D_{\rm{e}}}$/m²·s^–1	$7.5 \!\times\! {10^{ - 10}}$	$7.5 \!\times\! {10^{ - 10}}$	$7.5 \!\times\! {10^{ - 10}}$
${D_{\rm{s}}}$/m²·s^–1	$3.9 \!\times\! {10^{ - 14}}$	$1.0 \!\times\! {10^{ - 14}}$
k/mol·(mol·m^–3)^–1.5	$4.854 \!\times\! {10^{ - 6}}$	$2.252 \!\times\! {10^{ - 6}}$
${R_{\rm{s}}}$/m	$2 \!\times\! {10^{ - 6}}$	$2 \!\times\! {10^{ - 6}}$
x/m	$8.8 \!\times\! {10^{ - 5}}$	$8.0 \!\times\! {10^{ - 5}}$	$8.0 \!\times\! {10^{ - 5}}$
${R_{{\rm{SEI}}}}/\Omega$·m^–2	0.01
I/A·m^–2	20
$\alpha $	0.5	0.5
F/C·mol	96487
R/J·mol·K^–1	8.314
T/K	298.15

Table 2. Parameters lists of Li-ion battery.

Model	Average error at discharge rate 1C/V	Average error at discharge rate 3C/V
P2D	0	0
LSP2D	0.0056	0.014
SP	0.0052	0.142

Table 3. Average error of the battery terminal voltage is estimated by three models when the discharge rate is 1C and 3C.

Model	Time for 50 cycles/s
P2D	7860
LSP2D	21
SP	12

Table 4. Comparison of the estimated speeds of the three models.

Zheng-Yu Liu, Kun Yang, Zi-Hong Wei, Li-Yang Yao. Electrochemical model of lithium ion battery with simplified liquid phase diffusion equation[J]. Acta Physica Sinica, 2019, 68(9): 098801-1

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