A modified pseudo-steady-state analytical expression for battery modeling

K. Chayambuka, G. Mulder, D.L. Danilov, P.H.L. Notten (Corresponding author)

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

The solid-state spherical diffusion equation with flux boundary conditions is a standard problem in lithium-ion battery simulations. If finite difference schemes are applied, many nodes across a discretized battery electrode become necessary, in order to reach a good approximation of solution. Such a grid-based approach can be appropriately avoided by implementing analytical methods which reduce the computational load. The pseudo-steady-state (PSS)method is an exact analytical solution method, which provides accurate solid-state concentrations at all current densities. The popularization of the PSS method, in the existing form of expression, is however constrained by a solution convergence problem. In this short communication, a modified PSS (MPSS)expression is presented which provides uniformly convergent solutions at all times. To minimize computational runtime, a fast MPPS (FMPPS)expression is further developed, which is shown to be faster by approximately three orders of magnitude and has a constant time complexity. Using the FMPSS method, uniformly convergent exact solutions are obtained for the solid-state diffusion problem in spherical active particles.

LanguageEnglish
Pages49-53
Number of pages5
JournalSolid State Communications
Volume296
DOIs
StatePublished - 1 Jul 2019

Fingerprint

electric batteries
solid state
time constant
Current density
lithium
communication
grids
Boundary conditions
boundary conditions
current density
Fluxes
Electrodes
electrodes
Communication
approximation
Battery management systems
ions
simulation
mangion-purified polysaccharide (Candida albicans)
Lithium-ion batteries

Keywords

  • Analytical methods
  • Porous electrodes
  • Pseudo-steady state
  • Spherical diffusion

Cite this

@article{6df667bacc364f7e8d301bcaea0cbb83,
title = "A modified pseudo-steady-state analytical expression for battery modeling",
abstract = "The solid-state spherical diffusion equation with flux boundary conditions is a standard problem in lithium-ion battery simulations. If finite difference schemes are applied, many nodes across a discretized battery electrode become necessary, in order to reach a good approximation of solution. Such a grid-based approach can be appropriately avoided by implementing analytical methods which reduce the computational load. The pseudo-steady-state (PSS)method is an exact analytical solution method, which provides accurate solid-state concentrations at all current densities. The popularization of the PSS method, in the existing form of expression, is however constrained by a solution convergence problem. In this short communication, a modified PSS (MPSS)expression is presented which provides uniformly convergent solutions at all times. To minimize computational runtime, a fast MPPS (FMPPS)expression is further developed, which is shown to be faster by approximately three orders of magnitude and has a constant time complexity. Using the FMPSS method, uniformly convergent exact solutions are obtained for the solid-state diffusion problem in spherical active particles.",
keywords = "Analytical methods, Porous electrodes, Pseudo-steady state, Spherical diffusion",
author = "K. Chayambuka and G. Mulder and D.L. Danilov and P.H.L. Notten",
year = "2019",
month = "7",
day = "1",
doi = "10.1016/j.ssc.2019.04.011",
language = "English",
volume = "296",
pages = "49--53",
journal = "Solid State Communications",
issn = "0038-1098",
publisher = "Elsevier",

}

A modified pseudo-steady-state analytical expression for battery modeling. / Chayambuka, K.; Mulder, G.; Danilov, D.L.; Notten, P.H.L. (Corresponding author).

In: Solid State Communications, Vol. 296, 01.07.2019, p. 49-53.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - A modified pseudo-steady-state analytical expression for battery modeling

AU - Chayambuka,K.

AU - Mulder,G.

AU - Danilov,D.L.

AU - Notten,P.H.L.

PY - 2019/7/1

Y1 - 2019/7/1

N2 - The solid-state spherical diffusion equation with flux boundary conditions is a standard problem in lithium-ion battery simulations. If finite difference schemes are applied, many nodes across a discretized battery electrode become necessary, in order to reach a good approximation of solution. Such a grid-based approach can be appropriately avoided by implementing analytical methods which reduce the computational load. The pseudo-steady-state (PSS)method is an exact analytical solution method, which provides accurate solid-state concentrations at all current densities. The popularization of the PSS method, in the existing form of expression, is however constrained by a solution convergence problem. In this short communication, a modified PSS (MPSS)expression is presented which provides uniformly convergent solutions at all times. To minimize computational runtime, a fast MPPS (FMPPS)expression is further developed, which is shown to be faster by approximately three orders of magnitude and has a constant time complexity. Using the FMPSS method, uniformly convergent exact solutions are obtained for the solid-state diffusion problem in spherical active particles.

AB - The solid-state spherical diffusion equation with flux boundary conditions is a standard problem in lithium-ion battery simulations. If finite difference schemes are applied, many nodes across a discretized battery electrode become necessary, in order to reach a good approximation of solution. Such a grid-based approach can be appropriately avoided by implementing analytical methods which reduce the computational load. The pseudo-steady-state (PSS)method is an exact analytical solution method, which provides accurate solid-state concentrations at all current densities. The popularization of the PSS method, in the existing form of expression, is however constrained by a solution convergence problem. In this short communication, a modified PSS (MPSS)expression is presented which provides uniformly convergent solutions at all times. To minimize computational runtime, a fast MPPS (FMPPS)expression is further developed, which is shown to be faster by approximately three orders of magnitude and has a constant time complexity. Using the FMPSS method, uniformly convergent exact solutions are obtained for the solid-state diffusion problem in spherical active particles.

KW - Analytical methods

KW - Porous electrodes

KW - Pseudo-steady state

KW - Spherical diffusion

UR - http://www.scopus.com/inward/record.url?scp=85065427220&partnerID=8YFLogxK

U2 - 10.1016/j.ssc.2019.04.011

DO - 10.1016/j.ssc.2019.04.011

M3 - Article

VL - 296

SP - 49

EP - 53

JO - Solid State Communications

T2 - Solid State Communications

JF - Solid State Communications

SN - 0038-1098

ER -