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It is very important to accurately model Li-ion battery and estimate the corresponding parameters that can be used for battery management system (BMS) of electric vehicles (EVs). However, the rigorous pseudo-two-dimensional (P2D) model of Li-ion battery is too complicated to be adopted directly to online state estimation and real-time control of stage-of-charge in BMS applications. To solve this problem, in this study we present a simplified pseudo-two-dimensional (SP2D) model by the electrolyte dynamic behaviors of electrochemical battery model, which is based on the porous electrode theory and concentration theory. First, the classical concentration equations of Li-ion battery P2D model are investigated and introduced, based on which, the approximated method of describing the concentration distributions of Li-ion battery described by the SP2D model is given by ignoring the variation of Li-ion wall flux density across the electrode thickness; then, the Li-ion battery terminal output voltage, the solid phase concentration and potential diffusion, the electrolyte concentration and potential distribution can be calculated based on the averaged electrochemical dynamic behaviors of Li-ion battery. Moreover, by employing some concentration assumptions:1) the solid-phase lithium concentration in each electrode is constant in spatial coordinate x, and uniform in time; 2) the exchange current density can be approximated by its averaged value; 3) the total amount of lithium in the electrolyte and in the solid phase is conserved; with the averaged dynamics of SP2D model, the simplified calculation expression for Li-ion battery terminal voltage is derived. Finally, a case study of Sony NMC 18650 Li-ion battery is conducted, and the simulated comparisons among the battery voltages at different-C-rate galvanostatic discharges, and the related electrolyte concentration of Li-ion at 1 C-rate are conducted. Moreover, the proposed SP2D model is used to predict the battery voltage and electrolyte concentration distribution with respect to the P2D model under hybrid pulse power characterization condition and urban dynamometer driving schedule condition, and the corresponding test data are used to verify the accuracy of the SP2D model. It is observed that the simulated data of SP2D model are in good accord with those of the P2D model and test curve under these two operation conditions, which further validates the effectiveness of the proposed electrochemical model of Li-ion battery. Accordingly, the proposed SP2D model in this paper can be used to estimate real-time state information in advanced battery management system applications, and can improve the calculation efficiency significantly and still hold higher accuracy simultaneously than that from the P2D model.
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Keywords:
- electric vehicles /
- Li-ion batteries /
- electrochemistry /
- model reduction
[1] Wang M, Li J J, Wu H, Wan C R, He X M (in Chinese)[王铭, 李建军, 吴扞, 万春荣, 何向明 2011 电源技术 7 862]
[2] Cheng J, Li Z, 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 64 210202]
[3] Wang J P, Guo J G, Ding L 2009 Energy Convers. Manag. 50 318
[4] Fleischer C, Waag W, Bai Z, Sauer D U 2013 J. Power Sources 243 728
[5] Domenico D D, Stefanopoulou A, Fiengo G 2010 J. Dyn. Sys. Meas. Control 132 768
[6] Prada E, Domenico D D, Creff Y, Bernard J, SauvantMoynot V, Huet F 2012 J. Electrochem. Soc. 159 A1508
[7] Prada E, Domenico D D, Creff Y, Bernard J, Sauvant-Moynot V, Huet F 2013 J. Electrochem. Soc. 160 A616
[8] Chaturvedi N A, Klein R, Christensen J, Ahmed J, Kojic A 2010 Control Syst. IEEE 30 49
[9] Guo M, Sikha G, White R E 2011 J. Electrochem. Soc. 158 A122
[10] Huang L, Li J Y 2015 Acta Phys. Sin. 64 108202 (in Chinese)[黄亮, 李建远 2015 64 108202]
[11] Kemper P, Li S E, Kum D 2015 J. Power Sources 286 510
[12] Han X, Ouyang M, Lu L, Li J 2015 J. Power Sources 278 814
[13] Guo M, Jin X F, White R E 2017 J. Electrochem. Soc. 164 E3001
[14] Doyle M, Newman J 1995 Electrochim. Acta 40 2191
[15] Luo W L, Lu C, Wang L X, Zhang L Q 2013 J. Power Sources 241 295
[16] Joel C F, Saeid B, Jeffrey L S, Hosam K F 2011 J. Electrochem. Soc. 158 A93
[17] Venkat R S, Vijayasekaran B, Venkatasailanathan R, Mounika A 2009 J. Electrochem. Soc. 156 A260
[18] Cai L, White R E 2009 J. Electrochem. Soc. 156 A154
[19] Subramanian V R, Diwakar V D, Tapriyal D 2005 J. Electrochem. Soc. 152 A2002
[20] Subramanian V R, Boovaragavan V, Diwakar V D 2007 Electrochem. Solid-State Lett. 10 A255
[21] Santhanagopalan S, Guo Q Z, Ramadass P, White R E 2006 J. Power Sources 156 620
[22] Smith K A, Rahn C D, Wang C Y 2007 Energy Convers. Manag. 48 2565
[23] Di Domenico D, Stefanopoulou A, Fiengo G 2010 J. Dyn. Syst. Meas. Control 132 061302
[24] Prada E, Domenico D D, Creff Y, Bernard J, Sauvant-Moynot V, Huet F 2012 J. Electrochem. Soc. 159 A1508
[25] Rahimian S K, Rayman S, White R E 2013 J. Power Sources 224 180
[26] Moura S J, Chaturvedi N A, Krstic M E 2013 J. Dyn. Sys. Meas. Control 136 011015
[27] Moura S J, Argomedo F B, Klein R, Mirtabatabaei A, Krstic M 2017 IEEE Trans. Contr. Syst. T. 2 453
[28] Diwakar V D 2009 Ph. D. Dissertation (St. Louis:Washington University)
[29] Fan G, Pan K, Canova M, Marcicki J, Yang X G 2016 J. Electrochem. Soc. 163 A666
[30] Ma J H, Wang Z S, Su X R 2013 J. Power Supply 1 30 (in Chinese)[马进红, 王正仕, 苏秀蓉 2013 电源学报 1 30]
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[1] Wang M, Li J J, Wu H, Wan C R, He X M (in Chinese)[王铭, 李建军, 吴扞, 万春荣, 何向明 2011 电源技术 7 862]
[2] Cheng J, Li Z, 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 64 210202]
[3] Wang J P, Guo J G, Ding L 2009 Energy Convers. Manag. 50 318
[4] Fleischer C, Waag W, Bai Z, Sauer D U 2013 J. Power Sources 243 728
[5] Domenico D D, Stefanopoulou A, Fiengo G 2010 J. Dyn. Sys. Meas. Control 132 768
[6] Prada E, Domenico D D, Creff Y, Bernard J, SauvantMoynot V, Huet F 2012 J. Electrochem. Soc. 159 A1508
[7] Prada E, Domenico D D, Creff Y, Bernard J, Sauvant-Moynot V, Huet F 2013 J. Electrochem. Soc. 160 A616
[8] Chaturvedi N A, Klein R, Christensen J, Ahmed J, Kojic A 2010 Control Syst. IEEE 30 49
[9] Guo M, Sikha G, White R E 2011 J. Electrochem. Soc. 158 A122
[10] Huang L, Li J Y 2015 Acta Phys. Sin. 64 108202 (in Chinese)[黄亮, 李建远 2015 64 108202]
[11] Kemper P, Li S E, Kum D 2015 J. Power Sources 286 510
[12] Han X, Ouyang M, Lu L, Li J 2015 J. Power Sources 278 814
[13] Guo M, Jin X F, White R E 2017 J. Electrochem. Soc. 164 E3001
[14] Doyle M, Newman J 1995 Electrochim. Acta 40 2191
[15] Luo W L, Lu C, Wang L X, Zhang L Q 2013 J. Power Sources 241 295
[16] Joel C F, Saeid B, Jeffrey L S, Hosam K F 2011 J. Electrochem. Soc. 158 A93
[17] Venkat R S, Vijayasekaran B, Venkatasailanathan R, Mounika A 2009 J. Electrochem. Soc. 156 A260
[18] Cai L, White R E 2009 J. Electrochem. Soc. 156 A154
[19] Subramanian V R, Diwakar V D, Tapriyal D 2005 J. Electrochem. Soc. 152 A2002
[20] Subramanian V R, Boovaragavan V, Diwakar V D 2007 Electrochem. Solid-State Lett. 10 A255
[21] Santhanagopalan S, Guo Q Z, Ramadass P, White R E 2006 J. Power Sources 156 620
[22] Smith K A, Rahn C D, Wang C Y 2007 Energy Convers. Manag. 48 2565
[23] Di Domenico D, Stefanopoulou A, Fiengo G 2010 J. Dyn. Syst. Meas. Control 132 061302
[24] Prada E, Domenico D D, Creff Y, Bernard J, Sauvant-Moynot V, Huet F 2012 J. Electrochem. Soc. 159 A1508
[25] Rahimian S K, Rayman S, White R E 2013 J. Power Sources 224 180
[26] Moura S J, Chaturvedi N A, Krstic M E 2013 J. Dyn. Sys. Meas. Control 136 011015
[27] Moura S J, Argomedo F B, Klein R, Mirtabatabaei A, Krstic M 2017 IEEE Trans. Contr. Syst. T. 2 453
[28] Diwakar V D 2009 Ph. D. Dissertation (St. Louis:Washington University)
[29] Fan G, Pan K, Canova M, Marcicki J, Yang X G 2016 J. Electrochem. Soc. 163 A666
[30] Ma J H, Wang Z S, Su X R 2013 J. Power Supply 1 30 (in Chinese)[马进红, 王正仕, 苏秀蓉 2013 电源学报 1 30]
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