锂离子电池已成为重要的电化学能源储存设备，其性能的评估与监测对实际应用有着重要的指导意义。锂离子电池电化学反应模型是评估电池性能的有效手段。本文介绍了文献中依据电化学反应、离子扩散及电迁移过程建立的原始物理模型，通过引入电极副反应，两相反应，应力和能量等因素，进一步发展的锂离子电池电化学反应模型。较详细的说明了这些模型的电池充放电过程、锂离子浓度分布、电流分布、电极材料荷电状态、应力及循环容量衰减等模拟在电池实际运行中的应用。简要的介绍了物理模型的数学处理和简化，比较了各种处理方法的优缺点。
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.
[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.
