ANL-11/XX

ARGONNE NATIONAL LABORATORY

9700 S. Cass Ave. Argonne, IL 60439 USA

DRAFT REPORT SUBMITTED TO THE ENVIRONMENTAL PROTECT ION
AGENCY FOR PEER-REVIEW



### Modeling the Performance and Cost of Lithium-Ion Ba tteries for

Electric-Drive Vehicles

by

Paul Nelson, Kevin Gallagher and Ira Bloom

Electrochemical Energy Storage Theme Chemical Sciences and Engineering Division

January 15, 2011ii This Page Intentionally Left Blankiii 

### TABLE OF CONTENTS

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

................................................... ................... vii

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

................................................... ..................... ix

ABBREVIATIONS .....................................

................................................... ................... x

LIST OF SYMBOLS ...................................

................................................... ................. xii

ACKNOWLEDGEMENTS ..................................

................................................... ........ xv

EXECUTIVE SUMMARY .................................

................................................... ........ xvi

1. Introduction ...................................

................................................... ...............................1

2. Battery and Cell Design Format .................

................................................... .................2

2.1 Cell Design...................................

................................................... ...................3

2.2 Module Design ................................

................................................... ...............4

2.3 Battery Pack Design ..........................

................................................... .............5

3. Modeling of Battery Design and Performance .....

................................................... .......6

3.1 Criteria for Power, Energy, and Life .........

................................................... ....6

3.2 Voltage at Maximum Power .....................

................................................... .....8

3.3 Governing Equations ..........................

................................................... .........14

3.4 Calculation of the ASI .......................

................................................... ..........15

3.4.1 Current Collection Resistance ............. .............................................17

3.4.2 Potential and Current Distribution ........ ...........................................19

3.4.3 Determination of Module Terminal Size ...... ....................................21

3.5 Calculation of Battery Dimensions ............

................................................... ..21

3.5.1 Cell Dimensions ...........................

................................................... .22

3.5.2 Module Dimensions ......................... ................................................22iv

3.5.3 Battery Pack Dimensions ................... ..............................................23

3.6 Additional Considerations ....................

................................................... .......23

3.6.1 Maximum Electrode Thickness ............... ........................................23

3.6.2 Accounting for Parallel Cell Arrangements . ....................................24

4. Modeling of Battery Pack Manufacturing Cost ....

................................................... .....25

4.1 Approach .....................................

................................................... .................25

4.2 Materials Costs and Purchased Items ..........

................................................... 26

4.2.1 Battery Specific Materials Cost ........... ............................................26

4.2.2 Purchased Items Cost ...................... .................................................30

4.3 Baseline Manufacturing Plant .................

................................................... .....31

4.3.1 Receiving and Shipping .................... ...............................................32

4.3.2 Electrode Materials Preparation ........... ............................................34

4.3.3 Electrode Coating .........................

................................................... .34

4.3.4 Calendering ...............................

................................................... ....35

4.3.5 Inter-Process Materials Handling .......... ..........................................35

4.3.6 Electrode Slitting ........................

................................................... ..36

4.3.7 Final Electrode Drying .................... .................................................36

4.3.8 Control Laboratory ........................

................................................... 36

4.3.9 Cell Stacking .............................

................................................... ....37

4.3.10 Current Collector Welding ................ .............................................37

4.3.11 Enclosing Cell in Container .............. .............................................37

4.3.12 Electrolyte Filling and Cell Sealing ..... ..........................................38

4.3.13 Dry Room Management ...................... ...........................................38v

4.3.14 Formation Cycling, Final Cell Sealing, etc ....................................38

4.3.15 Module and Battery Assembly .............. .........................................39

4.3.16 Rejected Cell and Scrap Recycle .......... .........................................40

4.3.17 Baseline Plant Summary ................... .............................................41

4.4 Adjustment of Costs for Rates ................

................................................... .....41

4.5 Plant Investment Costs .......................

................................................... ..........43

4.6 Unit Costs for Battery Pack ..................

................................................... .......44

4.6.1 Variable Costs ............................

................................................... ...44

4.6.2 Fixed Expenses ............................

................................................... .45

4.6.3 Profits ...................................

................................................... .........46

4.6.4 Battery Pack Warranty Costs ............... ............................................46

4.7 Summary of Baseline Battery Cost .............

................................................... .46

5. Description of Spreadsheet Model and Instruction s for Use ........................................4 9

5.1 Background ...................................

................................................... ...............49

5.2 Instructions .................................

................................................... ..................49

5.2.1 Enabling Calculation ...................... ..................................................4 9

5.2.2 System Selection Worksheet ................ ............................................50

5.2.3 Battery Design Worksheet .................. .............................................50

5.2.4 Remaining Worksheets ...................... ..............................................54

5.3 Battery Design Format Requirements ........... ..................................................5 7

5.4 Troubleshooting and General Advice ........... ..................................................5 7

6. Illustrated Results ............................

................................................... ...........................58

6.1 Number of Cells in Series ....................

................................................... ........58vi

6.2 Battery Packs for HEVs........................

................................................... ........58

6.3 Battery Packs for EVs ........................

................................................... ..........61

6.4 Parallel-Connected Cell Groups and Electrode T hickness .............................63

6.5 Effects of Manufacturing Scale on the Price of the Pack ...............................64

7. Future Work ....................................

................................................... ...........................67

7.1 Thermal Modeling .............................

................................................... ..........67

7.2 Optimum Battery Voltage for Minimum Drivetrain Cost ..............................67

7.3 Multipurpose Battery Manufacturing Plants .... ...............................................68

7.4 Stand-Alone Graphical User Interface for Model ...........................................68

References ........................................

................................................... ..............................69vii 

### LIST OF FIGURES

2.1 Prismatic cell and module design for battery p acks .............................................. ..............2

2.2 Cell sandwich inside of prismatic pouch cells

................................................... .................3

2.3 Coated current collector foil for prismatic el ectrodes .......................................... ...............4

3.1. Summary flow of the design model ............

................................................... .....................7

3.2 a) Required change in [V/U] to maintain rated power with increases in internal resistance over the life of the battery. b) Increa se in current due to lowered [V/U] .........10

3.3 Change in heat rejection requirement from incr eases in resistance for batteries with different designed voltages at maximum power .....

................................................... .......11

3.4 Efficiencies for batteries designed to achieve maxi mum power at different fractions of their open-circuit voltage .......................

................................................... ........................13

3.5 The change in current and potential within the posi tive and negative foils. The current collection design results in a uniform current dist ribution along the length of the foil ....20

4.1 Metal ingot cost contribution to the current c ollector foils over a 20 year period ............30

4.2 Baseline lithium-ion battery manufacturing pla nt schematic diagram .............................3 2

4.3 Breakdown of installed capital equipment costs for the baseline plant ........................... .43

4.4 Breakdown of unit costs for baseline battery w ith total price to OEM of $2428 .............48

5.1 Iteration must be enabled for the spreadsheet model to function ................................ .....49

5.2 The specific cell chemistry for the battery design is selected on the System Selection
worksheet ........................................

................................................... ...............................50

5.3 System Selection worksheet ...................

................................................... .......................51

5.4 Top portion of Battery Design worksheet .......

................................................... ...............52

5.5 Middle portion of Battery Design worksheet ....

................................................... .............53

5.6 Bottom portion of Battery Design worksheet ....

................................................... ............55

5.7 Summary of Results worksheet ..................

................................................... ...................56viii

6.1 The effect of the number of cells for LMO-Gr, 60-kW , PHEV20 packs with 7.14 kWh total energy (70% useable) .......................

................................................... ......................58

6.2 Cell area-specific impedance (ASI) for various cell chemistries for 25-kW HEV battery packs delivering full power at about 238 A for 2 sec at 80% OCV .....................59

6.3 Volume, voltage and maximum current for 1.6-kWh lit hium-ion battery packs as a function of pack power for packs delivering full p ower .............................................. .....60

6.4 Battery pack price to OEMs at 100,000 packs per yea r manufacturing rate for 1.6-kWh lithium-ion battery packs as a function of pack pow er ................................................ .....61

6.5 Weight and volume of electric vehicle battery packs with LFP, LMO, and NMC electrodes versus graphite designed to deliver 15 0 kW of power at about 425 A ...........62

6.6 Battery pack price to OEM for LFP-G, LMC-G and NMC-G battery packs ...................63

6.7 Battery pack cost as a function of number of pa rallel cells and for different maximum
electrode thicknesses ............................

................................................... ..........................64

6.8 The effects of manufacturing rate on the price calc ulated by the model for battery packs of various cell chemistries, power capabilit ies and vehicle types ..........................65ix 

### LIST OF TABLES

3.1 Criteria for designing batteries for a specifi c end-use application .............................. ........6

4.1 Details of stated costs for cathodes, anodes, electrolyte, and separator ........................ ...27

4.2 Cost equations for purchased items ...........

................................................... ....................31

4.3 Summary table of the baseline plant ..........

................................................... ....................33

4.4 Materials yields during electrode and cell fab rication .......................................... ............40

4.5 The effect of processing rate (R) on cost for various scale factors ............................. ......42

4.6 Battery pack manufacturing investment costs ..

................................................... .............44

4.7 Unit cost of battery pack ....................

................................................... ............................45

4.8 Summary of results for cost of baseline battery and that of similar batteries with double the power and double the capacity of the ba seline battery ....................................4 7x 

### ABBREVIATIONS

ASI area specific impedance

BOL beginning of life

DMC dimethyl carbonate

EC ethylene carbonate

EMC ethyl methyl carbonate

EOL end of life

EV electric vehicle

Gr graphite

GSA General, Sales, and Administration

HEV hybrid electric vehicle

HEV-HP high-power assist hybrid electric vehicle

LCO lithium cobalt oxide

LFP lithium iron phosphate

Li lithium

Li-ion lithium-ion

LMO lithium manganese spinel

LMR lithium and manganese rich

LTO lithium titanate spinel

microHEV micro or mild power assist hybrid electric vehicle

NCA lithium nickel cobalt aluminum oxide

NMC lithium nickel manganese cobalt oxide

NMP N-Methyl-2-pyrrolidonexi

OCV open-circuit voltage

OEM original equipment manufacturer

PE polyethylene

PEP polyethylene terephthalate

PHEV plug-in hybrid electric vehicle

PP polypropylene

R&D research and development

SOC state of charge

USGS United States Geological Surveyxii 

### LIST OF SYMBOLS

Section 3 and 5

a ratio of interfacial area to electrode volume, cm -1

A pos area of the positive electrode, cm 2

A term area of the terminal, cm 2

ASI energy area specific impedance for energy, ohm cm 2

ASI power area specific impedance for power, ohm cm 2

C cell capacity, Ah.

C p specific heat capacity, J/g K

E total energy, Wh

F Faraday constant, 96485.3 C/mol

H j height of j , cm

H/W aspect ratio of pouch cell

i
o exchange current density related to the interfacial area, A/cm 2

I average current density, A/cm 2

I lim ionic ionic limiting current density, A/cm 2

I
n local current density, A/cm 2

L j thickness of j , cm

m j mass of j , g

N j number of j

P battery power, W

P batt maximum designed battery power, W

q heating rate, Wxiii

Q specific capacity of the electrode, mAh/g

r C C-rate, h -1

r C,lim limiting C-rate, h -1

r j radius of j , cm

R universal gas constant, 8.3144 J/mol K

R j resistance of j , ohm

T temperature, K

t time, s

U ocv,P open-circuit voltage at SOC for power, V

U ocv,E open-circuit voltage at SOC for energy, V

V cell cell voltage, V

v square root of dimensionless exchange current

[V/U] fraction of the open-circuit voltage

W j width of j

X comp compression factor

α constant, ohm cm 3

β constant, ohm cm 2

ε act volume fraction of active material

Φ 1,k metal potential of foil k , V

ρ j density of j , g/cm 3

σ j conductivity of j , S/cmxiv

Section 4

C capital cost of an installed equipment for the desi gned battery, $

C
o capital cost of an installed equipment for the base line plant battery, $

p power factor

R designed battery processing rate for specific proce ss step

R
o baseline plant processing rate for specific proce ss stepxv 

### ACKNOWLEDGEMENTS

Support from the Vehicle Technologies Program, Hybr id and Electric Systems, initially under Tien Duong and now David Howell, at the U.S. Depart ment of Energy, Office of Energy Efficiency and Renewable Energy, is gratefully ackn owledged. The submitted manuscript has been created by UChicago Argonne, LLC, Operator of Argonne National Laboratory (“Argonne”). Argonne, a U.S. Department of Energy O ffice of Science laboratory, is operated
under contract no. DE-AC02-06CH11357. The U.S. Gove rnment retains for itself, and others acting on its behalf, a paid-up nonexclusive, irrev ocable worldwide license in said article to reproduce, prepare derivative works, distribute cop ies to the public, and perform publicly and display publicly, by or on behalf of the Government . We especially thank Danilo Santini of Argonne’s Transportation R&D Center for his support and suggestions in carrying out this study. Ralph Brodd reviewed our baseline plant and made se veral suggestions which we have incorporated in the present design. Fritz Kalhammer and Haresh Kamath of the Electric Power
Research Institute have reviewed our work over seve ral years and made suggestions that resulted in improvements. The work was done under the direc tion of Dennis Dees and Gary Henriksen of Electrochemical Energy Storage who provided guidanc e in carrying out the work and preparing this manuscript.xvi 

### EXECUTIVE SUMMARY

This report details a design and cost model develop ed at Argonne National Laboratory for lithium-ion battery packs used in automotive transp ortation. The model designs the battery for a specified power, energy, and degree of powertrain e lectrification. The cost of the designed battery is then calculated by accounting for every step in the lithium-ion battery manufacturing process. The assumed annual production level direct ly affects each process step. The total cost to the original equipment manufacturer calculated by t he model includes the materials, manufacturing, and warranty costs for a battery pro duced in the year 2020. At the time this report is written, this calculation is the only publically available model that performs a bottom-up lithium-ion battery design and cost calculation.

The purpose of the report is to document the equati ons and assumptions from which the model
has been created. A user of the model will be able to recreate the calculations and perhaps more importantly, understand the driving forces for the results. Instructions for use and an illustration of model results are also presented. Almost every v ariable in the calculation may be changed by the user to represent a system different from the d efault values pre-entered into the program.

The model will be openly distributed to the public in the year 2011. Currently, the calculations
are based in a Microsoft ® Office Excel spreadsheet. Instructions are provide d for use; however, the format is admittedly not user-friendly. Future work is proposed to create a more intuitive user-interface with tools to prevent inappropriate values from being entered. A version that is more user-friendly will allow for wider adoption of the model.1 

### 1. Introduction

The recent penetration of lithium-ion (Li-ion) batt eries into the vehicle market has prompted interest in projecting and understanding the costs of this family of chemistries being used to electrify the automotive powertrain. The model desc ribed here-in is a calculation method that was developed at Argonne for estimating the manufac turing cost and performance of Li-ion batteries for electric-drive vehicles including hyb rid-electrics (HEV), plug-in hybrids (PHEV), and pure electrics (EV). To date, a number of cost models of various levels of detail have been published in different forms. 1-10 Most available cost models for batteries are based on a single linear equation dependent on the power and energy r equired such as $/kWh = a + b *kW. While a simplistic relation like this is attractive, it is only approximate and provides little guidance in reducing costs. The cost of a battery will change d epending upon the materials chemistry, battery design, and manufacturing process. 11,12 Therefore, it is necessary to account for all three areas with a bottom-up cost model. Other bottom-up cost m odels exist but are not available to the general public and have not been explicitly detaile d in an open document. The motivation for this work is based on a need for a battery cost model th at meets the following requirements:

1. Open and available to the entire community 2. Transparent in the assumptions made and method of calculation 3. Capable of designing a battery specifically fo r the requirements of an application 4. Based on a bottom-up calculation approach to a ccount for every cost factor

The model is the product of long-term research and development at Argonne National Laboratory. Over a period of years, Argonne has dev eloped methods to design Li-ion batteries for electric-drive vehicles based on modeling with Microsoft ® Office Excel spreadsheets. 11-18
These design models provided all the data needed to estimate the annual materials requirements for manufacturing the batteries being designed. Thi s facilitated the next step, which was to extend the effort to include modeling of the manufa cturing costs of the batteries. In the following sections of this document, a model is presented tha t meets the above criteria and may be used to analyze the effect of battery design and materials properties on the cost of the final battery pack. Use of the model requires some basic knowledge of b attery packs; however, a user does not need to be an expert. For instance, the number of cells and thus battery pack voltage must be specified by the user. However, default values are available for more specific requirements such as experimentally measured values. In this way, a pers on with reasonable knowledge of batteries may be able to conduct cost comparisons and “what i f” studies.

The battery pack design and cost calculated by the model represent projections of a 2020 production year and a specified level of annual bat tery production, 10,000-1,000,000. As the goal is to predict the future cost of manufacturing batt eries, a mature manufacturing process is assumed. The model designs a manufacturing plant wi th the sole purpose of producing the battery being modeled. The assumed battery design a nd manufacturing facility are based on common practice today but also assume some problems have been solved to result in a more efficient production process and a more energy dens e battery. Our proposed solutions do not have to be the same methods used in the future by i ndustry. We simply assume the leading battery manufacturers, those having successful oper ations in the year 2020, will reach these ends by some means.2 

### 2. Battery and Cell Design Format

Various cell and battery design concepts are under development at battery manufacturers. The exact design of the battery does not have an import ant effect on the cost for a set cell chemistry system; the amounts of electrode materials and the number, capacity and electrode area of the cells, are the determining cost factors. The most c ommon cell designs for batteries nearing largescale production are cylindrical wound cells, flat wound cells, and prismatic cells with flat plates. Cylindrical cells probably have a slight advantage for the assembly of the electrode-separator unit because of the ease of making a cylindrical wi nding. For the different cell designs, there are small differences in the weights of the terminal ex tensions and the procedures for connecting these extensions to the current collector sheets, w ith a small advantage for flat plate cells. The flat-wound and flat-plate cells form a more compact module and have better heat rejection capabilities than the cylindrical cells; although, each cell design can be adequately cooled for most applications. These small differences would ha ve minor effects on the cost of batteries produced in high volume in a mature, automated prod uction plant. We conclude that the cost
calculations would be relevant for batteries differ ing considerably from the selected design approach.

To provide a specific design for the calculations, a prismatic cell in a stiff-pouch container and a double-seamed module container was selected (Fig. 2 .1). For this design, calculation of the
current collector and terminal resistances are easi ly done. The electrical performance is near optimum in a compact, light-weight configuration. I t is unlikely that we have selected the most viable design in this short study; there may be ser ious flaws in some details. However, the overall performance and low cost for the selected d esign will be challenging to match and will only be met by the most successful manufacturers, t hose that will dominate the market.

Figure 2.1 Prismatic cell and module design for battery packs Terminal Seal Polymer Seal of

Cell Container

to Terminal

Ultrasonic Welds

of Terminal to
Collector Foils

Cell Cross-Section Battery Module Double-Seamed

Module Closure Heat Transfer Surfaces on Top and Bottom of
Container in Contact with Cell Edge Seals

Cell Terminal

Connections

Cell with Stiff, MultiLayer Container Polymer Edge Seal3

2.1 Cell Design

The prismatic cell of this design embodies individu al positive and negative electrodes consisting
of current collector foils coated with electrode ma terials on both sides. The current collectors are usually solid copper and aluminum foils for the pos itive and negative electrodes respectively. An illustration of a segment of the cell is detailed i n Figure 2.2. Each electrode is made up of active material particles held together by a polymeric bin der. A conductive additive, carbon black and/or graphite, is added to the positive electrode and sometimes to the negative electrode. The electrodes and separator each have porosity that is filled with the electrolyte solution. During discharge, the Li-ions move from the negative elect rode particles into the electrolyte, across the separator, and then insert into the particles compo sing the opposite positive electrode. The electrons simultaneously leave the cell through the current collection system and then enter through the opposite side after doing external work . The materials currently used in Li-ion cells are based on an intercalation mechanism. In this pr ocess, the Li-ion is inserted into or removed from the crystal structure of the active material. The oxidation state of the active material, or host, is concurrently changed by gaining or losing an electron. Other electrode materials based on conversion reactions or electrodeposition could be implemented into the model if desired.

separator negative
electrode + +

–

Li + positive
electrode e -

separator negative
electrode + +

–

Li + positive
electrode e -

Figure 2.2 Cell sandwich inside of prismatic pouch cells.

The electrodes are efficiently prepared by coating wide sheets of foil (up to 2-meters in width) with uncoated strips running the lengths of the foi l being coated. The individual electrodes can
be cut from these sheets with little waste of elect rode coating material or foil (Fig. 2.3). The separator for these cells can be handled as a singl e sheet that is folded back and forth as the
electrodes are inserted. The electrodes are inserte d so that all of the positive tabs extend beyond the separator sheet in one direction and the negati ve tabs extend in the opposite direction. The design model selects the number of electrodes for a set cell thickness determined by the type of cell: HEV, 6 mm; PHEV, 12 mm; EV, 14 mm. The cell terminals are formed from flat stock to be almost as wide as the entire cell. They are bent to the shape shown in Fig. 2.1 and ultrasonically welded to the current collector tabs . The cell stack is then sealed between the two halves of the cell container. The cell housing mate rial is a tri-layer consisting of an outer layer of4

polyethylene terephthalate (PEP) for strength, a mi ddle layer of 0.1-mm aluminum for stiffness and impermeability to moisture and electrolyte solv ent vapors and an inner layer of polypropylene (PP) for sealing by heating. 19,20 The two halves of the cell container are preshaped to facilitate assembly. The aluminum foil in the cell container material provides stiffness and it may be increased in thickness to assist in c onducting heat to the module container.

Figure 2.3 Coated current collector foil for prismatic electro des

2.2 Module Design

The model designs a module casing of 0.5 mm aluminu m that is sealed by double seaming, a process that is well established and inexpensive be cause it is automated, rapid, and uses low-cost capital equipment. The sealing of the module provid es an additional barrier to the loss of electrolyte solvent from the cells and the entrance of water vapor. These deleterious transfers through the seals of pouch cells may shorten their lives to less than the desired fifteen years. 19
The cells are placed on their sides in the module a nd the terminals of adjacent cells are connected either mechanically with small bolts and flat sprin gs to maintain contact or by laser welding.

Space is provided within the module casing on the l eft side, as sketched in Fig. 2.1, for an electronics package that includes cell monitoring f or malfunctions (temperature and voltage) and for state-of-charge (SOC) control. The SOC control is activated whenever the battery is at rest and it diverts charge from the cells at highest vol tage to those at lowest voltage.

In the model, we assume the module is cooled only b y air flowing over the upper and lower surfaces of the module. This method of cooling is m ost practical if the amount of heat generated is kept to moderate levels by defining full power a s that provided at 80 % or higher fraction of the open-circuit voltage. To enhance heat flow from the cells to the cooled walls of the module casing, the edge seals, which include two layers of 0.1 mm thick aluminum foil (one from each half of the cell container), can be pressed against the walls of the casing by springs shaped as hoops. The heat transfer can be further enhanced by increasing the thickness of the aluminum 

### Electrode Coating

Lines Showing

Places to Cut for

Electrodes Uncoated Area

for CC Tabs5

layer in the cell pouches or by adding an aluminum plate between the cells. The modules can also be cooled internally by a dielectric fluid suc h as a transformer coolant. For that approach, the fluid would be brought to the module through me tal tubing or be supplied to the battery jacket and enter the modules through slots. Corruga ted plates inserted between the cells would provide flow channels for the cooling fluid. In the current model, only air cooling on the outside of the module is provided. Further discussion of th ermal issues may be found in Section 7.

2.3 Battery Pack Design

The model designs the battery pack in sufficient de tail to provide a good estimate of the total weight and volume of the pack and the dimensions of the battery jacket so that its cost can be estimated. The modules are arranged within the batt ery jacket either in a single row, with the terminals facing the same side of the pack, or in a n even number of rows with the terminals in one row facing the terminal of an adjacent row. The terminals are laid out on the module so as not to interfere with those on the opposite row of modules, thus conserving space in the battery pack. The modules in a row are interconnected, nega tive to positive terminals, by copper connectors. The modules casings are compressed toge ther by two steel sheets bound with steel straps at the front and back of the battery pack. T he compression is necessary to ensure intimate contact between the active layers that make up the pouch cells that are tightly fit into the modules. The compressive force also serves to add s tructural support to the module casing.

The battery jacket consists of a sheet of aluminum on each side of a 10-mm thick layer of ridged, light-weight high-efficiency insulation. The thickn ess of each of the aluminum layers is selected by the modeling program to be 1- to 2-mm thick, dep ending on the total volume of the modules. The insulation slows the interaction of the battery with the external environment that cools the battery in the winter and heats it in the hot summe r weather. 146 

### 3 Modeling of Battery Design and Performance

The design portion of the model calculates the phys ical properties of a battery based on userdefined performance requirements and minimal experi mental data. An illustration of the model is shown in Figure 3.1. The user is asked to enter a n umber of design parameters such as the battery power, number of cells and modules, and target volt age at maximum power, etc. In addition, the user must enter one of the following three measures of energy: battery pack energy, cell capacity, or vehicle electric range. Defining one of these va lues will determine the value of the other two. An iterative procedure then solves for the user def ined energy parameter (energy, capacity, or range) and remaining battery properties by varying the cell capacity and electrode thickness. The result is the dimensions, mass, volume, and materia ls requirements for the cells, modules, and battery pack.

The model has been designed to allow the user to en ter as many customized values as desired. In this way, the model allows flexibility in the batte ry chemistries studies and some of the cell, module, and battery design aspects. Hence, the focu s of this report is on the method of
calculation and not the exact values chosen for a s pecific capacity or cell thickness. However, the default cell design parameters as well as experimen tal data measured at Argonne National Laboratory, for a number of different battery chemi stries, are available for use within the model. There are five governing equations for battery perf ormance that calculate the current density, battery energy, electrode area, electrode thickness , and resistance. The voltage at maximum power and the area specific impedance (ASI) are two important parameters in the design model for calculating the battery performance. Most of th e discussion will be spent on these two properties.

3.1 Criteria for Power, Energy, and Life

In order to fully specify a battery design, the use r of the design model must supply criteria for power, energy, and life. These criteria will depend on the application for which the battery will be used. While the user may change some of the sett ings as they prefer, we list our suggestions in Table 3.1. The battery type is defined by the end-u se application. Hybrid electric vehicles (HEVs), plug-in hybrid electric vehicles (PHEVs), a nd electric vehicles (EVs) have increasing
levels of electrification of the vehicle drivetrain . The model will use Table 3.1 or the user’s explicit inputs to size the battery correctly for t he chosen application.

Table 3.1 Criteria for designing batteries for a specific en d-use application Battery Type microHEV HEV-HP PHEV EV SOC for Rated Power, % 50 50 25 25
Power Duration, sec 2 10 10 10
SOC Range for Useable Energy, % 40-65 40-65 25-95 1 5-95

Cell Thickness, mm 6 6 10 147



# Battery Design Model

Iterative Spreadsheet
Solves for cell capacity and designs battery pack by varying:

1. Cell area

2. Electrode thickness

3. Internal resistance 

# Pack Requirements

• power

• energy or range • number of cells



# Cell Chemistry
Measured Properties • pulse power ASI • discharge ASI • mAh/g, g/cm 3 

## • electrode porosity

• SOC window • physical properties

ASI = area specific impedance 

# Key Constraints

• max electrode thickness • target cell potential, V, at peak power • cell/module format



# Calculated Battery Pack Properties

• dimensions

• volume & mass • specific energy,

power • materials required

Figure 3.1 Summary flow of the design model8

The microHEV is a micro or mild-hybrid that provide s a moderate power level, ~25 kW, for two seconds. This design is best suited for cell chemis tries capable of very high power-to-energy (P/E) ratios. The HEV-HP is a power-assist hybrid t hat provides the rated power for a full 10 second pulse. The power for both HEV applications i s rated at 50 % state-of-charge (SOC). The energy available for discharge and charging is 25 % of the total energy to ensure long cycle life. As the capacity of the HEV cells is typically small , a cell thickness of 6 mm is used. The PHEV utilizes a much larger portion of the total energy, 70 %. At the end of discharge, the PHEV battery is operated in a charge sustaining mode. Th erefore, the power rating for the battery is
determined at 25 % SOC. PHEV cells should be much l arger than HEV cells and thus a cell thickness of 10 mm is assumed. Finally, EV batterie s use 80 % of their total energy with their power rated near the end of discharge. Cell thickne sses are set to 14 mm to accommodate a high capacity design. As noted later in the report, sele cting a parallel arrangement of cells automatically assumes a cell thickness of 6 mm rega rdless of the end-use application. Additionally, the use of negative electrodes operat ing at potentials high above the lithium metal potential may extend the upper end of the available SOC range from 95 to 100 %. The lithium titanate spinel, Li 4 Ti 5 O 12 (LTO), negative electrode is an example of interca lation electrode with almost no risk of plating lithium metal during a ch arge pulse. On this basis, the available energy for LTO-based Li-ion chemistries is suggested to be 75 % for PHEVs and 85 % for EVs.

Accounting for capacity and power fade in the batte ry requires the user to design the battery with the appropriate excess energy and power at the begi nning-of-life (BOL). Defining the voltage at which maximum power is achieved at BOL is one way t o set the allowable power fade over the life of the battery. This is discussed in detail in the following section. Capacity or energy fade must be accounted for by over-sizing the battery at BOL. If the user has a certain fade requirement, then the BOL energy may be increased t o meet the end-of-life (EOL) target. The design model does not attempt to predict fade rates or even suggest an allowable fade for a specific application. It is our view that many aspe cts of materials chemistry, cell design, and battery use directly affect the decay of the batter y pack. Hence, we allow the user to make accommodations for decay as he or she believes is n ecessary.

3.2 Voltage at Maximum Power

The voltage at which a cell reaches the designed ma ximum power is one of the most important factors in the design of a battery. However, this s pecification is one of the least discussed aspects of battery design. The voltage at maximum power, V cell , is a measure of the largest polarization the cell will undergo during operation at the BOL. This initial value has a direct effect on roundtrip battery efficiency, heat removal requirements, cold-cranking power, and allowable power
fade. A basic calculation shows the maximum achieva ble power for a battery at BOL is at 50 % of the open-circuit voltage (OCV). Operating at the se conditions would result in an inefficient battery and require a significant cooling system to reject heat. More importantly, the battery will never be able to reach this power level after any i ncrease in impedance occurs. With all certainty, the impedance of a battery will rise with time and the power rating of battery will no longer be accurate. The remainder of this section presents a discussion for setting the BOL voltage at maximum power at no less than 80 % of the open-circ uit voltage. Defining the voltage as a fraction of the OCV, [V/U], allows for direct calcu lation of all the necessary battery properties (see for example Eq. 3.6 or 3.8 in the section 3.3)

.9

The allowable increase in battery resistance over t he life of the battery is a function of the designed voltage for maximum power. In general, des igning the battery to achieve maximum power at a higher [V/U] allows for larger resistanc e or impedance increases over the lifetime of the battery. Figure 3.2 created from Eq 3.1 display s how the voltage at maximum power will change to meet the designed power as the internal r esistance of the battery increases. Clearly, achieving BOL power at a high fraction of the OCV a llows for greater degradation within the usable lifetime of a battery. If the minimum voltag e is 55 % of the OCV, the allowable increase in resistance for batteries designed for BOL max po wer at 70, 80, and 90 % OCV is 18, 55, and 175 %. The consequence of achieving the power at lo wer and lower fractions of the open-circuit voltage is that both electric current and heat gene ration will increase over the lifetime of the battery, Figure 3.2b and Figure 3.3. The proper des ign of a battery will account for the changes over the entire lifetime and not just desired behav ior at BOL.

    

                  

−      

− + =      

1 1 1 2

2 1

4 1 1 2 1

U V

U V

R R

U V (3.1)

The level of heat production is significantly diffe rent at BOL for batteries designed to meet maximum power at differing fractions of the open-ci rcuit voltage. We may compare the differences in designed [V/U] by assuming the resis tive heating (joule heating) is the most significant factor in determining the heat generati on, Eq. 3.2. We also reasonably assume the ASI will not change significantly in the range of curre nt densities and electrode thickness we vary in the comparisons. From this point, we can analyze th e difference in heat generation from different designed [V/U] values, Eq 3.3.



# ( )

j j

j pos j R U V U

R I A q 2

2

2 1 

            

−

= = (3.2)

2

1 2 2

2 1

1 2

1 1

             

−              

−

=

U

V R U V R

q q (3.3)

The ratio of resistances may be found by equating t he power for the two cases. Then the resistances, and areas if the ASIs are equivalent, are determined solely by the fraction of the open-circuit voltage at which they achieve maximum power, Eq 3.4. Then substitution will give the ratio of heat production at maximum power for t he two cases, Eq. 3.5. A battery that achieves maximum power at 80 % of OCV will have a heat produ ction at maximum power that is 2.3 times higher than one designed at [V/U] = 90 %. A battery producing power at 70 % of the OCV will have 3.9 time higher heat generation than at [ V/U] = 90 %.10

Figure 3.2 a) Required change in [V/U] to maintain rated powe r with increases in internal resistance over the life of the battery. b) Increas e in current due to lowered [V/U]. 50 55 60 65 70 75 80 85 90 95

0 25 50 75 100 125 150 175 200

Increase in Resistance, %Fraction of OCV at Full Power, %



### 90%

80%

70% Designed BOL [V/U] at

max Power

0 10 20 30 40 50 60 70 80



### 0 25 50 75 100 125 150 175 200

Increase in Resistance, %Increase in Current, %



### 90%

80%

70% Designed BOL [V/U] at

max Power11



## 0 50 100 150 200 250 300 350 400 450 500

0 25 50 75 100 125 150 175 200

Increase in Resistance, %Increase in Heat Generation, %



## 90%

80%

70% Designed BOL [V/U] at

max Power

Figure 3.3 Change in heat rejection requirement from increase s in resistance for batteries with

different designed voltages at maximum power.

             

−       

            

−      

= =

2 2 1 1

1 2 2 1

2 1

1 1

U V

U V U

V

U V

A ASI A ASI

R R

pos

power pos power (3.4)

             

−       

            

−      

=

1

2 2 1

1 2

1

1

U V

U V U V

U V

q q (3.5)12

Two straightforward design changes will enable oper ating a battery at 90 % of OCV compared to 80 % while maintaining the same power output. First , a second identical battery may be connected in parallel to the original battery. This will lower the resistance of the battery pack by one half but will also double the energy and cost o f the battery. A more realistic approach is to reduce the electrode thickness by coating a larger separator area. The capacity of the cell is maintained while minimizing increases in cost from a larger separator, current collector and packaging area. This approach is feasible as long a s the reduced electrode thickness is above the increase in ASI, > 20 microns as discussed in detai l below.

The efficiency of a battery defines the heat reject ion requirements and may be measured or calculated. Measurement of round-trip efficiency of a battery is best performed by using a calorimeter to measure the heat given off during th e cycling of the battery. The calorimeter removes the requirement of knowing the exact SOC of a battery during the entire drive cycle. Calculation of the round-trip efficiency of a batte ry requires a detailed transient battery model within a vehicle simulation program to exercise the battery over the many acceleration and deceleration periods that occur during a drive cycl e. The interesting result is that the same battery will have different power ratings depending on what level of round-trip efficiency the user is willing to accept.

Figure 3.4 shows the efficiency of a battery as a f unction of the designed potential at which the battery reaches maximum power. The figure is create d using Equations 3.1 and 3.4 above. Each line may be considered a different drive cycle, or duty load, for a battery with the same energy but different impedance (changing separator area). The straight, solid black line represents the efficiency of the battery operated only at maximum power, P/P
max = 1. In example, a battery designed at [V/U] = 0.8 will have 80 % efficiency f or a single discharge pulse at maximum power. Likewise, a battery designed at 0.9 will be 90 % efficient at maximum power. Batteries are normally operated in the area above the line of the maximum power. Therefore, the other curves represent the efficiency of discharging a ba ttery at power levels below maximum power (typical driving conditions). Consider two batterie s each designed for a maximum power of 100 kW although one achieves this power at a [V/U] = 0. 9 and the other at 0.7. If the two batteries are discharged at 45 kW, P/P
max = 0.45, the battery designed at [V/U] = 0.9 will b e 6.4 % more efficient. This is significantly less than the 20 % efficiency improvement realized when operated at maximum power. The efficiency penalty is reduced as the battery operates less and less near the designed maximum power.13

Figure 3.4 Efficiencies for batteries designed to achieve max imum power at different fractions of their open-circuit voltage. Comparative efficien cy lines are shown for equivalent power demands over a period of battery operation. 

### 50% 60% 70% 80% 90% 100%

0.5 0.6 0.7 0.8 0.9 1

Designed [V/U] at Max PowerEfficiency During Discharge



### 0.10

0.20

0.30

0.45

0.60

0.80

1.00 

## P/P max14

3.3 Governing Equations

The five coupled, algebraic equations that govern t he battery design are presented in this section. While these equations are perhaps the most importan t, many other equations are used to fully define the battery mass and volume. These other equ ations will be specified where necessary in the following subsections.

The user of the model specifies the required maximu m power, P batt , of the battery. This power is translated to a current density, I , in Eq 3.6 using the area of the positive electrod e, A pos , the number of cells, N cell , the open-circuit voltage at the SOC for power, U ocv,P , and the fraction of the open-circuit voltage at which maximum power is achieved, [V/U].

      =

U

V U N A P I

P ocv cell pos batt

, (3.6)

The relationship between capacity and battery energ y is described by Equation 3.7. Formally, the energy of a battery is the product of the capacity and the average voltage at which the energy is obtained. The average cell voltage is approximated in Eq. 3.7 by subtracting the polarization from discharging the battery at a C/3 rate from the open-circuit voltage at the SOC for energy,

U ocv,E . The energy for all batteries designed by the desi gn model is calculated at a C/3 rate and the average open-circuit voltage at 50 % SOC. The r emaining necessary values are the capacity of the cell, C , ASI for energy, ASI energy , number of cells, and area of positive electrode. Either the battery energy or capacity may be specified. The en ergy may alternatively be determined from a stated range, fraction of total energy available, a nd energy usage rate for the vehicle (Wh/mile).

       

− =

pos energy

E ocv cell A

ASI C U C N E 3 , (3.7)

The area of the positive electrode in Eq. 3.8 is de termined largely by the area specific impedance for power, ASI

power , and resulting voltage drop. The voltage of cell a t max power, V cell,P , is found from the product [V/U] U ocv,P . In general, the area of the cell will increase if the ASI for power increases. The areas of the negative electrode and separator are determined from the area of the positive electrode. The negative electrode is taken to be 1 mm larger than the positive electrode in both height and width to alleviate concerns of l ithium plating during charge pulses. The separator area is slightly larger than the negative electrode to prevent the electrical shorting of
the two electrodes.



# ( )              

−       =

U V

U V U N P ASI A

P

ocv cell batt

power

pos 1 2

, (3.8)

The positive electrode thickness, L pos , in Eq. 3.9 is determined from the capacity of the cell, C

, specific capacity of the electrode, Q , volume fraction of active material, ε act , bulk density of the15

active material, ρ , and the positive electrode area. The negative ele ctrode thickness is determined by its specific reversible-capacity and the designe d excess-capacity to prevent lithium plating during charging. We have chosen a ratio of 1.25 neg ative to positive reversible-capacity (N/P ratio) for the default value for the cells with gra phite negative electrodes. LTO negative electrode based cells are designed at a 1.1 N/P ratio because of the previously mentioned minimal possibility of lithium deposition. The maximum allo wable electrode thickness is a user defined value. The calculation for the electrode area chang es when the designed thickness is greater than the maximum allowed (Section 3.6.1).

pos act pos A Q C L ρε = (3.9)

Finally, the ASI for power (and for energy to a les ser extent) is calculated using an expression that is based on the electrode thicknesses, the cur rent density, and the C-rate. The exact expression will be discussed in the next session. T he ASI in Eq 3.10 shows the basic dependencies with α and β being constant valued parameters.



## ( ) β α + +

=

pos L I f ASI (3.10)

3.4 Calculation of the ASI

In most battery design scenarios, the ASI directly determines the electrode thickness to meet a specified power-to-energy (P/E) ratio. From this el ectrode thickness, the area of the electrode is set to meet the capacity requirements. Clearly, the ASI plays a significant role in the design of a battery and particularly in the case of the P/E rat ios required by automotive applications. However, the ASI is not an inherent constant of a s pecific battery chemistry or cell design. The measured value of the ASI is a complex combination of resistances within the battery resulting from the physical processes occurring at different length and time scales. Consequently, the measured value is a function of many factors (state of charge, pulse length, current density, Crate, particle size, transport and kinetic paramete rs, etc). The calculation used for the ASI in this battery design model has been discussed in detail e lsewhere. 18 The physical meaning of the equation will be discussed but those interested in the derivation are directed to the separate publication. We note that the ASI described here is slightly different than the one addressed in the paper. The thermodynamic component is removed t hat originated from the change in opencircuit potential with concentration for the interc alation materials. Equation 3.11 contains the
definition of the ASI used in this document. I t1 is a positive valued current density for a discharge pulse. I t2 is equal to zero as it is during the relaxation pe riod after the pulse. Time 0, t0

, is the time just before a current pulse begins, tim e 1, t1 , is the time just before the current pulse ends, and time 2, t2 , is the time long after the current pulse when the cell is at open-circuit and the concentration gradients have relaxed. Therefore , this ASI measurement is not troubled by accounting for a change in open-circuit voltage wit h the passage of current. In general, the ASI measured with this definition is similar, although smaller, in value to those produced using the
more standard definition used elsewhere.16 2 1 1 2

t t t t I I V V ASI

−

−

= (3.11)

The ASI for the electrochemical charge and discharg e process is referred here-in as ASI echem . Our calculation approach for both the ASI for power and for energy involves adding three components together to reach the ASI echem , Eq. 3.12. The first two factors include impedance that arises from the interfacial charge transfer and tra nsport. The third factor is a lumped parameter used to capture the remaining impedance.

const intf intf echem ASI

ASI ASI ASI neg pos + + = (3.12)

The interfacial impedance for positive and negative electrodes both contain the charge transfer resistance component RT /( i
o aLF ) as shown in Eq. 3.13 and 3.14. Here, i
o is the exchange current density related to the interfacial area and a is the ratio of interfacial area to electrode volu me. An approximation often used for a relates the parameter to the volume fraction of th e active material and the particle radius, a = 3 ε act /r p . The variables i
o and a should be specified to relate to the same area as they are often not independently deter mined. R and T correspond to the universal gas constant and absolute temperature respectively. F is Faraday’s constant. The influence of the interfacial impedance is that the ASI echem increases as the electrode thickness is reduced. T his behavior is typically observed at electrode thickne sses less than 30 microns for common Li-ion battery materials.

F aL i T R ASI

neg

o = neg intf (3.13)

5.0

– 2

lim, lim pos intf 1

1 

   

    

 
 

 
 


      

−        

− =

C C

ionic

pos o r r

I I

F aL i T R ASI (3.14)

The positive electrode interfacial impedance also i ncludes two factors that account for the physical limitations that occur from depleting the concentration of the reactants within the porous electrode. The ionic

I lim term is the limiting ionic current for lithium cat ion transport through
the porous separator. The lim, C r term is the limiting C-rate for solid state diffusi on of lithium in
the active materials. The C-rate may be related to the current density with Eq. 3.15. Here, the specific capacity, Q , the active material density, ρ , active material volume fraction, ε act , and the electrode thickness, L , are used. If either the limiting C-rate or limiti ng ionic current are approached, the ASI will begin to approach an infin ite value. The parameters required for the ASI expression are fit to experimental measurements . The ASI values are corrected for the interfacial contributions present during measuremen t so that the correct ASI may be determined
at different electrode thicknesses.17 pos act C L Q r I ρε = (3.15)

The cell ASI for energy, ASI energy , and power, ASI power , are determined by adding the ASI echem to that of the current collectors, ASI
cc , as discussed in the next subsection. The differen ce between

ASI energy and ASI

power is that the limiting currents are not important du ring the C/3 discharge for energy and the ASI const is a different value for two cases. ASI energy will always be higher than

ASI power if a battery is operated far from the limiting cur rent. The higher impedance is due to the formation of significant concentration polarization s during the longer time scale of the energy discharge. A reasonable rule-of-thumb is that the ASI const for energy is 2.2x the value for power in layered oxide materials such as LiNi 0.80 Co 0.15 Al 0.05 O 2

.

3.4.1 Current Collection Resistance

The resistance from the conductors used to collect the current must be accounted for as they can contribute significant ohmic drop to the battery. T he ASI used to calculate the required cell
separator area, ASI power , is larger than the ASI for the electrochemical ch arge and discharge

processes, ASI

echem,P , as shown in Equation 3.16. The ASI echem value is typically measured from experiments and must be added to the external resis tances that arise from the materials used to
conduct the electric current. These resistances com e from current collection in the cell and also those on the module and battery pack level.

cells pos cnct cell

term cc echem,P power N A R ASI ASI ASI ASI + + + = (3.16)

The current collector foil impedance, ASI
cc , is determined from an analytical expression, Eq. 3.17, which accounts for the coated and uncoated re gion of the foil, labeled act for active and tab respectively. The resistance factor, R f , and the resistance of the current collector foils

, R
cc , are also shown for clarity in Eq 3.18 and 3.19. The fac tor of 2 in the R f term is due to assuming half of the foil thickness carries the current produced on one side of the foil. While all of the current passes through the tab region, the magnitude of the current varies along the height of the coated foil as the reaction area continually contributes c urrent to the foil. An equivalent length for the resistance calculation may be determined so that mu ltiplication by the total current for a cell will give the correct ohmic drop. This equivalent length is H/3 if the current density is relatively
constant over the entire area. The derivation of th is equivalent length as well as an in-depth discussion of the voltage and current distribution in the foils may be found in subsection 3.4.2. Also in the later subsection, the assumption of con stant current density is verified with numerical modeling.



## ( )        

+ = = tab act act f cc act act cc H H H R R W H ASI 3 2 (3.17)

       

+ =

pos foil pos foil neg foil neg foil f L

L R

, , , , 2 2

σ σ (3.18)18        

+ = W

H

W H R R tab

act act f cc 3 (3.19)

The cell terminals are ultrasonically welded to the ends of the current collector foil tabs. While the welding removes this contact resistance, the AS I of the terminal must be included in the total
cell resistance. The ASI of the cell terminals, cell

term ASI , is the summation of the positive and
negative cell terminals as shown in Eq 3.20. The di mensions for these terminals are set by the
calculated width of the cell and the user defined t erminal thickness and height.

pos

term term term

pos term neg term A

L W H ASI        

+ =

,

, cell

term 1

1

σ σ (3.20)

The ASI for connection losses is the last term in t he ASI summation stated in Eq. 3.16. This ASI value is calculated by multiplying the ratio of cel l positive electrode area to number of cells by the summation of the resistances, R cnct , for cell terminals, module terminals, module interconnects, and batteries terminals. In this way , each cell shares in the burden of overcoming the system losses from carrying the electric curren t. The calculation of R cnct is detailed in Eq.
3.21 with the individual sources of connection loss es shown. The voltage drop resulting from
cell-to-cell contact resistance, cell

cntct R , is taken to be 10 -4 U ocv,E in Eq. 3.22, a small fraction of the
open-circuit voltage. A battery manufacturer would only tolerate a minimal voltage drop from cell-to-cell contact. One connection method is to p hysically press the two cell terminals together. This resistance could be lowered by increasing the physical pressure and contact area, or by laser welding the terminals together. Regardless, the val ue used in the model is left to the choice of the user to leave as is or to change to a different val ue.



## ( ) batt

term incnt term cell

cntct cell cnct R R N R N R N R +

− + + = mod

mod mod

mod 1 (3.21)

pos E ocv cell cell

cnct IA

U N R ,

4 10

− = (3.22)

The module terminal resistance, mod

term R , calculation in Eq. 3.23 is shown as an example of how the

terminal and interconnect resistances are calculate d for the module and battery pack. The size of
the terminals and thus their resistance are determi ned from a calculation based on a predetermined allowable rate of temperature rise for t he conductor. This approach is explained in
more detail in subsection 3.4.3.



## ( ) mod

2 mod

term term

term term term N

r H R

π σ = (3.23)19

3.4.2 Potential and Current Distribution in the Cur rent Collection Foils

The designed current collection system was evaluate d using a numerical simulation package. Equations 3.24-3.26 were solved for a steady state, isothermal, and 1-D simulation. Here, the conductivity, σ

j , is the effective conductivity of 1⁄2 of the foil (t he other half carries the current from the opposite side). The bulk conductivity valu e, σ j 0 , is multiplied by the thickness of the conductor, L

j /2, to lower the dimension of transport.



## ( ) ( ) 

# ( )

echem neg pos ocv

n 

### ASI x

x U I ,1

,1 

### Φ

− Φ

−

= (3.24)



# ( )

n

pos pos I

− = Φ ∇

⋅ ∇ ,1 σ (3.25)



# ( )

n

neg neg I

= Φ ∇

⋅ ∇ ,1 σ (3.26)

The boundary conditions were set for both ends of e ach foil. The tab ends of the foils were set to a specified voltage and the opposite ends of the fo ils were restricted to a no flux condition. The simulation was performed using the foils defined in our battery design: 12 micron thick copper foil and 20 micron thick aluminum. The cell length was 20 cm, the ASI echem was 30 ohm cm 2 , and
the U
ocv and V

cell were set to 3.72 and 3.57 V respectively. Figure 3 .5 shows the current and potential distribution in the foils and in the cell resulting from the simulation. The cell potential along the length of the foil varies only by 1.5 mV from maximum to minimum difference. The 0.4 % variation in voltage results in a 0.9 % varia tion in current density. This verifies the current density is uniform along the length of the foil. Th is is also obvious from the linear relationship of current with foil height in Fig. 3.5. The assumptio n of constant current density was tested in cell heights up to 100 cm and found to be satisfactory. The assumption should be reasonable as long
as the ASI

echem is at least twice the value of ASI
cc . The simulated resistance of the foils is found
to raise the ASI

echem by 0.7 for an ASI power of 30.7 ohm cm 2 . Additionally, the numerical result verified that H/3 is the correct equivalent length to represent the ASI
cc for the cell. This may also be found analytically, Eq. 3.27-3.29, if you assume an even current distribution as we have shown is a reasonable assumption.



# ( ) 2 2 ,1 2 x

H I V

pos

n cell pos − + = Φ

σ (3.27)

       

− = Φ xL

x I

neg n

neg 2

2

,1 σ (3.28)

       

+ + = Φ

− Φ

= + 

# ∫

neg pos cell H

n neg pos

cc echem H

I V dx I H ASI ASI

σ σ 1 1

3 1 2

0 ,1 ,1 (3.29)20

Figure 3.5 The change in current and potential within the pos itive and negative foils. The current collection design results in a uniform current dist ribution along the length of the foil.

3.5690 3.5700 3.5710 3.5720 3.5730 3.5740 3.5750

0 0.2 0.4 0.6 0.8 1



### x/HPositive foil and cell potential, V

-0.0060 -0.0050 -0.0040 -0.0030 -0.0020 -0.0010 0.0000Negative foil potential, V



### Cell

Positive foil

Negative foil

0.00 0.02 0.04 0.06 0.08 0.10 0.12

0 0.2 0.4 0.6 0.8 1



### x/HFoil current per width, A/cm

0.00486 0.00487 0.00488 0.00489 0.00490 0.00491 0.00492Current density, A/cm2 

### Negative foil

Positive foil
current density21

An analogous problem has been solved by Euler and N onnemacher and then communicated repeatedly by Newman et al

. 21, 22 The analytical solution they presented may be used after a slight alteration to dimensionalize the current den sity to the geometry of our concern, Eq. 3.30 and 3.31. This solution was reached assuming linear polarization behavior and is valid for cases where the current density varies along the height o f the current collector foil. Thus, this approach is a more general solution than the one we use in t he design model.



# ( )

    

 

    

  

      

+ +

+ + = Φ

− Φ

−

= +

v v v H

I U
neg pos

pos neg

pos neg neg pos ocv

cc echem sinh cosh 2

1 ASI ASI 2 ,1 ,1 σ σ

σ σ

σ σ (3.30)

       

+ =

neg

pos echem ASI H

v σ

σ 1 1 2
2 (3.31)

3.4.3 Determination of Module Terminal, Battery Ter minal, and Module Inter-connect Size

An important factor for setting the resistances of a module terminal, battery terminal, or module interconnect is the allowable rate of temperature r ise in the conductor at full power. We set the acceptable rate of temperature rise, dT/dt, at 0.2 °C/sec or a 2 °C rise for a 10-sec power burst under adiabatic conditions. The heating rate, q , is then used to determine the mass, m , of the terminal required for the designed battery in Eq. 3 .32. Since the heating rate may also be determined by Eq. 3.33, we may determine the cylind rical terminal radius and mass by assuming a length, H

term . In this way, the size of the module terminal is r edesigned during each simulation to meet the specified power requirements and allowa ble temperature rise, Eq. 3.34. The mass of the conductor is found to be inversely proportional to the allowable temperature rise.

dt dT mC q p = (3.32)



# ( ) 2

pos

term term term IA A H q σ = (3.33)

2/1

−      

= dt

dT C IA A

p term term pos term σ

ρ (3.34)

3.5 Calculation of Battery Dimensions

The goal of the model is to quantify how the variou s components of a specific battery design sum to make the mass and volume of the battery pack . In this way, a true energy and power density can be calculated as well as the exact mate rials requirement to meet this design.22

Summing the mass of the components is relatively st raight forward. Determining the total volume that contains the components and required fr ee volume is not as obvious. The exact calculations used in the design model are detailed below for the cell, module, and battery pack.

3.5.1 Cell Dimensions

The number of layers in each cell is approximated i n Eq. 3.35 by accounting for the compression factor, X

comp , and the individual thicknesses of the current col lector foils, L foil , electrodes, L pos and L neg , separator, L sep , and container, L cont . X comp is usually taken to be 0.97. The Li-ion battery chemistries this model was designed for are assumed to undergo negligible volume change on the cell level. No effort was made to address possi ble changes in electrode volume upon cell discharge or charge.

) (2 2

pos

neg sep pos foil neg foil neg foil cont cell

comp layers L L L L L L

L L X N

+ + + + +

−

= (3.35)

The N layers approximation is necessary as the cell thickness i s a user defined parameter. The aspect ratio of the cell is also user defined; ther efore, solving for the width also determines the height of the cell as seen in Eq. 3.36. The width i s calculated from the number of layers and the aspect ratio, H/W

. The factor of 2 enters the denominator as both si des of the foil are assumed to
be coated.

layers pos

pos N W H A W

2 = (3.36)

Having determined the width and height of the elect rode, the rest of the cell dimensions are relatively straightforward, Eq. 3.37 and 3.38. The width of the cell, W cell , is 8 mm wider than the positive electrode to allow for the larger separato r area and pouch seals. The pouch seals are folded up, pressing along the inside wall of the mo dule casing. The height of the cell, H cell , is the height of the positive electrode in addition to the distance for the terminals and connections to the foil tab, L term,cnt . Our assumed design requires 15 mm for this distan ce. The volume of the cell is the product of the three dimensions.

8 + = pos cell W W (3.37)

cnt term pos cell L H H

,

2 + = (3.38)

3.5.2 Module Dimensions

The module dimensions are defined by Eq. 3.39-3.41. The height and length of the module are both just 2 mm wider than the cell dimension. The w idth of the module is related to the total
thickness from all of the cells with allowance for a SOC controller at one end.

2 mod + = cell W H (3.39)23 2 mod + = cell H L (3.40)



## ( ) 1

1 mod / mod +

+ = cell cell N L W (3.41)

3.5.3 Battery Pack Dimensions

The battery pack volume includes all of the modules , spacing for connections between modules, channel for the cooling air to flow, H air , thickness of the module compression plates, L comp , and the battery pack jacket, L jack (Eq. 3.42-3.44). L jack includes a 10 mm thick insulation layer
sandwiched between two aluminum walls for the conta iner. The thickness of the aluminum wall increases from 1 to 1.5 to 2 mm as the battery volu me increases from < 20 L to < 40 L to larger dimensions. The layout of the modules, number per r ow, N mod/row , and number of rows, N
row , is also included. The final volume of the battery is t he product of the three dimensions. The space left for connections between modules, L gap , is a function of the number of rows of modules. L gap is equal to 8, 10, or 20 depending if there is one, two, or four rows of modules. Three rows of modules are not allowed as the positive and negativ e terminal for the battery would be on opposite ends and thus not very practical. A number greater than four rows of modules is deemed

unnecessary.

jack air batt L

H H H 2

2 mod + + = (3.42)

jack comp air row batt L L H W N L 2 2 mod mod/ +

+ + = (3.43)

jack gap row batt L

L L N W 2

mod + + = (3.44)

3.6 Additional Considerations

A few situations may arise that require a change in the calculation method. These situations are
addressed in the subsections below. The inclusions of these calculations into the model allow for a more realistic depiction of limitations often enc ountered by cell manufactures.

3.6.1 Maximum Electrode Thickness

A practical limitation exists for the maximum achie vable electrode thickness. This limitation may be set by manufacturing capabilities, ionic and electronic current transport within the porous electrode, or aging characteristics related to adhe sion to the current collector. When the maximum electrode thickness, L
max , has been reached on either the positive or negati ve electrode, the electrode area equation is modified as shown in Eq 3.45. The electrode thickness, L tgt , is the largest electrode thickness, negative or positive, calculated at the targeted fraction of the OCV [V/U].

pos tgt L

pos A L L A

max max = (3.45)24

The area of the electrode is now determined by the cell capacity requirement to meet the battery energy demands and not the target voltage at maximu m power. As a consequence, the battery pack will operate at a higher [V/U] than originally selected by the battery designer. The new [V/U] may then be calculated from Eq. 3.46 which is the solution to the quadratic found in Eq.

3.47.



## ( )    

   

− + =      

pos cells power batt

cell cell

cell A N ASI P U U U U V 4 2 1 2 (3.46)

pos cells cell power batt

cell cell A

N V ASI P U V

− = (3.47)

The maximum electrode thickness has a large impact on the energy density and cost of cells designed for high energy and range. Nelson et al. d emonstrated this concept in 2009 assuming a
100 micron maximum electrode thickness. 11,17 In 2010, Santini et al. relaxed this assumption to 300 micons; although, the thickest electrode discus sed in the paper was a 225 micron graphite electrode in the LMO-Gr EV with 100 mile range. 12 In conversations with manufactures, 100 microns appears to be the general electrode thickne ss used for EV type cells at the present time. However, Santini et al. has shown substantial incre ases in energy density and decreases in cost if larger electrode thicknesses may be utilized. The c hallenges to achieving thick electrodes, in addition to those already mentioned, relate to fast charging while avoiding lithium metal deposition, removing gases formed during formation cycling, wetting the full porosity of the electrode, achieving defect free coatings, and dryi ng the thick electrode at high rates. Our opinion is that the successful cell manufacturers w ill engineer ways to overcome these challenges to increase energy density and lower cos t.

3.6.2 Accounting for Parallel Cell Arrangements

The user of the design model may wish to use a para llel arrangement of cells within the larger series arrangement of the battery pack. Several mot ivations exist for a parallel cell arrangement. For example, a battery supplier may wish to only pr oduce cells of a specific capacity. The manufacturer may only have the equipment to produce a certain size cell or they may encounter engineering design problems for very large cells ( > 60 Ah). Thus, a cell group composed of parallel connected cells may be necessary to meet t he energy requirements while staying within battery pack voltage and current requirements.

When the user chooses to have cells connected in pa rallel, the design model calculation includes the appropriate factors necessary to account for ch anges in the resistance, volume, and mass of the battery. The end result is a lower energy densi ty for the battery from including the cell group
interconnects and additional inactive material for each cell. Furthermore, the thickness of the
cells is reduced to 6 mm to better suit the smaller cell format.25 

### 4. Modeling of Battery Pack Manufacturing Cost

4.1 Approach

The manufactured cost of a battery pack is calculat ed with input from the design information generated in modeling the cell and battery pack per formance. The design modeling determines the annual materials and purchased items requiremen ts. The manufacturing cost is then added to these materials costs, along with a warranty cost, to reach the unit cost of a single battery pack. The manufacturing costs for the designed battery ar e scaled from a baseline plant. The baseline plant was designed for a battery of intermediate si ze and production scale so as to establish a center-point for other designs. The baseline plant accounts for the size, speed, number of units, direct labor, and depreciation of the capital cost for each processing step. These costs are adjusted to meet the requirements for a plant produ cing the battery under study. The process expenses are summed with the additional costs of op erating the manufacturing facility. These costs include launch costs, working capital, variab le overhead, general, sales, administration (GSA), research and development, depreciation, and profit.

In this analysis, all costs are evaluated for 2020 when large battery manufacturing plants are built. All dollar values are brought back to 2010 w ith allowance for inflation. Some materials and battery manufacturing costs are lower than rece nt values, where we judged that processing improvements for high volume production of material s would reduce costs.

The baseline manufacturing plant was calculated for an annual production rate of 100,000
batteries. The cost model accounts for different sc ales of manufacture by recalculating the costs of each individual step in the manufacturing proces s. The changes in capital and operating costs will change the calculated unit cost of the battery pack. However, the parameters were determined to provide reasonable estimates for manu facturing rates of 20-500 % of the baseline rate. Thus, for a plant that is far different in si ze from the baseline plant, for instance a pilot pl ant having an annual production of only 5,000 battery p acks per year, the estimate from this study would be expected to be less accurate than if deter mined in a study dedicated to that purpose.

To simplify the cost calculations, it was assumed t hat all hardware items for the cells, modules and battery will be purchased from a vendor special izing in similar products. The costs for these items were estimated to be a fixed value plus an ad ditional value proportional to the weight of the item, which is calculated during the battery de sign. In mature manufacturing plants in 2020, toward which this study is directed, some items whi ch are assumed to be purchased in this study might actually be internally manufactured from raw materials. This would increase the number of processing steps needed in our manufacturing sim ulation and thus complicate the cost calculations. Assuming that some parts would be pur chased if they would actually be produced from raw materials would tend to underestimate capi tal and labor costs and overestimate purchased items expenses. However, the net effect w ould be a very small change to the overall unit cost of the battery pack.26

4.2 Materials Costs and Purchased Items

The end battery pack cost depends significantly on the cost of both the active and inactive materials that compose the design. In this subsecti on, the assumed material costs and the rational behind them are presented. While we state suggested materials costs, the user of the cost model may enter any value that they desire.

4.2.1 Battery Specific Materials Cost

The largest contributions to the materials cost of the battery are from the following components: positive and negative electrode active material, se parator, electrolyte, and current collector foils.
The choice of the materials often defines the size and performance of the battery as well as the cost. Many different variations of materials are po ssible in the Li-ion family of chemistries. However, we have chosen to focus on the different a vailable positive electrode materials with less attention on the negative electrode. This refl ects the current research and manufacturing activities. The separator and the electrolyte are a lso both active areas of development. However, the following battery designs are based on a single electrolyte and separator combination. Including the cost and effect of additives and enha nced separators is beyond the scope of this work. The user is always able to modify the dimensi ons, cost, and ASI that may be required to account for changes in these materials.

The price of specific battery materials is of some debate. The values presented in Table 4.1 compare our suggested costs to those reported recen tly in the open literature. Our values, as well as the others in the table, are derived from conver sations with material, cell, and original equipment manufacturers. The sources are commonly a nonymous and the accuracy of the values is generally unknown. We present the comparison of published values so that the user of the cost model may appreciate the accepted range of values f or commonly used materials.

4.2.1.2 Positive Electrode Active Materials

The cost of positive electrode materials is driven to a large extent by the cost of the raw materials from which it is made. The archetype Li-ion positiv e electrode material, lithium cobalt oxide (LCO), was the original material commercialized in Li-ion batteries for consumer electronics. LCO has many excellent characteristics but is not c onsidered a viable choice for use in Li-ion batteries for automotive applications. One of the l argest drawbacks of LCO, other than safety concerns, is the cost of the cobalt. While tolerabl e in the consumer electronics market, the cost is too high for use in an automobile battery. Many oth er materials are in a commercially viable state of development and are currently utilized in Li-ion batteries produced today (Table 4.1). 3,6
The relative advantages and disadvantages of each m aterial will not be discussed here.

The amount of cobalt and nickel, as well as ease of manufacture, controls the end price for a positive electrode material. For example, the NMC-4 41 is less expensive than the NMC-333 as the cobalt quantity is significantly reduced. The m arket price for cobalt and nickel metal varies dramatically from year to year. Reducing the quanti ties of these materials will reduce the27ANL TIAX CARBMaterial Chemistry Abbreviation unit 2010 2010 2007Manganese spinel cathodeLi1.06Mn1.94O4LMO $/kg 10 12 - 16 - 20 8 - 10Phospholivine cathodeLiFePO4LFP $/kg 20 15 - 20 -25 16 - 20Layered oxide cathodeLiNi0.80Co0.15Al0.05O2NCA $/kg 36 34 - 40 - 54 28 - 30Layered oxide cathodeLi1.05(Ni1/3Mn1/3Co1/3)0.95O2NMC-333 $/kg 40 40 - 45 -53 22 - 25Layered oxide cathodeLi1.05(Ni4/9Mn4/9Co1/9)0.95O2NMC-441 $/kg 33 - -Li & Mn rich layered cathodexLi2MnO3·(1-x)LiNiyMnzCo1-y-zO2LMR-NMC $/kg 25 24 - 31 - 39 -Layered oxide cathodeLiCoO2LCO $/kg - - 30 - 40Graphite anodeC6Gr $/kg 19 17 - 20 - 23 -Titanate spinel anodeLi4Ti5O12LTO $/kg 12 9 - 10 - 12 -Electrolyte1.2 M LiPF6in EC:EMC$/kg 19 18.5 - 21.5 -24.5 -Separator PP/PE/PP$/m22 1 - 2.5 -2.9 -Current collector foil Copper$/m23.00 - -Current collector foil Aluminum$/m20.80 - -Table 4.1Details of stated costs for cathodes, anodes, electrolyte, and separator.3,628

positive electrode material price and price volatil ity. Researchers at TIAX LLC have treated this variation and shown the significant effect on end b attery cost. 10 The average metal prices for the last 20 years is 48 $/kg and 15 $/kg for cobalt and nickel respectively. These numbers are based on historical prices for the metals as collected by the United States Geological Survey (USGS). 23
The metal prices are best used as indicators for ho w the intercalation material cost will relate when compared to one another. The fact these materi als are not earth abundant means they will
not benefit as much as other materials from increas ed scales of production.

In general, earth abundant elements should be the d ominate transition metal used if a low positive electrode cost is desired. Both iron and m anganese are abundant and inexpensive transition metals for intercalation materials. Comp arison of the iron phosphate, LFP, to manganese spinel, LMO, reveals how processing costs contribute to the end price of a material. LMO is relatively easy to manufacture. In contrast, LFP requires a reducing atmosphere and a carbon coating step to reach the end product. The i ncreased complexity in the manufacturing process is realized in the price. However, one coul d argue that the manufacturing cost will decrease with increased knowledge from larger scale s of production.

4.2.1.2 Negative Electrode Active Materials

While multiple negative electrode materials exist f or Li-ion batteries, carbon materials in the form of graphite and/or hard carbon are still used in the vast majority of commercial cells. Graphite offers the greatest energy density while h ard carbon is said to enable high rate capability with decreased risk of lithium plating ( an undesired side reaction) during high charge rates. We have chosen synthetic graphite as a gener ic carbon electrode in our model. The price of graphite is much better understood than that of mos t of the positive electrode materials. However, significant differences in cost and perfor mance will exist between synthetic, natural, and coated-natural graphite. The method of producti on and necessary heat-treatment will control the end cost. Graphite, although in different purit y grades or microstructure forms, is used in many industries. This is in stark contrast to the p ositive electrode materials.

The lithium titanate electrode, LTO, offers an inte resting option compared to graphite. Unlike graphite, LTO operates within the stability window of the electrolyte. The higher electrode potential dramatically reduces or eliminates the fo rmation of the solid electrolyte interphase (SEI). As a result, nanoparticle-based LTO may be i mplemented without concerns of increased side reactions with the electrolyte. The reduced di mensions increase the available surface area for reaction while simultaneously shortening the di ffusion length. Both of these factors combined with the lack of SEI dramatically reduce the impeda nce of the electrode.

4.2.1.3 Electrolyte and Separator

The electrolyte used in this model is based on a li thium hexafluorophosphate salt, LiPF 6 , dissolved in a carbonate based solvent system. The carbonate solvent system is a blend of ethylene carbonate, EC, and a linear carbonate such as ethyl methyl carbonate, EMC, or dimethyl carbonate, DMC. Other chemical additives may be use d to lower the capacity and power fade of the battery over time. Polymers may be added to the electrolyte as either a minor or major29

component. This is not discussed in any further det ail in this work. The price of $16/L, about $19/kg, is only for the base electrolyte (i.e. no a dditional additives).

The separator is typically a porous membrane based on polypropylene (PP) and sometimes includes a polyethylene (PE) middle layer. PP and P E are very inexpensive raw materials and thus the suggested cost of $2/m 2 is in large part due to the manufacturing process required to form the porous network in the membrane. As competi tion and scale of manufacture increase, the prices of the separator may fall closer to $1/m 2 . However, the cost of improved technology may offset some of this cost reduction, so we have retained our cost estimate of $2/m 2

.

As safety is a major concern for Li-ion batteries, the separator plays a key role in isolating the oxidant from the fuel. If the two charged electrode s contact each other (short), then a run-away reaction is possible. Separators have been designed to “shut-down” or melt at key temperatures. The middle PE layer is the shut-down feature in our proposed separator. Ceramic coatings have also been used to ensure structural integrity. Many other approaches are being developed to increase the safety of Li-ion batteries. The user o f the cost model should account for the increased technology in the price and dimensions of the separator as needed.

4.2.1.3 Current Collector Foils

The current collector foils are based on copper met al for the negative electrode and aluminum for the positive electrode. However, the LTO anode mate rial, because of its high voltage relative to lithium, enables the use of aluminum as the negativ e electrode current collector. The price of
these foils is based on raw materials and manufactu ring costs. The foils are 12 microns and 20 microns thick for the copper and aluminum current c ollectors respectively. The foils used in batteries have additional requirements beyond the c heapest product available. Surface treatments are often necessary to promote adhesion of the elec trode to the foil surface. In addition, alloying of the foil may be necessary to achieve the require d material properties for long life.

The raw material contributions to the foil price wi ll vary with the volatility of the market price for the metals. Figure 4.1 displays the metal ingot price contribution on a $/m 2 basis. These numbers are based on historical prices for the meta ls as collected by the USGS. 23

The values for both aluminum and copper tend to var y significantly over the time period examined. The price for copper is more volatile and always more expensive than aluminum. Analysis of Figure 4.1 reminds the user of the cost model that cost quotes are only valid for a short period. As the market price for raw materials changes, so will the price for the finished product.

Conversations with manufacturers and suppliers lead us to take a price of 3.00 and 0.80 $/m 2 for battery grade copper and aluminum foil respectively . We point out that the current metal ingot price is only a small contribution to the end foil price being about 15 % of the aluminum foil price and 25 % of the copper foil price. Thus, a do ubling of the ingot prices would only moderately increase the foil prices. The aluminum f oil is produced by rolling of thicker stock
foils into thinner and thinner sheets. On the other hand, copper foil is more likely to be produced through an electrodeposition process.30 

### 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90

1985 1990 1995 2000 2005 2010



## YearMetal Ingot Cost in 2010 $/m2 

### Copper
Copper 20 yr avg

Aluminum
Aluminum 20 yr avg

Figure 4.1 Metal ingot cost contribution to the current colle ctor foils over a 20 year period. The average for that period is also shown. All costs ar e in 2010 US$.

4.2.1.4 Additional Electrode Components

The binder and conductive additive in the positive and negative electrodes add a small but real cost to the battery. The conductive additive, more common for the positive electrode, was priced at 6.80 $/kg for a high purity and moderate surface area carbon black material. The binder, perhaps PVDF or CMC based, is assumed to be 10 $/kg . The N -Methyl-2-pyrrolidone (NMP)
solvent for the PVDF binder is estimated to be 3.20 $/kg. Most of the NMP is recovered after evaporation and recycled as discussed in section 4. 3.3. Only the small amount lost in processing need be replaced. No cost is assumed for water.

4.2.2 Purchased Items Cost

Table 4.2 lists the purchased items for the cell mo dule and battery jacket. The cost of a SOC controller for each cell, or group of parallel cell s, is $1.80 plus a small factor for the cell capaci ty (Ah), which allows for higher cell balancing curren ts for larger cells. The other components cost31

a fixed amount plus an additional factor, which is proportional to their mass, m i . The cell negative terminal and parallel cell group connectio n are both made from nickel plated copper sheet and thus have the same cost equation.

Table 4.2 Cost equations for purchased items

Component, i Cost Equation, $/unit Cost per unit

SOC controller 1.80 + 0.005 C cell or parallel cell group Cell positive terminal 0.10 + 4 m i cell Cell negative terminal 0.10 + 5 m i cell

Cell container 0.10 + 5 m i cell Parallel cell group connection 0.10 + 5 m i parallel cell group

Module terminals 0.75 + 4 m i module Balance of module (casing) 1.00 + 3 m i module Battery enclosure & cooling 50.00 + 7 m i battery pack

4.3 Baseline Manufacturing Plant

The baseline plant is designed to produce 100,000 N CA-Gr baseline battery packs per year. The baseline battery pack produced by the plant has six ty, 40-Ah capacity cells, providing a total pack power of 50 kW and total energy of 8.7 kWh. Th e battery will power 24.4 miles of vehicle travel at 70% of the pack energy and 250 Wh/mile. T he schematic diagram of the plant (Fig. 4.2) is designed to illustrate the flow of materials thr ough the plant and the relative floor areas for the processing steps rather than representing a realist ic plant layout. The overall manufacturing rate of 100,000 battery packs per year is achieved by op erating for three shifts at the equivalent of 300 days per year of fully effective production. Th ere will be more than 300 days of operation, but some days will have less than 100% effectivenes s. The exceptions to three-shift operation are the Receiving and Shipping sections, which are acti ve for only two shifts per day. The cost factors for the individual manufacturing steps in t he baseline plant are summarized in Table 4.3
and discussed in detail in the sections that follow . Most of the operations are carried out with normal factory atmosphere, but the cell assembly pr ocess steps are completed in a dry room atmosphere.32

Figure 4.2 Baseline lithium-ion battery manufacturing plant s chematic diagram. Manufacturing rate: 100,000 NCA-Gr battery packs per year, 50-kW pack power, 40-Ah capacity, 60 cells per battery. Operating year: 300 days with three 8-h sh ifts (two shifts for receiving and shipping)

4.3.1 Receiving and Shipping

These operations require the moving equipment and s torage facilities common to any such factory facilities. The Receiving section handles s lightly less than 6,000,000 kg of materials per year and also has facilities to handle and store so me of the electrode materials in a dry atmosphere. The Shipping section is required to enc lose the battery packs in crates, which requires some automated equipment and more labor th an is required for Receiving. Shipping also handles about 400,000 kg of scrap each year, which is broken down and prepared for shipping in the Rejected Cell and Scrap Recycle section. The es timated resources needed for the Receiving and Shipping sections are shown in the table below.

Rate Factor Direct Labor Capital Equip.* Plant Area, m 2
Receiving Off-loading Moving Storage 870,000 kWh/y 3 per shift 3.60 mil$ total

0.60

1.20

1.80 600

Shipping 870,000 kWh/y 6 per shift 5.0 mil$ total 600 *Total cost including installation The areas in this diagram for each processing step are approximately proportional to the estimated plant areas in the baseline plant. Shipping

Cell and Scrap Recycling Receiving

Control Laboratory

Assembly Route Battery Pack Assembly and Testing Module

Assembly Formation

Cycling Current
Collector Welding Enclosing
Cell in
Container

Electrolyte Filling and Cell Closing Cell Stacking Solvent Evaporation

Positive

Negative Electrode Coating

Positive

Negative Electrode Slitting

Vacuum Drying Electrode Materials Preparation

Positive

Negative Calendering Solvent Recovery

Air

Locks

ChargeRetention Testing Final

Cell Sealing

Dry Room Materials Handling

Outdoor dry-room air

processing equipment33No./shift Hours/yr p Factor $MM p Factorm2p FactorReceiving (two-shift operation) 869,420kWh energy 3 14,4000.4 3.600.6 6000.5Materials preparationPositive electrode 1,712,524kg active material 3 21,6000.5 4.000.7 4000.6Negative electrode 1,208,957kg active material 3 21,6000.5 4.000.7 4000.6Electrode coatingPositive electrode 8,169,835m2cell area4 28,8000.5 6.000.8 (0.2)* 5000.8Negative electrode 8,169,835m2cell area4 28,8000.5 6.000.8 (0.2)* 5000.8Solvent recovery 2,309,021kg NMP 2 14,4000.4 3.000.6 1500.6CalenderingPositive electrode 8,169,835m2cell area1 7,2000.5 1.000.7 1500.6Negative electrode 8,169,835m2cell area1 7,2000.5 1.000.7 1500.6Materials handling#8,169,835m2cell area4 28,8000.7 1.500.7 6000.6Electrode slitting 8,169,835m2cell area4 28,8000.5 2.000.7 2000.6Vacuum drying 8,169,835m2cell area2 14,4000.5 1.600.7 2000.6Control laboratory 869,420kWh energy 4 28,8000.5 1.500.7 2000.6Cell Assembly in Dry RoomCell stacking 6,315,789total cells 6 43,2000.7 5.000.8 (0.3)** 4000.8Current collector welding 6,315,789total cells 6 43,2000.7 5.000.8 4000.8Enclosing cell in container 6,315,789total cells 4 28,8000.5 3.000.7 4000.6Electrolyte filling, and cell sealing 6,315,789total cells 6 43,2000.5 6.000.7 6000.6Dry room control and air locks 2,000m2operating area#2 14,4000.4 20.000.6 750.4Formation cycling 6,315,789total cells 8 57,6000.7 30.000.8 (0.3)** 1,5000.8Final cell sealing 6,315,789total cells 2 14,4000.5 7.500.7 3000.6Charge retention testing 6,315,789total cells 3 21,6000.4 4.750.7 6000.6Module assembly 6,000,000finished cells 6 43,2000.5 6.000.7 4000.6Battery pack assembly and testing 100,000battery packs 6 43,2000.5 6.000.7 (0.3)*** 6000.6Rejected cell and scrap recycle 6,315,789total cells 5 36,0000.7 2.500.7 4000.6Shipping (two-shift operation) 869,420kWh energy 6 28,8000.5 5.000.7 6000.6Total95 662,400135.9510,325#One-third of the space for materials handling is within the dry room.*The baseline capital cost electrode coating, Co, is based on the evaporation of the baseline annual solvent weight (Rso). For batteries requiringdifferent solvent evaporation rates Rs, the cost is multiplied by ratio of rates raised to the 0.2 power. Thus, Cost = Co*(R/Ro)^0.8*(Rs/Rso)^0.2.**The baseline costs of the capital equipment for cell stacking and formation cycling is for 40-Ah cells. To correct the baseline cost (Co) for cellsof different capacity, the cost is multiplied by the capacity ratio, (Cap)/ 40 Ah, raised to the 0.3 power. Thus, Cost = Co*(R/Ro)^0.8*(Cap/40)^0.3.***The baseline cost of the capital equipment for battery assembly is for a battery with four modules.To correct the baseline cost for a differentnumber of modules (Mod), the cost is multiplied bythe ratio of modules, (Mod)/4 raised to the 0.3 power. Cost = Co*(R/Ro)^0.7*(Mod/4)^0.3.Annual Baseline Rate (Ro)Direct LaborCap. EquipmentPlant AreaTable 4.3Summary table of the baseline plant34

4.3.2 Electrode Materials Preparation and Delivery to Coating

The electrode materials, which consist of active ma terial, carbon (if necessary), binder and binder solvent, are well mixed in small batches in portable tanks. At the design production rate in the baseline plant, each shift requires three ta nks each holding about 1000 liters of positive electrode material mix and three tanks each holding about 900 liters of negative electrode material mix. The section must be capable of exceed ing this design rate of production by at least 25% to catch up in case of unscheduled downtime in Materials Preparation or in some of the section immediately following that section. The ta nks of prepared materials are moved to the Coating section and pressurized to push the coating paste into the coating mechanism. The estimated resources needed are the following:

Materials Prep. Rate Factor Direct Labor Capital Eq uip.* Plant Area, m 2

Positive
Materials Storage tanks Mixing tanks Moving equip. 1,710,000 kg/y

active material 3 per shift 4.0 mil$ total

2.00 mil$

1.00

1.00 400

Negative
Materials 1,210,000 kg/y

active material 3 per shift 4.0 mil$ total 400

*Total cost including installation

4.3.3 Electrode Coating on Current-Collector Foil

The positive and negative electrode structures are formed by coating both sides of the current collector foil. In the baseline plant, the coating lines are 1.5 meter wide continuous roll-to-roll coating processes carried out at a line speed of 10 m/min. The first set of coating and drying
stations coats one side of the current collector fo il, drives off the solvent in a heated oven, and turns the foil over while transferring it to a seco nd set of stations. The second set of coating and drying stations applies and dries the remaining coa ting before the coated foil is wound into a large roll at the end of the line. The negative and positive coating lines are very similar. However, some of the negative material is coated on ly on one side to provide the electrodes at the end of the cell stacks. For the baseline plant, a total of 8,170,000 m 2 /y of coating (annual cell area) is required for the positive electrode (sligh tly more for the negative electrode), which allows for the 5% loss of cells expected to fail te sting and inspection. A larger area of foil than
the coated area must be fed to the coaters to allow for the part of the foil that is not coated so as to provide tabs for welding to the terminals (about 10%) and to allow for trimming losses during electrode slitting (8%). Also, about 30% excess coa ting capacity must be provided to allow for unscheduled downtime. Only one coating line is need ed for each electrode type to meet these needs. If one coating line breaks down, the other c oating line may change over temporarily to
coat the other electrode material.

The oven sections of the coating line are designed to dry coatings about 100 microns thick at the coating speed of 10 m/min. A thicker coating will r equire longer ovens at additional capital cost which is provided in the adjustment of costs discus sed in section 4.4. For the same annual area throughput, a coating line that coats both sides wi th a 300-micron coating would cost $7,500,00035

rather than the $6,000,000 cost for the 100-micron coater. The binder solvent for the positive electrode in the baseline plant is NMP, which must be recovered by condensation and recycled.
About 0.5% of the binder solvent is combusted with a thermal oxidizer and must be replaced. For the negative electrode the binder is water, which n eed not be recovered. The estimated resources to meet these needs are the following:

Electrode Coating Rate Factor Direct Labor Capital Equip.* Plant Area, m 2

Positive Electrode

Uncoated area
Width of coater Coating speed
Number of coaters
Maximum rate Excess capacity 8,170,000

m 2 /y cell area 4 per shift 6.0 mil$ total

18%
1.5 m
10 m/min

One 13,000,000 m 2 /y

30% 500

Negative Electrode 8,170,000

m 2 /y cell area 4 per shift 6.0 mil$ total 500

Solvent Recovery &
Oxidation 1,527,000 kg NMP/y 2 per shift 3.0 mil$ total 150

*Total cost including installation

4.3.4 Calendering

The materials leaving the coating lines may be stor ed on large rolls (see next section). However, typically the materials leaving the coaters would g o directly to the calendering process in which the coatings are compressed by rolling to meet the specified void volume fraction, which will later be filled with electrolyte. The calendering e quipment must match the output of the coating equipment producing 8,170,000 m 2 /y of cell area with a maximum rate of 13,000,000 m 2 of foil per year to meet contingencies as in coating. The e stimated resources to meet these needs are the following:

Calendering Rate Factor Direct Labor Capital Equip. * Plant Area, m 2

Positive Electrode 8,170,000

m 2 /y cell area 1 per shift 1.0 mil$ total 150

Negative Electrode 8,170,000

m 2 /y cell area 1 per shift 1.0 mil$ total 150

*Total cost including installation

4.3.5 Inter-Process Materials Handling

For all processes (Fig. 4.2), work in progress must be transported and occasionally stored to permit nearly-continuous operation of the equipment . Storage areas must be provided both inside and outside of the dry room. Raw materials must als o be moved to the processing sites, which for those in the dry room means through a separate air lock for materials transfer. One-third of the36

total space for Inter-Process Materials Handling is within the dry-room for the baseline plant and also for all other plants. The estimated resources to meet these needs are the following:

Materials Handling Rate Factor Direct Labor Capital Equip.* Plant Area, m 2

8,170,000

m 2 /y cell area 4 per shift 1.5 mil$ total 600

*Total cost including installation

4.3.6 Electrode Slitting

The coated electrode foils are slit into strips bet ween the coated sections and then into individual electrodes as shown in Fig. 2.2. The estimated scra p loss of foil for this process is about 8%. The
estimated resources to meet these needs are the fol lowing:

Electrode Slitting Rate Factor Direct Labor Capital Equip.* Plant Area, m 2

8,170,000

m 2 /y cell area 4 per shift 2.0 mil$ total 200

*Total cost including installation

4.3.7 Final Electrode Drying

In the absence of electrolyte, no harm is done by e xposing the electrodes to normal factory air; however, the electrodes must be dried by heating un der vacuum prior to cell assembly. Maintaining extremely low moisture conditions durin g cell assembly is believed to be very important in achieving long battery life. The final drying step coupled with dry room conditions ensures a minimal quantity of moisture will exist i n the final product. The pertinent processing rate in determining the resources necessary for dry ing is the total amount of active materials processed per year (other electrode materials are a pproximately proportional), which for the baseline plant is 2,950,000 kg/y or 3,275 kg/shift. The individual electrodes exiting from the electrode slitting process are separated into stack s by polarity, loaded into vacuum drying ovens, dried for several hours, and unloaded directly into the dry room. The estimated resources to meet these needs are the following:

Electrode Drying Rate Factor Direct Labor Capital E quip.* Plant Area, m 2

Dryer capacity Number of dryers
Maximum rate 2,950,000 kg/y

active material 2 per shift 1.6 mil$ total

600 kg/shift

8 4,320,000 kg/y 200

*Total cost including installation

4.3.8 Control Laboratory

The purpose of the control laboratory is to ensure that the raw materials and the electrodes being fabricated meet specifications. Laboratory personne l collect or supervise collection of samples and carry out analyses. The estimated resources to meet these needs are the following:37

Rate Factor Direct Labor Capital Equip.* Plant Are a, m 2

Control Lab 869,000 kWh/y 4 per shift 1.5 mil$ total 200

*Total cost including installation

4.3.9 Cell Stacking

The cells are assembled in four steps, which are ca rried out in a dry room. The first of these steps is cell stacking. The primary rate factor that dete rmines the cost for all steps in cell assembly is the number of cells assembled per year. For cell st acking an additional cost factor is the capacity of the cells; large cells usually require more elec trodes of larger area and thus a more capable, faster cell stacking machine. The method used to de termine the extra costs of stacking equipment in detailed in Table 4.3. The capacity of the cells is deemed to have only a minor effect on the other steps in cell assembly and is not taken into account for those steps. The electrodes are inserted in a folded separator sheet, the positive electrodes tabs protrude on one side and the negative electrodes tabs on the other. As in other parts of the plant, excess capacity is provided to allow catching up after unscheduled downtime. The e stimated resources to meet these needs for the baseline plant are the following:

Cell Stacking Rate Factor Direct Labor Capital Equi p.* Plant Area, m 2

Stacking rate
Number of units
Maximum rate 6,320,000 cells/y 6 per shift 5.0 mil$ total

4 cells/min
5 8,640,000 cells/y 400

*Total cost including installation

4.3.10 Current Collector Welding

The current collector tabs for the negative and pos itive electrodes are welded to their respective terminals by ultrasonic welding. This procedure ach ieves a connection of near-zero resistance and avoids overheating the electrodes during the we lding process. The estimated resources to meet these needs are the following:

Tab Welding Rate Factor Direct Labor Capital Equip. * Plant Area, m 2

Cell rate
Number of units
Maximum rate 6,320,000 cells/y 6 per shift 5.0 mil$ total

4 cells/min
5 8,640,000 cells/y 400

*Total cost including installation

4.3.11 Enclosing Cell in Container

The aluminum foil in the pouch container is suffici ently thick (100 microns default thickness) to permit the use of stiff, pre-shaped pouch halves. T he pouches are assumed to be purchased as38

finished parts. Each cell is enclosed in these cont ainers, which are then partially sealed prior to injecting electrolyte. The estimated resources to meet these needs are the following:

Enclosing cells Rate Factor Direct Labor Capital Eq uip.* Plant Area, m 2

Cell rate
Number of units
Maximum rate 6,320,000 cells/y 4 per shift 3.0 mil$ total

4 cells/min
5 8,640,000 cells/y 400

*Total cost including installation

4.3.12 Electrolyte Filling and Cell Sealing

At this station, the cells are evacuated, filled wi th electrolyte and temporarily sealed. The
estimated resources to meet these needs are the fol lowing:

Filling & 1 st

Seal Rate Factor Direct Labor Capital Equip.* Plan t Area, m 2

Cell rate
Number of units
Maximum rate 6,320,000 cells/y 6 per shift 6.0 mil$ total

4 cells/min
5 8,640,000 cells/y 600

*Total cost including installation

4.3.13 Dry Room Management

Excellent dry-room atmosphere is required for lithi um-ion cell assembly. A maximum dew point temperature of –40 °C is maintained in the room. Th e load on the dry-room drying apparatus is determined by diffusion of water vapor through the walls, entry of air through the air locks, the number of workers in the room, and the need to admi t some fresh air to limit the build up of contaminants such as electrolyte solvent vapor. The se load factors are approximately a function of the room area. Because of the importance of the proper functioning of the dry room, two workers are on duty at all times to monitor its per formance. The equipment for circulation and purification of the dry air will be located outside of the plant building, adjacent to the dry room.
The estimated resources to meet these needs are the following:

Operating
Area Direct Labor Capital Equip.* Air Locks, m 2

Dry Room 2,000 m 2 2 per shift 20.0 mil$ total 75

*Total cost including installation

4.3.14 Formation Cycling, Final Cell Sealing and Ch arge Retention Testing

Formation cycling is expensive because it takes con siderable time and each cell must be monitored separately. For plants to be operated in 2020, we expect some improvements from present day operations because of the urgency to im prove and thus save cost. We project that the entire formation cycling and testing can be done in two shifts. These operations consist of39

charging the cell, discharging to full depth to mea sure capacity and impedance, followed by fully recharging the cells. These tests will be carried o ut in large temperature controlled cycling units that test 500 cells simultaneously, monitor each ce ll and automatically identify failed cells. The capital cost of the cycling equipment is primarily a function of the annual number of cells to be tested, but to a lesser extent on the capacity of t he cells.

The short-term testing described above does not det ect cells that have self-discharge rates that are slightly above normal, which could lead to cata strophic failures later. To detect such defects, the cell charge is topped off and the cells are sto red for two weeks and then checked for loss of charge. Most of the test period is spent in large r acks in compact arrays, without electronic monitoring. Incidentally, the two-week long self-di scharge testing requires less floor space than for formation cycling, which lasts only two shifts.

The final cell sealing occurs between the formation cycling and charge-retention storage test. Gas generated during formation cycling may accumula te in the reservoir space that was created during the temporary sealing step. This gas is remo ved by creating the final seal below the reservoir and trimming off the unwanted portion.

The estimated resources to meet these needs are the following:

Rate Factor Direct

Labor Capital Equip.* Plant Area,

m 2
Formation Cycling Cell capacity Number of cyclers Cells per cycler Length of test Testing capacity 6,320,000 cells/y 8 per shift 30.0 mil$ total

40 Ah
35
500

2 shifts 7,875,000 cells/y 1500

Final Cell Sealing 6,320,000 cells/y 2 per shift 2.0 mil$ total 300

Charge Retention Testing rack capacity Racks per stack
Number of racks Length of test Testing capacity 6,320,000 cells/y 3 per shift 4.75 mil$ total

500 cells
5
750 14 days 8,040,000 600

*Total cost including installation

4.3.15 Module and Battery Assembly

Approximately 5% of the cells are expected to fail the formation cycling and charge-retention tests and these are sent to the Rejected Cell and S crap Recycle section. The accepted cells (6,000,000 finished cells per year) are assembled i nto modules by attaching the terminals through laser welding or mechanical joining with sp ring loaded devices. Electronic circuit packs are attached that occupy about the same volume as a cell. These operations are carried out at four40

automated stations each capable of handling about 2 80 cells per hour. For the module design being cost estimated in this model, the module is e nclosed in an air-tight aluminum container by double seaming. The processing rate that determines the cost of module assembly is the number of finished cells that must be handled per year.

The finished modules are assembled into battery pac ks with the aid of automated stations. The total cost of these stations is dependant mainly on the number of battery packs to be assembled per year (100,000 for the baseline plant), but to a lesser extent on the number of modules per pack. After assembly, the packs are moved to testin g stations where they are discharged as a final check of impedance and to lower the state of charge to a level suitable for shipping. The
estimated resources to meet these needs are the fol lowing:

Rate Factor Direct

Labor Capital Equip.* Plant Area,

m 2

Module Assembly
Number of stations
Cells/h/station Capacity 6,000,000 cells/y 6 per shift 6.0 mil$ total

4

280 8,060,000 cells/y 400

Battery Pack Assembly Modules/pack
Number of stations
Packs/h/station Capacity 100,000 packs/y 4 per shift 3.0 mil$ total

4

3
6 130,000 packs 300

Battery Pack Testing 100,000 packs/y 2 per shift 3.0 mil$ total 300

4.3.16 Rejected Cell and Scrap Recycle

Scrap is generated in preparing the electrodes and by the rejection of 5% of the cells that go through formation cycling and charge-retention test s. This scrap is gathered and packaged for shipment for recycling of the materials having valu e. No credit is taken for the value of the scrap in this model except that the costs of gathering, s orting, packaging and shipping are understated by about that value. The main factor in determining the cost of scrap recycle is the number of cells rejected, which have to be disassembled to re cover the scrap, a labor intensive process. The yields of materials in the various processing steps are shown in Table 4.4.

Table 4.4 Materials yields during electrode and cell fabric ation

Material Material

Mixing Coating Electrode

Slitting Cell

Stacking Electrolyte

Filling Total

Positive Electrode 99 95 99 99 92.2 Negative Electrode 99 95 99 99 92.2

Positive Current Coll. 99 92 99 90.2 Negative Current Coll. 99 92 99 90.2 Separator 98 98.0 Electrolyte 94 94.041

The estimated resources needed for scrap recycle ar e the following:

Rate Factor Direct

Labor Capital Equip.* Plant Area, m 2

Scrap Recycle Scrap rate 6,320,000 cells/y 5 per shift 2.5 mil$ total 441 kg/shift 400

4.3.17 Baseline Plant Summary

The processing rates and the primary cost factors f or the baseline plant are summarized in Table 4.3. The main cost-determining rate of processing f or each step is shown in the second column. The requirements for direct labor, capital equipmen t and plant area, which are shown in detail in the subsections above, are summarized in the table. It is seen that the plant requires a total of 95 workers per shift, $130,450,000 worth of capital eq uipment, and 10,325 square meters of plant area to manufacture the baseline battery at a rate of 100,000 battery packs per year.

4.4 Adjustment of Costs for Rates Different than th ose of the Baseline Rates

As noted in Table 4.3, there are many processing ra tes that must be considered in addition to the overall number of battery packs manufactured per ye ar. Each of these rates affects the costs of one or more steps in the process and may have no ef fect upon the costs of other steps in the process. For instance, when the user of the model i ncreases the power of the battery packs without increasing the number of cells or their cap acity, the model increases the area of the cells and decreases the electrode coatings thicknesses. S uch changes would result in an increase in the cost of the coating equipment, the floor area occup ied by the equipment, and in the direct labor for that step in the process. It would have no effe ct on the cost of mixing the materials to be coated because the amounts of these materials per b attery back are unchanged under the assumed
conditions.

The general approach to cost estimation of multiply ing a known cost by the ratio of processing rates raised to a power has also been applied to th e capital cost of individual items of equipment. 24

C = C
o ( R / R
o ) p (4.1)

Here, C
o is the capital cost of an installed equipment item designed for the baseline processing

rate, R
o. The power factor, p , relates the capital investment cost and the proce ssing rate for the manufacturing step.

If the value of p were 1.0, it would imply that the cost of the equi pment item, or the equipment items if there are several in parallel, would be di rectly proportional to the processing rate. However, the value of p for the cost of equipment is frequently about 0.6 to 0.7 for many manufacturing process steps because the equipment i s larger for the higher processing rates and its cost is less than if it were directly proportio nal to the processing rate. For process steps42

requiring the addition of many identical pieces of equipment for scale up, such as may be true for formation cycling of battery cells, the value of p may be as high as 0.9. The value of p is unlikely to reach 1.0 because the equipment cost includes in stallation, for which there is some savings even in installing multiple units of the same proce ssing capacity. The relationship between cost and processing rate for two-fold and three-fold rat e changes is illustrated in Table 4.5.

Table 4.5 The effect of processing rate ( R ) on cost for various scale factors

C / C
o = ( R / R
o ) p

Cost Ratio, C / C
o Scale Factor, p R / R
o = 2 R /

R
o = 3

0.25 1.19 1.32

0.3 1.23 1.39

0.4 1.32 1.55

0.5 1.41 1.73

0.6 1.52 1.93

0.7 1.62 2.16

0.8 1.74 2.41

0.95 1.93 2.84

1.0 2.00 3.00

Similar equations have been applied for determining the effect of processing rate on the annual hours of labor and the plant area required for a ma nufacturing step. In general, the value of p is low for the labor equation, usually only 0.4 to 0.5 , because only a relatively small addition to the labor crew permits operation of larger equipment or of operating several more units of the same processing capacity. 24 The value of p for the plant area required for a processing step is slightly less than that for equipment. The floor area requir ed for larger equipment or for more equipment items of the same size is proportionately less than the increase in the processing rate because of the more efficient use of the space occupied by the equipment and the savings in aisle area.

The value of the scale factors (i.e. p factors) for labor, capital equipment, and floor a rea were estimated for each of the processing steps (Table 4 .3). The scale factors selected for the direct labor requirement are usually only 0.4 to 0.5, whic h indicates considerable unit cost reduction for increasing the plant throughput.

For most processing steps, increasing the processin g rate beyond that in the baseline plant would
result in a decision to increase automation or use faster equipment to mitigate the costs of higher levels of throughput. Decreasing the processing rat e would have the opposite effect. Some steps in the process such as cell stacking, welding of cu rrent collectors, and formation cycling do not appear to be easily automated beyond the level inte nded in the baseline plant and, thus require a higher value for the scale factor of 0.8. This high er scale factor results in achieving fewer reductions in the cost per battery pack with increa sing production volume. Additionally, a higher

p factor results in a less severe penalty for lower production scale for an individual step in the

process.43

There are five steps for which the cost of the capi tal equipment is affected by other factors than the main processing rate for the process step. Thes e are discussed in the footnotes at the bottom of Table 4.3. For these steps, the costs that have been adjusted for the changes in the processing rate from the baseline rate are further adjusted to take into account the other cost factors. The cost of the coating equipment is adjusted for the a mount of solvents to be driven off of the positive and negative electrodes; thicker coatings need longer, more expensive ovens to drive off
the additional binder solvent or the coater most be operated at lower speeds. The cost of the cell stacking equipment and that of the formation cyclin g equipment, for which the main cost factor
in both cases is the number of cells to be fabricat ed annually, are also adjusted for the capacity of the cells; larger cells require more expensive equi pment. The cost of the capital equipment for battery assembly is primarily a function of the num ber of cells in the battery, but it is also a
function of the number of modules that must be inte rconnected. This dependence is accounted for in the model with an additional multiplying fac tor.

A breakdown of the baseline plant capital equipment costs listed in Table 4.3 is illustrated in Fig. 4.3. The largest costs for capital equipment are fo r formation cycling and testing, cell assembly in the dry room and electrode coating. These capita l costs are likely to be dominant in any lithium-ion battery plant in the near future.

Receiving and shipping

Materials preparation

Electrode coating

Calendering

Materials handling

Electrode slitting

Vacuum drying

Control laboratory

Cell assembly in dry room

Formation cycling and testing

Module and pack assembly

Rejected cell and scrap recycle

Figure 4.3 Breakdown of installed capital equipment costs for the baseline plant

4.5 Plant Investment Costs

In this model, the calculated investment costs are defined as those directly related with building and operating the plant (Table 4.6). Other costs th at may require investment, such as research44

and development, are added separately to the unit c ost of the battery. The largest investment cost is for the installed capital equipment. Each cost i tem for the battery under design is adjusted from the estimate of the baseline plant. The plant cost is done in a similar way with a cost of $1,500 per square meter ($140/sq. ft) including land and u tilities. Launch costs include plant start-up, employee training and materials that are lost or re cycled in early stages of production, beyond
the normal amounts. Launch costs are estimated to b e 5 % of annual materials costs plus 10 % of annual direct labor and variable overhead (Section 4.6). Working capital is needed to cover the costs of payroll, receivables, and the inventories of raw materials, work in progress and finished product. These working capital costs are partially offset by bills that are payable. We estimate the working capital to be 15 % of the annual variab le costs.

Table 4.6 Battery pack manufacturing investment costs

Investment Costs Description Method of Calculation Capital Equipment Equipment costs including
installation Estimates of costs for each processing step at baseline rates adjusted for actual rates. Plant Floor Space Space includes aisles and space for unfinished processing inventory plus land and utility

costs. Estimates of costs for each processing step at baseline rates adjusted for actual rates.

Launch Costs Plant start-up, training, out-ofspec product. 5% of annual materials cost, 10% of direct labor plus
variable overhead. Working Capital Cash to meet payroll, receivables, inventories of raw
materials and of unfinished and finished product, minus payables. 15% of annual variable costs.

4.6 Unit Costs for Battery Pack

The unit costs of the battery pack are calculated a s summarized in Table 4.7.

4.6.1 Variable Costs

The costs of the materials and purchased items are based on the costs discussed in section 4.2, and the annual amounts of materials are adjusted fo r the yields of materials (section 4.3) and yield of cells. The direct labor is the sum of the labor cost for each step in the process, which are each calculated for the baseline plant and adjusted for the rate associated with the battery under study. Variable overhead is the cost of indirect ma terials and labor, utilities, and plant
maintenance. It is estimated to cost 60 % of direct labor costs.45

4.6.2 Fixed Expenses

Fixed expenses include General, Sales, and Administ ration (GSA), research and development, and depreciation. The cost of GSA includes the plan t office, taxes on income and property, cost of sales and insurance. It is estimated by the mode l as 25 % of direct overhead plus 35 % of depreciation. Research and development (R&D) must b e carried out to ensure that the battery packs that are produced in the plant and the means of production continue to be competitive in the world market with respect to performance and pr ice. The greater the investment in the plant and its equipment, the greater is the need to be su ccessful in the R&D effort. Thus, the expenditure has been set at 50 % of the depreciatio n expense. Depreciation expense provides funding available for future investment in this pla nt or another venture to replace deteriorating plant and equipment. The equipment and plant are de preciated at straight-line rates for 8-year life (12.5 % per year) and 20-year life (5 % per year).

Table 4.7 Unit cost of battery pack Variable Costs Description Method of Calculation

Materials and Purchased

Items All materials and purchased items in finished product and lost in processing. Based on prices of materials, cost equations for purchased items and yields. Direct Labor Labor costs for operations and immediate supervision. Estimates of costs for each processing step at baseline rates adjusted for actual rates. Variable Overhead Indirect materials, labor, utilities, plant maintenance 60% of direct labor cost.

Fixed Expenses General, Sales, and Administration (GSA) Plant office, taxes on income and property, cost of sales and insurance expenses. 25% of direct labor and variable overhead plus 35% of depreciation. Research and Development On-going research needed t o upgrade product and maintain competitive position. 50% of depreciation

Depreciation Provides funds for new investments to replace those in current equipment and plant. 12.5% of capital equipment cost plus 5% of plant floor space

cost.
Profit Return on invested capital after

taxes. 5% of total investment costs.

Warranty Funds set aside for reimbursing

customers for battery pack
failures. 5.6% added to price based on present worth of projected
payments.46

4.6.3 Profits

The profit goal for this type of venture varies wit h the financial structure of the company, especially regarding long-term debt. For the model, the profit is set to provide a 5 % return on the total investment, which is an approximate avera ge for mature manufacturing as vehicle battery production is expected to be in 2020.

4.6.4 Battery Pack Warranty Costs

If a battery module or an entire pack fails, the re placement will cost much more than the original price paid by the OEM. It is important that such ev ents are rare, but provision must be made to reimburse the vehicle owner, especially in the earl y years of the projected battery life. The extra costs of replacing the battery will result from lab or for testing and replacing the battery, inventory costs for stocking replacement batteries, and servicing the battery controller if the new battery is slightly different than the old battery. It is likely that the battery manufacturer will be responsible for the cost of the new battery, which we assume will be equal to the cost of the original battery. The other costs of replacing the battery, to the extent that they are covered by the warranty, are assumed here to be covered by the automobile manufacturer and the dealer. The goal for average battery life is 15 years and a warranted life of 10 years, with full replacement in the first five years and shared cost of replacement for the last five years seems appropriate. The vehicle owner would pay an increas ing share of the cost from between 0 % at 5 years to 100 % at 10 or more years. With these assu mptions, the cost to the battery manufacturer will be equal to the present worth of the future co sts of the new battery or modules as provided in the warranty. The rate of battery failure will vary over the life of the battery with a slightly higher rate early in life, then a low failure rate followed by a gradually increasing failure rate. For purposes of calculation we assume a failure rat e of 1.0 % per year throughout the warranty period. With an internal rate of return of 8 % and calculated on a monthly basis, the present value of the future costs would be about 5.6 % of the pri ce of the battery before adding the warranty

cost.

4.7 Summary of Baseline Battery Cost

The spreadsheet version of the model, which is disc ussed in more detail in sections 5 and 6, provides a summary sheet which is illustrated in Ta ble 4.8 for the cost of the baseline battery and that of two others. This breakdown of the battery c osts, with a brief summary of the design values, illustrates the effects of the cost factors . The second battery has twice the power of the baseline battery and the third battery has the same power as the baseline battery, but twice the capacity. The number of cells is the same for each battery. The energy storage is slightly higher for the battery with double power because the volta ge would be slightly higher during the discharge to determine capacity. The battery with d ouble the capacity has fewer electrodes which are longer and wider, because the cell thickness in maintained, resulting in higher resistance in the current-collector structure. The higher impedan ce lowers the voltage during the discharge capacity measurements and results in slightly less than twice the energy storage of the baseline battery.47 Baseline Double Power Double Capacity Calculated Battery Parameters
Battery energy storage, kWh 8.7 8.8

17.1 Battery power at 80 % OCV, kW 50.0 100.0

50.0 Required battery power, kW 50.0 100.0

50.0 Capacity, Ah 40 40

80
Number of cells 60 60

60 Battery weight, kg 55.8 69.2

96.9 Battery volume, L 35.9 42.0

58.3 Vehicle electric range, miles 24.3 24.6

47.9 Investment Costs Capital equipment cost including installation, mil$ 130 149

152 Building, Land and Utilities
Area, m 2 10,325 12,193

11,744 Cost, $/m 2 1,500 1,500

1,500 Building investment, mil$ 15 18

18
Launch Costs 10 13

15 Working capital, mil$ 28 36

42 Total investment, mil$ 184 216

227 Unit Cost of Battery Pack, $

Variable Cost

Materials and Purchased Items
Cell materials 1,350 1,864

2,232 Cell purchased Items 75 75

90 Module and battery 228 234

276
Total 1,652 2,173

2,598
Direct Labor Electrode processing 36 52

40 Cell assembly 31 31

31 Formation cycling, testing and sealing 17 17

17 Module and battery assembly 16 16

16 Rejection and recycling 6 6

6 Receiving and shipping 8 8

11 Control laboratory 5 5

7
Total 119 135

128
Variable Overhead 72 81 77
Total Variable Cost 1,843 2,389 2,803 Fixed Expenses General, Sales, Administration 107 122 121 Research and Development 85 98 99 Depreciation 171 195 199 Total Fixed Expenses 364 415 419
Profits after taxes 92 108 113 Total unit cost per battery not including warranty, $ 2,299 2,912 3,335 Summary of Unit Costs, $

Materials 1,350 1,864

2,232
Purchased Items 303 309

366
Direct Labor 119 135

128
Variable Overhead 72 81

77 General, Sales, Administration 107 122

121 Research and Development 85 98

99 Depreciation 171 195

199
Profit 92 108

113 Warranty 129 163

187 Price, $ 2,428 3,075

3,522 Table 4.8. Summary of results for cost of baseline battery and that of similar batteries with double the power and double the capacity of th e baseline battery48

Doubling the power does not add as much cost to the materials and purchased parts as doubling the cell capacity. Most of the labor costs for the three batteries are similar with the major difference being for the labor cost for electrode p rocessing. The double power battery requires greater labor costs principally for coating the lar ger electrode area. Capital equipment and depreciation costs are higher for both the high pow er and high capacity battery packs. The increases in capital equipment cost for the high-po wer battery are for coating, calendering, materials handling and vacuum drying equipment. For the high-capacity battery, the main additional capital equipment costs are for the mate rials mixing, binder solvent recovery, cell staking and formation cycling steps in the process.

Overall, doubling the power of the battery increase s the cost by only 27 %. Doubling the capacity of the cells increases the cost by 45 %, c onsiderably more than for doubling the power. Alternatively, doubling the number of baseline cell s and modules within a larger battery jacket (two rows of modules instead of one, twice the volt age, energy, and power) would increase the cost by 83 %.

The summary of unit costs for the baseline battery pack, which is shown at the bottom of Table 4.8, is illustrated in Fig. 4.4. The materials and purchased items are the largest costs for the battery. For larger levels of production, these cos ts are even more dominant because the scale
factors for these items are close to one.

Figure 4.4 Breakdown of unit costs for baseline battery with t otal price to OEM of $2428. 

### 56%

12% 5% 3% 4% 4% 7% 4% 5% Materials

Purchased Items

Direct Labor

Variable Overhead

General, Sales, Administration

Research and Development

Depreciation

Profit

Warranty49



### 5 Description of the Spreadsheet Model and Instru ctions for Use

5.1 Background

Historically, the model has been based on Microsoft ® Office Excel spreadsheets. The flexibility afforded by a spreadsheet approach has been extreme ly useful to the development of the calculations. Until now, the model had been in a co nstant state of development. Changes to parameters and equations were made rapidly and freq uently. The publication of this report represents the first time a version of the model wi ll be “frozen” for open distribution to the public. Advances will continue to be made with the model, such as those discussed in the last section of this report. However, distributions of t he revised model will be made in an orderly fashion rather than the continuous improvement appr oach taken over the last number of years.

5.2 Instructions

The following subsections are a brief explanation o f how one may operate the spreadsheet based model. The user is advised to save the original doc ument separately as a back-up copy. Corruption of the calculation is possible and will likely occur during use by someone unfamiliar
with the model.

5.2.1 Enabling Calculation

This Microsoft ® Office Excel workbook requires the use of iteratio n. To enable this feature, go to the “Tools” drop-down menu and select “Options.” On the calculation tab, check the box next to “Iteration” and change the maximum number of ite rations to 1000 (Figure 5.1). Also ensure

the calculation is set to automatic and not manual. If the iteration is not turned on, the software will present an error complaining about circular re ferences.

Figure 5.1 Iteration must be enabled for the spreadsheet mode l to function.50

5.2.2 System Selection Worksheet

The cell chemistry is selected by copying the syste m designated at the top of a column, for instance NCA-G in cell F3, pasting it into cell E3 (Figure 5.2). Any of the values in row E can be overridden by entering the desired value in column L. The selection of the cell chemistry also includes the associated prices at the bottom of the page. These prices can also be overridden by entering the desired values in column L. A full scr een shot of the system selection worksheet is in Figure 5.3.

Figure 5.2 The specific cell chemistry for the battery design is selected on the System Selection worksheet. Any value may be overridden by entering a value in column L.

5.2.3 Battery Design Worksheet

The Battery Design worksheet designs five or more b atteries for any type of electric-drive vehicle (Figure 5.4–5.6). The calculated designs ar e specific for the end batteries requirements specified by the user. From the result, the amounts of materials and the purchased items required for manufacture are easily available to be used in the manufacturing cost calculations found on subsequent worksheets. Although a cell and module f ormat is assumed, the exact format (prismatic, pouch, can, etc) of the battery does no t have a dominant effect on the cost for a set cell chemistry system. Our experience teaches us th at the amounts of electrode materials and the number, capacity and electrode area of the cells, a re the determining cost factors. Nevertheless, a specific design format was selected and is shown on the Cell Design worksheet to provide a basis for calculating the entire cell and battery related costs.51 Figure 5.3 System Selection worksheet52 Figure 5.4 Top portion of Battery Design worksheet.53 Figure 5.5 Middle portion of Battery Design worksheet54

The Battery Design worksheet automatically receives input from the System Selection worksheet. These values are shown in purple (Figure s 5.4 and 5.6) and must not be altered on the Battery Design worksheet. As explained above, cell chemistry values may be adjusted on the System Selection worksheet. The operator provides b attery design input in the aqua colored cells (Figures 5.4 and 5.6). It is expected that the def ault values for the cell design (lines 27 to 30) an d the thickness of the battery insulation (line 57) s hould serve well for most batteries. The battery input parameters on lines 50 to 54 (Figure 5.4) and lines 141 to 143 (Figure 5.6) are the only input values that the operator is required to provi de to study a group of batteries. An important variable is the type of vehicle battery, (microHEV, HEV-HP, PHEV, or EV) on line 48 in Figure 5.4. One performs the selection by typing the name of the vehicle battery type in cell F48. While the correct spelling is important, capitalization i s not. This selection automatically determines the state of charge at which full power is designated ( thus, the open-circuit voltage and ASI for full power) and the length of the power burst (2 seconds for microHEV and 10 seconds for all others).

The cell capacity (lines 141 to 143 in Figure 5.6) can be set in any of three ways: (1) directly specifying the capacity (Ah) on line 141, (2) speci fying the total battery energy on line 142 or (3) specifying the electric range of the vehicle (miles ). Only one of the three lines should be filled in
and the others should be blank. The model will foll ow the directions of the top-most line with
non-zero values.

The number of batteries manufactured per year is se lected on line 59 in Figure 5.4. Changing this value from the default value of 100,000, which is t he manufacturing rate for the baseline plant, will change the manufacturing cost.

If it is desired to study more than five batteries in the same workbook it is only necessary to add additional columns by copying the battery 5 column to the right as many times as desired. Care should be taken that the appropriate values are mai ntained when the cells are copied over. The aqua colored cells are typically the source of any problems. The same column additions most also be done for the worksheets on Summary of Resul ts and Manufacturing Cost Calculations.

5.2.4 Remaining Worksheets

The cost calculations are done on the Manufacturing Cost worksheet and the results for the model are shown on the Summary of Results worksheet (Figure 5.7). No parameters need to be entered on these worksheets by the operator; all of the input for these worksheets is from the Battery Design and the Cost Input worksheets. Table s for presentations or for preparing graphs
of the data can be assembled at the bottom of eithe r the Battery Design or the Summary of
Results worksheet. These tables can be transferred to a blank worksheet for more complex studies. For instance, results for different cell c hemistries can be copied and pasted (special paste, values and numbers formats) to a blank works heet. Preparing a chart has been illustrated in the initial configuration by graphing the data t abulated at the bottom of the Battery Design worksheet. The X-axis description will have to be a djusted if the cell capacity is selected by one
of the alternative methods. On the last two workshe ets, the cell design and the baseline plant are
sketched.55 Figure 5.6 Bottom portion of Battery Design worksheet56 Figure 5.7 Summary of Results worksheet57

5.3 Battery Design Format Requirements

As the battery design is based off an assumed forma t (Section 2), certain design requirements are necessary to ensure the modeled battery is physical ly realistic. For a battery based on a single module, no additional restrictions are required. Ho wever, most batteries for transportation applications will use multiple modules. For these a pplications, the following rules should be followed by the user of the model. An even number o f cells should compose each module and an even number of modules should compose each battery pack. These two requirements are to ensure the electrical connections are in the approp riate places in the final battery pack. Finally, the dimensions of the resulting battery pack should be examined. Some final designs may benefit from changing the cell aspect ratio, H/W , to fit the end-use application. One example would be, to change the height of the battery pack. Also, for a set number of cells in the pack, changing the number of modules, thus cells per module, allows fo r adjustment of the pack dimensions.

5.4 Troubleshooting and General Advice

The spreadsheet iterates to find the solution and t his sometimes causes error messages to appear after an entry is changed. These errors can usually be removed by first correcting any erroneous entries (non-numeric, two decimal points, etc.). Th en the cells may be reset to default values by entering a “0” (i.e. zero) in the restart cell, F14 9 in Figure 5.6. Finally, entering a “1” in F149 restarts the iteration process leading to a success fully converged answer.

At some point, a user will ask the model to design a battery that is outside the bounds of what is allowable for the selected cell chemistry. The most common error is when too large of a P/E ratio is requested. Two different physical limitations ar e approached with increasing P/E ratio. First, the electrode thickness is shrinking. At some point , the value will become unrealistic and eventually approach 0 crashing the calculation. At the same time, the C-rate for the active material is approaching the limiting C-rate defined in the Cell Chemistry Worksheet. As this value is approached, the ASI will increase to large r and larger values, which thus demands
smaller and smaller electrode thicknesses. Eventual ly, the calculation will crash.

Common sense approaches to resolve these issues are to use lower designed power or higher designed energy. The C-rate and electrode thickness are easily viewed in the model output. These are found on the Battery Design worksheet in row 120 for the C-rate and rows 81 and 82 for the electrode thickness. Therefore, the user ma y try designs of increasing P/E ratios and
watch to see how the electrode thickness and C-rate is changing. Different cell chemistries will have different sensitivities to the P/E ratio depen ding on the defined limiting C-rate and calculated ASI for power. What is possible with the LMO-G system will not always be possible with the NCA-G system. P/E ratios that satisfy the expression in Eq. 5.1 generally result in successful battery designs. Higher P/E ratios are a llowable in some situations. Note that selecting the microHEV design doubles the allowable C-rate si nce only two second pulses are used. The limiting C-rate, r C,lim , may be found in cell E48 on the System Selection worksheet and is carried over to row 71 in the Battery Design worksheet.

35

. 1 lim, C r

E P < (5.1)58 

### 6. Illustrated Results

The model may be used to study the effects of batte ry parameters on the performance and the manufactured cost of the designed battery packs. A few examples are given below for the effects of various parameters on battery pack volume, weigh t and cost.

6.1 Number of Cells in Series

For a set battery pack power, the number of cells i n the pack has substantial effects on the price of the pack, the pack voltage and the maximum curre nt. These effects are illustrated (Figure 6.1) for LMO-Gr PHEV20 batteries (providing 20-mile elec tric range) with 60-kW power. The price of the battery increases by 26% in changing the num ber of series-connected cells in the pack from 32 to 96. The change in the maximum current wo uld also affect the cost of the motor and the electronic converter and controller, but in the opposite direction. As a result of these offsetting effects on the total cost of the electri c drivetrain, a study needs to be done to determine the optimum current at maximum power as a function of the total battery pack power and other parameters (see the Future Work section).

0 500 1,000 1,500 2,000 2,500

0 20 40 60 80 100 120

Number of Cells per PackPrice to OEM ($)

0 200 400 600 800 1,000Pack Current (A) and Voltage (V) Price
Max Current Voltage

Figure 6.1 The effect of the number of series-connected cells for LMO-Gr, 60-kW, PHEV20 packs with 7.14 kWh total energy (70% useable).

6.2 Battery Packs for HEVs

Lacking a definitive study on the cost of the entir e drivetrain to establish the appropriate relationship for battery current, voltage and power , Equation 6.1 is employed in the HEV59

examples that follow. Equation 6.1 strikes a balanc e between very high current and a large number of cells, to aid in selecting the number of cells for a battery of 25 to 150 kW of pack

power:

Battery Current at full Power (A) = 1.5 x Power (kW ) + 200 (6.1)

The number of cells required to match this relation ship will differ for each cell chemistry to match the cell open-circuit voltage and impedance o f the cell. Also, the selection of the current by this means is only approximate because the volta ge is not continuous being defined in terms of a discrete number of cells, which must be an eve n number for the module design in the model except for single-module battery packs.

Low-powered (25-kW) battery packs for HEVs need to deliver only about 0.15 to 0.25 kWh of energy or a total of about 0.6 to 1.0 kWh. Thus, a cell chemistry that is capable of a high P/E ratio is paramount for these batteries in achieving minimum cost. Some battery chemistries perform much better under these conditions than oth ers as illustrated in Fig. 6.2. The number of cells in these single-module HEV battery packs vari es from 33 to 52 to provide a maximum current at full power of 238 ± 2 A, in agreement wi th Eq. 6.1. It is apparent that the NMC-Gr and NCA-Gr systems studied here are not as well suited to very high P/E requirements as the other
systems.

0 5 10 15 20 25 30 35 40

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Total Pack Energy (kWh)Area-Specific Impedance, ohm-cm2 NMC-Gr

NCA-Gr

LFP-Gr

LMO-Gr

LMO-LTO

Figure 6.2 Cell area-specific impedance (ASI) for various cel l chemistries for 25-kW HEV battery packs delivering full power at about 238 A for 2 sec at 80% OCV60

HEV battery packs of about 0.4 kWh of useable energ y may be utilized for high power-assist applications. High-powered HEV battery packs of 40 to 100 kW may be required to deliver maximum power for up to 10 seconds. Also, they may be required to deliver moderate power to drive the vehicle electrically at 30 to 50 mph. Thi s latter requirement would also require more useable energy than for the standard HEV battery pa ck. For this illustration of high-powered HEV battery packs, we have set the energy requireme nt at 1.6-kWh total energy and 0.4-kWh useable energy. For a moderate-weight sedan with a n average energy requirement of 0.25 kWh/mile, the battery pack could power the vehicle for 1.6 miles before being recharged. The battery pack could then be recharged in 1.2 minutes at a rate of 20 kW or at a higher rate if
desired.

A comparison of some of the characteristics of LMO- LTO, LFP-Gr, and LMO-Gr battery packs with power capabilities of 25-kW to 100-kW and with 1.6 kWh total energy is shown in Fig. 6.3. As the power of the battery pack is increased, we h ave increased the number of cells so that both the voltage and the current increase as determined by the relationship of Eq. 6.1. The unevenness in the plotted lines for pack volume results from c hanges in the number of modules and the dimensions of the packs. The volumes for these high -powered battery packs (Fig. 6.3) as well as their weights (not shown in Fig. 6.3) are all well below the USABC targets for 25-kW battery packs even though most of the battery packs are muc h more powerful than 25 kW.

0 5 10 15 20 25

0 20 40 60 80 100 120

Battery Pack Power (kW)Battery Pack Volume (L)

0 100 200 300 400 500 600 700 800 900 1000 LMO-LTO
LFP-Gr
LMO-Gr
Pack OCV
Max CurrentVoltage (V) and Current (A)

Figure 6.3 Volume, voltage and maximum current for 1.6-kWh l ithium-ion battery packs as a function of pack power for packs delivering full po wer for 10 sec at 80% OCV and 50% SOC. Battery packs have 10-mm insulation thickness.61

Many factors affect the costs of manufacturing lith ium-ion battery packs. For batteries of high P/E, the chief factors are cell chemistry and pack power as shown in Fig. 6.4, where the prices are plotted for the same batteries as shown in Fig. 6.3, with the addition of the NCA-Gr system. In our attempt to provide high power with a minimum amount of electrode materials with the NCA-Gr system, the area-specific impedance (ASI) be came very high as the power was increased resulting in large cell areas and high co sts (Fig 6.4). The LMO-Gr system has a significant cost advantage over the other systems i n this illustration. These battery chemistries do not have the same probability of meeting the life g oal of 15 years, but work is underway throughout the world to meet this need for all of t hese systems.

0 500 1,000 1,500 2,000 2,500

0 20 40 60 80 100 120

Battery Pack Power (kW)Price of Battery Pack to OEM ($)

NCA-Gr

LFP-Gr

LMO-LTO

LMO-Gr

Figure 6.4 . Battery pack price to OEMs at 100,000 packs per year manufacturing rate for 1.6- kWh lithium-ion battery packs as a function of pack power for the same battery packs as in Fig. 6.3 with the addition of the NCA-Gr system.

6.3 Battery Packs for EVs

Lithium-ion batteries for PHEVs and EVs do not requ ire a high P/E ratio or low ASI to meet their goals. The most important factors for perform ance are high specific capacity (mAh/g), high cell voltage, and high electrode density. To compar e the performance of EV battery packs made from various Li-ion chemistries, we designed the pa cks to provide 150 kW of power at 80% OCV at a maximum current of 425 A, which is consist ent with Eq. 6.1. Each pack consisted of four modules containing 28, 30, and 32 cells for th e cell chemistries LMO-Gr, NMC-Gr, and LFP-Gr, respectively. These selections resulted in nominal (OCV) pack voltages of 429 to 443 V62

and within 2 to 13 A of the targeted maximum curren t of 425 A (Eq. 6.1) for these 150 kW battery packs. On this basis, the NMC-Gr system has excellent power and energy density (Fig. 6.5). The LMO-Gr system does well, despite only mod erate specific capacity because of its high voltage. The LFP positive electrode has higher capa city than the LMO chemistry but is hindered by a lower cell voltage and greater electrode poros ity resulting from the use of nanostructure particles.



### 0

50 100 150 200 250 300 350 400 450

50 100 150 200 250

Electric Range, milesBattery Pack Weight (kg) and Volume (L) LFP (155 mAh/g)
LMO (100 mAh/g)
NMC (175 mAh/g)



### Volume Weight

Figure 6.5 Weight and volume of electric vehicle battery packs with lithium iron phosphate (LFP), lithium manganese-spinel (LMO) and lithium n ickel-manganese-cobalt (NMC) positive electrodes versus graphite designed to deliver 150 kW of power at about 425 A.

The LMO-Gr system appears to have the lowest price of the three systems in this illustration (Fig. 6.6). By experimenting with the parameter val ues, it was found that EV battery packs of the NMC-Gr type could match the low price of those in t he LMO-Gr system. However, that would require that the specific capacity would be substan tially increased and, more importantly, the cost of the NMC would have to be reduced to about $ 20/kg from $33/kg, perhaps by reducing the cobalt content and increasing the manganese lev el.63



### 4,000 5,000 6,000 7,000 8,000 9,000 10,000 11,000

50 100 150 200 250

Electric Range, milesBattery Pack Price to OEM ($) LFP (155 mAh/g, $20/kg)

NMC (175 mAh/g, $33/kg)

LMO (100 mAh/g, $10/kg)

Figure 6.6 Battery pack price to OEM for LFP-G, LMC-G and NMC- G battery packs for same designs as in Fig. 6.5.

6.4 Parallel-Connected Cell Groups and Electrode Th ickness Limits

The model also allows the user to create parallel c ell groups and to set a maximum electrode thickness. The effect these two unique design facto rs have on cost are illustrated below in Figure 6.7 for the LMO-Gr and NCA-Gr systems. In this illu stration, the EV battery pack design parameters are 100 kW of power, 31 kWh of total ene rgy, and 100 mile range. The nominal battery pack voltage (OCV at 50% SOC) is around 340 V. Two maximum electrode thicknesses
of 100 and 200 microns are shown for the two cell c hemistries. The thickness of the positive electrode is limiting the LMO-Gr chemistry while th e thickness of the negative electrode limits the NCA-Gr chemistry. The LMO-Gr is the least expen sive in all cases. However, the difference
between the two chemistries lessens with smaller li miting electrode thickness. The costs will become even closer for lower designed P/E ratios. I n general, thicker electrodes reduce the cost of the battery pack by lessening the amount of inac tive materials used (separator, current collector, etc). Moving to 300 microns allows for g reater savings in the LMO-Gr design but not the NCA-Gr design. However, a lower P/E ratio desig n for NCA-Gr would take advantage of electrode thicknesses greater than 200 microns.

The cell capacity is shown for the NCA-Gr case limi ted to 100 microns. While the exact values will change with cell chemistry, they will all be s imilar. The cell capacity is reduced by one half as a single cell is added in parallel. This approac h is commonly used by cell manufacturers and64

OEMs that cannot reliably produce or successfully o perate cells of high capacity for transportation applications (> 60 Ah). However, thi s approach also increases the price of the battery pack. In this example, the price is increas ed by ~ $500 when an additional string of cells is incorporated in a parallel arrangement.

The model calculations show that the lowest cost ba ttery pack will utilize thick electrodes and large capacity cells. In current practice, these tw o approaches have yet to be successfully implemented within the entire community. In the cha llenge of lowering costs, it is useful to point out the largest gains come from the initial advance s (e.g. moving from 100 to 200 micron limit). After that point, the benefits are diminishing.

2,000 4,000 6,000 8,000 10,000 12,000

0 1 2 3 4 5

Number of Parallel CellsBattery Pack Price to OEM ($)

20 40 60 80 100 120Cell Capacity, Ah NCA 100 micron LMO 100 micron

NCA 200 micron LMO 200 micron

Cell capacity, Ah

Figure 6.7 Battery pack cost as a function of number of paral lel cells and for different maximum electrode thicknesses. The cell capacity is also sh own for the NCA-Gr limited to 100 micron
electrode thickness.

6.5 Effects of Manufacturing Scale on the Price of the Pack

The effects of manufacturing scale come into the co st calculation even if the annual number of packs produced is unchanged, but the design is alte red (e.g. power is increased). For a fixed design, the effect of changing the scale of operati ons depends on the fraction of the total price that is made up of materials costs. Unit materials costs change little with scale whereas the costs per pack for labor, capital and plant area may decl ine substantially with increasing production rates, especially at low production rates, Fig. 6.8

.65 

### y = 20771x -0.0862



### y = 19490x -0.0906

5,000 5,500 6,000 6,500 7,000 7,500 8,000 8,500 9,000 9,500

0 100,000 200,000 300,000 400,000 500,000 600,000

Annual Manufacturing Rate (packs/y)Price per Pack to OEM ($) LMO-Gr, EV150 mile, 150 kW

NMC-Gr, EV150 mile, 150 kW



### y = 10298x -0.1367



### y = 7387.8x -0.2011

0 500 1,000 1,500 2,000 2,500 3,000

0 100,000 200,000 300,000 400,000 500,000 600,000

Annual Manufacturing Rate (packs/y)Price per Pack to OEM ($) LMO-Gr,PHEV20 mile, 60 kW

LMO-Gr, HEV-25 kW

Figure 6.8 The effects of manufacturing rate on the price calc ulated by the model for battery packs of various cell chemistries, power capabiliti es and vehicle types66

The lines in the graphs are for the best-fit power relationships through the data with power factors of -0.086, -0.091, -0.137, and -0.201 from the top curve to that at the bottom. The least negative power factor is for the battery pack with the highest fraction of materials cost in the total pack cost. The more negative power factors re sult from a decreasing contribution of materials cost as a fraction of the total pack cost . These power factors for equations of the cost of a single unit can be converted to factors relating the total annual cost of manufacturing similar to Eq. 4.1 by adding 1.0 to each power factor. Thus th e factors become 0.914, 0.909, 0.863, and 0.799. These large factors show only a small to mod erate effect of scale. When the power curves are compared to the points in each of the graphs of Fig. 6.8, it is apparent that the scale factors approach one as the scale increases. This is becaus e the model assigns a value of 0.95 for the
active materials and 1.0 for the balance of the mat erials. As the production level increases and the materials costs become a larger fraction of the total price of the battery, the scaling power approaches 1.0 and the effect of scale become very small. Likewise, the effect of scale on battery price is much larger for HEV batteries than for EVs because materials costs constitute a smaller portion of the total cost for HEV batteries. Increa sing the production rate for HEV batteries will
result in a more dramatic reduction in cost than in creasing the production rate for EV batteries.67 

### 7. Future Work

7.1 Thermal Modeling

The battery design format used in this report provi des cooling to the battery pack by blowing air over the top and bottom of the modules. The heat is transferred through the stiff, aluminum pouch material to the module walls. An additional a luminum plate may be placed between cells to enhance heat transfer. This method of cooling wi ll be sufficient for some battery applications, but other applications might require that the batte ry pack be over-designed to reduce heat generation. Over-design would include providing a b attery pack of higher power than called for by the application or providing the power at a very high fraction of the open-circuit voltage (>85%OCV).

We intend to develop an alternative battery design that provides liquid cooling directly to the cells inside the modules. Means of distributing a d ielectric coolant to the interior of the modules will be studied. We will carry out thermal modeling studies on the heat generation during vehicle operation on various driving cycles and on the remo val of heat from both air-and liquid-cooled battery packs. We intend to investigate the feasibi lity and cost of these options. The results of these studies will be incorporated into the model i n a separate thermal modeling section. This work will be carried out in a cooperative effort wi th Argonne’s Transportation Technology R&D Center, which will perform vehicle simulation tests to determine the rate of heat generation in the battery pack.

7.2 Optimum Battery Voltage for Minimum Drivetrain Cost

For a set cell chemistry and set battery pack power , the cost of the pack increases as the number of cells and the pack voltage are increased (Fig. 6 .1). The additional cost results primarily from the cost of additional state-of-charge equalization circuits and the additional number of cells needing formation cycling and testing. The increase in battery pack cost is almost linear with the
increase in the number of cells. As the number of c ells is decreased, the pack current at maximum power becomes very high and the cost of the balance of the drivetrain increases at an accelerating rate. Thus, there must be a number of cells and an associated pack current at maximum power for which the total cost of the drive train is at a minimum. This minimum would be for the current at full power for which the slop e of the cost curve for the balance of the drivetrain versus current was equal to the negative of slope of the cost of the pack versus current. This optimum current will increase with the pack po wer because the slope of the cost-versuscurrent curve increases with increasing power and, therefore, the optimum current will also
increase.

To represent these phenomena in illustrating the mo del in Section 6, we used an equation (Eq. 6.1) for selecting the current at full power as a f unction of the battery pack power. This equation is just an estimate and it does not provide for dif ferences in the optimum current that would result from differences in cell chemistries, which are known to affect the battery cost versus power function.68

A study is needed to determine the cost of electric motors and the electronic control equipment required for the vehicle and battery pack as a func tion of power and maximum current capability. Once appropriate cost curves are established, we wi ll determine equations relating the optimum battery current to the desired battery power taking into account the battery chemistry. We intend to do this study with the cooperation of Argonne’s Transportation Technology R&D Center.

7.3 Multipurpose Battery Manufacturing Plants

Our cost modeling is based on the concept that a ma nufacturing plant is constructed to produce a single type of battery pack at a predetermined leve l of production. In practice, manufacturers will have to produce several types of batteries within t he same manufacturing plant and the levels of production may fluctuate. We intend to investigate how this increased flexibility requirement will affect the various manufacturing costs. For ex ample, the cell filling and sealing equipment may be required to handle cells of different dimens ions. This would most likely increase the capital cost for this equipment. Alternatively, add itional packaging and sealing lines might be
needed. We intend to evaluate combinations of vehic le battery packs that are easily integrated into the same plant. The manufacturing cost will mo st likely increase after these considerations
are built into the model.

7.4 Stand-Alone Graphical User Interface for Model

The spreadsheet program described here-in allows ve rsatility in designing the battery and in calculating the costs, but like all complex spreads heet programs it is not user-friendly to those
unfamiliar with the details of calculation. In addi tion, the model is easily corrupted by a poor choice of input parameters. As a result, the final spreadsheet program will be converted to a stand-alone user-friendly application, primarily wi th the efforts of Ira Bloom. Visual Basic for Applications will be used to hard code in the model calculations and to also create the graphical
interface. The new user interface should allow for a wide distribution of the model while maintaining the ability to change the vast majority of input parameters. The retention of this flexibility should make the model a valuable tool f or those interested in batteries regardless of the specific material property or manufacturing cos t structure the user seeks to analyze.69 

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