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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 Theory. (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, E-ISSN 1872-8480, Vol. 40, no 17-18, 7901-7915 p.Article in journal (Refereed) 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
Mathematics
Research subject
Mathematics with specialization in Applied Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-282025DOI: 10.1016/j.apm.2016.03.049ISI: 000381541100031OAI: oai:DiVA.org:uu-282025DiVA: diva2:916243
Available from: 2016-04-01 Created: 2016-04-01 Last updated: 2017-11-30Bibliographically approved

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Kaj, Ingemar

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