Asymptotic Reduction of a Lithium-Ion Pouch Cell Model

A three-dimensional model of a single-layer lithium-ion pouch cell is presented which couples conventional porous electrode theory describing cell electrochemical behaviour with an energy balance describing cell thermal behaviour. Asymptotic analysis of the model is carried out by exploiting the small aspect ratio typical of pouch cell designs. The analysis reveals the scaling that results in a distinguished limit, and highlights the role played by the electrical conductivities of the current collectors. The resulting model comprises a collection of one-dimensional models for the through-cell electrochemical behaviour which are coupled via two-dimensional problems for the Ohmic and thermal behaviour in the planar current collectors. A further limit is identified which reduces the problem to a single volume-averaged through-cell model, greatly reducing the computational complexity. Numerical simulations are presented which illustrate and validate the asymptotic results.

[1]  Adrien M. Bizeray,et al.  State and parameter estimation of physics-based lithium-ion battery models , 2016 .

[2]  A. Jossen,et al.  A Computationally Efficient Multi-Scale Model for Lithium-Ion Cells , 2018 .

[3]  M. Verbrugge,et al.  Temperature and Current Distribution in Thin‐Film Batteries , 1999 .

[4]  K. Smith,et al.  Three dimensional thermal-, electrical-, and electrochemical-coupled model for cylindrical wound large format lithium-ion batteries , 2013 .

[5]  N. Ramakrishnan,et al.  Effect of the electrode particle shape in Li-ion battery on the mechanical degradation during charge–discharge cycling , 2012 .

[6]  M. Doyle,et al.  Simulation and Optimization of the Dual Lithium Ion Insertion Cell , 1994 .

[7]  Mohammed M. Farag,et al.  Combined electrochemical, heat generation, and thermal model for large prismatic lithium-ion batteries in real-time applications , 2017 .

[8]  Richard D. Braatz,et al.  Modeling and Simulation of Lithium-Ion Batteries from a Systems Engineering Perspective , 2010 .

[9]  Gregory J. Offer,et al.  Surface Cooling Causes Accelerated Degradation Compared to Tab Cooling for Lithium-Ion Pouch Cells , 2016 .

[10]  Martin Z. Bazant,et al.  Homogenization of the Poisson-Nernst-Planck equations for Ion Transport in Charged Porous Media , 2012, SIAM J. Appl. Math..

[11]  Chaoyang Wang,et al.  Thermal‐Electrochemical Modeling of Battery Systems , 2000 .

[12]  J. Newman,et al.  Theoretical Analysis of Current Distribution in Porous Electrodes , 1962 .

[13]  Chang-wan Kim,et al.  The Effect of Tab Attachment Positions and Cell Aspect Ratio on Temperature Difference in Large-Format LIBs Using Design of Experiments , 2020, Energies.

[14]  Chaoyang Wang,et al.  Micro‐Macroscopic Coupled Modeling of Batteries and Fuel Cells I. Model Development , 1998 .

[15]  Scott G. Marquis,et al.  Python Battery Mathematical Modelling (PyBaMM) , 2021 .

[16]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

[17]  B. Scrosati,et al.  Lithium batteries: Status, prospects and future , 2010 .

[18]  U. Kim,et al.  Effect of electrode configuration on the thermal behavior of a lithium-polymer battery , 2008 .

[19]  Venkat R. Subramanian,et al.  Efficient Simulation and Model Reformulation of Two-Dimensional Electrochemical Thermal Behavior of Lithium-Ion Batteries , 2015 .

[20]  R. Ranom,et al.  Generalised single particle models for high-rate operation of graded lithium-ion electrodes: Systematic derivation and validation , 2019, Electrochimica Acta.

[21]  Simon V. Erhard,et al.  Multi-Dimensional Modeling of the Influence of Cell Design on Temperature, Displacement and Stress Inhomogeneity in Large-Format Lithium-Ion Cells , 2016 .

[22]  M. Armand,et al.  Building better batteries , 2008, Nature.

[23]  Valentin Sulzer.  Mathematical modelling of lead-acid batteries , 2019 .

[24]  Scott G. Marquis,et al.  A Suite of Reduced-Order Models of a Single-Layer Lithium-Ion Pouch Cell , 2020, Journal of The Electrochemical Society.

[25]  John Newman,et al.  A General Energy Balance for Battery Systems , 1984 .

[26]  Shriram Santhanagopalan,et al.  Multi-Domain Modeling of Lithium-Ion Batteries Encompassing Multi-Physics in Varied Length Scales , 2011 .

[27]  J. C. Jaeger,et al.  Conduction of Heat in Solids , 1952 .

[28]  Frank P. Incropera,et al.  Fundamentals of Heat and Mass Transfer , 1981 .

[29]  Richard Van Noorden.  The rechargeable revolution: A better battery , 2014, Nature.

[30]  Andreas Jossen,et al.  Simulation and Measurement of the Current Density Distribution in Lithium-Ion Batteries by a Multi-Tab Cell Approach , 2017 .

[31]  Giles Richardson,et al.  Multiscale modelling and analysis of lithium-ion battery charge and discharge , 2012 .

[32]  Rachel E. Gerver,et al.  Three-Dimensional Modeling of Electrochemical Performance and Heat Generation of Lithium-Ion Batteries in Tabbed Planar Configurations , 2011 .

[33]  Scott G. Marquis,et al.  An Asymptotic Derivation of a Single Particle Model with Electrolyte , 2019, Journal of The Electrochemical Society.

[34]  P. Bruce,et al.  Degradation diagnostics for lithium ion cells , 2017 .

[35]  Gregory L. Plett.  Battery Management Systems , 2015 .

[36]  James Marco,et al.  A systematic approach for electrochemical-thermal modelling of a large format lithium-ion battery for electric vehicle application , 2018 .

[37]  M. Doyle,et al.  Modeling of Galvanostatic Charge and Discharge of the Lithium/Polymer/Insertion Cell , 1993 .

[38]  Ralph E. White,et al.  Mathematical modeling of lithium-ion and nickel battery systems , 2002 .