© fraunhofer thermisch-elektrische batterie- modellierung w. beckert, christian freytag, t....
TRANSCRIPT
© Fraunhofer
THERMISCH-ELEKTRISCHE BATTERIE-MODELLIERUNG
W. Beckert, Christian Freytag, T. Frölich, M. Wolter
© Fraunhofer 2
Fraunhofer Institut f. Keramische Technolog. u. Systeme DresdenArbeitsgruppe 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
© Fraunhofer 3
Our Model Approach
for
Batteries
© Fraunhofer 4
Homogenisation model for winding body
uc
elecanoanoeff h
jU ,σ
PDE: anode side charge balance/ potential
uc
eleccathcatheff h
jU ,σ
PDE: cathode side charge balance/ potential
,...,
,...0
jTR
TUUUj
Ael
anocathelec
Constitutive equ.:electric characteristics
winding
...)( 1,
dddeffeff T jjσλ),,( eleccathanod
PDE:
thermal balance
current collectorporous 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:Uano
Ucath
T
composite
homogen.composite
volume element
combine into
transverse (electrolyte) current density
© Fraunhofer 5
Model for local electrical characteristics
Constitutive equation for el.-chem. active phase:
elecAelelec jSoCTRSoCTUU ,,0
[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]
elec
Ael
SoCbselec j
SoCTR
TlSoC
Tk
SoCTU
SoCSoC
TkTdeTaUU
,
1
1
,
1
1''
0
intrinsic electrochemical potential
cell polarisation resistivity
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Introduction into SHEPHERD-Model*
Discharge:
Charge:
* ref.: [1]
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Discharge example from SHEPHERD-Paper (NiCd-cell):
0,8
0,9
1
1,1
1,2
1,3
1,4
0 0,2 0,4 0,6 0,8 1 1,2
Introduction into SHEPHERD-Model
© 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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Thermal-dependence of SHEPHERD-parameters:
3,2803,2853,2903,2953,3003,3053,3103,3153,3203,3253,330
260 270 280 290 300 310 320
Vs/V
T/K
Vs_e_Vs_e
0,000
0,050
0,100
0,150
0,200
0,250
260 270 280 290 300 310 320
A/V
T/K
A_e_A
42,000
44,000
46,000
48,000
50,000
52,000
54,000
260 270 280 290 300 310 320B
T/K
B_e_B
0,026
0,028
0,030
0,032
0,034
0,036
0,038
0,040
260 270 280 290 300 310 320
K'/V
T/K
K'_e_K'
0,000
0,020
0,040
0,060
0,080
0,100
0,120
0,140
260 270 280 290 300 310 320
K/(V/A)
T/K
K_eK3_
-0,03
-0,02
-0,01
0,00
0,01
0,02
0,03
0,04
0,05
0,06
260 270 280 290 300 310 320
L/(V/A)
Titel
L_eL_g
LFP-6745135-30C-Cell
Introduction into SHEPHERD-Model
© Fraunhofer 10
transient battery model [3, 4, 5]: extended SHEPHERD-Modell (i≠const)
transient term
+
Introduction into SHEPHERD-Model
non-galvanostatic partgalvanostatic part(i=const)
open circuit voltage (equilibrium)
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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
© Fraunhofer 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)
thermal problem: 3D frame T(x,y,z)
Map 3D 2D Temperature
Map 2D 3D Dissipation Heat
ly
T(x,y,z)
jelek(l,y)
TQ diss
COMSOL: allows
integrated mapping +
simultaneous cosimulation
Mapping Operation
(unrolled electric film composite)
(thermal composite)
information transfer
( )44 344 21
&44 344 21
&
&
rev
uc
elec
diss
ddddeffth
Q
h
j
T
UT
Q
QT ׶¶
×-××==Ñ×-Ñ å 0, )( jjσλ
( )Tkk ss =
( )TUU 00 =
© Fraunhofer 14
Dt= 6 s
Transient analysis with current pulse
CT
high dynamic load + small area contacts hot spot formation
(LiFePo4, 26650, Ri= 10 mW)
pattern of hot spots, induced by contacting structure
dynamic analysis
current pulse: duration 6 s
Imax = 95 A = 40 C
reasonable magnitude for practical operation
50.2
47.8
KTloc 4.2
temperature
Hybrid-Model Results: 3D-thermal model branch
© 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
© Fraunhofer 16
3-D Model with Housing: Results
Temperature [°C]
41.9°C
21.9°C
41.9°C<T<29.0°C
35°C
30°C
25°C
20°C
40°C
dynamic analysis I 130 A 54 C Dt= 6 s
succesfull analysis of full cell geometry
computation time: 2-6 h
comparable results(hot spot formation) to winding body analysis
© Fraunhofer 17
Models and Results
(System Level)
© Fraunhofer 18
Implementation in SimulationX 3.5
SimulationX 3.5
Modelica 3.2
© Fraunhofer 19
Implementation in SimulationX 3.5
+
1 2
3
5
7
6
transient term
4
© 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)
© Fraunhofer 21
Application on External Data
Terminal voltage from a LFP-6745135-30C-Cell
2,2
2,4
2,6
2,8
3,0
3,2
3,4
0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0
volta
ge/V
DoD
V_shep@1C
V_t@1C
V_shep@5C
V_t@5C
V_shep@10C
V_t@10C
1C
5C
10C
1C 2,1A
5C 10,5A
10C
21A
© Fraunhofer 22
Application on External Data
Temperature profile during discharge of a LFP-6745135-30C-Cell
15171921232527293133
0 500 1000 1500 2000 2500 3000 3500 4000
T/°C
time/s
T_Batt_1C
T_Batt_5C
T_Batt_10C
1C
5C
10C
© Fraunhofer 23
Application on External Data
1C - pulse discharge for COMSOL-Model:
peak 17,5A
duty cycle
300s
periode 2000s
3
3,2
3,4
3,6
3,8
4
4,2
0 5000 10000 15000 20000
volta
ge/V
time/s
V_shep/V
V_comsol/V
© Fraunhofer 24
Application on External Data
5C - pulse discharge for COMSOL-Model:
peak 87,5A
duty cycle
100s
periode 2000s
2,2
2,4
2,6
2,8
3
3,2
3,4
3,6
3,8
4
4,2
0 5000 10000 15000 20000
volta
ge/V
time/s
V_shep/V
V_comsol/V
© 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
CT
50.2
47.8
© 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
© Fraunhofer 27
Wish List to Modelica
simple data import to Modelica
simple data fit function in Modelica
(bidirectional) interface to FEM
…
© 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.
© Fraunhofer 29
Fraunhofer IKTS: Georg Fauser
Adrian Goldberg
Diana Leiva Pinzon
IAV GmbH Chemnitz: Carolus GrünigMirko Taubenreuther
Daniel Tittel
Acknowledgments
This work was kindly funded by:
Europäische Fond für regionale Entwicklung (EFRE) and the Freistaat Sachsen