Efficient Reformulation of Solid-Phase Diffusion in Physics-Based Lithium-ion Battery Models

Lithium-ion batteries are typically modeled using porous electrode theory coupled with various transport and reaction mechanisms with an appropriate discretization or approximation for the solid phase. One of the major difficulties in simulating Li-ion battery models is the need for simulating solid-phase diffusion in a second dimension r. It increases the complexity of the model as well as the computation time/cost to a great extent. Traditional approach toward solid-phase diffusion leads to more difficulties, with the use of emerging cathode materials, which involve phase changes and thus moving boundaries. A computationally efficient representation for solid-phase diffusion is discussed in this paper. The operating condition has a significant effect on the validity, accuracy, and efficiency of various approximations for the solid-phase diffusion. This paper compares approaches available today for solid-phase reformulation and provides two efficient forms for constant and varying diffusivities in the solid phase. This paper introduces an efficient method of an eigenfunction based Galerkin collocation and a mixed order finite difference method for approximating/representing solid-phase concentration variations within the active materials of porous electrodes for a pseudo-two-dimensional model for lithium-ion batteries.

[1]  Yonathan Bard,et al.  Nonlinear parameter estimation , 1974 .

[2]  T. Brubaker,et al.  Nonlinear Parameter Estimation , 1979 .

[3]  R. Huggins.  Solid State Ionics , 1989 .

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

[5]  M. Verbrugge,et al.  Lithium intercalation of carbon-fiber microelectrodes , 1996 .

[6]  J. Weidner,et al.  Proton Diffusion in Nickel Hydroxide: Prediction of Active Material Utilization , 1998 .

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

[8]  Linda R. Petzold,et al.  Consistent Initial Condition Calculation for Differential-Algebraic Systems , 1998, SIAM J. Sci. Comput..

[9]  C. Floudas,et al.  Global Optimization for the Parameter Estimation of Differential-Algebraic Systems , 2000 .

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

[11]  G. Botte,et al.  Modeling Lithium Intercalation in a Porous Carbon Electrode , 2001 .

[12]  B. Popov,et al.  Modeling lithium diffusion in nickel composite graphite , 2001 .

[13]  Ralph E. White,et al.  New Separation of Variables Method for Composite Electrodes With Galvanostatic Boundary Conditions , 2001 .

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

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

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

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

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

[19]  Venkat R. Subramanian,et al.  Towards "Real-Time" Simulation of Physics Based Lithium Ion Battery Models , 2007 .

[20]  Lorenz T. Biegler,et al.  Global Optimization of Highly Nonlinear Dynamic Systems , 2008 .

[21]  Ralph E. White,et al.  Thermodynamic model development for lithium intercalation electrodes , 2008 .

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

[23]  Richard D. Braatz,et al.  Parameter Estimation and Capacity Fade Analysis of Lithium-Ion Batteries Using First-Principles-Based Efficient Reformulated Models , 2009 .