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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)
Uppsala University, Disciplinary Domain of Science and Technology, För teknisk-naturvetenskapliga fakulteten gemensamma enheter, International Science Programme (ISP). University of Ougadougou, Burkina Faso.
2016 (English)In: Applied Mathematical Modelling, 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 characteristics ofa specific battery cell chemistry, starting with the coupled ODE linear dynamics of thekinetic battery model. We show that a related system of PDE with Robin type boundaryconditions arises in the limiting regime of a spatial kinetic battery model, and provide anew probabilistic representation of the solution in terms of Brownian motion with drift re-flected at the boundaries on both sides of a finite interval. To compare linear and nonlineardynamics in kinetic and stochastic battery models we study Markov chains with states rep-resenting available and remaining capacities of the battery. A natural scaling limit leads toa class of nonlinear ODE, which can be solved explicitly and compared with the capacitiesobtained for the linear models. To indicate the potential use of the modeling we discussbriefly comparison of discharge profiles and effects on battery performance.

Place, publisher, year, edition, pages
Elsevier, 2016. Vol. 40, no 17-18, 7901-7915 p.
National Category
Mathematical Analysis
Research subject
Applied Mathematics and Statistics
Identifiers
URN: urn:nbn:se:uu:diva-301331OAI: oai:DiVA.org:uu-301331DiVA: diva2:954020
Available from: 2016-08-19 Created: 2016-08-19 Last updated: 2016-08-19

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http://dx.doi.org/10.1016/j.apm.2016.03.049

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Kaj, Ingemar
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Department of MathematicsInternational Science Programme (ISP)
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