Change search
ReferencesLink to record
Permanent link

Direct link
Modeling battery cells under discharge using kinetic and stochastic battery models
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics. (Analysis and Probability)ORCID iD: 0000-0002-7672-190X
Uppsala University, Disciplinary Domain of Science and Technology, För teknisk-naturvetenskapliga fakulteten gemensamma enheter, International Science Programme (ISP). Univ Ouagadougou, Dept Math, Ouagadougou, Burkina Faso.
2016 (English)In: Applied Mathematical Modelling, ISSN 0307-904X, Vol. 40, no 17-18, 7901-7915 p.Article in journal (Other academic) Published
Abstract [en]

In this paper we review several approaches to mathematical modeling of simple batterycells and develop these ideas further with emphasis on charge recovery and the responsebehavior of batteries to given external load. We focus on models which use few param-eters and basic battery data, rather than detailed reaction and material characteristicsof a specific battery cell chemistry, starting with the coupled ODE linear dynamics ofthe kinetic battery model. We show that a related system of PDE with Robin typeboundary conditions arises in the limiting regime of a spatial kinetic battery model,and provide a new probabilistic representation of the solution in terms of Brownianmotion with drift reflected at the boundaries on both sides of a finite interval. Tocompare linear and nonlinear dynamics in kinetic and stochastic battery models westudy Markov chains with states representing available and remaining capacities of thebattery. A natural scaling limit leads to a class of nonlinear ODE, which can be solvedexplicitly and compared with the capacities obtained for the linear models. To indicatethe potential use of the modeling we discuss briefly comparison of discharge profilesand effects on battery performance.

Place, publisher, year, edition, pages
2016. Vol. 40, no 17-18, 7901-7915 p.
Keyword [en]
battery lifetime; state-of-charge; charge recovery; probabilistic solution of PDE; Robin boundary condition; nonlinear ODE
National Category
Research subject
Mathematics with specialization in Applied Mathematics
URN: urn:nbn:se:uu:diva-282025DOI: 10.1016/j.apm.2016.03.049ISI: 000381541100031OAI: diva2:916243
Available from: 2016-04-01 Created: 2016-04-01 Last updated: 2016-10-05Bibliographically approved

Open Access in DiVA

fulltext(1598 kB)11 downloads
File information
File name FULLTEXT01.pdfFile size 1598 kBChecksum SHA-512
Type fulltextMimetype application/pdf

Other links

Publisher's full text

Search in DiVA

By author/editor
Kaj, Ingemar
By organisation
Department of MathematicsInternational Science Programme (ISP)

Search outside of DiVA

GoogleGoogle Scholar
Total: 11 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 24 hits
ReferencesLink to record
Permanent link

Direct link