Document [original]

Electrochemical Impedance Spectroscopy as an

Analytical Tool for Dynamic Charge Acceptance

Prediction

vorgelegt von

M. Sc.

Sophia Bauknecht

ORCID: 0000-0001-6054-7268

an der Fakultät IV – Elektrotechnik und Informatik

der Technischen Universität Berlin

zur Erlangung des akademischen Grades

Doktor der Ingenieurwissenschaften

– Dr.-Ing. –

genehmigte Dissertation

Promotionsausschuss:

Vorsitzender: Prof. Dr.-Ing. Ronald Plath

Gutachterin: Prof. Dr.-Ing. Julia Kowal

Gutachter: Prof. Dr. rer. nat. Dirk Uwe Sauer

Gutachter: Angel Kirchev PhD, HDR

Tag der wissenschaftlichen Aussprache: 14. September 2023

Berlin 2023

Vorwort

Diese Doktorarbeit entstand in meiner Zeit als Wissenschaftliche Mitarbeiterin

von Dezember 2017 bis März 2023 am Fachgebiet Elektrische Energietechnik

(EET) der TU Berlin.

Prof. Dr. Julia Kowal, meine Doktormutter, hat mich für mein erstes Projekt

am Fachgebiet und damit für Batterien und Elektrochemische Impedanzspek-

troskopie begeistert. Ich möchte mich bei ihr dafür bedanken, dass sie mich auf

diesen Weg gebracht und mich begleitet hat, immer ein offenes Ohr hatte und

mich unterstützt hat, wann immer es nötig war.

Während meiner Arbeit am Fachgebiet EET habe ich unter anderem zwei Pro-

jekte die durch das Consortium for Battery Innovation (CBI) gefördert wurden

bearbeitet. Deshalb möchte ich mich vor allem bei Dr. Matt Raiford, aber auch

allen anderen CBI Mitgliedern bedanken, die mich so herzlich in die CBI-Familie

aufgenommen haben und immer großes Interesse an meiner Forschungsarbeit

gezeigt haben. Durch das CBI war es mir möglich meine Forschungsergebnis-

se regelmäßig in den CBI-Workshops vorzustellen und mit führenden Wissen-

schaftlern zu diskutieren. Die Ergebnisse aus den CBI-Projekten finden sich

zu einem großen Teil in meiner Doktorarbeit wieder. Mit Dr. Eckhard Karden

habe ich so gut wie alle meine Ergebnisse besprochen, ausgewertet und disku-

tiert. Durch seine Nachfragen und Vorschläge ist es mir gelungen das Beste

aus meinem Forschungsauftrag rauszuholen. Deshalb möchte ich mich ganz

herzlich bei ihm bedanken, dass er nie aufgehört hat, noch mehr wissen zu

wollen. Des Weiteren möchte mich bei Dr. Eberhard Meißner bedanken, der

seinen wohlverdienten Ruhestand dafür nutzt, Grünschnäbeln wie mir die Welt

der Batterien zu erklären und sich nicht nur mit Messergebnissen zufrieden-

gibt, sondern auch ganz genau verstehen möchte, welche chemischen oder phy-

III

sikalischen Prozesse diese auslösen. Durch den Einfluss von Dr. Julia Kowal,

Dr. Matt Raiford, Dr. Eckhard Karden und Dr. Eberhard Meißner werde ich wohl

immer eine heimliche Blei-Batterie-Lobbyistin bleiben.

Ich danke meiner Projektleidensgenossin Dr. Begüm Bozkoya für die gute und

fruchtbare Zusammenarbeit und die moralische Unterstützung in hektischen

Workshop-Vorbereitungs-Zeiten. Jederzeit wieder würde ich ein Projekt mit ihr

angehen und wüsste, dass die Ergebnisse großartig werden würden.

Außerdem möchte ich meinen Kollegen danken, die mich auf dem langen Weg

der Dissertation begleitet haben und mir so gute Freunde geworden sind. Beson-

ders hervorheben möchte ich die folgenden drei: Meinen Büronachbarn, Mar-

cel Franke der bei allem wissenschaftlichen Ernst Spaß, Ironie und Witz nie

vergessen hat, Dr. Julian Long der mir gezeigt hat, wie man in effektiven und

automatisierten Arbeiten wahre Meisterschaft erlangt und Paul Martin Luc der

mit seiner akribischen Art den Qualitätsstandart von jedem meiner Vorträge und

Plakate erhöht hat.

Insbesondere möchte ich meinen Eltern für ihre Unterstützung danken. Schon

immer haben sie mir mit viel Liebe ein sicheres Netz geboten und mich moralisch

unterstützt, wodurch ich alles ausprobieren und schaffen konnte. Ich kann nicht

ausdrücken, wieviel mir ihre Hilfe und Führsorge bedeutet. Ohne sie wäre ich

nicht da, wo ich heute bin.

Schluss endlich möchte ich mich bei meinem Seelenverwandten Bastian Matthies

aus tiefsten Herzen bedanken. Für die tollen Jahre, die wir miteinander ver-

bracht haben, die abenteuerlichen Reisen, die wir gemeinsam gemacht haben

und für die Ratschläge, mit denen er mich immer unterstützt. Du und ich – wir

gehören einfach zusammen.

Berlin, 30.09.2023

Sophia Bauknecht

Abstract

Electrochemical storage systems support a wide range of applications in modern

life. Particularly when aligning towards renewable energy sources batteries be-

come indispensable. Batteries were utilized in automotive applications e.g. for

starting, lighting, and ignition (SLI) purposes for many years. However, the re-

cent push towards clean mobility and energy have changed the requirements. To

accomplish the reduction of fuel consumption and CO2emissions regenerative

braking is utilized. Therefore, energy available during braking is stored within

the SLI battery and can be used for starting the vehicle and on-board supply.

However, this raises the necessity to significantly improve the SLI batteries. One

of the most pressing issues is to enhance the dynamic charge acceptance (DCA),

the batteries’ ability to store high amounts of energy in a very short amount of

time. Typically used SLI batteries often have an insufficient DCA. By adding car-

bon additives to the negative electrode [1] an increase of up to three times higher

DCA can be enabled [2]. However, extensive material screenings are needed to

investigate different carbon additives. These are not carried out with mass pro-

duced batteries, but with smaller laboratory test cells, e.g., 2V, 4.5Ah [1]. The

improvement is hampered by the lack of predictability between small test cells

and batteries under realistic long-term vehicle usage conditions. Therefore, new

testing procedures have to be considered.

Within this work several measurement test procedures for DCA determination

have been defined, tested, evaluated, and compared with each other. Influenc-

ing factors on the DCA, such as the state of charge, prior usage, electrolyte con-

centration, temperature, and carbon additives were investigated with these test

procedures. Furthermore, DCA results of various cell layouts were correlated

with battery level tests. Thereby, a best practice methodology for cell-level DCA

measurements was derived. However, these measurement test procedures for

DCA determination are time consuming. Therefore a different approach using

Electrochemical Impedance Spectroscopy (EIS) was investigated.

EIS is a powerful characterization technique to identify electrochemical pro-

cesses, materials, device, and reveal transient behaviour of systems. The influ-

ence of different carbon additives, various cell layouts, and different working

points, such as state of charge, or prior usage, were systematically studied using

EIS. A correlation between material properties found in the parameters of the

EIS measurements and the DCA could be found. Resulting in the development

of a fast prediction method for DCA using EIS, which can decrease the testing

time from several weeks down to less than a day.

Kurzfassung

Elektrochemische Energiespeichersysteme werden überall für verschiedenste

Anwendungen genutzt. Insbesondere im Hinblick auf die Energiewende und

durch die Verwendung von erneuerbare Energiequellen steigen die Anforderun-

gen und die Anzahl der Einsatzgebiete von Batterien. Gerade im Verkehrssektor

sind Batterien ein unverzichtbares Instrument um die Energiewende durchzu-

führen. Batterien werden bereits seit vielen Jahre als Starterbatterien in Fahrzeu-

gen verwendet. Die jüngsten Bestrebungen hin zu sauberer Mobilität haben

jedoch auch die Anforderungen an diese Batterien verändert. Um den Kraft-

stoffverbrauch und die CO2-Emissionen zu reduzieren, wird beispielsweise das

rekuperative Bremsen eingesetzt. Dabei wird die beim Bremsen verfügbare En-

ergie in der Starterbatterie gespeichert und kann anschließend wieder für das

Anfahren und die Bordversorgung verwendet werden. Dies erfordert jedoch

eine erhebliche Verbesserung der Starterbatterien. Die Verbesserung der Ladeak-

zeptanz, d.h. die Fähigkeit der Batterien, große Mengen an Energie in kürzester

Zeit zu speichern, stellt dabei eines der dringendsten Probleme dar. Aktuell

verwendete Starterbatterien weisen oft eine unzureichende Ladeakzeptanz, für

die Nutzung des rekuperativen Bremsens, auf. Doch durch die Zugabe von

Kohlenstoffen an der negativen Elektrode [1] kann eine bis zu dreifach höhere

Ladeakzeptanz erreicht werden [2]. In der Entwicklung dieser Batterien sind

umfangreiche Materialtests erforderlich, um möglichst viele verschiedene Koh-

lenstoffzusätze zu untersuchen. Diese Tests werden mit kleinen Labortestzellen,

z.B. 2V, 4.5Ah durchgeführt [1]. Die Verbesserung der Starterbatterien wird

aber durch die mangelnde Vergleichbarkeit zwischen kleinen Labortestzellen

und ganzen Batterien unter realistischen Langzeitbedingungen im Fahrzeugbe-

trieb erschwert. Daher müssen neue Testverfahren in Betracht gezogen werden.

VII

Im Rahmen dieser Arbeit wurden mehrere Messverfahren zur Bestimmung der

Ladeakzeptanz definiert, getestet, bewertet und miteinander verglichen. Ein-

flussfaktoren auf die Ladeakzeptanz, wie der Ladezustand, die vorherige Nut-

zung, die Elektrolytkonzentration, die Temperatur und verschiedene Kohlen-

stoffzusätze, wurden mit Hilfe dieser Testverfahren untersucht. Darüber hinaus

wurde die Ladeakzeptanz verschiedener Testzellen und -layouts mit Starterbat-

terien verglichen. Die Messverfahren zur Bestimmung der Ladeakzeptanz sind

jedoch zeitaufwändig. Daher wurde ein weiterer Ansatz mit Hilfe der elektro-

chemischen Impedanzspektroskopie (EIS) verfolgt.

EIS ist eine leistungsstarke Charakterisierungstechnik zur Identifizierung von

elektrochemischen Prozessen, Materialien und zur Bestimmung des transien-

ten Verhaltens von Systemen. Der Einfluss verschiedener Kohlenstoffzusätze,

Testzelllayouts und Betriebspunkte, wie z.B. der Ladezustand oder die vorherige

Nutzung, wurde systematisch mittels EIS untersucht. Dabei konnte eine Kor-

relation zwischen den Materialeigenschaften, die in den Parametern der EIS-

Messungen gefunden wurden, und der Ladeakzeptanz von Starterbatterien fest-

gestellt werden. Dies führte zur Entwicklung einer schnellen Vorhersagemetho-

de für die Ladeakzeptanz mittels EIS, die die Testzeit von mehreren Wochen auf

weniger als einen Tag verkürzen kann.

VIII

Contents

List of Abbreviations XIII

List of Variables XV

List of Figures XIX

List of Tables XXIX

1 Introduction and Motivation 1

2 Starting-Lighting-Ignition Batteries 7

2.1 Fundamentals and Functionality . . . . . . . . . . . . . . . . . . . 7

2.1.1 Starting-Lighting-Ignition Battery Design . . . . . . . . . . 8

2.1.2 Main Chemical Reactions . . . . . . . . . . . . . . . . . . . 10

2.1.3 SideReactions.......................... 12

2.2 State-of-the-Art: SLI Battery . . . . . . . . . . . . . . . . . . . . . . 13

2.3 Technology Comparison for SLI Batteries . . . . . . . . . . . . . . 19

2.3.1 Low current Capacity . . . . . . . . . . . . . . . . . . . . . 21

2.3.2 First Pulse of the Cold Cranking Ability . . . . . . . . . . . 24

2.3.3 Second Pulse of the Cold Cranking Ability . . . . . . . . . 31

2.3.4 Charging Regime of LFPs and LABs . . . . . . . . . . . . . 34

2.3.5 Final Comparison for SLI Batteries . . . . . . . . . . . . . . 35

3 Test Cell Preparation and Pretests 37

3.1 Test Cell Preparation with Top-Down Approach . . . . . . . . . . 38

3.2 Test Cell Preparation with Bottom-Up Approach . . . . . . . . . . 41

3.2.1 Deviations between Test Cells . . . . . . . . . . . . . . . . . 46

3.3 Test Cells Built for Testing . . . . . . . . . . . . . . . . . . . . . . . 48

Contents

3.4 Parameters for Testing Diverse Cell Layouts . . . . . . . . . . . . . 50

3.4.1 Electrical Test Plan to examine relevant Parameters . . . . 50

3.4.2 Initial Scaling Parameters . . . . . . . . . . . . . . . . . . . 52

3.4.3 Electrolyte Concentration Correlation with SoC during Con-

stant Current Discharge . . . . . . . . . . . . . . . . . . . . 53

3.4.4 Adjustment of the Electrolyte Concentration . . . . . . . . 57

3.4.5 Verification of the Capacity Scaling Factor . . . . . . . . . . 58

4 Dynamic Charge Acceptance 63

4.1 Standard Measurement Test Procedures for DCA . . . . . . . . . . 63

4.1.1 Single Pulse Charge Acceptance Test . . . . . . . . . . . . . 64

4.1.2 DCA test defined by the European standard . . . . . . . . 68

4.1.3 Ford long-term Run-in DCA Test B . . . . . . . . . . . . . . 74

4.1.4 Comparing the different DCA Test methods . . . . . . . . 77

4.2 Modified Test Procedures for DCA . . . . . . . . . . . . . . . . . . 80

4.2.1 CA2 Test at various SoC after Prior Charge and Discharge 81

4.2.2 DCA Test at 80% SoC after Prior Charge and Discharge . . 82

4.3 Influencing Factors on the DCA . . . . . . . . . . . . . . . . . . . . 84

4.3.1 StateofCharge ......................... 86

4.3.2 Short-term Usage . . . . . . . . . . . . . . . . . . . . . . . . 87

4.3.3 Long-termUsage........................ 96

4.3.4 Electrolyte Concentration . . . . . . . . . . . . . . . . . . . 97

4.3.5 Temperature........................... 100

4.3.6 VoltageLevel .......................... 102

4.3.7 TestCellDesign......................... 103

4.3.8 Carbon Additives at the negative Electrode . . . . . . . . . 106

4.3.9 Technology ........................... 108

4.3.10 Comparing the Influencing Factors . . . . . . . . . . . . . . 110

4.4 Limits of the DCA Measurement Methods . . . . . . . . . . . . . . 111

5 EIS - Fundamentals and Measurement 115

5.1 Literature Survey: What is EIS used for in LABs? . . . . . . . . . . 116

5.2 EIS Measurement on Batteries . . . . . . . . . . . . . . . . . . . . . 117

5.3 EIS at various SoC and Superimposed DCs . . . . . . . . . . . . . 124

5.3.1 Ideal EIS Procedure . . . . . . . . . . . . . . . . . . . . . . . 124

5.3.2 Restrictions for EIS because of Over Voltages . . . . . . . . 126

Contents

5.3.3 Final EIS Procedure . . . . . . . . . . . . . . . . . . . . . . . 132

5.4 Pre-Processing of EIS data . . . . . . . . . . . . . . . . . . . . . . . 135

5.4.1 Kramers-Kronig......................... 136

5.4.2 Distribution of Relaxation Times . . . . . . . . . . . . . . . 137

5.5 Equivalent Electric Circuit Model . . . . . . . . . . . . . . . . . . . 141

5.6 Literature Survey: Interpretation of Equivalent Circuit Elements . 146

5.7 Influencing Factors on the EIS . . . . . . . . . . . . . . . . . . . . . 151

5.7.1 StateofCharge ......................... 151

5.7.2 Superimposed DC . . . . . . . . . . . . . . . . . . . . . . . 152

5.7.3 Short-term Usage . . . . . . . . . . . . . . . . . . . . . . . . 152

5.7.4 Electrolyte Concentration . . . . . . . . . . . . . . . . . . . 153

5.7.5 Temperature........................... 154

5.7.6 Carbon Additives at the negative Electrode . . . . . . . . . 154

5.7.7 StateofHealth ......................... 155

5.8 LimitsofEIS............................... 155

5.8.1 Errors caused by the EIS measurement device . . . . . . . 156

5.8.2 Errors caused by the measurement setup . . . . . . . . . . 160

5.8.3 Errors caused by non-stationary factors . . . . . . . . . . . 161

5.8.4 Errors caused by the current used for preconditioning and

superposition.......................... 170

6 EIS as Analytical Tool 179

6.1 Feasibility Study: EIS as Analytical Tool for Predicting DCA . . . 181

6.2 Correlation between EIS and DCA for Cell with Various Additives 192

6.2.1 Fitting for all Parameters . . . . . . . . . . . . . . . . . . . 195

6.2.2 Fitting for selected Parameters . . . . . . . . . . . . . . . . 205

6.3 Correlation between EIS and DCA for different SoC . . . . . . . . 212

6.3.1 Fitting for all Parameters . . . . . . . . . . . . . . . . . . . 214

6.3.2 Fitting for selected Parameters . . . . . . . . . . . . . . . . 222

7 Conclusion 229

Bibliography 235

List of Abbreviations

AC Alternating Current

A/D Analog-to-Digital

AM Active Mass

AFM Atomic Force Microscopy

AGM Absorbent Glass Mat

BMS Battery Management System

C20 20h discharge Capacity

CA2 Charge Acceptance Test 2

CCA Cold Cranking Ability

CPE Constant Phase Element

D/A Digital-to-Analog

DC Direct Current

DCA Dynamic Charge Acceptance

DCRss Dynamic Charge Real Start-Stop

DL Detection Limit

DRT Distribution of Relaxation Times

ECM Equivalent Circuit Model

EIS Electochemical Impedance Spectroscopy

EFB Enhanced Flooded Batteries

EFB+C Enhanced Flooded Batteries with Current increasing Additive

EN European Standard

H+Hydrogen Ions

H2O Water

H2SO4Diluted Sulphuric Acid

I20 20h Discharge Current

IDC Superimposed DC

ICE Internal Combustion Engine

K-K Kramers-Kronig

KOL Key-Off Load

LAB Lead-Acid Battery

LFP Lithium Iron Phosphate Battery

XIII

List of Abbreviations

LSB Least Significant Bit

LSM Laser Scanning Microscope

N Negative Plate

NAM Negative Active Mass

OCV Open Circuit Voltage

OCV80 Open Circuit Voltage at 80% SoC

P Positive Plate

PAM Positive Active Mass

Pb Lead

PbO2Lead Dioxide

PbSO4Lead Sulfate

PSoC Partial State of Charge

qDCA Quick Dynamic Charge Acceptance

qOCV Quasi Open Circuit Voltage

RC test Reverse Capacity Test

R-C Resistance and Capacitance

Ref-CB Reference, Carbon-Black

RH Relative Humidity

RMS Root Mean Square

RSS Sum of Squares of Residuals

sext Specific External Surface Area

SLI Starting-Lighting-Ignition

SoC State of Charge

SoH State of Health

TSS Total Sum or Squares

VRLA Valve-Regulated Lead-Acid

XIV

List of Variables

AMatrix

bVector

cFactor

CCapacitance

Cform,N Theoretically required Capacity for the formation of N

Cform,P Theoretically required Capacity for the formation of P

CH2OMolar Heat Capacity of Water

CH2SO4Molar Heat Capacity of Sulfuric Acid

CnNominal Capacity

Cn,bat Nominal Capacity of the Battery

Cmol(SoC)SoC dependent Molar Heat Capacity

CPb Molar Heat Capacity of lead

CPbO2Molar Heat Capacity of lead dioxide

CPbSO4Molar Heat Capacity of lead sulfate

cspec(SoC)SoC dependent Specific Heat Capacity

CT(SoC)SoC dependent Heat Capacity

cspez,NAM Specific Capacity for Formation of the NAM

cspez,PAM Specific Capacity for Formation of the PAM

dpart Average Particle Size

∆GFree Reaction Enthalpy

∆HReaction Enthalpy

∆SoC SoC Difference

∆TTemperature Difference

∆VVoltage Difference

∆ZQuantization step of the Impedance

EEnergy

E25◦CEnergy at 25 ◦C

EEff Energy Efficiency

Etotal Total Energy

Euse Usable Energy

err tolerance

List of Variables

fFrequency

F Farady Constant

FScal Scaling Factor

ICurrent

IAC Alternating Current

IAC,LSB Least Significant Bit of the Alternating Current

IAC,max Maximum Measurable Alternating Current

IcAverage Charge Current after prior Charging

IdAverage Charge Current after prior Discharging

IDCA Resulting Dynamic Charge Acceptance Current

IrAverage Charge Current during Real-world micro cycles

I(t)Measured Current

LInductance

LSB Least Significant Bit

mMass

Mtotal Molar Mass

nNumber of Electrons

N Negative Plate

NfNumber of measured Frequencies

NτMultiple of the Number of measured Frequencies

NAM Negative Active Mass

P Positive Plate

PAM Positive Active Mass

φPhase Shift

QHeat

QHeat Flow

QAC,Joule Joule Heat Flow by AC

QDC,Joule Joule Heat Flow by DC

Qrev Reversible Heat

qspec Specific Heat

Qrev Reversible Heat Flow

RResistance

R0Internal Resistance

R2Correlation Coefficient

RKOL Key-Off Load Resistance

sext Specific external surface area

σWarburg coefficient

tTest Duration

τTime Constant

VVoltage

Vav Average OCV

V(t)Measured Voltage

VAC Alternating voltage

VAC,ideal Ideal Alternating Voltage

XVI

VAC,LSB Least Significant Bit of the Alternating Voltage

VAC,max Maximum Measurable Alternating Voltage

ωAngular Frequency

xVector of unknown distribution function

ξCompression Factor

z Number of cells

ZImpedance

Z(jω) Impedance

ZRC Impedance of the R-C

ZARC Impedance of the ZARC element

ZCPE Impedance of the CPE

ZLImpedance of the inductive part

Zmax Maximum Impedance measurable

Zideal,max Maximum Impedance for ideal AC voltage

Zideal,min Minimum Impedance for ideal AC voltage

ZWImpedance of the Warburg element

XVII

List of Figures

1.1 Graphicalabstract. ........................... 3

2.1 The lead-acid (a) cell and (b) battery (adapted from Ref. [7]). . . . 8

2.2 Electrochemical processes at the negative electrode in LABs (own

schematic based on [30]). . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3 (a) The processes within the LAB [36], (b) dissolution of a fine

PbSO4crystal structure during charging (own schematic based on

[34]), and (c) dissolution of a coarse PbSO4crystal structure dur-

ing charging (own schematic based on [34]). . . . . . . . . . . . . . 12

2.4 C20 capacity test at (a) 25◦C, (b) 0 ◦C, and (c) −18◦C (adjusted

fromRef.[6]). .............................. 22

2.5 (a) Capacity and (b) energy of the C20 test (adjusted from Ref. [6]). 23

2.6 First pulse of the CCA at 0◦C (a) voltage, (b) current, and (c) power

(adjusted from Ref. [6]). . . . . . . . . . . . . . . . . . . . . . . . . 25

2.7 First pulse of the CCA at −10 ◦C (a) voltage, (b) current, and (c) power

(adjusted from Ref. [6]). . . . . . . . . . . . . . . . . . . . . . . . . 25

2.8 First pulse of the CCA at −18 ◦C (a) voltage, (b) current, and (c) power

(adjusted from Ref. [6]). . . . . . . . . . . . . . . . . . . . . . . . . 26

2.9 First pulse of the CCA at −30 ◦C (a) voltage, (b) current, and (c) power

(adjusted from Ref. [6]). . . . . . . . . . . . . . . . . . . . . . . . . 26

2.10 Voltage used for total and usable energy determination during the

first pulse (adjusted from Ref. [6]). . . . . . . . . . . . . . . . . . . 27

2.11 (a) Total energy and (b) usable energy during the first pulse of the

CCA test (adjusted from Ref. [6]). . . . . . . . . . . . . . . . . . . . 29

2.12 Energy efficiency during the first pulse of the CCA test (adjusted

fromRef.[6]). .............................. 29

XIX

List of Figures

2.13 Internal resistance (a) absolute values and (b) normalized values

(adjusted from Ref. [6]). . . . . . . . . . . . . . . . . . . . . . . . . 31

2.14 Complete CCA test at 0◦C (a) voltage, (b) current, and (c) power

(adjusted from Ref. [6]). . . . . . . . . . . . . . . . . . . . . . . . . 31

2.15 Complete CCA test at −10 ◦C (a) voltage, (b) current, and (c) power

(adjusted from Ref. [6]). . . . . . . . . . . . . . . . . . . . . . . . . 32

2.16 Complete CCA test at −18 ◦C (a) voltage, (b) current, and (c) power

(adjusted from Ref. [6]). . . . . . . . . . . . . . . . . . . . . . . . . 32

2.17 Complete CCA test at −30 ◦C (a) voltage, (b) current, and (c) power

(adjusted from Ref. [6]). . . . . . . . . . . . . . . . . . . . . . . . . 33

3.1 Cell counting (adapted from Ref. [7]). . . . . . . . . . . . . . . . . 39

3.2 Step by step plate reduction: (a) lifting plate stack, (b) disconnect-

ing unnecessary plates, and (c) replacement with spacers (adapted

fromRef.[7]). .............................. 40

3.3 builting test cells: (a) enveloping the positive plate, (b) merging

the electrodes, (c) adding spacers, (d) electrodes inside the cell

case and (e) assembled test cells. . . . . . . . . . . . . . . . . . . . 44

3.4 Voltage in different EFB cell layouts during the RC test (adapted

fromRef.[7]). .............................. 55

3.5 Electrolyte concentrations in different EFB cell layouts during the

RC test (adapted from Ref. [7]). . . . . . . . . . . . . . . . . . . . . 55

3.6 Voltage in different EFB cell layouts during the C20 test (adapted

fromRef.[7]). .............................. 56

3.7 Electrolyte concentration in different EFB cell layouts during the

C20 test (adapted from Ref. [7]). . . . . . . . . . . . . . . . . . . . . 56

3.8 C20 test results in different EFB cell layouts with (a) current based

on Cnregarding the number of active half plates and acid adjust-

ment and (b) based on the effective capacity C20 given in Table 3.11

(adapted from Ref. [7]). . . . . . . . . . . . . . . . . . . . . . . . . . 59

3.9 CA2 test results in different EFB cell layouts (a) based on Cnre-

garding the number of active half plates and (b) based on effective

capacity C20 given in Table 3.11 (adapted from Ref. [7]). . . . . . . 60

4.1 Graphical visualization of the CA2 test. . . . . . . . . . . . . . . . 65

List of Figures

4.2 CA2 test results in (a) EFB+CAcomplete battery and different test

cells layouts and (b) the middle size cell using different additives

(adjusted from Ref. [10]). . . . . . . . . . . . . . . . . . . . . . . . . 66

4.3 The 10s normalized charge current of the CA2 test (adjusted from

Ref.[10]).................................. 67

4.4 The qDCA and DCRss part of the DCA EN test (adjusted from

Ref. [10], based on [9]). . . . . . . . . . . . . . . . . . . . . . . . . . 68

4.5 Partial results (a) Ic, (b) Id, and (c) Irof the DCA EN test of the

EFB+CAbattery and different cell layouts (adjusted from Ref. [10]). 71

4.6 Partial results (a) Ic, (b) Id, and (c) Irof the DCA EN test of four

different EFB+C middle size cells (adjusted from Ref. [10]). . . . . 71

4.7 EFB+CA: (a-c) Partial and (d) final result of the DCA EN test. . . . 73

4.8 EFB+CB: (a-c) Partial and (d) final result of the DCA EN test. . . . 73

4.9 EFB+CC: (a-c) Partial and (d) final result of the DCA EN test. . . . 73

4.10 EFB+CD: (a-c) Partial and (d) final result of the DCA EN test. . . . 73

4.11 The normalized charge currents and voltages after 6h pause of

the (a,b) EFB+CA, (c,d) EFB+CB, (e,f) EFB+CC, and (g,h) EFB+CD

during 1 week of DCRss and 3 weeks of Ford long-term run-in

DCA test B (adjusted from Ref. [10]). . . . . . . . . . . . . . . . . . 76

4.12 EFB+CA: (a) CA2, (b) DCA EN, and (c) long-term DCA run-in test

B (adjusted from Ref. [10]). . . . . . . . . . . . . . . . . . . . . . . . 78

4.13 EFB+CB: (a) CA2, (b) DCA EN, and (c) long-term DCA run-in test

B (adjusted from Ref. [10]). . . . . . . . . . . . . . . . . . . . . . . . 78

4.14 EFB+CC: (a) CA2, (b) DCA EN, and (c) long-term DCA run-in test

B (adjusted from Ref. [10]). . . . . . . . . . . . . . . . . . . . . . . . 78

4.15 EFB+CD: (a) CA2, (b) DCA EN, and (c) long-term DCA run-in test

B (adjusted from Ref. [10]). . . . . . . . . . . . . . . . . . . . . . . . 78

4.16 Correlation CA2 and DCA EN test (adjusted from Ref. [10]). . . . 79

4.17 Correlation DCA EN test and DCA run-in test (adjusted from Ref.

[10]). ................................... 79

4.18 (a) The preconditioning used for the modified CA2 test (adjusted

from Ref. [26]) and (b) the preconditioning proposed by Smith et

al. (adjusted from Ref. [81]). . . . . . . . . . . . . . . . . . . . . . . 81

4.19 The modified DCA EN test. . . . . . . . . . . . . . . . . . . . . . . 82

4.20 Influences on the DCA (lower part is based on [9]). . . . . . . . . . 85

XXI

List of Figures

4.21 Influence of the short-term usage on the DCA (green [82], purple

[64] and light blue EFB+C1[71] and red EFB+C5[71]). . . . . . . . 88

4.22 Influence of the SoC and the short-term usage on the DCA on an

EFB+CXmiddlesizecell......................... 90

4.23 (a) Fine PbSO4crystals after short pause (b) growing to coarse

PbSO4crystals after a long pause, and (c) the distribution of PbSO4

crystal size over time (adjusted from Ref. [34]). . . . . . . . . . . . 91

4.24 Influence of the pause before the DCA (green [82] and purple [9]). 92

4.25 Distribution of PbSO4crystals after prior (a) charge, (b) discharge,

and (c) pause (adjusted from Ref. [34]). . . . . . . . . . . . . . . . 93

4.26 The average electrolyte concentration and maximum stratification

within two EFB+CXand EFB+CYmiddle size cell after prior (a) charge

and (b) discharge (measured during the modified DCA EN test). . 94

4.27 Modified DCA EN test of the EFB+CXand EFB+CYmiddle size

cell after prior (a) charge and (b) discharge. . . . . . . . . . . . . . 94

4.28 LSM picture of the negative plate surface (a) after charge, (c) after

discharge of the EFB+CXand (b) after charge, and (d) after dis-

charge of the EFB+CY(1-3) at the top, middle, and bottom. . . . . 95

4.29 Electrolyte concentration of the EFB+CXmiddle size cell (a) after

1h charge and (b) after discharge. . . . . . . . . . . . . . . . . . . . 99

4.30 The DCA of the EFB+CXmiddle size cell (a) after 1h charge and

(b)afterdischarge. ........................... 99

4.31 Temperature influence on the DCA at 80% after prior charge [64]. 101

4.32 The electrolyte concentration adjusted to battery level at 80% SoC

in EFB+CXcells (a) after charge from 0% SoC and (b) after dis-

chargefrom100%SoC.......................... 104

4.33 The DCA with electrolyte concentration adjustment to battery level

at 80% SoC in EFB+CXcells (a) after charge from 0% SoC and

(b) after discharge from 100% SoC. . . . . . . . . . . . . . . . . . . 104

4.34 Influence of the SoC on the DCA of different technologies (turquoise

and orange [81], blue [95], red (own measurements) and black [9]). 109

5.1 Galvanostatic EIS measurement principle. . . . . . . . . . . . . . . 118

5.2 (a) Sinusoidal current, and (b) with superimposed DC. . . . . . . 120

5.3 The micro cycling regime at one target SoC and one superimposed

DC (a) cell voltage, (b) superimposed DC, and (c) SoC. . . . . . . 121

XXII

List of Figures

5.4 Simulated EIS example (a) Nyquist plot, (b) absolute value, and

5.5 (a) Ideal EIS procedure, (b) current, and (c) SoC development dur-

ing the micro cycles at any target SoC. . . . . . . . . . . . . . . . . 125

5.6 First trials of the EIS procedure, starting at 95% SoC, adjusting the

SoC via discharge, resulting in voltage overshoots at all SoC. . . . 128

5.7 CC discharge with 1·I20 to 70% SoC and micro cycles with ±1·I20,

not resulting in voltage overshoots. . . . . . . . . . . . . . . . . . 129

5.8 EIS procedure starting at 90% SoC (a-c) after complete charge ac-

cording to the EN, and (d-f) after an incomplete charge without

constant voltage phase. . . . . . . . . . . . . . . . . . . . . . . . . . 130

5.9 The EIS procedure without voltage overshoots. . . . . . . . . . . . 132

5.10 Nyquist plots of the middle size EFB+CXcell (a) complete, (b) pos-

itive, and (c) negative half-cell spectra. . . . . . . . . . . . . . . . . 134

5.11 Negative half-cell spectra of a middle size EFB+CXcell at 50%

SoC, adjusted via discharge, +0.5·I20 superimposed DC, and at

25◦C (a) Nyquist plot, (b) absolute value, and (c) phase angle

withintheBodeplot........................... 136

5.12 EIS measurement, shown in Figure 5.11, its K-K transformation,

and the resulting validated spectra (a) Nyquist plot, (b) absolute

value, and (c) phase angle within the Bode plot. . . . . . . . . . . 137

5.13 DRT of the spectra visualized in Figure 5.11. . . . . . . . . . . . . 140

5.14 Spectra of a R-L series connection. . . . . . . . . . . . . . . . . . . 142

5.15 Spectra of two R-C parallel connections. . . . . . . . . . . . . . . . 143

5.16 Spectra of a R-C parallel connection with and without the depres-

sionfactor................................. 144

5.17 EIS measurement shown in Figure 5.11, its K-K transformation,

the resulting validated spectra, and the fitting result. . . . . . . . . 146

5.18 The chosen ECM (adjusted from Ref. [25]). . . . . . . . . . . . . . 146

5.19 The inductive curl of the middle size EFB+C1negative half-cell

EIS at 50% SoC, 25 ◦C and with -0.5·I20 superimposed DC. . . . . 149

5.20 SoC influence on the (a) internal resistance and (b) the negative

half-cell spectra of the middle size EFB+CXcell using a discharge

current for SoC adjustment, +0.5·I20 superimposed DC, and at 25◦C.151

XXIII

List of Figures

5.21 Influence of the superimposed DC on the negative half-cell EIS

measurement of the middle size EFB+CXat 50% SoC using a dis-

charge current for SoC adjustment, and 25 ◦C............. 152

5.22 Influence of prior usage on the negative half-cell EIS measurement

of the middle size EFB+CXcell at 50% SoC, 25 ◦C, and (a) -0.5·I20,

(b) without, and (c) +0.5·I20 superimposed DC. . . . . . . . . . . . 153

5.23 Influence of the temperature on the negative half-cell EIS mea-

surement of the middle size EFB+CXcell at 50% SoC using a dis-

charge current for SoC adjustment, and (a) -0.5·I20, (b) without,

and (c) +0.5·I20 superimposed DC. . . . . . . . . . . . . . . . . . . 154

5.24 Influence of different tailored carbon additives on the negative

half-cell EIS measurement at 80% SoC, 25 ◦C and with +0.5·I20

superimposedDC. ........................... 155

5.25 The normalized quantisation error of the AC and voltage on the

negative half-cell EIS measurement of the middle size EFB+CXcell

at 25◦C without superimposed DC. . . . . . . . . . . . . . . . . . 159

5.26 The normalized error of the ambient temperature deviation on the

negative half-cell EIS measurement of the middle size EFB+CXcell

at 25◦C without superimposed DC. . . . . . . . . . . . . . . . . . 160

5.27 Influence of the SoC change during measuring one spectra (thick

line = measurement, thin line = maximum possible deviation) of

the middle size EFB+CXcell at 25◦C with +0.5 I20 superimposed

DC (a) the negative half-cell spectra, zoom into (b) high-frequency

part, (c) low-frequency part, and (d) the normalized error. . . . . 162

5.28 The normalized error of the temperature change during one EIS

spectra on the negative half-cell EIS measurement of the middle

size EFB+CXcell at 25◦C with a superimposed DC of (a) -0.5·I20,

(b) -1·I20, and (c) -3·I20.......................... 168

5.29 The normalized error of the temperature change during one EIS

spectra on the negative half-cell EIS measurement of the middle

size EFB+CXcell at 25◦C with a superimposed DC of (a) +0.5·I20,

(b) +1·I20, and (c) +3·I20. ........................ 169

5.30 Ideal (green) and error prone (pink) SoC changes during the EIS

measurement procedure, caused by the quantization error of the

preconditioning current. . . . . . . . . . . . . . . . . . . . . . . . . 170

XXIV

List of Figures

5.31 The normalized quantization error of the preconditioning current

on the negative half-cell spectra of the middle size EFB+CXcell at

25◦C without superimposed DC. . . . . . . . . . . . . . . . . . . . 172

5.32 Ideal (green) and the error prone SoC change caused by the quan-

tization error of the preconditioning (pink) and superimposed cur-

rent (blue) during the EIS procedure. . . . . . . . . . . . . . . . . . 174

5.33 Influence of the quantization error of the preconditioning and the

superimposed DC (thick line = measurement, thin line = maxi-

mum possible deviations) on the middle size EFB+CXcell at 25◦C

without superimposed DC (a) the negative half-cell spectra, zoom

into (b) high-frequency part, (c) low-frequency part, and (d) the

normalizederror. ............................ 175

6.1 DCA EN test results (a) complete cell, (b) middle size cell, and

6.2 EIS procedure used for the feasibility study. . . . . . . . . . . . . . 183

6.3 EIS measurements at 80% SoC (a) complete, (b) middle, and (c) small

size test cells (adjusted from Ref. [25]). . . . . . . . . . . . . . . . . 183

6.4 Zoom into Figure 6.3 (a) complete, (b) middle, and (c) small size

test cells (adjusted from Ref. [25]). . . . . . . . . . . . . . . . . . . 184

6.5 DRT of Figure 6.3 (a) complete, (b) middle, and (c) small size test

cells (adjusted from Ref. [25]). . . . . . . . . . . . . . . . . . . . . . 186

6.6 The chosen ECM (adjusted from Ref. [25]). . . . . . . . . . . . . . 187

6.7 EIS and fit of Figure 6.3 (feasibility study): (a) complete, (b) mid-

dle, and (c) small size cells (adjusted from Ref. [25]). . . . . . . . . 188

6.8 DCA compared to R1(feasibility study): (a) complete, (b) middle,

and (c) small size test cells. . . . . . . . . . . . . . . . . . . . . . . . 190

6.9 DCA compared to CPE1(feasibility study): (a) complete, (b) mid-

dle, and (c) small size test cells. . . . . . . . . . . . . . . . . . . . . 190

6.10 DCA compared to τ1(feasibility study): (a) complete, (b) middle,

and (c) small size test cells. . . . . . . . . . . . . . . . . . . . . . . . 190

6.11 DCA EN test results (a) Icat 80% SoC, (b) Idat 90% SoC, and (c) Id

at 80% SoC of the modified DCA EN test (adjusted from Ref. [26]). 193

6.12 EIS procedure and details at 80% SoC. . . . . . . . . . . . . . . . . 194

6.13 EIS at 80% SoC adjusted via discharge (a) -0.5·I20, (b) without, and

XXV

List of Figures

6.14 DRT of Figure 6.13 (a) -0.5·I20, (b) without, and (c) +0.5·I20 super-

imposedDC................................ 196

6.15 EIS and fit of Figure 6.13 (all parameters) (a) -0.5·I20, (b) without,

and (c) +0.5·I20 superimposed DC. . . . . . . . . . . . . . . . . . . 197

6.16 Absolute error of the fits in Figure 6.15 with (a) -0.5·I20, (b) with-

out, and (c) +0.5·I20 superimposed DC. . . . . . . . . . . . . . . . . 198

6.17 Relative error of the fits in Figure 6.15 with (a) -0.5·I20, (b) without,

and (c) +0.5·I20 superimposed DC. . . . . . . . . . . . . . . . . . . 199

6.18 Modified DCA EN compared to R0(fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC. . . . . 200

6.19 Modified DCA EN compared to L(fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC. . . . . 200

6.20 Modified DCA EN compared to λ(fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC. . . . . 200

6.21 Modified DCA EN compared to Rmin (fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC. . . . . 201

6.22 Modified DCA EN compared to τmin (fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC. . . . . 201

6.23 Modified DCA EN compared to R1(fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC. . . . . 202

6.24 Modified DCA EN compared to CPE1(fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC. . . . . 202

6.25 Modified DCA EN compared to ξ1(fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC. . . . . 202

6.26 Modified DCA EN compared to R2(fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC. . . . . 203

6.27 Modified DCA EN compared to CPE2(fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC. . . . . 203

6.28 Modified DCA EN compared to ξ2(fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC. . . . . 203

6.29 EIS and fit (only fitting selected parameters) at 80% SoC adjusted

via discharge with (a) -0.5·I20, (b) without, and (c) +0.5·I20 super-

imposed DC (adjusted from Ref. [26]). . . . . . . . . . . . . . . . . 207

6.30 Absolute error of the fits in Figure 6.29 with (a) -0.5·I20, (b) with-

out, and (c) +0.5·I20 superimposed DC. . . . . . . . . . . . . . . . . 208

XXVI

List of Figures

6.31 Relative error of the fits in Figure 6.29 with (a) -0.5·I20, (b) without,

and (c) +0.5·I20 superimposed DC. . . . . . . . . . . . . . . . . . . 208

6.32 Modified DCA EN compared to R0(only fitting selected param-

eters) with (a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed

DC (reprint from Ref. [26]). . . . . . . . . . . . . . . . . . . . . . . 209

6.33 Modified DCA EN compared to R1(only fitting selected param-

eters) with (a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed

DC (reprint from Ref. [26]). . . . . . . . . . . . . . . . . . . . . . . 209

6.34 Modified DCA EN compared to R2(only fitting selected param-

eters) with (a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed

DC (reprint from Ref. [26]). . . . . . . . . . . . . . . . . . . . . . . 210

6.35 Modified DCA EN compared to CPE1(only fitting selected pa-

rameters) with (a) -0.5·I20, (b) without, and (c) +0.5·I20 superim-

posed DC (reprint from Ref. [26]). . . . . . . . . . . . . . . . . . . 210

6.36 Modified DCA EN compared to CPE2(only fitting selected pa-

rameters) with (a) -0.5·I20, (b) without, and (c) +0.5·I20 superim-

posed DC (reprint from Ref. [26]). . . . . . . . . . . . . . . . . . . 210

6.37 Modified CA2 test (adjusted from Ref. [26]). . . . . . . . . . . . . . 212

6.38 EIS at 80% SoC adjusted via discharge for the 3P2N EFB+C1test

cell with +0.5·I20 superimposed DC. . . . . . . . . . . . . . . . . . 213

6.39DRTofFigure6.38. ........................... 215

6.40 EIS and fit (all parameters) of Figure 6.38 (a) Nyquist, (b) absolute

valueand(c)phase. .......................... 216

6.41 (a) Relative and (b) absolute error of the fits in Figure 6.40. . . . . 216

6.42 Modified CA2 test compared to R0(fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC. . . . . 218

6.43 Modified CA2 test compared to L(fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC. . . . . 218

6.44 Modified CA2 test compared to λ(fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC. . . . . 218

6.45 Modified CA2 test compared to Rmin (fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC. . . . . 219

6.46 Modified CA2 test compared to τmin (fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC. . . . . 219

6.47 Modified CA2 test compared to ξmin (fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC. . . . . 219

XXVII

List of Figures

6.48 Modified CA2 test compared to R1(fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC. . . . . 220

6.49 Modified CA2 test compared to CPE1(fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC. . . . . 220

6.50 Modified CA2 test compared to ξ1(fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC. . . . . 220

6.51 Modified CA2 test compared to R2(fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC. . . . . 221

6.52 Modified CA2 test compared to CPE2(fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC. . . . . 221

6.53 Modified CA2 test compared to ξ2(fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC. . . . . 221

6.54 EIS and fit (only selected parameters) for a 3P2N EFB+C1test cell

with +0.5·I20 superimposed DC (a) Nyquist, (b) absolute value

and(c)phase............................... 223

6.55 (a) Relative and (b) absolute error of the fits in Figure 6.54. . . . . 223

6.56 Modified CA2 test compared to R0(only fitting selected parame-

ters) with (a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed

DC. .................................... 225

6.57 Modified CA2 test compared to R1(only fitting selected parame-

ters) with (a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed

DC (reprint from Ref. [26]). . . . . . . . . . . . . . . . . . . . . . . 225

6.58 Modified CA2 test compared to R2(only fitting selected parame-

ters) with (a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed

DC (reprint from Ref. [26]). . . . . . . . . . . . . . . . . . . . . . . 225

6.59 Modified CA2 test compared to CPE1(only fitting selected param-

eters) with (a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed

DC (reprint from Ref. [26]). . . . . . . . . . . . . . . . . . . . . . . 226

6.60 Modified CA2 test compared to CPE2(only fitting selected param-

eters) with (a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed

DC (reprint from Ref. [26]). . . . . . . . . . . . . . . . . . . . . . . 226

XXVIII

List of Tables

2.1 Test matrix for the technology comparison for SLI batteries. . . . 20

2.2 The C20 continuous discharge capacity (adjusted from Ref. [6]). . 21

2.3 Comparison of the normalized capacity and energy degradation

during the low discharge current capacity test. . . . . . . . . . . . 23

2.4 The currents used for the CCA test (adjusted from Ref. [6]). . . . . 24

2.5 Comparison of the total energy, unable energy and efficiency degra-

dation during the first pulse of the CCA test. . . . . . . . . . . . . 30

2.6 Passing the standard test and average power during first and sec-

ond pulse of the CCA test (adjusted from Ref. [6]). . . . . . . . . . 34

3.1 Cell layout used for investigating layout effects with the Top-Down

approach (adapted from Ref. [7]). . . . . . . . . . . . . . . . . . . . 38

3.2 Electrolyte analyses in g cm−3before and after the cutting proce-

dure (37%-38% electrolyte concentration), the detection limit (DL)

and the requirement of the VDE 0510 (adapted from Ref. [7]). . . 41

3.3 Textural properties of five synthesized carbon materials, two un-

known additives, and a commercial reference (adapted from Ref.

[71]). ................................... 42

3.4 Formation criteria dependent of cell layout. . . . . . . . . . . . . . 46

3.5 Test cells built from the Top-Down approach. . . . . . . . . . . . . 48

3.6 Test cells built from the Bottom-Up approach. . . . . . . . . . . . . 49

3.7 Test plan to identify basic scaling factors, using an EFB test cell. . 51

3.8 Cnscaling factor based on plate count of complete cell. . . . . . . 53

3.9 Absolute acid volume and nominal acid volume for all cell layouts

(adjusted from Ref. [7]). . . . . . . . . . . . . . . . . . . . . . . . . 57

3.10 Electrolyte concentration at 80% SoC ρ80%H2SO4before and after

adjustment for all cell layouts (adjusted from Ref. [7]). . . . . . . . 58

XXIX

List of Tables

3.11 Comparison of the nominal capacity Cnbased on plate count and

C20 capacity (adjusted from Ref. [7]). . . . . . . . . . . . . . . . . . 59

3.12 CA2 test results with current based on Cnand with current scaled

with C20 (adjusted from Ref. [7]). . . . . . . . . . . . . . . . . . . . 61

4.1 Test plan for DCA of EFB+CA, EFB+CB, EFB+CCand EFB+CDbat-

teries, complete cells, middle and small size cells. . . . . . . . . . 64

4.2 The normalized charge current of the CA2 (adjusted from Ref. [10]). 67

4.3 RKOL depending on cell type and layout (adjusted from Ref. [10]). 70

4.4 Final results of the DCA test according to EN 50342-6:2015. . . . . 72

4.5 Test plan for investigating influencing factors on DCA using the

EFB+CXand EFB+CYcomplete cell, middle and small size cell. . 80

4.6 Preconditioning of DCA tests. . . . . . . . . . . . . . . . . . . . . . 112

4.7 DCAvariation. ............................. 113

5.1 Pre tests for deriving the EIS procedure using an EFB complete

cells, middle, and small size cells. . . . . . . . . . . . . . . . . . . . 127

5.2 EIS test parameters (adapted from Ref. [25]). . . . . . . . . . . . . 134

5.3 EIS test plan for the EFB+C1, EFB+C2, EFB+C3, EFB+C4, EFB+C5,

EFB+Ref, EFB+CX, and EFB+CYmiddle size cells. . . . . . . . . . 135

5.4 EISmeter specific technical data. . . . . . . . . . . . . . . . . . . . . 158

5.5 Temperature change during the EIS measurement on a middle

sizecell................................... 163

5.6 SoC error caused by preconditioning current on a middle size cell. 172

5.7 SoC error caused by preconditioning and superimposed DC dur-

ing all EIS measurements at each SoC on a middle size cell. . . . . 173

5.8 SoC error caused by the preconditioning and the superimposed

DC during the EIS measurements on a middle size cell. . . . . . . 176

5.9 SoC error over time caused by preconditioning and the superim-

posed DC during all EIS measurements at each SoC on a middle

sizecell................................... 177

6.1 Scaling factors according to the number of active plates within a

cell (adjusted from Ref. [25]). . . . . . . . . . . . . . . . . . . . . . 185

6.2 Time constants determined with DRT, Figure 6.5 (adjusted from

[25]). ................................... 186

XXX

List of Tables

6.3 Starting parameters, lower and upper limits for the ECM fit (ad-

justedfromRef.[25])........................... 187

6.4 EFB+CAEIS parameters and errors (adjusted from Ref. [25]). . . . 188

6.5 EFB+CBEIS parameters and errors (adjusted from Ref. [25]). . . . 189

6.6 EFB+CCEIS parameters and errors (adjusted from Ref. [25]). . . . 189

6.7 Correlation coefficient between the DCA EN test results and the

EIS parameters within the first feasibility study. . . . . . . . . . . 191

6.8 EIS parameters, their boundaries and starting values if all param-

etersarefitted............................... 197

6.9 Error between measurements and fit if all parameters are fitted. . 199

6.10 Correlation coefficient between DCA EN partial results and EIS

parameters if all parameters are used for fitting. . . . . . . . . . . 204

6.11 EIS parameters, their boundaries and starting values if only se-

lected parameters are fitted. . . . . . . . . . . . . . . . . . . . . . . 206

6.12 Errors between measurements and fit if only selected parameters

arefitted.................................. 209

6.13 Correlation coefficient between DCA EN and EIS parameters if

only selected parameters are fitted (adjusted from Ref. [26]). . . . 211

6.14 Error between EFB+C1EIS measurements and fit if all parameters

arefitted.................................. 217

6.15 Correlation coefficient between the CA2 test and the EIS parame-

ters after previous discharge if all parameters are used for fitting. 222

6.16 Error between EFB+C1EIS measurements and fit if only selected

parametersarefitted........................... 224

6.17 Correlation coefficient between the CA2 test and EIS parameters

after previous discharge if only selected parameters are fitted. . . 227

XXXI

Introduction and Motivation

Chapter 1

Electrochemical storage devices support various applications of today’s life, such

as wireless communication, power tools, and mobile computing. Batteries have

a high cost compared to other energy sources. However, they decouple the pro-

duction and usage on the time scale and enable wireless energy transportation.

Especially when energy production is aligned towards renewable energy sources

to reduce the emission of pollutants, batteries are unavoidable. Stationary en-

ergy storage devices will be important for stabilizing the grid with volatile en-

ergy production and consumption. Nevertheless, they are and will become even

more prominent in automotive applications.

Lithium-ion batteries are the most popular technology within research. How-

ever, lead-acid batteries (LABs) are still heavily used. LABs had a market share

of 422GWh, compared to 404GWh of Li-ion batteries in 2021 [3]. Following the

predictions, this order will change in 2023 to 660GWh of Li-ion batteries and

450GWh of LABs [3]. In conventional vehicles with an internal combustion en-

gine (ICE), LABs have been used as SLI batteries for over 100 years. LABs are still

used for SLI batteries due to there distinct properties such as 99% recycling rate

in Europe [4], which reduces mining, environmental stress, production energy

and pollutant emission [4]. Especially due to their low costs, which is three to

four times lower than for lithium-ion batteries, the LAB is favored in automotive

applications [5]. Furthermore, LABs are intrinsically safe, which makes system

integration cheaper and easier. And even electric vehicle still contains a LAB for

redundancy of the security attributes, such as steering booster, lightning, or the

antilock braking system when the high voltage system needs to be disconnected.

Thereby a LAB is installed in every vehicle independent of the propulsion sys-

tem.

1 Introduction and Motivation

Since the LABs are still widely used and needed for automotive applications fur-

ther investigations on the dynamic charge acceptance (DCA) of LABs are needed

for micro-hybrid vehicles. Therefore, the following research goals are addressed

within this thesis:

• Investigating the future perspective of the LAB as SLI battery.

• The comparison between different DCA test procedures.

• Translating the standard DCA test procedures form battery to cell level

with and without reduced plate count.

• Investigations on the effects of the cell layout compared to battery results

and thereby the ratio between the positive active mass (PAM), the negative

active mass (NAM), and the electrolyte.

• Definition of an electrochemical impedance spectroscopy (EIS) test proce-

dures at multiple SoC, different prior usage, and various superimposed

direct current (DC) for cell with and without reduced plate count.

• Analysis and prediction of the DCA using EIS.

Figure 1.1 shows the graphical visualization of the content of this thesis, con-

sisting of five main sections. Starting with the comparison between LABs and

Li-ion batteries in SLI applications (Section 2), followed be test cell preparation

(Section 3) used for testing the DCA (Section 4) and EIS (Section 5). Concluding

in the comparison between the DCA and EIS test results (Section 6). Each section

is described in more detail in the following, also including information on where

each of the research goals was addressed and what content was previously pub-

lished.

Figure 1.1: Graphical abstract.

Section 2 summarizes the fundamentals and functionality of the lead-based SLI

battery, such as the design, main reactions, and side reactions. Furthermore, the

LAB is compared with the lithium iron phosphate battery (LFP) within the SLI

application, to answer the first research goal in Section 2.3. The methodology

and the results of this section where previously published by S. Bauknecht, F.

Wätzold, A. Schlösser, and J. Kowal in Batteries 2023, 9(3), 176 "Comparing the

Cold Cranking Performance of Lead-Acid and Lithium-Iron Phosphate Batteries

at temperatures below 0 ◦C" [6].

Even though LFPs might replace LAB-based SLI batteries in the undetermined

future, the LABs are currently the State-of-the-Art SLI technology. Therefore, fur-

ther improvements, investigation, material screenings, and research are needed.

In this work LAB-based test cells are built with two different procedures: the

Top-Down (Section 3.1 summarizes how industrial-manufactured and formatted

batteries are cut into single cells with reduced plate count) and the Bottom-Up

1 Introduction and Motivation

approach (Section 3.2 describes the pasting and preparation of grids and combin-

ing these plates to form cells). The Top-Down approach and first testing results

were previously published by S. Bauknecht, J. Kowal, B. Bozkaya, J. Settelein,

and E. Karden in the Journal of Energy Storage Volume 45, January 2022, 103667

"Effects of Cell Layout and Scaling Factors on Constant Current Discharge and

Dynamic Charge Acceptance" [7]. Section 3.3 summarizes all test cells, their ad-

ditives, cell layout, plate count, and which section describes the test procedure

and the results. Investigations have been carried out with a battery and test cells

with different layouts (3P2N and 2P1N). That way, the influence of the reduced,

asymmetric set of plates on steady-state and dynamic properties could be inves-

tigated.

Test definitions often exist for batteries but not for cell level. The research goal

arises to still get comparable test results at the cell level. Therefore, parameters,

such as voltage, current, capacity, electrolyte amount, and concentration, need

to be adjusted when tests are downscaled from battery to cell level. These pa-

rameters and their influence are investigated in Section 3.4. Moreover, the effects

caused by the plate count and the ratio between PAM, NAM, and the electrolyte

are evaluated, which was also one of the main research goals of this work. These

finding were investigated using test cells build with the Top-Down approach

and were previously published [7]. With the results all standardized battery test

procedures could also be used on the cell level and still result in comparable

DCA results.

While the technology has been known for a long time and the design of bat-

teries for SLI applications did not change much over several decades, new ve-

hicle requirements like electrically assisted brakes and steering systems, cabin

pre-heating during key-off, and micro-hybridization confronts the SLI battery

with substantially increased energy throughput and lead to significant develop-

ments. The newly invented micro-hybrid cars use brake energy recuperation

and stop/start to enable fuel savings up to 5% with little additional costs [8].

Therefore, high DCA, characterized as the rechargeability of vehicle starter bat-

teries [9], is desired to enable the additional functionalities and is an up-to-date

topic for battery and automotive industries. In Section 4, standard DCA test

procedures and the modified DCA procedures for batteries and cells with var-

ious layouts are presented, evaluated, and compared. This way, the research

goal to compare and find correlations between different DCA test procedures

was addressed. Moreover, the correlation between battery and different cell lay-

outs was analyzed. It is known that the negative electrode is the limiting fac-

tor as it cannot accept high charge currents during short pulses [1]. Therefore,

enhanced flooded batteries (EFBs) and various additives were investigated to

improve their performance and meet the new demands. The comparison of dif-

ferent standard measurement test procedures for DCA, the influence of different

cell layouts, and additives was previously published by S. Bauknecht, J. Kowal,

B. Bozkaya, J. Settelein, and E. Karden in Energy Technology 2022, 2101053 "The

Influence of Cell Size on Dynamic Charge Acceptance Tests in Laboratory Lead-

Acid Cells" [10]. The modified DCA tests, presented in Section 4.2, were used to

enable DCA tests at multiple states of function (SoF). Therefore, DCA influenc-

ing factors, such as the state of charge (SoC), prior usage, electrolyte concentra-

tion, temperature, and additives, can be investigated in Section 4.3. Section 4.4

analyzes the limitations and errors introduced during DCA measurements.

To gain a more detailed understanding of the processes within the battery, EIS is

used as an analytical tool. EIS is a widely used standard characterization tech-

nique to identify electrochemical processes to characterize materials or devices

[4], to measure the polarization behavior, non-linear processes, and dynamics

in the frequency domain [11]. Research fields like medicine, biology, and ge-

ology have used EIS for various applications [12]. The first studies on battery

impedance were made in the 1940s with a limited frequency range [13] identify-

ing the AC resistance. This approach is still used to estimate the SoC and state

of health (SoH) of lead-acid batteries [14, 15]. By increasing the frequency range,

the capacitive behavior of the impedance could also be used to estimate SoC [16,

17, 18], SoH [19, 20, 21, 22, 23] and, SoF [24] estimation.

Section 5 summarizes what EIS is and can be used for and how it is applied for

batteries and cells. One goal of this thesis was to investigate test cells at various

SoC, adjusted with charge, or discharge current, with and without superimposed

DC. Therefore, an EIS procedure is suggested in Section 5.3. The pre-processing

of the obtained data is summarized in Section 5.4. Furthermore, EIS is used to

develop and parameterize battery simulation models. The evaluation using an

equivalent circuit model (ECM) is illustrated in Section 5.5. The ECM’s interpre-

tation of the parameters obtained and conclusions on the processes shown with

1 Introduction and Motivation

the spectra are stated in Section 5.6. Section 5.7 investigated the most important

influencing factors on the EIS. The possible error sources during EIS measure-

ments are investigated in Section 5.8.

Screening active materials with different additive combinations for DCA im-

provements is time-consuming. The processes limiting the DCA and mecha-

nisms by which additives achieve substantially higher DCA are not fully under-

stood yet. Since EIS with a wide frequency range can show the electrochemical

processes within a battery or cell, it was used as an analytical tool to predict the

DCA, summarized in Section 6. The correlation between the ECM fitting param-

eters obtained from the EIS and the DCA test results were investigated within

a first feasibility study by S. Bauknecht, J. Kowal, B. Bozkaya, J. Settelein, and

E. Karden in Batteries 2022, 8(7), 66 "Electrochemical Impedance Spectroscopy

as an Analytical Tool for the Prediction of the Dynamic Charge Acceptance of

Lead-Acid Batteries" [25], and described in Section 6.1.

Since the results of the first feasibility study were reasonably good, a more de-

tailed EIS procedure was investigated. 2V, 20Ah (3P2N) test cells, containing

eight different negative electrodes, were analyzed with multiple superimposed

DC, various SoC adjusted via a charge, or discharge current, summarized in Sec-

tions 6.2 and 6.3. These results have been previously published by S. Bauknecht,

J. Kowal, J. Settelein, M. Föhlisch, and E. Karden in Batteries 2023, 9(5), 263

"Dynamic Charge Acceptance Compared to Electrochemical Impedance Spec-

troscopy Parameters: Dependencies on Additives, State of Charge and Prior Us-

age" [26].

Two different fitting procedures were used. Firstly, the fitting of all parameters

was executed, resulting in minimal fitting errors. On the downside, many free

variables impacting each other need to be evaluated, which hinders identify-

ing a correlation between the EIS parameters and the DCA. Therefore, a second

approach was evaluated where parameters identified as independent of the ad-

ditives or the current SoF and the compression factors of the constant phase ele-

ments (CPEs) were kept constant thought out all fits. Consequently, only a few

parameters were left for fitting, increasing the error between the measurement

and the fit but enabling the identification of a correlation between the remaining

EIS parameters and the DCA.

Starting-Lighting-Ignition

Batteries

Chapter 2

In 1859, Gaston Planté discovered 1859 that a useful discharge current could

be drawn from a pair of lead plates immersed in a sulfuric acid solution and

subjected to a charge current [27]. This can be seen as the birth of the lead-

acid battery (LAB). In the 19th century, the LAB was already used for electric

propulsion and starting-lighting-ignition (SLI) of vehicles. Thereby, the SLI bat-

tery describes the central part of the multiple functions of a LAB in automotive

applications. Nowadays, LABs continue to be used within all automotive appli-

cations.

Section 2.1 explains the fundamentals and functionality of the lead-based SLI

battery, such as the design, main reactions and side reactions. Section 2.2 dis-

cusses the State-of-the-Art; requirements, additives at the electrodes, future chal-

lenges and opportunities. Furthermore, the first research goal is adressed, dis-

cussing a possible replacement of the State-of-the-Art lead-acid-based SLI tech-

nology with lithium iron phosphate (LFP) batteries. This is summarized in Sec-

tion 2.3. Therefore, six batteries, namely two LABs and four LFPs, have been

tested regarding their capacity at 25 ◦C, 0 ◦C, and −18 ◦C and regarding their

cold crank capability at 0◦C, −10◦C, −18 ◦C, and −30 ◦C.

2.1 Fundamentals and Functionality

Although design adjustments have been necessary, fundamental electrochem-

istry remained unchanged for over 150 years. Even with changing demands, the

LAB continues to be a crucial factor in automobile applications in the future [28].

2 Starting-Lighting-Ignition Batteries

2.1.1 Starting-Lighting-Ignition Battery Design

A lead-acid cell, shown in Figure 3.3 (a), contains several positive and negative

plates (N), where the active mass (AM) is pasted on grids that work as a current

collector. Either of them is placed inside envelopes which act as separators and

prohibit short circuits on the one hand but have to provide ionic conductivity on

the other hand. At the top of each plate is a lug, which allows to connect all plates

of the same polarity by a strap. Intercell connectors built a series connection of

multiple cells. an SLI battery consists of six cells, visualized in Figure 3.3 (b).

(a) (b)

Figure 2.1: The lead-acid (a) cell and (b) battery (adapted from Ref. [7]).

At a fully charged state, the positive active mass (PAM) consists of lead dioxide

(PbO2), and the negative active mass (NAM) consists of lead (Pb). Both masses

are highly porous to provide a maximum electrode surface. The electrolyte of

LABs is diluted sulphuric acid (H2SO4).

The electrolyte in LABs provides ionic conductivity and serves as an electro-

chemical reactant. Batteries with a fluid electrolyte are called flooded or vented

LABs. This design allows an interchange of gas and fluid with the surroundings.

Previously each cell was closed by a screw-in plug which could be removed for

a refill of the cell with distilled water. Nowadays, flooded batteries used for SLI

applications have a closed container because the water loss is low (<3g Ah−1

[29]) and refilling water is no longer necessary. In this work, only flooded bat-

teries have been tested. They are separated into three types:

• conventional flooded batteries,

2.1 Fundamentals and Functionality

• enhanced flooded batteries (EFBs), with additional design features for micro-

hybrid applications, to significantly improve the starting performance, cy-

cling capability, and service-life [28] and

• EFB with improved performance of the negative electrode (EFB+C), where

the +C stands for higher current rates due to an improved dynamic charge

acceptance (DCA).

Both battery types; EFB and EFB+C, are tested during this thesis. Conventional

flooded batteries are not tested during this thesis.

Another alternative battery design is the sealed or valve-regulated lead-acid

(VRLA) battery. The development of the VRLA battery in the 1970s was a ma-

jor breakthrough. If the electrolyte is immobilized as gel or inside an absorbent

glass mat (AGM) and pressure-relief valves are used, this battery was designed

for a higher cycle lifetime, was shake-proven, and enabled variable positioning.

However, a refill is impossible. Therefore, water loss due to gassing has to be re-

duced to a minimum, and the VRLA batteries are inherently more heat sensitive

than their flooded counterparts.

The nominal capacity Cnof a typical flooded automotive battery for passenger

cars ranges from 35Ah to 135Ah. This value corresponds to the dischargeable

amount of Ahs during a 20h constant-current discharge. The cell potential of a

single lead-acid cell is approximately 2V at equilibrium state. The typical design

of a flooded automotive battery is a series connection of six cells, resulting in a

voltage of 12V. The cells are connected by inter-cell-connectors which are not

accessible to the user. Only the current collectors of the negative electrode of the

first cell and the current collectors of the positive electrode of the sixth cell have

terminals outside the battery and can therefore be connected.

Safety is one of the biggest concerns of the car making-industry nowadays. How-

ever, potentially hazardous sulfuric acid and lead are the main components within

a LAB. As long as these materials are inside a battery, they do not present signifi-

cant risks to customers or the environment [28]. Even more, the LAB technology

is currently the only battery technology that is operated in a closed loop with

more than 99% collected and recycled batteries in Europe [28]. This way, a LAB

is comprised of 85% recycled material [28].

2 Starting-Lighting-Ignition Batteries

2.1.2 Main Chemical Reactions

The main chemical equations within a LAB are:

Negative electrode: Pb +H2SO4←→ PbSO4+2H++2e−

Positive electrode: PbO2+H2SO4+2H++2e−←→ PbSO4+2H2O

Overall battery reaction: Pb +PbO2+2H2SO4←→ 2PbSO4+2H2O

Figure 2.2 schematically shows the electrochemical processes at the negative

electrode in LABs. During discharge, the sulfuric acid ions (HSO−

4) within the

electrolyte migrate to the negative electrode and react with the lead (Pb) to pro-

duce the nonconductive, solid product of lead sulfate (PbSO4) and hydrogen

ions (H+). Two electrons (2e−) are released during this process. Thereby, a flow

of electrons through the external circuit to the positive electrode is enabled. Only

the electrochemical processes at the negative electrode are visualized because

one of the main targets of this work is the DCA, limited mainly by the negative

electrode.

Figure 2.2: Electrochemical processes at the negative electrode in LABs (own

schematic based on [30]).

At the positive electrode lead dioxide (PbO2) reacts with the sulfuric acid (H2SO4)

and the two electrons to PbSO4and water (H2O). Thus, during discharge, PbSO4

progressively develops in equal quantities at both electrode polarities, which

is also revered to as ‘double-sulfate theory’ first suggested by Gladstone and

Tribe in 1882 [31]. At the beginning of discharging, fine PbSO4crystals are grow-

ing, and with time, they grow further to coarse crystals. The crystal size highly

depends on time, state of charge (SoC), temperature, and discharging current.

2.1 Fundamentals and Functionality

These influencing factors are discussed further in Section 4.3 if the crystals de-

veloped during discharging also affect the charging reaction.

Fine crystals are of the size < 100nm while coarse crystals are > 100nm [32]. The

pore diameter (of NAM ≈1µm, while for PAM only ≈0.1µm [33]) is limiting the

maximum crystal size through the pore walls [33] but is also determining the ac-

tive reaction surface area, which is ten times higher at the positive electrode [34].

Moreover, the bigger pore volume in the NAM causes much farther distances for

transport between the dissolved PbSO4crystals with a pore to the reaction sur-

face of the active material. At 80% SoC the NAM consists of 37vol% Pb, 6vol%

PbSO4and 57vol% pores. The PAM composition consists of a similar order of

magnitude at 80% SoC: 45vol% PbO2, 7vol% PbSO4and 48vol% pores. The

processes within a LAB and a visualization of different PbSO4crystal structures

at the negative electrode are shown in Figure 2.3. The electrolyte concentration

(flooded SLI: ρH2SO4=1.28 gcm−3at 100% SoC and VRLA SLI: 1.29 - 1.33g cm−3

at 100% SoC) decreases linearly during discharging. Thereby, the relative elec-

trolyte concentration can be correlated with the SoC of the cell. Since the sulfuric

acid electrolyte is an active participant in the cell reaction of LABs, greatly im-

pacts discharge and charge processes [35] on both electrodes. It is known that in

modern SLI flooded battery designs, the capacity is limited by the sulfuric acid

[35].

The electrochemical processes at the electrodes are reversed during the charg-

ing process, visualized in Figure 2.3. The fine PbSO4crystals are first dissolved

during charging events. Because of their higher reaction surface area, the sol-

ubility of fine crystals is bigger than the solubility of coarse crystals. Moreover,

the average dissolution distance of fine PbSO4crystals is shorter, further increas-

ing the charging reaction rate. As the cell is almost fully charged, the majority

of the PbSO4will have been converted back to Pb or PbO2and further charging

will increase the evolution of hydrogen at the negative electrode and oxygen at

the positive electrode. With traditional cell designs, this will result in a loss of

water from the cell electrolyte solution. In contrast to the discharge process, the

relative electrolyte concentration cannot be correlated with the SoC of the cell

until near the end of the charge when gassing provides a good mixture of the

electrolyte solution [35].

2 Starting-Lighting-Ignition Batteries

Figure 2.3: (a) The processes within the LAB [36], (b) dissolution of a fine PbSO4

crystal structure during charging (own schematic based on [34]), and

(own schematic based on [34]).

2.1.3 Side Reactions

In addition to the main reaction, there permanently exist side reactions. There

are two side reactions that are referred to as gassing reactions. Firstly, the oxygen

evolution at the positive electrode

2H20−→ O2+4H++4e−

and secondly, the hydrogen evolution at the negative electrode

4H++4e−−→ 2H2.

Overall, this cases water loss

2H20−→ 2H2+O2

exist as long as the cell voltage is higher than the equilibrium potential of this

reaction of 1.23V. Since the equilibrium potential of the gassing reaction is be-

low the equilibrium potential of the LAB system, water is electrolysed perma-

nently. This results in self-discharge of the battery because the electrons released

at the negative electrode, according to the main equation, are accepted by the

hydrogen, and the oxygen evolved during the gassing reaction at the positive

electrode provides the necessary electrons for the main reaction. However, the

rate of gassing during discharge and the open-circuit conditions is relatively low,

and therefore, the self-discharge is also low.

2.2 State-of-the-Art: SLI Battery

In VRLA batteries, the electrolyte is immobilized, thereby small gas channels

allow a gas transport of oxygen to the negative electrode where recombination

of oxygen with hydrogen to water is possible:

O2+4H++4e−−→ 2H2O.

As a consequence, the water loss is primarily suppressed in VRLA batteries.

Oxygen can recombine in a flooded cell as well. However, the gaseous diffu-

sion is by an orders of magnitude faster compared with the oxygen diffusion in

dissolved form. Therefore, the recombination rate in flooded LABs is negligible

compared to the rate in VRLA batteries.

Corrosion is one of the main aging effects of LABs but is also counted as a side

reaction at the positive electrode

Pb +2H2O−→ PbO2+4H++4e−.

2.2 State-of-the-Art: SLI Battery

From 1910 to 1930, internal combustion engine (ICE) vehicles gained market

share rapidly, and manual cranking became unnecessary after Cadillac’s intro-

duction of electric starter motors in 1912. The initially used magnetic ignition

was replaced in 1925 by a lower-cost battery ignition introduced by Bosch. This

new invention required a rechargeable battery. Since then, the LAB has been

used for electric propulsion, and SLI of vehicles [37, 38, 39] and remained the

most widely used energy storage system for ICE vehicles up to today. The en-

ergy storage system used for ICE vehicles always used to have a broad range of

requirements [28]:

• high safety demand

• simple control

• low cost

• light weight

• reliability under a broad range of ambient conditions such as:

–temperature rage from −18 ◦C up to 75◦C

–mechanical robustness like tilting and vibration resistance

2 Starting-Lighting-Ignition Batteries

–safety against leakage over cycle life

–no or at least low water consumption level

• discharging ability for various operation conditions:

–starting the ICE with more than 200A for several seconds

–cold-cranking ability

–high voltage quality during regular operation

–key-off load supply with some mA over hours and days

–supply energy in emergency mode during generator break down

–resistance to deep discharge

• charging ability for various operation conditions:

–limited voltage supply

–a complete recharge is not always possible

–endurance ability against overcharge

Even though the fundamental electrochemistry of the LAB remained unchanged

over the last 150 years, it has been continuously and successfully adapted to meet

new performance requirements. Over the last years, LAB improvements have

concentrated on reducing lead consumption, corrosion resistance, cold crank

performance, water loss reduction, and reliability. For example, a lower paste

density results in a higher cold crank, and changes in mass quantities and ra-

tios were used to overcome premature capacity loss effects. The thickness of

the grids has been reduced from 2mm in the 1960s to about 0.8mm nowadays

[28]. This was only possible due to the improvements of the casting technol-

ogy and enhancements of the charge control systems for batteries, prohibiting

over charge and thereby minimizing corrosion of the positive grid. Removing

antimony from the grid drastically reduced water consumption within the LAB.

However, other alloys had to be found to maintain mechanical hardness, im-

prove paste adhesion and corrosion protection. Moreover, the usage of non-

woven scrims attached to the positive plate (P) allowed higher mass loading,

mass density and has significantly improved cycle-life by the provision of me-

chanical support and, to some extent, reduced acid stratification [40]. The scrims

consist of glass or synthetic fibers or a combination of both and typically replace

the pasting paper.

2.2 State-of-the-Art: SLI Battery

The driving force behind the lead acid battery innovation has been cost reduc-

tion. This has resulted in many process optimizations. Two of the most signifi-

cant cost-saving improvements have been the automatizing the battery assembly

lines and introducing modern cost- and energy-efficient formation [28]. The con-

tinuous plate-making technology is probably the most recent advancement [28]

resulting in a very low-cost battery technology nowadays.

Shortly after introducing the electric self-starters for automobiles in 1912, various

chemical solutions were proposed to overcome the biggest threat to the power

performance; the tendency of the sponge-like lead active material of the negative

plate to densify during service. For automotive LABs, it has become standard

practice to use a combination of three additive expanders; barium sulfate, ligno-

sulfonate, and carbon (less than 1wt% of the negative mass, with carbon content

less than 0.2wt% [28]). Willihnganz et al. showed that lignin and barium sulfate

are responsible for improving the capacity [41, 42] . The barium sulfate parti-

cles act as nuclei for the formation of lead sulfate during discharge. This way,

lead sulfate cristals are smaller and more uniformly distributed throughout the

spongy lead active-mass [41, 42]. Now barium sulfate includes the nanoscale

to improve the discharge performance and recovery from discharge, and the

cold cranking ability (CCA) [43]. Organic additives, like wood flour and sub-

sequently lignin extracts from the paper-making industry, were first used by

accident as leachate from wooden battery cases and separators. However, the

life cycle performance crashed without its presence when advancing to plastic

cases and separators [43]. Therefore, organic additives were added to the neg-

ative plates to stabilize the cycle life and the capacity markedly, increasing the

performance under engine-starting conditions [44]. The fiber was historically

added as a rheological paste strengthening agent during drying with no chem-

ical or electrochemical performance inferred [43]. Fiber is now used to enhance

long-term plate robustness in cycling [43]. The carbon additive was originally

used as a pigment to differentiate between the positive and the negative plates

visually [43]. Nowadays, amorphous carbon, also known as lampblack or gas

carbon black, is a hotly discussed and highly diversified performance additive

offering functional gains across many applications and is thereby used with a

loading up to 5wt% [43]. For example, it improves the conductivity of the dis-

charge product and assists in the formation of pasted plates [28]. More and more

carbon additives are also used for enhancement of the DCA.

2 Starting-Lighting-Ignition Batteries

Recent developments have revealed that including additional carbon in the NAM

beyond normal expander level enhances charge efficiency under high-rate charge

conditions, occurring in vehicles with regenerative braking, and obtains a longer

life under the same operating conditions. These benefits were already demon-

strated in VRLA batteries operating under partial state of charge (PSoC) con-

ditions in electric vehicle and photo voltaic power applications [45, 46]. These

works have shown that batteries with standard levels of carbon failed during

short bursts of charge at high current densities due to the builtup of lead sul-

fate in the negative plate. Whereas the positive plate was fully charged. More-

over, reference electrode measurements during charge events visualized a lim-

iting role of the negative electrode because of its larger polarization magnitude

[43].

Starting in 2008 in Japan, carbon additives found their way into 12V EFB bat-

teries for stop-start and micro-hybrid applications. However, the new carbon

NAM additives come with increased water consumption and gassing within

over-charge test specifications in Europe, and North America [47] and decreased

capacity and cold-cranking performance [48]. Nevertheless, some carbon types

enable up to three times higher stabilized DCA [49] and improve the cycle-life

at PSoC but have only minimal effect on the hydrogen overvoltage. In recent

years, there have been many discussions on the functions by which the carbon

component can enhance the battery performance [50], also visualized with other

DCA influencing factors in Figure 4.20:

• Carbon enhances the utilization of the AM during charge, and discharge

events by improving the electronic conductivity [43].

• Carbon additives may obtain the optimal pore structure within the AM

[50].

–Thereby obtaining a higher surface area of the AM. By increasing the

active surface area the capacitive function [28] is also increased as well

as the charge transfer reactions. Both lead to an increased DCA.

–Maintain continuous electrolyte access through the channels of the

structure. A supply of lead ions is only possible with access to the

electrolyte deposit.

2.2 State-of-the-Art: SLI Battery

–It is significantly responsible for obstructing the growth of lead sul-

fate crystals, mainly deposited inside the pores. Smaller PbSO4crys-

tals positively affect the dissolution and diffusion processes. Smaller

PbSO4crystals have a higher surface area and, due to Ostwald-Ripen-

ing, also a higher solubility but a smaller crystal size also decreases the

diffusion distance [34]. All are resulting in a higher lead ion supply

and thereby increased DCA.

• Recent research investigations have suggested that the effectivity of DCA

improving carbons is based on their usage as a deposit for lead ions. This

would enable a sufficient supply of lead ions during charging, increasing

the DCA [43].

Most research efforts have improved the NAM [9] as this seems to be the DCA

limiting factor. However, there has also been an investigation on the PAM [51],

where lead dioxide was formed on a pure lead substrate with an antimony alloy.

It was found that by increasing the antimony amount, the lead dioxide particles

became smaller, increasing the positive electrode’s reaction surface area. How-

ever, antimony in the alloy does not affect the size of lead sulfate crystals. Since

the surface area of the PAM is greater compared to the NAM [50], the relative

effect is smaller than the NAM improvement.

To overcome the limits of the classic automotive flooded battery and make it

suitable for micro-hybrid applications, the battery designs and materials have

been improved and resulted in EFBs. This new technology almost matches the

performance and durability of automotive VRLA batteries at substantially lower

cost [28]. A huge advantage of the newly developed EFB is the similar design to

an SLI battery which allows using the same production machinery to increase the

productivity [28]. The new technology combines the following advances [28]:

• less shedding of AM through scrims to reinforce the positive plate,

• reduced acid stratification by the utilization of construction elements that

use the natural movement of the vehicle to agitate the electrolyte,

• increased deep- and partial SoC cycling capability via advancements in cell

design, mass ratios, and mass densities,

• improved protection of the negative lugs against corrosion through grid

alloys,

2 Starting-Lighting-Ignition Batteries

• optimized usage of lead by including more and/or thinner plates and

• enhanced negative-plate performance for improved charge acceptance by

adding extra carbon additives.

It has been forecast that LABs most likely continue to play a key factor in auto-

mobile applications in the future [28] with an increase of a world wide demand

of 2 −3% per year [52, 53]. To achieve this, the LAB will need to adapt to the

future trend of [28]:

• An increasing number of loads:

–Introducing new electric functions which are essential for safety e.g.,

autonomous driving.

–Further replacement of mechanical functions by electric devices.

–A new level of voltage quality, power performance, and storage sys-

tem reliability.

• The battery operation under PSoC condition:

–Enabling energy recuperation through regenerative braking.

–Allowing to switch off the engine at car stop events via the stop/start

functions.

–Continuous decrease of fuel consumption and the CO2emissions.

Even though the ongoing adaptation of new demands and the stated forecasts

draw a bright future for LABs as SLI batteries, it can not be ignored that, for the

first time since its introduction as SLI battery a century ago, the LAB does not

only have to meet the challenges imposed by new vehicle technologies but is also

confronted with the competition from other battery chemistries [28, 54]. This

development is because advanced battery technologies are progressing from the

initial niche markets like luxury sports cars which can afford a very high price

for the imposed improvements [55]. However, lithium-ion batteries would not

only provide desirable weight savings, improved charge acceptance, and cycling

capability [28] but would also introduce safety risks, questionable reliability, and

high controlling complexity. LABs are considered extremely safe because of their

aqueous electrolyte that makes battery fires, and explosions an extremely rare

event [28]. A comparison between lithium-based and LAB-based SLI batteries

was made in the following section.

2.3 Technology Comparison for SLI Batteries

Nowadays, a typical SLI battery is based on LABs. The ability of this technology

of uncompromised CCA at low temperatures ensured a reliable engine start at

any ambient temperature over the last decades. A comparison of the State-of-

the-Art LAB-based SLI battery with lithium-based batteries has been published

[6]. The results will be discussed in the following.

Passenger car gasoline engines require up to 2kW for the ignition process [56].

Diesel engines require even more, up to 2.6kW, for starting the engine [56]. Av-

erage currents during engine start range from 290A to 620 A [57] for a period of

0.3s to 3s depending on the motor type and the ambient temperature. Temper-

atures below 0 ◦C increase the current requirement and duration of the process

[56, 57]. Discharging at these currents results in relatively high voltage drops,

and therefore, most onboard power supply consumers are designed for voltages

down to 6V [58].

Optimization of all automotive components, e.g., weight reduction, bring lithium-

ion batteries into the focus of SLI applications. Porsche announced 2009 an LFP

starter battery as an add-on option for selected models. This reduces the weight

by approximately 10kg [55]. Despite higher cost LFPs have become an alterna-

tive for premium vehicles in Europe, America, and Asia [59]. However, there

is no common standard to evaluate the suitability of LFP starter batteries, espe-

cially for low temperatures. Cold-cranking tests are described for 12V LABs in

the European Standard (EN) [60].

Technologies based on lithium can provide a very high energy and power den-

sity. This could result in the opportunity to drastically decrease volume and

mass in relation to the power while increasing the available energy. A weight

reduction of 50% is predicted using Li-ion batteries [59]. However, the general

downside of lithium technologies is their narrow temperature range for opera-

tions, and it is lacking safety. For this reason, LFPs, a suitable technology for SLI

applications, are chosen for the subsequent investigation. LFPs are known to be

one of the safest lithium technologies because they do not produce oxygen dur-

ing thermal runaway. Furthermore, the nominal voltage of four LFPs in series is

4·3.3V = 13.2V which is close to the nominal voltage of LAB 6·2V = 12V. Both

2 Starting-Lighting-Ignition Batteries

charging voltages 4·3.6V = 14.4V and 6·2.4 V = 14.4V are identical. Therefore,

using an LFP as an SLI battery would minimize additional vehicle adaptations.

Table 2.1: Test matrix for the technology comparison for SLI batteries.

Test

order Procedure Details in Visualized in

1 C20 Test at 25◦C Section 2.3.1

2 C20 Test at 25◦C Section 2.3.1 Figures 2.4 (a), 2.5,

Table 2.3

3 C20 Test at 0◦C Section 2.3.1 Figures 2.4 (b), 2.5,

Table 2.3

4 C20 Test at −18 ◦C Section 2.3.1 Figures 2.4 (c), 2.5,

Table 2.3

5 CCA Test at 0◦C Sections 2.3.2, 2.3.3 Figures 2.6, 2.11, 2.12, 2.14,

Tables 2.5, 2.6

6 CCA Test at −10 ◦C Sections 2.3.2, 2.3.3 Figures 2.7, 2.11, 2.12, 2.15,

Tables 2.5, 2.6

7 CCA Test at −18 ◦C Sections 2.3.2, 2.3.3 Figures 2.8, 2.11, 2.12, 2.16,

Tables 2.5, 2.6

8 CCA Test at −30 ◦C Sections 2.3.2, 2.3.3 Figures 2.9, 2.11, 2.12, 2.17,

Tables 2.5, 2.6

Even though LFPs seem to have a promising opportunity to be used as future SLI

batteries, some questions remain unclear until now. It needs to be proven if LFPs

have similar or even better CCA at low temperatures than LAB. Therefore, two

test regimes were evaluated to answer this question [6]. First, the comparison

of the low current discharge capacity at different temperatures. Moreover, the

comparison of the CCA using the EN at different temperatures. The test matrix,

including cross-references to the corresponding sections and figures, is shown in

Table 2.1. Using the EN, LFPs must demonstrate if they can meet the demand

met by the LABs used in vehicles during the last year [60].

2.3 Technology Comparison for SLI Batteries

2.3.1 Low current Capacity

In order to compare LABs and LFP technologies, six batteries were tested. Two

LABs, a 12V, 50Ah (6s1p) and a 12 V, 92Ah (6s1p), both from the same com-

pany, were tested. For the LFP battery packs, four different batteries were eval-

uated. The LFP packs were built using two different 26650 cells: two 12 V, 25Ah

(4s10p) batteries from different companies, a 12V, 40Ah (4s15p), and a 12 V,

50Ah (4s20p). The battery capacity was determined at 25◦C for all six batteries.

The discharging currents used are summarized in Table 2.2.

LFPs 1 and 2 were equipped with an internal BMS whose operations are un-

known. During discharging tests, the BMS of LFP 1 was bypassed. For LFP 2,

the cut-off voltage during discharge was reprogrammed from the initial value of

10V to 8V (cell cut-off voltage is 2V). The LFPs 3 and 4 as well as the LABs did

not have an internal BMS.

Table 2.2: The C20 continuous discharge capacity (adjusted from Ref. [6]).

ID Battery size Nominal

capacity

Capacity

at 25◦C

Small, constant

discharge current

LAB 1 6s1p 50Ah 53.3Ah 2.5A

LAB 2 6s1p 92Ah 98.4Ah 4.6A

LFP 1 4s15p 40Ah 39.2Ah 2A

LFP 2 4s10p 25Ah 25.8Ah 1.25A

LFP 3 4s10p 25Ah 24.6Ah 1.25A

LFP 4 4s20p 50Ah 50.5Ah 2.5A

Before any testing, all batteries were conducted two full capacity turnovers at

25◦C to ensure the functionality and fully charged batteries before conducting

any further tests at lower temperatures. Further detail on the charging regime

is given in Section 2.3.4. The second discharge at 25◦C will be further used as a

capacity baseline. For any other temperature then 25◦C the batteries are cooled

down to the discharging test temperature of 0 ◦C or −18 ◦C respectively for 24h

before starting the capacity test. The capacity at all temperatures was tested

using very low constant currents, normalized to the batteries Cn, of 1

20·C, or in

LABs terms I20, till a cut-off voltage of 10.5V as defined in the EN for LABs [60].

A low current, stated in Table 2.2, is chosen to minimize the temperature gra-

2 Starting-Lighting-Ignition Batteries

dient within the battery and the temperature changes during the test. After all

tests, the batteries were warmed up to 25◦C for 24h and then charged according

to the standard [60] or their datasheet, before performing the next capacity test.

Figure 2.4 shows the voltage decline during the constant current discharging

test to determine the capacity of the batteries. The data indicate that regard-

less of temperature, all voltages of the same technology behave similarly. Fig-

ure 2.4 (a) shows the C20 test results at 25◦C. At this temperature, all batteries

are almost reaching their target capacity. Additionally, it should be noted that

despite having similar nominal voltages, LFPs exhibit higher voltage levels and

a more consistent voltage plateau during operation at all ambient temperatures.

At lower temperatures, shown in Figure 2.4 (b) and (c), the capacity decreases for

all technologies while the spread between the technologies increases. However,

this trend is more distinct for LABs compared to LFPs. Therefore, the LFPs have

a higher power and higher energy output even at temperatures below 0 ◦C.

(a) (b) (c)

0 5 10 15 20

Time / h

Voltage / V

0 5 10 15 20

Time / h

Voltage / V

0 5 10 15 20

Time / h

Voltage / V

LAB 1 LAB 2 LFP 1 LFP 2 LFP 3 LFP 4

Figure 2.4: C20 capacity test at (a) 25◦C, (b) 0◦C, and (c) −18◦C (adjusted from

Ref. [6]).

Figure 2.4 (a) evaluates the measured C20 capacity normalized to their Cnat dif-

ferent temperatures. At 25◦C all batteries are close to their Cn. Both LABs reach

107% at 25◦C while the LFPs range between 98% and 103%. At lower tempera-

tures, the capacity of both technologies gets lower, and the spread between the

batteries increases. At 0◦C, shown in Figure 2.4 (b), the capacity of both tech-

nologies is still highly comparable, all batteries still have around 91% to 102%

usable capacity. However, at −18 ◦C LABs have a low usable capacity, shown in

2.3 Technology Comparison for SLI Batteries

Figure 2.4 (c). The capacity of all batteries and different temperatures are com-

pared in Figure 2.5 (a). The LFPs have a higher power and energy output than

LABs. In Figure 2.5 (b), the usable energy degradation, normalized to the energy

at 25◦C, is shown for lower temperatures. While the usable energy degradation

between LABs and LFP is still comparable at 0◦C, the usable energy decreases

drastically for LABs at even lower temperatures. At −18◦C LABs have usable

energy between 51% and 61% compared to the LFPs, which still have usable

energy between 76% and 86%. Concluding, for low constant current discharge

tests at temperatures below 0 ◦C, the LFPs are superior.

For all six different test batteries, the capacity degradation normalized to Cnat

different temperatures as well as their energy degradation normalized to the

usable energy at 25 ◦C are summarized in Table 2.3.

Table 2.3: Comparison of the normalized capacity and energy degradation dur-

ing the low discharge current capacity test.

Technology −18◦C 0 ◦C 25 ◦C

LABs capacity C/Cn55% - 76% 97% 107%

LFPs capacity C/Cn82% - 91% 91% - 102% 98% - 103%

LABs energy E/E25◦C51% - 61% 82% - 92% 100%

LFPs energy E/E25◦C76% - 86% 92% - 99% 100%

(a) (b)

-18 0 25

100

110

-18 0 25

100

LAB 1 LAB 2 LFP 1 LFP 2 LFP 3 LFP 4

Figure 2.5: (a) Capacity and (b) energy of the C20 test (adjusted from Ref. [6]).

2 Starting-Lighting-Ignition Batteries

2.3.2 First Pulse of the Cold Cranking Ability

The CCA test was executed according to the EN [60]. After fully charging the

battery, it was cooled down to the test temperature and held for 24h. Within the

standard, only −18 ◦C is investigated [60]. Within this work, test temperatures

are 0 ◦C, −10◦C, −18◦C and −30 ◦C. The first 10s discharging pulse of 9AAh−1

is followed by a 10s pause, and then a second discharging pulse of 5.4A Ah−1.

This second discharging pulse typically lasts until the voltage limit is reached

or for a maximum time of 170s has passed. The discharging currents during

the CCA test’s first and second pulse are stated in Table 2.4. Even though the

batteries are typically not completely discharged after a CCA test, all batteries

were warmed up to 25 ◦C for 24h and then completely charged according to the

EN [61] or their datasheet before and between any of the following tests. Further

details are given in Section 2.3.4.

Table 2.4: The currents used for the CCA test (adjusted from Ref. [6]).

ID Battery size Nominal

capacity

Current

1st pulse

Current

2nd pulse

LAB 1 6s1p 50Ah 450A 270A

LAB 2 6s1p 92Ah 828A 497A

LFP 1 4s15p 40Ah 360A 216A

LFP 2 4s10p 25Ah 225A 135A

LFP 3 4s10p 25Ah 225A 135A

LFP 4 4s20p 50Ah 450A 270A

The CCA at 0◦C is shown in Figure 2.6 and at −10 ◦C in Figure 2.7. All batter-

ies were able to supply the desired discharging current during the first pulse at

0◦C and −10 ◦C. However, the voltage drop varied significantly with temper-

ature and increased as the temperature decreased for both technologies. LFPs

exhibited higher voltage levels than LABs and provided a higher power level.

2.3 Technology Comparison for SLI Batteries

(a) (b) (c)

0 10 20 30

Time / s

Voltage / V

0 10 20 30

Time / s

-10

-8

-6

-4

-2

Current / A Ah-1

0 10 20 30

Time / s

100

120

Power / W Ah-1

LAB 1 LAB 2 LFP 1 LFP 2 LFP 3 LFP 4

Figure 2.6: First pulse of the CCA at 0◦C (a) voltage, (b) current, and (c) power

(adjusted from Ref. [6]).

(a) (b) (c)

0 10 20 30

Time / s

Voltage / V

0 10 20 30

Time / s

-10

-8

-6

-4

-2

Current / A Ah-1

0 10 20 30

Time / s

100

120

Power / W Ah-1

LAB 1 LAB 2 LFP 1 LFP 2 LFP 3 LFP 4

Figure 2.7: First pulse of the CCA at −10 ◦C (a) voltage, (b) current, and

Figure 2.8 shows the CCA results for −18◦C, as specified by the EN standard

[60]. While the LABs only have a safety limit of 6V, which is not reached during

the CCA test at −18 ◦C, two out of four LFPs reach their safety limit of 8V during

the first discharging pulse. It should be noted that the safety limit has been

reduced from the original battery voltage limits of 10.5V (2.63 V per cell) to the

datasheet cell voltage limit of 2V per cell. The discharging current is regulated

as soon as any of the cells’ voltage limit is reached. This way, two LFPs can not

deliver the requested current demanded by the EN [60].

2 Starting-Lighting-Ignition Batteries

(a) (b) (c)

0 10 20 30

Time / s

Voltage / V

0 10 20 30

Time / s

-10

-8

-6

-4

-2

Current / A Ah-1

0 10 20 30

Time / s

100

120

Power / W Ah-1

LAB 1 LAB 2 LFP 1 LFP 2 LFP 3 LFP 4

Figure 2.8: First pulse of the CCA at −18 ◦C (a) voltage, (b) current, and

However, it is important to note that the minimum power required for the igni-

tion process in a typical gasoline engine is a function of both voltage and current.

Therefore, a lower voltage limit for LABs, which allows delivering the current

demanded by the standard, can still impact the reliability of the ignition process

[56]. All batteries deliver more than 60WAh−1power during the first 10s pulse

at −18◦C, implying that a battery with a capacity between 33.3Ah and 43.3Ah

could deliver the required power of 2kW to 2.6kW for the ignition process [56],

regardless of the technology.

(a) (b) (c)

0 10 20 30

Time / s

Voltage / V

0 10 20 30

Time / s

-10

-8

-6

-4

-2

Current / A Ah-1

0 10 20 30

Time / s

100

120

Power / W Ah-1

LAB 1 LAB 2 LFP 1 LFP 2 LFP 3 LFP 4

Figure 2.9: First pulse of the CCA at −30 ◦C (a) voltage, (b) current, and

2.3 Technology Comparison for SLI Batteries

At −30◦C, shown in Figure 2.9, all batteries reach their safety limit during the

first discharging pulse and fail to deliver the requested current defined by the

standard [60]. Although the LABs approach the safety limit much later than the

LFPs, they still fail to meet the criteria. The power delivered by the batteries

during the first discharging pulse is between 60W Ah−1and 50WAh−1, with

the power level of the LFPs being lower than that of the LABs.

Figure 2.10: Voltage used for total and usable energy determination during the

first pulse (adjusted from Ref. [6]).

Furthermore, the energy output has been evaluated since the current and voltage

levels alone are not very informative. To make a qualitative comparison between

the two battery technologies, the total and usable energy is considered, as the

power must be sustained for a certain amount of time to start an engine [56]. The

total energy Etotal can be calculated by taking the average open circuit voltage

(OCV) Vav, shown in Figure 2.10, and the discharging current I(t)during the

10s pulse.

Etotal =Vav Z10s

0I(t)dt (2.1)

To determine the average OCV voltage, the voltage level before the first dis-

charging pulse and the relaxation voltage at the end of the 10s pause are used to

determine the average. Since the relaxation processes are not complete after the

10s pause, the average voltage will be underestimated. The usable energy Euse

is determined using the actual voltage, shown in Figure 2.10, and current during

2 Starting-Lighting-Ignition Batteries

the first 10s discharging pulse.

Euse =Z10s

0V(t)·I(t)dt (2.2)

Figure 2.11 (a) visualizes the total energy degradation from 0 ◦C to −30 ◦C nor-

malized to the total energy at 0 ◦C. The LABs have a total energy decrease of

max. 2% for all tested temperatures. The LFPs, on the other hand, have a total

energy decrease of 1% to 6% at temperatures above and including −18◦C. Below

−18◦C the total energy of the LFPs decreases by 15% to 60%. Thus, the investi-

gated LABs provide higher total energy over the tested temperature range.

The usable energy degradation, visualized in Figure 2.11 (b), shows a higher de-

crease for all batteries compared to the total energy. Even for the short test time

of 10s, this energy loss can be explained by heating. Since the battery’s internal

heating consumes part of the energy, the usable energy is lower than the total en-

ergy. It should be noted that for the investigated temperatures below 0◦C, LABs

deliver higher usable energy values compared to LFPs. LFPs show a similar de-

crease in usable energy at temperatures above and including −18◦C. However,

at −30◦C, the usable energy of LFPs significantly decreased.

Combining the total and usable energy allows the calculation of the efficiency,

EEff =Euse

Etotal (2.3)

shown in Figure 2.12. The efficiency decreases as the temperature decreases for

both LABs and LFPs. However, LFPs have a higher energy efficiency than LABs

for all investigated temperatures.

However, the efficiency increases at −30 ◦C. This can be explained by the longer

relaxation time at lower temperatures, which causes a significant voltage under-

estimation at −30 ◦C. As a result, the calculated average open circuit voltage

decreased for some batteries at −30◦C. This leads to a decreased total energy,

resulting in an increased efficiency. Table 2.5 summarizes the total and usable en-

ergy values, as well as the resulting efficiency during the first pulse, depending

on the ambient temperature.

2.3 Technology Comparison for SLI Batteries

(a) (b)

-30 -18 -10 0

100

-30 -18 -10 0

100

LAB 1 LAB 2 LFP 1 LFP 2 LFP 3 LFP 4

Figure 2.11: (a) Total energy and (b) usable energy during the first pulse of the

CCA test (adjusted from Ref. [6]).

-30 -18 -10 0

100

LAB 1 LAB 2 LFP 1 LFP 2 LFP 3 LFP 4

Figure 2.12: Energy efficiency during the first pulse of the CCA test (adjusted

from Ref. [6]).

2 Starting-Lighting-Ignition Batteries

Table 2.5: Comparison of the total energy, unable energy and efficiency degra-

dation during the first pulse of the CCA test.

Technology −30◦C−18 ◦C−10 ◦C 0 ◦C

LABs Etotal/E0◦C> 98% > 98% > 98% 100%

LFPs Etotal/E0◦C15% - 60% 94% - 99% > 97% 100%

LABs Euse/E0◦C> 71% 84% - 94% 95% - 97% 100%

LFPs Euse/E0◦C13% - 47% 73% - 84% 88% - 93% 100%

LABs efficiency 49% 57% - 63% 64% - 65% 67%

LFPs efficiency 61% - 69% 63% - 68% 68% - 76% 74% - 82%

Figure 2.13 visualizes the internal resistance of various batteries measured at

different ambient temperatures using a Hioki BT3554 (measuring the 1kHz re-

sistance). It is shown that the internal resistance of all batteries increases with

decreasing temperature. This is one of the reasons why the CCA also decreases

with decreasing temperature. However, the internal resistances of LABs and

LFPs are comparable for all temperatures. Therefore, the internal resistance

alone does not explain why the LABs have a higher power output and their

voltage limit is reached later than LFPs during the first discharge pulse. LABs

and LFPs have different electrochemical systems with distinct temperature de-

pendencies of the chemical reaction rate and diffusion speed, which also impact

the CCA.

The electrolyte significantly impacts the internal resistance and, thereby, low-

temperature performance. The electrolyte of the LABs consists of sulfuric acid,

which can freeze depending on its SoC at low temperatures. In contrast, the elec-

trolyte in most commercially available LFPs consists of ethylene carbonate and

dimethyl carbonate EC/DMC with conducting salt, e.g., LiPF6. For LFPs, the

electrolyte decomposition significantly affects ionic mobility in the electrolyte so-

lution, creating suitable surface films [62, 63]. As temperature decreases, the ion

conductivity of the electrolyte reduces [62, 63] for both LABs and LFPs, thereby

increasing the battery’s internal resistance.

2.3 Technology Comparison for SLI Batteries

(a) (b)

-30 -18 -10 0 25

0.1

0.2

0.3

0.4

0.5

LAB 1 LAB 2 LFP 1 LFP 2 LFP 3 LFP 4

Figure 2.13: Internal resistance (a) absolute values and (b) normalized values

(adjusted from Ref. [6]).

2.3.3 Second Pulse of the Cold Cranking Ability

Despite the decrease in the starting voltage level at lower temperatures, all LFPs

demonstrated sufficient current outputs during the second pulse of the CCA test

conducted at 0◦C, −10◦C, and −18 ◦C, shown in Figures 2.14, 2.15, and 2.16.

(a) (b) (c)

0 20 50 100 150 200

Time / s

Voltage / V

0 20 50 100 150 200

Time / s

-10

-8

-6

-4

-2

Current / A Ah-1

0 20 50 100 150 200

Time / s

100

120

Power / W Ah-1

LAB 1 LAB 2 LFP 1 LFP 2 LFP 3 LFP 4

Figure 2.14: Complete CCA test at 0◦C (a) voltage, (b) current, and (c) power

(adjusted from Ref. [6]).

During the second discharging pulse, all LFPs exhibit a significant increase in

voltage, likely caused by self-heating. At the end of the 200s CCA test, the volt-

2 Starting-Lighting-Ignition Batteries

age levels for all LFPs are similar, regardless of the ambient temperature. Con-

versely, the CCA test results for the LABs at 0◦C, −10 ◦C, and −18 ◦C show a

lower voltage curve compared to the LFPs. Unlike the LFPs, the voltage level

of the LABs does not increase during the second pulse of the CCA test due to

their higher heat capacity. The higher heat capacity of the LABs results in slower

temperature changes which cannot affect the 200s test duration. LAB 1 exhibits

a significantly shorter discharging time than LAB 2 at all ambient temperatures,

but LAB 2 is still capable of providing the required current at 0 ◦C, −10 ◦C, and

−18◦C.

(a) (b) (c)

0 20 50 100 150 200

Time / s

Voltage / V

0 20 50 100 150 200

Time / s

-10

-8

-6

-4

-2

Current / A Ah-1

0 20 50 100 150 200

Time / s

100

120

Power / W Ah-1

LAB 1 LAB 2 LFP 1 LFP 2 LFP 3 LFP 4

Figure 2.15: Complete CCA test at −10 ◦C (a) voltage, (b) current, and (c) power

(adjusted from Ref. [6]).

(a) (b) (c)

0 20 50 100 150 200

Time / s

Voltage / V

0 20 50 100 150 200

Time / s

-10

-8

-6

-4

-2

Current / A Ah-1

0 20 50 100 150 200

Time / s

100

120

Power / W Ah-1

LAB 1 LAB 2 LFP 1 LFP 2 LFP 3 LFP 4

Figure 2.16: Complete CCA test at −18 ◦C (a) voltage, (b) current, and (c) power

(adjusted from Ref. [6]).

2.3 Technology Comparison for SLI Batteries

Figure 2.17 illustrates that all LFPs reach the 8V limit at the beginning of the

second pulse when tested at −30◦C. After a few seconds, the voltage rises again,

allowing the requested current to be delivered by the end of the second pulse. In

contrast, the LABs can provide the requested current but experience a significant

voltage decrease during the initial moments of the second pulse. As a result,

the power output during the first seconds of the second discharging pulse for

the LABs at −30 ◦C is slightly lower than that of the LFPs at both −30 ◦C and

−18◦C.

(a) (b) (c)

0 20 50 100 150 200

Time / s

Voltage / V

0 20 50 100 150 200

Time / s

-10

-8

-6

-4

-2

Current / A Ah-1

0 20 50 100 150 200

Time / s

100

120

Power / W Ah-1

LAB 1 LAB 2 LFP 1 LFP 2 LFP 3 LFP 4

Figure 2.17: Complete CCA test at −30 ◦C (a) voltage, (b) current, and (c) power

(adjusted from Ref. [6]).

Table 2.6 summarizes the average power output for all batteries during the first

and second pulses at the tested temperatures. Additionally, whether the batter-

ies passed the EN-defined test or not is identified.

2 Starting-Lighting-Ignition Batteries

Table 2.6: Passing the standard test and average power during first and second

pulse of the CCA test (adjusted from Ref. [6]).

ID Ambient

temperature

Passing

the standard

Average power

1st pulse

Average power

between 20s - 60s

LAB 1 0◦C passed 77.4WAh−151.7WAh−1

−10◦C passed 74.8WAh−150.3WAh−1

−18◦C passed 72.8WAh−149.4WAh−1

−30◦C not passed 55.1WAh−120.6WAh−1

LAB 2 0◦C passed 77.3WAh−152.3WAh−1

−10◦C passed 73.6WAh−150.2WAh−1

−18◦C passed 64.8WAh−146.6WAh−1

−30◦C not passed 54.6WAh−141.7WAh−1

LFP 1 0◦C passed 96.8WAh−161.1WAh−1

−10◦C passed 85.8WAh−155.8WAh−1

−18◦C not passed 70.8WAh−149.7WAh−1

−30◦C not passed 35.0WAh−127.1WAh−1

LFP 2 0◦C passed 85.3WAh−155.2WAh−1

−10◦C passed 79.6WAh−152.9WAh−1

−18◦C not passed 71.2WAh−150.5WAh−1

−30◦C not passed 11.3WAh−113.5WAh−1

LFP 3 0◦C passed 99.4WAh−162.2WAh−1

−10◦C passed 89.8WAh−158.1WAh−1

−18◦C passed 80.4WAh−154.0WAh−1

−30◦C not passed 44.0WAh−138.2WAh−1

LFP 4 0◦C passed 97.1WAh−161.5WAh−1

−10◦C passed 85.6WAh−156.8WAh−1

−18◦C passed 77.6WAh−152.7WAh−1

−30◦C not passed 45.8WAh−140.4WAh−1

2.3.4 Charging Regime of LFPs and LABs

The batteries were warmed up to 25 ◦C and held for 24h. Subsequently, the LABs

were charged according to the EN standard, with a current of 5·I20 for 24h at a

maximum voltage of 16V (2.66V per cell) for flooded batteries [61]. For AGM

LABs, the standard specifies a charging current of only 1·I20 and a maximum

2.3 Technology Comparison for SLI Batteries

charging voltage of 14.8V (2.47V per cell) for 24h [61]. The LFPs were charged

using a charging current of 1C and a voltage target of 14.4V (3.6V per cell) until

a cut-off current of 0.05AAh−1was reached.

LFPs 1 and 2 were equipped with an internal BMS whose operations are un-

known. LFPs 3 and 4 were charged with the external battery management sys-

tem (BMS), KISS active BMS from Faktor GmBH, for procurement reasons. This

BMS has the feature of active balancing during charging, but it was disconnected

during the discharging tests. The LABs do not need a BSM during charging or

discharging.

Using the standard or the definitions of the datasheets, the LFPs are much faster

while charging than the LABs. However, the long overcharge for LABs does

ensure the dissolution of lead sulfate crystals, which will enhance the lifetime

of LABs and enable comparable results between the tests. This process is not

needed for LFPs. On the other hand, a complex BMS is needed while charging

any lithium-based battery. This BMS needs to keep voltage and current limits

and enable balancing between different parallel connections. This kind of com-

plex control is not needed for LABs.

2.3.5 Final Comparison for SLI Batteries

LFPs exhibit higher voltage levels at low discharging currents than LABs, re-

sulting in higher power and energy output irrespective of ambient temperature.

LFPs also have a lower capacity decline (82% - 91% C/Cnat −18◦C) and lower

energy decline (76% - 86% E/Enat −18◦C) compared to LABs (55% - 76% C/Cn,

51% - 61% E/Enat −18◦C). Therefore, for low discharging currents, the LFPs

are superior to LABs within a temperature range of 25 ◦C to −18◦C.

Regarding the CCA standard test definition, the LABs met the requirements for

the first pulse at 0◦C, −10◦C, and −18◦C by supplying the necessary current

of 9AAh−1for 10s while maintaining a voltage above 6V. During the second

pulse of the CCA test, the LABs also satisfied the test criteria. However, the volt-

age decreases rapidly during the second pulse of the CCA test. At −30 ◦C, the

LABs nearly met the requirements for the first pulse. However, the voltage limit

was reached, and the current needed to be decreased, still providing more than

2 Starting-Lighting-Ignition Batteries

8AAh−1. There was a significant decrease in the LABs’ voltage during the sec-

ond pulse at −30 ◦C.

The LFP batteries met the requirements for the CCA standard test for the first

and second pulses at 0◦C and −10 ◦C. At −18 ◦C, only two of the four LFPs

could pass the current requirement without dropping below the LFP-specific

cut-off voltage of 8V. Despite this, when looking at power instead of current,

during the first pulse, all LFPs could provide a similar power output to the LABs

at −18◦C. Furthermore, all LFPs passed the requirements of the second pulse at

−18◦C. During the second pulse of the CCA test, the voltage level of the LFPs

increased at all temperatures due to self-heating. While all LFPs failed the first

and second pulse tests at −30 ◦C, they were able to provide the required current

through self-heating at the end of the second pulse.

However, using minimum voltage as the decision criterion for passing the CCA

standard test does not allow good comparison between different battery tech-

nologies. The LFP batteries have a higher cut-off voltage of 8V compared to the

6V for LABs, which makes it difficult to compare them. A better way would be

to redefine the requirements of the test in terms of energy or power. The LFP

batteries performed similarly to the LABs in terms of energy and power output

at temperatures down to −18◦C, but the LABs were superior at −30◦C. The

future will determine whether the low-cost, safe, and reliable LAB technology

will remain the state-of-the-art SLI battery or if the expensive and complex LFP

technology will dominate the market.

Test Cell Preparation and Pretests

Chapter 3

Even though LAB-based SLI batteries might be replaced by LFPs in the undeter-

mined future, the LABs are currently the State-of-the-Art SLI technology. For this

reason, further improvements, investigation, material screenings, and research

are needed. Investigations on the factors that influence DCA (for 12V-61Ah bat-

teries) [64], modeling processes in LABs [65, 66], and test definitions [60, 61, 67,

68] often exist for industrially manufactured complete batteries. On the other

hand, new material screenings and research are often performed using hand-

made test cells with only a few plates. Therefore, the following three research

questions have developed and will be answered within this section:

• How can electrical tests defined for battery level be used on cell level?

• How is the ratio between PAM, NAM, and electrolyte of test cells effecting

electrical test results?

• Can cell level results be scaled to match battery test results?

The preparation of test cells with the Top-Down approach is described in the

following Section 3.1. During the Top-Down approach, test cells are cut from

industrial-manufactured and already formatted batteries. Therefore, industri-

ally manufactured cell components are used rather than introducing sources of

errors by using handmade cells. Section 3.2 describes the preparation with the

Bottom-Up approach. With the Bottom-Up approach, test cells were built by

pasting grids and combining these plates to form cells. This approach is the

standard way laboratory test cells are built and gives a high degree of freedom

on components or pastes used. A summary of all test cells, their additives, cell

layout, plate count, and in which section the test description and the results

are given in Section 3.3. Afterward, Section 3.4 compares parameters that need

to be adjusted when tests are downscaled from battery to cell level to still get

comparable test results at the cell level. Thereby, parameters such as voltage,

3 Test Cell Preparation and Pretests

current, capacity, electrolyte amount, and concentration are investigated. More-

over, effects caused by the plate count and the ratio between PAM, NAM, and

the electrolyte are evaluated.

3.1 Test Cell Preparation with Top-Down Approach

Experiments in Section 3.4 had been carried out with test cells prepared with

the Top-Down approach. This approach was already described in a paper pre-

viously published [7]. For this approach, 12V, 70Ah EFB with and without ad-

ditives significantly enhancing the DCA of different battery manufacturers had

been cut into single cells with different layouts. All test cells produced from the

battery are listed in Table 3.1.

Table 3.1: Cell layout used for investigating layout effects with the Top-Down

approach (adapted from Ref. [7]).

Cell layout Negative

limited

Electrolyte

limited

Positive

limited

Complete cell - 8P8N 8P9N

Middle size cell 3P2N - -

Small size cell 2P1N - -

Different cell layouts were used to investigate size and symmetry effects of the

PAM, the NAM, and the electrolyte. A complete cell contains as many plates

as the original battery cell would contain, differing between different produc-

ers, e.g., 8 positive (P), and 9 negative (N) plates (8P9N). Furthermore, smaller

cell layouts such as 3P2N and 2P1N, which laboratory material investigations

typically use, have been investigated. Since additives in the NAM were to be in-

vestigated, the negative electrodes were bound to be the limiting factor. Finally,

the cell results were compared with the data obtained from complete batteries.

A commercial EFB contains six single cells. They can be numbered 1 to 6, where

cell 1 is the cell at the end with the negative pole, and cell 6 is the cell at the end

of the positive pole, visualized in Figure 3.1.

3.1 Test Cell Preparation with Top-Down Approach

To remove single cells from a completely functional battery, it was impossible to

retain all cells for later testing. Therefore, test cells 1, 3, and 5 were chosen as

test cells, while the other cells had to be destroyed during the cutting procedure.

Holes were drilled into the lid above cells 2, 4, and 6. This way, the electrolyte

could be sampled for future analysis shown in Table 3.2. Afterward, the elec-

trolyte was drained, and the plastic housing of the test cells 2, 4, and 6 was cut

off completely. During cutting, it was crucial to avoid damaging the straps of

cells 2, 4, and 6. The electrodes in cells 2, 4, and 6 were removed from the straps

by cutting the lugs. After all electrodes were removed, cells 1, 3, and 5 were

completely separated. The lid of cell 1 was not opened since it was to keep all its

original plates. From now on, cell 1 will be referred to as a complete cell.

Figure 3.1: Cell counting (adapted from Ref. [7]).

After separating all cells, the leftover straps were prepared to create satisfactory

connections for the subsequent electrical tests. Additional preparation was nec-

essary for cells 3 and 5, shown in Figure 3.2. Test cells 3 and 5 will be reduced

in plate count, resulting in a 3P2N and a 2P1N, respectively. These test cells are

referred to as middle or small size cells. For further preparation, the electrolyte

was removed from cells 3 and 5, such that all plates were still covered with acid,

but the intercell connections were not. The lid was cut off halfway through the

intercell connector in the next step. The plate stack was lifted from the case, visu-

alized in Figure 3.2 (a). All unnecessary plates were disconnected by cutting off

the lugs (Figure 3.2 (b). The remaining space, which is not filled with plates any-

more was replaced with spacers (inserted plastic shims), shown in Figure 3.2 (c).

This was the remaining plate stack remains with a sligth compression and mini-

mized excess acid volume.

3 Test Cell Preparation and Pretests

(a) (b) (c)

Figure 3.2: Step by step plate reduction: (a) lifting plate stack, (b) disconnecting

unnecessary plates, and (c) replacement with spacers (adapted from

Ref. [7]).

After reassembling, the cell housing was refilled with the original electrolyte,

and the lid was closed. After 5h of rest time, another electrolyte sample was

taken and analyzed for metallic impurities, given in Table 3.2. Analyzing the

acid before and after the cutting procedure allowed investigating the acid for

foreign metals (such as Co, Cr, Fe, Mo, and Ni), which are introduced during

the cutting procedure. Despite careful handling, microscopic swarfs from the

cutting equipment (horizontal bandsaw, oscillating multitool) contaminated the

test cells during reassembly. When precipitated at the negative electrode, they

would most likely reduce the hydrogen overvoltage, accelerating the hydrogen

gassing reaction. It is unknown whether the foreign metals found are influenc-

ing the DCA test results. Nevertheless, since the same cutting procedure was

used on all batteries, the effect will be similar between the standard EFB and

all different kinds of EFB with enhanced charge acceptance. This contamination

could have only affected the middle and small size cells but not the complete

cell, for which the cell housing and lid remained sealed. These test cells could

enter the pretests right after reassembling since the formation procedure was al-

ready executed on the complete battery. All tests were conducted in a climate

chamber, minimizing outer influences.

3.2 Test Cell Preparation with Bottom-Up Approach

Table 3.2: Electrolyte analyses in g cm−3before and after the cutting procedure

(37%-38% electrolyte concentration), the detection limit (DL) and the

requirement of the VDE 0510 (adapted from Ref. [7]).

Additive Al Co Cr Cu Fe Mo Ni Zn

Before

cutting

EFB+CA72.200 <DL 0.041 0.002 1.540 <DL <DL 1.470

EFB+CB45.900 <DL 0.035 <DL 1.280 0.011 <DL 3.080

After

cutting

EFB+CA68.400 0.189 0.203 0.029 36.900 0.161 0.062 2.260

EFB+CB54.100 0.314 0.266 0.017 16.800 0.322 0.071 2.860

DL 0.000 0.002 0.001 0.001 0.001 0.006 0.005 0.001

VDE 0510 req. 0.200 0.500 30.000

The test cells, their additives, cell layout, and plate count, built with the Top-

Down approach, are summarized in Table 3.5.

3.2 Test Cell Preparation with Bottom-Up Approach

A total of eight different NAM formulations are studied with the Bottom-Up ap-

proach. Among them, five different amorphous carbon powders (referred to as

C1to C5), provided by the Bavarian Center for Applied Energy Research, are

used [69]. The synthesis of these five carbons is described in the literature [70].

The physical properties are also characterized in literature [71]. The specific sur-

face area and the specific pore volume of the five different amorphous carbon

powders are very similar [71], while the specific external surface area (sext) and

thereby the average particle size (dpart) [71] significantly varies. The character-

istics of the additives used for the Bottom-Up approach are listed in Table 3.3.

Next to the five synthesized amorphous carbons, two unknown additive mixes

(referred to as CXand CY) and a commercially available carbon black used as

reference (Ref), are included in this study. All test cells built with the Bottom-Up

approach used the same industrial manufactured positive plates.

3 Test Cell Preparation and Pretests

Table 3.3: Textural properties of five synthesized carbon materials, two un-

known additives, and a commercial reference (adapted from Ref. [71]).

Cell

additive

sext

of carbon dpart

EFB+C17.1m2g−1633nm

EFB+C220.3m2g−1221nm

EFB+C350.4m2g−188nm

EFB+C492.1m2g−148nm

EFB+C5159.3m2g−127nm

EFB+CX- -

EFB+CY- -

EFB+Ref 28m2g−1104nm

Paste mixing was done on a laboratory scale with the identical mixing routine

for all additives under inspection. The basis of the paste recipe was not changed.

Only the added amount of water was varied to maintain constant mass penetra-

tion and generate a fixed paste viscosity throughout all mixtures. The amount of

water needed is not directly linked to carbon’s external surface area. The paste

mix included:

• Leady oxide (1500 g)

• Water (194 ±16g, depending on water absorption of carbon)

• Diluted sulfuric acid (1.4 gcm−3, 120g)

• Barium sulfate (12 g)

• Vanisperse (3g)

• Carbon additive (1.0 wt% = 15g, for CXand CYunknown)

After the paste mixing, the AM was pasted manually on industrial lead grids

(143mm x 113mm). At each test cell 106 g ±1 g of AM is applied. Up to ten

negative electrodes have been prepared for each of the formulations. The elec-

trodes were cured under moderate temperatures and a defined atmosphere. In

the first step a high humidity of >95% RH at 40 ◦C was kept for 18h to form

tribasic lead sulfate. During the second curing step, the electrodes dried, and

residual lead content was reduced at temperatures being increased from 50 ◦C

to 60◦C throughout 24h. The humidity decreased during the second step from

3.2 Test Cell Preparation with Bottom-Up Approach

>95% RH until approximately 10% RH due to opening the vent of the curing

box. The completed plates were weighted, and only the superior plates, closest

to 154g, were used for cell preparation.

Pouring a lead-antimony alloy into a cast and inserting the lugs of either the

negative or the positive plates connected them with the current collector. Each

plate of the finished positive electrode had to be enveloped. Afterward, the pos-

itive and negative plates are merged. Spacers were added to each side and at the

bottom of the plate stack while inserting the stack into the cell case. This way,

the excess acid was reduced, and compression to the plate stack was provided

without mechanically pressuring it into a tight case. Before filling the test cell

with any electrolyte, the lid was mounted to the case, ensuring tightness using a

rubber ring and numerous well distributed bolts. The lid contains several open-

ings for the current collector, the gassing tube, the reference electrode, and for

electrolyte filling purposes. The tube was used for imitating the condensation

and recombination maze in the lid of a commercially sold battery. It allows the

recombination of hydrogen and oxygen and prevents pressure increase caused

by gassing. The reference electrode can be used to differentiate between the neg-

ative and the positive half-cell voltage, giving a higher degree of understanding

electrochemical behavior inside the test cell. All openings but the one for filling

in the electrolyte are sealed. The same current collector and cell cases were used

for all test cells.

Sulfuric acid with a concentration of 1.2gcm−3was used to fill up the test cell till

the current collectors were slightly covered. The amount of electrolyte inside the

test cell was determined by weighing the test cell and all additional inventory

before mempty and after filling mfilled.

melec =mfilled −mempty (3.1)

3 Test Cell Preparation and Pretests

(a) (b)

(d)

Figure 3.3: builting test cells: (a) enveloping the positive plate, (b) merging the

electrodes, (c) adding spacers, (d) electrodes inside the cell case and

(e) assembled test cells.

A relatively soft formation procedure was used, with constant current charging

of 3·I20 at room temperature of 25◦C. However, formation processes take longer

for cells with lower plate count because the NAM:PAM ratio is much higher. To

determine the theoretically required capacity Cform to complete the formation,

the number of plates (N,P) and the mass of both the NAM and the PAM are mul-

tiplied with the specific theoretical required capacity Cspec [72]. This procedure

has to be performed for both electrodes, where the electrode with the higher

formation criteria is the regulating factor.

Cform,P =P·PAM ·Cspez,PAM (3.2)

3.2 Test Cell Preparation with Bottom-Up Approach

Cform,N =N·NAM ·Cspez,NAM (3.3)

For a complete cell (7P8N), this theoretical calculation would result in a theoret-

ically required capacity of

Cform,P =7·0.1117kg ·226.2 Ah

kg =176.87Ah (3.4)

Cform,N =8·0.0764kg ·226.6 Ah

kg =139.04Ah. (3.5)

However, experimental evaluations have shown that this theoretical criterion is

insufficient for formation due to losses, e.g., by gassing. Table 3.4 gives the cho-

sen formation criteria and therefore formation time in rounded values. The Cn

of a test cell has been scaled for test cells with reduced plate count. Further ex-

planation is given in Section 3.4.2.

After formation, the leftover electrolyte amount mAwas determined by subtract-

ing the cell weight after formation mafter from the cell weight after filling.

mA=mfilled −mafter (3.6)

The electrolyte concentration of all cells was adjusted to dC= 1.29gcm−3at 100%

SoC by adding electrolyte with the concentration of 1.42g cm−3. The ratio be-

tween the leftover electrolyte amount after formation and the refilling acid can

be determined as follows: mB

mA=dC−dA

dB−dC(3.7)

The amount of refilling electrolyte was exemplary determined for a 20Ah 3P2N

test cell, which had remaining 250g of electrolyte after formation with a density

of 1.254gcm−3:

251g =1.29gcm−3−1.254gcm−3

1.42gcm−3−1.29gcm−3=36

13 (3.8)

mB=250g ·36

130 ≈70g (3.9)

Afterward, the 20Ah 3P2N test cell was filled with 30g of 1.29gcm−3electrolyte

to ensure, that all test cells had an equal electrolyte level.

3 Test Cell Preparation and Pretests

After the acid adjustment, all test cells are finalized by charging with a constant

current of 0.5·I20 = 0.5A for 10h. This will guarantee finalized formation. More-

over, the stirring effect of overcharging will avoid acid stratification caused by

the acid adjustment. Afterward, the cells are ready for testing, starting with the

pretests, e.g., C20 test.

Table 3.4: Formation criteria dependent of cell layout.

Cell layout Cell

size

Nominal

capacity

Formation

current

Formation

criteria

Formation

time

Complete cell 7P8N 70Ah 10.5A 5 ·Cn= 350Ah 33h

Middle size cells 3P2N 20Ah 3.0A 6 ·Cn= 120Ah 40h

Small size cells 2P1N 10Ah 1.5A 7 ·Cn= 70Ah 46.7h

In Table 3.6, all test cells, their additives, cell layout, and plate count, built with

the Bottom-Up approach, are summarized.

3.2.1 Deviations between Test Cells

In experimental research, reproducibility refers to the repeatability of results

achieved by an experiment when replicated [73]. It was recently highlighted that

more than 70% of researchers trying to replicate experiments from others are un-

able to reproduce the findings [74]. More than half are even unable to reproduce

their own results [74]. To reproduce, learn or built upon others experiments, it

is essential to eliminate as many unknown disturbance variables as possible and

tracing each experiment with a high level of detail in the reporting.

Evaluations on influencing factors on the DCA (Section 4.3), and on the electro-

chemical impedance spectroscopy (EIS) (Section 5.7), have been conducted with

cells produced from the Bottom-Up approach. These tests have only been con-

ducted with a small number (up to three) of test cells each. Therefore, errors and

deviations of single cells from the same production charge cannot be excluded.

Variations between the cells, e.g., amount of lead, additives, amount of added

water to the dry past, amount of active material per plate, storage and trans-

portation conditions of the plates, and the accurateness of the assembler can

3.2 Test Cell Preparation with Bottom-Up Approach

hardly be distinguished because they add up along every single step of the cell

production. Some noticeable variations are to be stated in more detail:

• The amount of water added to the dry paste (194g ±16g) depends on the

water absorption of the carbon. This variation was accepted to maintain a

constant mass penetration and generate a fixed paste viscosity throughout

all mixtures.

• All other stated weights also contain small-scale inaccuracies of ±0.1g.

• After the paste mixing, the active material is pasted manually on ten in-

dustrial lead grids (143mm x 113mm), where 106g ±1g of active material

is used per plate.

• After curing, the variation between the single plates is already significant.

The average weight of a negative plate is 154.3g with a variation of ±4.3g

and a standard deviation of 2.6g.

• The positive plates are industrially manufactured and only introduce ne-

glectable sources of errors compared to the negative handmade plates.

• Further unspecific variation occurs due to the handmade current collector

of the negative and the positive plates.

• The variation originating from the cell building and formation is kept as

minimal as possible. The same spacers and the same cases have been used

for all cells. The amount of electrolyte for the formation and after was

kept the same. Depending on the number of plates, the same formation

program has been used for all cells.

Even though multiple variations between different cells have been identified,

the significance of the influence of these was not investigated. It is unfeasible to

predict if these differences influence the capacity of the cell or the EIS and the

charge acceptance as well. To offer a small outline on the reproducibility of the

test cells, the C20 capacity is investigated. All 2V, 20Ah 3P2N EFB Bottom-Up

cells (independent of their additive) have a maximum variation of ±0.88Ah and

a standard deviation of ±0.5Ah during the first C20 capacity test. However, the

deviation increases already after some cycles. This effect is caused by the addi-

tives, of which some increase the water loss, which will thereby increase the acid

density within these cells.

3 Test Cell Preparation and Pretests

3.3 Test Cells Built for Testing

The test cells, their additives, cell layout, and plate count, built with the Top-

Down approach, are summarized in Table 3.5. The test cells built from the

Bottom-Up approach, their additives, cell layout, and plate count are summa-

rized in Table 3.6.

Table 3.5: Test cells built from the Top-Down approach.

Cell

additives Cell layout Plate

count Test matrix Results in

EFB Battery unknow Section 3.4

Complete cell 8P9N Table 3.7 Section 3.4

Middle size cell 3P2N Table 3.7 Section 3.4

Small size cell 2P1N Table 3.7 Section 3.4

EFB+CABattery unknow Section 4.1

Complete cell 8P8N Table 4.1 Section 4.1

Middle size cell 3P2N Table 4.1 Sections 4.1 and 6.1

Small size cell 2P1N Table 4.1 Section 4.1

EFB+CBBattery unknow Section 4.1

Complete cell 8P8N Table 4.1 Section 4.1

Middle size cell 3P2N Table 4.1 Sections 4.1 and 6.1

Small size cell 2P1N Table 4.1 Section 4.1

EFB+CCBattery unknow Section 4.1

Complete cell 8P9N Table 4.1 Section 4.1

Middle size cell 3P2N Table 4.1 Sections 4.1 and 6.1

Small size cell 2P1N Table 4.1 Section 4.1

EFB+CDBattery unknow Section 4.1

Complete cell 8P9N Table 4.1 Section 4.1

Middle size cell 3P2N Table 4.1 Section 4.1

Small size cell 2P1N Table 4.1 Section 4.1

The test cells built from the Top-Down approach have been used for pretest-

ing, such as parameter determination (e.g., current, voltage, electrolyte concen-

tration) for comparable test results between different cell layouts and batteries.

The test cells built from the Top-Down approach have also been used to inves-

tigate size and symmetry effects. Furthermore, the first investigations on cor-

3.3 Test Cells Built for Testing

relations between DCA and electrochemical impedance spectroscopy (EIS) have

been evaluated. In Table 3.5 not only the list of different test cells is given, but

cross-references to the sections describing their test procedure and the tables giv-

ing their test plan are listed as well.

Table 3.6: Test cells built from the Bottom-Up approach.

Cell

additives Cell layout Plate

count Test matrix Results in

EFB+CXComplete cell 7P8N Table 4.5 Section 4.3

Table 5.1 Section 5.3.2

Middle size cell 3P2N Table 4.5 Sections 4.3, 6.2, 6.3

Table 5.1 Section 5.3.2

Table 5.3 Sections 5.4, 5.5, 5.7, 5.8,

6.2 and 6.3

Small size cell 2P1N Table 4.5 Section 4.3

Table 5.1 Section 5.3.2

EFB+CYMiddle size cell 3P2N Table 4.5 Sections 4.3, 6.2, 6.3

Table 5.3 Sections 6.2, 6.3

EFB+C1Middle size cell 3P2N Table 4.5 Sections 5.7, 6.2, 6.3,

Table 5.3 Sections 5.6, 5.7, 6.2, 6.3

EFB+C2Middle size cell 3P2N Table 4.5 Section 6.2

Table 5.3 Section 6.2

EFB+C3Middle size cell 3P2N Table 4.5 Section 6.2

Table 5.3 Section 6.2

EFB+C4Middle size cell 3P2N Table 4.5 Sections 5.7, 6.2

Table 5.3 Sections 5.7, 6.2

EFB+C5Middle size cell 3P2N Table 4.5 Sections 5.7, 6.2

Table 5.3 Sections 5.7, 6.2

EFB+Ref Middle size cell 3P2N Table 4.5 Section 6.2

Table 5.3 Section 6.2

Test cells built with the Bottom-Up approach were used to further investigate

influencing factors on the DCA and EIS. Cells with CXand CYwere used for cell

size and symmetry studies and test cells using C1to C5and CRef−CB were used to

test DCA influencing factors and comparing the DCA and the fitting parameters

of the EIS measurement. Therefore, for C1to C5and CRef−CB only 3P2N test

3 Test Cell Preparation and Pretests

cells were built. Cross-references to the sections describing their different test

procedures and to the test matrices can be found in Table 3.6.

3.4 Parameters for Testing Diverse Cell Layouts

New AMs are often tested and selected at the cell level. However, the compara-

bility between cell to battery-level performance is not always good. The aim of

this section, which had been published before [7], outlines how the test results

at the cell level are influenced and how test cells have to be prepared to provide

comparable results to the battery level. Therefore, industrially manufactured

cell components, as described in the Top-Down approach (Section 3.1), are used

rather than introducing sources of errors by using handmade cells. However,

with a reduced, asymmetric set of plates, the test cell design generates an acid

surplus and a PAM surplus (Section 3.1). This will have not only major effects on

steady-state properties such as the constant current discharge but also on short-

term high current charging pulses, e.g., used in the DCA (EN) [61] and the CA2

test [68].

3.4.1 Electrical Test Plan to examine relevant Parameters

Changing the cell layout from complete battery to complete cell and to cells with

reduced plate count influences several cell variables. Therefore, several tests re-

garding the basic scaling factors (e.g., voltage, current, and capacity) and the

electrolyte (e.g., acid amount and electrolyte concentration) were carried out us-

ing the test cells built with the Top-Down approach described in Section 3.1.

Table 3.7 schematically represents the electrical test plan.

The freshly cut and fully charged cells first conducted a reserve capacity (RC) test

[60], shown in Figure 3.4. The RC test discharges the cells with a constant current

of 25A for a complete battery or cell and a down-scaled current according to

the factor given in Table 3.8. To avoid a deep discharge of the AM, the RC test

used in this work had an additional cutoff condition. Next to the minimum

voltage of 1.75V per cell, a time limit of 180min was used. During the RC test,

the electrolyte concentration was measured at three heights (top, middle, and

bottom). Afterward, the cells were charged according to the EN 50342.1 [60]:

3.4 Parameters for Testing Diverse Cell Layouts

5·I20 (also given in Table 3.8), for 24h with a maximum voltage limit of 2.66V

per cell followed by the cells resting for at least 16h before starting the next test.

Table 3.7: Test plan to identify basic scaling factors, using an EFB test cell.

Test

order Procedure Description in Visualized in

1 Cutting 12V battery into Section 3.1 Figure 3.2

cells with different layouts

2 RC test (scaled to Cn) Section 3.4.1 Figure 3.4, Figure 3.5

3 C20 test (scaled to Cn) Section 3.4.1 Figure 3.6, Figure 3.7

4 Adjustment of the electrolyte Section 3.4.4 Table 3.10

concentration to 1.247gcm−3

at 80% SoC

5 C20 test (scaled to Cn) Section 3.4.1 Figure 3.8 (a), Table 3.11

6 CA2 test (scaled to Cn) Section 4.1.1 Figure 3.9 (a), Table 3.12

7 C20 test (scaled to Section 3.4.1 Figure 3.8 (b), Table 3.11

effective C20 capacity)

8 CA2 test (scaled to Section 4.1.1 Figure 3.9 (b), Table 3.12

effective C20 capacity)

Next, a 20 h capacity (C20) test was carried out, where the test cell was discharged

at a constant current of I20 (according to Table 3.8). Acid concentration profiles

during constant current discharge at 25 ◦C show that the end of discharge is

caused by acid depletion in the positive electrode [75]. However, the used test

cells have excess acid within the outer half of the outer plates, preventing a de-

pletion. To avoid a deep discharge of the AM again, the cutoff conditions for the

C20 test were firstly the minimum voltage limit of 1.75V and a time limit of 22h.

The voltage development during discharge for all cell sizes and the complete

battery is shown in Figure 3.6. The electrolyte concentration was also measured

during this test at three different heights for different SoCs (shown in Figure 3.7).

Afterward, the cells were charged according to the standard again [60]. The elec-

trolyte concentration was adjusted according to the acid measurements during

the C20 test in the next step. Thereby, the middle and small size cell’s electrolyte

were adjusted to the electrolyte concentration of the complete cell at 80% SoC.

The adjustment procedure, the reasons which make this adjustment necessary,

3 Test Cell Preparation and Pretests

and the goals of the adjustment are described in Section 3.4.4. Afterward, the C20

test was repeated twice more: with the newly adjusted electrolyte concentration

(Figure 3.8 a) but otherwise unchanged; and a second time with a constant cur-

rent based on the effective C20 capacity (Figure 3.8 b).

To reveal the influences of different cell sizes on the charge acceptance, a charge

acceptance test, from the Japanese standard SBA S0101 2014, known as Charge

Acceptance Test 2 (CA2), was conducted [68]. This DCA test discharges the bat-

tery from a fully charged condition with 3.42·I20 for 30min to approximately

90% SoC, rests the battery for 20±4h and conducts a single charge pulse to test

the DCA. The charge pulse is defined at battery level with a maximum current of

200A (irrespective of battery size) and a voltage set point of 14.5V = 2.42V/cell.

The charging current was evaluated for the first 10s of the charging pulse, where

the integral of the 10s charge gives the performance value in relation to the nom-

inal capacitance of the battery. This test had to be adjusted to cell level by chang-

ing voltage and current values. Figure 3.9 depicts the results of the CA2 test at

a 90% SoC based on a cell capacity regarding the number of active half-plates

and based on the effective C20 capacity given in Table 3.11. Again, the cells were

charged according to the EN [60] followed by a resting period of at least 16h

before the next test was started.

3.4.2 Initial Scaling Parameters

Scaling the parameters defined for battery level when using them for cell tests

to get representative results was already discussed [7]. Within the following

section, three basic LAB tests are used to identify parameters that need to be

scaled to adapt the tests and to improve their accuracy at the cell level. The

chosen tests are the RC test [60], the C20 test [60], and the CA2 test [68]. The most

basic factors which need to be scaled are the voltage and the capacity:

• Standard tests are defined for batteries containing six cells each. The bat-

tery has a nominal voltage of 12V and thereby 2V per cell.

• All tests are defined for the nominal capacity (Cn) of the battery. Cnof

a complete test cell is the same as for the battery. However, if the cell is

reduced in plate count, the Cnhas to be scaled. Using a first-order approx-

imation, Cnis scaled according to the number of “active half-plates”. An

3.4 Parameters for Testing Diverse Cell Layouts

outer plate only has one active half-plate because it only participates partly

during charging and discharging, while a plate in the center has two active

half-plate”. For example, a complete cell (8P9N) contains 16 active half-

plates. A small size cell (2P1N) made out of this complete cell contains two

active half-plates. Consequently, the capacity for the small size cell can

be calculated using a factor of 2/16. The scaling factors for all test cells,

depending on their original cell size, are given in Table 3.8.

•Cnis also used to determine the SoC of the battery or test cell.

• Furthermore, the scaling factor determines the charging and discharging

current rates.

Table 3.8: Cnscaling factor based on plate count of complete cell.

Cell additive Cell layout Plate

count

Scaling

factor

Nominal

capacity Cn

I20 based

on Cn

EFB, EFB+CC, Complete cell 8P9N 1 70.00Ah 3.50A

and EFB+CDMiddle size cell 3P2N 4/16 17.50 Ah 0.88A

Small size cell 2P1N 2/16 8.75Ah 0.44A

EFB+CAand Complete cell 8P8N 1 70.00Ah 3.50A

EFB+CBMiddle size cell 3P2N 4/15 18.67 Ah 0.93A

Small size cell 2P1N 2/15 9.33Ah 0.47A

EFB+C1−5, Complete cell 7P8N 1 70.00 Ah 3.50A

EFB+Ref, Middle size cell 3P2N 4/14 20.00Ah 1.00A

EFB+CXand Small size cell 2P1N 2/14 10.00Ah 0.50A

EFB+CY

The internal resistance of all test cells was carefully minimized to decrease losses

at connections and enable charging currents up to 33.3·In. Furthermore, all con-

tacts have been carefully observed regarding corrosion, which could lead to ar-

tifacts in the test results at high current rates.

3.4.3 Electrolyte Concentration Correlation with SoC during

Constant Current Discharge

Figure 3.4 shows the result of the RC test of a complete battery and different cell

sizes. The complete test cell showed very similar behavior to that of a battery

3 Test Cell Preparation and Pretests

(the voltage of the original battery divided by six is visualized), which reaches

the voltage limit at about 150min. The complete cell reaches its voltage limit

after about 140min. All downsized cells exceed this time. The down-sized cells

even exceed the additional time limit of 180min. The voltage level of the small

size cell is higher compared to the middle size cell throughout the test. To iden-

tify reasons for the difference in the discharge curves, the electrolyte concentra-

tion at different heights was measured, as depicted in Figure 3.5.

A digital density meter DMA 35 from Anton Paar Germany GmbH was used to

measure the concentration of the electrolyte. The tube connected with the built

in manual pump was put in the investigated spot for the measurement. For all

measurements, three heights (top, middle, and bottom) were measured to inves-

tigate the electrolyte concentration and stratification. Due to chemical reactions

during discharge, the density of the electrolyte decreases. Measuring the con-

centration, therefore, gives information about the charging status of the battery.

As expected, Figure 3.5 shows that the sulphuric acid concentration decreases

during battery discharge. The capacity of an EFB is typically limited by the

amount of sulphuric acid [35]. The electrolyte concentration decreases for all

cell layouts. The lower the plate count of test cells, the smaller the electrolyte

concentration degradation during the test. Since the downsized cells contain an

excess volume of acid within and outside the outer plates, which is discussed

further in Section 3.4.4, this observation was to be expected. Larger nominal

capacities in test cells with reduced plate count during the RC test can also be

explained with the excess acid within these test cells. Similar observations can

be made for the C20 test shown in Figures 3.6 and 3.7.

3.4 Parameters for Testing Diverse Cell Layouts

0 50 100 150

Time / min

1.8

1.9

2.1

2.2

Voltage per Cell / V

Battery

Complete cell

Middle size cell

Small size cell

Figure 3.4: Voltage in different EFB cell layouts during the RC test (adapted from

Ref. [7]).

0 50 100 150

Time / min

1.1

1.15

1.2

1.25

1.3

1.35

Electrolyte Concentration / g cm-3

Complete cell

Middle size cell

Small size cell

Top

Middle

Bottom

Figure 3.5: Electrolyte concentrations in different EFB cell layouts during the RC

test (adapted from Ref. [7]).

3 Test Cell Preparation and Pretests

0 5 10 15 20 25

Time / h

1.8

1.9

2.1

2.2

Voltage per Cell / V

Battery

Complete cell

Middle size cell

Small size cell

Figure 3.6: Voltage in different EFB cell layouts during the C20 test (adapted from

Ref. [7]).

0 5 10 15 20 25

Time / h

1.1

1.15

1.2

1.25

1.3

1.35

Electrolyte Concentration / g cm-3

Complete cell

Middle size cell

Small size cell

Top

Middle

Bottom

Figure 3.7: Electrolyte concentration in different EFB cell layouts during the C20

test (adapted from Ref. [7]).

3.4 Parameters for Testing Diverse Cell Layouts

3.4.4 Adjustment of the Electrolyte Concentration

The acid amount for the different cell sizes is given in Table 3.9. After ini-

tial capacity cycles, the electrolyte concentration of all cells was approximate

1.31gcm−3at 100% SoC. However, the variation of electrolyte concentration af-

ter discharge to 80% between the cell layouts and at different heights are shown

in the previous Section 3.4.3 and are summarized in Table 3.10. This variation

can be explained by the higher acid:AM ratio of the down-sized cell layouts.

The excess acid is particularly stored outside of the outer plates and within the

additional positive separator envelopes on the outside. This can not be avoided

entirely through inserting spacers. The nominal capacities (shown in Table 3.9)

were scaled according to the number of active geometric plate surfaces. A similar

chemical composition of the NAM state-of-charge as in the battery was achieved.

However, differences in PAM state-of-charge, electrolyte concentration, and con-

sequently OCV characteristics were generated. Even though the amount of acid

significantly affects on small current capacity tests [35], it does not significantly

influence the charge acceptance tests, as long as the electrolyte concentration

was adjusted for the respective SoC operating point. Since the diffusion process

is slow, any excess acid from the outside of the outer plates, which could diffuse

into the cell during a long-term discharge, showed little effect on a reaction that

occurs within only seconds of charging pulses.

Table 3.9: Absolute acid volume and nominal acid volume for all cell layouts

(adjusted from Ref. [7]).

Cell layout Plate

count

Nominal

capacity Cn

Acid

volume

Nominal

acid volume

Complete cell 8P9N 70.00Ah 0.679l 9.70mlAh−1

Middle size cell 3P2N 17.50 Ah 0.178l 10.17mlAh−1

Small size cell 2P1N 8.75Ah 0.115l 13.13mlAh−1

Before further testing, the electrolyte concentration was adjusted to the typical

automotive PSoC operating point of 80% SoC to enhance the comparability be-

tween test cells with different plate counts during the charge acceptance tests.

This eliminates the first-order electrolyte concentration effects in the run-in and

DCA (EN) tests for cells with lower plate counts. The voltage at 80% SoC of

complete batteries is usually around 12.54V, which resulted in a cell voltage of

3 Test Cell Preparation and Pretests

2.09V. Resulting in an electrolyte concentration of approximately 1.247gcm−3

at 80% SoC [76].

The acid densities were adjusted by refilling the cells with diluted acid of the

same battery sample. Afterward, the cells were charged for an hour and were left

over the night. Therefore, the acid inside the pores could diffuse to the outside

and mix with the refilled acid. The procedure was repeated twice. The electrolyte

concentration at 80% SoC before and after the acid adjustment was measured at

three different heights and is shown in Table 3.10.

Table 3.10: Electrolyte concentration at 80% SoC ρ80%H2SO4before and after ad-

justment for all cell layouts (adjusted from Ref. [7]).

Cell layout Plate

count

Original

ρ80%H2SO4

Adjusted

ρ80%H2SO4

Complete cell 8P9N 1.265 ±0.008gcm−31.253 ±0.002 gcm−3

Middle size cell 3P2N 1.283 ±0.007g cm−31.258 ±0.003gcm−3

Small size cell 2P1N 1.289 ±0.001gcm−31.252 ±0.019gcm−3

3.4.5 Verification of the Capacity Scaling Factor

Since the correct capacity and current scaling have a significant impact regard-

ing the scalability and comparability of DCA tests for different cell layouts, addi-

tional tests with various scaling factors for capacity and current were performed.

In Table 3.11 Cnbased on the number of active half-plates is shown. The voltage

level lasts longer on a higher value for cells with lower plate counts since the

acid limitation was eliminated due to the excess acid in smaller test cells. As dis-

cussed in Section 3.4.4 the electrolyte concentration for the following tests was

adjusted at 80% SoC. First, the C20 test was repeated after the acid adjustment,

Figure 3.8 (a). Based on the C20 test results shown in Figure 3.8 (a) the I20 cur-

rent for middle and small size cells were increased to measure the C20 capacities

based on the effective capacity, shown in Figure 3.8 (b). The Cnand effective C20

capacities of the second experiment are both given in Table 3.11, where the ef-

fective capacity exceed Cnby 4to 34%. The capacities of both experiments, were

then used for one CA2 test each.

3.4 Parameters for Testing Diverse Cell Layouts

Table 3.11: Comparison of the nominal capacity Cnbased on plate count and C20

capacity (adjusted from Ref. [7]).

Cell layout Plate

count

Nominal

capacity Cn

Effective

capacity C20

Comparison

Cnand C20

Complete cell 8P9N 70.00Ah 72.8 Ah 104%

Middle size cell 3P2N 17.50 Ah 22.5Ah 129%

Small size cell 2P1N 8.75Ah 11.77Ah 134%

(a) (b)

0 5 10 15 20 25

Time / h

1.8

1.9

2.1

2.2

Voltage per Cell / V

0 5 10 15 20 25

Time / h

1.8

1.9

2.1

2.2

Voltage per Cell / V

Figure 3.8: C20 test results in different EFB cell layouts with (a) current based

on Cnregarding the number of active half plates and acid adjust-

ment and (b) based on the effective capacity C20 given in Table 3.11

(adapted from Ref. [7]).

The results of the CA2 test when scaling currents and thereby the SoC based

on the number of active half-plates shown in Figure 3.9 (a) versus the effective,

NAM-limited capacity shown in Figure 3.9 (b) and Table 3.12, respectively. Both

CA2 tests result in very similar levels of nominal charge-current per cell even

thought the current scaling factors differ substantially, from 4to 34%. Similar re-

sults were also published by Pavlov et al. [35], in which they tested charge accep-

tance using 10-second charging pulses at various (NAM-based) SoC and for mul-

tiple acid densities. The charge acceptance variation in the case of 1.24gcm−3

was 0.06AAh−1per 10% SoC change [35], implying that the influence of NAM

3 Test Cell Preparation and Pretests

SoC was relatively low. In particular, the highly geometric trend that cells with

lower plate count or with higher acid-to-mass ratio resulting in a higher DCA

was clearly shown in both experiments. However, the CA2 test results for the

complete cell had little in common with those of the battery for both scaling

factors. Artefacts due to impurities cannot have been the cause of this lack of

comparability if the complete cell was kept intact and was, therefore, still sealed.

The unexpected differences between the battery and the complete cell results

might be explained by the position of the complete cell, which was an outer cell

during the battery cutting procedure of the Top-Down approach. Outer cells

always experience different temperatures and pressures during production, for-

mation and testing and are therefore not perfectly comparable to other cells and

certainly not comparable to a complete battery.

(a) (b)

-2 0 2 4 6 8 10

Time / s

0.5

1.5

2.5

Normalized Charge Current / A Ah-1

-2 0 2 4 6 8 10

Time / s

0.5

1.5

2.5

Normalized Charge Current / A Ah-1

Figure 3.9: CA2 test results in different EFB cell layouts (a) based on Cnregard-

ing the number of active half plates and (b) based on effective capac-

ity C20 given in Table 3.11 (adapted from Ref. [7]).

The reason for the relatively low effect of the scaling factor in the case of the CA2

test could be explained by the counteraction of influencing factors. In the case

of the small size cell, the difference between the nominal and effective capacity

was 34%, resulting in a 3.4% difference in the SoC when adjusted to 90% SoC.

The lower SoC, when using the effective cell capacity, increases the charge accep-

tance. However, the increased normalisation factor diminishes the higher charge

acceptance, dividing the measured charging current by 134% battery capacity. It

3.4 Parameters for Testing Diverse Cell Layouts

was shown that the scaling factor did not significantly impact on the quantita-

tive results of charge acceptance tests. Further, the scaling factor was certainly

not the reason for the increased DCA for cells with lower plate counts. Possible

reasons for the increased charge acceptance for cells with lower plate counts are

further discussed in Section 4.3.

Table 3.12: CA2 test results with current based on Cnand with current scaled

with C20 (adjusted from Ref. [7]).

Cell layout Plate

count

CA2 results

based on Cn

CA2 results

based on C20

Complete cell 8P9N 0.638 AAh−10.614AAh−1

Middle size cell 3P2N 0.772AAh−10.686AAh−1

Small size cell 2P1N 1.292AAh−11.159AAh−1

Dynamic Charge Acceptance

Chapter 4

Micro-hybrid cars are the lowest hybridization types. They usually use brake

energy recuperation and stop/start to enable fuel savings with little additional

costs. High dynamic charge acceptance (DCA), characterized as the recharge-

ability of vehicle starter batteries, is desired to enable the additional functional-

ities and is, therefore an up-to-date topic for battery and automotive industries.

The first introduction of the term DCA was used for short charging periods with

high currents at partial state of charge (PSoC) [77]. This work defines the DCA

as the average charging current over all recuperation events during a represen-

tative trip [9]. Furthermore, for all shown test results, the DCA is normalized

with the nominal capacity Cnof the battery or cell to make the DCA results com-

parable between different cell layouts.

In Section 4.1, standard test procedures for investigating the DCA of batteries

and cells are evaluated and compared, which relates to two of the originating

research goals. The first is to translate the DCA tests from battery to cell level

and the second is to compare different DCA test methods with each other. On

the basis of these standard tests, two new DCA tests are introduced in Section 4.2

to enable DCA tests at multiple SoC and after different prior usage. Test results

are shown for both test procedures. Based on literature and measurements, the

influencing factors on the DCA are analyzed in Section 4.3. Within Section 4.4,

the limitations and errors introduced during DCA measurements are analyzed.

4.1 Standard Measurement Test Procedures for DCA

The DCA of lead-acid batteries (LABs) is highly dependent on the battery’s oper-

ational history and hard to predict during ongoing operation. Therefore, various

test methods have been introduced for micro-hybrid starter batteries [64]. Within

4 Dynamic Charge Acceptance

this section, three different test methods of different complexities are presented;

the charge acceptance test 2 (CA2) SBA S 0101 2014 [68], DCA test defined by the

European standard (EN) 50342-6:2015 [61] and the Ford long-term run-in DCA

test B. The test plan for these standardized tests is shown in Table 4.1. Further-

more, Table 4.1 contains cross-references to the sections where tests are described

in detail as well as figures and tables visualizing the test results. The EFB+CA,

EFB+CB, EFB+CCand EFB+CDcomplete, middle and small size cells, build with

the Top-Down approach, where used to compare the standard DCA tests.

Table 4.1: Test plan for DCA of EFB+CA, EFB+CB, EFB+CCand EFB+CDbatter-

ies, complete cells, middle and small size cells.

Test

order Procedure Description in Visualized in

1 C20 test (scaled to Cn) Section 3.4.1

2 CA2 test Section 4.1.1

3 DCA EN test Section 4.1.2

4 EIS at 80% SoC

5 Adjustment of the electrolyte Section 3.4.4

conc. to 1.247gcm−3at 80% SoC

6 C20 test (scaled to Cn) Section 3.4.1

7 CA2 test Section 4.1.1 Table 4.2,

Figures 4.2, 4.3

8 DCA EN test Section 4.1.2 Table 4.4,

Figures 4.5, 4.6, 4.7,

4.8, 4.9, 4.10, 6.1

9 EIS at 80% SoC Section 6.1 Figures 6.3, 6.4

10 long-term run-in DCA test B Section 4.1.3 Figure 4.11

4.1.1 Single Pulse Charge Acceptance Test

For simple charge acceptance forecasts, a short-term test like the CA2 from the

Japanese standard can be used [68]. The following test description is based on

this test [68], which will be referred to as CA2 test. This test consists of a single

charge pulse applied to a battery that has been discharged to a working state of

charge (SoC) and rested. The discharge is conducted with 3.42·I20 for 30min, i.e.,

4.1 Standard Measurement Test Procedures for DCA

with an estimated I5by 10%. The Japanese battery standards are about to grad-

ually transition from C5 to C20 as a capacity rating. Within the test standard, the

rest period is defined as 20h ±4h. To shorten the test procedure but guarantee

reproducibility, a pause of 16 h was used on every test battery or cell. The charge

pulse (at the battery level) is defined to have a maximum current of 200A (irre-

spective of battery size) and a voltage set point of 14.5V = 2.417 V/cell. The CA2

definition calls for determining the charge integral of the first 10s and scaling it

to the nominal capacity (Cn) of the battery or cell. A schematic visualization of

the test procedure is shown in Figure 4.1.

Figure 4.1: Graphical visualization of the CA2 test.

This test definition enables a fast and easy DCA prediction. However, the charge

acceptance is highly dependent on external conditions, the short-term and long-

term usage. Therefore, this single pulse test is not capable of predicting the DCA

expected during real-world application.

Within Figures 4.2 and 4.3, and Table 4.2, the test results of the CA2 test of

enhanced flooded battery cells with current increasing additives (EFB+C), pre-

pared with the Top-Down approach, are presented. In Figure 4.2 (a) the 10s-

charging pulses of the CA2 results are compared between diverse cell layouts

and Figure 4.2 (b) using different additives. The EFB+CAcomplete battery and

the EFB+CAcomplete cell have very similar test results. This test result would

be expected since, apart from a voltage level difference, the two units are very

similar. The middle size and small cells of the EFB+CAcells reveal higher nor-

malized charge currents for lower plate counts. Furthermore, clear differences

between cell additives can be identified for the middle size cell layout.

4 Dynamic Charge Acceptance

However, the high comparability between the battery and the complete cell can-

not be found for every additive under investigation. Figure 4.3 and Table 4.2

summarize all normalized charging currents, respectively. Only the EFB+CAand

the EFB+CDbatteries and complete cells have comparable test results in the CA2

test. The reasons for differences between the battery and the complete cell test

results for EFB+CBand the EFB+CCmight be explained by the unknown usage

of the batteries before the Top-Down approach was used to make test cells out of

them. Possible reasons are the temperature and pressure differences during the

formation of inner and outer cells. Therefore, the outer cell (which is later the

complete test cell) acts differently than the four inner cells. Nevertheless, when

testing the complete battery, all six test cells contribute to the charge acceptance.

(a) (b)

0 5 10

Time / s

0.5

1.5

2.5

Normalized Charge Current / A Ah-1

EFB+CA complete battery

EFB+CA complete cell

EFB+CA middle size cell

EFB+CA small size cell

0 5 10

Time / s

0.5

1.5

2.5

Normalized Charge Current / A Ah-1

EFB+CA middle size cell

EFB+CB middle size cell

EFB+CC middle size cell

EFB+CD middle size cell

Figure 4.2: CA2 test results in (a) EFB+CAcomplete battery and different test

cells layouts and (b) the middle size cell using different additives (ad-

justed from Ref. [10]).

All single-cell results of the EFB+CBcells, shown in Figure 4.3, were lower than

those of the original battery. Moreover, the cell results do not show the typi-

cal increase of charge current for lower plate counts. All EFB+CA, EFB+CCand

4.1 Standard Measurement Test Procedures for DCA

EFB+CDcells show that the normalized charge current will increase with lower

plate count. Possible reasons for this behavior are stated in Section 4.3. One

of the stated reasons is the electrolyte concentration. For all test cells, the acid

was adjusted to 80% SoC before the test. However, the CA2 is conducted at

91.5% SoC. Therefore, the acid densities would differ slightly between cell lay-

outs. This can introduce additional variation in the charge acceptance results but

would not invert the order from poorest to best results.

Complete battery Complete cell Middle size cell Small size cell

0.5

1.5

Normalized Charge Current / A Ah-1

EFB+CA battery

EFB+CB battery

EFB+CC battery

EFB+CD battery

EFB+CA complete cell

EFB+CB complete cell

EFB+CC complete cell

EFB+CD complete cell

EFB+CA middle size cell

EFB+CB middle size cell

EFB+CC middle size cell

EFB+CD middle size cell

EFB+CA small size cell

EFB+CB small size cell

EFB+CC small size cell

EFB+CD small size cell

Figure 4.3: The 10s normalized charge current of the CA2 test (adjusted from

Ref. [10]).

Table 4.2: The normalized charge current of the CA2 (adjusted from Ref. [10]).

Cell layout EFB+CAEFB+CBEFB+CCEFB+CD

Complete battery 0.41AAh−10.9AAh−11.29AAh−11.37AAh−1

Complete cell 0.45AAh−10.41 AAh−10.77AAh−11.23A Ah−1

Middle size cell 0.62 AAh−10.75AAh−11.11A Ah−11.4AAh−1

Small size cell 0.69AAh−10.72AAh−11.22AAh−11.48AAh−1

Comparing the CA2 results, the normalized charging current is higher for cells

with lower plate count. Conflicting with the expectations, the battery and com-

plete cell results do not show a clear correlation. But the normalized charg-

4 Dynamic Charge Acceptance

ing currents show a similar line up regarding their type: EFB+CA< EFB+CB

< EFB+CC< EFB+CD.

4.1.2 DCA test defined by the European standard

Since a single charge pulse does not represent the DCA in real-world applica-

tions, a more complex DCA test method for LABs in micro-hybrids was pro-

posed and applied to both flooded and absorbent glass mat (AGM) batteries

[78]. The results were similar to the tests with stop/start in real-world appli-

cations [64, 79]. However, the test included several capacity tests and no stable

level for DCA was reached. The great capacity turnover by cycling results in acid

stratification. This is highly influencing the DCA, which is further evaluated in

Section 4.3.4.

Figure 4.4: The qDCA and DCRss part of the DCA EN test (adjusted from Ref.

[10], based on [9]).

Investigations on real-time run-in driving cycle simulations on more than 60 bat-

tery types were carried out [80]. Consequently, the gained experience was used

to define the DCA EN test [61]. In contrast to single-pulse tests, the DCA EN

test is specially designed to forecast the run-in DCA after several months of cus-

tomer usage. The advantage of this definition is the test duration of about two

weeks. The DCA EN test consists of three parts, which will be described in detail

based on the DCA EN definition [61]. Starting with a precycling part, including

two times the reserve capacity (RC) test and one time the 20h discharge capacity

4.1 Standard Measurement Test Procedures for DCA

(C20) test. Secondly, the quick DCA (qDCA) measures the average pulse charge

acceptance during a series of 20 cycles after prior charge and prior discharge.

Concluding with the last part, the dynamic charge real start-stop (DCRss) sim-

ulates five days of real-world stop/start operation with periods, designed to

depict vehicle parking with an slight quiescent load. The second and third parts

of the DCA EN test are visualized in Figure 4.4.

The LAB was discharged for 22h using 1·I20 to 0% SoC. Afterwards, the battery

or cell was charged with 5·I20 up to to 80% SoC, according to Ah-counting. The

DCA after charge (tested in the qDCA part) was investigated after the batteries

or cell was charged to 80% SoC and 20h rested. The average charge current after

charge was calculated for 20 cycles as Ic, where the index c represents a prior

charge. Subsequently, the battery or cell was fully charged, using 5·I20 and a

voltage limit of 2.66V for 12h. Afterwards, the battery or cell was discharged to

90% SoC, rested for 20h, and the 20 cycles were repeated. The average charge

current after prior discharge is called Id, where the index d represents a prior

discharge.

The last part of the DCA EN test investigates the DCA during small cycles

at 80% SoC, simulating real-world stop/start vehicle operation. The average

charge current during real-world stop/start operation is referred to as Ir. This

part simulated five days, three trips per day, where one trip consists of 19 small

cycles, incorporating periods of regular engine operation, regenerative brak-

ing (5s charging at 15V; 2.5V/cell), and stop/start events (9s+1s discharge).

During the periods of regular engine operation, a simplified alternator control

strategy was simulated that chose among charging the battery at a lower volt-

age (14.4V; 2.4V/cell), maintaining zero-current control (here, simulated as a

pause), or discharging the battery into the vehicle load (creating fuel savings by

utilizing recuperated brake energy), depending on the batteries charge balance.

Each trip was preceded and followed by discharge events that simulate vehicle

activation, engine start, and rest times after usage. For the first 58s after en-

gine start and before the 19 stop/start cycles, conventional alternator charging

(14.4V; 2.4V/cell) was simulated.

During the DCRss test sequence, a resistor is connected to the battery or cell,

simulating the key-off loads (KOL) in a parked vehicle. The KOL resistance RKOL

4 Dynamic Charge Acceptance

will discharge the battery or cell by approximately 0.8% Cnper day. It consists

of two E96 resistors in parallel, calculated by:

RKOL =75000 Ω·Ah

Cn,bat (4.1)

where Cn,bat is the nominal capacity of the complete battery. For the single cells,

the formula needs to be modified

RKOL =75000 Ω·Ah

FScal ·Cn,bat ·6(4.2)

by dividing by the cell number and multiplying the battery capacity with the

scaling factor FScal, given in Table 3.8. The resulting KOL resistances RKOL are

given in Table 4.3.

Table 4.3: RKOL depending on cell type and layout (adjusted from Ref. [10]).

Cell layout Plate count Capacity RKOL

Complete cell 7P8N/8P8N/8P9N 70 Ah 180 Ω

Middle size cells 3P2N 20.0 /17.5 /18.7 Ah 625 /680 /715 Ω

Small size cells 2P1N 10.0 /8.8 /9.3 Ah 1.3 /1.3 /1.5 kΩ

All partial results (Ic,Id, and Ir) of the DCA EN test are weighted and added

IDCA =0.512 ·Ic

Cn+0.223 ·Id

Cn+0.218 ·Ir

Cn−0.181A

Cn(4.3)

to the DCA combined result (IDCA). For a better comparison between different

batteries and cell layouts, all partial results and the combined result are normal-

ized to Cn. The DCA has, therefore, the unit A Ah−1.

The impact of the prior usage on the DCA and differences between cell layouts

is shown in Figure 4.5. The charge currents after prior charge Ic, shown in Fig-

ure 4.5 (a), are lower than after discharge Id, Figure 4.5 (b). Ir, shown in Fig-

ure 4.5 (c), is at the same level as Idbut has a much broader variety between

cell layouts. The influence of the short-term usage before the DCA is further

discussed in Section 4.3.2, next to other influencing factors. It is also shown that

disregardless of the short-term usage, the charging currents are always higher

for lower plate counts.

4.1 Standard Measurement Test Procedures for DCA

(a) (b) (c)

1 5 10 15 20

Cycle Number

0.5

1.5

Normalized Charge Current / A Ah-1

EFB+CA complete battery

EFB+CA complete cell

EFB+CA middle size cell

EFB+CA small size cell

1 5 10 15 20

Cycle Number

0.5

1.5

Normalized Charge Current / A Ah-1

12345

Time / d

0.5

1.5

Normalized Charge Current / A Ah-1

Figure 4.5: Partial results (a) Ic, (b) Id, and (c) Irof the DCA EN test of the

EFB+CAbattery and different cell layouts (adjusted from Ref. [10]).

(a) (b) (c)

1 5 10 15 20

Cycle Number

0.5

1.5

Normalized Charge Current / A Ah-1

1 5 10 15 20

Cycle Number

0.5

1.5

Normalized Charge Current / A Ah-1

12345

Time / d

0.5

1.5

Normalized Charge Current / A Ah-1

EFB+CA middle size cell

EFB+CB middle size cell

EFB+CC middle size cell

EFB+CD middle size cell

Figure 4.6: Partial results (a) Ic, (b) Id, and (c) Irof the DCA EN test of four dif-

ferent EFB+C middle size cells (adjusted from Ref. [10]).

4 Dynamic Charge Acceptance

Differences between additives are shown in Figure 4.6 for the middle size cells.

For Icand Idthe DCA results line up the same way as they did within the CA2

EFB+CA< EFB+CB< EFB+CC< EFB+CD. Only for the Irthe results for the

EFB+CAand EFB+CBtest cells are switched.

Table 4.4: Final results of the DCA test according to EN 50342-6:2015.

Cell layout EFB+CAEFB+CBEFB+CCEFB+CD

Complete battery 0.3AAh−10.4AAh−10.54AAh−10.53AAh−1

Complete cell 0.19AAh−10.23 AAh−10.39AAh−10.44A Ah−1

Middle size cell 0.33 AAh−10.4AAh−10.61A Ah−10.77AAh−1

Small size cell 0.41AAh−10.47AAh−10.71AAh−10.8 AAh−1

In Figures 4.7 to 4.10, the average results of the (a) Ic, (b) Id, (c) Irpartial results

and (d) the final IDCA are visualized and summarized in Table 4.4. With only a

few exceptions, the final IDCA result aligns with increased DCA for test cells with

lower plate count.

Basically, from the Figures 4.7 to 4.10 the same conclusions can be drawn as

from Figure 4.5. The charge currents after prior charge Icare lower than after

discharge Idfor all battery and cell types. Iris at approximately the same level

as Id. It can further be concluded that all partial and complete DCA results are

quantitatively higher for lower plate counts. The only exception is observed for

the EFB+CAand EFB+CB, in which the middle size cells accept slightly higher

Idthan the small size cells of the respective same type. Small size cells of the

EFB+CCand EFB+CD, the Idand Irreach a limited value due to the test definition

(charge limitation at 33.3·I20).

4.1 Standard Measurement Test Procedures for DCA

0.5

1.5

Normalized Charge

Current / A Ah-1

(a)

0.5

1.5 (b)

0.5

1.5 (c)

IDCA

0.5

1.5 (d) Battery

Complete cell

Middle size cell

Small size cell

Figure 4.7: EFB+CA: (a-c) Partial and (d) final result of the DCA EN test.

0.5

1.5

Normalized Charge

Current / A Ah-1

(a)

0.5

1.5 (b)

0.5

1.5 (c)

IDCA

0.5

1.5 (d) Battery

Complete cell

Middle size cell

Small size cell

Figure 4.8: EFB+CB: (a-c) Partial and (d) final result of the DCA EN test.

0.5

1.5

Normalized Charge

Current / A Ah-1

(a)

0.5

1.5 (b)

0.5

1.5 (c)

IDCA

0.5

1.5 (d) Battery

Complete cell

Middle size cell

Small size cell

Figure 4.9: EFB+CC: (a-c) Partial and (d) final result of the DCA EN test.

0.5

1.5

Normalized Charge

Current / A Ah-1

(a)

0.5

1.5 (b)

0.5

1.5 (c)

0.5

1.5 (d) Battery

Complete cell

Middle size cell

Small size cell

Figure 4.10: EFB+CD: (a-c) Partial and (d) final result of the DCA EN test.

4 Dynamic Charge Acceptance

4.1.3 Ford long-term Run-in DCA Test B

During the development of the DCA EN test, a so-called “Test B” was used to es-

tablish a realistic battery performance in the field operation [9, 80]. Research on

batteries showed that the DCA at the beginning of usage is high but gets lower

and stabilizes at this low value after a few weeks of usage [9]. This effect is called

the run-in effect [9]. The recuperation currents observed in typical customer ve-

hicles under moderate temperature, moderate and predominatly urban traffic

usage can be reproduced using the DCA run-in test B [64]. Even though this

test takes several weeks, it delivers precise DCA results compared to the vehicle

operation in exchange. The test procedure applied in this work is slightly ab-

breviated. Essentially containing one week of the DCRss sequence described in

Section 4.1.2 followed by three weeks of a modified DCRss test sequence. Only

this short test duration needs to be evaluated since the test cells have stabilized

much faster, resulting in stabilized DCA run-in values after four weeks of testing.

Further differences between the DCRss run-in DCA test versus the EN version

include the following:

• Quasi-open circuit voltage (qOCV) correction every morning. The open

circuit voltage (OCV) is measured after more than 15h without trips but

still with the KOL resistor continuously connected, and hence consistently

below thermodynamic equilibrium voltage. This value corrects the charge-

balance target, compensating for side reactions, self-discharge, and Ah bal-

ance measurement errors. All of the named might be neglected for five

days in the DCRss part but not for several weeks or months during the

run-in DCA test B.

• The KOL resistor will only be compensated to a certain degree (to about

a third during run-in vs. completely in the DCRss part) in the ongoing

Ah balance calculation. This ensures that qOCV corrections will always

occur at the low end of the OCV tolerance interval. After days with a pos-

itive charge balance, the OCV will not be affected if it remains high due to

slowly relaxing positive half-cell overpotentials. A weekly SoC swing by

several percent of Cnwill develop. This behavior is expected in vehicles

due to SoC or SoF measurement errors and variability in vehicle usage.

4.1 Standard Measurement Test Procedures for DCA

Furthermore, the DCA run-in test B needs to be adjusted from battery to cell

level:

• All other voltages (e.g., the OCV and the qOCV after a pause for more than

6h) were divided by six.

• The OCV at 80% SoC (OCV80) was adjusted to the cell layout.

• The KOL resistor is scaled to the cell level (as described for the DCRss part

in the EN test).

• The KOL resistor compensation is scaled to the cell layout.

• The KOL resistor must be checked regularly for corrosion effects over the

extremely long duration of the run-in DCA test.

Figure 4.11 presents the results of the run-in DCA test procedure. The moving

average of the recuperation current is visualized in Figures 4.11 (a), (c), (e), and

(g) for the different additives investigated. All cell and battery types except the

EFB+CBunits showed the typical DCA decline during the first few weeks of

vehicle usage, i.e., the run-in effect. All recuperation currents have stabilized

after two or three weeks of DCA run-in test B. Furthermore, the comparabil-

ity between the battery and the complete cell is very high. However, not all

battery types show the typical increase of the DCA for lower plate counts. Fig-

ures 4.11 (b), (d), (f), and (h) show the V6h values for the different additives

investigated, compared to the horizontal OCV target. The target OCV values at

80% SoC depend on the battery technology. For the EFB+CAand EFB+CBcells it

is 2.085V and for the EFB+CCand EFB+CDit is 2.09V, respectively. The dashed

lines (battery voltage) represent the normal OCV swing once a week during the

run-in DCA test. On day seven, where the first SoC correction occurs for the

cells, all cells have a higher voltage level than the batteries. Therefore the cells

had not to be recharged as much, resulting in a lower OCV swing on the cell

level. One extreme example is shown in Figure 4.11 (d), where the EFB+CBcom-

plete cell has a voltage at day seven even higher than the target level. The cells

need a longer time than the batteries before the self-discharge brings down the

voltage level. At the beginning of the third week, all cells can take charge and

show the typical OCV swing. Moreover, only if the OCV swing occurs compa-

rable DCA results in the run-in DCA test B are generated.

4 Dynamic Charge Acceptance

0 7 14 21 28

Time / d

0.5

1.5

Irecu / A Ah-1

(a)

0 7 14 21 28

Time / d

0.5

1.5

Irecu / A Ah-1

(c)

0 7 14 21 28

Time / d

0.5

1.5

Irecu / A Ah-1

(e)

0 7 14 21 28

Time / d

0.5

1.5

Irecu / A Ah-1

(g)

0 7 14 21 28

Time / d

2.05

2.1

2.15

V6h per Cell / V

(b)

0 7 14 21 28

Time / d

2.05

2.1

2.15

V6h per Cell / V

(d)

0 7 14 21 28

Time / d

2.05

2.1

2.15

V6h per Cell / V

(f)

0 7 14 21 28

Time / d

2.05

2.1

2.15

V6h per Cell / V

(h)

Figure 4.11: The normalized charge currents and voltages after 6h pause of the

(a,b) EFB+CA, (c,d) EFB+CB, (e,f) EFB+CC, and (g,h) EFB+CDduring

1 week of DCRss and 3 weeks of Ford long-term run-in DCA test B

(adjusted from Ref. [10]).

4.1 Standard Measurement Test Procedures for DCA

4.1.4 Comparing the different DCA Test methods

Figures 4.12 to 4.15 compare the three different DCA measurement results (a)

CA2, (b) DCA EN, and (c) DCA run-in test. Most tests showed a systematically

higher DCA for lower plate counts. Indeed, this behavior is more distinct for

the CA2 and the DCA EN than for the run-in test. However, the DCA run-in

test results are chosen at the end of the four weeks of testing for cells without

failures or prior to any failure, e.g., for the EFB+CCmiddle and small size cells.

The comparability between the complete battery and the complete cell results is

relatively low for the CA2 but higher for the DCA EN and the DCA run-in test

B. For the latter two, the battery DCA results slightly exceeds the complete cell

DCA.

The CA2 results correlate highly with the DCA EN test, as seen in Figure 4.16.

The results obtained from the CA2 test are generally higher than those accord-

ing to the DCA EN test for all battery/cell types. The test procedure itself can

explain this general trend. The CA2 determines the charge acceptance using

a single pulse after discharging the battery. This approach results in a much

higher DCA than after prior charge. Since the DCA EN test combines the DCA

after prior discharge, after prior charge, and during micro cycles, this value is

lower. Furthermore, the quantitative ranking of the CA2 and the DCA EN is the

same for all types and layouts: EFB+CA< EFB+CB< EFB+CC< and EFB+CD.

Both test methods would therefore deliver qualitatively similar results during

material screenings as long as similar test cell layouts are compared.

The DCA EN test and the DCA run-in test B are qualitatively comparable for

complete batteries and cells for three out of four types: EFB+CA, EFB+CC, and

EFB+CD, as shown in Figure 4.17. The run-in test B results of the EFB+CBbattery

and cells were higher than the DCA EN test results. However, these correlations

were only examined for test cells without failures or prior to any failure (e.g., the

EFB+CCmiddle and small size cells).

4 Dynamic Charge Acceptance

ISBA

0.5

1.5

Normalized Charge

Current / A Ah-1

(a)

IDCA

0.5

1.5 (b)

IRun-in

0.5

1.5 (c) Battery

Complete cell

Middle siz cell

Small size cell

Figure 4.12: EFB+CA: (a) CA2, (b) DCA EN, and (c) long-term DCA run-in test B

(adjusted from Ref. [10]).

ISBA

0.5

1.5

Normalized Charge

Current / A Ah-1

(a)

IDCA

0.5

1.5 (b)

IRun-in

0.5

1.5 (c) Battery

Complete cell

Middle siz cell

Small size cell

Figure 4.13: EFB+CB: (a) CA2, (b) DCA EN, and (c) long-term DCA run-in test B

(adjusted from Ref. [10]).

ISBA

0.5

1.5

Normalized Charge

Current / A Ah-1

(a)

IDCA

0.5

1.5 (b)

IRun-in

0.5

1.5 (c) Battery

Complete cell

Middle siz cell

Small size cell

Figure 4.14: EFB+CC: (a) CA2, (b) DCA EN, and (c) long-term DCA run-in test B

(adjusted from Ref. [10]).

ISBA

0.5

1.5

Normalized Charge

Current / A Ah-1

(a)

IDCA

0.5

1.5 (b)

IRun-in

0.5

1.5 (c) Battery

Complete cell

Middle siz cell

Small size cell

Figure 4.15: EFB+CD: (a) CA2, (b) DCA EN, and (c) long-term DCA run-in test B

(adjusted from Ref. [10]).

4.1 Standard Measurement Test Procedures for DCA

0 0.5 1 1.5

Normalized Charge Current from CA Test 2 / A Ah-1

0.5

Normalized Charge Current

from DCA (EN) Test / A Ah-1

Figure 4.16: Correlation CA2 and DCA EN test (adjusted from Ref. [10]).

0 0.5 1 1.5

Normalized Charge Current from End of Run-in Test / A Ah-1

0.5

Normalized Charge Current

from DCA (EN) Test / A Ah-1

Figure 4.17: Correlation DCA EN test and DCA run-in test (adjusted from Ref.

[10]).

4 Dynamic Charge Acceptance

4.2 Modified Test Procedures for DCA

The standard test methods are highly restricted in terms of investigated SoC and

prior usage. On the other hand, they are hardly comparable because too many

influencing factors are changed at once. Standard tests were used as a baseline

to create new test procedures for investigations on influencing factors. Namely,

using the CA2 single pulse test but instead of only investigating 91% SoC after

prior discharge, it will be extended to investigate various SoC after prior charge

and after prior discharge. Therefore, a broad range of influencing factors can be

investigated. Secondly, the DCA EN test is changed to investigate the DCA after

prior charge and discharge both at 80% SoC. This way, only one factor, the prior

usage, is changed, and better comparisons can be drawn.

Table 4.5: Test plan for investigating influencing factors on DCA using the

EFB+CXand EFB+CYcomplete cell, middle and small size cell.

Test

order Procedure Description in Visualized in

1 C20 test (scaled to Cn) Section 3.4.1

2 Modified CA2 test Section 4.2.1 Figure 4.30

2.1 Determine electrolyte concentration Section 3.4.3 Figure 4.30

3 Adjustment of the electrolyte Section 3.4.4

conc. to 1.247gcm−3at 80% SoC

4 Modified CA2 test Section 4.2.1 Figures 4.22, 4.30,

4.33, 4.34, 6.37

4.1 Determine electrolyte concentration Section 3.4.3 Figures 4.30, 4.33

5 DCA EN test Section 4.1.2 Figure 6.11(a), (b)

6 Modified DCA EN test Section 4.2.2 Figures 4.27, 6.11(c)

6.1 Determine electrolyte concentration Section 3.4.3 Figure 4.26

7 Repetition of modified DCA EN test Section 4.2.2

7.1 LSM pictures after prior discharge Section 4.3.2 Figure 4.28

7.2 LSM pictures after prior charge Section 4.3.2 Figure 4.28

The most significant influences on the DCA are investigated in Section 4.3, using

the modified DCA tests. The test plan used is listed in Table 4.5, containing

cross-references to the detailed descriptions and figures showing the test results.

4.2 Modified Test Procedures for DCA

4.2.1 CA2 Test at various SoC after Prior Charge and Discharge

The CA2 single pulse test originally only tests the charge acceptance after prior

discharge at one specific SoC. To investigate the SoC influences and the effects

of the short-term usage, the test procedure was modified. Therefore, the fully

charged test cell was discharged with 1·I20 = 1A until the target (between 95%

SoC and 50% SoC) was reached. Afterward, the cells were rested for 16h before

the pulse test (charging for 10s with a voltage limit of 2.4V). This way, the charge

acceptance after prior discharge is determined for various SoC. To determine the

charge acceptance after prior charge, the cells were discharged to 0% SoC and

charged with 1·I20 = 1A, with a voltage limit of 2.6V, until the target SoC. After

charging, the test cells were rested for 16h, and the pulse test (charging for 10s

with a voltage limit of 2.4V) was executed.

(a) (b)

Figure 4.18: (a) The preconditioning used for the modified CA2 test (adjusted

from Ref. [26]) and (b) the preconditioning proposed by Smith et al.

(adjusted from Ref. [81]).

A similar preconditioning for testing the influence of prior usage and SoC on

valve-regulated lead-acid (VRLA) batteries was proposed by Smith et al. [81].

In contrast to their procedure, the test cells within this work were recharged

between all charge acceptance tests. This way, it can be assured that the tar-

geted SoC was investigated without any summed-up errors of previous pulses.

A graphical comparison between the preconditioning used in this work and the

preconditioning proposed by Smith et al. is shown in Figure 4.18. Test results

are partly shown in Section 4.3 investigating influencing factors on the DCA. A

summary of the CA2 single pulse test results at different SoC after prior charge

and discharge are given in Section 6.

4 Dynamic Charge Acceptance

Additionally, the charge acceptance after prior charge of 1h was investigated.

Therefore, the cells were discharged to 5% SoC less than the target SoC and

charged with 1·I20 = 1A for 1h to reach the target SoC. Within this step, a voltage

limit of 2.6V and Ah counting was used to reach the target limit. A comparison

between the test results after prior discharge, after prior charge from 0% SoC,

and after prior charge of 1h is given in Figure 4.22.

4.2.2 DCA Test at 80% SoC after Prior Charge and Discharge

A modified charge acceptance test based on the DCA EN 50342-6:2015 was also

conducted. For this modified DCA EN test, only two parts out of the standard

test were executed. The first, is the DCA after prior charge (Ic) at 80% SoC, sim-

ilar to the standard. The second is the DCA measurement after prior discharge

(Id). However, Idwas conducted at 80% SoC SoC rather than 90% SoC (as de-

fined within the standard). This way, both histories are comparable without any

SoC influence. The modified DCA EN test is visualized in Figure 4.19.

Figure 4.19: The modified DCA EN test.

Further experiments during the modified charge acceptance test are executed for

investigations on the structural differences of the negative plates depending on

the short-term usage. Therefore, the test procedure was to be carried out twice.

First, the complete modified DCA test sequence was executed, and in the pause

before the DCA cycling, the electrolyte concentration was measured at the top,

middle, and bottom of the test cell. Afterward, the modified DCA test was re-

4.2 Modified Test Procedures for DCA

peated but stopped at 80% SoC after prior charge and 20h rest time before the

DCA cycling started. The cells from the same production charge were stopped

at 80% SoC after the prior discharge before the DCA cycling started. Laser scan-

ning microscopy (LSM) was used to imaging the surface of the negative plate

once after charge and once after discharge.

In the work of Budde-Meiwes, the washing procedure was done using conven-

tional tab water [9]. The long washing time using water could cause the forma-

tion of new crystals [9]. This could explain why the lead sulfate crystal struc-

ture on the surface of the negative plate could not be distinguished depending

on their prior usage using LSM pictures [9]. Compared to the work of Budde-

Meiwes, the preconditioning, the washing, and drying procedure used within

this work differs.

For LSM measurements, the examined cells were opened, the cell stack was

taken out, and a negative electrode was separated. Keeping the exposure to air

as short as possible (less than 1min), the plates were cleaned in a beaker using

isopropanol. Exposure to air and water must be avoided if the active material

is highly reactive and the plate surface area might be changed. Therefore, iso-

propanol can be used, as a none reactive substance, to clean off the electrolyte

(sulphuric acid) from the negative plate and avoid any further reactions such

as the growing of lead sulfate crystals. One washing consisted of five steps.

Each step took 30min with continuous stirring. This way, the electrodes were

rinsed off without using mechanical forces and possibly destroying the micro-

scopic structure of the negative electrode. The isopropanol was replaced after

each step, keeping the concentration gradient between the washing medium and

the substance left in the pores high. Right after the washing procedure, the elec-

trodes were dried in a vacuum oven at 60 ◦C for 24h.

Test results are partly shown in Section 4.3 investigating the influencing factors

on the DCA. A summary of the DCA results at 80% SoC after prior charge and

discharge are given in Section 6.

4 Dynamic Charge Acceptance

4.3 Influencing Factors on the DCA

Identifying and understanding the influencing factors on the DCA is worth hav-

ing a closer look at the processes during charge and discharge. These processes

can be expressed as a combination of an electrochemical, physical, and chemical

processes [82]. The three processes, shown in the bottom part of Figure 4.20, and

the factors which they are affected by are further explicated in the following [9,

82]:

• The electrochemical process is rate limited by the terminals’s current. At

the negative plate (N), two electrons are removed from a Pb atom during

discharge, leaving a Pb+

2ion. During charge, this procedure is reversed.

A Pb+

2ion combined with two electrons form a lead atom. Since the elec-

trochemical process depends on the current and the reaction speed, this

process is defined by the conductivity of the grid and active mass (AM),

temperature, and the surface area of the AM.

• The physical process is the diffusion process. The concentration gradient

caused by the formation or reduction of Pb+

2ions close to the electrode

arising during charge or discharge causes diffusion. Diffusion depends

on temperature, the deposition, and thereby the concentration gradient of

Pb+

2, the diffusion distance, the electrolyte concentration, and stratification.

• Last but not least, the chemical process of the dissolution of PbSO4crys-

tals, which takes place as long as the concentration of Pb+

2ions is higher

than the saturation concentration. The dissolution process is dependent on

the electrolyte concentration and stratification, the concentration of ions,

and thereby diffusion constant, SoC, time, crystal size, temperature, and

potential [82].

For a good DCA, these three processes need to be running equally well. Sauer

et al. state reasons for the dissolution of PbSO4crystals as the limiting process

for DCA [82]. While Pilatowicz et al. supplemented a model with diffusion for

valid results during charging [24].

4.3 Influencing Factors on the DCA

Figure 4.20: Influences on the DCA (lower part is based on [9]).

4 Dynamic Charge Acceptance

Since the electrochemical, physical, and chemical process determine the charg-

ing and discharging speed, the driving or prohibiting factor for DCA must be

found among the influencing factors of these three processes. SoC, temperature,

short-term usage, pauses, voltages, electrolyte concentration, and stratification

are only a few factors that have been identified to influence the DCA [9]. The

main influencing factors and their effects on the charging process are visualized

in Figure 4.20 and further discussed in this section. Poor DCA and inefficient

charging have been reported before [77, 82, 83]. However, the processes and

how to influence them are not yet fully understood.

The negative electrode is known to be the limiting factor for DCA [9, 32, 33, 34,

84]. Moreover, it is also the key to improve the DCA [82]. The negative active

mass (NAM) pore diameter is bigger, determining the active reaction surface

area (which is four times smaller than of a positive plate (P) [85]), the PbSO4

crystal size and the distances for ion diffusion [33, 34]. Higher polarisation of

the negative electrode during charge pulses has been shown [86]. An additional

factor for the DCA limitation of the negative is the small double-layer capaci-

tance typically up to 1.0FAh−1of the negative and 70.0FAh−1of the positive

electrode [37]. Therefore, the positive electrode has a greater ability to absorb

short, sharp charge pulses, while the negative does not [85]. Therefore, further

investigations will mainly focus on the NAM.

The most significant influencing factors are determined and shown in the fol-

lowing subsections. For this reason, test results obtained from the literature were

evaluated and compared to own measurements. The test procedure used is listed

in Table 4.5, containing cross-references to the sections describing the tests and

figures showing the test results.

4.3.1 State of Charge

The influences of SoC were analyzed by Schaeck et al. in a test series on AGM

batteries [87]. Immediately after step wise (10% steps) discharging the battery

from 100% SoC to 60% SoC, single high-rate charge pulses were performed [87].

Smith et al. also investigated the effects of different SoC-levels on the DCA at

90%, 70% and 50% SoC, using the DCApp procedure on VRLA test cells [81].

For both DCA test procedures and battery types, a clear trend of increased DCA

4.3 Influencing Factors on the DCA

at lower SoC can be seen [81, 87]. However, the test procedure from Schaeck et

al. does not consider that the high-rate charge pulses at each investigated SoC

step will influence all following SoC values [87]. Furthermore, the test results of

AGM batteries do not have the same influencing factors than EFBs. Neverthe-

less, quantitative conclusions, such as increasing DCA at lower SoC, can still be

drawn for all types of LABs [87]. For evaluating EFB, the DCA at different SoC

and with charge and prior discharge has also been tested within this work. The

results are visualized in Figure 4.22.

Reasons for higher DCA at lower SoC have been stated in literature [9, 82]. Only

small amounts of lead sulfate are available at high SoC. With a lower number of

PbSO4, its active surface area and, thereby, its solubility gets lower [9]. Moreover,

the solubility rises with low acid concentrations, which decreases with decreas-

ing SoC [9]. Further analyses of the electrolyte concentration can be found in

Section 4.3.4. Concluding, at high SoC, the dissolution of the lead-sulfate crys-

tals becomes the limiting step during charging [82]. Moreover, the dissolution

rate is inversely proportional to the crystal radius. That means the DCA in-

creases when the crystal size is smaller. This can be adjusted by increasing the

discharging current during SoC adjustment. The higher the discharging current,

the smaller the lead sulfate crystals, thereby the higher the DCA [9].

Contradicting the SoC influence on the DCA observations on small cycles (ap-

proximately 1% SoC) have been made. If a battery is cycled this way, the charge

acceptance decreases with increased cycling time even though the SoC is ap-

proximately stable [88]. The recently formed lead sulfate crystals appear to have

a higher dissolution rate than older crystals [88]. This phenomenon is also re-

ferred to as hardening crystals [88].

4.3.2 Short-term Usage

The short-term usage was defined by Kowal et al. as a time period of up to

two or three days, maybe even a week [89]. The short-time usage includes prior

charge or discharge, current rates, the lowest SoC, rest periods, and many more

influencing factors affecting the DCA [89]. The influence of the operating history

on the DCA is called the "DCA memory effect" [9]. Figure 4.21 compares the

DCA after charge, and prior discharge [9, 71, 82]. Sauer et al. investigated the

4 Dynamic Charge Acceptance

influence of the short-term usage on flooded batteries at 90% SoC [82], while

Budde-Meiwes also investigated flooded batteries but at 80% SoC [9]. Bozkaya

et al. evaluated the DCA using the DCA EN test [61], which tests the DCA after

prior charge at 80% SoC and after prior discharge at 90% SoC [71]. The DCA

after prior discharge achieved values up to ten times higher compared to the

DCA after prior charge [82]. Comparable work about VRLA batteries show two

to five times higher DCA values for the prior discharge [87, 90]. This effect was

further analyzed by Meissner [34, 36]. The effects of the short-term usage on the

DCA were summarized as follows [9]:

• higher DCA after prior discharge than after prior charge

• poorer DCA after prior discharge at a low current rate compared to a high

current rate

• DCA degrades significantly after rest time

• all effects are reversible

100

Charge Current / %

0.09 A Ah-1

0.15 A Ah-1

0.25 A Ah-1

1.09 A Ah-1

0.54 A Ah-1

1.15 A Ah-1

After Prior Charge After Prior Discharge

Single pulse at 90% SoC

Simulated drive cycles at 80% SoC

qDCA: After charge at 80%, after discharge at 90% SoC

Figure 4.21: Influence of the short-term usage on the DCA (green [82], purple

[64] and light blue EFB+C1[71] and red EFB+C5[71]).

4.3 Influencing Factors on the DCA

To test the influence of the short-term usage, an EFB+CXmiddle size cell (3P2N)

with an electrolyte concentration of 1.25gcm−3at 80% SoC, which correlates

with the electrolyte concentration of a complete battery at 80% SoC, was tested.

First, the DCA after prior discharge. Therefore, the fully charged test cell was

discharged using I20 until the target SoC was reached, rested for 16h, and charged

with high-rate charge pulses for 60s, limited by 2.4V. The first 10s are evaluated

to determine the DCA at each target SoC after prior discharge. 5% SoC steps are

investigated, starting from 95% SoC down to 50% SoC. Between every investi-

gated SoC, the test cell was fully charged again. The charging regime takes 24h

with 5·I20 and finishes with a 16h rest before the DCA determination for the next

SoC can be started.

For the DCA measurement after prior charge, the fully charged test cell was dis-

charged using I20 till 0% SoC and then charged using I20 till the target SoC. Af-

terward, the test cell is rested for 16h and charged with high-rate charge pulses

for 60s, limited by 2.4V. Only the first 10s are evaluated. 5% SoC steps are in-

vestigated in a range between 95% SoC to 50% SoC. Also, for the prior charge,

the test cell was fully charged between every investigated SoC.

Lead sulfate crystals are formed, during discharging, while they are dissolved

during charging. Thereby, the form and amount of lead sulfate crystals have a

direct effect on rechargeability and, thereby, on DCA. Atomic force microscopy

(AFM) images can be used to observe an electrode, showing fine crystals after

discharging and coarse crystals after charging [91]. This can be explained by

investigating the charging and discharging process itself. During a discharging

event, first fine and later coarse PbSO4crystals are created. The crystal size de-

pends on the discharging current and time. The higher the discharging current,

the finer the lead sulfate crystals [92]. This could also be shown using AFM

images [91]. High discharging currents create crystal sizes < 100nm while low

discharging currents mainly create crystals with a size > 100nm [32]. The growth

of coarse crystals could be related to a high Pb2+ion concentration on the surface

of the electrode [93]. However, if a higher discharge current is used, the Pb2+ion

concentration on the surface of the electrode decreases, and thereby, the crystals

will stay smaller [93]. The shorter the discharging time, the finer the lead sul-

fate crystals, growing more coarse as the discharging time exceeds. However, all

crystals always exhibit a distribution around an average crystal size.

4 Dynamic Charge Acceptance

During a charging event, the finest PbSO4crystals are completely dissolved

first because of there higher solubility through a bigger reaction surface area.

Thereby, fine crystals can be found [91] and high DCA is observed after prior

discharge [82, 90, 94, 95]. Immediately after a charge event, however, the fine

lead sulfate crystals are already consumed, and only material of coarse crystals

with a low reaction surface area and lower solubility remains, also visible in the

mentioned AFM images [91]. Only a poor DCA is observed after prior charging

[82, 90]. However, Budde-Meiwes could not visualize fine and coarse crystals

after discharge and charge, respectively, using laser scanning microscope (LSM)

pictures [9]. One possibility why it was not possible to find crystals of different

size could be that most of the reaction surface lies within the pores, while only

the surface of the plate but not the inside of the pores can be pictured using LSM.

5060708090100

SoC / %

0.2

0.4

0.6

0.8

1.2

Normalized Charge Current / A Ah-1

After discharge

After 1h charge

After charge from 0% SoC

Figure 4.22: Influence of the SoC and the short-term usage on the DCA on an

EFB+CXmiddle size cell.

The deposition process of PbSO4crystals during discharging is faster compared

to the dissolution process of PbSO4crystals during charging [91, 92]. This is one

more explanation for low DCA. If the process without any limitations is slow,

the DCA will also be low. All of the stated observations explain the higher DCA

4.3 Influencing Factors on the DCA

after prior discharge compared to prior charge, shown in Figure 4.22 for differ-

ent SoC for an exemplary EFB+CXmiddle size cell (3P2N).

Next to prior charging or discharging, the short-term usage of a battery or cell

also consists of the rest time between preconditioning and the DCA test. AFM

images of the negative plate that was discharged and rested afterwards show

that within a few minutes, some crystals grew bigger while the smaller ones

disappeared [91]. Within Figure 4.23, this behavior is visualized. Figure 4.23 (a)

shows fine PbSO4crystals after none or after a short pause to (b) coarse PbSO4

crystal structure after a long pause. In Figure 4.23 (c), the distribution of PbSO4

crystal size over time is visualized [34].

Figure 4.23: (a) Fine PbSO4crystals after short pause (b) growing to coarse

PbSO4crystals after a long pause, and (c) the distribution of PbSO4

crystal size over time (adjusted from Ref. [34]).

The surface tension of small crystals is higher than the one of coarse crystals

[34]. In an electrolyte with homogeneous lead sulfate solubility and lead ion

concentration, the small crystals combine to larger crystals to reduce the surface

tension and reach a lower energy state [9, 30, 34]. Thereby, the average crystal

radius rises and the number of crystals decreases, but the total lead sulfate vol-

ume stays constant during a pause [9, 30, 34]. This results in less lead sulfate

surface area, and thereby, lower DCA [64, 91]. Figure 4.24 shows the influence

of the rest time after discharge for flooded batteries [9, 82]. Only when the bat-

tery was discharged, and small lead sulfate crystal were created, the rest period

significantly influences the resulting DCA [64]. The DCA is not as dependent on

the rest time after prior charge because only coarse crystals are left, and DCA is

low independent of the rest time [9, 90].

4 Dynamic Charge Acceptance

0 20 40 60 80 100

Rest Time / h

100

Charge Current / %

Single pulse after discharge at 90% SOC

Simulated drive cycles after discharge at 80% SOC

Figure 4.24: Influence of the pause before the DCA (green [82] and purple [9]).

The knowledge of crystal behavior during a pause has to be combined with the

knowledge of the PbSO4crystal size after charge and after discharge. All three

parts of Figure 4.25 start the same [34]. Starting with a discharge from 100% SoC

to Figure 4.25 (a) 70%, (c) 80% or (b) 90% SoC, where the average crystal size is

small, and the distribution is narrow. During a rest time of 16h - 24h, the average

crystal size gets bigger, and the distribution gets wide as well. Up to this point,

only small differences develop due to different discharging depths. In the lower

parts of Figure 4.25 (a) the dissolving of fine PbSO4crystals during the charging

from 70% SoC to 80% SoC and the distribution of the leftover PbSO4crystals

after prior charge is shown. Only large PbSO4crystals are left. Therefore, for

any future charging step, the dissolving will be slower, resulting in a low DCA

after prior charge [34, 82, 90]. The low part of Figure 4.25 (b) shows the old

(coarse) and the newly developed fine PbSO4crystals after the next discharging

step from 90% to 80% SoC. For any future charging step, the dissolving will be

very fast if these newly formed, fine PbSO4crystals can be dissolved quickly.

This results in a high DCA after prior discharge [34, 82, 90]. In Figure 4.25 (c),

no more charging or discharging happens, just an even longer pause, resulting

in only large PbSO4crystals with a broader distribution [82, 92] via the Ostwald

Ripening process. Thereby, a low DCA after prior charge can be observed [34,

4.3 Influencing Factors on the DCA

43, 82, 87, 90]. Next to the influences of charging or discharge, it was shown by

Schack et al. and Sauer et al. that the influence of the duration of the rest period

is relatively small [82, 87].

(a) (b) (c)

Figure 4.25: Distribution of PbSO4crystals after prior (a) charge, (b) discharge,

and (c) pause (adjusted from Ref. [34]).

The electrolyte concentration is measured at the test cell’s top, middle, and bot-

tom shortly before the two test sequences. In Figure 4.26, the measuring re-

sults of the electrolyte concentration and the stratification of the EFB+CXand the

EFB+CYcells after (a) charge and (b) discharge are compared. It can be shown

that the average electrolyte concentration is lower after prior charge. Even more

outstanding is the high acid stratification after prior charge, which does not exist

after prior discharge. The differences in the electrolyte concentration as well as

the stratification after charge compared to after discharge, might be the source

of different DCA. However, both will be discussed in Section 4.3.4.

In Figure 4.27, the DCA of a middle size 3P2N EFB+CXand EFB+CYcell is com-

pared (a) after prior charge at 80% SoC and (b) after prior discharge at 80% SoC.

As expected, the DCA after discharging is about four times higher than after

charging. The DCA of the EFB+CYcell is moderately higher for both histories.

4 Dynamic Charge Acceptance

(a) (b)

EFB+CXEFB+CY

1.1

1.15

1.2

1.25

1.3

Electrolyte Concentration / g cm-3

EFB+CXEFB+CY

1.1

1.15

1.2

1.25

1.3

Electrolyte Concentration / g cm-3

Figure 4.26: The average electrolyte concentration and maximum stratifica-

tion within two EFB+CXand EFB+CYmiddle size cell after prior

(a) charge and (b) discharge (measured during the modified DCA

EN test).

(a) (b)

EFB+CXEFB+CY

0.5

1.5

Normalized Charge Current / A Ah-1

EFB+CXEFB+CY

0.5

1.5

Normalized Charge Current / A Ah-1

Figure 4.27: Modified DCA EN test of the EFB+CXand EFB+CYmiddle size cell

after prior (a) charge and (b) discharge.

Figure 4.28 shows the LSM pictures after prior charge and after prior discharge

for the two different EFB+CXand EFB+CYtest cells at three different heights

(top, middle, and bottom). For the bottom part, the existence of superficial dense

4.3 Influencing Factors on the DCA

sulfate layers results from stratification and stand times during initial cycling.

This structure seems independent of the additives used and remains unchanged

after charge and subsequent discharge test. After prior charge, Figure 4.28 (a)

and (b), both cell types show many lead-sulfate crystals of several µm sizes at

the surface at the top of the cell. While after prior discharge, Figure 4.28 (c) and

(d), the PbSO4 crystals are largely dissolved, and the crystal size at the top of the

negative plates is fine.

Figure 4.28: LSM picture of the negative plate surface (a) after charge, (c) after

discharge of the EFB+CXand (b) after charge, and (d) after discharge

of the EFB+CY(1-3) at the top, middle, and bottom.

Five different frames have been compared at each height to ensure a uniform

surface. One, representative frame was chosen for vizualization in Figure 4.28.

It was expected to identify coarse crystals after charging and fine crystals after

discharging. However, differences between EFB+CXand EFB+CYshould also be

noticeable, at least after discharge where the EFB+CXand EFB+CYcells conduct

different DCA as well. Major differences between EFB+CXand EFB+CYafter

prior charge could not be identified within the LMS pictures. Slightly finer lead

sulfate crystals could be identified for the EFB+CYcell after discharge. However,

further experiments with different additives would be needed for confirmation.

On the other hand, it is known that at 80% SoC, the active material consists of

60% pores [96]. For this reason, it is most likely that most of the DCA-relevant

4 Dynamic Charge Acceptance

processes are conducted within the pores, which would not be visible with an

LSM. In the LSM pictures, only the negative plate surfaces can be shown, which

should not be misinterpreted to show a situation representative of the overall

active material if the surface inside of the pores cannot be presented.

4.3.3 Long-term Usage

Next to short-term usage, long-term usage also influences the DCA. The long-

term real vehicle application operates at PSoC where the typical cycling ampli-

tude is around one percent of the SoC or less [9]. The DCA of new LABs cur-

rently lies between 0.5AAh−1and 1.5AAh−1[9]. The DCA should be sustained

through its complete operational life to meet the State-of-the-Art requirements

for automotive batteries. However, after a relatively short PSoC vehicle opera-

tion, the DCA decreases to around 0.1AAh−1or even lower values [64, 89]. This

is called the run-in effect and should not be misinterpreted as aging since the

battery can fulfill all power-supply system functions for years, even at this low

DCA level [28]. Moreover, employing a complete full charge can restore the high

DCA of the fresh battery [82]. However, the improvement of LABs is hampered

by the lack of predictability for DCA under realistic long-term vehicle operation

based on laboratory cell-level tests. That means the same benefits found dur-

ing cell-level laboratory tests would not necessarily be experienced after several

months of vehicle operation within a battery. At least two methodological issues

may cause such problems [7]:

• The DCA of small test cells may not linearly scale up to full automotive cell

designs due to factors like plate size, plate structure, plate count, utiliza-

tion, mass to acid ratios, assembly, and connections. This will be further

discussed in Section 4.3.7.

• DCA test methods, even the more complex Ford long-term run-in test, may

be over-simplified, yielding non-representative results even for full-size

batteries [64].

Compared to conventional applications, where the battery is operated at 100%

SoC, long-term real vehicle application operates at PSoC. This application cre-

ates large lead sulfate crystals, which are seldom or are never entirely converted

back to lead, especially at the negative electrode [97]. High sulfation will sig-

nificantly reduce the usable surface area during charging and the solubility of

4.3 Influencing Factors on the DCA

the lead sulfate crystals [9]. Therefore, batteries lose their high DCA. Additives

(whose effect on the DCA will be discussed separately in Section 4.3.8) could

slow down sulfation [9]. Nevertheless, the longer the time period before the

next full recharge, the higher the degree of sulfation [98]. After several weeks

a LAB is hardly rechargeable because the lead sulfate crystals are massive and

become irreversible [88, 98]. Therefore, refresh charge events are triggered regu-

larly in some vehicle applications to dissolve the sulfated crystals and thus keep

the level of DCA constantly high [82, 87]. The effect of dissolving sulfate crystals

can be even improved by charging at higher temperatures [82].

4.3.4 Electrolyte Concentration

In contrast to other battery technologies, the electrolyte of LABs, which is sul-

phuric acid, takes part in the main reaction. During discharge, the AMs are con-

verted from PbO2or from Pb to PbSO4at both electrodes by using sulfate ions

from the electrolyte. This results in a depletion of sulfate ions during discharg-

ing. Otherwise, they are produced during charging. Hence, acid concentration

changes during charging and discharging. The average acid concentration in the

battery cell is directly related to the SoC [99].

The accessible electrolyte is important for providing lead sulfate ions, the lead

sulfate solubility, and influencing the diffusion rate [43]. However, the lead sul-

fate solubility decreases for higher acid concentration [100]. All three factors

are influencing the DCA. Pavlov et al. investigated the charge acceptance using

10s charging pulses at various SoC and for multiple acid densities [35]. If the

electrolyte limits the cell, e.g., due to its electrolyte concentration, the charge ac-

ceptance depends only slightly on SoC [35]. However, if the electrolyte is not

the limiting factor (which is the case for the test cells in this work since both the

acid concentration and the acid amount are high), the NAM needs to be the lim-

iting factor for charge acceptance [35], visualized in Figure 4.22. Furthermore, it

has been found that larger lead sulfate crystals are formed at low acid concen-

trations, which are difficult to reduce [91, 93, 101]. Many authors consider the

solubility of lead sulfate crystals, which depends on acid concentration, as the

main factor limiting lead sulfate reduction speed, limiting DCA on the negative

plate [88, 93, 101, 102].

4 Dynamic Charge Acceptance

Next to electrolyte concentration changes during charge and discharge, there are

significant gradients within the cell as well. These concentration gradients can be

either observed in a horizontal direction throughout the pores of the active mate-

rial or in a vertical direction caused by gravity forces, known as acid stratification

[30]. Acid stratification can develop when a battery or cell is discharged, where

the electrodes consume the sulfuric acid. The leftover water lifts to the top of

the cell, decreasing the density of the acid in the upper region [103]. In extreme,

a deep discharge would lead to a low electrolyte concentration throughout the

cell, except the volume below the electrodes [104]. Diffusion homogenizes the

concentration gradients, but can hardly homogenise acid stratification because

this effect is much slower than the reverse during operation.

Even though diffusion can only slowly homogenize acid stratification, the gassing

effect caused by charging can. The emerging gas bubbles result in mixing, and

thus a homogenization of the electrolyte [89]. However, the gassing has no mix-

ing effect in the electrolyte volume below the electrodes. As gas bubbles emerge

evenly at the whole plate surface but all gas bubbles rise to the top, the mixing

process is most efficient in the upper part [89].

If a battery is charged below the hydrogen evolution voltage, and no bubbles

are emerging to mix the electrolyte, the flooded batteries will also rapidly suf-

fer from acid stratification [105, 106]. The acid stratification develops during

voltage-limited charging because the new sulfuric acid produced at the elec-

trode will sink to the bottom of the battery or cell due to its high density [103].

Therefore, the DCA EN test procedure, which charges the battery or cell only to

80% SoC [9] and afterward uses voltage-limited charging steps for DCA mea-

surements will cause extreme acid stratification [78]. Since the acid stratification

can be considered a local change in acid concentration, this will have a big, neg-

ative impact on the local DCA and the DCA of the complete battery or cell [35,

64, 78].

To investigate the influence of the electrolyte concentration an EFB+CXmiddle

size cell with a original concentration of 1.3gcm−3at 100% SoC, which correlates

with the concentration of a battery at 100% SoC, was compared to a middle size

cell with an electrolyte concentration of 1.25gcm−3at 80% SoC. This correlates

with the concentration of a battery at 80% SoC.

4.3 Influencing Factors on the DCA

After 1h charge:

Electrolyte concentration adjusted to battery level at 100%

Electrolyte concentration adjusted to battery level at 80%

After discharge:

Electrolyte concentration adjusted to battery level at 100%

Electrolyte concentration decreased to battery level at 80%

(a) (b)

5060708090100

SoC / %

1.18

1.2

1.22

1.24

1.26

1.28

1.3

1.32

1.34

Electrolyte Concentration / g cm-3

5060708090100

SoC / %

1.18

1.2

1.22

1.24

1.26

1.28

1.3

1.32

1.34

Electrolyte Concentration / g cm-3

Figure 4.29: Electrolyte concentration of the EFB+CXmiddle size cell (a) after 1h

charge and (b) after discharge.

(a) (b)

5060708090100

SoC / %

0.2

0.4

0.6

0.8

1.2

Normalized Charge Current / A Ah-1

5060708090100

SoC / %

0.2

0.4

0.6

0.8

1.2

Normalized Charge Current / A Ah-1

Figure 4.30: The DCA of the EFB+CXmiddle size cell (a) after 1h charge and

(b) after discharge.

4 Dynamic Charge Acceptance

In Figure 4.29, the electrolyte concentration for different SoC is shown for prior

(a) charge and (b) discharge. The influence of the electrolyte concentration on

the DCA is shown in Figure 4.30 for prior (a) charge and (b) discharge for vari-

ous SoC. The test procedures was described in Section 4.3.2. It can be concluded

that the higher the electrolyte concentration, the lower the DCA.

Acid stratification can also enhance an inhomogeneous current distribution. The

inhomogeneous current distribution will increase differences in the location of

charging and discharging [89], increasing acid stratification even more. Finally,

the lower part of the negative electrode will become less active [9, 82]. The devel-

opment and the consequences of the current distribution over the electrode have

been evaluated [107, 108, 109, 110, 111]. The inhomogenities of both electrolyte

concentration and charge distribution grow with the current rate [89]. Next to

decreasing the DCA, the acid stratification and the inhomogeneous current also

cause a reduction in performance, and premature aging of the battery [30].

Many factors affect the occurrence and strength of acid-stratification, such as

current rate, deep discharges, and temperature. Acid stratification forms during

cycling at all temperatures, but the effect is more pronounced at lower temper-

atures because the temperatures cause a change in gassing and the diffusion

constant. A lower temperature will increase the acid’s viscosity, reducing the

homogenizing effect of the gassing [104].

4.3.5 Temperature

The operating temperature is one of the key influencing factors of the DCA. It

has been shown that for moderate and low temperatures, the voltage limit dur-

ing charging is almost entirely reached by the overvoltage at the negative elec-

trode, limiting further charging [9]. In contrast, at elevated temperatures (e.g.,

45◦C), the negative electrode is not immediately reaching the voltage limit, and

the positive electrode shows polarisation as well [9]. Since the voltage limit is

reached later at elevated temperatures, the DCA is increasing. For pulses longer

than 20s, it was even shown that the negative polarisation would decrease while

the positive polarisation increases [9]. The double layer capacitance of electrodes

explains this effect. Since the surface area of the positive electrode is ten times

larger compared to the negative electrode [112], the double layer capacitance is

100

4.3 Influencing Factors on the DCA

also ten times larger [37]. Therefore, the negative polarization is visible at short

pulses as a lower double-layer capacitance cannot absorb short, sharp charge

pulses [85], limiting the DCA. The double layer capacitance of both electrodes re-

mains unchanged for all temperatures. Nevertheless, at elevated temperatures,

the DCA increases, extending pulse times and allowing the positive electrode to

take over some of the polarization as well [9].

-20 -10 0 10 20 30 40 50

Temperature / °C

0.2

0.4

0.6

0.8

1.2

1.4

Normalized Charge Current / A Ah-1

Simulated drive cycles after charge at 80% SOC

Figure 4.31: Temperature influence on the DCA at 80% after prior charge [64].

At low temperatures, the charging and discharging reactions are slowed down

[113] by the lower conductivity of the electrolyte, the reduced solubility of the

lead sulfate, and the slower transport of the reactants to the surface of the elec-

trodes [104]. Reasons for enhanced DCA with higher temperature originated

within all three charging processes (electrochemical, physical, and chemical).

The higher the temperature, the higher the electrical conductivity, the higher

the diffusion constant, and the higher the dissolution of lead sulfate crystals,

thereby the higher the DCA [9]. This is mainly caused by the increased thermal

energy, which results in a higher reaction rate and thereby increases the dissolu-

tion rate of lead sulfate crystals during charging [28, 114]. It was found that the

dissolution rate doubles with an increase of 5◦C temperature [82]. Moreover, the

solubility rises with lower acid concentrations, linked to rising temperature [9].

Consequently, the DCA is doubled each time the temperature rises by approxi-

101

4 Dynamic Charge Acceptance

mately 12.5◦C [9], visualized in Figure 4.31. However, during discharging, lead

sulfate crystals grow quicker at higher temperatures [9]. Larger sulfate crystals

lead to lower DCA [9, 76, 82, 87, 88, 98].

Next to the real DCA enhancement by the temperature, also side reaction can

be enhanced during charging at high temperatures. If gassing is enhanced by

higher temperatures, the DCA only seems to be increased, but in reality, the

battery is not charged, but higher gassing currents are lost. It was shown that the

gassing rate is doubled at about 10◦C higher temperature [82]. Next to gassing,

side effects such as self-discharge cannot be prevented at higher temperatures

and influence the DCA as well [9].

4.3.6 Voltage Level

The influence of the voltage limit during charging on the DCA is only minor

[115]. At 100mV/cell higher voltage, the gassing rate is tripled [82, 115]. Which

leads to a higher gassing current at higher voltages [35, 85] but does not increase

the DCA. This effect is extreme for charging voltages higher than 16V (2.66V

per cell). The overvoltage consists of the ohmic voltage drop, the reaction over-

voltage, described by the Butler-Volmer equation, and the diffusion overvoltage

[82]. The latter is caused by the concentration gradient of ions in the electrolyte

[82]. When the battery is almost fully charged, the concentration of lead ions

decreases. Therefore, all ions are consumed directly by the charging reaction,

which increases the concentration gradient and, therefore, the diffusion over-

voltage [82]. Finally, the battery voltage rise as well [82]. However, high charg-

ing current does not necessarily result in a higher dissolution rate. That means

a higher voltage above a certain level (from 14V to 15V or from 2.3V per cell to

2.5V per cell) does not significantly increase the DCA [9].

It has been stated that the negative electrode limits the DCA. Emphasizing this

Budde-Meiwes showed that higher pulse voltage almost solely increases the

negative half-cell polarization but hardly charging current [9]. This indicates

that the rate-limiting step is not the transfer reaction, but lead sulfate dissolution

and transport [9].

102

4.3 Influencing Factors on the DCA

4.3.7 Test Cell Design

Different test cell layouts have been tested. However, the test cell layout signif-

icantly impacts several influencing factors and is therefore also influencing the

DCA. 2V EFB+CXtest cells, as a complete cell and with a reduced number of

plates (3P2N and 2P1N), are compared in the following. Due to the asymmetric

design for cells with lower plate count, the negative electrode is stronger polar-

ized during constant voltage charging than in a symmetric design. The cell lay-

out also influences the amount of acid and, thereby, the acid concentration and

the stratification at PSoC operation. Last but not least, the capacities of the test

cells are determined through a calculation (summarized in Table 3.8). Therefore,

all rated currents and SoCs could differ slightly between cell layouts. However,

the latest was discussed, and concluded to be neglectable [7].

Figure 4.32 shows the electrolyte concentration for three different EFB+CXcell

layouts after the adjustment of the electrolyte concentration to battery level at

80% SoC (a) after charge and (b) after prior discharge. The electrolyte concentra-

tion of the complete cell was not changed since it contained the same electrolyte

amount as the battery cell. It is shown that for high SoC, the acid densities are

very similar for all three cell layouts. While for lower SoCs, the electrolyte con-

centration differs. At low SoCs, the electrolyte concentration for the complete

test cells is the lowest and for the small cell layout, the highest.

Figure 4.33 shows the resulting influence of cell layout on the DCA of the same

EFB+CXcells. It can be shown that the DCA of all cell layouts is similarly low

after prior charge. Moreover, they also show similar DCA results throughout

the whole SoC range. After prior charge, the DCA seems almost independent

of cell layout, electrolyte concentration, and SoC. The DCA after prior discharge

varies highly between different cell layouts. After discharge, a higher charge

acceptance can be measured for cells with a lower plate count, independent of

the SoC. This result was already shown for different cell layouts using the single

pulse CA2 test after prior discharge to 91% SoC [7].

103

4 Dynamic Charge Acceptance

After charge:

Complete cell

Middle size cell

Small size cell

After discharge:

Complete cell

Middle size cell

Small size cell

(a) (b)

5060708090100

SoC / %

1.18

1.2

1.22

1.24

1.26

1.28

1.3

1.32

1.34

Electrolyte Concentration / g cm-3

5060708090100

SoC / %

1.18

1.2

1.22

1.24

1.26

1.28

1.3

1.32

1.34

Electrolyte Concentration / g cm-3

Figure 4.32: The electrolyte concentration adjusted to battery level at 80% SoC in

EFB+CXcells (a) after charge from 0% SoC and (b) after discharge

from 100% SoC.

(a) (b)

5060708090100

SoC / %

0.2

0.4

0.6

0.8

1.2

1.4

1.6

1.8

Normalized Charge Current / A Ah-1

5060708090100

SoC / %

0.2

0.4

0.6

0.8

1.2

1.4

1.6

1.8

Normalized Charge Current / A Ah-1

Figure 4.33: The DCA with electrolyte concentration adjustment to battery level

at 80% SoC in EFB+CXcells (a) after charge from 0% SoC and (b) af-

ter discharge from 100% SoC.

104

4.3 Influencing Factors on the DCA

To determine the influences of cell layout on the DCA, as well as its influence

on the change of other cell parameters, four different but related aspects are

identified [7]:

• Polarisation of the negative electrode

• Slow dissolution and diffusion processes

• Electrolyte concentration

• Acid stratification

The first mentioned cause of higher normalized charge acceptance in cells with a

lower plate count is the increasing polarisation of the negative electrode [7]. As

discussed before, during charging with a maximum voltage restriction, negative

electrode polarization becomes the DCA limiting factor. The positive electrode

only polarises slightly due to its high double-layer capacitance [79, 112]. This be-

havior is even intensified due to the more asymmetric design of the smaller-sized

cells compared to the symmetric design of a complete cell or battery. Conse-

quently, the negative electrode will polarise more strongly and thereby increase

the DCA of small test cells. However, the current could not be increased in-

finitely because it is also limited by the Pb2+supply [7].

The second aspect of cell size effects on the DCA states that the slow dissolution

and diffusion processes which hamper the charge acceptance [64], were not as

dramatic in cells with lower plate counts [7]. Previous research had asserted that

the supply of Pb2+ions from chemically dissolved lead sulfate limit the rate of

the negative charging reaction [35]. Indeed, even if the solubility was low, there

were already Pb2+ions dissolved within the pores, which could be used during

the charging event first, unaffected by neither solubility nor diffusion. How-

ever, the Pb2+ions would be exhausted within milliseconds during charging.

In small test cells, a surplus of Pb2+ions dissolved in the electrolyte localized

outside the pores of the negative plate could be used if the diffusion constant

was high enough. However, the only excess usable Pb2+ions would accrue in

the positive outer plates, but the diffusion path would be too long, and the dif-

fusion processes too slow for it to arrive at the reaction surface of the negative

plates within 10s. Therefore, it can be concluded that freshly dissolved Pb2+

ions were needed. However, this process is slow and will not be affected by the

plate count. This is not the reason for enhanced DCA for lower plate counts.

105

4 Dynamic Charge Acceptance

The third aspect, explaining the higher DCA with the decreased electrolyte con-

centration for cells with lower plate count at 90% SoC after adjusting them all to

the same electrolyte concentration at 80% SoC [7]. The electrolyte concentration

differs among the cell sizes because of the total acid amount within the cells.

Measurements shown in Figure 4.33 (b) also show a higher DCA for cells with

lower plate count at 80% SoC, when the electrolyte concentration of all cells was

adjusted.

The last aspect influencing the DCA in different cell layouts is the acid stratifi-

cation [7]. Flooded batteries rapidly suffer from acid stratification during pre-

conditioning and DCA tests [64, 78]. However, due to the excess acid in cells

with lower plate count, their acid stratification decreases, leading to an overall

increased DCA for cells with low plate count.

It is impossible to separate all aspects resulting from the test cell layout from

each other since they are all related [7].

4.3.8 Carbon Additives at the negative Electrode

The negative electrode is known to be the limiting factor for DCA [9, 32, 33, 34,

84]:

• The NAM pore diameter is bigger than that of a positive active mass (PAM)

[32, 85]. Resulting four times smaller reaction surface area of the NAM.

However, even worst is that PbSO4crystals can grow bigger within the big

pores during discharge, slowing the dissolution during charging. This also

increases the distance for the Pb2+transport.

• The negative plate has only a small double-layer capacitance (1.0FAh−1)

compared to the positive electrode (70.0FAh−1) [37].

• Resulting higher polarisation of the negative electrode during charge pulses

have been shown [86].

Since these limit the negative electrode in DCA, they are also the primary target

for improvement. The research in the last years concentrated on the negative

electrode by adding additives to the negative electrode. One widely employed

additive is carbon. It has become common to incorporate elevated concentra-

tions of carbon to increase charge acceptance and performance, such as capacity

106

4.3 Influencing Factors on the DCA

or cycle lifetime in PSoC [45, 46, 50, 116, 117, 118, 119, 120]. Many types of car-

bon additives are used, such as carbon black, activated carbon, graphite, flake,

expanded and synthetic graphite, isotropically graphitized carbon or mixture

of them [120, 121]. Within the various carbon types, an even broader range of

properties can be found within these carbons, such as surface area, pore vol-

umes, chemical stability, electrical, and thermal conductivity [122, 123].

The presence of the carbon can decrease the NAM pore diameter and extend the

surface area on which the charge and discharge reactions can occur [50, 117, 124,

125]. With enhancing the specific surface area of NAM, the reactions can take

place faster, and the potential of the negative plates decreases, which prevents

hydrogen evolution [126].

Furthermore, additives can decrease the NAM pore diameter, and thereby, im-

pede the growth of lead sulfate crystals [71, 110, 117, 119, 124, 127, 128]. With

small lead sulfate crystals, their surface area remains high, and thereby, recharge

is facilitated [110, 117, 119, 124]. This cannot only be accomplished by using

carbon but also by adding isolated titanium dioxide [110, 129]. Various types of

carbon [120] but also lignin [15] can be used on the negative plate, which will

both result in more homogeneous lead sulfate crystals after discharge. An even

distribution of the lead sulfate keeps the path open for acid diffusion and allows

a more homogeneous current distribution [130]. Forming homogeneously dis-

tributed lead sulfate crystals also prevents irreversible lead sulfate growth [131].

Even for medium SoC, the DCA during dynamic operation is more restricted of

the negative electrode [93, 132, 133]. On the other hand, the positive electrode

only polarizes slightly due to its high double layer capacitance [64, 112]. The-

oretically, the DCA is highest if the negative and positive plate capacitance are

the same [71]. However, by nature, the negative plate has a very small double-

layer capacitance compared to the positive electrode [37]. Therefore, carbons

that provide good contact with lead and a low-ohmic resistance should be cho-

sen [119]. Carbons with a high conductivity provide an electric double layer at

the crossing from carbon to the electrolyte [9, 50, 119]. Protons from peak charge

currents can be stored first in this double layer and convert lead sulfate to lead

[50]. The potential over the electrode surface would be inhomogeneous [50].

This way, hydrogen evolution can be avoided and could be used as charge cur-

107

4 Dynamic Charge Acceptance

rent [9]. On the downside certain carbon may contain impurities which would

lower the over potential of hydrogen evolution and eventually reduce the effi-

ciency of charge [119, 134].

Bringing this to the next level was the design of the ultra-battery [50, 133, 135,

136]. The ultra-battery is a lead-acid battery (LAB) hybrid, and an asymmetric

double-layer capacitor [133, 136]. The negative electrode does not contain car-

bon, but is covered with a porous layer [136]. As a result, two advantages merge.

Firstly, the carbon layer acts as a capacitive buffer for high charge currents, but

otherwise low capacity [125]. Moreover, the lead electrochemical system, which

has a high capacity but low charge acceptance, might continuously charge the

negative active material with the energy stored in the capacitor [125].

Even though carbon has a lower conductivity than lead, it has a higher conduc-

tivity than lead sulfate, which is an insulator. Therefore, carbon can build a con-

ductive network on lead sulfate crystals, allowing reactions even at PSoC where

many lead sulfate crystals have formed [45, 46, 50, 126]. This would lower the

charge voltage and enhance the DCA at PSoC [126]. It was found that with cy-

cling under PSoC conditions, the electrochemical and chemical processes at the

negative plates proceed not only on the lead surface but on the carbon surface as

well [117]. Furthermore, it has been found that carbons influence the structure

of the lead NAM [1, 118, 119, 125].

Next to all the structural changes due to the carbon, it was also found that some

carbons keep the lead ion concentration in the electrolyte at a higher level, which

is also beneficial for charging [117].

Test DCA of 3P2N test cells at 80% SoC after prior charge and discharge contain-

ing various additives at the negative electrode is shown in Figure 6.11.

4.3.9 Technology

Within this section, differences and similarities between different technologies

regarding the DCA are investigated. For conventional flooded batteries [9], as

well as EFB [9], enhanced EFB+C, VRLA batteries [81], AGM [95] and lithium

iron phosphate (LFP) batteries [81] the DCA is increasing with lower SoC, vi-

108

4.3 Influencing Factors on the DCA

sualized in Figure 4.34. All lead-based batteries have comparable low DCA for

high SoC. However, it is shown that the increase of the DCA with lower SoC is

much more distinct for VRLA batteries compared to EFB and EFB+C batteries.

Only the LFP batteries differ significantly, starting with a high DCA for high SoC

but remaining almost constant as SoC decreases.

5060708090100

State of Charge / %

Normalized Charge Current / A Ah-1

LFP battery

VRLA battery

AGM battery

EFB+Cx middle size cell

Conventional flooded battery

Figure 4.34: Influence of the SoC on the DCA of different technologies (turquoise

and orange [81], blue [95], red (own measurements) and black [9]).

The results shown in Figure 4.34 might be surprising because earlier published

literature showed significantly lower charge acceptance for VRLA batteries ver-

sus flooded batteries [137]. However, starting-lighting-ignition (SLI) batteries

used nowadays in the market do not show this phenomenon anymore. One

explanation could be the shift to antimony-free grids for the flooded batteries

resulting in a lower DCA [82].

Furthermore, all lead-based battery types evaluated show an increasing DCA

after prior discharge than prior charge. AGM batteries, which have an immo-

bile electrolyte, usually do not show any acid stratification. This most likely

explains higher DCA, especially after prior charge, compared to flooded and

EFB+C batteries [9]. Only the LFP battery does not show differences between

prior charge and discharge [81]. However, comparing the DCA of different tech-

nologies based on short-term tests is not sufficient for classification of DCA for

109

4 Dynamic Charge Acceptance

real-world applications [9]. For example, the AGM shows higher DCA after

prior discharge (Figure 4.34). However, simulated in the real-world test, both

technologies are at similar low DCA [9].

All battery technologies show a decreasing DCA with an exceeding rest period

before the DCA test. However, the effect of the rest period is much more stable

after prior charge, while the decreasing DCA with a longer rest period after dis-

charging is much more distinct.

While all lead-based batteries show the typical DCA run-in effect, other commer-

cial storage devices, such as supercapacitors [138] or lithium-ion batteries [139]

can keep their originally high DCA throughout their lifetime.

Another lead-based technology is the UltraBattery, a flooded or VRLA battery

that contains a capacitive element as part of the negative plate [37, 133]. The

capacitor acts as a buffer for the negative plate and thus prevents it from being

discharged and charged at full current rates without decreasing the DCA [85].

With this design, the negative characteristics of the negative electrode compared

to the positive electrode can be made up for. Whereas conventional lead-based

batteries periodically require a full recharge to dissolve the sulfate crystals, re-

capture the originally high DCA, and therefore continue to operate successfully,

the UltraBattery has been demonstrated to operate for extremely long periods

without this kind of conditioning [140].

Despite their disadvantages the EFBs are still used within many vehicles because

of their low price compared to AGM batteries, or even more expensive Li-ion

batteries, as well as highly expensive supercapacitors [9].

4.3.10 Comparing the Influencing Factors

The list of influencing factors on the DCA is everlasting, and many more could

be evaluated. However, the factors described above are the most influential to

the DCA. They can be divided into two main categories:

• manipulable influencing factors and

• internal influencing factors.

110

4.4 Limits of the DCA Measurement Methods

Manipulable influencing factors could be affected as they influence the battery’s

behavior from the outside, such as temperature. Internal influencing factors can-

not be affected because the battery behavior is affecting itself, such as SoC. How-

ever, some factors remain in between if they could be manipulated with the cell

or battery design (e.g., electrolyte concentration or additives) and will internally

influence the DCA.

Furthermore, many of the investigated influencing factors depend on each other

and/or influence each other. For example, the acid concentration is highly de-

pendent on the SoC, and the acid stratification depends on the short-term usage.

Nevertheless, the sensitivity of the influences is essential.

4.4 Limits of the DCA Measurement Methods

For measuring the DCA and all pretests the Digatron power electronics MCT

50/100/200-06-13(12) ME was used. It contains several 50A channels used for

small and middle size cells as well as two 200A channels which were used for

DCA tests on complete test cells. The analog signal of this test device has a

tolerance of err =±0.1% of the voltage and the current measurement. The quan-

tisation error of the Analog-to-Digital (A/D) converter used in the test device is

determined by the least significant bit (LSB) = 1.5mA for the current and 2.5mV

for the voltage. The errors introduced by the test device are exemplary calcu-

lated for a 3P2N middle size cell, with a nominal capacity Cn= 20Ah. The I20 of

a 3P2N test cell is 1A. Depending on the absolute value of the current either the

tolerance of ±0.1 % or the quantisation error of 1.5mA dominates the resulting

error. For small currents such as 1.5A the error of the tolerance and the quantisa-

tion error are similar. For higher current the error of the tolerance predominates.

For lower currents the quantisation error predominates.

The SoC range ∆SoC(SoCtarget)caused by the LSB error is calculated by

∆SoC(SoCtarget) = 2·h∆SoCtarg −(Itarget +LSB

2)·tadjust

Cn·100i (4.4)

where ∆SoCtarg indicates the targeted SoC change, Itarget is the errorless current,

111

4 Dynamic Charge Acceptance

tadjust is the time used to adjust the targeted SoC with the chosen current, and

LSB indicates the quantisation error. The error prone current can maximal vari-

ate by LSB/2 from the targeted current.

The SoC range ∆SoC(SoCtarget)caused by the tolerance is calculated by

∆SoC(SoCtarget) = 2·h∆SoCtarg −(Itarget +Itarget ·|err|)·tadjust

Cn·100i (4.5)

where errorless current Itarget needs to be multiplied with the absolute value of

the tolerance |err|to determine the error.

All preconditioning steps for the different DCA tests and the resulting SoC de-

viation of each step are summarized in Table 4.6.

Table 4.6: Preconditioning of DCA tests.

DCA test Preconditioning current time ∆SoC

SBA discharge from 100% to 91% 3.42A 30min 0.017%

Icat 80% discharge from 100% to −10% 1A 22h 0.165%

and charge from −10% to 80% 5A 3.6h 0.180%

Idat 90% discharge from 100% to 90% 1A 2h 0.015 %

Idat 80% discharge from 100% to 80% 1A 4h 0.030 %

Since the DCA is SoC dependent, the inaccurate adjusted SoC will affect the re-

sulting DCA. However, the investigations of different cell layouts and additives

has shown, that the SoC influence on the DCA varies. It is largest for small size

cells and smallest for the complete cell. Concluding the example, only the DCA

range cased by the error prone SoC range for a middle size is given in Table 4.7.

Since the DCA dependency on the SoC also varies between different additives,

the DCA error is given for the additive with the strongest (EFB+CX) and the low-

est (EFB+C1) SoC dependency.

Moreover, the tolerance of the test device and the quantization errors for current

and voltage will also be present during the DCA measurement. For the DCA

tests the cells were charged with voltage limitations and relatively high currents.

Therfore, is the influence of the tolerance much bigger than the LSB. The toler-

ance of the test device influences both, the voltage and the current. However,

112

4.4 Limits of the DCA Measurement Methods

Table 4.7: DCA variation.

Cell additives EFB+C1EFB+CX

SoC influence low strong

SBA 0.139mAAh−10.412mAAh−1

Icat 80% 2.818mAAh−18.370mAAh−1

Idat 90% 0.123 mAAh−10.364mAAh−1

Idat 80% 0.245 mAAh−10.728mAAh−1

the influence of the voltage limit during charging on the DCA is only minor

[115] and can thereby be neglected. The CA2 test consists of a 10s pulse with

a voltage limit of 2.4V and a maximum current of 50A for the middle size test

cells. With a tolerance of ±0.1% the current deviation is ±0.05 A. Since the tests

only lasts 10s, the accumulated error during the CA2 test is neglectable.

Both the DCA EN test and the modified DCA test involve 20 cycles for Icand

20 cycles for Id, where each cycle consists of a charging pulse lasting 10s with a

voltage limit of 2.5V, followed by a discharging pulse regulated by Ah-counting.

For the middle size cells, the maximum charging current is 33.3A and the max-

imum discharging current is 20A. Since the maximum charging current is not

sustained for the entire 10s, the discharging pulse is shorter than the charging

pulse. The discharging pulses during Icare approximately 2s and during Id

8s long. Therefore, the cycles of Icare combined 120s and the cycles of Idare

combined 180s long. The accumulated error during the DCA EN test and the

modified DCA test can also be neglected.

Furthermore, it needs to be taken into account, that part of the charging current

goes into the gassing reaction. This effects the preconditioning and thereby the

SoC adjusting. Moreover, it does also occur during the charge acceptance test

itself, which will lead to over estimated DCA.

113

EIS - Fundamentals and

Measurement

Chapter 5

Electrochemical impedance spectroscopy (EIS) is a widely used standard char-

acterization technique in electrochemistry to measure the polarization behavior,

non-linear processes, and dynamics of electrochemical systems in the frequency

domain [11]. Its main applications are identifying electrochemical processes and

characterizing materials or devices [4]. Research fields like medicine, biology,

and geology have used EIS for various applications [12]. EIS can be used to de-

velop and parameterize battery simulation models. Differences between battery

and cell characteristics can be visualized, and processes can be investigated.

Section 5.1 summarizes what EIS was and can be used for. Section 5.2 explains

the method for valid EIS measurements on a battery or test cell. To measure

multiple EIS spectra at various SoC, adjusted with charge, or discharge current,

with and without superimposed direct current (DC), an EIS procedure is sug-

gested in Section 5.3. The pre-processing of the obtained data is summarized in

Section 5.4, and the evaluation using an equivalent circuit model (ECM) is illus-

trated in Section 5.5. The interpretation of the parameters obtained by the ECM

and conclusions on the processes shown with the spectra are stated in Section 5.6.

Section 5.7 investigated the most important influencing factors on the EIS. The

possible error sources during EIS measurements are investigated in Section 5.8.

115

5 EIS - Fundamentals and Measurement

5.1 Literature Survey: What is EIS used for in LABs?

1940 the first studies on battery alternating current (AC) resistance, refered to

as impedance (Z), were conducted with a limited frequency range because only

analog measurement technologies were known at that time. One of these first

works was the measurement of the internal resistance of the negative electrode

of a lead-acid battery (LAB) using a Wheatstone bridge at 3kHz [42]. The inter-

nal resistance was measured while discharging the electrode at different current

rates, thereby separating the ohmic voltage drop from the electrochemical po-

larization of the electrode [42]. Since 1998 the AC resistance has been the main

scope of attention for the state of charge (SoC) and state of health (SoH) estima-

tion of LABs [141, 142, 143]. Some battery testers could accomplish reliability in

identifying cell failures by measuring the impedance at 1kHz [144, 145]. This

works especially well for battery types and applications where the failure is re-

lated to a sharp increase of ohmic resistance, e.g., absorbent glass mat (AGM)

batteries in stand-by applications with permanent float charging where grid cor-

rosion and water loss in the separator are expected to be the dominating aging

mechanisms [146]. Even though significant changes in the AC resistance value

indicate changes in the cell, which might reflect its performance, small or no

changes do not ensure that the cell is free of defects or deterioration [147]. More-

over, values at a specific frequency may change their location in the spectrum

during aging since aging changes processes could change time constants [148].

This may explain why some authors rate the attempt to use the AC resistance at

a specific frequency as an inaccurate prediction tool for SoC and SoH [141].

The capacitive behavior of the impedance, mainly belonging to the negative elec-

trode, could be shown by increasing the frequency range to 30 Hz [149]. Lower

frequencies, down to 1mHz, have been accessible since the late 1970s, were digi-

tal frequency-response analyzers were developed. However, until the end of the

last century, no monitoring of starting-lighting-ignition (SLI) batteries existed.

Indeed it was not necessary. Until recently, the battery was only considered as an

energy buffer that is used to start the vehicle. However, the number of loads in-

stalled and the maximal required power increased, an automatic start/stop func-

tion and brake energy regeneration were implemented, and many safety-related

functionalities were included [150]. Nowadays, EIS with a wide frequency range

can be conducted. This technique provides a non-destructive cell-level monitor-

116

5.2 EIS Measurement on Batteries

ing that shows the electrochemical processes and can serve as a basis for dynamic

battery models. EIS has thereby been identified as one of the most promising

tools to predict battery lifetime and control and understande the battery itself,

even for SLI. Thereby, EIS was investigated for SoC [16, 17, 18] and SoH estima-

tion [19, 20, 21, 22, 23]. Next to SoC and SoH also, the state of function (SoF)

is of significant interest during battery operation [24]. Piłatowicz used the well-

known physico-chemical approach of the Butler-Volmer equation for accurate

battery dynamic response estimation to calculate the SoF of a battery [24]. Even

a novel intelligent charger with an embedded diagnosis function for SoH esti-

mation using online impedance spectroscopy was proposed [151].

The impedance-based models of batteries persist of networks of simple passive

electrical components that can represent electrochemical processes. The Ran-

dles circuit among the first and most widely used equivalent circuits [152]. The

impedance-based model’s applicability to several battery technologies, such as

supercaps, lithium-ion batteries, and LABs, was developed using non-linear

components [153, 154]. A physics and chemistry-based model for LABs was

created [30]. Even though the parameter for this model is not measurable by

impedance spectroscopy, adding these submodels to the impedance-based model

can further improve simulations of dynamic battery operations [155].

5.2 EIS Measurement on Batteries

The EIS is a standard characterization technique to measure the polarization be-

havior, non-linear processes, and dynamics of electrochemical systems in the

frequency domain [11]. The basic concept and the experimental setup of EIS is

described in this section.

There are two distinct measurement principles: galvanostatic, as shown in Fig-

ure 5.1, and potentiostatic. To perform galvanostatic EIS, a sinusoidal alternating

current (IAC) with a defined frequency (f) is applied to the battery or cell under

investigation, and the alternating voltage response (VAC) is measured. This mea-

surement principle is schematically shown in Figure 5.1. In the case of potentio-

static measurement, a sinusoidal voltage with a defined frequency is applied to

the battery or cell, and the current response is measured. Generally, the gal-

117

5 EIS - Fundamentals and Measurement

vanostatic method is used for batteries and cells because voltage excitation can

introduce systematic errors especially under non-equilibrium conditions. The

voltage does not sufficiently define the SoC of the battery. In extreme cases, a

battery may be discharged or charged at the same voltage, depending on its SoC

and prior usage [156]. The frequency is varied over a wide range to obtain the

complete spectrum . However, since low frequencies require long measurement

periods, the frequency range is chosen depending on the expected range of in-

terest or other conditions, such as limitations of the measurement device. The

resulting impedance Zis the correspondent transfer function of the AC IAC and

the AC voltage VAC in the frequency domain:

Z(jω) = VAC

IAC =v(ω)·sin(ωt+φ(ω))

i(ω)·sin(ωt)=|Z(jω)|·ejωφ (5.1)

Figure 5.1: Galvanostatic EIS measurement principle.

The system under inspection must be stationary, linear, and causal for utiliz-

able EIS measurements. In reality, these three conditions cannot be fulfilled on

batteries [112]. Therefore the battery or cell under investigation has to be kept

in a quasi-stationary condition since EIS is highly dependent on the operational

state, and the signals amplitudes must be at least able to be linearized. However,

the reaction of batteries is always non-linear [157]. It follows the Butler–Volmer

equation. Therefore, it is necessary to operate the battery or cell at small cur-

rents to ensure that the nonlinearity of transport and reaction processes can be

118

5.2 EIS Measurement on Batteries

neglected [156]. The most significant influencing factors, further discussed in

Section 5.7, on the EIS measurement are [114]:

• Temperature (T),

• SoC,

• SoH,

• electrolyte concentration and stratification,

• superimposed DC (IDC) and

• short-term usage (e.g., after prior charge or discharging or the length of a

pause).

Keeping a (quasi-) steady state during a measurement is hardly manageable

since the measurements require a certain amount of time. Regardless, tempera-

ture, SoC, and SoH changes should be avoided or kept as small as possible dur-

ing the measurement. Due to the voltage-dependent processes, the amplitude of

IAC has to be as small as possible. Otherwise, this will result in a non-linear volt-

age response. In this case, the voltage response is not just one sinusoidal curve

with the same frequency as the sinusoidal current; instead, it contains infinite

sinusoidal curves of various frequencies.

Another problem may arise when applying EIS to a battery or cell caused by ge-

ometry effects, reaction kinetics, and mass transport. Neither batteries nor cells

are ideal, and the reaction zone may move during discharge from the surface of

the electrode down the pores or from the top part of the electrode to the bottom.

Parasitic reactions like the decomposition of the electrolyte may occur [156].

EIS is often performed without superimposed charging or discharging current

[131, 158, 159, 160, 161, 162, 163]. This is beneficial since the SoC of the battery

or cell will not change even during long measurement times. However, a su-

perimposed charging or discharging current IDC prohibits hardly reproducible

local concentrations of reactants, which generate overpotentials caused by the

short-term usage [164]. On the other hand, the superposition of a charging or

discharging current is used to avoid a change of polarity during the measure-

ment and thereby force only one reaction direction upon the battery [21, 155].

Therefore, the superposed current IDC defines the overall working point of the

119

5 EIS - Fundamentals and Measurement

battery and guarantees the full participation of the electrode surface in the reac-

tion. The performance of EIS with superimposed DC has developed to the con-

temporary measurement method [20, 21, 24, 112, 155, 156, 157, 165, 166, 167, 168,

169, 170, 171, 172, 173]. Figure 5.2 compares the schematic measurement prin-

ciple of (a) an EIS measurement input with only sinusoidal current with (b) an

additionally superimposed DC. It is necessary to choose the superimposed DC

wisely. For example: If IDC of 0.5·I20 is used for a cell with 10Ah capacity, it

results in IDC = 0.25A for this cell. On the other hand, the AC is chosen to ensure

a voltage response VAC of around 3mV/cell [174]. If the voltage response VAC

is smaller than 3mV, measurement errors dominate the measurement and ham-

per the evaluation. If the cell has an ohmic resistance of 3mΩ, a current IAC of

1A is chosen to generate a voltage response of 3mV. Therefore, the amplitude

of IAC is more significant than the amplitude of IDC. Thereby, it would not pre-

vent a change of polarity during the measurement. In this case, the minimum

IDC usable would be 2·I20. However, when a superimposed DC is applied, each

impedance, measured one after another, belongs to a slightly different SoC. This

will result in a reduction of the frequency range to guarantee quasi-stationary be-

havior. Nevertheless, if high current processes are meant to be investigated, e.g.,

dynamic charge acceptance (DCA), it might be superior to increase the IDC even

further and limit SoC changes by limiting the measurement time and thereby the

frequency range. Ultimately, the demand on the (quasi-) steady state still needs

to be met, whereas the SoC of the battery or cell should not deviate more than

10% SoC [156] from the targeted SoC.

(a) (b)

Figure 5.2: (a) Sinusoidal current, and (b) with superimposed DC.

120

5.2 EIS Measurement on Batteries

A significant influencing factor is the short-term usage of the battery or cell be-

fore taking the EIS. If a battery or cell was continuously charged or discharged

previously paused different lengths, the spectra will have significant differences.

Especially in LABs, slow dynamic processes like acid diffusion exceedingly mask

the charge transfer reactions of the electrodes [112]. Therefore, it would be de-

sirable to eliminate diffusion from the measurement to obtain a good model of

all processes. Therefore, a micro-cycle approach was introduced [156]. The basis

of this approach is still kept the same but was adjusted according to the require-

ments of this work.

5 10 15 20

2.1

2.2

2.3

2.4 (a)

5 10 15 20

-1

-0.5

0.5

1(b)

5 10 15 20

95 (c)

Figure 5.3: The micro cycling regime at one target SoC and one superimposed

DC (a) cell voltage, (b) superimposed DC, and (c) SoC.

The measurement procedure is schematically visualized in Figure 5.3. Starting

from a given SoC, the cell is cycled by approximately 5% SoC around the tar-

geted state, shown in Figure 5.3 (c). Thereby, a maximum of ±2.5% SoC change

is expected. The desired ±IDC is used as charging and discharging current, visu-

alized in Figure 5.3 (b). Meanwhile, one impedance spectrum is recorded during

each discharging period and one during each charging period, always starting

by recording the high frequencies. The battery voltage changes most at the be-

121

5 EIS - Fundamentals and Measurement

ginning of a new superimposed DC. In order to have a more stable voltage dur-

ing an EIS measurement, the beginning of the spectrum is delayed till after the

first ohmic drop. To wait for an SoC change of 1% before starting a spectrum has

been suggested [157] and will also be done within this work. It was shown that

influences of diffusion or migration are canceled out after two micro cycles [156].

Therefore, irrespective of the previous LAB usage at intermediate SoC, the mea-

sured spectra are easily reproducible from the second micro-cycle onward. The

micro-cycles are repeated three times, and only the impedance spectrum (with

superimposed charging and discharging current, respectively) taken during the

last cycle is used for later investigation. Next to the SoC limit, a voltage limit of

2.4V was set during the charging steps of the micro-cycles. If the voltage limit

was reached, the cell was discharged by only the Ah of the prior charge step.

Even though this additional limit may decrease the frequency range, it ensures

a (quasi-) steady state during the measurement. Figure 5.3 (a) shows the voltage

during EIS without superimposed current, followed by three micro-cycles with

±0.5·I20 superimposed DC. The beginning of the spectra, after 1% SoC [157],

can be seen within this voltage measurement.

For meaningful EIS measurements, a four-point measurement is unavoidable.

Suppose the cables of the voltmeter are connected to the cables of the current

path (two-point measurement). In that case, the voltage drop over the resistance

of the connection to the battery and the resistance of the current cables are mea-

sured as well, leading to a measuring error. Therefore, the voltage measurement

cables are connected directly to the battery terminals (four-point measurement)

and should always be closest to the battery. That way, no current flows through

the voltage cables, and a current-free voltage measurement is possible since sep-

arate cable pairs are used for power supply and voltage measurement. The mea-

surement cables should always be closest to the battery. The bolted connection

should be mounted with the same torque for comparable results.

The impact of electromagnetic noise, namely inductive or capacitive coupling,

is described in Section 5.8. To minimize these noise effects, measurement se-

tups need to be adjusted. To minimize inductive coupling, all channels should

be twisted as closely as possible to minimize the area between the channels. To

minimize capacitive coupling, channels with a current signal should not be par-

allel to each other and be separated as far as possible or shielded.

122

5.2 EIS Measurement on Batteries

The Digatron power electronics MCT 50/100/200-06-13(12) ME, the EISmeter 2-

20-4, and the Battery Manager are used as test equipment for EIS measurements.

With the EISmeter, a spectrum from 6.5 kHz to a few µHz can be taken with

very high accuracy. The high long-term stability of the instrumentation allows

for measurements at low frequencies. Since impedance measurements down to

the µHz-region are very time-consuming, the frequency range is finally limited

by the measurement time for one spectrum. For each frequency, three periods

are measured, and eight frequencies per decade are evaluated. Therefore, a test

duration of t≈12 min for the complete spectra is to be expected [112]. The

EISmeter uses a quasi-galvanostatic mode during the impedance measurement

performance.

Since the dynamic behavior of the negative electrode is of high interest, hydro-

gen reference electrodes from Gaskatel 88010 were used. Since the location of a

reference electrode becomes a crucial factor during the measurement, especially

for comparability and reprehensibility, it was kept at the same position in each

test cell during all measurements.

The complex plane representation via Nyquist plot, shown in Figure 5.4 (a), only

represents the real part of the impedance Zon the horizontal axis and the imag-

inary part of the impedance Zon the vertical axis. Each measurement point

represents the impedance for one frequency. The frequency increases from right

to left. Since all batteries show a capacitive behavior within EIS measurements,

the imaginary axis is reversed for evaluations.

The Bode diagram shows the absolute value of the impedance in Figure 5.4 (b) and

the phase angle in Figure 5.4 (c) against the employed frequencies. On the other

hand, it does not directly show the distribution into real and imaginary parts of

the impedance.

123

5 EIS - Fundamentals and Measurement

0 10 20 30 40

-20

-10

(a)

10-2 10-1 100101102103

40 (b)

10-2 10-1 100101102103

-20

(c)

Figure 5.4: Simulated EIS example (a) Nyquist plot, (b) absolute value, and

5.3 EIS at various SoC and Superimposed DCs

5.3.1 Ideal EIS Procedure

The ideal procedure for investigating the used enhanced flooded battery (EFB)

test cells with EIS would include various SoC, adjusted with charge, or discharge

current, and different superimposed DCs.

Since the EFB test cells are used for SLI applications, where they are at high SoC

levels at all times, an SoC range from 50% to 100% SoC should be analyzed.

However, EIS uses a sinusoidal AC, overcharging the battery or at least reaching

the maximum voltage limit when used at 100% SoC. Therefore, investigations

from 50% to 95% SoC in 5% steps would be desired.

For later correlation analyses of the EIS with the DCA, especially high superim-

posed DCs are desired. On the other hand, the ±2, 5% SoC limit during micro cy-

cling limits the measurement frequency range for superimposed DCs. Further-

more, high superimposed DCs will mainly cause gasing, which is not the process

under inspection. As a trade-off between good comparability with DCA and a

wide frequency range under investigation, superimposed DCs of IDC = 0A, ±

0.5·I20,±1·I20,±2·I20, and ±3·I20 are investigated.

124

5.3 EIS at various SoC and Superimposed DCs

Last but not least, the SoC adjustment before the micro cycles should be made

with discharge and charge. Since the DCA highly relies on the prior usage, sim-

ilar short-term usage should be simulated with the EIS procedure.

Figure 5.5: (a) Ideal EIS procedure, (b) current, and (c) SoC development during

the micro cycles at any target SoC.

Figure 5.5 visualizes the ideal EIS procedure. Each SoC between 50% and 95% is

targeted once using a discharging current to adjust the SoC and afterward using

a charging current. At each SoC, the same micro cycles (±2.5% SoC around tar-

get SoC), marked with red rectangles, are executed with IDC = 0A, ±0.5·I20,±

1·I20,±2·I20, and ±3·I20, visualized in Figure 5.5 (b) and (c). The micro-cycling

approach [156] was already used in previously published work [25, 26]. One

spectrum is recorded during each discharge and charge period. Budde-Meiwes

suggested starting the EIS measurement after 1% SoC change during each new

125

5 EIS - Fundamentals and Measurement

superimposed DC [157]. This way, the rapid voltage change, where the cell is in

a non-stationary state, will not be recorded during EIS [157].

Unexpected problems occurred deriving the ideal test procedure. Voltage over-

shoots occurred at any SoC when superimposing a DC. For quasi-stationary EIS

measurements, these voltage overshoots must be avoided or at least not be eval-

uated. However, further analyses in an attempt to identify their origin have been

made in Section 5.3.2.

5.3.2 Restrictions for EIS because of Over Voltages

Pretests were conducted to derive an EIS test procedure including various, es-

pecially high SoC, adjusted using charge, or discharge currents, with multiple

superimposed DCs, minimizing or avoiding voltage overshoots. Table 5.1 sum-

marizes the pretests investigating the voltage overshoots and thereby deriving

the required EIS procedure. During these pretests, the micro-cycling regime was

used. During the micro cycles, Ah-counting was used to keep the SoC level con-

stant. Additionally, the voltage was limited to a maximum of 2.6V throughout

the test. If this limit was reached, the discharging part of the micro cycle was

started immediately. Therefore, the micro cycles at high SoCs and for higher su-

perimposed DCs were shortened. The findings, shown within this section, were

conducted using the complete battery, the middle, and the small size cells and

were qualitatively the same for all layouts.

An essential condition for EIS is that the system must contain stationary or at

least quasi-stationary conditions. However, if a current is superimposed during

the EIS measurement, keeping the voltage in a stationary condition is impossi-

ble since the voltage depends on the state of charge. The superimposed DC is

toggled between charging and discharging during the micro-cycling procedure.

This leads to ohmic voltage drops right after changing the current. To avoid mea-

suring EIS during this rapid voltage change, where the cell is in a non-stationary

state, each measurement only starts after a 1% SoC change after each new super-

imposed DC occurs.

126

5.3 EIS at various SoC and Superimposed DCs

Table 5.1: Pre tests for deriving the EIS procedure using an EFB complete cells,

middle, and small size cells.

Test

order Procedure Visualized in

1 EIS procedure starting at 95% SoC, SoC adjustment Figure 5.6

via discharge (voltage overshoots at all SoC)

2 Small constant current (CC) discharge to 70% SoC,

micro cycles with ±0.5·I20 (no voltage overshoots)

3 CC discharge with 1·I20 to 70% SoC and micro cycles Figure 5.7

with ±1·I20 (no voltage overshoots)

4 EIS procedure starting at 90% SoC, SoC adjustment Figure 5.8 (a-c)

via discharge (no voltage overshoots)

5 EIS procedure starting at 95% SoC, SoC adjustment Figure 5.6

via discharge, (voltage overshoots are reproducible)

6 EIS procedure starting at 95% SoC, SoC adjustment

via discharge, 48h pauses (voltage overshoots)

7 EIS procedure starting at 90% SoC after incomplete Figure 5.8 (d-f)

charge (voltage overshoot at all SoC)

8 EIS procedure, SoC adjustment via charge (voltage

overshoots at high SoC)

9 Final EIS procedure, SoC adjustment via discharge Figure 5.9

and charge (no voltage overshoots)

When the first 1% SoC change is left out, the voltage changes are linearizable

during the rest of the period at medium SoC. Therefore, the batteries or cells con-

tained a quasi-stationary condition, and EIS measurements could be evaluated.

However, high SoC and high superimposed DCs result into voltage overshoots

at the end of the 5% SoC micro cycles. The voltage overshoots depend on the am-

plitude of the superimposed DC and the SoC. The first overshoots are marked

with a black dotted circle in Figure 5.6 (a) the cell voltage, (b) the positive, and

that the voltage incline already starts during the first micro cycles. However,

extreme cell polarization only occurred after some cycles, especially at higher

superimposed DC. While the positive half-cell potential did not significantly in-

crease during cycling, the negative half-cell potential mainly enables the voltage

overshoots.

127

5 EIS - Fundamentals and Measurement

Figure 5.6: First trials of the EIS procedure, starting at 95% SoC, adjusting the

SoC via discharge, resulting in voltage overshoots at all SoC.

However, excluding all EIS data points taken during a voltage overshoot from

further investigations, as they are not in a quasi-steady state, is insufficient. The

micro cycles at 90% SoC and 70% SoC are also shown in Figure 5.6. The voltage

overshoots at 90% SoC with +0.5·I20 superimposed DC are much worse than at

95% SoC, increasing right from the first micro cycle.

128

5.3 EIS at various SoC and Superimposed DCs

Figure 5.7: CC discharge with 1·I20 to 70% SoC and micro cycles with ±1·I20, not

resulting in voltage overshoots.

Figure 5.7 shows a CC discharge from 100% to 70% SoC, followed by ten EIS

micro cycles with a superimposed DC of ±1·I20. These micro cycles were con-

ducted at the same SoC and with the same superimposed DC as the last three

micro cycles shown in Figure 5.6. However, the micro cycles after CC discharge

to 70% SoC, shown in Figure 5.7, do not have a voltage overshoot. It is also vi-

sualized that the voltage overshoots did not always evolve during micro cycles.

129

5 EIS - Fundamentals and Measurement

Concluding that the voltage overshoots during the high SoC must influence the

voltage during the rest of the test and cause voltage overshoots at medium SoC.

They were possibly affecting EIS measurements within the quasi-steady state as

well. Therefore, it seems necessary to avoid voltage overshoots at any cost.

Figure 5.8: EIS procedure starting at 90% SoC (a-c) after complete charge accord-

ing to the EN, and (d-f) after an incomplete charge without constant

voltage phase.

Figure 5.8 (a-c) compares the consequences of a relatively small voltage over-

shoot, appearing after some cycles, with the consequences of a voltage overshoot

>2.6V, shown in Figure 5.8 (d-f), developed through a incomplete charge with-

out a constant voltage section. Both tests used ±0.5·I20 for preconditioning and

cycling. The first voltage overshoots accrued at 90% SoC. The relatively small

voltage overshoot <2.6V did not result in voltage overshoots during later cycles

at 80% SoC. On the other hand, the high voltage overshoot >2.6V did result in

voltage overshoots during all later cycles at 80% SoC. It can be concluded that

the maximum voltage during an overshoot determines if later cycles are affected.

130

5.3 EIS at various SoC and Superimposed DCs

Further tests have shown that the first voltage overshoot already occurred at

lower SoC when the SoC was adjusted via charge than via discharge. Moreover,

it was necessary to avoid voltage overshoots during SoC adjustment via charge,

as they would also influence later cycles. It was not possible to avoid voltage

overshoots via prior capacity throughputs. Furthermore, a pause could not min-

imize the consequences a voltage overshoot causes on all following cycles.

The findings can be explained by an inhomogeneous current distribution during

micro cycling over the height of the electrodes [89]. During short discharges, the

lead sulfate crystals are preferably developing at the bottom of the electrodes.

During short and incomplete charging (lack of the constant voltage phase), the

lead sulfate crystals are preferably dissolved at the top of the electrodes. There-

fore, micro cycles create SoC inhomogeneities between the top and the bottom

of the cell [89]. If the cell is only discharged for a short time, e.g., to 95% SoC, the

following micro cycles increase the SoC inhomogeneities and, therefore, an SoC

of 100% and inactive top part of the electrode develops. This leads to voltage

overshoots at 95% SoC and during all micro cycles to come, shown in Figures 5.6

and 5.8 (d-f). If the cell once comes into this state, it can not be resolved during

the EIS process anymore. Only a complete charge, including a constant voltage

step, will dissolve all lead sulfate crystals. Suppose the first discharging step is

long enough to develop enough lead sulfate crystals all over the electrode. In

that case, there will be no voltage overshoot during the following micro cycles,

as shown in Figure 5.8.

Figure 5.9 (a) shows the resulting EIS procedure avoiding any voltage overshoots

for SoC adjustment via discharge and charge. In Figure 5.9 (b) the cell voltage,

dure allows EIS measurements between 90% SoC and 50% SoC in 5% SoC steps

with superimposed DCs of ±0.5 to ±3·I20. However, not every SoC could be

investigated with every superimposed DC. Furthermore, the voltage limit was

adjusted to a maximum of 2.4V.

131

5 EIS - Fundamentals and Measurement

5.3.3 Final EIS Procedure

Figure 5.9: The EIS procedure without voltage overshoots.

Since the investigation of very high SoC is impossible using the micro cycling

approach with high superimposed DCs without developing voltage overshoots,

two measurements have been taken. Firstly, a safety limit of 2.4V was set. Sec-

ondly, a compromise was found between investigating high SoC and high su-

perimposed DCs. Figure 5.9 shows that the maximum SoC was limited to 90%

for SoC adjustment via discharge and to a maximum of 80% when the SoC was

adjusted via charge. Furthermore, EIS measurements at very high SoC (e.g.,

90% and 85%) were conducted only superimposing IDC = 0A and ±0.5·I20,

Figure 5.9 (b). For lower SoC, higher currents could be superimposed without

132

5.3 EIS at various SoC and Superimposed DCs

risking voltage overshoots. Adjusting 80% and 75% SoC via discharge the 0DC

spectrum, ±0.5·I20, and ±1·I20 superimposed DCs were evaluated. ±2·I20 was

included at 70% and 65% SoC. At 60% and for lower SoC, a DC of ±3·I20 could

be superimposed as well, Figure 5.9 (c)

To exclude all errors (discussed in Section 5.8), which may arise during the dis-

charging phase of the EIS procedure, the cell were recharged according to Euro-

pean standard (EN) [60] before starting the next phase. This dissolves all sulfate

crystals and ensured a fully charged cell. Afterward, the cell was discharged to

0% SoC and recharged to 50% SoC, thereby all following spectra are taken after

prior charge.

One spectrum was recorded during each discharge, and charge superimposed

DC. Only starting the EIS measurement after 1% SoC change during each new

superimposed DC. Since the micro cycles stabilize the EIS test results, only the

EIS measurement during the third micro cycle of each superimposed DC were

evaluated.

On the one hand, these voltage overshoots provoked a non-stationary state of

the cell. However, investigations have shown that voltage overshoots measured

at one SoC also affected all following measurements, even at much lower SoCs,

where the voltage overshoots did not resemble with inconspicuous usage. There-

fore, these voltage overshoots must be avoided at all costs. Resulting of these

findings, at high SoCs, only an EIS measurement without and with low super-

imposed DCs (IDC = 0A and ±0.5I20) could be taken.

All EIS measurements were performed within a climate chamber, regulating the

ambient temperature to either 25 ◦C, 35◦C or 45◦C. The most important param-

eters for the EIS measurement are summarized in Table 5.2.

133

5 EIS - Fundamentals and Measurement

Table 5.2: EIS test parameters (adapted from Ref. [25]).

Parameter Values

IDC 0A, ±0.5·I20,±1·I20,±2·I20, and ±3·I20

investigated SoC 50% to 90% in 5% steps

SoC adjustment via ±1·I20 charge or discharge current

IAC,max 0.5A

fmin 10mHz

fmax 6.5kHz

nr. of measurement points 8 frequencies per decade

T 25◦C, 35◦C and 45 ◦C

∆SoC ±2.5%

The EIS test plan for the Bottom-Up approach EFB+C1, EFB+C2, EFB+C3, EFB+C4,

EFB+C5, EFB+Ref, EFB+CX, and EFB+CYmiddle size cells is shown in Table 5.3.

It contains the pretests executed before starting the EIS procedure at different

temperatures. Figure 5.10 exemplarily shows the (a) complete, (b) positive, and

to investigate NAM additives with EIS, only the negative half-cell spectra are

evaluated.

0 2 4 6 8 10 12

-8

-6

-4

-2

0 2 4 6 8 10 12

-8

-6

-4

-2

0 2 4 6 8 10 12

-8

-6

-4

-2

Figure 5.10: Nyquist plots of the middle size EFB+CXcell (a) complete, (b) posi-

tive, and (c) negative half-cell spectra.

134

5.4 Pre-Processing of EIS data

Table 5.3: EIS test plan for the EFB+C1, EFB+C2, EFB+C3, EFB+C4, EFB+C5,

EFB+Ref, EFB+CX, and EFB+CYmiddle size cells.

Test

order Procedure Description in Visualized in

1 C20 test (scaled to Cn) Section 3.4.1

2 CA2 test Section 4.1.1

3 DCA EN test Section 4.1.2 Figure 6.11 (a), (b)

4 EIS procedure at 25◦C Section 5.3 Figures 5.20 - 5.33,

6.13, 6.38

5 EIS procedure at 35◦C Section 5.3 Figure 5.23

6 EIS procedure at 45◦C Section 5.3 Figure 5.23

5.4 Pre-Processing of EIS data

In Figure 5.11, an exemplary impedance spectrum is shown in the Nyquist and

Bode plots. In both representations, every third measurement point is marked.

As shown, while the measurement points are evenly distributed along the fre-

quencies in the Bode plot, there are more measurement points close to the origin

in the Nyquist diagram. This lack of measurement points in the second semicir-

cle results in a lower weighting of model errors for the concerned frequencies.

Interpolation of the measured impedance data on an equidistant logarithmic is

one opportunity to overcome this problem.

Before any other evaluation of the EIS data, e.g., identifying an ECM, they are

pre-processed to avoid systematic errors. These measurement errors may de-

velop by violations of stationarity, time-invariance, or linearity. Non-stationary

batteries can cause large residuals at low frequencies. To reliably detect and elim-

inate irregularities in the measurement data, the Kramers-Kronig (K-K) transfor-

mation can be used.

135

5 EIS - Fundamentals and Measurement

0 6 12 18

-12

-6

(a)

10-3 10-2 10-1 100101102103104

(b)

10-3 10-2 10-1 100101102103104

-20

(c)

Figure 5.11: Negative half-cell spectra of a middle size EFB+CXcell at 50% SoC,

adjusted via discharge, +0.5·I20 superimposed DC, and at 25◦C

(a) Nyquist plot, (b) absolute value, and (c) phase angle within the

Bode plot.

5.4.1 Kramers-Kronig

If the real and the imaginary parts of an EIS measurement are interdependent,

it can be concluded that the system investigated is linear and stable [175, 176].

This can be verified using the K-K transformation [175, 176]. It reconstructs the

spectrum using the K-K test [177] by calculating the real part from the imaginary

part [178, 179]. A comparison between the measurement and the reconstruction

via the K-K test is visualized in Figure 5.12.

Next to the K-K transformation, the Z-hit method can also be used. Thereby,

the impedance amplitude Zis calculated from the measured phase shift (φ)

based on the Hilbert transformation [180]. For both tests, an ECM consisting of

a series connection of a single resistance and an unlimited number of resistance

and capacitance (R-C) parallel connections, only containing linear parameters,

is used. Each single R-C element fulfills the K-K condition. Therefore, a model

only consisting of those does as well. The range of the time constants investi-

gated should exceed that of the measurement by some decades to minimize the

residuals at the ends of the frequency dispersion. The measured spectrum is

valid only if it can be reconstructed using the R-C circuit components and their

136

5.4 Pre-Processing of EIS data

residuals are evenly distributed. However, the difference between the measure-

ment and the reconstruction is never zero if the noise in the measurement can

not be avoided. If the absolute error is higher than 1.5mΩor the relative error is

higher than 3%, the data points are considered to not fulfilling the K-K transfor-

mation. These are not evaluated any further. Errors between the measurement

and the K-K transformation can be induced by diffusion processes [148].

0 6 12 18

-12

-6

(a)

10-3 10-2 10-1 100101102103104

(b)

10-3 10-2 10-1 100101102103104

-20

(c)

Figure 5.12: EIS measurement, shown in Figure 5.11, its K-K transformation, and

the resulting validated spectra (a) Nyquist plot, (b) absolute value,

and (c) phase angle within the Bode plot.

5.4.2 Distribution of Relaxation Times

Identifying characteristic points and properties within a spectrum requires expe-

rience and a deep level of understanding of the electrochemical processes within

the battery. Moreover, this is needed to determine an ECM and its parameters

for representing the spectrum, as described in Section 5.5. The distribution of

relaxation times (DRT) provides a model-free approach to identifying single pro-

cesses [181]. Consequently, the DRT reveals the number of involved processes

and even allows their quantification by their location of time constants. Thereby,

it is a reproducible way to determine a suitable ECM for modeling and starting

parameters for later fitting.

137

5 EIS - Fundamentals and Measurement

The spectra are transferred from the frequency into the time domain using the

Fourier transformation [11]. Even when overlapping in the frequency domain,

the separation and quantification of their single polarization contribution are

visible in the time domain [11]. How to generate the DRT from the measured

impedance spectra [10, 11, 181] an optimization problem needs to be solved

min||A·x−b||2. (5.2)

where xis the vector of unknown distribution function, matrix Aand vector b

need to be determined. Solving the algorithm allows only non-negative values

since only positive resistance values have a physical meaning. Non-resistive-

capacitive contributions in the spectrum cannot be modeled because of the re-

strictions to positive resistance values. A common way to solve this problem is

the shift and cut-off approach: All the measurements with positive imaginary

parts are discarded. The ohmic offset is subtracted from all measurements, leav-

ing only R-C elements. Danzer introduced the generalized distribution of re-

laxation times (GDRT) analysis for complex superposed impedance spectra that

include ohmic, inductive, capacitive, resistive-capacitive, and resistive-inductive

effects. Thus, the entire spectrum can be reproduced [11].

As an example to briefly describe the determination of the DRT, the reconstruc-

tion of a series of R-C elements is described. For an R-C element, the imaginary

and real parts are described with

ImZRC=ω·τ·R

1+ (ω·τ)2(5.3)

and

ReZRC=R

1+ (ω·τ)2. (5.4)

For the transformation procedure, both imaginary and real parts of the measured

spectrum are used for the optimization function.

b=



ReZRC

ImZRC

(5.5)

138

5.4 Pre-Processing of EIS data

The unknown distribution function of the DRT is

x=[h1...hk...hNτ]T(5.6)

here Nτis chosen as a multiple of the number of measured frequencies Nfin

the impedance spectra Nτ= c·Nf[11] with c ∈1, 2,3to get a smoother distri-

bution function [181]. The matrix A that needs to be calculated for the different

measured frequencies and predefined time constants includes the real and imag-

inary parts.







Re1

1+(j·ω1·τ1). . . Re1

1+(j·ω1·τNτ)

.....

Re1

1+(j·ωNf·τ1). . . Re1

1+(j·ωNf·τNτ)

.....

Im1

1+(j·ω1·τ1). . . Im1

1+(j·ω1·τNτ)

.....

Im1

1+(j·ωNf·τ1). . . Im1

1+(j·ωNf·τNτ)







(5.7)

The number of the R-C elements used to display the spectra with an equivalent

circuit model must usually be chosen to be higher than the number of measure-

ments to achieve adequate resolution. Using a regularization term is one way

to solve this ill-posed optimization problem. For example, the Tikhonov regu-

larization can determine the DRT, adding the term to the optimization function

[182] is the regularization parameter. The sum of squared errors of the recon-

structed spectrum indicates the optimal selection of the regularization parame-

ter [182].

Involving the regularization term into the optimization problem, the matrix A

and vector b are complemented:

AReg =



λ·l∈Rnxn 

(5.8)

139

5 EIS - Fundamentals and Measurement

and

bReg =



0∈Rn

(5.9)

Each peak represents a single process. Thereby, the DRT help to identify the

number of processes and to choose the equivalent circuit model elements and

their starting parameters. Assuming a Gaussian distribution within the DRT, the

occurring peaks respectively process can be assigned to a single Gaussian bell.

Thereby, the location of the peak corresponds to the characteristic time constant

of the process. The area which a bell covers equals the polarization resistance

of the process. The variance and width correlate with the frequency range of

the process. A process with a sharp peak occurs at a small range of frequencies,

while broad peaks point out more distributed processes.

10-2 10-1 100101102

0.5

1.5

2.5

Figure 5.13: DRT of the spectra visualized in Figure 5.11.

Figure 5.13 shows the DRT of the spectra visualized in Figure 5.11. However,

the peak for the highest time constant τ= 17s is an edging effect caused by

a small number of measurement points in the Nyquist and can be neglected.

The other two main peaks reveal the time constants of the two semicircles. The

time constant of τ= 0.166 s equals to the frequency of f= 1/0.166s = 6Hz, and

τ= 3.22s equals to the frequency of f= 1/3.22s = 0.3Hz. These characteristic

frequencies can also be found in the Nyquist diagram as the frequencies for the

minimum imaginary part of the impedance. However, in Nyquist, inaccuracies

may accrue, while in the DRT, a determination is elementary.

140

5.5 Equivalent Electric Circuit Model

A suitable equivalent circuit topology must be defined to model the measured

EIS. Based on the underlying physical processes, the ECM allows a good rep-

resentation of the measured spectra within a minimum set of model parame-

ters. The ECM can persist of simple passive electrical components like resis-

tors, capacitors, and inductors. These components are interconnected to net-

works representing the electrochemical processes. The ECM for batteries and

cells is mainly based on Randles circuit [152]. Randles circuit can be employed

with different levels of modifications. Compared to other modeling approaches,

the ECM offers high computation speed. Therefore, it is used to simulate com-

plex systems or to implement small simulation step sizes [155] needed for dy-

namic battery operations. However, parameterization measurements must be

executed, and the ECMs have a restricted validity range within these parameter-

ization measurements [155].

In an ECM, simple passive electrical components are interconnected to a net-

work. Starting with the ohmic resistance, the physical meaning of the ohmic re-

sistance R0corresponds to the sum of the limited conductance of the contacts, the

intercell connections, the grid, the active masses (AM), and the electrolyte [143].

The internal resistance depends on the SoC, SoH, prior usage, and temperature

of the battery or cell. This originates from chemical and morphological changes

in the active material, grid corrosion, and electrolyte concentration [112]. The

internal resistance is easily measured as the real part of the impedance. Mainly

the internal resistance is determined in a frequency range where the phase angle

of the impedance equals zero. In other words, all electrochemical reactions are

shunted by the double-layer capacitance.

At high frequencies, the imaginary part of any battery impedance becomes pos-

itive. It often grows linearly while the real part remains constant [183, 184].

This behavior is modeled with an inductance L. The inductive branch of the

impedance plot has to be included in the model, or at least the effect of the in-

ductance has to be compensated numerically [183]. If the inductive branch is

suppressed, a systematic error is introduced into the evaluation because the ex-

istence of an inductance leads to a characteristic deformation of the capacitive

branch [185]. Karden observed impedances that were not strictly vertical but

141

5 EIS - Fundamentals and Measurement

curved with growing Re{Z}with increasing frequencies [156]. Therefore, an

alternative representation within the ECM was given

ZL=L·(jω)ξL·L(5.10)

without physical interpretation [156]. The porosity of an electrode might lead to

this inductive behavior at high frequencies [186]. However, in [156] was shown

that this contribution is relatively small. Three different spectra with different

values for the resistance and the inductance are shown in Figure 5.14.

0 5 10 15 20 25

-10

-5

R = 5 m , L = 4.3 mH, L= 1

R = 10 m , L = 4.3 mH, L= 1

R = 10 m , L = 4.3 mH, L= 0.65

Figure 5.14: Spectra of a R-L series connection.

The parallel connection of a resistance and a capacitor represents the charge

transfer resistance Rct and the double-layer capacitance Cdl [187, 188]. Both val-

ues result in a time constant τ

τ=R·C. (5.11)

The interface between the electrolyte and the AMs determines the value of the

double-layer capacitance. The interface of the positive and negative electrode

surfaces is thereby significantly different. The inner surface of the negative

electrode is approximately a tenth part of the surface of the positive electrode.

Thereby, the double-layer capacitance of the negative electrode is smaller. By

connecting the charge transfer resistance in parallel to the double-layer capaci-

142

5.5 Equivalent Electric Circuit Model

tance, the energy stored in the electrochemical double layer can be dissipated by

the charge transfer processes after the interruption of the charge current. Dur-

ing pulse charges, this loop of charge and self-discharge of the electrochemical

double layer is repeated several times. Different spectra consisting of two R-C

parallel connections with different values for the resistances and the time con-

stants are shown in Figure 5.15.

0 2 4 6 8 10 12

-10

-8

-6

-4

-2

R1= 5 m , 1= 10 ms, R2= 5 m , 2= 10 ms

R1= 5 m , 1= 10 ms, R2= 5 m , 2= 100 ms

R1= 5 m , 1= 10 ms, R2= 5 m , 2= 1 s

R1= 7 m , 1= 10 ms, R2= 5 m , 2= 1 s

Figure 5.15: Spectra of two R-C parallel connections.

Next to the passive electrical components, also frequency-dependent compo-

nents are known. Diffusion processes are often seen at small frequencies. In

the case of unlimited diffusion, this is visualized within the spectrum by a con-

stant incline ϕ= const. = -π/4 = −45◦C. The component used to illustrate this

behavior is called the Warburg element

ZW=√2·σ

pj·ω, (5.12)

where σis the Warburg coefficient. Since the Warburg element is not used in this

work, it will not be further discussed.

The constant phase element (CPE) represents a generalized capacitive element,

143

5 EIS - Fundamentals and Measurement

with the impedance formula

ZCPE =1

A(jω)ξC(5.13)

where 0 ≤ξC≤1. If ξC= 1, the CPE element becomes a pure capacitor. When

ξCgoes to 0, it behaves like a resistor [31].

0 2 4 6 8 10 12

-10

-8

-6

-4

-2

R = 5 m , 1= 10 ms, C= 1

R = 10 m , 1= 10 ms, C= 1

R = 10 m , 1= 10 ms, C= 0.75

R = 10 m , 1= 10 ms, C= 0.5

Figure 5.16: Spectra of a R-C parallel connection with and without the depres-

sion factor.

Suppose the spectra do not consist of a perfect semicircle on the Nyquist plot

but a depressed semicircle, as shown in Figure 5.16. In that case, imitating this

behavior with parallel R-C elements is hard. This non-ideal capacitive behavior

does not consist of one relaxation time τ= 1/RC but is distributed around a

mean value [174]. Such a distribution mainly arises from the spatial extension

of the electrode to electrolyte interface in rough or porous electrodes [174]. Such

a deformed semicircle can be modeled when a CPE replaces the double-layer

capacitance within the R-C connection. The parallel connection of a CPE and a

resistance is called a ZARC element. The impedance of a ZARC element can be

calculated by the means of the equation

ZARC =R·ZCPE

R+ZCPE =R·CPE−1(jω)−ξ

R+CPE−1(jω)−ξ=R

R·CPE(jω)ξ+1(5.14)

144

5.5 Equivalent Electric Circuit Model

where 0 ≤ξ≤1. For ξ=1, the porous character of the electrodes vanishes, and

the distributed low-frequency elements can be represented by an R-C circuit.

The lower ξ, the higher the deformation. Formally, ξis unit less and the physical

unit of CPE·(j·ω)ξis F/s. Therefore, F·sξ−1is the unit of the CPE. Furthermore,

R·CPE can also be combined and represented as τ, where the unit of τis sξ. For a

ZARC element, the distance between the real-axis intersection and the point with

the lowest imaginary part of the impedance is still characterized by R. However,

the absolute value of all impedance values is reduced for all frequencies. Differ-

ent spectra consisting of one R-C parallel connection with different depression

factors are shown in Figure 5.15.

An explanation for the non-ideal capacitor is a non-uniform current distribution

[189]. Measurement showed that the ZARC element represents an actual capaci-

tor for measurements close to the center of the electrode. In contrast, it showed

a depression at the edge of the electrode, where the current density is perturbed

[189]. Calborean verified this hypothesis using EIS measurements in cells with

various acid-filling levels [190]. The lower the acid level, the more homogeneous

the current and acid distribution and the closer the ZARC element to a perfect

semicircle. Moreover, the depression level also depends on acid stratification

[190]. Earlier hypotheses on the reasons for depressed semicircles, such as the

roughness of the electrodes [191] or the thickness variation or composition of

the coating [192], could be ruled out since by adding/removing electrolyte, such

parameters would not vary [190].

The measured EIS data consist of an inductive part, a shift along the real axis,

and three semicircles. One spectrum is shown in Figure 5.17. Even though the

complete measurement is shown, only the valid measurement points are high-

lighted in red. The part of the spectra which fails the K-K transformation is only

illustrated with light blue dots. The three semicircles within the valid measure-

ment points are marked, leading to the chosen ECM shown in Figure 5.18. The

ECM consists of an R0, defined as the minimum of the real part of the impedance.

However, in all figures, the spectra will be shifted according to this internal re-

sistance for better comparison.

145

5 EIS - Fundamentals and Measurement

Figure 5.17: EIS measurement shown in Figure 5.11, its K-K transformation, the

resulting validated spectra, and the fitting result.

Figure 5.18: The chosen ECM (adjusted from Ref. [25]).

5.6 Literature Survey: Interpretation of Equivalent

Circuit Elements

EIS measurement results conducted and the results shown in the literature show

different shapes for battery, cell, and half-cell spectra. Thereby, the shape mainly

depends on the measurement regime, e.g., SoC, superimposed DC, and fre-

quency range. The assignment of physical meaning to single equivalent circuit

elements is relatively difficult. They are sometimes resulting in contradictory in-

terpretations.

146

5.6 Literature Survey: Interpretation of Equivalent Circuit Elements

It is generally agreed that the high-frequency behavior (f> 100Hz), representable

by the internal resistance and the inductivity, can be explained from electrode

geometry effects such as connections inside the cell or battery, the separator, the

electrolyte resistivity and the surface coverage of the electrode by crystallized

lead sulfate [16, 17, 19, 112, 141, 143, 159, 168, 185, 193, 194]. Additionally, the

interconnected sponges lead together with external contributions was suggested

as a reason for the high-frequency behavior [195]. The inclination of the induc-

tive branch was attributed to the skin effect or current displacement [196].

Generally, each semicircle is connected with one separate electrochemical reac-

tion process, which could be charge transfer, chemical reactions, mass trans-

port, or adsorption processes [169]. If those steps differ in their time constants,

the spectra will result in several semicircles. Furthermore, one reaction can re-

sult in several separate semicircles if it executes several consecutive or parallel

steps [197]. Within some works, only one semicircle could be identified. Others

showed a semicircle and a 45 ◦C slope or the beginning of a second semicircle

[16, 170, 190, 195, 198]. Most EIS measurements are represented with two capac-

itive semicircles [141, 156, 159, 168, 169, 170, 193, 195, 198, 199, 200, 201, 202]. The

identification of the electrochemical reaction for each semicircle varies between

the sources. However, it is hard to compare different interpretations since the

frequency range of each semicircle is not always provided. It is mostly agreed

that one of the capacitive semicircles is related to the charge transfer reaction

while the other relates to the double-layer capacitance. Both reactions are re-

lated to the porosity of the electrodes and take place at the electrode-electrolyte

interface [19]. However, there is no consensus on which of the semicircle belongs

to which electrochemical reaction.

Within several works, the high-frequency semicircle is assigned to the reactions

inside the porous structure of both electrodes [16, 141, 148, 151, 159, 168, 190,

193, 195, 199, 203]. Thereby, the semicircle is described by the charge transfer

resistance, depending on the porosity or the effective surface area of the elec-

trode, respectively [143, 204] and the double-layer capacitance. With lower SoC,

the active surface decreases, increasing the semicircle [199]. Furthermore, the

current dependency of the semicircle suggests its connection to charge transfer.

However, Kowal et al. described the SoC dependency of all found semicircles

147

5 EIS - Fundamentals and Measurement

[170] and pointed out the current dependency on the low-frequency capacitive

semicircle, which was already found by Karden et al. [156, 170]. Beketaeva et

al. measured the negative active mass (NAM) porosity for different SoCs and

related the pore volume with the real part of the impedance [205].

Some sources propose that the second or low-frequency semicircle relates to the

sulphation reaction, whose rate is mainly controlled by the rate-limiting diffu-

sion of Pb2+ions [16, 141, 151, 190, 193, 204]. Without further indication, if the

diffusion occurs inside or outside the pores of the plates. Alao et al. measured

a 45◦line at low frequencies, down to 0.1Hz, their interpretation was that the

diffusion of Pb2+ions only inside the pores is the shape-forming process [198].

While others explicitly attribute the second semicircle to the diffusion in and

outside the porous electrode [16, 19, 168]. D’Alkaine et al. pointed out the inho-

mogeneous current distribution stimulating the diffusion inside the macroscopic

pore structure and outside the electrodes [195]. Kirchev et al. interpreted the

low-frequency semicircle as the adsorption impedance, representing the trans-

port of Pb2+ions from the pore to the adsorption layer in the outer Helmholtz

layer [159].

While the analysis presented so far separates the two semicircles into two pro-

cesses, various authors assign one semicircle to the negative and the other to

the positive half-cell instead [20, 159]. At the same time, Kowal presented half-

cell measurements of the negative electrode, consisting of two small semicircles,

and the positive half-cell electrode consisting mainly of one big semicircle [169].

The complete cell impedance’s first semicircle would be made up of the negative

electrode and the second of both electrodes but mainly the positive [169]. This

could be justified if the impedance of the positive electrode consists mainly of

the pore diffusion impedance and the charge transfer process is not visible in

the impedance of the positive electrode. Another possible reason was given by

Tenno et al., who stated the essentially different charging rates for the positive

and the negative electrodes as the reason for the two semicircles [200]. Also,

Kwiecien et al. interpreted the first semicircle as the charge-transfer process of

the negative electrode, the second semicircle as a slower (not further defined)

process of the negative electrode, and the third semicircle as the charge-transfer

process of the positive electrode [148].

148

5.6 Literature Survey: Interpretation of Equivalent Circuit Elements

Whenever an electrochemical process is relatively heterogeneous, a suppressed

semicircle is found instead of a perfect semicircle [143].

0 2 4 6 8 10 12

-10

-8

-6

-4

-2

Figure 5.19: The inductive curl of the middle size EFB+C1negative half-cell EIS

at 50% SoC, 25 ◦C and with -0.5·I20 superimposed DC.

Some authors identified next to the capacitive semicircle a low-frequency induc-

tive loop [112, 156, 159, 169, 170, 190, 194, 206], exemplary shown in Figure 5.19.

However, calling this phenomenon an inductive loop might not be a good decli-

nation because it suggests the presence of an inductivity that could not accrue at

low frequencies [207]. Therefore, it is more appropriate to call this behavior neg-

ative capacitance [208], [209], [210], which is equivalent to calling it an inductive

loop [207]. The pseudo-inductive loop may have a negative resistance and a neg-

ative capacitance [211]. However, both interpretations (a low-frequency induc-

tivity or a negative capacity) are extremely hard to describe by electrochemical

processes. While most did not comment on this finding or suggested measure-

ment errors as a reason for the low-frequency inductive loop, some tried to find

the physical processes that are its phenomenological origin. An easy way to

eliminate the possibility of measurement artifacts is the usage of the K-K test, as

it indicates the errors if the system is not linear, stable, causal, and finite system

[175, 176, 177]. Further information are given in Section 5.4.1. One possible ex-

planation for a low-frequency inductive loop is that there are two different time

constants, one for the electronic charge transport and one for the ions gathering

149

5 EIS - Fundamentals and Measurement

at the interface, thereby changing the stoichiometry or oxidation state [212]. It

should be noted that a DC of the opposed sign will cause a capacitive semicircle

and not an inductive low-frequency loop [207]. A second possible explanation

for a low-frequency loop is a two-step reaction, competing for reaction or ab-

sorption, where the secondary effect is much slower than the main reaction [213,

214]. Hampson discovered that the oxidation from lead to Pb2+must occur in a

two step electron transfer reaction [215, 216]. That a multi-step reaction would

strongly resemble an EIS of a lead electrode was also shown by Maddala et al.

[210]. Huck compared the spectra resulting from two charge transfer reaction

steps with two additional adsorbates and with a different intermediate step pro-

posed by Hampson [197], [215], [216]. The latter two can result in a double capac-

itance loop with a negative capacitance. Stoynov et al. attributed both capacitive

semicircles of the negative half-cell to nucleation and the inductive semicircle of

the negative half-cell to propagation [194]. While two capacitive semicircles and

an inductive loop were found for lower SoC, the inductive loop was replaced by

a third capacitive semicircle at high SoC. The appearance of the third capacitive

semicircle was attributed to the further growth of the already-formed crystals

[194]. However, when the potential reached the hydrogen-gassing activation

stage, the impedance changed its shape corresponding to hydrogen evolution

[194].

150

5.7 Influencing Factors on the EIS

5.7.1 State of Charge

Figure 5.20 shows the SoC influence on the negative half-cell EIS measurement.

No SoC dependency is visible for the inductive part of the spectra [165]. In Fig-

ure 5.20 (a), the increase of the internal resistance with decreasing SoC is visual-

ized [16, 17, 18, 141, 156, 165, 193, 198, 217, 218]. The increase of the internal resis-

tance with decreasing SoC can be related to the change of the electrolyte density

and it’s decreasing conductivity, and the increasing electrode surface coverage

by insulating crystallized lead sulfate [17, 141, 193, 217, 218].

(a) (b)

1234

0 2 4 6 8 10 12

-8

-6

-4

-2

Figure 5.20: SoC influence on the (a) internal resistance and (b) the negative half-

cell spectra of the middle size EFB+CXcell using a discharge current

for SoC adjustment, +0.5·I20 superimposed DC, and at 25◦C.

In Figure 5.20 (b), the internal resistance was neglected to better compare the

semicircles. It is shown in Figure 5.20 (b) that the semicircles increase with lower

SoC. This behavior can be found for all additive types and superimposed DCs.

The increase of the semicircles with decreasing SoC was already found in earlier

literature [17, 141, 156, 157, 165, 193, 199, 217, 218]. The increasing semicircle

with lower SoC can be related to the decreasing active surface area [199], partly

caused by blocked pores by PbSO4crystals and bubbles during overcharging

[141, 193, 217].

151

5 EIS - Fundamentals and Measurement

5.7.2 Superimposed DC

It has been shown that the internal resistance and the inductive part are not de-

pendent on the superimposed DC [165]. Comparing spectra, taken with super-

imposed DCs, show that the charging currents generally result in larger semicir-

cles than the corresponding discharging currents [22, 154, 156, 157, 165]. This is

also visualized in Figure 5.21, where the highest charging currents result in the

largest semicircles. Several investigations have shown a reduced diameter of the

semicircle as the absolute value of the discharging current increases [198, 219].

That the spectra taken without a superimposed DC serves as an asymptote for

both discharging and charging currents tending towards zero can also be seen in

Figure 5.21 [156].

0 5 10 15 20 25 30

-20

-15

-10

-5

0DC

+0.5 I20

+1 I20

+2 I20

+3 I20

-0.5 I20

-1 I20

-2 I20

-3 I20

Figure 5.21: Influence of the superimposed DC on the negative half-cell EIS mea-

surement of the middle size EFB+CXat 50% SoC using a discharge

current for SoC adjustment, and 25 ◦C.

5.7.3 Short-term Usage

The effects of previous charge or discharge can be minimized but not neglected

completely using micro cycles, as described in Section 5.2, [157]. The remaining

differences caused by the history are visualized in Figure 5.22 for different su-

perimposed DCs. The short-term usage influences mainly the first and second

semicircles at the negative half cell. When the SoC is adjusted via charging, the

152

5.7 Influencing Factors on the EIS

impedance is larger than via discharge for superimposed charging and discharg-

ing current [157].

(a) (b) (c)

0 5 10 15

-10

-5

after prior discharge after prior charge

0 5 10 15

-10

-5

0 5 10 15

-10

-5

Figure 5.22: Influence of prior usage on the negative half-cell EIS measurement

of the middle size EFB+CXcell at 50% SoC, 25 ◦C, and (a) -0.5·I20,

(b) without, and (c) +0.5·I20 superimposed DC.

No significant effect of a pause (10s - 1min) before an EIS measurement was

determined for spectra with a superimposed charge or discharged current [157].

5.7.4 Electrolyte Concentration

After some cycles, the acid density irreversibly increases from top to bottom of

the electrode. This acid stratification causes different effective reaction constants

within the system, changing the spectra [16]. The local current density, which is

smaller at the bottom because of the finite conductivity of the grid and thereby

enhancing acid stratification, defines the charge-transfer resistance. The mea-

sured impedance increases with higher acid density or distinct acid stratifica-

tion [148]. It was shown that a few distributed R-C elements connected through

ohmic resistances can represent this behavior [169].

When the acid stratification is minimized, e.g., by bubbling nitrogen through

a cell, the semicircles in the negative half-cell spectra are smaller and less de-

pressed [157].

153

5 EIS - Fundamentals and Measurement

5.7.5 Temperature

The internal resistance and the radius of the first semicircle tend to decrease with

temperature rise [198, 219]. The lower values for the charge transfer resistance

and the double-layer capacitance imply that higher temperatures increase the

reaction rate and the active surface area of the PbO2layer [198]. These observa-

tions can also be made in Figure 5.23. Especially within Figure 5.23 (a), with a

superimposed discharging current, the decreasing radius of the semicircles for

higher temperatures can be seen. In Figure 5.23 (b) without a superimposed DC

and in (c) with a superimposed charging current, the radius of the semicircle at

35◦C and 45◦C are similar.

(a) (b) (c)

0 5 10 15

-10

-5

0 5 10 15

-10

-5

0 5 10 15

-10

-5

Figure 5.23: Influence of the temperature on the negative half-cell EIS mea-

surement of the middle size EFB+CXcell at 50% SoC using a dis-

charge current for SoC adjustment, and (a) -0.5·I20, (b) without, and

5.7.6 Carbon Additives at the negative Electrode

High electrode surface areas are a key parameter to get a high power and dy-

namic charge as well as low internal resistance [71, 128, 204]. If these new and

highly porous active materials can be seen within the EIS measurement was ana-

lyzed at 80% SoC [25] and is also visualized in Figure 5.24. Further investigations

are shown in Section 6.

154

5.8 Limits of EIS

0 2 4 6 8 10

-6

-4

-2

EFB+C1 (Sext = 7.1 m2 g-1)

EFB+C4 (Sext = 92.1 m2 g-1)

EFB+C5 (Sext = 159.3 m2 g-1)

Figure 5.24: Influence of different tailored carbon additives on the negative half-

cell EIS measurement at 80% SoC, 25 ◦C and with +0.5·I20 superim-

posed DC.

5.7.7 State of Health

Since the SoH of a LAB is not the scope of this work, no further investigations are

made. The EIS procedure was always conducted on newly built test cells, only

conducting a few capacity throughputs, such as the C20, the CA2 test, and the

DCA EN test, before the EIS procedure. Therefore, SoH should not be relevant

for the EIS procedure used. However, EIS is affected by the SoH and could also

be used as a prediction tool for SoH [20, 21, 141, 167, 193, 220, 221].

5.8 Limits of EIS

Executing EIS measurement on batteries and cells is an error-prone method. The

measurement principle can minimize some. Others are caused by the measure-

ment device itself and cannot be influenced. In the following, the various sources

of errors are identified, determined, and illustrated for the 2V, 20Ah, middle

size (3P2N) EFB+CXcell used within this work. The estimation principle for

every error source can be used on all cell layouts or additives of interest. More-

over, the relevant estimations are also valid for EIS measurements on other bat-

tery technologies. The investigated sources of errors are divided into five main

155

5 EIS - Fundamentals and Measurement

categories.

• Errors caused by the EIS measurement device, Section 5.8.1:

–Discretization in Time

–Timing Error

–Quantization Errors

• Errors caused by the measurement setup, Section 5.8.2:

–Electromagnetic Noise

–Cabling

–Ambient Temperature

• Errors caused by non-stationary factors, Section 5.8.3:

–SoC Drift

–Temperature Drift

–Voltage Non-linearity

• Errors caused by the current used for preconditioning and superposition,

Section 5.8.4:

–Preconditioning

–Superimposed Current

–Timing Error during Superposition

5.8.1 Errors caused by the EIS measurement device

The EIS measurement device used in this work is called the EISmeter 2-20-4 pro-

vided by Digatron power electronics. Errors caused by the EISmeter are dis-

cussed and verified by Karden [112]. The primary sources of errors are dis-

cretization in time, errors in the time measurement, and quantization errors in

voltage and current.

Discretization in Time

The continuous voltage and current signals are recorded with a finite sampling

rate. Thereby, the maximum frequency investigated during the EIS measure-

ment is limited by the sample rate to avoid Aliasing. Aliasing will occur when

the signal frequency is higher than half of the sample rate, provoking a differ-

ent reconstructed signal from the samples than the original continuous signal.

156

5.8 Limits of EIS

However, Aliasing is generally avoided by applying a low-pass filter to the in-

put signal before sampling. Thereby, it only limits the maximum frequency in-

vestigated but will not cause any errors.

Timing Errors

Whenever signals are sampled, timing errors occur. For example, the interval

between two samples might not be constant, or voltage and current might not

be sampled simultaneously. Sampling is made equidistant using a timer clock

controlling the hardware. However, this timer clock might also have minor time

measurement errors. Voltage and current sampling must occur at the same in-

stant or, at least, with a constant delay. Any of these will result in proportional

errors, impacting the results of the phase shift between current signal input and

voltage response during the EIS measurement. Even though it is known that this

error will occur, it is only possible to investigate this source of error further if the

time error is known for the used device. Nevertheless, the error is expected to

be neglectable.

Quantization Errors

Apart from the limited sampling rate, quantization errors in the voltage and cur-

rent measurements occur due to their limited resolution. The quantization errors

are determined by the least significant bit (LSB) of the digital-to-analog (D/A)

converter controlling the current and the analog-to-digital (A/D) converter mea-

suring the voltage. By determining the impedance, both quantization errors will

impact the EIS result. The LSB for AC, voltage, the maximum allowed current,

and the ideal voltage amplitude during an EIS measurement are given in Ta-

ble 5.4.

157

5 EIS - Fundamentals and Measurement

Table 5.4: EISmeter specific technical data.

Technical Parameter EISmeter Specific Value

IAC,LSB 30 µA

IAC,max 0.5A

VAC,LSB 10 µV

VAC,ideal 6mV

VAC,LSB 10mV

∆Z10 µΩ

Zmax 666 Ω

Furthermore, ∆Z, the quantization step of the impedance, and Zmax, the maxi-

mum impedance measurable during an EIS measurement, are given in Table 5.4.

Where

∆Z=VAC,LSB/2

IAC,max (5.15)

the quantization step of the impedance is determined by the minimum voltage

step measurable when the AC with the highest allowed amplitude is inserted

[112]. Moreover,

Zmax =VAC,max

IAC,LSB/2 (5.16)

the maximum impedance measurable during an EIS will be recorded when the

highest voltage is measured when the AC with the smallest possible amplitude

is inserted [112]. However, whenever an impedance close to ∆Zor Zmax is mea-

sured, the relative error would be close to 100% because either the voltage or the

current amplitude would approach its resolution limit. The relative error

∆Z

Z=sVAC,LSB/2

VAC 2

+IAC,LSB/2

VAC/Z2

(5.17)

for all measurements depends on the values of the impedance [112]. Whenever

possible, the EISmeter will adjust the amplitude of the AC to result in an ampli-

tude of 6mV for the AC voltage signal. However, the AC impedance, which will

not be tracked during EIS measurement and must be calculated with VAC/IAC,

158

5.8 Limits of EIS

can only be varied between IAC,LSB/2 ≤IAC ≤IAC,max. Thereby, between

Zideal,min =VAC,ideal

IAC,max =12mΩ(5.18)

and

Zideal,max =VACideal

IAC,LSB/2 =400Ω(5.19)

it is possible to keep the AC voltage amplitude at its ideal value of 6mV [112].

While the current value decreases between its maximum value IAC,max, and the

minimum value ILSB/2. For an impedance smaller than 100 Ω, the error in volt-

age dominates the relative error. Therefore, in the range of 12mΩ≤Z≤100 Ω,

where VAC ∼VAC,ideal, the relative error is very small with

∆Z

Z=sVAC,LSB/2

VAC 2

=10 µV/2

6mV =0.08%. (5.20)

For lower impedance values than ZV=ideal,min the amplitude for VAC will de-

crease, resulting in an increasing relative error. For higher impedance values,

the current is reduced so far that the current error predominates the relative er-

ror and will increase as well. The quantization error is shown in Figure 5.25. It

is too minor to have visible effects on the spectra.

10-3 10-2 10-1 100101102103

-2

-1

Figure 5.25: The normalized quantisation error of the AC and voltage on the neg-

ative half-cell EIS measurement of the middle size EFB+CXcell at

25◦C without superimposed DC.

159

5 EIS - Fundamentals and Measurement

5.8.2 Errors caused by the measurement setup

Electromagnetic Noise

Inductive or capacitive coupling is caused by the measurement setup as cross-

talk between cables. Two conductors are said to be inductively coupled when

the AC through one conductor creates a changing magnetic field which induces

a voltage in the second conductor. Capacitive coupling is the energy transfer

between channels or within an electrical network through the displaced current

induced by an electric field. If the inductive and capacitive coupling is mini-

mized as described within Section 5.2, e.g., by shielding and twisting the cables,

the electrochemical noise can be neglected.

Cabling

The resistive coupling can be minimized using four-point measurements for EIS

measurements, allowing a current-free voltage measurement.

Ambient Temperature

10-3 10-2 10-1 100101102103

-1

-0.5

0.5

Figure 5.26: The normalized error of the ambient temperature deviation on the

negative half-cell EIS measurement of the middle size EFB+CXcell

at 25◦C without superimposed DC.

To avoid additional errors in the EIS measurement caused by the measurement

setup, the ambient temperature should be stabilized by performing all EIS mea-

surements in a climate chamber. The climate chamber, which is set to 25 ◦C

varies between 24.79◦C and 25.28◦C and has thereby a temperature deviation

160

5.8 Limits of EIS

of ∆T= 0.49◦C = ±0.25 ◦C. The temperature deviation within the temperature

chamber is independent of the adjusted temperature. The effect of the tempera-

ture deviation on the impedance measurement results is shown in Figure 5.26.

5.8.3 Errors caused by non-stationary factors

For meaningful EIS, the battery or cell must be kept stationary, or at least in

a quasi-stationary working point. Influencing factors that could easily change

or even change automatically during the measurement of one spectrum are the

SoC, temperature, and voltage level. Other influences (e.g., SoH, electrolyte con-

centration, electrolyte stratification, superimposed DCs, and short-term usage)

are usually unchanged during one single EIS measurement. However, they must

be kept constant to allow comparison between spectra.

SoC Drift

The influence of the SoC on the EIS measurements has been shown in Section 5.7.1.

Figure 5.27 (a) shows nine impedance spectra in 5% SoC steps. However, all

these spectra have been taken with a superimposed charge current of +0.5·I20.

Whenever a superimposed DC is applied, each impedance, measured one after

another during a spectrum, belongs to a slightly different SoC. To still fulfill the

demand on the (quasi-) steady state, the SoC change must be limited. Within this

work, the SoC only deviates ±2.5% from the targeted SoC. Thereby, for spectra

taken with a superimposed charge current of +0.5·I20, as shown in Figure 5.27,

the latest EIS measurement points are closer to the higher SoC than they would

be at the target SoC. Vice versa, for superimposed discharging currents, the lat-

est EIS measurement points would be closer to the lower SoC than they would

be at the target SoC. Figure 5.27 (d) also visualizes that the error caused by the

SoC drift is minimal between 1Hz and 6500Hz and has a higher impact on the

low-frequency region than on the high-frequency region, where the spectra show

minimal deviation.

161

5 EIS - Fundamentals and Measurement

(a)

0 2 4 6 8 10 12 14

-4

-2

90% SoC

85% SoC

80% SoC

75% SoC

70% SoC

65% SoC

60% SoC

55% SoC

50% SoC

(b) (c)

123

-2

-1

8 9 10

-2

-1

(d)

10-3 10-2 10-1 100101102103

Figure 5.27: Influence of the SoC change during measuring one spectra (thick

line = measurement, thin line = maximum possible deviation) of the

middle size EFB+CXcell at 25◦C with +0.5 I20 superimposed DC

(a) the negative half-cell spectra, zoom into (b) high-frequency part,

162

5.8 Limits of EIS

Temperature Drift

The influence of the ambient temperature on the EIS measurements has been

shown in Section 5.7.5. All EIS measurements have been conducted within a cli-

mate chamber, preventing ambient temperature drifts during one measurement.

However, when an EIS measurement with a superimposed DC is conducted,

the inner cell temperature will rise. The change in cell temperature is shown in

Table 5.5.

Table 5.5: Temperature change during the EIS measurement on a middle size

cell.

IDC time ∆V˙

QDC,Joule ˙

Qrev ˙

Q˙

T(50%) ∆T(50%)

+0.5A 2h 0.13V 33mW 30mW 65mW 0.349 mK

min 0.042K

−0.5A 2h 0.13V 33mW −30mW 5mW 0.027 mK

min 0.003K

+1A 1h 0.16V 80mW 61mW 143mW 0.768 mK

min 0.046K

−1A 1h 0.16V 80mW −61mW 21mW 0.113 mK

min 0.007K

+2A 30min 0.21V 210mW 121mW 333mW 1.788 mK

min 0.054K

−2A 30min 0.21V 210mW −121mW 91 mW 0.489 mK

min 0.015K

+3A 20min 0.26V 390mW 182mW 574mW 3.083 mK

min 0.062K

−3A 20min 0.26V 390mW −182mW 210 mW 1.128 mK

min 0.023K

The reversible heat Qrev is the part of the reaction enthalpy which cannot be used

but is converted into heat. It is determined by

Qrev =∆H−∆G(5.21)

subtracting the free reaction enthalpy ∆Gfrom the reaction enthalpy ∆H. The

free reaction enthalpy ∆Gand the reaction enthalpy ∆Hof the LAB can be deter-

mined by subtraction the values of the molecules before and after the discharg-

ing reaction:

∆H=2·H0,PbSO4+2·H0,H2O−H0,PbO2−H0,Pb −2·H0,HSO−

4−2·H0,H+(5.22)

∆H=−2·920 kJ

mol −2·285.8 kJ

mol +277.4 kJ

mol +0kJ

mol +2·887.3 kJ

mol +2·0kJ

mol

∆H=−359.6 kJ

mol

163

5 EIS - Fundamentals and Measurement

∆G=2·G0,PbSO4+2·G0,H2O−G0,PbO2−G0,Pb −2·G0,HSO−

4−2·G0,H+(5.23)

∆G=−2·813 kJ

mol −2·237.2 kJ

mol +217.3 kJ

mol +0kJ

mol +2·755.9 kJ

mol +2·0kJ

mol

∆G=371.3 kJ

mol

For LABs the reversible heat is thereby

Qrev =−359.6 kJ

mol +371.3 kJ

mol =11.7 kJ

mol

for complete discharge. The positive sign indicates that the battery changes ther-

mal energy into chemical energy and thereby cools down. The reversible heat is

−11.7kJmol−1for a charging current. The heat flow ˙

Qwithin the cell during

one EIS measurement consists of the Joule heat flow and the reversible heat flow

Qrev.

Q=˙

QDC,Joule +˙

QAC,Joule +˙

Qrev (5.24)

Q=|IDC|· ∆VDC

2+IAC,peak ·VAC,peak

2+z·Qrev

n·F·|IDC|(5.25)

The Joule heat flow consists of two parts: the DC part ˙

QDC,Joule and the super-

imposed AC part ˙

QAC,Joule. Since the superimposed DC IDC is changed between

its negative to its positive value, it will result in a higher voltage change than

when starting at 0A. Therefore, the superimposed DC will be multiplied by half

of the resulting voltage change during one EIS measurement ∆V. The second

part of the Joule heat flow, resulting from the AC signal, can be calculated using

the root mean square (RMS) value. The peak current (IAC,max = 0.5A) and the

peak voltage (VAC,ideal = 6mV) are multiplied and each divided by root of two

to result in the joule power loss caused by the AC signal.

QAC,Joule =IAC,max

√2·VAC,ideal

√2=1.5mW (5.26)

The values for ˙

QAC,Joule will stay the same for all EIS measurements, indepen-

dent of the superimposed DC. The reversible heat flow caused by the super-

imposed DC composites of the number of cell z = 1, the reversible heat, the

number of electrodes participating in the reaction n = 2, the Faraday’s constant

F = 96485Asmol−1, and superimposed DC. The reversible heat flow caused by

the AC can be neglected because the positive and the negative generated heat

164

5.8 Limits of EIS

during each half period of the sinusoidal function will cancel each other out.

The heat flow ˙

Qand the partial results ˙

QDC,Joule,˙

QAC,Joule, and ˙

Qrev are given in

Table 5.5 for different superimposed DCs.

The electrolyte of a LAB participates in the reaction, changing from H2O to

H2SO4, the molar heat capacity Cmol(SoC)of the electrolyte and thereby the cell

or battery is highly dependent on the SoC and which molecules are present to

which amount at that distinct SoC. At 100% SoC, the heat capacity Cmol(100%)

mainly consists of the heat capacity of the AMs and the electrolyte.

Cmol (100%) = 640.38 J

molK

If the chemical reaction would be completely finished while discharging and

all components left at 0% SoC would be PbSO4and H2O. The heat capacity at

0% SoC Cmol (0%)would be

Cmol (0%) = 357.52 J

molK.

However, LABs are limited by the amount of electrolyte, while an acid overage

is present in test cells with reduced plate count. In both cases, not all com-

ponents are completely used up at 0% SoC. Thereby, a heat capacity low as

357.52Jmol−1K−1will never be reached within a cell but it will be used for fur-

ther calculations as an extreme case evaluation.

The molar mass Mtotal is independent of the SoC. And can thereby be calculated

from the reaction equation of the full battery

Mtotal =MPb +MPbO2+2·MH2SO4, (5.27)

or from the reaction equation of the discharged battery

Mtotal =2·MPbSO4+2·MH2O. (5.28)

Splitting the molecules into single elements

Mtotal =2·MPb +6·MO+2·MH+MS(5.29)

165

5 EIS - Fundamentals and Measurement

and inserting the molar masses of all elements results in a molar mass of the lead

battery of

Mtotal =2·207.2 g

mol +6·16 g

mol +2·1g

mol +32.1 g

mol =642.56 g

mol.

The specific heat capacity c(SoC)is determined by

c(SoC) = Cmol(SoC)

Mtotal . (5.30)

c(100%) = 0.997 J

gK and c(0%) = 0.556 J

The weight of one cell is determined by the nominal capacity Cn, the number of

cells z, and the specific capacity qspec

m=Cn·z

qspec . (5.31)

The specific capacity qspec can be calculated with

qspec =n·F

Mtotal (5.32)

qspec =2·96485 As

mol

642.56 g

mol

=83.42Ah

kg .

Inserting all values in the formula, the weight of one cell can be determined

m=20Ah ·1

83.42 Ah

=239.7g

and thereby, the heat capacity CT(SoC), dependent on the SoC,

CT(SoC) = c(SoC)·m(5.33)

CT(100%) = 239.0 J

Kand CT(0%) = 133.4 J

behaving linearly between these marginal values. To determine the temperature

change rate ˙

Twithin the cell during one EIS measurement, the resulting heat

166

5.8 Limits of EIS

flow ˙

Qneeds to be normalized to the heat capacity CTof the cell.

T=1

CT(SoC)·˙

Q(5.34)

Using the lowest heat capacity would result in the worst possible temperature

increase during the EIS measurement. Since only EIS measurements down to

50% SoC have been measured, the resulting temperature change will be given in

Table 5.5, estimated using CT(50%)= 186.2JK−1.

The EIS measurements are limited by the maximum allowed SoC change of

5% SoC. Thereby, an EIS with superimposed ±0.5 A will take 2h and the EIS

with superimposed ±3A will take 20min. The maximum increase in tempera-

ture can be calculated by

∆T=Zt

Tdt. (5.35)

Following the calculation, the maximum possible temperature increase during

one EIS measurement is 0.11K. This temperature change is insignificant. Espe-

cially since the heat is generated throughout 2h, giving plenty of time to emit the

heat to its surrounding environment. All temperature changes for the different

superimposed DCs are given in Table 5.5. The errors resulting from the temper-

ature changes depending on the superimposed DC and the measurement time

of the spectra are shown in Figures 5.28 and 5.29. However, they do not inte-

grate the errors resulting from several EIS measurements. The previous calcula-

tion only determined the heat production of the cell but not the heat conduction

into the surrounding environment, which would cool down the cell again. Since

the heat production is small, even with the maximum evaluation used, and the

resulting error can be neglected, the heat conduction will not be investigated.

Furthermore, the error will not integrate over several different SoCs investi-

gated during one EIS procedure. Since there is a pause of 4h at the beginning

of each new SoC investigation, which is long enough for the heat conduction,

and thereby, cooling down of the test cell, each SoC can be evaluated separately

regarding the heat production.

167

5 EIS - Fundamentals and Measurement

(a)

10-3 10-2 10-1 100101102103

-0.05

0.05

0.10

(b)

10-3 10-2 10-1 100101102103

-0.05

0.05

0.10

(c)

10-3 10-2 10-1 100101102103

-0.05

0.05

0.10

Figure 5.28: The normalized error of the temperature change during one EIS

spectra on the negative half-cell EIS measurement of the middle size

EFB+CXcell at 25◦C with a superimposed DC of (a) -0.5·I20, (b) -

1·I20, and (c) -3·I20.

168

5.8 Limits of EIS

(a)

10-3 10-2 10-1 100101102103

0.2

0.4

0.6

0.8

(b)

10-3 10-2 10-1 100101102103

0.2

0.4

0.6

0.8

(c)

10-3 10-2 10-1 100101102103

-0.05

0.05

0.10

Figure 5.29: The normalized error of the temperature change during one EIS

spectra on the negative half-cell EIS measurement of the middle

size EFB+CXcell at 25◦C with a superimposed DC of (a) +0.5·I20,

(b) +1·I20, and (c) +3·I20.

169

5 EIS - Fundamentals and Measurement

Voltage Non-linearity

When a charging or discharging current is superimposed, the resistive voltage

drop at the beginning of a new superimposed DC is very high. This is already

visualized in Figure 5.3 for a superimposed DC of ±0.5A. In order to have a rel-

atively stable voltage during an EIS measurement, the beginning of the spectrum

is delayed till after the first ohmic drop. The EIS measurement will thereby only

start after 1% SoC change, as already suggested by Budde-Meiwes [157]. Fur-

thermore, the charging steps are stopped when reaching 2.4V to avoid voltage

overshoots that appear for high superimposed DC and/or high SoC. If this volt-

age limit is reached during one charging step, the cell will only be discharged by

the amount of Ah of the prior charge step. By respecting these voltage limits, no

additional measurement errors will be provoked.

5.8.4 Errors caused by the current used for preconditioning and

superposition

Preconditioning

Figure 5.30: Ideal (green) and error prone (pink) SoC changes during the EIS

measurement procedure, caused by the quantization error of the

preconditioning current.

The current used for preconditioning (SoC adjustment) and superposition in-

troduces an error caused by its quantization. The accumulated error affects the

investigated SoC. Furthermore, the error margin can increase during the test,

and later spectra would be affected more. A visualization of the accumulated

error during SoC adjustment via discharging current is shown in Figure 5.30.

170

5.8 Limits of EIS

To estimate the accumulated error, first, only the error within the current used

for preconditioning the cell and thereby adjusting the SoC will be determined.

The analog signal of this test device has a tolerance of ±0.1 % of the current mea-

surement. The A/D converter has a quantisation error of 1.5mA. The quan-

tization error is dominating the tolerance for small currents such as 1·I20 for

adjusting the SoC. Thereby, only the influence of the LSB is investigated. The

resulting error prone current can maximal variate by LSB/2 from the targeted

current. It results in a maximum current of 1.0015A and a minimum current of

0.9985A throughout the preconditioning phase. The maximum, error prone SoC

SoCmax(SoCtarget)can be calulated with

SoCmax(SoCtarget) = SoCstart −(Itarget +LSB

2)·tadjust

Cn·100(5.36)

where SoCstart indicates the starting SoC, which is 100% when starting with a

fully charged test cell and adjusting the SoC via discharge. Itarget is the errorless

current chosen for SoC adjustment, which is 1·I20. For a 3P2N cell (with a nom-

inal capacity Cn= 20Ah), Itarget is 1A. The time to adjust the targeted SoC with

the chosen current is indicated by tadjust. For a 10% SoC change, 2h are needed.

SoCmax(90%) = 100% −(1A+1.5 mA

2)·2h

20 Ah ·100%=90.0075%

To determine the minimum error prone SoC possible the LSB factor has to be

subtracted.

SoCmin(SoCtarget) = SoCstart −(Itarget −LSB

2)·tadjust

Cn·100(5.37)

Resulting in

SoCmin(90%) = 100% −(1A−1.5 mA

2)·2h

20 Ah ·100%=89.9925%.

∆SoC gives the resulting SoC range.

∆SoC =SoCmax(SoCtarget)−SoCmin(SoCtarget)(5.38)

For each following 5% SoC step, the adjustment takes 1h, resulting in the error

accumulation of ∆SoC = 0.0038% per step. The resulting error range is summa-

171

5 EIS - Fundamentals and Measurement

rized in Table 5.6 and shown in Figure 5.31.

Table 5.6: SoC error caused by preconditioning current on a middle size cell.

Targed SoC ∆SoC SoCmin SoCmax

90% 0.015% 89.99% 90.01%

85% 0.023% 84.99% 85.01%

80% 0.030% 79.99% 80.02%

75% 0.037% 74.98% 75.02%

70% 0.045% 69.98% 70.02%

65% 0.053% 64.97% 65.03%

60% 0.060% 59.97% 60.03%

55% 0.067% 54.97% 55.03%

50% 0.075% 49.96% 50.04%

10-3 10-2 10-1 100101102103

-0.10

-0.05

0.05

0.10

Figure 5.31: The normalized quantization error of the preconditioning current

on the negative half-cell spectra of the middle size EFB+CXcell at

25◦C without superimposed DC.

172

5.8 Limits of EIS

Superimposed Current

However, the superimposed DC used during the impedance measurement also

induces a quantization error, as visualized in Figure 5.32. The error of each mi-

cro cycle must be accumulated over the EIS procedure for each validated SoC.

Thereby, a maximum SoC error of ±1.43% is reached after the EIS measurements

at 50% SoC. The accumulated errors for each SoC before and after all EIS mea-

surements at given SoC are summarized in Table 5.7 and shown in Figure 5.33.

Table 5.7: SoC error caused by preconditioning and superimposed DC during

all EIS measurements at each SoC on a middle size cell.

Targed

SoC Superimposed DCs Ideal EIS

meas. time

∆SoC

start of EIS

∆SoC

end of EIS

90% 0A and ±0.5A 13h 0.02% 0.11%

85% 0A and ±0.5A 13h 0.12% 0.22%

80% 0A, ±0.5A, ±1A 19h 0.23% 0.37%

75% 0A, ±0.5A, ±1A 19h 0.38% 0.52%

70% 0A, ±0.5 A, ±1A, ±2A 22h 0.53% 0.69 %

65% 0A, ±0.5 A, ±1A, ±2A 22h 0.70% 0.86 %

60% 0A, ±0.5A, ±1A, ±2A, ±3A 24h 0.87% 1.05%

55% 0A, ±0.5A, ±1A, ±2A, ±3A 24h 1.06% 1.24%

50% 0A, ±0.5A, ±1A, ±2A, ±3A 24h 1.25% 1.43%

Table 5.7 shows the measurement time, including all impedance spectra with su-

perimposed DCs for each SoC. The spectra without any superimposed DC are

named for completion but do not have any influence on the following error pre-

diction. At 90% SoC, the time includes 1h discharge (to 87.5% SoC) with 0.5A

to the minimum SoC followed by six micro cycles around the target SoC, 2h

each, with ±0.5A superimposed DC, 13h in total. The 1h discharge with 0.5A

are part of the micro cycling approach at each target SoC. Lower SoC contain

additional superimposed DCs, given in Table 5.9, resulting in longer EIS mea-

surement times. Therefore, the measurement time increases for lower SoC.

The quantization error of the voltage will not introduce any further errors since

the voltage is only used for measurement limits, as described before.

173

5 EIS - Fundamentals and Measurement

Figure 5.32: Ideal (green) and the error prone SoC change caused by the quanti-

zation error of the preconditioning (pink) and superimposed current

(blue) during the EIS procedure.

Figure 5.33 shows the influence of the quantization error of the preconditioning

and superimposed DC on a middle size cell. Mainly, low SoC and low frequen-

cies show a deviation.

174

5.8 Limits of EIS

(a)

0 2 4 6 8 10 12 14

-4

-2

90% SoC

85% SoC

80% SoC

75% SoC

70% SoC

65% SoC

60% SoC

55% SoC

50% SoC

(b) (c)

123

-2

-1

8 9 10

-2

-1

(d)

10-3 10-2 10-1 100101102103

-2

-1

Figure 5.33: Influence of the quantization error of the preconditioning and the

superimposed DC (thick line = measurement, thin line = maximum

possible deviations) on the middle size EFB+CXcell at 25 ◦C with-

out superimposed DC (a) the negative half-cell spectra, zoom into

(b) high-frequency part, (c) low-frequency part, and (d) the normal-

ized error.

175

5 EIS - Fundamentals and Measurement

Timing Errors during Superposition

Whenever signals are sampled, small timing errors occur. This phenomenon was

already discussed in Section 5.8.1 within the context of errors caused by the EIS

measurement device. Within this section, the influence of the timing errors of

the superimposed DC and, thereby, on the SoC during the whole measurement

procedure is validated. The ideal measurement time for one EIS measurement

depends on the superimposed DC, given in Table 5.8. The ideal measurement

time results in a maximum SoC change of 5% SoC during each measurement.

This way, the SoC varies by ±2.5% around the target SoC. However, the time er-

ror, limiting each superimposed DC, also influences the SoC change during each

measurement. The time error and the resulting influences on the SoC change are

summarized in Table 5.8.

Table 5.8: SoC error caused by the preconditioning and the superimposed DC

during the EIS measurements on a middle size cell.

Superimposed

Ideal EIS

meas. time

SoC change

during EIS

Max. time

deviation ∆SoC

0A 0Ah 4h irrelevant irrelevant

±0.5A 1Ah = 5% 2h ±0.0078h ±0.0039Ah = ±0.020%

±1A 1Ah = 5% 1h ±0.0022h ±0.0022 Ah = ±0.011 %

±2A 1Ah = 5% 30min ±0.0003h ±0.0006Ah = ±0.003%

±3A 1Ah = 5% 20min ±0.0003h ±0.0009Ah = ±0.005%

A small time error is also introduced during each EIS measurement, this error

will be neglectable. In Table 5.9, the measurement time, including all impedance

spectra with superimposed DCs for each SoC, is given. The actual measurement

time for each target SoC exceeds the ideal measurement time. The maximum

measurement times at each SoC are also given in Table 5.9. These extended mea-

surement times will also increase the maximum error caused by the superim-

posed DC, which will integrate overall measurements and SoCs. The maximum

error of 0.0034% is thereby at 50% SoC.

176

5.8 Limits of EIS

Table 5.9: SoC error over time caused by preconditioning and the superimposed

DC during all EIS measurements at each SoC on a middle size cell.

Targed

SoC

Superimposed

Ideal EIS

meas. time

Real EIS

meas. time

Time error

end of EIS

90% 0A and ±0.5A 13h 13.03h 0.0001%

85% 0A and ±0.5A 13h 13.03h 0.0002%

80% 0A, ±0.5A, ±1A 19h 19.05h 0.004%

75% 0A, ±0.5A, ±1A 19h 19.05h 0.006%

70% 0A, ±0.5 A, ±1A, ±2A 22h 22.07h 0.009 %

65% 0A, ±0.5 A, ±1A, ±2A 22h 22.07h 0.0011 %

60% 0A, ±0.5A, ±1A, ±2A, ±3A 24h 24.08h 0.0014%

55% 0A, ±0.5A, ±1A, ±2A, ±3A 24h 24.08h 0.0017%

50% 0A, ±0.5A, ±1A, ±2A, ±3A 24h 24.08h 0.0020%

177

EIS as Analytical Tool

Chapter 6

Screening active materials with different additive combinations to enhance the

dynamic charge acceptance (DCA) is a time-consuming task. The DCA Euro-

pean standard (EN) test [61], described in Section 4.1.2, can be used for attempt-

ing a DCA forecast in real applications with reasonable but not perfect corre-

lation [222]. However, The DCA EN test consists of several weeks of testing.

This is a challenging task for material screenings, especially if the aim is a high

additive-throughput. The processes limiting the DCA have yet not been fully

understood. Furthermore, the mechanisms additives use to increase the DCA

substantially are not understood either. However, it might be possible to visual-

ize the effects via electrochemical impedance spectroscopy (EIS). Using EIS with

a wide frequency range can show the electrochemical processes within a battery

or cell. Thus, EIS has been identified as one of the most promising tools for pre-

dicting battery behavior and will be the scope of this section.

Therefore, the research goal to identify the correlation between the parameters

obtained from the EIS and the DCA test results was investigated [25, 26]. A

first feasibility study [25], described in Section 6.1, was conducted on test cells

extracted from industrially manufactured automotive batteries. The DCA was

tested using the European standard [61] with these test cells and correlated with

the EIS results after prior discharge at 80% SoC with different superimposed

currents. A correlation between the DCA and the first/high-frequency semicir-

cle could be identified for all cell types and layouts [25]. The resistance of the

first semicircle (R1) is smaller for cells with higher DCA [25].

Since the results of the first feasibility study were reasonably good, a more de-

tailed EIS procedure containing various superimposed direct currents (DC), var-

ious states of charge (SoC) adjusted via a charge, or discharge current was inves-

179

6 EIS as Analytical Tool

tigated as part of the research goal of this thesis [26]. Therefore, 2V, 20Ah test

cells, containing three positive and two negative plates (3P2N), built from the

Bottom-Up approach were used as a tradeoff between good battery correlation

and the total number of plates which need to be constructed. Eight different neg-

ative electrode additives were investigated; five included specially synthesized

amorphous carbons, two with unknown additive mixes, and one with a com-

mercially available carbon black. The correlation between the modified DCA

test (DCA after prior charge and discharge both at 80% SoC), described in Sec-

tion 4.2.2, and the EIS parameters obtained at the same state of function (SoF)

are summarized in Section 6.2. Three out of the eight negative electrode ad-

ditives were further tested regarding their SoC influence after prior charge and

discharge on the DCA and EIS. The results of the modified single pulse DCA test,

described in Section 4.2.1, were compared with the EIS parameters obtained at

the same SoF. The used EIS procedure is described in Section 5.3. The correla-

tions are shown in Section 6.3.

The fitting procedure was the same in both Sections 6.2 and 6.3. Firstly, the fit-

ting of all parameters was executed, resulting in minimal fitting errors. On the

down side, many free variables, all having an impact on each other, need to be

evaluated, which hinders identifying a correlation between the EIS parameters

and the DCA. Therefore, a second approach was evaluated where parameters

identified as independent of the additives or the current SoF (SoC and prior us-

age) were kept constant thought out all fits. Moreover, the compression factors

of the CPEs were also kept constant. Consequently, only a few parameters were

left for fitting, increasing the error between the measurement and the fit but en-

abling the identification of a correlation between the remaining EIS parameters

and the DCA.

A good correlation between the DCA and the parameters of the EIS measure-

ments could be found for the eight different negative electrode additives [26].

Furthermore, the correlation was found for various SoCs after discharge [26].

Since the DCA after prior charge only changes marginal [26], a correlation at this

SoF was not feasible. For all SoF investigated, the best parameters for predicting

the DCA were found within the negative half-cell spectra measured during a

superimposed charging current [26]. Therefore the research goal to analyse and

predict the DCA using EIS was accomplished.

180

6.1 Feasibility Study: EIS as Analytical Tool for Predicting DCA

6.1 Feasibility Study: EIS as Analytical Tool for

Predicting DCA

A first feasibility study investigating if EIS can be used as an analytical tool to

predict the DCA of batteries and test cells [25] will be summarized within this

Section.

For this study, three different cell types and three different cell layouts (a total of

9 cells) from the Top-Down approach have been tested. The test cells are listed

in Table 3.5. Within the Top-Down approach, commercial enhanced flooded bat-

teries (EFBs) 12V, 70Ah batteries were separated into test cells with different

layouts (complete, middle, and small size cells). To match the acid to mass ratio

of the original battery, excess acid was minimized by using spacers, and the acid

density was adjusted to 80% SoC. Further details about the test cell preparation

using the Top-Down approach can be found in Section 3.1. A test matrix in Ta-

ble 4.1 summarizes the test procedure for the test cells used in this section. The

same test cells executed the DCA EN test and the EIS measurements.

The DCA was tested according to the standard described in Section 4.1.2. During

the recuperation phase, a voltage restriction of 2.5V was used. Hence, the charg-

ing current could not increase infinitely, as it was limited by the supply of lead

ions. The average charging currents were used as good indicators for charge-

ability. The average of the charging currents during the DCA EN test are shown

in Figure 6.1 for the different cell layouts. Independent of the cell layout, the

normalized charge currents increase in the following order: EFB+CA< EFB+CB

< EFB+CC. Reasons for enhanced DCA depending on the additives used at the

negative electrode have yet to be fully understand. A possible explanation is that

additives increase the porosity of the negative electrode. This would increase the

electrochemically active surface and decrease the maximum lead sulfate crystal

size. Thus, increasing its dissolution and decreasing the distance for the lead

ion transport. Consequently, this would increase the charge current. Moreover,

these effects should be visible within EIS as well.

Even though the test results are normalized to their capacity (as described in

Section 3.4.2), the DCA is quantitatively higher for lower plate count. This was

181

6 EIS as Analytical Tool

explained by the influence of unavoidable acid surplus within the small and

middle size test cells [7]. The amount of electrolyte per Ah has been found to

be the most relevant influencing factor for the DCA [7]. It affects the electrolyte

concentration during test at different SoC and decreases the acid stratification.

Consequently, the normalized DCA increases with lower plate count [118, 223,

224].

(a) (b) (c)

0.2

0.4

0.6

0.8

Normalized Charge Current / A Ah-1

EFB+CA complete cell

EFB+CB complete cell

EFB+CC complete cell

0.2

0.4

0.6

0.8

Normalized Charge Current / A Ah-1

EFB+CA middle cell size

EFB+CB middle cell size

EFB+CC middle cell size

0.2

0.4

0.6

0.8

Normalized Charge Current / A Ah-1

EFB+CA small cell size

EFB+CB small cell size

EFB+CC small cell size

Figure 6.1: DCA EN test results (a) complete cell, (b) middle size cell, and

For this first feasibility study, the complete EIS procedure, investigating various

SoC, different prior usages, and several superimposed DCs, described in Sec-

tion 5.3 was not executed. Only a shortened version was used, schematically

visualized in Figure 6.2. The test cells are investigated at 80% SoC via EIS since

the processes affecting the DCA are expected to be most visible in EIS measure-

ments at the same SoC as the DCA test is conducted. Therefore, the fully charged

and rested test cells were discharged to 80% SoC, and EIS was executed using

the micro cycling approach [156]. Three small, 4% SoC cycles using a DC cur-

rent of ±0.5I20 around 80% SoC were conducted. Meanwhile, one spectrum was

recorded during each discharging and charging period. Only the spectrum with

superimposed charging current measured during the third period was used to

investigate the charging processes.

182

6.1 Feasibility Study: EIS as Analytical Tool for Predicting DCA

Figure 6.2: EIS procedure used for the feasibility study.

A reference electrode was used to measure the half-cell potentials as well. The

negative half-cell spectra at 80% SoC are visualized in Figure 6.3.

(a) (b) (c)

0123

-2

-1

0 1 2 3

-2

-1

0 1 2 3

-2

-1

EFB+CA complete cell

EFB+CB complete cell

EFB+CC complete cell

EFB+CA middle cell size

EFB+CB middle cell size

EFB+CC middle cell size

EFB+CA small cell size

EFB+CB small cell size

EFB+CC small cell size

Figure 6.3: EIS measurements at 80% SoC (a) complete, (b) middle, and (c) small

size test cells (adjusted from Ref. [25]).

For all cell layouts, the negative half-cell spectra at 80% SoC consist of several

semicircles, where each semicircle relates to one process of the electrochemical

reaction. For the three types shown, the EFB+CAcells exhibit the biggest first

semicircle, followed by the EFB+CBand the smallest first semicircle for EFB+CC.

Comparing those results with the DCA charging currents (shown in Figure 6.1),

183

6 EIS as Analytical Tool

the conclusion can be drawn that the higher the DCA, the smaller the first semi-

circle of the EIS.

The first semicircle, zoomed in in Figure 6.4, can be related to the charge transfer

reaction alongside the double layer capacitance Cdl, which is associated with the

porosity of the electrodes and, therefore, with the electrochemical reaction at the

electrode-electrolyte interface [151]. Consequently, the charge transfer process

might be situated in the same semicircle where the impact of additives at the

DCA is noticeable.

Moreover, the DCA EN contains very short charging pulses of 10s, where the

most significant part of the accepted current is taken within the first second.

This would correspond with frequencies higher than 0.1Hz. The first semicircles

within the shown spectra are at frequencies between 1Hz and 365Hz. Therefore,

the processes influencing the DCA are most likely visual within the first semicir-

cle of the EIS.

(a) (b) (c)

0 0.1 0.2 0.3 0.4 0.5 0.6

-0.4

-0.3

-0.2

-0.1

0.1

0.2

0 0.1 0.2 0.3 0.4 0.5 0.6

-0.4

-0.3

-0.2

-0.1

0.1

0.2

0 0.1 0.2 0.3 0.4 0.5 0.6

-0.4

-0.3

-0.2

-0.1

0.1

0.2

EFB+CA complete cell

EFB+CB complete cell

EFB+CC complete cell

EFB+CA middle cell size

EFB+CB middle cell size

EFB+CC middle cell size

EFB+CA small cell size

EFB+CB small cell size

EFB+CC small cell size

Figure 6.4: Zoom into Figure 6.3 (a) complete, (b) middle, and (c) small size test

cells (adjusted from Ref. [25]).

For comparability, all spectra are shifted along the real axis by the internal resis-

tance (R0), the smallest real part of the impedance (Z). To enable the comparison

between the spectra of different battery types the number of active half plates

must be used to scale the negative half-cell spectra. In the reduced cell layouts,

the positive plates are on the outside. Therefore, all negative half plates are ac-

184

6.1 Feasibility Study: EIS as Analytical Tool for Predicting DCA

tive. A middle size cell contains four active negative half plates, and a small

size cell contains two active negative half plates. The original cell layout of the

EFB+CAand EFB+CBcontains 8P8N, which makes a total of 16 negative half

plates but only 15 active negative half plates. The EFB+CCcomplete cell con-

tains 8P9N resulting in 16 active negative half plates out of 18. The middle size

cell must be scaled with 4/16 or 4/18, respectively. The resulting factors are

given in Table 6.1. If the complete spectra were evaluated instead of the nega-

tive half-cell spectra and only one cell layout was under observation, this scaling

would be unnecessary.

Table 6.1: Scaling factors according to the number of active plates within a cell

(adjusted from Ref. [25]).

Battery type EFB+CAand EFB+CBEFB+CC

Original plate count 8P8N 8P9N

Complete cell 15/16 16/18

Middle size cell 4/16 4/18

Small size cell 2/16 2/18

Before fitting, the EIS data were evaluated using Kramers-Kronig (K-K) trans-

formation to avoid systematic errors e.g., due to violations of the stationarity

or causality, further detailed in Section 5.4.1. Only data points that pass the K-

K transformation condition are further evaluated. To determine the equivalent

circuit model (ECM), the distribution of relaxation times (DRTs), described in

Section 5.4.2, was determined to analyze the number of processes and their char-

acteristic frequencies. In Figure 6.5, the DRT of the EIS at 80% SoC are shown.

The generated DRT is similar for all three types of cells. The main difference

is based on the layout. The number of peaks gives evidence of the number of

processes involved. Therefore, for every peak, one resistance-capacitive (R-C)

element or Zarc element should be used [11, 225]. Moreover, a peak’s location

correlates with the characteristic time constant of that process. The complete

cells contain four peaks within the DRT, meaning four processes are involved.

The peaks are found at the time constants τ0≈0.003s, τ1≈0.07s, τ2≈1s, and

τ3≈10s. For the middle and small size cells, the peak at the small time constant

is not as distinct anymore and, therefore, not determined. However, peaks τ1,τ2,

and τ3with similar values were also found for the middle and small size cells.

185

6 EIS as Analytical Tool

(a) (b) (c)

10-3 10-2 10-1 100101102

0.02

0.04

0.06

0.08

0.10

0.12

10-3 10-2 10-1 100101102

0.02

0.04

0.06

0.08

0.10

0.12

10-3 10-2 10-1 100101102

0.02

0.04

0.06

0.08

0.10

0.12

EFB+CA complete cell

EFB+CB complete cell

EFB+CC complete cell

EFB+CA middle cell size

EFB+CB middle cell size

EFB+CC middle cell size

EFB+CA small cell size

EFB+CB small cell size

EFB+CC small cell size

Figure 6.5: DRT of Figure 6.3 (a) complete, (b) middle, and (c) small size test cells

(adjusted from Ref. [25]).

The exact time constants identified by the DRT for all cell types and layouts are

given in Table 6.2. The DRT results were used to choose the ECM model. Since

τ0was only distinct for complete cells, only τ1,τ2, and τ3are considered for

the ECM. The ECM consists of a resistance R0, an inductive part, and three Zarc

elements, shown in Figure 6.6. The Zarc elements contain a compression factor,

which fits the spectra better than R-C elements. The time constants determined

with the DRT were directly used as set parameters for the Zarc elements.

Table 6.2: Time constants determined with DRT, Figure 6.5 (adjusted from [25]).

τ0τ1τ2τ3

EFB+CAComplete cell 0.003sξ0.072sξ2.359sξ13.495sξ

Middle size cell - 0.080 sξ2.320sξ11.190sξ

Small size cell - 0.100 sξ1.094sξ5.838sξ

EFB+CBComplete cell 0.002sξ0.060sξ1.094sξ7.415sξ

Middle size cell - 0.054 sξ2.816sξ15.900sξ

Small size cell - 0.044 sξ0.568sξ3.629sξ

EFB+CCComplete cell 0.003sξ0.073sξ2.984sξ19.025sξ

Middle size cell - 0.056 sξ1.436sξ19.025sξ

Small size cell - 0.056 sξ0.451sξ2.283sξ

186

6.1 Feasibility Study: EIS as Analytical Tool for Predicting DCA

Figure 6.6: The chosen ECM (adjusted from Ref. [25]).

The remaining values of the ECM were fitted. The starting parameter used for

fitting for the internal resistance R0equals the removed offset along the real part

of the impedance. However, for some spectra, it is impossible to determine R0

in a frequency range where the phase of the impedance crosses zero. To enable

compensation, the upper limit is extended.

Table 6.3: Starting parameters, lower and upper limits for the ECM fit (adjusted

from Ref. [25]).

EIS parameter lower boundary starting value upper boundary

R0R0R0R0+0.05mΩ

L0Hs(ξ+1)0Hs(ξ+1)0.010Hs(ξ+1)

ξL0 0.40 1.00

R10 mΩ0.30 mΩ1.00 mΩ

τ1τ1τ1τ1

ξ10.85 0.85 0.85

R20 mΩ0.40 mΩ1.00 mΩ

τ2τ2τ2τ2

ξ20.66 0.66 0.66

R30 mΩ0.50 mΩ2.00 mΩ

τ3τ3τ3τ3

ξ30.75 0.75 0.75

The fitting was executed twice. The first time all ξ-parameters could be fitted in

a range between 0 and 1. However, for comparability, the average value for each

ξ1,ξ2, and ξ3was taken. The fit was repeated with set values for the compression

factor for all cell types and layouts. The starting values and the boundaries for

the final fit are given in Table 6.3.

187

6 EIS as Analytical Tool

The fitting results of the first semicircle of the negative half-cell EIS at 80% SoC

are shown in Figure 6.7. The first semicircle is well represented by the fit. The

resulting fitting parameters used are stated in Tables 6.4, 6.5, and 6.6. Since the

time constants are not fitted, they are not listed. It can be noted, that the param-

eters for the inductivity are very different for different cells even with the same

cell layout. This can be caused by a lack of data points within this region. For

later parameterization the inductivity was kept constant for each cell layout.

(a) (b) (c)

0 0.2 0.4 0.6

-0.4

-0.2

0.2

0 0.2 0.4 0.6

-0.4

-0.2

0.2

0 0.2 0.4 0.6

-0.4

-0.2

0.2

EFB+CA complete cell

EFB+CB complete cell

EFB+CC complete cell

EFB+CA middle cell size

EFB+CB middle cell size

EFB+CC middle cell size

EFB+CA small cell size

EFB+CB small cell size

EFB+CC small cell size

Figure 6.7: EIS and fit of Figure 6.3 (feasibility study): (a) complete, (b) middle,

and (c) small size cells (adjusted from Ref. [25]).

Table 6.4: EFB+CAEIS parameters and errors (adjusted from Ref. [25]).

EIS parameter Complete cell Middle size cell Small size cell

EFB+CAR00.44 mΩ0.19 mΩ0.19 mΩ

L420 µHs(ξ+1)108 µHs(ξ+1)11.8 µHs(ξ+1)

ξL0.94 0.98 0.97

R10.40 mΩ0.42 mΩ0.52 mΩ

R20.53 mΩ0.53 mΩ0.30 mΩ

R30.22 mΩ0.62 mΩ1.16 mΩ

error 4.2% 2.9% 6.6%

188

6.1 Feasibility Study: EIS as Analytical Tool for Predicting DCA

Table 6.5: EFB+CBEIS parameters and errors (adjusted from Ref. [25]).

EIS parameter Complete cell Middle size cell Small size cell

EFB+CBR00.37 mΩ0.23 mΩ0.16 mΩ

L249 µHs(ξ+1)46.8 µHs(ξ+1)13.1 µHs(ξ+1)

ξL0.94 0.94 0.95

R10.34 mΩ0.30 mΩ0.20 mΩ

R20.30 mΩ0.60 mΩ0.30 mΩ

R30.41 mΩ1.45 mΩ0.37 mΩ

error 5.1% 4.7% 3.4%

Table 6.6: EFB+CCEIS parameters and errors (adjusted from Ref. [25]).

EIS parameter Complete cell Middle size cell Small size cell

EFB+CCR00.48 mΩ0.31 mΩ0.28 mΩ

L257 µHs(ξ+1)277 µHs(ξ+1)2500 µHs(ξ+1)

ξL0.95 1.00 0.18

R10.31 mΩ0.28 mΩ0.16 mΩ

R20.38 mΩ0.30 mΩ0.30 mΩ

R30.37 mΩ0.10 mΩ0.10 mΩ

error 3.6% 2.3% 5.1%

Figures 6.8, 6.9, and 6.10 show the comparison of the fit parameters with the

DCA. The parameters 1/R1and CPE1have a positive correlation to the normal-

ized DCA for all cell layouts. Even though this is a very positive result for the

feasibility study, a final conclusion cannot be drawn yet. A verification with

more test cells would be needed.

The time constants have very similar values for all cell layouts, and additives.

Therefore, the time constant behaves as expected since neither the cell layout nor

the additives should change the time constant of the chemical process within a

battery or cell. However, for this reason, the time constant cannot be used to find

a correlation between the EIS parameters and the DCA.

189

6 EIS as Analytical Tool

(a) (b) (c)

0 0.2 0.4 0.6 0.8

Figure 6.8: DCA compared to R1(feasibility study): (a) complete, (b) middle,

and (c) small size test cells.

(a) (b) (c)

0 0.2 0.4 0.6 0.8

100

200

300

400

0 0.2 0.4 0.6 0.8

100

200

300

400

0 0.2 0.4 0.6 0.8

100

200

300

400

Figure 6.9: DCA compared to CPE1(feasibility study): (a) complete, (b) middle,

and (c) small size test cells.

(a) (b) (c)

0 0.2 0.4 0.6 0.8

0.05

0.1

0.15

0 0.2 0.4 0.6 0.8

0.05

0.1

0.15

0 0.2 0.4 0.6 0.8

0.05

0.1

0.15

Figure 6.10: DCA compared to τ1(feasibility study): (a) complete, (b) middle,

and (c) small size test cells.

190

6.1 Feasibility Study: EIS as Analytical Tool for Predicting DCA

Next to the linear fit, visualizing the correlation between the parameters and the

DCA results, the determination of the correlation coefficients (R2) can be used

to identify how good the correlation is. The correlation coefficients illustrate the

statistical relationship between two parameter sets and are determined by

R2=1−RSS

TSS (6.1)

where RSS is the sum of squares of residuals and TSS is the total sum of squares.

The correlation coefficient is in the range from −1to +1, where ±1 indicate the

strongest correlation.

The correlation coefficients between the DCA EN test results and the EIS param-

eters are summarized in Table 6.7. The highest correlation between DCA and the

fitting parameters is obtained within the first semicircle. Comparing the inverse

of the resistance R1, and the capacitance CPE1, with the DCA test results, a good

correlation was found for both. The resistance R1, the parameter indicating the

size of the high-frequency semicircle, increases for larger semicircles. For all cell

layouts, the highest R1is found for EFB+CA, followed by the R1of EFB+CBand

the smallest value R1of EFB+CCtest cells. The highest correlation coefficients

are up to 0.999 between the capacitance constant phase element of the first semi-

circle (CPE1) and the DCA could also be found. All values for the CPE1are in

the range of the Cdl, which is associated with the electrochemical reaction at the

electrode-electrolyte interface [151]. Therefore, it is most likely to be influenced

by additives. No clear correlation between DCA and the time constant τ1or the

parameters of the second and third semicircle could be found.

Table 6.7: Correlation coefficient between the DCA EN test results and the EIS

parameters within the first feasibility study.

Parameter Complete cell Middle size cell Small size cell

1/R10.893 0.826 0.975

τ10.430 -0.637 -0.500

CPE10.975 0.663 0.999

Concluding, EIS measurements could be usable to predict a high or low DCA

for test cells. However, the evaluation of only three battery types is insufficient.

Therefore, further investigations regarding the predictability of the DCA for test

191

6 EIS as Analytical Tool

cells with different additives are needed, which are summarized in Section 6.2.

Moreover, various SoCs and prior usages (prior charge or prior discharge) were

investigated and compared to DCA under multiple conditions, Section 6.3.

6.2 Correlation between EIS and DCA for Cell with

Various Additives

This section compares the DCA EN test results with the fitting parameters ob-

tained from EIS measurements at 80% SoC adjusted via charge and discharge,

investigating various superimposed DCs [26]. Therefore, 2V, 20Ah 3P2N test

cells built from the Bottom-Up approach, described in Section 3.2, were used. In

total, eight different additives were investigated; five including specially synthe-

sized amorphous carbon (EFB+C1−5), two unknown additive mixes (EFB+CX,

and EFB+CY), and one commercially available carbon black served as a reference

(EFB+Ref). All test cells used within this and Section 6.3 are listed in Table 3.6.

The middle size test cells were used as a tradeoff between good battery corre-

lation and the number of plates necessary to build a test cell, as there is only a

limited amount of active mass preparation within one batch.

The complete DCA EN test (described in Section 4.1.2), followed by the mod-

ified DCA EN test (described in Section 4.2.2), were executed, as listed in the

test plan given in Table 4.5. In Figure 6.11, the DCA after prior charge (Ic) at

80% SoC, DCA after prior discharge (Id) at 90% SoC, and at 80% SoC is shown

for 20Ah 3P2N test cells with various additives (EFB+C1−5, EFB+Ref, EFB+CX,

and EFB+CY).

The original DCA EN results, shown in Figure 6.11 (a) and (b), are thereby com-

pared with the modified DCA test, shown in Figure 6.11 (c). Therefore, the DCA

after prior charge and discharge can be compared at 80% SoC. This way, only

one factor, either the SoC influence or the influence of prior usage, is investi-

gated, and better comparisons can be drawn in comparison to changing both

influencing factors simultaneously. Icat 80% SoC and Idat 90% SoC were tested

using three similar test cells for each additive type (except C2, which could only

be tested with one test cell). The average DCA result and the variation are visu-

alized. Idat 80% SoC was only conducted with one test cell each. The results of

192

6.2 Correlation between EIS and DCA for Cell with Various Additives

the test cells in Figure 6.11 were ordered according to their expected DCA result.

Icis small compared to Id. The DCA after prior discharge is higher at 80% SoC

than at 90% SoC. Idat 80% SoC is increasing in the following order: EFB+C2<

EFB+C1< EFB+Ref < EFB+C3< EFB+C4< EFB+CX< EFB+C5< EFB+CY. The

results of the five tailored carbons for Idat 80% SoC are lining up (except CPE1

and EFB+CPE2which DCA test results are reversed) according to their external

surface areas [226]. The higher the external surface area, the higher the DCA.

EFB+C1

EFB+C2

EFB+Ref

EFB+C3

EFB+C4

EFB+CX

EFB+C5

EFB+CY

0.2

0.4

0.6

0.8

1.2

1.4

Normalized Charge Current / A Ah-1

(a)

EFB+C1

EFB+C2

EFB+Ref

EFB+C3

EFB+C4

EFB+CX

EFB+C5

EFB+CY

0.2

0.4

0.6

0.8

1.2

1.4

Normalized Charge Current / A Ah-1

(b)

EFB+C1

EFB+C2

EFB+Ref

EFB+C3

EFB+C4

EFB+CX

EFB+C5

EFB+CY

0.2

0.4

0.6

0.8

1.2

1.4

Normalized Charge Current / A Ah-1

(c)

Figure 6.11: DCA EN test results (a) Icat 80% SoC, (b) Idat 90% SoC, and (c) Id

at 80% SoC of the modified DCA EN test (adjusted from Ref. [26]).

The EIS test procedure, described in Section 5.3, allows to measure EIS at various

SoC and with different superimposed DCs. The EIS test plan, containing details

about pretests before starting the EIS procedure, such as the C20 test, the single

pulse DCA test, and the DCA EN test, is given in Table 5.3. Even thought the

complete EIS procedure measured spectra at various SoC, within this section,

only the spectra at this state of function (SoF) as the DCA results were evalu-

ated. For comparing the EIS spectra with Idand Icat 80% SoC only the spectra

at 80% SoC and without or with ±0.5·I20 superimposed DC were analyzed. For

lower SoC also higher superimposed DCs were measured. However, voltage

overshoots prohibited using higher superimposed DCs when adjusting 80% SoC

via charging current. Therefore, only spectra without or with ±0.5·I20 superim-

193

6 EIS as Analytical Tool

posed DC are shown in this section. A visualization of the EIS procedure used

and details about the EIS at 80% SoC for analyzing the influence of the additives

are given in Figure 6.12.

Figure 6.12: EIS procedure and details at 80% SoC.

The data preprocessing using K-K transformation was described in Section 5.4.1.

In Figure 6.13 complete EIS measurements for a 3P2N EFB+C1test cell at various

SoCs and without and with ±0.5·I20 superimposed DCs are shown. However,

only the part of the spectra which was further validated is highlighted in color.

The part of the spectra, which failed the K-K transformation, is only illustrated

with gray dots.

After the first preprocessing, the EIS data could be fitted. In the following Sec-

tions 6.2.1 and 6.2.2 two different approaches are discussed. The first, in Sec-

tions 6.2.1, shows the fitting results if all parameters were fitted. This way,

good fitting results with only small errors were accomplished. On the down-

side, many free variables, all having an impact on each other, need to be eval-

uated which hinders identifying a correlation between the EIS parameters and

the DCA. Therefore, a second approach, shown in Section 6.2.2, was evaluated.

For this approach, parameters that were identified as independent of the addi-

tives or the current SoF (SoC and prior usage) were kept constant thought out

all fits. Moreover, the compression factors of the CPEs were also kept constant

194

6.2 Correlation between EIS and DCA for Cell with Various Additives

since these parameters interfere with the resistance and the capacitance of each

semicircle, impeding the evaluation. Consequently, only a few parameters were

left for fitting, increasing the error between the measurement and the fit. But this

enabled the identification of a correlation between the remaining EIS parameters

and the DCA.

(a) (b) (c)

0 5 10 15

-10

-5

0 5 10 15

-10

-5

0 5 10 15

-10

-5

Figure 6.13: EIS at 80% SoC adjusted via discharge (a) -0.5·I20, (b) without, and

6.2.1 Fitting for all Parameters

The DRT is shown in Figure 6.14 for all test cells at 80% SoC adjusted via dis-

charge for different superimposed DCs. Based on the evaluation of the DRT for

all test cells, SoC, and prior usage, the number of processes and the range of their

time constants were analyzed. Three areas were identified where peaks evolve

within the DRT. One at very small time constants, which referes to a very small

semicircle within the spectra and is therefore subscripted with "min". The other

two semicircles are refered to as first and second semicircles. One of the time

constants can be found between 0.1s and 1s, and the last between 2s and 100s.

195

6 EIS as Analytical Tool

(a) (b) (c)

Figure 6.14: DRT of Figure 6.13 (a) -0.5·I20, (b) without, and (c) +0.5·I20 superim-

posed DC.

Similar to the feasibility study, summarized in Section 6.1, the resulting ECM

consists of a resistance R0, an inductive part, and three Zarc elements. Each Zarc

element consists of a parallel connection of a resistance Rand a CPE. The CPE

contains a capacitive value and a compression factor. In the first feasibility study,

the time constants determined with the DRT were directly used as set parame-

ters within the ECM. In this section, the time constants found in the DRT were

used as the starting value for fitting, with defined fitting boundaries, given in

Table 6.8. The same goes for the parameter R0, which has the starting value of

the minimum real part of the fit but is also fitted within defined boundaries,

given in Table 6.8. The capacitive values of the CPE are not fitted but result out

of the correlating resistance Rand time constant τ. Next to the values for the

three semicircles, the starting values and boundaries for the high-frequency part

of the spectra are given in Table 6.8.

196

6.2 Correlation between EIS and DCA for Cell with Various Additives

Table 6.8: EIS parameters, their boundaries and starting values if all parameters

are fitted.

EIS parameter lower boundary starting value upper boundary

R00mΩmin(Re{Z}) 10.00mΩ

L0mHs(ξ+1)1.00mHs(ξ+1)5.00mHs(ξ+1)

ξL0.80 1.00 1.00

Rmin 0mΩ0.50mΩ3.00mΩ

Cmin 0.33F s (ξ−1)variable 1000.00Fs (ξ−1)

τmin 0.001sξvariable 0.100sξ

ξmin 0 0.74 1.00

R10.25mΩ4.00mΩ10.00mΩ

CPE18Fs (ξ−1)variable 4000 Fs (ξ−1)

τ10.1sξvariable 1.00sξ

ξ10 0.70 1.00

R20.75mΩ5.00mΩ26.00mΩ

CPE277Fs (ξ−1)variable 40000Fs (ξ−1)

τ22.00sξvariable 100.00sξ

ξ20 0.80 1.00

(a) (b) (c)

0 1 2 3 4 5

-4

-3

-2

-1

0 1 2 3 4 5

-4

-3

-2

-1

0 1 2 3 4 5

-4

-3

-2

-1

Figure 6.15: EIS and fit of Figure 6.13 (all parameters) (a) -0.5·I20, (b) without,

and (c) +0.5·I20 superimposed DC.

197

6 EIS as Analytical Tool

The fitting results if all parameters are free to fitting, are shown in Figure 6.15.

Since all parameters were used for fitting, the results are very accurate. While

the mini semicircle is very similar between the spectra containing different car-

bon additives, the first and second semicircles vary. The ECM and the resulting

parameters could fit all spectra with reasonable accuracy. This was obtained us-

ing the DRT results as starting values for the time constants and carefully chosen

boundaries for the parameters.

For better evaluation of the accuracy, the absolute and relative errors between

EIS measurements and fit were determined. The absolute error Eabs is the abso-

lute value out of the subtraction of each EIS measurement data point with the

corresponding fit data point:

Eabs =∆x=xmeas −xfit(6.2)

If the absolute error is normalized to the corresponding EIS measurement data

point, the relative error Erel can be determined in percentage.

Erel =∆x

xmeas ·100% (6.3)

In Figures 6.16 and 6.17 the relative and the absolute errors for these fits are

shown. The absolute error is highest for edge frequencies since the fit has fewer

data points in these regions. The relative error is highest for high frequencies

because these data points are close to the origin and have low absolute values.

Therefore, even small absolute errors result in high relative errors.

(a) (b) (c)

10-3 10-2 10-1 100101102103104

0.2

0.4

0.6

0.8

10-3 10-2 10-1 100101102103104

0.2

0.4

0.6

0.8

10-3 10-2 10-1 100101102103104

0.2

0.4

0.6

0.8

Figure 6.16: Absolute error of the fits in Figure 6.15 with (a) -0.5·I20, (b) without,

and (c) +0.5·I20 superimposed DC.

198

6.2 Correlation between EIS and DCA for Cell with Various Additives

(a) (b) (c)

10-3 10-2 10-1 100101102103104

Figure 6.17: Relative error of the fits in Figure 6.15 with (a) -0.5·I20, (b) without,

and (c) +0.5·I20 superimposed DC.

The average of the absolute and relative errors of all investigated spectra were

determined. In Table 6.9 the average values of all investigated spectra (not only

the ones shown within this section) are shown. Furthermore, the averaged er-

rors for each spectrum were used to determine the standard, and the maximum

deviations of the errors.

Table 6.9: Error between measurements and fit if all parameters are fitted.

Average

error

Standard

deviation

Maximum

deviation

Relative error

per spectra 1.5% 0.7 % 3.0%

Absolute error

per spectra 0.07mΩ0.03mΩ0.08mΩ

The resulting EIS parameters are correlated to the DCA results at the same SoF,

shown in Figures 6.19 to 6.28. For each parameter set, a linear fit of the parame-

ters indicates the correlation between the EIS parameters and the DCA.

199

6 EIS as Analytical Tool

(a) (b) (c)

0 0.2 0.4 0.6 0.8 1 1.2

0.5

1.5

0 0.2 0.4 0.6 0.8 1 1.2

0.5

1.5

0 0.2 0.4 0.6 0.8 1 1.2

0.5

1.5

Figure 6.18: Modified DCA EN compared to R0(fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC.

(a) (b) (c)

0 0.2 0.4 0.6 0.8 1 1.2

0.5

1.5

2.5

0 0.2 0.4 0.6 0.8 1 1.2

0.5

1.5

2.5

0 0.2 0.4 0.6 0.8 1 1.2

0.5

1.5

2.5

Figure 6.19: Modified DCA EN compared to L(fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC.

(a) (b) (c)

0 0.2 0.4 0.6 0.8 1 1.2

0.7

0.8

0.9

1.1

0 0.2 0.4 0.6 0.8 1 1.2

0.7

0.8

0.9

1.1

0 0.2 0.4 0.6 0.8 1 1.2

0.7

0.8

0.9

1.1

Figure 6.20: Modified DCA EN compared to λ(fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC.

200

6.2 Correlation between EIS and DCA for Cell with Various Additives

(a) (b) (c)

0 0.2 0.4 0.6 0.8 1 1.2

0.5

1.5

0 0.2 0.4 0.6 0.8 1 1.2

0.5

1.5

0 0.2 0.4 0.6 0.8 1 1.2

0.5

1.5

Figure 6.21: Modified DCA EN compared to Rmin (fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC.

(a) (b) (c)

0 0.2 0.4 0.6 0.8 1 1.2

0.02

0.04

0.06

0.08

0.10

0 0.2 0.4 0.6 0.8 1 1.2

0.02

0.04

0.06

0.08

0.10

0 0.2 0.4 0.6 0.8 1 1.2

0.02

0.04

0.06

0.08

0.10

Figure 6.22: Modified DCA EN compared to τmin (fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC.

201

6 EIS as Analytical Tool

(a) (b) (c)

0 0.2 0.4 0.6 0.8 1 1.2

0.5

1.5

0 0.2 0.4 0.6 0.8 1 1.2

0.5

1.5

0 0.2 0.4 0.6 0.8 1 1.2

0.5

1.5

Figure 6.23: Modified DCA EN compared to R1(fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC.

(a) (b) (c)

0 0.2 0.4 0.6 0.8 1 1.2

100

200

300

400

500

0 0.2 0.4 0.6 0.8 1 1.2

100

200

300

400

500

0 0.2 0.4 0.6 0.8 1 1.2

100

200

300

400

500

Figure 6.24: Modified DCA EN compared to CPE1(fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC.

(a) (b) (c)

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0.8

Figure 6.25: Modified DCA EN compared to ξ1(fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC.

202

6.2 Correlation between EIS and DCA for Cell with Various Additives

(a) (b) (c)

0 0.2 0.4 0.6 0.8 1 1.2

0.1

0.2

0.3

0.4

0.5

0 0.2 0.4 0.6 0.8 1 1.2

0.1

0.2

0.3

0.4

0.5

0 0.2 0.4 0.6 0.8 1 1.2

0.1

0.2

0.3

0.4

0.5

Figure 6.26: Modified DCA EN compared to R2(fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC.

(a) (b) (c)

0 0.2 0.4 0.6 0.8 1 1.2

2000

4000

6000

8000

0 0.2 0.4 0.6 0.8 1 1.2

2000

4000

6000

8000

0 0.2 0.4 0.6 0.8 1 1.2

2000

4000

6000

8000

Figure 6.27: Modified DCA EN compared to CPE2(fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC.

(a) (b) (c)

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0.8

Figure 6.28: Modified DCA EN compared to ξ2(fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC.

203

6 EIS as Analytical Tool

Table 6.10: Correlation coefficient between DCA EN partial results and EIS pa-

rameters if all parameters are used for fitting.

Parameter IDC = -0.5·I20 IDC = 0DC IDC = +0.5·I20

at 80% SoC R00.359 0.356 0.42

adjusted via

charge

λ0.568 -0.382 -0.074

Rmin 0.462 -0.210 -0.498

CPEmin 0.360 -0.004 -0.419

τmin 0.234 -0.137 0.230

ξmin 0.469 0.084 -0.424

1/R10.264 -0.112 0.748

CPE10.451 0.102 0.538

ξ10.160 -0.286 -0.239

1/R20.536 0.102 -0.154

CPE20.087 0.503 -0.251

ξ20.339 0.102 -0.445

at 80% SoC after at R00.658 -0.092 0.446

adjusted via

discharge

L-0.164 -0.553 0.007

λ0.066 0.545 -0.658

Rmin -0.211 0.181 0.598

CPEmin -0.013 -0.272 0.710

τmin -0.052 -0.545 0.458

ξmin 0.694 0.405 0.063

1/R10.822 0.270 0.627

CPE10.004 0.217 0.704

ξ1-0.158 -0.473 -0.808

1/R20.542 0.755 0.918

CPE20.180 0.473 0.762

ξ2-0.082 -0.665 0.600

The correlation factors of each parameter set are summarized in Table 6.10. The

correlation coefficient ranges from -1 to +1, where ±1 indicates the strongest pos-

sible correlation. Within this data set, the only correlation between the DCA EN

partial results and the EIS parameters at 80% SoC after prior charge and with su-

perimposed DC could be found within the first semicircle, where 1/R1and CPE1

204

6.2 Correlation between EIS and DCA for Cell with Various Additives

show good correlations. A correlation after prior discharge could be found for

the first and the second semicircle. However, this is not a clear trend throughout

all superimposed DCs. Moreover, even though the compression factor ξdoes

correlate with the other parameters of the same semicircle (Rand CPE), it does

not show a clear correlation. The parameters ξ2at 80% SoC after prior discharge

varies from -0.665 for no superimposed DC, and 0.6 for +0.5·I20 superimposed

DC, for example.

Correlations could hardly be found after prior charging. Not only the DCA after

prior charging is only slightly affected but the EIS spectra are not affected either.

Better correlations could be identified after prior discharging. The parameters

most affected by the additives are the parameters of the three semicircles. How-

ever, all parameters interact with each other, which makes it hard to find clear

correlations. Therefore, a fitting attempt with reduced number of variables was

executed in Section 6.2.2.

6.2.2 Fitting for selected Parameters

Based on the test results of Section 6.2.1 the number of fitting parameters was re-

duced step wise. In the first step, all values regarding the high-frequency part of

the spectra (L,ξL,Rmin,τmin, and ξmin) were averaged. Furthermore, the param-

eter R0no longer had a fitting range but the minimum real part of the impedance

was used. The fitting procedure was repeated with this set values, leaving only

the parameters of the two semicircles free for fitting. For the resulting fits, the

values of the compression factors ξ1and ξ2were averaged for each superim-

posed DC as well. In the following and last fitting step, the values for ξ1and ξ2

were also set values but differ depending on the superimposed DC. Only four

variables were left for fitting: R1,τ1,R2and τ2. The DRT determined the start-

ing values for fitting the time constants for the two CPE. All set values of the

ECM and the boundaries of the fitting parameters are summarized in Table 6.11.

Since many fitting parameters depend on the prior usage, the values are split

into previous discharge or charge.

205

6 EIS as Analytical Tool

Table 6.11: EIS parameters, their boundaries and starting values if only selected

parameters are fitted.

EIS parameter set value lower boundary upper boundary

R0R0

L4.3mHs(ξ+1)

ξL0.65

τmin 0.01sξ

ξmin 0.74

adjusted via discharge:

Rmin 0.5mΩ

R10.25mΩ10.00mΩ

τ10.1sξ1.00sξ

ξ1with 0DC 0.72

ξ1with +0.5·I20 0.77

ξ1with -0.5·I20 0.78

R20.75mΩ26.00mΩ

τ22.00sξ100.00sξ

ξ2with 0DC 0.50

ξ2with +0.5·I20 0.80

ξ2with -0.5·I20 0.80

adjusted via charge:

Rmin 1mΩ

R11mΩ50mΩ

τ10.08sξ2.00sξ

ξ1with 0DC 1.00

ξ1with +0.5·I20 0.78

ξ1with -0.5·I20 0.69

R25mΩ300mΩ

τ21sξ40sξ

ξ2with 0DC 1.00

ξ2with +0.5·I20 0.76

ξ2with -0.5·I20 0.67

206

6.2 Correlation between EIS and DCA for Cell with Various Additives

The resulting fits for 3P2N test cells containing different additives at the negative

electrode are shown in Figure 6.29. The deviation between the EIS measurement

and the fit with only few selected fitting parameters is larger compared to the

fitting result when all parameters are fitted. To name only a few examples: the

fits for EFB+CYspectra with -0.5·I20 superimposed DC show significant errors

at the beginning of the second semicircle, while the fits for EFB+C1, EFB+C2,

and EFB+C3spectra without and with +0.5·I20 superimposed DC lag precision

within the first semicircle.

(a) (b) (c)

012345

-4

-3

-2

-1

012345

-4

-3

-2

-1

012345

-4

-3

-2

-1

Figure 6.29: EIS and fit (only fitting selected parameters) at 80% SoC adjusted

via discharge with (a) -0.5·I20, (b) without, and (c) +0.5·I20 superim-

posed DC (adjusted from Ref. [26]).

The corresponding absolute errors are shown in Figure 6.30, and the relative

errors are shown in Figure 6.31. The absolute errors are up 2mΩhigh, which

is twice as high compared to the fits when all parameters are used for fitting.

Similar to the fits with all parameters used, the absolute errors are still highest

for low frequencies. The relative error increased as well. For the fits using only

selected parameters, the relative errors reach up to 40%, especially in the high-

frequency region, where the averaged values were used for the parameters.

207

6 EIS as Analytical Tool

(a) (b) (c)

10-3 10-2 10-1 100101102103104

Figure 6.30: Absolute error of the fits in Figure 6.29 with (a) -0.5·I20, (b) without,

and (c) +0.5·I20 superimposed DC.

(a) (b) (c)

10-3 10-2 10-1 100101102103104

Figure 6.31: Relative error of the fits in Figure 6.29 with (a) -0.5·I20, (b) without,

and (c) +0.5·I20 superimposed DC.

The average relative and absolute error, their standard deviation, and their max-

imum deviation if only selected parameters are used for fitting are summarized

for all evaluated spectra (not only the spectra shown within this section) in Ta-

ble 6.12. The errors between all EIS measurements and fits when only selected

parameters are fitted are more than doubled compared to when all parameters

are fitted (Table 6.9).

The correlations between the EIS parameters and the DCA are shown in Fig-

ure 6.32 for R0, in Figure 6.33 for 1/R1, in Figure 6.34 for 1/R2, in Figure 6.35 for

CPE1, and in Figure 6.36 for CPE2. Within all stated figures, the linear fit for all

data points after previous charge and one fit for the data points after previous

discharge is given.

208

6.2 Correlation between EIS and DCA for Cell with Various Additives

Table 6.12: Errors between measurements and fit if only selected parameters are

fitted.

Average

error

Standard

deviation

Maximum

deviation

Relative error

per spectra 4.7% 1.9 % 8.7%

Absolute error

per spectra 0.11mΩ0.04mΩ0.11mΩ

(a) (b) (c)

0 0.2 0.4 0.6 0.8 1 1.2

0.5

1.0

1.5

0 0.2 0.4 0.6 0.8 1 1.2

0.5

1.0

1.5

0 0.2 0.4 0.6 0.8 1 1.2

0.5

1.0

1.5

Figure 6.32: Modified DCA EN compared to R0(only fitting selected parame-

ters) with (a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC

(reprint from Ref. [26]).

(a) (b) (c)

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0.8

Figure 6.33: Modified DCA EN compared to R1(only fitting selected parame-

ters) with (a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC

(reprint from Ref. [26]).

209

6 EIS as Analytical Tool

(a) (b) (c)

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

Figure 6.34: Modified DCA EN compared to R2(only fitting selected parame-

ters) with (a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC

(reprint from Ref. [26]).

(a) (b) (c)

0 0.2 0.4 0.6 0.8 1 1.2

100

120

0 0.2 0.4 0.6 0.8 1 1.2

100

120

0 0.2 0.4 0.6 0.8 1 1.2

100

120

Figure 6.35: Modified DCA EN compared to CPE1(only fitting selected parame-

ters) with (a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC

(reprint from Ref. [26]).

(a) (b) (c)

0 0.2 0.4 0.6 0.8 1 1.2

1000

2000

3000

4000

0 0.2 0.4 0.6 0.8 1 1.2

1000

2000

3000

4000

0 0.2 0.4 0.6 0.8 1 1.2

1000

2000

3000

4000

Figure 6.36: Modified DCA EN compared to CPE2(only fitting selected parame-

ters) with (a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC

(reprint from Ref. [26]).

210

6.2 Correlation between EIS and DCA for Cell with Various Additives

The correlation coefficients of the selected parameters are summarized in Ta-

ble 6.13. The best correlation was found between the DCA EN partial results and

the EIS parameters 1/R1, 1/R2, and CPE2at 80% SoC adjusted via discharge.

Moreover, a good correlation between the DCA results and the EIS parameters

at 80% SoC adjusted via charge and with +0.5·I20 superimposed DC could be

found within the first semicircle (1/R1and CPE1). The parameters of the second

semicircle adjusted via charge and the CPE1adjusted via discharge show only

marginal correlation.

Comparing the DCA (EN) test results with the EIS measurements, the first semi-

circle, consisting of R1and CPE1, shows a higher correlation than the second

semicircle [25, 26]. The AC resistance of the test cells is likely to directly impact

on the charging current under voltage restricted charging. Furthermore, the ca-

pacitance values CPE1is in the range of the Cdl (≈100F), which is related to

the electrochemical active surface area of the electrodes [151] and might be influ-

enced by additives in the NAM. The resistance values correlate better compared

to their corresponding capacitive values [25, 26]. The highest correlation was

found between the DCA, and the EIS parameters of the first semicircle with a

+0.5·I20 superimposed charging current [25, 26]. When charging processes are

promoted, the DCA most likely shows its correlations with the EIS parameters

[25].

Table 6.13: Correlation coefficient between DCA EN and EIS parameters if only

selected parameters are fitted (adjusted from Ref. [26]).

Parameter IDC = -0.5·I20 IDC = 0DC IDC = +0.5·I20

at 80% SoC 1/R10.386 0.105 0.660

adjusted via 1/R20.641 -0.347 0.225

charge CPE1-0.036 0.524 0.435

CPE20.105 0.344 0.366

at 80% SoC 1/R10.706 0.499 0.876

adjusted via 1/R20.624 0.812 0.622

discharge CPE1-0.23 0.228 0.198

CPE20.337 0.600 0.521

211

6 EIS as Analytical Tool

6.3 Correlation between EIS and DCA for different

SoC

Instead of only using the standard single pulse DCA test, described in Sec-

tion 4.1.1, which only investigates one SoC after prior discharge, the test was

extended to investigate influencing factors such as the SoC and prior usage. The

modified single pulse DCA test was presented in Section 4.2.1. A detailed test

procedure is given in Table 4.5. Partial results have already been shown in Sec-

tion 4.3. Figure 6.37 shows the test results of this modified test procedure ex-

emplary for three 2V, 20Ah 3P2N test cells built from the Bottom-Up approach,

described in Section 3.2, containing different additives (EFB+C1, EFB+CX, and

EFB+CY).

5060708090100

SoC / %

0.2

0.4

0.6

0.8

1.2

Normalized Charge Current / A Ah-1

EFB + C1 after prior discharge

EFB + CX after prior discharge

EFB + CY after prior discharge

EFB + C1 after prior charge

EFB + CX after prior charge

EFB + CY after prior charge

Figure 6.37: Modified CA2 test (adjusted from Ref. [26]).

The SoC influence on the DCA (higher DCA for lower SoC [9, 81, 227]), and dif-

ferences between additives are visible in the DCA EN test and in the single pulse

DCA test. For test cells with DCA enhancing additives, the increase of the DCA

when the SoC decreases flattens for lower SoC [9, 81, 227]. On the other hand,

the DCA almost linearly increases (between 90% and 50% SoC) for test cells with

an overall lower DCA. The influence of the prior usage (DCA after prior charge

< DCA after prior discharge [9, 10, 71, 81, 82, 227]) is also shown for the test cells

212

6.3 Correlation between EIS and DCA for different SoC

containing three different additives, shown in Figure 6.37. It is shown that the

influence of the prior usage is more distinct than the influence of the SoC. Fur-

thermore, the influence of the SoC and differences between additives are more

distinct after discharge than after charge, also shown in [10, 71]. Differences be-

tween the single pulse charge acceptance test at 80% SoC, shown in Figure 6.37,

and the results from EN standard Icat 80% SoC, shown in Figure 6.11, are to be

expected due to the different test procedures.

Within this section the modified single pulse DCA test results are compared with

the fitting parameters obtained from EIS measurements, investigating multiple

superimposed DCs, various SoC adjusted via charge, and discharge [26]. The

EIS test plan is given in Table 5.3. It must be noted that similar but not the same

test cells have executed the DCA EN, the modified DCA EN (Table 4.5), and the

EIS test procedure (Table 5.3). Since the DCA after prior charge only changes

marginally [26], a correlation between the DCA and the EIS parameters at this

SoF was not feasible.

0 5 10 15 20

-10

-5

Figure 6.38: EIS at 80% SoC adjusted via discharge for the 3P2N EFB+C1test cell

with +0.5·I20 superimposed DC.

213

6 EIS as Analytical Tool

The test procedure, described in Section 5.3, allows EIS measurements at the

same SoF as the single pulse DCA measurements; at various SoCs after prior

charge and discharge. Additionally, different superimposed DCs were investi-

gated during the EIS procedure. The data preprocessing was already described

in Section 5.4.1. In Figure 6.38 complete EIS measurements for a 3P2N EFB+C1

test cell at various SoCs with +0.5·I20 superimposed DC are shown. However,

only the part of the spectra which was further validated is highlighted in color.

The part of the spectra which fails the K-K transformation, is only illustrated

with gray dots.

After the first preprocessing, the EIS data could be fitted. In the following Sec-

tions 6.3.1 and 6.3.2 two different approaches are discussed. The first shows

the fitting results if all parameters were freely fitted. This approach was exe-

cuted similarly as described in Section 6.2.1. Thereby, good fitting results with

only small errors were accomplished. On the downside many free variables, all

having an impact on each other, need to be evaluated, which hinders identify-

ing a correlation between the EIS parameters and the DCA. Therefore, a second

approach was evaluated, already described in Section 6.2.2. Thereby, as much

parameters as possible were kept constant during all fits. Consequently, only a

few parameters were left for fitting, increasing the error between the measure-

ment and the fit. But a correlation between the remaining EIS parameters and

the DCA could be identified.

6.3.1 Fitting for all Parameters

Within this section, the single pulse DCA results are correlated with the corre-

sponding EIS results. This investigation will only be executed for test results

after prior discharge. Since the single pulse DCA results after prior charge only

change marginally for different SoC and additives, they would not deliver mean-

ingful results.

The DRT is exemplarily shown for a 3P2N EFB+C1test cell with +0.5·I20 super-

imposed DCs in Figure 6.39. Since the DRT for all evaluated spectra was very

similar, the same ECM, starting values, and boundaries for the parameters (al-

ready given in Section 6.2.1) could be used. The ECM consists of a resistance

R0, an inductive part, and three CPEs (each containing a resistance, a time con-

214

6.3 Correlation between EIS and DCA for different SoC

stant, and a compression factor). As described in Section 6.2.1, the time constants

found in the DRT were used as the starting value for fitting, with defined fitting

boundaries.

Figure 6.39: DRT of Figure 6.38.

The fitting results are shown in Figure 6.40 using a Nyquist plot and a Bode plot,

respectively. The fittings are highly accurate. In the Nyquist plot, Figure 6.40 (a),

only a minor deviation in the low-frequency part is visible. In the Bode plot,

Figure 6.40 (b) and (c), these deviations within the low-frequency part are also

visible. Moreover, the Bode plot reviles errors with the high-frequency part, es-

pecially above 10Hz.

For better evaluation of the accuracy, Figure 6.41 visualizes (a) the relative and

(b) the absolute error between EIS measurements and fit if all parameters are

fitted. The relative error shown in Figure 6.41 (a) is highest for high frequencies

since these data points are close to the origin, where already small errors greatly

impact the relative error.

215

6 EIS as Analytical Tool

0 5 10 15

-10

-5

(a)

10-3 10-2 10-1 100101102103104

-50

-25

Figure 6.40: EIS and fit (all parameters) of Figure 6.38 (a) Nyquist, (b) absolute

value and (c) phase.

(a) (b)

10-3 10-2 10-1 100101102103104

0.5

1.5

Figure 6.41: (a) Relative and (b) absolute error of the fits in Figure 6.40.

216

6.3 Correlation between EIS and DCA for different SoC

Table 6.14 summarizes the average, the standard, and maximum deviation of the

relative, and absolute error for only the EFB+C1EIS measurements and fit.

Table 6.14: Error between EFB+C1EIS measurements and fit if all parameters are

fitted.

Average

error

Standard

deviation

Maximum

deviation

Relative error

per spectra 2.4% 0.4 % 1.1%

Absolute error

per spectra 0.08mΩ0.03mΩ0.07mΩ

The comparison of EIS parameters with the single pulse DCA test results after

prior discharge is shown in Figures 6.42 to 6.53. Even though higher superim-

posed DCs have been measured at low SoC, only the spectra without and with

±0.5·I20 superimposed DC are shown. The spectra obtained with -1·I20, -2·I20, or

-3·I20 do not contain additional information. The spectra obtained with +1·I20,

+2·I20, or +3·I20, on the other hand, show a significant increase of the gassing

processes within the spectra, covering all other processes and thereby hamper-

ing the evaluation. Thereby, investigations of the spectra obtained without and

with ±0.5·I20 will show if the influence of different additives, the SoC, and prior

usage has a similar impact on the EIS results as it does on the DCA. If a good

correlation between the EIS parameters and the DCA can be drawn, EIS could

be used as an analytical tool for predicting DCA without long-term tests such as

the DCA EN or the Ford long-term run-in DCA test B.

217

6 EIS as Analytical Tool

(a) (b) (c)

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Figure 6.42: Modified CA2 test compared to R0(fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC.

(a) (b) (c)

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Figure 6.43: Modified CA2 test compared to L(fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC.

(a) (b) (c)

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0.8

Figure 6.44: Modified CA2 test compared to λ(fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC.

218

6.3 Correlation between EIS and DCA for different SoC

(a) (b) (c)

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Figure 6.45: Modified CA2 test compared to Rmin (fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC.

(a) (b) (c)

0 0.2 0.4 0.6 0.8 1 1.2

0.02

0.04

0.06

0.08

0.1

0 0.2 0.4 0.6 0.8 1 1.2

0.02

0.04

0.06

0.08

0.1

0 0.2 0.4 0.6 0.8 1 1.2

0.02

0.04

0.06

0.08

0.1

Figure 6.46: Modified CA2 test compared to τmin (fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC.

(a) (b) (c)

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0.8

Figure 6.47: Modified CA2 test compared to ξmin (fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC.

219

6 EIS as Analytical Tool

(a) (b) (c)

0 0.2 0.4 0.6 0.8 1 1.2

0.5

1.0

1.5

2.0

2.5

0 0.2 0.4 0.6 0.8 1 1.2

0.5

1.0

1.5

2.0

2.5

0 0.2 0.4 0.6 0.8 1 1.2

0.5

1.0

1.5

2.0

2.5

Figure 6.48: Modified CA2 test compared to R1(fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC.

(a) (b) (c)

0 0.2 0.4 0.6 0.8 1 1.2

100

200

300

400

500

600

700

0 0.2 0.4 0.6 0.8 1 1.2

100

200

300

400

500

600

700

0 0.2 0.4 0.6 0.8 1 1.2

100

200

300

400

500

600

700

Figure 6.49: Modified CA2 test compared to CPE1(fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC.

(a) (b) (c)

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0.8

Figure 6.50: Modified CA2 test compared to ξ1(fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC.

220

6.3 Correlation between EIS and DCA for different SoC

(a) (b) (c)

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

Figure 6.51: Modified CA2 test compared to R2(fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC.

(a) (b) (c)

0 0.2 0.4 0.6 0.8 1 1.2

500

1000

1500

2000

2500

0 0.2 0.4 0.6 0.8 1 1.2

500

1000

1500

2000

2500

0 0.2 0.4 0.6 0.8 1 1.2

500

1000

1500

2000

2500

Figure 6.52: Modified CA2 test compared to CPE2(fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC.

(a) (b) (c)

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0.8

Figure 6.53: Modified CA2 test compared to ξ2(fitting all parameters) with

(a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC.

221

6 EIS as Analytical Tool

Table 6.15 summarizes the correlation coefficients between the single pulse DCA

results and the EIS parameters after previous discharge for superimposed DC

-0.5·I20, +0.5·I20, and without. There was no clear correlation between the high-

frequency parameters (R0, L, λ,Rmin,τmin nor ξmin) and the DCA results. Better

correlations could be identified for the Rand CPE parameters of the first and sec-

ond semicircles. However, all parameters interact, especially ξ, making it hard

to find clear correlations. Therefore, a fitting attempt with a reduced number of

fitting parameters, as described in Section 6.2.2, was carried out for this data set

as well.

Table 6.15: Correlation coefficient between the CA2 test and the EIS parameters

after previous discharge if all parameters are used for fitting.

Parameter IDC = -0.5·I20 IDC = 0DC IDC = +0.5·I20

R0-0.369 -0.188 -0.063

L-0.141 -0.026 0.202

λ0.268 0.064 -0.419

Rmin 0.370 0.082 -0.025

τmin -0.299 -0.387 0.224

ξmin 0.008 0.175 0.200

1/R10.488 0.199 0.450

CPE10.344 0.127 0.412

ξ10.349 -0.153 0.161

1/R20.281 0.307 0.388

CPE20.449 0.490 0.490

ξ2-0.726 0.374 -0.818

6.3.2 Fitting for selected Parameters

This section used the fitting procedure to reduce the number of fitting param-

eters, described in Section 6.2.2. Therefore, parameters that were identified as

independent of the SoC and the compression factors of the CPEs were kept con-

stant thought out all fits. Consequently, only a few parameters were left for

fitting, increasing the error between the measurement and the fit. However, the

comparison between the remaining parameters and the DCA is more precise.

222

6.3 Correlation between EIS and DCA for different SoC

0 5 10 15

-10

-5

(a)

10-3 10-2 10-1 100101102103104

-50

-25

Figure 6.54: EIS and fit (only selected parameters) for a 3P2N EFB+C1test cell

with +0.5·I20 superimposed DC (a) Nyquist, (b) absolute value and

(a) (b)

10-3 10-2 10-1 100101102103104

0.5

1.5

Figure 6.55: (a) Relative and (b) absolute error of the fits in Figure 6.54.

223

6 EIS as Analytical Tool

In Nyquist, shown in Figure 6.54 (a), the highest variation between the EIS mea-

surement and the fit can be found in the second semicircle or the low frequencies,

respectively. However, in the Bode plot, shown in Figure 6.54 (b) and (c), the

biggest differences can be found in the phase between 10Hz and 6.5kHz. These

two areas of discrepancies are also visualized within the relative error, shown in

Figure 6.55 (a), and the absolute error, shown in Figure 6.55 (b). The relative er-

ror is especially high for the high-frequency area, where the absolute value of the

impedance is small, and even minor discrepancies within the phase shift result

in increased relative errors. The absolute error, on the other hand, is exception-

ally high for low frequencies. However, the resulting errors when only selected

parameters were used for fitting are very similar to the errors when all param-

eters were used. A summary of the average error, the standard, and maximum

deviation of the relative and the absolute error of the spectra for the EFB+C1are

given in Table 6.16. These errors are very similar to the errors of all test cells

(Table 6.12).

Table 6.16: Error between EFB+C1EIS measurements and fit if only selected pa-

rameters are fitted.

Average

error

Standard

deviation

Maximum

deviation

Relative error

per spectra 4.8% 1.1 % 2.9%

Absolute error

per spectra 0.11mΩ0.03mΩ0.07mΩ

The resulting fit parameters are shown in Figures 6.56 to 6.60 in correlation to

the single pulse DCA test results.

224

6.3 Correlation between EIS and DCA for different SoC

(a) (b) (c)

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0.8

1.2

1.4

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0.8

1.2

1.4

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0.8

1.2

1.4

Figure 6.56: Modified CA2 test compared to R0(only fitting selected parameters)

with (a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC.

(a) (b) (c)

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

Figure 6.57: Modified CA2 test compared to R1(only fitting selected parame-

ters) with (a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC

(reprint from Ref. [26]).

(a) (b) (c)

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

Figure 6.58: Modified CA2 test compared to R2(only fitting selected parame-

ters) with (a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC

(reprint from Ref. [26]).

225

6 EIS as Analytical Tool

(a) (b) (c)

0 0.2 0.4 0.6 0.8 1 1.2

100

120

0 0.2 0.4 0.6 0.8 1 1.2

100

120

0 0.2 0.4 0.6 0.8 1 1.2

100

120

Figure 6.59: Modified CA2 test compared to CPE1(only fitting selected parame-

ters) with (a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC

(reprint from Ref. [26]).

(a) (b) (c)

0 0.2 0.4 0.6 0.8 1 1.2

1000

2000

3000

4000

0 0.2 0.4 0.6 0.8 1 1.2

1000

2000

3000

4000

0 0.2 0.4 0.6 0.8 1 1.2

1000

2000

3000

4000

Figure 6.60: Modified CA2 test compared to CPE2(only fitting selected parame-

ters) with (a) -0.5·I20, (b) without, and (c) +0.5·I20 superimposed DC

(reprint from Ref. [26]).

The correlation coefficients between the DCA and the EIS parameters are shown

in Table 6.17. The correlation is highest for the EFB+C1and EFB+CXtest cells,

independent of the superimposed DC. However if the complete correlation coef-

ficient of all three evaluated test cells is evaluated, the correlation coefficient for

+0.5·I20 superimposed DC is highest. This was also observed in the feasibility

study [25], summarized in Section 6.1. It is explainable since the DCA will most

likely show correlations with the EIS parameters when charging processes are

promoted [25, 26].

226

6.3 Correlation between EIS and DCA for different SoC

Table 6.17: Correlation coefficient between the CA2 test and EIS parameters after

previous discharge if only selected parameters are fitted.

Parameter IDC = -0.5·I20 IDC = 0DC IDC = +0.5·I20

complete 1/R10.429 0.462 0.504

correlation 1/R20.511 -0.073 0.571

CPE10.440 0.406 0.467

CPE20.747 0.412 0.670

correlation of 1/R10.944 0.924 0.963

EFB+C11/R20.933 0.672 0.896

CPE10.988 0.968 0.985

CPE20.965 0.978 0.952

correlation of 1/R10.931 0.911 0.944

EFB+CX1/R20.995 0.187 0.994

CPE10.991 0.988 0.987

CPE20.976 0.886 0.939

correlation of 1/R1-0.777 -0.425 -0.653

EFB+CY1/R2-0.430 -0.953 0.036

CPE1-0.624 -0.532 -0.647

CPE2-0.437 -0.572 0.324

227

Conclusion

Chapter 7

In micro-hybrid vehicles, the lead-acid battery (LAB) is a crucial component for

improved fuel economy by using the stop/start function of the engine and re-

generative braking. For improving the dynamic charge acceptance (DCA) of the

LAB, new negative active mass (NAM) additives are tested. For further enhance-

ment of the future research the following research questions were investigated

within this thesis:

The first research goal was to investigating the future perspective of the LAB as

SLI battery. The typical State-of-the-Art SLI battery is based on LABs because

its uncompromised CCA at low temperatures always ensured a reliable engine

start. A comparison of the LAB-based SLI battery with lithium-based batteries

showed that LFPs exhibit higher voltage levels at low discharging currents than

LABs, resulting in higher power and energy output irrespective of the ambient

temperature. LFPs also have a lower capacity decline and lower energy decline

for decreasing temperatures during low current discharge. Regarding the CCA

test, the LABs met the requirements until −18 ◦C by supplying the necessary

current while maintaining a voltage above 6V. The LFP batteries only met the

requirements for the CCA standard test until −10◦C.

Translating the standard DCA test procedures form battery to cell level with

and without reduced plate count was the second research goal. DCA standard

test procedures were only defined for battery testing until now. However, for a

higher throughput during material screening or compositional variation smaller

cell layouts would be feasible. Test cells have been derived using two different

procedures the Top-Down approach and the Bottom-Up approach. While the

Bottom-Up approach is the classical way of building test cells by hand pasting

plates and using these to construct and format cells. The Top-Down approach

229

7 Conclusion

used 12V, 70 Ah EFBs, which were pre-tested for DCA, to harvest 2V test cells,

though some with a reduced number of plates (3P2N and 2P1N). Since the DCA

is known to be restricted by the negative electrode [93, 132, 133], the NAM limits

the investigated test cells. For DCA tests on cell level with and without reduced

plate count, identifying operational conditions and scaling factors, e.g., voltages,

currents, acid amount, and concentration was necessary.

Following up by the next research goal to investigate the effects of the cell lay-

out compared to battery results and thereby the ratio between the positive active

mass (PAM), the negative active mass (NAM), and the electrolyte. Test cells were

used to study the effects of changing cell count, plate count, the ratio between

the PAM, the NAM, and the electrolyte and correlate their results with the bat-

tery results.

The influence of the cell layout compared to battery results on the DCA tests was

compared for different DCA test procedures: the CA tests 2 [68], the DCA EN

test [61], and the Ford long-term run-in DCA test B [9, 80]. All three test proce-

dures conducted correlating results for all different test cell layouts. Thereby all

three test procedures showed the DCA increase with reduced plate count.

A mayor research goal was to investigate the influencing factors on the DCA, es-

pecially within cells with reduced plate count. Next to the standard DCA tests,

new DCA test procedures were contrived to investigate influencing factors on

the DCA, such as cell layout, short-term history, state of charge (SoC), electrolyte

concentration, and NAM additives. The main influence factors on DCA in elec-

trical tests are the short-term usage (prior charge, discharge, or rest period), the

SoC, and additives. After prior discharge, the DCA is high and decreases with

a more extended rest period. After prior charge, the DCA is at its lowest level

and almost independent from the following rest period. The DCA increases with

decreasing SoC.

A clear proportionality was found between the external surface area of carbon

additives used at the NAM and DCA [26, 71]. The external surface area of car-

bon additives seems to be a crucial parameter in adjusting the short-term and

long-term DCA.

230

The electrochemical behavior influencing the DCA at 80% SoC after prior charge

and discharge was analyzed by applying post-mortem-analysis of the active

masses using a laser scanning microscope. Therefore, the cells at the chosen

state of function (SoF) were opened, and a negative electrode was separated and

cleaned in a beaker using isopropanol as a nonreactive substance. The electrodes

were rinsed off without using mechanical forces and possibly destroying the mi-

croscopic structure of the negative electrode. After washing, the electrodes were

dried in a vacuum oven and investigated via laser scanning microscope (LSM)

at three different heights.

LSM pictures from the bottom showed superficial dense sulfate layers resulting

from stratification and stand times during initial cycling. This structure seems

independent of the additives used and remains unchanged after prior charge

and subsequent discharge test. After prior charge, the LSM showed many lead

sulfate (PbSO4) crystals of several µm sizes at the top of the cell. While after prior

discharge, the PbSO4crystals are primarily precipitated, and the crystal size at

the top of the negative plates is fine. Since smaller crystals are easier to dissolve,

the LSM showed one reason for higher DCA after prior discharge compared to

prior charge.

Cells constructed with a reduced, asymmetric electrode system generate an acid

surplus and PAM surplus, which enormously affect steady-state properties such

as 20h discharge capacity (C20). On the other hand, they only have minimal

impact on DCA. In the process, the nominal DCA increases as the plate count

falls. Ultimately two aspects introduced the most significant influence on the

increased DCA in test cells with lower plate counts and, thereby, a more asym-

metric NAM-PAM-to-acid ratio. The first is the increasing polarisation of the

negative electrode in cells with lower plate counts. The second is that the acid

stratification significantly impacts the DCA, that the decreased acid stratification

due to the excess acid in small cells increased the normalized DCA.

The definition of an electrochemical impedance spectroscopy (EIS) test proce-

dures at multiple SoC, different prior usage, and various superimposed direct

current (DC) for cell with and without reduced plate count was accomplished.

This test definition was used to analyse and predict the DCA using EIS, which

was the final research goal of this work. The DCA-enhancing influence of addi-

231

7 Conclusion

tives can be visualized via electrochemical impedance spectroscopy (EIS). Neg-

ative half-cell EIS measurements have been conducted at various SoC, adjusted

via charge or discharge, and with multiple superimposed direct currents (DCs).

The micro-cycling approach was used to conduct reproducible EIS measure-

ments. The EIS measurements are pre-processed using Kramers-Kronig (K-K)

transformation to verify that all data evaluated were stable, causal, and that

real and imaginary parts are interdependent [175, 176]. Afterward, the distribu-

tion of relaxation times (DRT) was used to analyze the number of processes and

their characteristic frequencies [181], thereby determining the equivalent circuit

model (ECM) and the starting parameters of the fitting. The negative half-cell

spectra were fitted with an internal resistance, an inductance, and three constant

phase elements (CPEs) (one is refered to as mini CPE).

Two different fitting procedures were used and compared. The first allowed

the fitting of all parameters, resulting in many parameters interacting with each

other. The second fitting procedure reduced the number of fitting parameters

step-wise. In the first step, all values regarding the high-frequency part of the

spectra (L,ξL,Rmin,τmin, and ξmin) were averaged. Furthermore, the parameter

R0no longer had a fitting range, but the minimum real part of the impedance

was used. The fitting procedure was repeated with this new set of values, leav-

ing only the parameters of the two semicircles free for fitting. For the resulting

fits, the compression factors ξ1and ξ2were averaged for each superimposed

DC. Only four variables were left for fitting: R1,τ1,R2and τ2. Even though this

restriction will cause a noticeable deterioration of the fitting quality, this must

be accepted to validate such a brought range of test cells (additives) and bat-

tery states (SoC and prior usage). Artifacts during DCA prediction can only be

avoided if the model uses a minimal number of variable parameters. The re-

sulting EIS parameters are compared to DCA measurements at the same SoF.

The highest correlation between DCA and the EIS parameters is obtained within

the first semicircle while superimposing a charging current. The first semicir-

cle represents the charge transfer reaction, which can be differentiated by using

different additives for enhancing the DCA. However, a correlation between the

DCA and the second semicircle was also identified.

If not every reaction process is represented by a single semicircle, but one reac-

tion can occur in two separate semicircles if executed in several consecutive or

232

parallel steps, the second semicircle could represent the second of the two-step

electron transfer reaction [215, 216]. Huck modeled the EIS spectra with a two-

step charge transfer reaction [197]. Even though the impact was the highest in

the first semicircle, the measurement results indicate that the additives also affect

the low-frequency semicircle. The inverse of the resistance R1and R2, and thus

the conductivity, showed the highest correlation to the DCA. The relationship

between the capacitance CPE1and CPE2and the DCA is not as distinct. The EIS

measurements can be used to predict the DCA for different additives at various

SoF quantitatively.

233

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