Efficient Simulation and Model Reformulation of Two-Dimensional Electrochemical Thermal Behavior of Lithium-Ion Batteries

Lithium-ionbatteries areanimportanttechnologytofacilitate efficient energystorageandenablea shiftfrompetroleumbasedenergy to more environmentally benign sources. Such systems can be utilized most efficiently if good understanding of performance can be achieved for a range of operating conditions. Mathematical models can be useful to predict battery behavior to allow for optimization ofdesignandcontrol.Ananalyticalsolutionisideallypreferredtosolvetheequationsofamathematicalmodel,asiteliminatestheerror that arises when using numerical techniques and is usually computationally cheap. An analytical solution provides insight into the behavior of the system and also explicitly shows the effects of different parameters on the behavior. However, most engineering models, including the majority of battery models, cannot be solved analytically due to non-linearities in the equations and state dependent transport and kinetic parameters. The numerical method used to solve the system of equations describing a battery operation can have a significant impact on the computational cost of the simulation. In this paper, a model reformulation of the porous electrode pseudo three dimensional (P3D) which significantly reduces the computational cost of lithium ion battery simulation, while maintaining high accuracy, is discussed. This reformulation enables the use of the P3D model into applications that would otherwise be too computationally expensive to justify its use, such as online control, optimization, and parameter estimation. Furthermore, the P3D model has proven to be robust enough to allow for the inclusion of additional physical phenomena as understanding improves. In this paper, the reformulated model is used to allow for more complicated physical phenomena to be considered for study, including thermal effects. © The Author(s) 2015. Published by ECS. This is an open access article distributed under the terms of the Creative Commons Attribution Non-Commercial No Derivatives 4.0 License (CC BY-NC-ND, http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial reuse, distribution, and reproduction in any medium, provided the original work is not changed in any way and is properly cited. For permission for commercial reuse, please email: oa@electrochem.org. [DOI: 10.1149/2.0341506jes] All rights reserved.

[1]  J. Newman,et al.  A mathematical model of stress generation and fracture in lithium manganese oxide , 2006 .

[2]  W. Schiesser.  The Numerical Method of Lines: Integration of Partial Differential Equations , 1991 .

[3]  Y. Inui,et al.  Simulation of temperature distribution in cylindrical and prismatic lithium ion secondary batteries , 2007 .

[4]  Jinchao Xu,et al.  Newton-Krylov-Multigrid Algorithms for Battery Simulation , 2002 .

[5]  W. Craig Carter,et al.  Microstructural Modeling and Design of Rechargeable Lithium-Ion Batteries , 2005 .

[6]  Ralph E. White,et al.  Reduction of Model Order Based on Proper Orthogonal Decomposition for Lithium-Ion Battery Simulations , 2009 .

[7]  V. Subramanian,et al.  Efficient Macro-Micro Scale Coupled Modeling of Batteries , 2005 .

[8]  Richard D. Braatz,et al.  Optimal control and state estimation of lithium-ion batteries using reformulated models , 2013, 2013 American Control Conference.

[9]  J. Newman,et al.  Porous‐electrode theory with battery applications , 1975 .

[10]  Xibo Yuan,et al.  IECON 2012 - 38th Annual Conference on IEEE Industrial Electronics Society , 2013 .

[11]  U. Kim,et al.  Modeling for the scale-up of a lithium-ion polymer battery , 2009 .

[12]  Ralph E. White,et al.  Development of First Principles Capacity Fade Model for Li-Ion Cells , 2004 .

[13]  J. Newman,et al.  Heat‐Generation Rate and General Energy Balance for Insertion Battery Systems , 1997 .

[14]  Ralph E. White,et al.  Single-Particle Model for a Lithium-Ion Cell: Thermal Behavior , 2011 .

[15]  T. Fuller,et al.  Temperature-dependent electrochemical heat generation in a commercial lithium-ion battery , 2014 .

[16]  Venkatasailanathan Ramadesigan,et al.  Coordinate Transformation, Orthogonal Collocation, Model Reformulation and Simulation of Electrochemical-Thermal Behavior of Lithium-Ion Battery Stacks , 2011 .

[17]  V. Subramanian,et al.  Efficient Reformulation of Solid-Phase Diffusion in Physics-Based Lithium-ion Battery Models , 2009, ECS Transactions.

[18]  Ralph E. White,et al.  Thermal Model for a Li-Ion Cell , 2008 .

[19]  Chaoyang Wang,et al.  Solid-state diffusion limitations on pulse operation of a lithium ion cell for hybrid electric vehicles , 2006 .

[20]  T. Fuller,et al.  A Critical Review of Thermal Issues in Lithium-Ion Batteries , 2011 .

[21]  Mo-Yuen Chow,et al.  Adaptive parameter identification and State-of-Charge estimation of lithium-ion batteries , 2012, IECON 2012 - 38th Annual Conference on IEEE Industrial Electronics Society.

[22]  Jeffrey A. Reimer,et al.  A {sup 7}Li NMR study of lithium insertion into lithium manganese oxide spinel , 1999 .

[23]  M. Safari,et al.  Multimodal Physics-Based Aging Model for Life Prediction of Li-Ion Batteries , 2009 .

[24]  Martin Z. Bazant,et al.  Efficient Conservative Numerical Schemes for 1D Nonlinear Spherical Diffusion Equations with Applications in Battery Modeling , 2013 .

[25]  Ralph E. White,et al.  A generalized cycle life model of rechargeable Li-ion batteries , 2006 .

[26]  Li Jia,et al.  Two-dimensional electrochemical–thermal coupled modeling of cylindrical LiFePO4 batteries , 2014 .

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

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

[29]  Philip T. Krein,et al.  Electrical battery model for use in dynamic electric vehicle simulations , 2008, 2008 IEEE Power Electronics Specialists Conference.

[30]  Ralph E. White,et al.  Mathematical modeling of the capacity fade of Li-ion cells , 2003 .

[31]  Paul Ivey,et al.  A multi scale multi-dimensional thermo electrochemical modelling of high capacity lithium-ion cells , 2014 .

[32]  J. Tarascon,et al.  Comparison of Modeling Predictions with Experimental Data from Plastic Lithium Ion Cells , 1996 .

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

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

[35]  James W. Evans,et al.  Electrochemical‐Thermal Model of Lithium Polymer Batteries , 2000 .

[36]  Ralph E. White,et al.  Theoretical Analysis of Stresses in a Lithium Ion Cell , 2010 .

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

[38]  Venkatasailanathan Ramadesigan,et al.  A perturbation approach for consistent initialization of index-1 explicit differential-algebraic equations arising from battery model simulations , 2011, Comput. Chem. Eng..

[39]  Ralph E. White,et al.  Mathematical modeling of secondary lithium batteries , 2000 .

[40]  Young-Il Jang,et al.  TEM Study of Electrochemical Cycling‐Induced Damage and Disorder in LiCoO2 Cathodes for Rechargeable Lithium Batteries , 1999 .

[41]  J. Villadsen,et al.  Solution of differential equation models by polynomial approximation , 1978 .

[42]  Venkatasailanathan Ramadesigan,et al.  Model-based simultaneous optimization of multiple design parameters for lithium-ion batteries for maximization of energy density , 2013 .

[43]  Ralph E. White,et al.  Comparison between Computer Simulations and Experimental Data for High-Rate Discharges of Plastic Lithium-Ion Batteries , 2000 .

[44]  J. Newman,et al.  Thermal Modeling of the Lithium/Polymer Battery .1. Discharge Behavior of a Single-Cell , 1995 .

[45]  Ralph E. White,et al.  Review of Models for Predicting the Cycling Performance of Lithium Ion Batteries , 2006 .

[46]  W. Shyy,et al.  Numerical Simulation of Intercalation-Induced Stress in Li-Ion Battery Electrode Particles , 2007 .

[47]  J. Newman,et al.  Thermal modeling of the lithium/polymer battery. II: Temperature profiles in a cell stack , 1995 .

[48]  Ui Seong Kim,et al.  Modeling the Thermal Behaviors of a Lithium-Ion Battery during Constant-Power Discharge and Charge Operations , 2013 .

[49]  Linda R. Petzold,et al.  Numerical solution of initial-value problems in differential-algebraic equations , 1996, Classics in applied mathematics.

[50]  J. Christensen,et al.  An Efficient Parallelizable 3D Thermoelectrochemical Model of a Li-Ion Cell , 2013 .

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

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

[53]  M. Doyle,et al.  Relaxation Phenomena in Lithium‐Ion‐Insertion Cells , 1994 .

[54]  V. Subramanian,et al.  Mathematical Model Reformulation for Lithium-Ion Battery Simulations: Galvanostatic Boundary Conditions , 2009 .

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

[56]  Paul W. C. Northrop,et al.  A robust false transient method of lines for elliptic partial differential equations , 2013 .

[57]  R. Stephenson.  A and V , 1962, The British journal of ophthalmology.

[58]  James W. Evans,et al.  Three‐Dimensional Thermal Modeling of Lithium‐Polymer Batteries under Galvanostatic Discharge and Dynamic Power Profile , 1994 .

[59]  John Newman,et al.  Stress generation and fracture in lithium insertion materials , 2005 .

[60]  J. Newman,et al.  Thermal Modeling of Porous Insertion Electrodes , 2003 .

[61]  J. Meyers,et al.  Three-Dimensional Modeling of Electrochemical Performance and Heat Generation of Spirally and Prismatically Wound Lithium-Ion Batteries , 2013 .

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

[63]  M. A. Akanbi,et al.  Numerical solution of initial value problems in differential - algebraic equations , 2005 .

[64]  Shung-Ik Lee,et al.  Modeling on lithium insertion of porous carbon electrodes , 2002 .

[65]  Ralph E. White,et al.  Modeling Lithium Intercalation of a Single Spinel Particle under Potentiodynamic Control , 2000 .

[66]  Richard D. Braatz,et al.  Parameter Estimation and Capacity Fade Analysis of Lithium-Ion Batteries Using Reformulated Models , 2011 .

[67]  Matthew B. Pinson,et al.  Theory of SEI Formation in Rechargeable Batteries: Capacity Fade, Accelerated Aging and Lifetime Prediction , 2012, 1210.3672.