1. thermisch-elektrische Batterie-modellierung
W. Beckert, Christian Freytag, T. Frölich, M. Wolter

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,...)
High-Temperature-Fuel-Cell-Systems
Thermo-Electric-Generator
Diesel-Particulate-Filter

3. Our Model Approach
for
Batteries

4. Homogenisation model for winding body
current collector
porous cathode
porous anode
isolator
separator/ electrolyte
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:
Uano
Ucath T
composite
homogen.
volume element
combine into
PDE: anode side charge balance/ potential
PDE: cathode side charge balance/ potential
Constitutive equ.: electric characteristics
PDE:
thermal balance
transverse (electrolyte) current density

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

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

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

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

9. Introduction into SHEPHERD-Model
LFP C-Cell
Thermal-dependence of SHEPHERD-parameters:

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

11. Models and Results
(Batterie Cell Level)

12. Model Geometry:
Example: cylindrical cell with contact tabs (LiFePo4 , 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

13. Hybrid 2D-3D Model with Thermal  Electric Coupling
Concept: Combined 2D electric  3D thermal model for winding body
electric problem: 2D frame Uano(l,y), Ucath(l,y), jelek(l,y) Qdiss(l,y)
(unrolled electric film composite)
COMSOL: allows
integrated mapping simultaneous cosimulation ( ) T k s = ( ) T U = y
jelek(l,y) l
Mapping Operation T
information transfer
Qdiss
T(x,y,z)
Map 3D  2D
Temperature
Map 2D  3D
Dissipation Heat
thermal problem: 3D frame T(x,y,z)
(thermal composite) ( ) 4 3 2 1
&
rev uc
elec
diss d
eff th Q h j T U × - = Ñ å , σ λ

14. Hybrid-Model Results: 3D-thermal model branch
Transient analysis with current pulse
pattern of hot spots, induced by contacting structure
temperature
50.2
Dt= 6 s
dynamic analysis
current pulse: duration 6 s
Imax = 95 A = 40 C
reasonable magnitude for practical operation
47.8
(LiFePo4, 26650, Ri= 10 mW)
high dynamic load + small area contacts  hot spot formation

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

16. 3-D Model with Housing: Results
41.9°C
40°C
Temperature [°C]
35°C
succesfull analysis of full cell geometry
computation time: 2-6 h
comparable results (hot spot formation) to winding body analysis
30°C
25°C
20°C
21.9°C
41.9°C<T<29.0°C
dynamic analysis I  130 A  54 C Dt = 6 s

17. Models and Results
(System Level)

18. Implementation in SimulationX 3.5
Modelica 3.2

19. Implementation in SimulationX 3.57 3 4 6 5 2 1
transient term +

20. Application on External Data
Sources of used data:
experimental data for LFP C-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)

21. Application on External Data
Terminal voltage from a LFP C-Cell 1C
2,1A 5C
10,5A
10C
21A

22. Application on External Data
Temperature profile during discharge of a LFP C-Cell

23. Application on External Data
1C - pulse discharge for COMSOL-Model:
peak
17,5A
duty cycle
300s
periode
2000s

24. Application on External Data
5C - pulse discharge for COMSOL-Model:
peak
87,5A
duty cycle
100s
periode
2000s

25. Summary hybrid 2D-electric + 3D-thermal composite approach with
50.2
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
47.8

26. Outlook "Virtual Battery Thermal Lab"-Tool:
Prototype example: [IKTS]
curved LTCC substrate
thick-film resistor
electrolyte tolerant resolution: +/- 0.6 K
"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

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

28. References
[1] C. M. Shepherd: Theoretical design of primary and secondary cells part III - battery discharge equation NRL Report 5908
Washington, D.C
[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.

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