© 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

© Fraunhofer 6

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

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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

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)

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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