Elektrochemische Modelle für Lithium-Ionen Batterien MES 10 - Elektrochemische Modelle...

KIT – Universität des Landes Baden-Württemberg undnationales Forschungszentrum in der Helmholtz-Gemeinschaft www.iam.kit.edu/wet

Elektrochemische Modelle für Lithium -Ionen Batterien

André Weber

Institut für Angewandte Materialien - Werkstoffe der Elektrotechnik IAM-WETAdenauerring 20b, Geb. 50.40 (FZU), Raum 314

phone: 0721/608-7572, fax: 0721/608-7492andre.weber@kit.eduwww.iam.kit.edu/wet

Modellbildung elektrochemischer Systeme

Quelle:

Institut für Angewandte Materialien Werkstoffe der Elektrotechnik

Vorlesung MES 10 - Elektrochemische Modelle LiB - Zellen.pptx, Folie: 2, 10.07.2018

www.iam.kit.edu/wet

Elektrochemisches ModellStand der Technik & Motivation

IAM-WET

Verhaltensmodell

geringe örtliche AuflösungechtzeitfähigParametrierung einfach

grobe Verhaltensprädiktion im vermessenen Parameterraum

Differentialgleichungen & FEM

hohe örtliche Auflösungnicht echtzeitfähigParametrierung aufwendig

Simulation von unbekannten Strukturen und MaterialienInter-/Extrapolation des Parameterraums

( )cDt

c ∇⋅∇=∂∂

( ) ( )

−−= …00

1exp UU

physikalisch motiviertes Ersatzschaltungsmodell

geringe örtliche AuflösungechtzeitfähigParametrierung mittel

Diagnose durch Simulation Fehler-/DegradationsfälleInter-/Extrapolation des Parameterraums

Quelle:

www.iam.kit.edu/wet

Distribution of Relaxation Times as Basis for Time-Domain Models of Li-Ion Batteries

IAM-WET

Impedance Measurement

Physically MotivatedModel

Time-DomainSimulation

Model Targets:

Good Real-time Capabilities - model structure deployable on microcontroller

Scalability - accuracy and computational effort easy adaptable

Automization of Parameterization - model quality does not depend on human expertise

Quelle:

www.iam.kit.edu/wet

IntroductionBattery Modeling Today

IAM-WET

EIS Measurement

electrochemical impedance measurements

non parametric representation of linear dynamics

variation of operating points (SOC,T)

Quelle:

www.iam.kit.edu/wet

Model selection and fit

a priori knowledge necessary

stabilization of fit procedure critical

subtraction of differential capacity

R0 RQ1 RQ2 RQ3 ZGFLWC0

differential capacity

IAM-WET

EIS Measurement

R0 RQ1 RQ2 RQ3 ZGFLWC0 fractional impedance elements

Quelle:

www.iam.kit.edu/wet

IAM-WET

EIS Measurement

Approximation of fractional impedance elements

Fractional impedance elements cannot be simulated directly in time domain

Approximation with sum of RC-Elements:

empirical relation [1]

analytical expansion to sum

discretization of the distribution of relaxation times

RC1 RC2 RC3

Analytical expression for the measured impedance ha s to be known!

[1] Stephan Buller, Phd-Thesis, Aachener Beitrage des ISEA, Shaker Verlag GmbH, 2002

Quelle:

www.iam.kit.edu/wet

IAM-WET

EIS Measurement

Time Domain Model and Simulation

CV …+

PLECSt

Loss ofaccuracy

time effort

Quelle:

www.iam.kit.edu/wet

g(τ): Dirac pulses

τ1 τ2

ideal process: RC-Elements

RC1 RC2

The Distribution of Relaxation Times

IAM-WET

( )( )

Z j R djτω τωτ

+∫ g(τ): distribution function of relaxation times (DRT)

H. Schichlein, A.C. Müller, M. Voigts, A. Krügel and E. Ivers-Tiffée, Journal of Applied Electrochemistry, Vol. 32, No. 8, pp. 875-882, 2002

The Continuous Distribution of Relaxation Times

tτ1 τ2general distribution function

RQ1 RQ2

real process: RQ-Elements

Calculation of the Discrete Distribution of Relaxat ion Times

N is the Number of RC-Elementsdiscrete distribution: � is logarithmical equally spacedg(�n) = 0 at highest and lowest �n

log(τ)

ττω δωτ=

( )( )

Quelle:

www.iam.kit.edu/wet

IAM-WET

EIS Measurement

CV …+

PLECSt

Loss ofaccuracy

time effort

Quelle:

www.iam.kit.edu/wet

IAM-WET

EIS Measurement

Method of the Distribution of Relaxation Times

PLECSt

…Re(Zth)

deconvolution of EIS

τωωτ=

( )( )

polpolnn

distribution ofrelaxation times

Quelle:

www.iam.kit.edu/wet

Verification of the DRT ModelExperimental

IAM-WET

2 Ah Li-ion cell from KOKAM

Pouch-cell

Anode: Graphite

Cathode: NCA/LCO-Blend

REM: Anode

2µm 2µm

Anode: Graphite Cathode: NCA / LiCoO2 Blend

LiCoO2

Quelle:

www.iam.kit.edu/wet

pulse height 1C

pulse length = 10s

f = [100kHz … 5mHz]

Uampl = 10mV / 5mV

Verification of the DRT ModelExperimental

IAM-WET, D. Klotz, M. Schönleber, J. P. Schmidt, and E. Ivers-Tiffée, Electrochim. Acta, 56, 8763 (2011).

Electrochemical Measurements

quasi stationary OCV

discharge/charge at C/40

Variation of Imax = C/4 … 2C � 0.5A � 4A

average discharge with Imax/2

transformationto frequencydomain1

merger of high andlow frequency range

impedance spectraf = [100kHz …10µHz]

completely autom

ated process

Quelle:

www.iam.kit.edu/wet

impedance spectroscopy time domain measurements

Impedance Measurements in the Frequency and Time Domain

IAM-WET

0.1 0.2 0.3 0.40

Z´ [Ω]

-Z´´

Z´ [Ω]

-Z´´

Z´ [Ω]

-Z´´

0.1 0.2 0.3 0.40

Z´ [Ω]

-Z´´

SOC = 100 %

Û = 10 mV

fmin = 5,88 µHz

fmax = 10 kHzΔSOC = 1,95 %

tMess = 19 days

nIntegration = 3...8

LiCoO2 / C

C = 120 mAh

cellLiCoO2 / C

C = 120 mAh

SOC = 100 %

ΔU = 50 mV

fmin = 6,84 µHz

fmax,ZB = 8,63 Hzfmax = 10 kHz

ΔSOC = 5,01 %

tMess = 4 days

Quelle:

www.iam.kit.edu/wet

Measurement ResultsEIS

IAM-WET

f �0

f � ∞∞∞∞

SOC [%]

f �0

extended frequency range via pulse measurements

Quelle:

www.iam.kit.edu/wet

Measurement ResultsDRT

IAM-WET

SOC ↓

Quelle:

www.iam.kit.edu/wet

Measurement ResultsDRT

IAM-WET

complex SOC-dependence

beneficial use of the DRT for identification and se paration of Processes 1,2

interpretation not necessary for parameterization of time domain model

[1] J.P. Schmidt, T. Chrobak, M. Ender, J. Illig, D. Klotz, and E. Ivers-Tiffée, J. Power Sources, 196 (2010) 5342-5348.

[2] J. Illig, T. Chrobak, D. Klotz, and E. Ivers-Tiffée, ECS Trans., 33 (2011) 3-15.

Quelle:

www.iam.kit.edu/wet

Measurement ResultsComparison: EIS / DRT-Model

IAM-WET

SOC [%]

DRT Model

Measurement

Very good accordance of measurement and DRT-model

Quelle:

www.iam.kit.edu/wet

Verification of the DRT-ModelScalability

IAM-WET

EIS Measurement / DRT-Model Variation of N

τωωτ=

( )( )

Results

N = 100 � 11.6 RC / decade

20 RC-elements show no significant difference to 100 RC-elements

N = 20 � 2.3 RC / decade

10 RC-elements show slight deviations

N = 10 � 1.1 RC / decade

4 RC-elements result in a bad fit of the impedance data

N = 4 � 0.5 RC / decade

Quelle:

www.iam.kit.edu/wet

Verification of the DRT-ModelScalability – Time Domain Simulation

IAM-WET

Comparison of dynamic behavior

seconds-timescale shows significant differences for 4 RC-model

slight increase of accuracy between 10 and 20 RC-model

no visible difference for 20 and 100 RC-model

10 RC-Model shows good accordance and modest calcul ation effort

-Imax Currrent

Quelle:

www.iam.kit.edu/wet

Comparison of Simulation Time

DRT-ModelReal-Time Capability

IAM-WET

Model Order

RCs / decade

Tsim / Tmeas [%]

Simulation Environment

Matlab R2009awww.mathworks.com

PLECS 2.1www.plexim.com

Hardware:Intel® Core™ i7 CPU4GB RAM

��

Quelle:

www.iam.kit.edu/wet

Physically based models Behavioral models

Electrochemical models Equivalent circuit models Time -domain models

+ charge- and mass transport+ understand electrochemical

reactions+ high accuracy

+ dependence of battery characteristics on operating parameters

+ optimal battery design according to performance and capacity

+ estimation of the current battery condition

+ fast computation+ battery management systems

- time consuming computation - only applicable in the frequency domain

- no physical interpretation possible

Battery Models

IAM-WET

[1] Ma, Y. et al., RSC Advances, 6 (2016), 25435-25443

anode separator cathode

Quelle:

www.iam.kit.edu/wet

Physically based models Behavioral models

Electrochemical models Equivalent circuit models Time -domain models

Battery Models

IAM-WET

� New approach combines advantages

� High-resolution electrochemical characterisation needed for physical interpretability

physical interpretability fast computation in the time domain

Quelle:

www.iam.kit.edu/wet

Methodology

IAM-WET

Voltage behavior of a battery when applying a curre ntLoss processes that determine the overvoltage

< �� Open circuit voltage ��

Quelle:

www.iam.kit.edu/wet

Methodology

IAM-WET

< �� Open circuit voltage

�� Instantaneous voltage drop

��

Lithium transport in the electrolyte, electron transportin the electrodes and current collectors

Quelle:

www.iam.kit.edu/wet

Methodology

IAM-WET

�� Fast kinetic processes

��

�� ,�/��,�

Interface losses at anode and cathode2

Quelle:

www.iam.kit.edu/wet

Methodology

IAM-WET

�� Slow diffusion processes

��

�� ,�/��,�

�� ,�/�

Interface losses at anode and cathode

Lithium solid state diffusion in anode and cathode3

Quelle:

www.iam.kit.edu/wet

Methodology

IAM-WET

��

�� ,�/��,�

�� ,�/�

Lithium solid state diffusion in anode and cathode

Contact losses included in 4 1

Quelle:

www.iam.kit.edu/wet

Methodology

IAM-WET

��

�� ,�/��,�

�� ,�/�

Lithium solid state diffusion in anode and cathode

Contact losses included in 4 1

Quelle:

www.iam.kit.edu/wet

Methodology

IAM-WET

How to determine the operating voltage

„fast“ lossprocesses (< 1 Hz)

„slow “ lossprocesses (> 1 Hz)

ηloss

ηDiff

ηCT/SEI

Quelle:

www.iam.kit.edu/wet

Methodology

IAM-WET

Electrochemical Impedance Spectroscopy

DRT-Analysis:

Description of the loss processes over the frequency

Equivalent Circuit Modelling

Fast loss processes

� �� !" #$�%1 ' �� (�

ηloss

ηDiff

ηCT/SEI

�� Measurement of the frequency dependent resistance

�process identification

�� process quantification

Quelle:

www.iam.kit.edu/wet

Methodology

IAM-WET

Current interruption method in the time domain

Time domain model fit

Slow loss processes

η � , ∙ �. ∙ 1 exp 2�.

', ∙ �3 ∙ 1 exp 2�3

ηloss

ηDiff

ηCT/SEI

�� Measurement of the low-frequent loss contributions

�� process quantification

Quelle:

www.iam.kit.edu/wet

Investigated Cell

IAM-WET

anode:

graphite

LiNixCoyAl1-x-yO2LiCoO2carbon black

10 µm

SEM imagesHigh power pouch cell

Manufacturer KOKAM

Nominal capacity 350 mAh

Nominal voltage 3,7 V

Max. charge current 700 mA (≙ 2C)

Max. discharge current 7 A (≙ 20C)

Voltage limits (Umin- Umax) 2,7 - 4,2 V

cathode:

Quelle:

www.iam.kit.edu/wet

ηloss

ηDiff

ηCT/SEI

Experimental

IAM-WET

Fast loss processes

Quelle:

www.iam.kit.edu/wet

ExperimentalAnalysis of high and middle frequency Electrochemical Processes

IAM-WET

Electrochemical impedance spectroscopy: measurement of the frequency-dependent resistance

Excitation and response signal

( )( ) Re( ) Im( ) ' ''

( )juu t

Z e Z j Z Z j Zi t i

ϕω ⋅= = ⋅ = + ⋅ = + ⋅

T = 25 °CSOC = 60 %

Quelle:

www.iam.kit.edu/wet

IAM-WET

Electrochemical impedance spectroscopy: measurement of the frequency-dependent resistance

Excitation and response signal Impedance in a Nyquist diagram

( )( ) Re( ) Im( ) ' ''

( )juu t

Z e Z j Z Z j Zi t i

ϕω ⋅= = ⋅ = + ⋅ = + ⋅

T = 25 °CSOC = 60 %

Quelle:

www.iam.kit.edu/wet

Requirements for validity

IAM-WET

Kramers Kronig validity test to ensure the validity o f the measurement

http://www.iam.kit.edu/wet/Lin-KK.php

If all these requirements are fulfilled, the Kramers Kronigrelations can be derived:

Linearity of the measured system

Time invariance of the measured system

Causality of the measured system

2 ' Im( ( '))Re( ( )) '

ω ωω ωπ ω ω

∞ ⋅=−∫

2 ' Re( ( '))Im( ( )) '

ω ωω ωπ ω ω

∞ ⋅= −−∫

If Re(Z) is known, Im(Z) can be computed.

� Comparison of computed part and measured partreveals the Kramers Kronig residuals .

Quelle:

www.iam.kit.edu/wet

Requirements for validity

IAM-WET

Kramers Kronig validity test to ensure the validity o f the measurement

Example: change of SOC

http://www.iam.kit.edu/wet/Lin-KK.php

If all these requirements are fulfilled, the Kramers Kronigrelations can be derived:

Linearity of the measured system

Time invariance of the measured system

Causality of the measured system

2 ' Im( ( '))Re( ( )) '

ω ωω ωπ ω ω

∞ ⋅=−∫

2 ' Re( ( '))Im( ( )) '

ω ωω ωπ ω ω

∞ ⋅= −−∫

If Re(Z) is known, Im(Z) can be computed.

� Comparison of computed part and measured partreveals the Kramers Kronig residuals .

1. Approach the desired SOC

2. Wait for x hours until the cell is in stationary mode

� What is x ?

Quelle:

www.iam.kit.edu/wet

IAM-WET

Distribution of relaxation times for the clear sepa ration of loss processes

T = 25 °CSOC = 60 %

15 Hz100 Hz

Quelle:

www.iam.kit.edu/wet

IAM-WET

T = 25 °CSOC = 60 %

15 Hz100 Hz

relaxation time of process n

1111)(

ωτωτωωω

:nnn0, CR=τ

distribution function of relaxation timespol

( )( )

Z j R djτω τωτ

# � :[2]

Quelle:

www.iam.kit.edu/wet

IAM-WET

T = 25 °CSOC = 60 %

15 Hz100 Hz

1111)(

ωτωτωωω

:nnn0, CR=τ

( )( )

Z j R djτω τωτ

# � :[2]

process 1 process 2

ggeneraldistributionfunction

�*,3�*,. �

Quelle:

www.iam.kit.edu/wet

IAM-WET

T = 25 °CSOC = 60 %

15 Hz100 Hz

1111)(

ωτωτωωω

:nnn0, CR=τ

( )( )

Z j R djτω τωτ

# � :[2]

100 Hz

process 1 process 2

�*,3�*,. �

Quelle:

www.iam.kit.edu/wet

process 1 process 2

�*,3�*,. �

1111)(

ωτωτωωω

:nnn0, CR=τ

( )( )

Z j R djτω τωτ

# � :[2]

IAM-WET

T = 25 °CSOC = 60 %

15 Hz100 Hz

100 Hz

Physical meaning of P1, P2 and P3 ?Physical meaning of P1, P2 and P3 ?

Quelle:

www.iam.kit.edu/wet

IAM-WET

Experimental cells for the assignment of loss proce sses

3-electrode setup

IAM-WET-housing

6$2%78!!

6$2%98:3 ;$2%78!!6$2%98:.

Working electrode: Anode or Cathode

Reference electrode: Al-mesh with LTO coating

Counter electrode: Lithium

T = 25 °CSOC = 40 %

• inhouse development• 18 mm electrode diameter• 3-electrode setup[3,4]

Quelle:

www.iam.kit.edu/wet

IAM-WET

Experimental cells for the assignment of loss proce sses

3-electrode setup

IAM-WET-housing

6$2%78!!

6$2%98:3 ;$2%78!!6$2%98:.

Working electrode: Anode or Cathode

Reference electrode: Al-mesh with LTO coating

Counter electrode: Lithium

Measurement results

P1 P2 P3

T = 25 °CSOC = 40 %

• inhouse development• 18 mm electrode diameter• 3-electrode setup[3,4]

Charge transfer of the

cathode PCT,C

SEI-process / charge transfer

of the anode PSEI/CT,A: side

peaks due to the porous

electrode structure

Quelle:

www.iam.kit.edu/wet

IAM-WET

T = 25 °CSOC = 60 %

Quantification of loss processes by equivalent circ uit modeling

� Frequency dependent processes can be simplified simulated

with RQ elements

<=>,= <?@A/=>,B

Quelle:

www.iam.kit.edu/wet

IAM-WET

T = 25 °CSOC = 60 %

Quantification of loss processes by equivalent circ uit modeling

� Frequency dependent processes can be simplified simulated

with RQ elements

� Good fit quality despite simplified model

� Fit delivers resistance and time constant of each process

<=>,= <?@A/=>,B

Quelle:

www.iam.kit.edu/wet

Experimental

IAM-WET

Slow loss processes

ηloss

ηDiff

ηCT/SEI

Quelle:

www.iam.kit.edu/wet

ExperimentalAnalysis of low frequency Electrochemical Processes

IAM-WET

I = 350 mAT = 25 °C

Slow diffusion process PDiff,A/C takes place in the low frequency range

� EIS not applicable

Quelle:

www.iam.kit.edu/wet

IAM-WET

I = 350 mAT = 25 °C

� Time domain measurement

1. Start at OCV-level

2. Apply a current pulse

3. Analyze the voltage curve after cut-off of the current

� cell in stationary mode

Quelle:

www.iam.kit.edu/wet

IAM-WET

I = 350 mAT = 25 °C

� Time domain measurement

1. Start at OCV-level

2. Apply a current pulse

3. Analyze the voltage curve after cut-off of the current

� cell in stationary mode

4. Subtract η0, ηCT,C and ηCT/SEI,A from relaxing overvoltage

� diffusion overvoltage ηDiff,A/C remains

Quelle:

www.iam.kit.edu/wet

IAM-WET

I = 350 mAT = 25 °C

At least two diffusion processes in the cell: anode and cathode

� Fit delivers resistance and time constant :

CDE:: � , ∙ �DE::,. ∙ 1 exp GHIJKK,L ' , ∙ �DE::,3 ∙ 1 exp G

HIJKK,M

Time domain fit model

[5] Pop, V. et al., J. Electrochemical Society, 153 (2006), A2013-A2022

� Relative error below 0.1%

� good fit quality

Quelle:

www.iam.kit.edu/wet

Battery Model

IAM-WET

NOPQQ,B/=(SOC,T)ROPQQ,B/=(SOC,T)

OCV by linear interpolation ofcharge and discharge curve

EISDRT-AnalysisECM TDM

OCV(SOC,T) N (SOC,T)N=>,=(SOC,T)

R=>,=(SOC,T)

N?@A/=>,B(SOC,T)

R?@A/=>,B(SOC,T)

S � TUV, W, , �SXYZ TUV, W C* TUV, W, , C[\]/Y^,_ TUV, W, , CY^,Y$TUV, W, ,% CDE::,_/Y$TUV, W, ,%

Battery Model

Quelle:

www.iam.kit.edu/wet

Results

IAM-WET

�`a � �� /��,� ��,� ��,�/�Simulation of a cell discharge

I = 350 mAT = 25 °C

Quelle:

www.iam.kit.edu/wet

Results

IAM-WET

Simulation of a cell discharge

� Absolute residuals below 30 mV in 90% of the SOC range

� Only at SOCs < 10% the residuals are higher than 30 mV

I = 350 mAT = 25 °C

�`a � �� /��,� ��,� ��,�/�

Elektrochemische Modelle für Lithium-Ionen Batterien MES 10 - Elektrochemische Modelle...

Documents

Kompendium: Li-Ionen-Batterien - DKE

3 Elektrochemische Wandler - Baustelle / Under …whz-cms-10.zw.fh-zwickau.de/mth/praesentationen/Elektrochemische... · Elektronenabgabe = Oxidation Elektronenaufnahme = Reduktion

(# 5816) Elektrochemische Untersuchung biologisch ......(# 5816) Elektrochemische Untersuchung biologisch inspirierter molekularer Metalloxidcluster und deren Redoxverhalten Carsten

Lithium-Ionen Batterien · Lithium-Ionen Batterie neue Wege! Im Vergleich zu herkömmlichen Blei-Säure Batterien bietet die Lithium-Ionen Technologie wesentliche Vorteile. Eine vollständige

Elektrochemische Thermodynamik Wiederholung : Potentiale, Potentialbegriff

Elektrochemische Abscheidung von Metallen und Legierungen ... · Elektrochemische Abscheidung von Metallen und Legierungen aus nichtwässrigen Systemen und Aktivierung von passivierten

Brennstoffzelle - eduhi.at · Brennstoffzelle AK-05/2001 GB3: Elektrochemische Energiewandlung und -speicherung Abteilung ECW: Elektrochemische Wasserstofftechnik Gemeinnützige Stiftung

Fachdidaktische Modelle - Institut für Sportwissenschaft · Fachdidaktische Modelle • Einführung – Hintergrund • „klassische“ Modelle • 1. Sportartenprogramm (Söll)

Elektrochemische Grundlagen der Korrosion - schadenprisma · Zustand das elektrochemische Potential der Reaktion allein über den äußeren, als unendlich anzusetzenden, Widerstand

PRODUKTIONSPROZESS EINER LITHIUM-IONEN- BATTERIEZELLE

Die bio-elektrochemische Brennstoffzelle als Baustein

Magnetismus von Atomen und Ionen

COMSOL · Web viewSo ist der Anwender der Software z. B. in der Lage, Lithium-Ionen-, Blei-Säure- und Feststoffbatterien als physikalisch basierte Modelle zu erstellen und diese

Lithium-Ionen-Batterien für Elektrofahrzeuge

PRODUKT-ROADMAP LITHIUM-IONEN-BATTERIEN 2030

Simultane Elektrochemische Impedanzspektrometrie und ...ak-thermophysik.de/download/gefta/2015/Vortrag_Sarge.pdfSimultane Elektrochemische Impedanzspektrometrie und Kalorimetrie an

Elektrochemische Doppelschicht

10.3 Elektrochemische Gleichgewichte 189...10.3 Elektrochemische Gleichgewichte 189 10.2.3 Anwendung der Leitfähigkeitsmessung Werden bei chemischen Reaktionen in Lösungen Ionen

Elektrochemische und oberflächenanalytische Untersuchungen zur

Ionen: Verschränkung Nicole Stefanov 13.07.2011