Corresponding Author

Yong YANG(yyang@xmu.edu.cn)


Lithium ion battery has become an important and popular electrochemical device for energy storage.Suitable evaluation and understanding of electrochemical performance and state of charge play a key role in the applications of lithium ion batteries.Construction and utilization of engineering modeling for lithium ion batteries is an effective way to fulfill this target.In this paper,engineering models of lithium ion batteries based on electrochemical reaction,ionic diffusion and migration are introduced.The emphasis is placed on the development of engineering models by the introduction of side reaction,phase transition,stress and energy.The applications of engineering models in such simulations as charge-discharge,concentration distribution,current distribution,state of charge,stress and capacity fading are particularly presented.The mathematical treatments and simplifications are also briefly described.

Graphical Abstract


Lithium ion batteries, Battery reaction modeling, Cyclic capacity decay, Stress model

Publication Date


Online Available Date


Revised Date


Received Date



[1] Doyle M, Fuller T F, and Newman J. Modeling of Galvanostatic Charge and Discharge of the Lithium/Polymer/ Insertion Cell[J]. J. Electrochem. Soc. , 1993, 140(6): 1526-1533.

[2] Basu S and Worrell W L. Fast Ion Transport in Solids[C], Amsterdam: North-Holland Publishing Co. , 1979: 149-152.

[3] Sequeira C A C and A. Hopper. The Study of Lithium Electrode Reversibility Against (PEO)xLiF3CSO3 Polymeric Electrolytes[J]. Solid State Ionics, 1983, 9&10(2): 1131-1138.

[4] Fuller T F, Doyle M, and Newman J. Simulation and Optimazation of the Dual Lithium Ion Insertion Cell[J]. J. Electroehem. Soc. , 1994, 141(1): 1-10.

[5] R. Pollard and J. Newman. Transient Behaviour of Porous Electrodes with High Exchange Current Densities[J]. Electrochim. Acta, 1980, 25(3): 315-321.

[6] Feng Y(冯毅). 锂离子电池数值模型研究[D], 上海, 中国科学院研究生院, 2008.

[7] Albertus P, Christensen J, and Newman J. Experimentals on and Modeling of Positive Electrodes with Multiple Active Materials for Lithium-Ion Batteries[J]. J. Electrochem. Soc. , 2009, 156(7): 606-618.

[8] Ramadass P, White R E, and PoPov B N, et al. Development of First Principles Capacity Fade Model for Li-Ion Cells[J]. J. Electrochem. Soc. , 2004, 151(2): 196-203.

[9] Sikha G, Popov B N, and White R E. Effect of Porosity on the Capacity Fade of a Lithium-Ion battery[J]. J. Electrochem. Soc. , 2004, 151(7): 1104-1114.

[10] Darling R and Newman J. Modeling Side Reactions in Composite LiyMn2O4 Electrodes[J]. J. Electroehem. Soc. , 1998, 145(3): 990- 998.

[11] Reimers J N and Dahn J R. Electrochemical and In Situ X-Ray Diffraction Studies of Lithium Intercalation in LixCoO2[J]. J. Electrochem. Soc. , 1992, 139(8): 2091-2097.

[12] Zhang Q and White R E. Moving Boundary Model for the Discharge of a LiCoO2 Electrode[J]. J. Electrochem. Soc. , 2007, 154(6): 587- 596.

[13] Renganathan S, Sikha G, and White R E, et al. Theoratical Analysis of Stresses in a Lithium Ion Cell[J]. J. Electrochem. Soc. , 2010, 157(2): 155-163.

[14] Bernardi D, Pawlikowski E, and Newman J. A General Energy Balance for Battery Systems [J]. J. Electrochem. Soc. , 1985, 132(1): 5-12.

[15] Kumaresan K, Sikha G, and White R E. Thermal Model for a Li-Ion Cell[J]. J. Electrochem. Soc. , 2008, 155 (2): 164-171.

[16] Gu W B and Wang C Y. Thermal-Electrochemical Modeling of Battery Systems[J]. J. Electrochem. Soc. , 2000, 147(8): 2910-2022.

[17] Liu S Y. An Analytical Solution to Li/Li+ Insertion into a Porous Electrode[J]. Solid State Ionics, 2006, 177 (1&2): 53-58.

[18] Johan M R and Arof A K. Modeling of Electrochemical Intercalation of Lithium into a LiMn2O4 Electrode Using Green Function[J]. J. Power. Source, 2007, 170(2): 490-494.

[19] Doyle M and Newmen J. Analysis of Capacity-Rate Data for Lithium Batteries Using Simplified Models of the Discharge Process[J]. J. Appl. Electrochem. 1997, 27(7): 846-856 .

[20] Ali S A H, Hussin A, and Arof A K. Short- and Long-Time Solutions for Material Balance Equation in Lithium -ion Batteries by Laplace Transform[J]. J. Power source, 2002, 112(2): 435-442.

[21] Bhikkaji B and Soderstrom T. Reduced order models for diffusion systems[J]. Int. J. Control, 2001, 74(15): 1543-1557.

[22] Smith K A, Rahn C D, and Wang C Y. Model Order Reduction of 1D Diffusion Systems Via Residue Grouping [J]. J. Dyn. Syst. Control, 2008, 130(1): 1-8.

[23] Cai L and White R E. Reduction of Model Order Based on Proper Othogonal Decomposition for Lithium-Ion Battery Simulations[J]. J. Electrochem. Soc. , 2009, 156(3): 154-161.



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.