D1.1 – Report on electrochemical cell model...2018/11/30 · cell, which is the project cell of the EVERLASTING project. The experimental part is used to parameterize and validate

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Electric Vehicle Enhanced Range, Lifetime And Safety Through INGenious battery management

D1.1 – Report on electrochemical cell model November 2018

This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 713771

D1.1 – Report on electrochemical cell model Author: Sturm Johannes (TUM) - November 2018

EVERLASTING - Grant Agreement 71377 (Call: H2020-GV8-2015) Electric Vehicle Enhanced Range, Lifetime And Safety Through INGenious battery management

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PROJECT SHEET

Project Acronym EVERLASTING

Project Full Title Electric Vehicle Enhanced Range, Lifetime And Safety Through INGenious battery management

Grant Agreement

713771

Call Identifier H2020-GV8-2015

Topic GV-8-2015: Electric vehicles’ enhanced performance and integration into the transport system and the grid

Type of Action Research and Innovation action

Project Duration 48 months (01/09/2016 – 31/08/2020)

Coordinator VLAAMSE INSTELLING VOOR TECHNOLOGISCH ONDERZOEK NV (BE) - VITO

Consortium Partners

COMMISSARIAT A L’ENERGIE ATOMIQUE ET AUX ENERGIES ALTERNATIVES (FR) - CEA SIEMENS INDUSTRY SOFTWARE SAS (FR) - Siemens PLM TECHNISCHE UNIVERSITAET MUENCHEN (DE) - TUM TUV SUD BATTERY TESTING GMBH (DE) - TUV SUD ALGOLION LTD (IL) - ALGOLION LTD RHEINISCH-WESTFAELISCHE TECHNISCHE HOCHSCHULE AACHEN (DE) - RWTH AACHEN LION SMART GMBH (DE) - LION SMART TECHNISCHE UNIVERSITEIT EINDHOVEN (NL) - TU/E VOLTIA AS (SK) - VOLTIA VDL ENABLING TRANSPORT SOLUTIONS (NL) – VDL ETS

Website www.everlasting-project.eu

http://www.everlasting-project.eu/



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DELIVERABLE SHEET

Title D1.1 – Report on electrochemical cell model

Related WP WP1 (WP1 – Task 1.1 “Cell level detailed modelling”)

Lead Beneficiary Siemens PLM

Author Johannes Sturm (TUM)

Reviewers Matthieu Ponchant (Siemens PLM)

Didier Buzon (CEA)

Fabian Frie (RWTH Aachen)

Type Report

Dissemination level PUBLIC

Due Date M26

Submission date November 30, 2018

Status and Version Final, version 1.0



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REVISION HISTORY

Version Date Author/Reviewer Notes

V0.1 20/11/2018 Sturm Johannes (TUM)

Lead Beneficiary

Draft version 0.1

V0.2 21/11/2018 Didier Buzon (CEA) Peer review

V0.2 21/11/2018 Matthieu Ponchant (Siemens PLM) Peer review

V0.3 21/11/2018 Fabian Frie (RWTH Aachen) Peer review

V0.4 22/11/2018 Johannes Sturm (TUM) Quality check

V0.5 22/11/2018 Matthieu Ponchant (Siemens PLM)

WP1 leader

Final review

V1.0 30/11/2018 Carlo Mol (VITO)

Coordinator

Submission to the EC



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DISCLAIMER

The opinion stated in this report reflects the opinion of the authors and not the opinion of the European Commission.

All intellectual property rights are owned by the EVERLASTING consortium members and are protected by the applicable laws. Except where otherwise specified, all document contents are: “© EVERLASTING Project - All rights reserved”. Reproduction is not authorised without prior written agreement.

The commercial use of any information contained in this document may require a license from the owner of that information.

All EVERLASTING consortium members are committed to publish accurate information and take the greatest care to do so. However, the EVERLASTING consortium members cannot accept liability for any inaccuracies or omissions nor do they accept liability for any direct, indirect, special, consequential or other losses or damages of any kind arising out of the use of this information.

ACKNOWLEDGEMENT

This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 713771



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EXECUTIVE SUMMARY The report summarizes the activities and achievements of work package (WP) 1 regarding the “Cell level detailed modelling” task (Task 1.1). Over the first two years in the EVERLASTING project, different experimental methods were applied on electrode/electrolyte and cell level of the INR18650-MJ1 lithium-ion cell, which is the project cell of the EVERLASTING project. The experimental part is used to parameterize and validate the modelling and simulation part using different thermal-electrochemical models for lithium-ion batteries. The results of the cell level detailed modelling show accurate prediction of the cell’s behaviour under various charge and discharge scenarios, cyclic and calendric aging as well as under different applied cooling strategies and ambient temperature conditions. The report is mainly based on the related publication [1] in the Journal of Power Sources and the published data repository [2] at the TU Delft (i.e. Research Data Center). The publications are available under the following DOIs:

• Research Paper: https://doi.org/10.1016/j.jpowsour.2018.11.043 • Data Repository: https://doi.org/10.4121/uuid:e8735cd2-e478-4db5-80bc-b5051961a0ab



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TABLE OF CONTENTS EXECUTIVE SUMMARY .......................................................................................................................................................... 6

TABLE OF CONTENTS ............................................................................................................................................................ 7

LIST OF ABBREVIATIONS AND ACRONYMS ................................................................................................................... 8

LIST OF FIGURES .................................................................................................................................................................. 10

LIST OF TABLES .................................................................................................................................................................... 11

INTRODUCTION .................................................................................................................................................................... 12

1 ELECTROCHEMICAL-THERMAL CHARACTERIZATION ................................................................................... 13

1.1 HALF-CELL MEASUREMENTS .................................................................................................................................................... 13

1.1.1 Silicon-doped Graphitic Anode .......................................................................................................................................... 13

1.1.2 Nickel-rich NMC-type Cathode .......................................................................................................................................... 14

1.2 FULL-CELL MEASUREMENTS .................................................................................................................................................... 17

1.2.1 Open-circuit tests and Cell Balancing ............................................................................................................................ 17

1.2.2 Calorimetric tests..................................................................................................................................................................... 20

1.2.3 Thermographic Tests ............................................................................................................................................................. 20

1.2.4 Aging Tests .................................................................................................................................................................................. 21

2 CELL-LEVEL DETAILED MODELLING ..................................................................................................................... 22

2.1 SINGLE P2D MODEL ................................................................................................................................................................ .. 22

2.1.1 Model Description .................................................................................................................................................................... 22

2.1.2 Parameterization .................................................................................................................................................................... 24

2.2 MULTI-DIMENSIONAL MODEL APPROACH ............................................................................................................................. 26

2.2.1 Model Description .................................................................................................................................................................... 28

2.2.2 Parameterization .................................................................................................................................................................... 29

3 MODEL VALIDATION .................................................................................................................................................. 30

3.1 CALORIMETRIC TESTS ................................................................................................................................................................ 30

3.2 THERMOGRAPHIC TESTS ........................................................................................................................................................... 32

3.3 AGING TESTS ................................................................................................................................................................ ............... 38

CONCLUSIONS ....................................................................................................................................................................... 39

4 REFERENCES .................................................................................................................................................................. 40



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LIST OF ABBREVIATIONS AND ACRONYMS ACRONYM DEFINITION

18650 Cylindrical Cell Format with diameter of 18 mm and height of 65 mm

C Graphite

CC Constant Current

CR2032 Coin Cell standard setup/type

CV Constant Voltage

DAE Differential Algebraic Equation

DMC Dimethyl Carbonate

DOD Depth of Discharge

DVA Differential Voltage Analysis

EC Ethylene Carbonate

EMC Etyhl Methyl Carbonate

EIS Electrochemical Impedance Spectroscopy

FEM Finite Element Method

ICP-OES Inductively Coupled Plasma-Optical Emission Spectroscopy

LFP Lithium Iron Phosphate

LiPF6 Lithium Hexafluorophosphate

MJ1 Everlasting Project Cell – INR18650-MJ1 from LG Chem

MSE Mean Squared Error

MuDiMod Multi-Dimensional Model

NCA Nickel Cobalt Aluminum

NMC Nickel Manganese Cobalt

NMC-811 Nickel Manganese Cobalt oxide in relation 8-1-1 (wt.-%)

NMC-111 Nickel Manganese Cobalt oxide in relation 1-1-1 (wt.-%)

OCP Open Circuit Potential

OCV Open Circuit Voltage

p2D Pseudo Two-Dimensional

PC Polypropylene Carbonate



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RWTH Aachen Rheinisch-Westfaelische Technische Hochschule Aachen

SiC Silicon doped Graphite

SOC State of Charge

TUM Technische Universität München

WP Work package

WPL Work package leader



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LIST OF FIGURES Figure 1 Dismantled MJ1-cell for extracting coin-cell samples. ........................................................................................... 13

Figure 2 Open-circuit-potential (a) and entropic coefficient (b) measurement of the SiC coin-cell with depiction of the full-cell voltage range from 2.5 to 4.2 V [1]. ................................................................................................ 14

Figure 3 The Compression/Vacuum box in the argon-filled glovebox (left) was used to apply the pressure profile (right) for evacuating the pore of the cathode samples to ease the wetting of the porous structure. .. 15

Figure 4 Manufacturing process of using the vacuum assisted wetting process of the NMC811 coin blanks. 16

Figure 5 Open-circuit-potential (a) and entropic coefficient (b) measurement of the NMC-811 coin-cell with depiction of the full-cell voltage range from 2.5 to 4.2 V [1]. ................................................................................................ 16

Figure 6 DVA analysis of the full- and half-cells with analysing the balancing of the cell for the charge scenario [1]. ................................................................................................................................................................ .................................................. 18

Figure 7 DVA analysis of the full- and half-cells with analysing the balancing of the cell for the discharge scenario [1]. ............................................................................................................................................................................................... 19

Figure 8 Calculating the convective heat flow of the 18650 cell format [1]. .................................................................. 21

Figure 9 Overview of the fundamental equation system of the single p2D electrochemical-thermal cell model [1]. ................................................................................................................................................................ .................................................. 23

Figure 10 Summary of the electrochemical-thermal p2D model parameterization of the INR18650-MJ1 cell [1]. ................................................................................................................................................................ .................................................. 25

Figure 11 Parameterization of the electrolyte (see Ref. [50] = “I”) in the p2D model [1]. ........................................ 26

Figure 12 Overview of the fundamental equations incorporated in the 2D electrical and 3D thermal model in the MuDiMod [1]. ..................................................................................................................................................................................... 27

Figure 13 Model overview of the MuDiMod depicting the parallel-connected p2D models between the current collectors, the 2D electrical model and the 3D thermal model [1]. .................................................................................... 28

Figure 14 Parameterization of the 2D electrical model [1]. .................................................................................................. 29

Figure 15 Parameterization of the 3D thermal model [1]. .................................................................................................... 30

Figure 16 Calorimetric experimental and simulation results (single p2D-model and MuDiMod) for the charge (d, e, f) and discharge (a, b, c) scenario using the cell voltage (a, d), heat generation (b, e) and temperature (c, f) [1]. ................................................................................................................................................................................................ ............. 31

Figure 17 Cell voltage (a, d, e, g) validation of the MuDiMod and single p2D model at different charge and discharge rates with depiction of the simulation error (b, d, f, h) [1]. .............................................................................. 33

Figure 18 Validation of the volume-averaged temperature calculation in the single p2D model for different charge and discharge rates as well as different ambient temperatures [1].................................................................... 35

Figure 19 Validation of the locally calculated temperature in the MuDiMod for different charge and discharge rates as well as different ambient temperatures [1]. ............................................................................................................... 36



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Figure 20 Validation of the single p2D model using the thermography measurement under convective cooling I [1]. ................................................................................................................................................................ ............................................... 37

Figure 21 Validation of MuDiMod using the thermography measurement under convective cooling condition I [1]. ................................................................................................................................................................................................ ............... 37

Figure 22 Aging simulation study for the INR18650-MJ1 cell for SEI growth during cyclic aging referring to the cell voltage (a), overall capacity fade (b) and SEI-layer thickness growth (c). .............................................................. 38

LIST OF TABLES Table 1 Open-circuit test procedure [1] ........................................................................................................................................ 17

Table 2 Calorimetric test procedure [1] ........................................................................................................................................ 20

Table 3 Thermographic test procedure [1] .................................................................................................................................. 20

Table 4 Cyclic aging profile [23] ........................................................................................................................................................ 21

Table 5 Parameterization of the side reaction incorporated in the single p2D model to account for SEI growth during cyclic and calendric aging...................................................................................................................................................... 23



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INTRODUCTION Even if state of the art lithium-ion technologies offer the highest energy and power density among other battery chemistries, the requirements for the next decade [3] of large stationary storage systems and automotive applications exceed available capabilities. Extended operational performance will be required such as offering a range of more than 300 km [4] for a full-electric vehicle while maintaining lifetime and safety [5]. Preliminary estimates target at 300 Wh kg-1 on cell level [3,6] to achieve energy densities on battery pack level around 250 Wh kg-1. Referring to the geometrical format and the capacity of the cell, current automotive applications incorporate already larger-sized cells [7] via increasing the width and length of the electrodes and/or the coating thicknesses of the composites with standard chemistries such as Graphite (C), Nickel Manganese Cobalt (NMC) or Nickel Cobalt Aluminum (NCA) oxides [5]. Small formats such as the 18650 cell offer limited geometrical space but higher intrinsic safety due to their thermal behaviour compared to large-sized cell formats and higher capacities are achieved through advancements on the electrode level (>600 Whkg-1) and active material level (> 700 Wh kg-1) via highly densified electrodes yielding to low porosities (< 20%) and/or employing high-capacity active materials [3].

In order to meet these requirements [5], layered oxide-types such as high-energy NMC, nickel-rich NMC-types (e.g. NMC-811) and NCA [3] appear to be at the moment the most suitable choice in combination with silicon doped graphite (SiC) anodes [6]. To increase the intrinsic capacity of NMC-type electrodes, the content of nickel, manganese and cobalt is varied from an equalized, standard composition (i.e. NMC-111) to nickel-rich oxides which content nickel beyond 80 wt.-% [8]. Specific capacities up to 275.5 mAh g-1 [9] at a cut-off voltage of 5 V and approximately 200 mAh g-1 [8] at 4.3 V are achievable for a NMC-811 cathode and despite the possible capacity fading [9] due to gasing and oxygen release from the host lattice seen above 4 V, nickel-rich active materials turn out to provide high-capacity electrodes. In terms of the anodic active material, silicon containing graphite compounds offer capacities > 400 mAh g-1 [10–13] which exceed the standard graphite anodes (372 mAh g-1 [14–16]). Doping graphite with small amounts of silicon (1:93 wt.-% for Si:C) increases the specific capacity significantly [10]. However, the volumetric expansion of silicon during lithiation is a crucial issue. As the volumetric expansion of pure silicon (≈ 400% [17]) can only partly be accommodated by the graphitic matrix [13], decreasing the size of the particles [18], incorporating silicon nanowires [17] or using coatings with carbon [19] dilute the overall volume expansion [20] and limit the lithiation window of the Si component which makes silicon doped graphite to an appropriate high-capacity active material for anodes.

Considering nickel-rich and silicon doped graphite materials on the electrode level, an increase from ≈ 340 Wh kg-1 to > 600 Wh kg-1 [3] is attainable when the morphology [3], coating thicknesses [7] and the amount of inactive additives [21] are optimized. Standard electrodes reveal porosities of approximately 35% [3], whereas high-energy electrodes reveal porosities even below 20%, which may enhance unwanted liquid mass transport limitations [22] and reduce the charge and discharge-rate capability of the cell.

In short, next generation high-energy electrodes will incorporate high-capacity active materials (e.g. NMC-811/SiC) and low porous electrodes beside thicker coatings or longer electrodes.

In this report, a commercial 3.35 Ah NMC-811/SiC (INR18650-MJ1, LG Chem [23]) lithium-ion battery is characterized via calorimetry, infrared thermography and open-circuit potential (OCP) experiments. Based on



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the experimental part, a Newman-type [24] pseudo-two dimensional (p2D) model and a Multi-Dimensional Model (MuDiMod) [25–28] are parameterized and validated. While the single p2D model assumes ideal utilized electrodes with a constant areal current density along the current collectors and uses a lumped, volume averaged thermal model, the MuDiMod framework accounts for inhomogeneous electrode utilization along the electrodes (e.g. induced by different current collector tab pattern or collector thicknesses) together with local heat generation and temperature calculation.

Electrochemical-Thermal Characterization In order to parameterize the thermal-electrochemical models, both full- (i.e. INR18650-MJ1 – SiC vs. NMC-811) and half-cells (i.e. anode (SiC) and cathode (NMC-811) vs. pure lithium-metal reference electrode) were investigated towards OCP behaviour and its dependency towards temperature (i.e. entropic coefficient). To validate the simulation models, calorimetric and thermographic measurements of the full cell were conducted within WP1 at RWTH Aachen and TUM.

Half-cell Measurements The half-cells were built from several dismantled INR18650-MJ1 (MJ1) cells opened in an argon-filled glovebox (M.Braun Inertgas-Systeme GmbH). Figure 1 shows exemplarily an opened MJ1 cell with the extracted jelly roll (i.e. “+” and “-”), the unwound anode and cathode (with already extracted half-cell samples) and the fully dismantled and separated MJ1 cell (right). The unwounded electrodes seen in Figure 1 were used to extract electrode samples, which were used to build CR2032-type coin-cells.

Figure 1 Dismantled MJ1-cell for extracting coin-cell samples.

SILICON-DOPED GRAPHITIC ANODE The electrodes for the half-cells were extracted from full cell #4-MJ1 at 3 V, which was opened inside an argon-filled glovebox.



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Single-side coated electrode samples (∅ 14 mm) for the CR2032-type coin cell were gained from a single-coated area at the outer end of the anode and via mechanical abrasion using a scalpel for the continuously double-side coated cathode. The assembly included two aluminum spacers (0.5 mm/1 mm), two glasfiber separators each of 250 µm, a single lithium-metal coin (250 µm) and the remaining CR2032-type housing caps, wave spring and insulation ring.

The anode half-cells were filled with 90 µl of 1 M LiPF6 in 3:7 (wt.:wt.) ethylene carbonate (EC)/ethyl methyl carbonate (EMC) electrolyte (99.9 % purity, Solvionic) under ambient pressure (≈ 1 bar) in the glove-box. Open-circuit potential measurements for charge and discharge of the anode (SiC) were measured in a climate chamber (VT 4021, Vötsch Industrietechnik GmbH) at 25°C combined with a cycler (CTS, BaSyTec). The applied current was set to 80 µA (≈ 0.01C). As the electrodes of the coin cells were extracted from an already utilized cell, no formation cycles were necessary. The discharge capacity gained from the coin-cell summed up to 7.96 mAh (5.17 mAh cm-2).

The entropy profiles of the negative electrode (SiC) were measured using a potentiometric method [29]. The anode half-cells were initially set to 10 mV at 0.1C with a subsequent CV period and termination criterion of C/1000. Afterwards the anode was delithiated with C/30 at delithiation steps of 6.25 % referring to the capacity of the coin-cell, gaining 17 reference points in total. After resting for 6 h at 25°C, a positive temperature pulse of 10 K amplitude and 4h duration immediately followed by a negative pulse of the same amplitude and duration was applied according to the work of Zilberman et al. [29] at each lithiation step with a climate chamber (KT115, Binder) which ensured isothermal test condition at a temperature accuracy of ±15 mK. PT100 sensors were used to measure the temperature at the surface of each cell. As the half-cell voltage was not completely relaxed after 6 h, the voltage response to the temperature profile was corrected using the method presented in Osswald et al. [30]. Figure 2 shows the measured OCP- and entropic profiles of the SiC-anode over the lithiation level. The area in blue marks the delithiation and voltage range of the coin-cell used in the full-cell voltage range from 2.5 to 4.2 V.

Figure 2 Open-circuit-potential (a) and entropic coefficient (b) measurement of the SiC coin-cell with depiction of the full-cell voltage range from 2.5 to 4.2 V [1].

Nickel-rich NMC-type Cathode Similar procedure as presented in section 1.1.1 for the anode coin-cells was applied to the cathode coin-cells. In contrast to the anode coin-cells, the assembled NMC-811 half-cells did not function, when the electrolyte



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was inserted under ambient pressure. Wetting cathode samples under vacuum in a pressure chamber (see Figure 3) (Harro-Höfliger Verpackungsmaschinen GmbH) within the glovebox, the coin cells operated normally. The pressure profile shown in Figure 3 was used for the wetting process. As the NMC-811 electrode is even denser with a porosity of 17.1% than the SiC anode (21.6%) (Mercury porosimetry, PASCAL 140/440 with CD3 dilatometer), capillary and wettability effects may inhibit the electrolyte from entering the pore. After this first phase of wetting, another 70 µl of electrolyte were added to the coin-cells.

Figure 3 The Compression/Vacuum box in the argon-filled glovebox (left) was used to apply the pressure profile (right) for evacuating the pore of the cathode samples to ease the wetting of the porous structure.

Figure 4 gives an impression of the working space in side of the glovebox and the preliminary wetting results of the cathode samples is shown (see “before”), where dry, non-wetted parts appeared on the surface. After the vacuum-assisted wetting process (see “after”), the samples were stored in pouch bag-foils until the coin-cell assembly began.

The open-circuit potential measurements for charge and discharge of the cathode (NMC-811) half-cells were measured in a climate chamber (VT 4021, Vötsch Industrietechnik GmbH) at 25°C combined with a cycler (CTS, BaSyTec). The applied current for the cathode half-cells was set to 80 µA (≈ 0.01C). Again, as the electrodes of the coin-cells were extracted from an already utilized cell, no formation cycles were necessary. The discharge capacity gained from the coin-cell summed up to 8.43 mAh (5.48 mAh cm-2) for NMC-811 and the results are shown in Figure 6, where the area marked in blue refers to the full-cell voltage range from 2.5 to 4.2 V. The entropy profile was measured similarly to the anode profile presented in section 1.1.1. The cathode half-cells were initially set to 4.6 V at 0.1C with a subsequent CV period and termination criterion of C/1000. Afterwards the cathode was lithiated with C/30 at lithiation steps of 6.25 % referring to the measured coin-cell capacity, gaining 17 reference points in total. The entropy profile for the NMC-811 coin-cell is shown in Figure 6.



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Figure 4 Manufacturing process of using the vacuum assisted wetting process of the NMC811 coin blanks.

Figure 5 Open-circuit-potential (a) and entropic coefficient (b) measurement of the NMC-811 coin-cell with

depiction of the full-cell voltage range from 2.5 to 4.2 V [1].

b)

a)



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Full-Cell Measurements The full-cell measurements were used to determine the balancing of anode and cathode in the INR18650-MJ1 cell, as already indicated in Figure 2a and 5a. In addition, the full-cell data is used to validate the simulation results over varying applied current rates at different ambient temperatures for charge and discharge and to evaluate the simulated total heat generation. Therefore, open-circuit-potential-, calorimetric and thermographic measurements are used and shown in this work.

Open-circuit tests and Cell Balancing The test procedure for the open-circuit measurements of the full-cell is shown in Table 1 [1].

Table 1 Open-circuit test procedure [1]

Step Current rate Termination Ambient Temperature

Preconditioning CC 0.1C 2.5V – 4.2V

25°C

Preconditioning CV - Until 3.35 mA

Relaxation 0 4 h

CC 0.033C 2.5V – 4.2V

CV - Until 3.35 mA

The discharge capacity of the full cell (Q0) was measured to 3.560 Ah at C/30 constant current (CC) with additional constant voltage (CV) period. The measured OCP data from the half- and full-cells are used for a differential voltage analysis (DVA), which is shown for the charge scenario of the full-cell in Figure 6. The reconstructed OCP (“NMC811+SiC”) in Figure 6a is derived via extending and shifting [31] the measured half-cell OCPs towards the full-cell capacity level. The residual deviance is shown in Figure 6b, which reveals potential errors of less than 15 mV with an average error of 5.7 mV.

For the differential potential and differential capacity shown in Figure 6c and d, a capacity normalization by multiplying the differential potentials with Q0 is performed [32]. With the aid of the differential potential, the balancing of the full-cell revealed an oversized cathode (≈ 9.4%) and an almost complete use of the anode (> 99%) referring to the specified voltage ranges (see Table 1). The potential differential (see Figure 6b) showed slight deviances with a mean deviation of 230 mV Ah-1. The differential capacity vs. cell voltage for charge in Figure 6d matches the full-cell behaviour with marginal deviances. Four characteristic redox peaks can be observed at 3.42, 3.63, 3.91 and 4.1 V attributed to the NMC-811 cathode, which were seen similar in other works [8].

In sum, the DVA analysis for the charge scenario revealed accurate reconstruction of the full-cell OCP behaviour via the custom-built coin cells and the balancing analysis of the full-cell revealed a significantly oversized cathode. Similar results were gained for the discharge scenario, which is shown in Figure 7.



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Figure 6 DVA analysis of the full- and half-cells with analysing the balancing of the cell for the charge scenario [1].



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Figure 7 DVA analysis of the full- and half-cells with analysing the balancing of the cell for the discharge scenario [1].



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Calorimetric tests The test procedure for the calorimetric measurements of the full-cell is shown in Table 2 [1].

Table 2 Calorimetric test procedure [1]

Step Current rate Termination Initial Temperature

CC 0.2C 2.5V – 4.2V

25°C CV - Until 167.5 mA

Thermal relaxation 0 10 h

In terms of the calorimetry, the heat generation of a pristine MJ1 cell (#1-MJ1) was measured at a 0.2C, 0.5C and 1.0C CC charge- and discharge-rate with an accelerating rate calorimeter (EV-ARC, Thermal Hazard Technology) combined with a cycler (CTS, BaSyTec). Each charge and discharge step was followed by a CV period with a termination criterion of 0.05C at 4.2 V and 2.5 V, respectively. After each step the cell was rested for at least 10 h. The total heat capacity of the cell was determined during the adiabatic conditions in the calorimeter and via the thermography measurements during the period “Relaxation II” (see the following section, Table 3).

Thermographic Tests The test procedure for the thermographic measurements of the full-cell is shown in Table 3 [1].

Table 3 Thermographic test procedure [1]

Regarding the thermography measurements [33], the temperature distribution at the surface of the full-cell (#2-MJ1) and the adjacent copper connectors (1860C006, Feinmetall [34]) was measured during different charge- (0.2, 0,5 and 1.0) and discharge-rates (0.2, 0.5, 1.0 and 2.0) via an infrared camera (A655sc, FLIR Systems Inc.) with an accuracy of ±2 K at four different ambient temperatures (20, 25, 30 and 40°C). To increase temperature accuracy, the infrared thermography temperature data is referenced to a four-wire Pt100 sensor with an absolute accuracy of ±0.15 K at 0°C (DIN/IEC Class A). The optical resolution of 80x480 pixels provides a relative accuracy of ±30 mK between the pixels.


Preconditioning CC 1C 2.5V – 4.2V

20, 25, 30 and 40°C

Preconditioning CV - Until 33.5 mA

Relaxation I 0 4 h

CC 0.2, 0.5, 1 and 2C 2.5V – 4.2V

CV - Until 33.5 mA

Relaxation II 0 1 h



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Turbulent air-flow at 1.0 and 2.0 ms-1 guaranteed convective cooling with a heat transfer coefficient of 22.4 W m-2 K and 32.1 W m-2 K (see Figure 8) in a custom-built climate chamber [33] combined with a cycler (HPS, BaSyTec).

Figure 8 Calculating the convective heat flow of the 18650 cell format [1].

Aging Tests The aging test results were adopted from the data sheet [23,35] of the cell manufacturer, which applied a cyclic aging profile as shown in Table 4 for 500 cycles.

Table 4 Cyclic aging profile [23]


CC-Charge 0.45C 2.5V – 4.2V

25°C CV - Until 100 mA

CC-Discharge 1.20C 4.2V – 2.5V



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Cell-Level Detailed Modelling Two different thermal-electrochemical models were used in WP1 and implemented in the commercial FEM solver COMSOL Multiphysics 5.3a [36]. The first model is the widely applied Newman-type p2D model [24] which is based on porous electrode theory, reaction kinetics and concentrated solution theory [37]. This model was extended by a general energy balance [37] to calculate the volume-averaged temperature of the regarded MJ1 cell. The second model is a multidimensional framework, which incorporates several parallel-connected p2D models (i.e. between the current collectors of the cell), a single 2D electrical model for the current collectors and a single, locally coupled 3D thermal model of the jelly roll. In the following, the theory of both models and the implemented parameterization is discussed in short with reference to the related publication of this report [1].

Single P2D Model

Model Description The electrochemical model used in this work is the widely applied Newman-type p2D model [24]which is based on porous electrode theory, reaction kinetics and concentrated solution theory [37]. The model equations as well as the temperature calculation are summarized in Figure 9. For the single p2D model, this additional thermal model calculates the volume-averaged cell temperature from heat generation due to ohmic losses in the solid and liquid phase (Qs, Ql), reaction overpotential (Qr), entropy change (Qrev) and contact resistance (Qext). Heat transfer to the environment is considered via convection (Qconv) and radiation (Qrad). In case of the thermography measurements, heat conduction via the connectors is also described (Qcon). The reference temperature (Tcon) for the heat conduction was measured on the surface of the connectors.

In this work, the thermal-electrochemical model is extended towards aging mechanistics [38] in form of solid-electrolyte interphase (SEI) growth, which is incorporated in the p2D model as a side-reaction. The approach accounts for lithium-ion (𝜅𝜅𝑆𝑆𝑆𝑆𝑆𝑆) and electron (𝜎𝜎𝑆𝑆𝑆𝑆𝑆𝑆) transport through the SEI, which results in the distinction of the overpotential for the main reaction (i.e. de-/intercalalation, 𝜂𝜂𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚) and the SEI forming reaction (i.e. 𝜂𝜂𝑆𝑆𝑆𝑆𝑆𝑆). The ohmic drops and the related overpotentials can be described according to the work of Kindermann et al. [38]. Therefore, the main and side reaction current can be calculated as

𝑖𝑖𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 = 𝑖𝑖0,𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 ⋅ exp 𝛼𝛼𝑚𝑚 ⋅ 𝜂𝜂𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 ⋅ 𝐹𝐹

𝑅𝑅 ⋅ 𝑇𝑇−exp

−𝛼𝛼𝑐𝑐 ⋅ 𝜂𝜂𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 ⋅ 𝐹𝐹𝑅𝑅 ⋅ 𝑇𝑇

𝑤𝑤𝑖𝑖𝑤𝑤ℎ

𝜂𝜂𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 = Φ𝑠𝑠 − Φ𝑙𝑙 − 𝐸𝐸𝑒𝑒𝑒𝑒,𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑖𝑖𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 ⋅ 𝑅𝑅𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚

𝑖𝑖𝑆𝑆𝑆𝑆𝑆𝑆 = 𝑖𝑖0,𝑆𝑆𝑆𝑆𝑆𝑆 ⋅ −exp −𝛼𝛼𝑐𝑐,𝑆𝑆𝑆𝑆𝑆𝑆 ⋅ 𝜂𝜂𝑆𝑆𝑆𝑆𝑆𝑆 ⋅ 𝐹𝐹

𝑅𝑅 ⋅ 𝑇𝑇 𝑤𝑤𝑖𝑖𝑤𝑤ℎ 𝜂𝜂𝑆𝑆𝑆𝑆𝑆𝑆 = Φ𝑠𝑠 −Φ𝑙𝑙 − 𝐸𝐸𝑒𝑒𝑒𝑒,𝑆𝑆𝑆𝑆𝑆𝑆 − 𝑖𝑖𝑆𝑆𝑆𝑆𝑆𝑆 ⋅ 𝑅𝑅𝑆𝑆𝑆𝑆𝑆𝑆

The parameterization of the main reaction is the same as presented before in this report and the parameterization of the side reaction is defined according to Table 5.



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Table 5 Parameterization of the side reaction incorporated in the single p2D model to account for SEI growth during cyclic and calendric aging.

Figure 9 Overview of the fundamental equation system of the single p2D electrochemical-thermal cell model [1].

Parameter Value*

𝐸𝐸𝑒𝑒𝑒𝑒,𝑆𝑆𝑆𝑆𝑆𝑆 / V 0.4 [38]

𝑖𝑖0,𝑆𝑆𝑆𝑆𝑆𝑆 / A m-2 0.75E-6 *

𝑀𝑀𝑆𝑆𝑆𝑆𝑆𝑆 / kg mol-1 0.162 [39]

𝜌𝜌𝑆𝑆𝑆𝑆𝑆𝑆 / kg m-3 1690 [39]

𝑅𝑅0,𝑆𝑆𝑆𝑆𝑆𝑆 / Ω m2 1E-3 [39]

𝑠𝑠0,𝑆𝑆𝑆𝑆𝑆𝑆 / nm 5E-9 [39]

𝜎𝜎𝑆𝑆𝑆𝑆𝑆𝑆 / S m-1 1E-8 [38]

𝜅𝜅𝑆𝑆𝑆𝑆𝑆𝑆 / S m-1 1E-2 [38]

𝛼𝛼𝑐𝑐,𝑆𝑆𝑆𝑆𝑆𝑆 / - 1*

* Estimated



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Parameterization

Anode Parameterization The dry anode half-cell samples were weighed with a total mass of 37.3 mg (Quintix 224-1S, Sartorius Mechatronics) and with the calculated weight of the current collector (∅ 14 mm x 11 µm, 𝜌𝜌𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑒𝑒𝑐𝑐 =8.95 g cm-3 [40]), the weight of the dry electrode is estimated as 22.1 mg. The current collector thickness was derived from inductively coupled plasma-optical emission spectroscopy (ICP-OES, Varian 7XX-ES ICP-OES Spectrometer, Agilent Technologies), referring to the measured amount of copper and the sample size (∅ 20 mm). The total thickness of the electrode was measured via laser microscopy (VK9710K Violet Laser 408nm, KEYENCE CORPORATION) and micrometer caliper (Micromar 40 EWV, Mahr GmbH), resulting in a coating thickness of 86.7 µm. Mercury porosimetry (PASCAL 140/440 with CD3 dilatometer, PASCAL) revealed porosity values of 21.6% which leads to a total solid volume of 10.1 mm3 for the coin sample. The fraction of silicon in graphite could be determined via ICP-OES to ≈ 3.5 wt.-%. Specific gravimetric capacities of natural graphite [12] and nano-particle sized silicon [41] can be estimated to 330 mAh g-1 and 3600 mAh g-1. Referring to standard compositions of active and inactive material [3,42], 9 wt.-% are assumed to consist of binder and carbon black (combined density of ≈ 1.78 kg m-3 [43,44]), resulting in a content of graphite of 87.5 wt.-%. The maximum theoretical loading (bg) of the anode is calculated [13] to 415 mAh g-1, which is well in line with comparable gravimetric loadings for SiC [12]. Considering 21.6% porosity and the densities (𝜌𝜌) of binder, carbon black and 3.5-87.5 wt.-% SiC (2.24 g cm-3, derived from Ref. [12]), the total volumetric fractions can be calculated [12] to 9% (carbon black/binder) and 69.4 % (SiC) from the gravimetric composition.

The maximum lithium-ion concentration in the anode is estimated to 34684 mol m-3 according to the following equation:

𝑐𝑐𝑠𝑠,𝑚𝑚𝑚𝑚𝑚𝑚 = 𝑏𝑏𝑔𝑔 ∙ 𝜌𝜌 ∙ 𝐹𝐹−1

The particle radius (𝑅𝑅𝑐𝑐,𝐷𝐷50 ) was derived from the mercury porosimetry to 6.1 µm. Both lithiation and delithiation paths are considered to estimate the equilibrium potential [45,46] in the single p2D model for charge and discharge simulation of the full cell, as the silicon doped graphite shows distinct hysteresis effects which is well in line with other works [47]. In order to match the measured capacity of the coin cells to the lithiation level, two reference points were considered at 0 mAh and at the transition of LiC12 to LiC6 [48], which can be clearly seen in the derivative of the potential vs. capacity. Due to the hysteresis effect, the averaged value in capacity between both peaks in the lithiation and delithiation path was used to match approximately the 50% level [49].

Cathode Parameterization Similar to the anode half-cells, the weight of the cathode samples was derived to 37.1 mg with a thickness of 17.3 µm for the aluminum current collector (𝜌𝜌𝑚𝑚𝑙𝑙𝑎𝑎𝑚𝑚𝑚𝑚𝑚𝑚𝑎𝑎𝑚𝑚=2.71 g cm-3 [40]). The composition of 82%-6.3%-11.7% for nickel, manganese and cobalt was determined via ICP-OES and slightly differs from a strictly 80%-10%-10% ratio. Regarding the cathodic porosity of 17.1% and the coating thickness of 66.2 µm, the total solid volume accounts to 8.44 mm3 for the coin sample. A standard gravimetric composition of 96 wt.-% to 4 wt.-% [42] ratio for the active and inactive parts and a crystallographic density of 4.87 g cm-3 for NMC-811 [9] is assumed here. Considering the porosity of 17.1%, the volumetric fractions are calculated [12] to 74.5% (NMC-811) and 8.4% (carbon black/binder). The specific gravimetric capacity of the NMC-811 material is assumed



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to be 275.5 mAh g-1 [9]. The particle radius (𝑅𝑅𝑐𝑐,𝐷𝐷50) is derived as 3.8 µm and thus the theoretical maximum concentration is calculated to 50060 mol m-3.

The lithiation level during both lithiation and delithiation of the OCP is calculated via setting two points at the measured half-cell capacity and at 0 mAh in reference to 275.5 mAh g-1 [9]. The derived lithiation degrees are well in line with other findings [8].

The determination of the lithiation degree of both electrodes is applied similarly for the entropic coefficients. The complete parameterization of the NMC-811/SiC porous electrodes is given in Figure 10 as published in the research paper [1].

Figure 10 Summary of the electrochemical-thermal p2D model parameterization of the INR18650-MJ1 cell [1].



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Gas-chromatography combined with mass spectroscopy (Clarus 560/600 GC/MS, PerkinElmer LAS GmbH) of the electrolyte in the MJ1 revealed contents of EC, EMC and dimethyl carbonate (DMC) and the values for a 1 M LiPF6 in polypropylene carbonate (PC)/EC/DMC were used as the most appropriate set available in literature from Valøen and Reimers [50] (see Figure 11).

As transport correction for the liquid diffusion coefficient (𝐷𝐷𝑙𝑙 ), the ionic conductivity (𝜅𝜅𝑙𝑙 ) and the electrical conductivity in the active material (𝜎𝜎𝑠𝑠 ) [25], the Bruggeman correlation [51] was used with increased coefficients (≈ 23%) for the cathode to account for the low porosity of 17.1%.

Figure 11 Parameterization of the electrolyte (see Ref. [50] = “I”) in the p2D model [1].

Multi-Dimensional Model Approach The MuDiMod consists of several p2D models calculating electrochemical potentials and lithium-ion concentrations perpendicular to the current collectors, the 2D model accounting for the electrical potential along the current collectors and the 3D model calculating the local temperature within the jelly roll of the cylindrical cell. As the basic MuDiMod framework is already published in previous works [27,28] with an extension of using effective spatial discretization techniques [52], only novel implemented techniques or submodels are outlined here. An overview of the additionally solved DAE system for the 2D and 3D submodels is given in Figure 12.

An additional charge balance (see Figure 12) guarantees the charge transfer from the p2D models to be in agreement to the total current applied at the cell's tabs in the 2D model in order to avoid slight deviances in the SoC calculation.



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Figure 12 Overview of the fundamental equations incorporated in the 2D electrical and 3D thermal model in the MuDiMod [1].

Moreover, a fully spatially resolved 3D thermal model for cylindrical cells is incorporated which enables for local coupling of heat generation calculated in the p2D and 2D models and temperature distribution along the electrodes instead of using lumped thermal models [25]. The local coupling enables for analysing tab pattern influences on heat generation, temperature distribution and local differences in SoC [53].

In general, a computationally efficient mathematical description of the coordinate transformation between a spirally wound domain and its unwound representation is needed for a lean exchange of local states between the related submodels. A variable extrusion algorithm proofed to enable a coupling of a planar 2D and spirally wound 3D model whilst using only 35% of RAM and saving 97% of computation time with sufficient accuracy compared to fully-discretized models [54]. Based on this approach, an extended coupling algorithm transfers the local heat generation of the p2D and the 2D model forward to the 3D thermal model via coordinate mapping, incorporating a lumped finite element method (FEM) discretization-mesh in the 3D model. By implication, the local temperature is transferred backwards to the 2D model and the p2D models.



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Model Description The multiphysical coupling of the MuDiMod is illustrated in Figure 13.

Figure 13 Model overview of the MuDiMod depicting the parallel-connected p2D models between the current collectors, the 2D electrical model and the 3D thermal model [1].

The basic multi-dimensional model description is presented in previous work [25,27,52] and the extension for the local coupling of heat generation and temperature between the 2D and 3D model is explained here.

Similar to other works [54,54–56], the coordinate mapping (i.e. variable extrusion algorithm) of 2D-plain to 3D-spirally-wound geometries uses the correlation of arc length (Λ) and azimuthal angle (Ψ𝑚𝑚𝑐𝑐𝑐𝑐, see Sturm et al. [1]) of the spirally wound jelly roll as follows:

Λ(Ψ𝑚𝑚𝑐𝑐𝑐𝑐) =𝐿𝐿𝑠𝑠𝑠𝑠𝑚𝑚𝑐𝑐𝑠𝑠

4𝜋𝜋[(cosh(𝑎𝑎𝑎𝑎𝑐𝑐𝑠𝑠𝑖𝑖𝑎𝑎(𝛹𝛹𝑚𝑚𝑐𝑐𝑐𝑐 + 4𝜋𝜋)) ⋅ (𝛹𝛹𝑚𝑚𝑐𝑐𝑐𝑐 + 4𝜋𝜋)) + arcsin (𝛹𝛹𝑚𝑚𝑐𝑐𝑐𝑐 + 4𝜋𝜋) ]

Looking into the 3D-spiral geometry of the jelly roll, every point in the 𝑥𝑥′′ − 𝑦𝑦′′-plain is dened by an azimuthal angle and the radial distance from the starting point. Hence, every (𝑥𝑥′′,𝑦𝑦′′)-coordinate pair can be correlated to an (Ψ𝑚𝑚𝑐𝑐𝑐𝑐 ,𝑅𝑅𝑚𝑚)-coordinate pair according to



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𝑥𝑥′′𝑦𝑦′′ = cos(𝛹𝛹𝑚𝑚𝑐𝑐𝑐𝑐 ) ⋅ Ψ𝑚𝑚𝑐𝑐𝑐𝑐 ⋅

𝐿𝐿𝑠𝑠𝑠𝑠𝑚𝑚𝑐𝑐𝑠𝑠2𝜋𝜋

+ 𝑅𝑅𝑚𝑚

sin(𝛹𝛹𝑚𝑚𝑐𝑐𝑐𝑐 ) ⋅ Ψ𝑚𝑚𝑐𝑐𝑐𝑐 ⋅𝐿𝐿𝑠𝑠𝑠𝑠𝑚𝑚𝑐𝑐𝑠𝑠

2𝜋𝜋+ 𝑅𝑅𝑚𝑚

𝑓𝑓𝑓𝑓𝑎𝑎 Ψ𝑚𝑚𝑐𝑐𝑐𝑐 ∈ 0, 42.9𝜋𝜋

𝑅𝑅𝑚𝑚 ∈ 2 ⋅ 𝐿𝐿𝑠𝑠𝑠𝑠𝑚𝑚𝑐𝑐𝑠𝑠:𝐿𝐿𝑠𝑠𝑠𝑠𝑚𝑚𝑐𝑐𝑠𝑠

10: 3 ⋅ 𝐿𝐿𝑠𝑠𝑠𝑠𝑚𝑚𝑐𝑐𝑠𝑠

To discretize the azimuthal direction, 2148 nodes are used (≈ 0.3 mm element-length) to calculate the arc-length from inner start (Ψ𝑚𝑚𝑐𝑐𝑐𝑐 = 0) to the outer end (Ψ𝑚𝑚𝑐𝑐𝑐𝑐 = 49.2𝜋𝜋 ) of the 61.5 cm length of electrode in the INR18650-MJ1 cell. To discretize the radial direction (i.e. thickness of electrode stack), 10 spirals are defined by increasing the starting point (𝑅𝑅𝑚𝑚 = 2 ⋅ 𝐿𝐿𝑠𝑠𝑠𝑠𝑚𝑚𝑐𝑐𝑠𝑠) in 35.8 µm-steps 𝐿𝐿𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠

10. In sum, a total number of 21480

nodes were used to guarantee proper matching with the lumped FEM-mesh in the 3D model.

Looking into the unwound, plain electrode geometry in the 2D model, the 𝑥𝑥′-coordinate along the electrode corresponds directly to the arc length (Λ) and is correlated to the azimuthal angle as shown in the publication of Sturm et al. [1]. The height of the electrode (𝐻𝐻) corresponds to the 𝑦𝑦′- and 𝑧𝑧′′-coordinate in the 2D and 3D model and can be correlated directly.

The local heat generation is extruded from the 2D model to the 3D model using the FEM. Therefore, the calculated heat generation terms from the p2D models and the 2D model are referenced to the thickness of the corresponding layers and multiplied with the thickness ratio of corresponding layers and the total stack thickness.

Parameterization The parameterization of the 2D electrical model includes the electrical conductivities of copper ([57], II) and aluminium ([58], III) as shown with temperature dependency in Figure 14 [1]. The height and the length of the electrodes was measured after the disassembly procedure on the unwound anodes and cathodes of the INR18650-MJ1 cell.

Figure 14 Parameterization of the 2D electrical model [1].

The parameterization of the 3D thermal model is shown in Figure 15 [1]. The densities, heat capacities and heat conductivities are mainly adopted from the work Chen et al. [59] (see I Figure 15), beside other references (i.e. II= [40], III= [12], IV= [9], V= [60], VI= [61]). The effective values for the electrode stack (see “stack” in Figure 15) are calculated from superposition of the single layers of each material. For the perpendicular and lateral heat conductivity, calculations in parallel and in series superposition of the single layers and its related conductivities were considered [59].



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Figure 15 Parameterization of the 3D thermal model [1].

Model Validation The model validation part shows the accuracy of the simulation results in reference to the measured full-cell data including the calorimetric and thermographic experiments. Both the single p2D model and the MuDiMod framework are analysed and a comparison between these models will evaluate the error when electrode utilization is homogenized over length and width of the current collectors (i.e. single p2D model) instead of local potential, concentration and temperature calculation as implemented in the MuDiMod.

Calorimetric Tests The calorimetry measurements at C/5 discharge and charge are used to validate the simulated cell voltage, heat generation and temperature with focus on describing properly the thermal behaviour of the full-cell.

Using the calculated heat capacity of 42.1 J K-1 of the full-cell, the simulation results from the single p2D-model and the MuDiMod are shown in Figure 16 for discharge and charge at C/5.



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Figure 16 Calorimetric experimental and simulation results (single p2D-model and MuDiMod) for the charge (d, e, f) and discharge (a, b, c) scenario using the cell voltage (a, d), heat generation (b, e) and temperature (c, f)

[1].

The heat dip in Figure 16b (≈ 50% DoD) can be explained by the negative entropic heat of the SiC active material. The overall cell behaviour is predicted quite accurate by the single p2D and the MuDiMod simulation with an average error of 13.4/11.9 mV and 10.5/16.2 mV for the cell voltage under discharge/charge, respectively.

The average temperature errors under discharge/charge resemble the measured temperature with 0.3/0.1 K and 0.8/0.5 K for the single p2D and the MuDiMod. In terms of the C/5 charge simulation, both models show the fuzziness of the measured entropic coefficient [1] at low cell SoC levels (see Figure 16e), but the calculated temperature is nevertheless well in line with the measurement with an acceptable deviation below 1 K on average.



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The charge and discharge simulation of the calorimetry measurements show an accurate description of the measured electrical and thermal behaviour of the MJ1 cell and a proper validation especially for the calculated heat and temperature in the 0D- (single p2D) and 3D-thermal model (MuDiMod) was shown.

Thermographic Tests Thermography measurements of the full-cell are used to validate the simulated cell behaviour of both models in terms of varying constant charge- and discharge-rates under varying ambient temperatures and convective cooling conditions [33]. The experimental and simulated cell voltages at 25°C as well as the residual error are shown in Figure 17.

Following the data sheet [23], a 0.5C charging rate is advised for the MJ1 cell while the maximum C-rate during charge is set to 1C. Higher C-rates such as 2C were only applied for discharge. As shown in Figure 17, the simulated data (a, c, e and g) match the measured cell voltage quite well during charging and at 1C, an average error of 14.5 mV and 13.7 mV and a mean squared error (MSE) of ≈ 0.4 (mV)2 is seen for the single p2D model and the MuDiMod. The largest error during charge (see Figure 17 b, d, f and h) can be observed at the beginning due to the steep voltage increase referring to the anode OCP at low lithiation degrees. Similarly, the maximum error appears at the end of the discharge. The simulated cell voltages at discharge in Figure 17 match the measured data quite well and at 1C, an average error of 13.5 mV and 15.2 mV and a MSE of 0.3 (mV)2 and 0.5 (mV)2 appear for the single p2D and the MuDiMod.

Only marginal differences between the single p2D and the MuDiMod can be observed except for 2C (see Figure 17 g and h), where approximately 20% reduced errors for the mean cell voltage are seen in the MuDiMod simulation results. Regarding the MuDiMod simulation results, current distribution on the current collectors vary ±5% around the mean value of 9.4 mA cm-2, which cannot be described by a single p2D model assuming homogeneous electrode utilization, resulting in the appearing deviance between the two models.



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Figure 17 Cell voltage (a, d, e, g) validation of the MuDiMod and single p2D model at different charge and discharge rates with depiction of the simulation error (b, d, f, h) [1].

In terms of the cell voltage, accurate simulation results appeared for both models and the temperature calculation is validated in Figure 18 and 19 at different ambient temperatures for the single p2D model and the MuDiMod, respectively.

During charge at 25°C (see Figure 18a), maximum temperature errors of 0.4 K and 0.6 K with a mean deviance of 0.1 K and 0.2 K appear at 0.2C and 0.5C respectively.



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At 1C, the maximum and mean error account for 1.2 K and 0.34 K, still revealing sufficient accurate simulation results. The highest deviations during discharge shown in Figure 18b appear at 2C with 1.4 K and 0.27 K for the maximum and mean error.

Regarding the temperature profiles in the ambient temperature range from 20°C up to 40°C in Figure 20 c and f, the simulated temperatures at 1.0C reveal an accurate prediction of the cell behaviour with deviances in the range of ±1 K (see Figure 18 d and f).

Similar results were seen for the analysis of the MuDiMod simulation results in Figure 19.

The thermography validation under both (see Sturm et al. [1]) convective cooling conditions show accurate simulation of the temperature for charge and discharge and reveal errors, which are below 0.5 K on average and thus are in the range of the measurement accuracy.

The detailed error analysis of the thermography validation at 1 m s-1 for the single p2D model and the MuDiMod are given in Figure 20 and 21.



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Figure 18 Validation of the volume-averaged temperature calculation in the single p2D model for different charge and discharge rates as well as different ambient temperatures [1].



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Figure 19 Validation of the locally calculated temperature in the MuDiMod for different charge and discharge rates as well as different ambient temperatures [1].



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Figure 20 Validation of the single p2D model using the thermography measurement under convective cooling I [1].

Figure 21 Validation of MuDiMod using the thermography measurement under convective cooling condition I [1].



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Aging Tests As basic data for validating calendric and cyclic aging via SEI-growth at the SiC anode, the cell manufacturer’s provided aging study [23] was used as it covered the full SoC range of the cell (i.e. 2.5 to 4.2 V of the cell voltage). The simulation study referring to the procedure presented in Table 4 is shown in Figure 22 via the altering of the cell voltage (a), the overall capacity fade (b) and the SEI-layer thickness growth (c) at the anode/separator interface.

Figure 22 Aging simulation study for the INR18650-MJ1 cell for SEI growth during cyclic aging referring to the cell voltage (a), overall capacity fade (b) and SEI-layer thickness growth (c).

The results show sufficient accuracy to describe the aging behaviour of the INR18650-MJ1 cell and taking these preliminary results as basis for the future work on aging modelling, lithium-plating [62] and stripping [63] as well as cathode-electrolyte interphase (CEI) [64] can be included in the thermal electrochemical p2D model.



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CONCLUSIONS A full electrochemical-thermal parameterization of a Newman-type [24] p2D model for a high-capacity and highly densified NMC-811/SiC electrode pair is presented in this report, including measured open-circuit potentials, entropic coefficients, porosities and particle sizes gained from mercury porosimetry as well as ICP-OES analysis of the active material and the electrolyte.

For both charge and discharge, DVA analysis of full- and half-cells revealed marginal deviations and simulation results for calorimetry and thermography measurements in a range of 20°C up to 40°C ambient temperature showed the validity of the presented parameterization.

The extension of the thermal-electrochemical p2D model towards aging mechanistics such as SEI growth revealed accurate prediction of the capacity fade for cyclic aging. Future modelling work in the EVERLASTING project will focus on extending this approach for lithium plating and stripping mechanistics as well as cathode-electrolyte interphase growth and validate the simulation models with cyclic aging data at 0°C, 10°C, 25°C and 40 °C at different applied current rates.

Comparison of simulation results of the single p2D and the multi-dimensional model made it clear that a more detailed evaluation of the charge and discharge behaviour should be based on the multi-dimensional model. This is important, especially when higher current rates cause larger gradients for potentials and concentrations over the length and height of the electrode and the assumption of an homogeneously utilized electrode may not predict the overall cell behaviour sufficiently accurate enough anymore.



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D1.1 – Report on electrochemical cell model...2018/11/30 · cell, which is the project cell of the EVERLASTING project. The experimental part is used to parameterize and validate