THERMISCH-ELEKTRISCHE BATTERIEMODELLIERUNG
W. Beckert, Christian Freytag, T. Frölich, M. Wolter
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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
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Thermo-Electric-Generator
2
Diesel-Particulate-Filter
Our Model Approach
for
Batteries
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Homogenisation model for winding body
cell laminate
current collector
porous cathode
separator/ electrolyte
porous anode
current collector
isolator
winding
simplified 3-phase homogenised continuum approach
cathode side current distributor phase
combine into
DOF:
Uano
Ucath
T
composite
homogen.
composite
volume
element
"el.-chem." active phase:
transverse charge transfer


jelec
huc


  σ eff ,cath  U cath  
jelec
huc
transverse (electrolyte) current density
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intrins. potential
anode side current distributor phase
PDE: anode side charge PDE: cathode side charge Constitutive equ.:
balance/ potential
balance/ potential
electric characteristics
  σ eff ,ano  U ano  
polar. resistance
jelec 
4
U cath  U ano  U 0 T ,...
RelA T , j,...
PDE:
thermal balance


1
  λ eff  T  (σeff
,d  jd )  jd  ...
d  (ano, cath, elec)
Model for local electrical characteristics
Constitutive equation for el.-chem. active phase:
intrinsic electrochemical potential
Uelec  U0 T , SoC  R T , SoC jelec
A
el
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
1 
1



U elec  U s  aT   e bSoC   d ' T   k ' T  
 l T   jelec
  SoC   k T  

SoC

SoC
1
 1



U 0 T , SoC
RelA T , SoC
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Introduction into SHEPHERD-Model*
Discharge:
Charge:
* ref.: [1]
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Introduction into SHEPHERD-Model
Discharge example from SHEPHERD-Paper (NiCd-cell):
1,4
1,3
1,2
1,1
1
0,9
0,8
0
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0,2
0,4
0,6
7
0,8
1
1,2
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]
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Introduction into SHEPHERD-Model
LFP-6745135-30C-Cell
3,330
3,325
3,320
3,315
3,310
3,305
3,300
3,295
3,290
3,285
3,280
54,000
0,140
52,000
0,120
K/(V/A)
48,000
46,000
Vs_e
_Vs_e
B_e
_B
44,000
270
280
290
300
310
320
0,020
270
280
290
300
310
320
260
0,036
0,100
A_e
_A
300
0,032
320
320
0,01
0,00
L_e
L_g
-0,02
-0,03
260
270
280
290
T/K
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310
0,02
-0,01
0,028
310
320
0,03
0,034
0,026
290
310
0,04
0,030
0,000
300
0,05
L/(V/A)
A/V
K'/V
0,150
290
0,06
K'_e
_K'
0,038
0,200
280
280
T/K
0,040
270
270
T/K
0,250
260
0,060
0,000
260
T/K
0,050
0,080
0,040
42,000
260
K_e
K3_
0,100
50,000
B
Vs/V
Thermal-dependence of SHEPHERD-parameters:
T/K
9
300
310
320
260
270
280
290
Titel
300
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
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Models and Results
(Batterie Cell Level)
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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
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Hybrid 2D-3D Model with Thermal  Electric Coupling
Concept: Combined 2D electric  3D thermal model for winding body
Uano(l,y), Ucath(l,y), jelek(l,y) Qdiss(l,y)
electric problem: 2D frame
(unrolled electric film composite)
s k  s k T 
COMSOL: allows
U 0  U 0 T 
integrated mapping +
simultaneous cosimulation
y
l
information transfer
T
Map 3D  2D
Temperature
T(x,y,z)
Map 2D  3D
Dissipation Heat
thermal problem: 3D frame
(thermal composite)
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T(x,y,z)
U 0 jelec
  λ  T   Q& th   (σ eff , d  jd )  jd  T 


T
huc
d

 
 

&
Q& diss
Qrev
13
Hybrid-Model Results: 3D-thermal model branch
Transient analysis with current pulse
pattern of hot spots, induced by contacting structure
temperature
T C 
50.2
Tloc  2.4 K
dynamic analysis
t= 6 s
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
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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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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
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dynamic analysis I  130 A  54 C t = 6 s
Models and Results
(System Level)
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Implementation in SimulationX 3.5
SimulationX 3.5
Modelica 3.2
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Implementation in SimulationX 3.5
7
3
4
6
5
2
1
+ transient
term
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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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Application on External Data
Terminal voltage from a LFP-6745135-30C-Cell
3,4
1C
voltage/V
3,2
3,0
V_shep@1C
2,8
V_t@1C
2,6
V_shep@5C
2,4
V_shep@10C
5C
V_t@5C
10C
V_t@10C
2,2
0,0
0,1
0,2
0,3
0,4
0,5
0,6
DoD
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0,7
0,8
0,9
1,0
1C
2,1A
5C
10,5A
10C
21A
Application on External Data
Temperature profile during discharge of a LFP-6745135-30C-Cell
33
31
T_Batt_1C
10C
29
T_Batt_5C
T/°C
27
T_Batt_10C
25
5C
23
21
19
1C
17
15
0
500
1000
1500
2000
2500
time/s
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3000
3500
4000
Application on External Data
1C - pulse discharge for COMSOL-Model:
4,2
voltage/V
4
3,8
peak
17,5A
duty cycle
300s
periode
2000s
3,6
V_shep/V
3,4
V_comsol/V
3,2
3
0
5000
10000
15000
time/s
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20000
Application on External Data
5C - pulse discharge for COMSOL-Model:
4,2
4
3,8
voltage/V
3,6
3,4
peak
87,5A
duty cycle
100s
periode
2000s
3,2
3
2,8
V_shep/V
2,6
V_comsol/V
2,4
2,2
0
5000
10000
15000
time/s
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20000
Summary
T C 
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
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47.8
Outlook
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
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Wish List to Modelica

simple data import to Modelica

simple data fit function in Modelica

(bidirectional) interface to FEM
 …
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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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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
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