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The pseudo-two-dimensional (P2D) model is the most widely used electrochemical model for lithium-ion batteries. Because of the complexity and the difficulty in using the complete P2D model, many simplified P2D models, such as the single particle model (SP model) and the parabolic profile approximation model (PP model), have been proposed. However, the using of the SP model can cause a large amount of precision to lose in its simplified process, while the PP model has a high complexity. In this paper, we propose a liquid phase simplification P2D (LSP2D) model. The using of the LSP2D model has a small precision loss and a relatively low complexity. The LSP2D model is based on the electrochemical average kinetics of the lithium ion battery. We first simplify the terminal voltage into an equation containing only the solid phase concentration c sand the liquid phase concentration c e. Then we use the partial differential equation to represent the solid phase concentration c sand the liquid phase concentration c e, and then obtain a final model. The simulation environment is based on COMSOL, and the simulation results show that when the discharge rate is 1C, the estimation accuracy and speed from the LSP2D model are similar to those from the SP model. But when the discharge rate is 3C, the estimation time from the LSP2D model is reduced by 99.73% compared with that from the P2D model, and the estimation accuracy is greatly improved compared with the estimation accuracy from the SP model.
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Keywords:
- electrochemical model/
- battery management system/
- liquid phase diffusion equation/
- parabolic approximation
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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 $ 
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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 DownLoad:
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Model Average error at
discharge rate 1C/VAverage error at
discharge rate 3C/VP2D 0 0 LSP2D 0.0056 0.014 SP 0.0052 0.142 DownLoad:
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[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20]
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