An overview on the usage of some model reduction approaches for simulations of Li-ion transport in batteries

In this work, some model reduction approaches for performing simulations with a pseudo-2D model of Li-ion battery are presented. A full pseudo-2D model of processes in Li-ion batteries is presented following [3], and three methods to reduce the order of the full model are considered. These are: i) directly reduce the model order using proper orthogonal decomposition, ii) using fractional time step discretization in order to solve the equations in decoupled way, and iii) reformulation approaches for the diffusion in the solid phase. Combinations of above methods are also considered. Results from numerical simulations are presented, and the efficiency and the accuracy of the model reduction approaches are discussed.

[1]  Ralph E. White,et al.  Comparison of approximate solution methods for the solid phase diffusion equation in a porous electrode model , 2007 .

[2]  Jochen Zausch,et al.  Thermodynamic consistent transport theory of Li-ion batteries , 2011 .

[3]  Oliver Wirjadi,et al.  Survey of 3d image segmentation methods , 2007 .

[4]  Horst W. Hamacher,et al.  Inverse Radiation Therapy Planning: A Multiple Objective Optimisation Approach , 1999 .

[5]  M. Junk.  On the Construction of Discrete Equilibrium Distributions for Kinetic Schemes , 1999 .

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

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

[8]  Ann Marie Sastry,et al.  Mesoscale Modeling of a Li-Ion Polymer Cell , 2007 .

[9]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

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

[11]  Ralph E. White,et al.  Effect of Porosity on the Capacity Fade of a Lithium-Ion Battery Theory , 2004 .

[12]  K. Kunisch,et al.  Control of the Burgers Equation by a Reduced-Order Approach Using Proper Orthogonal Decomposition , 1999 .

[13]  Paul V. Braun,et al.  Three-dimensional bicontinuous ultrafast-charge and -discharge bulk battery electrodes. , 2011, Nature nanotechnology.

[14]  J. Orlik.  Homogenization for viscoelasticity of the integral type with aging and shrinkage , 1998 .

[15]  D. Kehrwald.  Parallel lattice Boltzmann simulation of complex flows , 2004 .

[16]  A. Becker.  A Review on Image Distortion Measures , 2000 .

[17]  H. Trinkaus,et al.  knowCube for MCDM – Visual and Interactive Support for Multicriteria Decision Making , 2003 .

[18]  Frank-Thomas Lentes,et al.  Three-dimensional radiative heat transfer in glass cooling processes , 1998 .

[19]  J. Orlik.  Homogenization for contact problems with periodically rough surfaces , 2004 .

[20]  Ann Marie Sastry,et al.  Micro-Scale Modeling of Li-Ion Batteries: Parameterization and Validation , 2012 .

[21]  Th. Hanne,et al.  Applying multiobjective evolutionary algorithms in industrial projects , 2006 .

[22]  M. Krekel.  Optimal Portfolios With A Loan Dependent Credit Spread , 2002 .

[23]  S. Kruse,et al.  On the Pricing of Forward Starting Options under Stochastic Volatility , 2003 .

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

[25]  H. Neunzert,et al.  Mathematics as a Technology: Challenges for the next 10 Years , 2004 .

[27]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[28]  Anton Winterfeld,et al.  Application of general semi-infinite programming to lapidary cutting problems , 2008, Eur. J. Oper. Res..

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

[30]  Chao-Yang Wang,et al.  Computational battery dynamics (CBD)—electrochemical/thermal coupled modeling and multi-scale modeling , 2002 .

[31]  Chaoyang Wang,et al.  Analysis of Electrochemical and Thermal Behavior of Li-Ion Cells , 2003 .

[32]  A. Unterreiter,et al.  Numerical evidance for the non-existing of solutions of the equations desribing rotational fiber spinning , 2007 .

[33]  Jochen Zausch,et al.  Modeling of Species and Charge Transport in Li-Ion Batteries Based on Non-equilibrium Thermodynamics , 2010, NMA.

[34]  A. Zemitis.  On interaction of a liquid film with an obstacle , 2002 .

[35]  H. Neunzert.  »Denn nichts ist für den Menschen als Menschen etwas wert, was er nicht mit Leidenschaft tun kann« , 2001 .

[36]  T. Hanne.  Eine Übersicht zum Scheduling von Baustellen , 2005 .

[37]  Shengyi Liu.  An analytical solution to Li/Li+ insertion into a porous electrode , 2006 .

[38]  Marc Doyle,et al.  Computer Simulations of a Lithium-Ion Polymer Battery and Implications for Higher Capacity Next-Generation Battery Designs , 2003 .

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

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

[41]  N. Ettrich.  Generation of surface elevation models for urban drainage simulation , 2005 .

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

[43]  H. Knaf.  Kernel Fisher discriminant functions – a concise and rigorous introduction , 2007 .

[44]  J. Linn.  On the Frame — Invariant Description of the Phase Space of the Folgar–Tucker Equation , 2004 .

[45]  V. Starikovicius,et al.  The multiphase flow and heat transfer in porous media , 2003 .

[46]  A. Naumovich.  On a Finite Volume Discretization of the Three-dimensional Biot Poroelasticity , 2006 .