Physically based modeling and simulation of a LiFePO4 ... - DLR ELIB

Physically based modeling and simulation of a LiFePO4-based lithium-ion battery C. Hellwig, D. N. Fronczek*, Ş. Sö Sörgel and W. G. Bessler German Aerospace Center (DLR), Institute of Technical Thermodynamics, Thermodynamics, Stuttgart, Germany *E-mail: [email protected]

Goal and approach

MultiMulti-scale modeling

Goal: ImpedanceImpedance-based SOC diagnostics of LiFePO4 cells LiFePO4based cell

e–

100 % 40 % 0%

Li+

E

Thermal modeling

Z'' [mOhm]

10 8 6 4 2 0 -2 -4 25

30

Positive electrode

Negative current collector

Negative electrode

LiFePO4 e–

LiC6

Li+

LiPF6

DLR MobilEMobilE-Pack 300 W continuous 1 kW peak

100 % 80 % 60 % 40 % 20 % 0%

20

Positive current collector

• Li+ charge transport in electrolyte: 100 µm scale • Li transport in solid phase: ~100– ~100–1000 nm scale

Electrochemical characterization

Structural characterization A123 26650

Battery management of LIB/PEFC LIB/PEFC hybrid system

T

Electrochemical Discharge and modeling impedance simulation

Mass and charge transport is modeled on particle and repeat unit scale.

Separator Electronically conductive coating

e–

Li+

Electrolyte Active material

Li

35

Z' [mOhm]

Model Thermodynamics ΔH (cLi )  TΔS(cLi ) ΔG Parameters:  eq (cLi )   zF zF • Empirical halfhalf-cell enthalpy, entropy 1.5 mol l–1 • LiPF6 Concentration:   F   (1   )F  – + – 10 2 – 1 Kinetics  i  i 0  exp  act   exp   act   • Li and PF6 - diffusion coefficient: 1·10 m s RT  RT     • ButlerButler-Volmer kinetics • Thickness (anode / separator / cathode): 40 µm / 20 µm / 80 µm RT  c 0  – 14 2 – 1 – 16 2 – 1       ( t )    ( c )   conc • Concentration overpotential  ln  act eq Li conc • Bulk diffusion coefficients (LiC6 / LiFePO4): 1· 1·10 m s / 1· 1·10 m s zF  c (t )  SolidSolid-state transport • Exchange current density: 3·105 A m–3 Diffusion Chemistry • Mass conservation • Particle radius (anode / cathode): 1 µm / 0.1 µm Li 1   2 Li  MLi  i r D  • Spherical diffusion in particle t r 2 r  r  zF Thermodynamic data: Electrolyte transport Diffusion Migration Chemistry • Separation in enthalpy and entropy • NernstNernst-Planck equation ∂c    ∂c  z F   ∂  D  D c   M s    ∂t y  ∂y  RT y  ∂y  • LiC6: Y. Reynier, Reynier, R. Yazami, Yazami, B. Fultz, Journal of Power Sources • Charge neutrality  c z   0  119– 119–121 (2003) 850– 850–855 Heat transport Conduction Sources Losses • LiFePO4: J. L. Dodd, PhD thesis, California Institute of Technology, • Ohmic, Ohmic, chemical heat production CPT   T    2007    QelchemQohmTcellTenv • Heat conduction and convection t y  y  Cell voltage E =  –  i

i

i

i

V i i

i i

i i

i

cathode

anode

Electrochemical behavior Experiment

3.6

2.6 2.4

Experiment Simulation

0.5

1.0

1.5

Capacity [Ah]

-5 15

2.0

20

25

30

35

40

1.60 0.7 +

c(Li )

x in LixFePO4

30

1.50

0.5

1.45

0.4

x in LixC6

0.3

1C, 25% SOC 0

20

35

40

-1.0

40

60

80

-0.5

0.0

0.5

1.0

Relative sensitivity

• Allows detailed insight into rateratelimiting processes. • Cathode is limiting component

• Promising system for highhigh-energy batteries (5× (5× specific energy) • Major challenge today: Limited cycle life • New model will account for side reactions and other degradation mechanisms, allowing the study of cell aging Positive electrode

+

1.55

Concentration Li [mol / l]

Stoichiometry x in LixC6 / LixFePO4

Separator Neg. El.

Pos. El.

0.6

25

0.1 C 5C

Outlook: LithiumLithium-sulfur batteries

Concentration variation at SOC 25 % with 1C discharge rate: 0.8

20

• Considerable influence of SOC on impedance spectrum • Impedance simulations are feasible, so far only qualitative agreement

Spatial concentration variations Electrolyte: • S-curve behavior of Li+concentration in electrolyte • No interaction with separator assumed Bulk: • Stoichiometry change during discharging in dependence on diffusion limitations in electrolyte

15

Z'[m]

Z' [mOhm]

• Flat discharge curve, voltage variation mainly from C6 electrode • Voltage losses at higher discharge rates due to transport limitations in electrodes

5 0

0 -5

2.2 0.0

5

100

120

Distance through repeat unit [µm]

1.40 140

Sulfur/carbon composite

Organic electrolyte

Li2S8

Positive current collector

Li2S6 Li2S4 Li2S3

Li2S2 Li2S

Sulfur redox chemistry

Negative electrode

Separator

S8

Charge

0.1C 1C 2C 5C 10C

Discharge

3.0

Anode bulk diffusion coefficient Anode particle diameter Anode exchange current density Anode thickness Cathode bulk diffusion coefficient Cathode particle diameter Cathode exchange current density Cathode thickness Separator thickness

100 % 40 % 0%

10

-Z'' [m]

-Z'' [mOhm]

Cell Voltage [V]

3.2

Simulation

100 % 40 % 0%

10

3.4

2.8

Sensitivity analysis • Sensitivity of cell parameters on discharge capacity

Electrochemical impedance spectra • Impedance spectra of an unpolarized cell at different SOC

Polysulfides diffusion (shuttle mechanism)

Lithium metal S8

Polysulfides reduction

Discharge curves • Discharge curves starting from 100 % SOC at different discharge rates

Li2S8

Negative current collector

Li2S6 Li2S4 Li2S3 Li

+

Li0

Lithium plating/stripping