包含液相扩散方程简化的锂离子电池电化学模型
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摘要
锂离子电池的电化学模型对于电池特性分析和电池管理具有重要意义,但是准二维(P2D)模型复杂度太高,为了在保证模型精度的基础上尽量降低复杂度,本文提出了一种包含液相简化的P2D (LSP2D)模型,该模型首先基于电化学平均动力学将电池端电压化简成为仅耦合固相Li+浓度c_s和液相Li+浓度c_e的方程,然后进一步对表达c_s和c_e演化规律的偏微分方程进行抛物线近似化简,使得最终的模型由多项式组成.COMSOL仿真表明在放电倍率为1C时该模型与单粒子(SP)模型的估算精度和速度相当,但在放电倍率为3C时,该模型的估算时间比P2D模型减少了99.73%,与SP模型相当,估算精度相比SP模型有大幅度提升.
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_s and the liquid phase concentration c_e. Then we use the partial differential equation to represent the solid phase concentration c_s and 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 1 C, the estimation accuracy and speed from the LSP2D model are similar to those from the SP model. But when the discharge rate is 3 C, 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.
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_s and the liquid phase concentration c_e. Then we use the partial differential equation to represent the solid phase concentration c_s and 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 1 C, the estimation accuracy and speed from the LSP2D model are similar to those from the SP model. But when the discharge rate is 3 C, 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.
引文
[1] Zou C F, Manzie C, Nesic D 2016 IEEE Trans. Control Syst.Technol. 24 1594
[2] Seaman A, Dao T S, McPhee J 2014 J. Power Sources 256 410
[3] Tang S X, Solorio L C, Wang Y, Krstic M 2017 Automatica83 206
[4] Pang H 2018 Acta Phys. Sin.67 058201(in Chinese)[庞辉2018物理学报67 058201]
[5] Hu L B, Choi J W, Yang Y, Jeong S, Mantia F L, Cui L F,Cui Y 2009 Proc. Natl. Acad. Sci. 106 51
[6] Lindgren J, Asghar I, Lund P D 2016 Int. J. Energy Res. 401576
[7] Bizeray A M, Kim J H, Duncan S R, Howey D A 2018 IEEE Trans. Control Syst. Technol.
[8] Doyle M, Fuller T F, Newman J 1993 J. Electrochem. Soc.140 1526
[9] Li J, Lotfi N, Landers R G, Park J 2017 J. Electrochem. Soc.164 A874
[10] Tanim T R, Rahn C D, Wang C Y 2015 J. Dyn. Syst. Meas.Contr. 137 011005
[11] Subramanian V R, Diwakar V D, Tapriyal D 2005 J.Electrochem. Soc. 152 A2002
[12] Cheng Y, Li J, Jia M, Tang Y W, Du S L, Ai L H, Yin B H,Ai L 2015 Acta Phys.Sin. 64 210202(in Chinese)[程昀,李劼,贾明,汤依伟,杜双龙,艾立华,殷宝华,艾亮2015物理学报64 210202]
[13] Santhanagopalan S, Guo Q Z, Ramadass P, White R E 2006J. Power Sources 156 620
[14] Farag M, Fleckenstein M, Habibi S 2017 J. Power Sources342 351
[15] Zheng L F, Zhang L, Zhu J G, Wang G X, Jiang J C 2016Appl. Energy 180 424
[16] Pang H 2017 Acta Phys. Sin. 66 238801(in Chinese)[庞辉2017物理学报66 238801]
[17] Prada E,Di-Domenico D,Creff Y, Bernard J, SauvantMoynot V, Huet F 2012 J. Electrochem. Soc. 159 A1508
[18] Han X B, Ouyang M G, Lu L G, Li J Q 2015 J. Power Sources 278 814
[19] Dawson-Elli N, Lee S B, Pathak M 2018 J. Electrochem. Soc.165 Al
[20] Ramadass P, Haran B, Gomadam P M, 2004 J. Electrochem.Soc. 151 A196
[2] Seaman A, Dao T S, McPhee J 2014 J. Power Sources 256 410
[3] Tang S X, Solorio L C, Wang Y, Krstic M 2017 Automatica83 206
[4] Pang H 2018 Acta Phys. Sin.67 058201(in Chinese)[庞辉2018物理学报67 058201]
[5] Hu L B, Choi J W, Yang Y, Jeong S, Mantia F L, Cui L F,Cui Y 2009 Proc. Natl. Acad. Sci. 106 51
[6] Lindgren J, Asghar I, Lund P D 2016 Int. J. Energy Res. 401576
[7] Bizeray A M, Kim J H, Duncan S R, Howey D A 2018 IEEE Trans. Control Syst. Technol.
[8] Doyle M, Fuller T F, Newman J 1993 J. Electrochem. Soc.140 1526
[9] Li J, Lotfi N, Landers R G, Park J 2017 J. Electrochem. Soc.164 A874
[10] Tanim T R, Rahn C D, Wang C Y 2015 J. Dyn. Syst. Meas.Contr. 137 011005
[11] Subramanian V R, Diwakar V D, Tapriyal D 2005 J.Electrochem. Soc. 152 A2002
[12] Cheng Y, Li J, Jia M, Tang Y W, Du S L, Ai L H, Yin B H,Ai L 2015 Acta Phys.Sin. 64 210202(in Chinese)[程昀,李劼,贾明,汤依伟,杜双龙,艾立华,殷宝华,艾亮2015物理学报64 210202]
[13] Santhanagopalan S, Guo Q Z, Ramadass P, White R E 2006J. Power Sources 156 620
[14] Farag M, Fleckenstein M, Habibi S 2017 J. Power Sources342 351
[15] Zheng L F, Zhang L, Zhu J G, Wang G X, Jiang J C 2016Appl. Energy 180 424
[16] Pang H 2017 Acta Phys. Sin. 66 238801(in Chinese)[庞辉2017物理学报66 238801]
[17] Prada E,Di-Domenico D,Creff Y, Bernard J, SauvantMoynot V, Huet F 2012 J. Electrochem. Soc. 159 A1508
[18] Han X B, Ouyang M G, Lu L G, Li J Q 2015 J. Power Sources 278 814
[19] Dawson-Elli N, Lee S B, Pathak M 2018 J. Electrochem. Soc.165 Al
[20] Ramadass P, Haran B, Gomadam P M, 2004 J. Electrochem.Soc. 151 A196