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© Fraunhofer THERMISCH-ELEKTRISCHE BATTERIE- MODELLIERUNG W. Beckert, Christian Freytag, T. Frölich, M. Wolter

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© Fraunhofer 2 Fraunhofer Institut f. Keramische Technolog. u. Systeme Dresden Arbeitsgruppe Modellierung und Simulation: Multiphysics-Feldsimulation (FEM, CFD); Reaktive Strömung; homogenisierter Ansatz für heterogene Mesostrukturen; (Systemsimulation) Thermisches Management von Energiesystemen,... (SOFC-Stacks + Komponenten, thermoelektrische Generatoren, Li-Ion-Batterien,...) H igh -T emperature -F uel -C ell -SystemsT hermo -E lectric -G enerator D iesel -P articulate -F ilter

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© Fraunhofer 3 Our Model Approach for Batteries

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© Fraunhofer 4 Homogenisation model for winding body PDE: anode side charge balance/ potential PDE: cathode side charge balance/ potential Constitutive equ.: electric characteristics winding PDE: thermal balance current collector porous cathode porous anode isolator separator/ electrolyte current collector cell laminate anode side current distributor phase cathode side current distributor phase "el.-chem." active phase: transverse charge transfer simplified 3-phase homogenised continuum approach intrins. potential polar. resistance DOF: U ano U cath T composite homogen. composite volume element combine into transverse (electrolyte) current density

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© Fraunhofer 5 Model for local electrical characteristics Constitutive equation for el.-chem. active phase: [C. M. Shepherd "Theoretical design of primary and secondary cells. Part 3: battery discharge equation" NRL Report 5908; May 1963 Empirical Approach: Shepherd's Model [1] intrinsic electrochemical potential cell polarisation resistivity

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© Fraunhofer 6 Introduction into SHEPHERD-Model* Discharge: Charge: * ref.: [1]

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© Fraunhofer 7 Discharge example from SHEPHERD-Paper (NiCd-cell): Introduction into SHEPHERD-Model

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© Fraunhofer 8 Extensions and adaptions to original SHEPHERD-Model: Introduction into SHEPHERD-Model only valid for isothermal and galvanostatic conditions for OCV* for linear range * ref.: [2]

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© Fraunhofer 9 Thermal-dependence of SHEPHERD-parameters: LFP-6745135-30C-Cell Introduction into SHEPHERD-Model

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© Fraunhofer 10 transient battery model [3, 4, 5]: extended SHEPHERD-Modell (i≠const) transient term + Introduction into SHEPHERD-Model non-galvanostatic part galvanostatic part(i=const) open circuit voltage (equilibrium)

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© Fraunhofer 11 Models and Results (Batterie Cell Level)

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© Fraunhofer 12 Model Geometry: Example: cylindrical cell with contact tabs ( LiFePo 4, ANR 26650) separated current collector tabs, embedded between windings nonhomogeneous contacting with current concentration toward cont. tabs helical current flow + current collection 3D-model approach

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© Fraunhofer 13 Hybrid 2D-3D Model with Thermal Electric Coupling Concept: Combined 2D electric 3D thermal model for winding body electric problem: 2D frame U ano (l,y), U cath (l,y), j elek (l,y) Q diss (l,y) thermal problem: 3D frame T(x,y,z) Map 3D 2D Temperature Map 2D 3D Dissipation Heat l y T(x,y,z) j elek (l,y) T Q diss COMSOL: allows integrated mapping + simultaneous cosimulation (unrolled electric film composite) (thermal composite) information transfer rev uc elec diss d dddeffth Q h j T U T Q QT 0, )( jjσλ T kk TUU 00

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© Fraunhofer 14 t= 6 s Transient analysis with current pulse high dynamic load + small area contacts hot spot formation (LiFePo4, 26650, R i = 10 m ) pattern of hot spots, induced by contacting structure dynamic analysis current pulse: duration 6 s I max = 95 A = 40 C reasonable magnitude for practical operation 50.2 47.8 temperature Hybrid-Model Results: 3D-thermal model branch

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© Fraunhofer 15 Completion: 3D-Model with Housing Geometry/ Mesh generation winding domain: Comsol-generated add housing + contact structure: CAD-Import connecting meshs by interface elements

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© Fraunhofer 16 3-D Model with Housing: Results Temperature [°C] 41.9°C 21.9°C 41.9°C

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© Fraunhofer 17 Models and Results (System Level)

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© Fraunhofer 18 Implementation in SimulationX 3.5 SimulationX 3.5 Modelica 3.2

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© Fraunhofer 19 Implementation in SimulationX 3.5 + 1 2 3 5 7 6 transient term 4

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© Fraunhofer 20 Application on External Data Sources of used data: experimental data for LFP-6745135-30C-Cell: discharge 1C, 5C, 10C including temperature data data from COMSOL build-in battery-model [6]: pulse discharge: 1C, 5C no temperature data included SHEPHERD-parameters via external data fit (Excel)

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© Fraunhofer 21 Application on External Data Terminal voltage from a LFP-6745135-30C-Cell 1C2,1A 5C10,5A 10C21A

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© Fraunhofer 22 Application on External Data Temperature profile during discharge of a LFP-6745135-30C-Cell

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© Fraunhofer 23 Application on External Data 1C - pulse discharge for COMSOL-Model: peak17,5A duty cycle300s periode2000s

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© Fraunhofer 24 Application on External Data 5C - pulse discharge for COMSOL-Model: peak87,5A duty cycle100s periode2000s

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© Fraunhofer 25 Summary hybrid 2D-electric + 3D-thermal composite approach with geometrical details thermo-electric coupling homogenised 3 phase model for winding composite simple empirical model for electrical characteristics result: contact structure acts as source for thermal hot-spots in dynamic loads approach has potential for use in multi-cell models good, robust and simple model for description of terminal voltage resolution for isothermal and galvanostatic restriction of original model sufficiently accurate match between experiment and model 50.2 47.8

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© Fraunhofer 26 Outlook "Virtual Battery Thermal Lab"-Tool: analyse/ understand internal thermal processes „benchmark" for simpler models tool for cell design optimisation IKTS activity: internal cell temperature sensor assist design process optimise sensor positioning analyse effects from interference of sensor-cell implementation of charge behaviour data fit in SimulationX/Modelica coupled thermal-electric model Prototype example: [IKTS] curved LTCC substrate thick-film resistor electrolyte tolerant resolution: +/- 0.6 K

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© Fraunhofer 27 Wish List to Modelica simple data import to Modelica simple data fit function in Modelica (bidirectional) interface to FEM …

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© Fraunhofer 28 References [1]C. M. Shepherd: Theoretical design of primary and secondary cells part III - battery discharge equation NRL Report 5908 Washington, D.C. 1963. [2]O. Tremblay, L.-A. Dessaint, A. I. Dekkiche: A Generic Battery Model for the Dynamic Simulation of Hybrid Electric Vehicles Vehicle Power and Propulsion Conference 2007. [3]A. Jossen: Fundamentals of battery dynamics Journal of Power Sources 154 (2006) 2, S. 530–38. [4]N. Sekushin: Equivalent circuit of Warburg impedance Russian Journal of Electrochemistry 45 (2009), S. 828–32. [5]F. M. González-Longatt: Circuit Based Battery Models: A Review 2do congreso iberoamericano de estudiantes de ingenieria electrica, 2006. [6] COMSOL Multiphysics User’s Guide: Rechargeable Lithium-Ion Battery Version 3.5a, 2008.

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© Fraunhofer 29 Fraunhofer IKTS:Georg Fauser Adrian Goldberg Diana Leiva Pinzon IAV GmbH Chemnitz: Carolus Grünig Mirko Taubenreuther Daniel Tittel Acknowledgments This work was kindly funded by: Europäische Fond für regionale Entwicklung (EFRE) and the Freistaat Sachsen

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