Modeling the Cost and Performance of 

Lithium-Ion Batteries for Electric-Drive 

Vehicles 

Final Report 
Modeling the Cost and Performance of 


Lithium-Ion Batteries for Electric-Drive 


Vehicles 


Final Report
 

Assessment and Standards Division 

Office of Transportation and Air Quality 

U.S. Environmental Protection Agency 

Prepared for EPA by
 

Argonne National Laboratory
 

Chemical Sciences and Engineering Division
 

Contract No. DE-AC02-06CH11357 


Submitted July 15, 2011
 

NOTICE 

This technical report does not necessarily represent final EPA decisions or 

positions. It is intended to present technical analysis of issues using data 

that are currently available. The purpose in the release of such reports is to 

facilitate the exchange of technical information and to inform the public of 

technical developments. 

EPA-420-R-12-023 

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TABLE OF CONTENTS
 

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

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

ABBREVIATIONS ............................................................................................................x
 

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

ACKNOWLEDGEMENTS ..............................................................................................xv
 

EXECUTIVE SUMMARY ............................................................................................ xvi
 

PREFACE TO THE FINAL REPORT .......................................................................... xvii
 

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

2. Battery and Cell Design Format .....................................................................................3
 

2.1 Cell Design.........................................................................................................4
 

2.2 Module Design ..................................................................................................5
 

2.3 Battery Pack Design ..........................................................................................6
 

3. Modeling of Battery Design and Performance ...............................................................9
 

3.1 Criteria for Power, Energy, and Life ................................................................9
 

3.2 Voltage at Maximum Power ...........................................................................11
 

3.3 Governing Equations ......................................................................................17
 

3.4 Calculation of the ASI ....................................................................................18
 

3.4.1 Current Collection Resistance ..........................................................20
 

3.4.2 Potential and Current Distribution ...................................................22
 

3.4.3 Determination of Module Terminal Size ..........................................24
 

3.5 Calculation of Battery Dimensions .................................................................25
 

3.5.1 Cell Dimensions ...............................................................................25
 

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3.5.2 Module Dimensions .........................................................................26
 

3.5.3 Battery Pack Dimensions .................................................................26
 

3.6 Additional Considerations ..............................................................................26
 

3.6.1 Maximum Electrode Thickness .......................................................27
 

3.6.2 Accounting for Parallel Cell Arrangements .....................................33
 

3.6.3 Accounting for Parallel Module Arrangements ...............................33
 

4. Thermal Management ...................................................................................................34
 

4.1 Heat Generation Rates in the Battery Pack during Driving ............................34
 

4.2 Heating under Adiabatic Conditions ...............................................................35
 

4.3 Active Cooling Systems ..................................................................................35
 

4.3.1 Heat Transfer from Cell to Module Wall .........................................36
 

4.3.2 Heat Transfer from Module Wall to Flowing Coolant ....................38
 

4.4 Cooling and Heating Required to Maintain Pack Temperature ......................42
 

4.5 Heat-up from Cold Ambient Conditions .........................................................43
 

5. Modeling of Battery Pack Manufacturing Cost ............................................................44
 

5.1 Approach .........................................................................................................44
 

5.2 Materials Costs and Purchased Items .............................................................45
 

5.2.1 Battery Specific Materials Cost .......................................................45
 

5.2.2 Purchased Items Cost .......................................................................50
 

5.2.3 Pack Integration Cost .......................................................................50
 

5.3 Baseline Manufacturing Plant .........................................................................53
 

5.3.1 Receiving and Shipping ...................................................................54
 

5.3.2 Electrode Materials Preparation .......................................................56
 

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5.3.3 Electrode Coating .............................................................................56
 

5.3.4 Calendering ......................................................................................57
 

5.3.5 Inter-Process Materials Handling ....................................................57
 

5.3.6 Electrode Slitting .............................................................................58
 

5.3.7 Final Electrode Drying .....................................................................58
 

5.3.8 Control Laboratory ...........................................................................58
 

5.3.9 Cell Stacking ....................................................................................59
 

5.3.10 Current Collector Welding .............................................................59
 

5.3.11 Enclosing Cell in Container ...........................................................59
 

5.3.12 Electrolyte Filling and Cell Sealing ...............................................60
 

5.3.13 Dry Room Management .................................................................60
 

5.3.14 Formation Cycling, Final Cell Sealing, etc ....................................60
 

5.3.15 Module and Battery Assembly .......................................................61
 

5.3.16 Rejected Cell and Scrap Recycle ...................................................62
 

5.3.17 Baseline Plant Summary ................................................................63
 

5.4 Adjustment of Costs for Rates ........................................................................63
 

5.5 Plant Investment Costs ....................................................................................66
 

5.6 Unit Costs for Battery Pack ............................................................................66
 

5.6.1 Variable Costs ..................................................................................66
 

5.6.2 Fixed Expenses ................................................................................67
 

5.6.3 Profits ...............................................................................................68
 

5.6.4 Battery Pack Warranty Costs ...........................................................68
 

5.7 Summary of Baseline Battery Cost .................................................................68
 

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6. Description of Spreadsheet Model and Instructions for Use ........................................71
 

6.1 Background .....................................................................................................71
 

6.2 Instructions ......................................................................................................71
 

6.2.1 Enabling Calculation ........................................................................71
 

6.2.2 System Selection Worksheet ............................................................73
 

6.2.3 Battery Design Worksheet ...............................................................73
 

6.2.4 Remaining Worksheets ....................................................................77
 

6.3 Battery Design Format Requirements .............................................................80
 

6.4 Troubleshooting and General Advice .............................................................80
 

6.5 Suggested Number of Cells, Modules, and Performance Inputs ....................80
 

6.6 Entering a New Material Couple .....................................................................81
 

7. Illustrated Results ..........................................................................................................83
 

7.1 Number of Cells in Series ...............................................................................83
 

7.2 Cathode Materials ............................................................................................84
 

7.3 Parallel-Connected Cell Groups and Electrode Thickness .............................84
 

7.4 Manufacturing Scale ........................................................................................86
 

8. Future Work ..................................................................................................................89
 

8.1 Initial Power Designed at Differing Fractions of the Open-Circuit Voltage ...89
 

8.2 Optimum Battery Voltage for Minimum Drivetrain Cost ..............................89
 

8.3 Multipurpose Battery Manufacturing Plants ...................................................90
 

8.4 Stand-Alone Graphical User Interface for Model ...........................................90
 

References .........................................................................................................................91
 

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LIST OF FIGURES
 

2.1	 Prismatic cell and module design for battery packs ............................................................3
 

2.2	 Cell sandwich inside of prismatic pouch cells ....................................................................4
 

2.3	 Coated current collector foil for prismatic electrodes .........................................................5
 

2.4	 Hermetically-sealed module ................................................................................................6
 

2.5	 Insulated battery jacket with enclosed modules that are cooled on their upper and lower
 

surfaces by ethylene glycol-water solution..........................................................................7
 

3.1. 	 Summary flow of the design model ..................................................................................10
 

3.2	 a) Required change in [V/U] to maintain rated power with increases in internal
 

resistance over the life of the battery. b) Increase in current due to lowered [V/U] .........13
 

3.3	 Change in heat rejection requirement from increases in resistance for batteries with
 

different designed voltages at maximum power ...............................................................14
 

3.4	 Efficiencies for batteries designed to achieve maximum power at different fractions of
 

their open-circuit voltage ..................................................................................................16
 

3.5	 The change in current and potential within the positive and negative foils. The current
 

collection design results in a uniform current distribution along the length of the foil ....23
 

3.6	 Cell capacity simulated at the C/1 and C/3 rate as a function of electrode thickness
 

(loading) for NCA-Gr. .......................................................................................................29
 

3.7	 Normalized electrolyte salt concentration at the end of discharge at the C/1 and C/3
 

discharge rates. ..................................................................................................................29
 

3.8	 Calculated ASI from a simulated 10-s, 5C discharge pulse for the NCA-Gr cell couple at
 

60% SOC. .........................................................................................................................30
 

3.9	 The potential of the negative electrode versus a hypothetical lithium reference electrode
 

located in the center of separator during a 5C charge pulse for the NCA-Gr couple ........31
 

4.1	 Plot comparing the estimated resistance to heat transfer from the cell center to the
 

cooled surface of the module to that calculated by the FlexPDE model ..........................38
 

4.2	 Heat transfer from the module wall to the laminar flow heat transfer fluid. The
 

temperature profile of the fluid is shown at different lengths down the path. ..................39
 

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4.3	 Temperature profile in the heat transfer fluid for various fractions of the dimensionless
 

path length..........................................................................................................................41
 

4.4	 Correlation of model simulation results relating the Graetz number and mean Nusselt
 

number for laminar flow between an insulated surface and the module casing ................41
 

5.1	 Metal ingot cost contribution to the current collector foils over a 20 year period ............49
 

5.2	 Baseline lithium-ion battery manufacturing plant schematic diagram .............................54
 

5.3	 Breakdown of installed capital equipment costs for the baseline plant ............................65
 

5.4	 Breakdown of unit costs for baseline battery with total price to OEM of $2428 .............70
 

6.1	 Iteration must be enabled for the spreadsheet model to function .....................................72
 

6.2	 The specific cell chemistry for the battery design is selected on the System Selection
 

worksheet ..........................................................................................................................73
 

6.3	 System Selection worksheet .............................................................................................74
 

6.4	 Top portion of Battery Design worksheet .........................................................................75
 

6.5	 Middle portion of Battery Design worksheet ....................................................................76
 

6.6	 Bottom portion of Battery Design worksheet ...................................................................78
 

6.7	 Summary of Results worksheet ........................................................................................79
 

7.1	 The effect of the number of cells for NMC441-Gr, 60-kW, PHEV25 packs with 10.7
 

kWh total energy (70% useable) .......................................................................................83
 

7.2	 Mass and volume of electric vehicle battery packs with lithium iron phosphate (LFP), 


lithium manganese-spinel (LMO) and lithium nickel-manganese-cobalt oxide (NMC441)
 

positive electrodes versus graphite designed to deliver 150 kW of power at 360 V (25%
 

SOC). ................................................................................................................................85
 

7.3	 Battery pack price to OEM for LFP-Gr, LMO-Gr and NMC441-Gr battery packs for
 

same designs as in Fig. 7.2. NMC441-Gr and LMO-Gr result in nearly the same price...85
 

7.4	 Battery pack cost as a function of number of parallel cells and for different maximum
 

electrode thicknesses..........................................................................................................87
 

7.5	 The effects of manufacturing rate on the price calculated by the model for battery packs
 

of various cell chemistries, power capabilities and vehicle types ....................................88
 

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LIST OF TABLES
 

3.1	 Criteria for designing batteries for a specific end-use application ......................................9
 

3.2	 The effect of electrode loading on the price of a 17 kWh NCA-Gr PHEV40
 

battery with 96 cells ..........................................................................................................32
 

4.1	 Sample calculations of composite thermal conductivities of cell structures
 

across layer and parallel to layers .....................................................................................37
 

4.2	 Range of parameter values for calculating heat transfer rates in FlexPDE model ...........37
 

5.1	 Details of stated costs for cathodes, anodes, electrolyte, and separator ...........................46
 

5.2	 Cost equations for purchased items ..................................................................................50
 

5.3	 Costs to integrate battery pack into vehicle drivetrain.......................................................51
 

5.4	 Summary table of the baseline plant .................................................................................55
 

5.5	 Materials yields during electrode and cell fabrication ......................................................62
 

5.6	 The effect of processing rate (R) on cost for various scale factors ...................................64
 

5.7	 Battery pack manufacturing investment costs ..................................................................66
 

5.8	 Unit cost of battery pack ...................................................................................................67
 

5.9	 Summary of results for cost of baseline battery and that of similar batteries with
 

double the power and double the capacity of the baseline battery ....................................69
 

6.1	 General suggestions for range of input parameters that change with battery type ...........81
 

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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 

MW molecular weight 

NCA lithium nickel cobalt aluminum oxide 

NMC lithium nickel manganese cobalt oxide 

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NMP N-Methyl-2-pyrrolidone 

OCV open-circuit voltage 

OEM original equipment manufacturer 

PE polyethylene 

PET polyethylene terephthalate 

PHEV plug-in hybrid electric vehicle 

PP polypropylene 

R&D research and development 

SOC state of charge 

USGS United States Geological Survey 

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LIST OF SYMBOLS
 

Section 3, 4 and 6
 

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

Apos area of the positive electrode, cm2 

Aterm area of the terminal, cm2 

ASIenergy area specific impedance for energy, ohm cm2 

ASIpower area specific impedance for power, ohm cm2 

C cell capacity, Ah. 

C1 parameter 

Cp specific heat capacity, J/g K 

dH hydraulic radius, cm 

E total energy, Wh 

E& energy usage rate, Wh/mile 

F Faraday constant, 96485.3 C/mol 

G mass flowrate, g/s 

h heat transfer coefficient, W/cm2

 K 

Hj height of j, cm 

H/W aspect ratio of pouch cell 

io exchange current density related to the interfacial area, A/cm2 

I average current density, A/cm2 

ionic Ilim ionic limiting current density, A/cm2 

In local current density, A/cm2 

Itotal total current density, A 

k thermal conductivity, W/cm K 

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lj	 length of j, cm 

Lj	 thickness of j, cm 

mj	 mass of j, g 

n	 parameter 

Nj	 number of j 

[N/P]	 negative to positive capacity ratio 

P	 battery power, W 

Pbatt	 maximum designed battery power, W 

q	 heating rate, W 

Q	 specific capacity of the electrode, mAh/g 

rC	 C-rate, h-1 

rC,lim	 limiting C-rate, h-1 

rj	 radius of j, cm 

R	 universal gas constant, 8.3144 J/mol K 

Rj	 resistance of j, ohm 

t	 time, s 

T	 temperature, K 

Uocv,P	 open-circuit voltage at SOC for power, V 

Uocv,E	 open-circuit voltage at SOC for energy, V 

square root of dimensionless exchange current 

Vcell	 cell voltage, V 

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

Wj	 width of j 

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x Cartesian coordinate, cm 

Xcomp compression factor 

α constant, ohm cm3 

β constant, ohm cm2 

εact volume fraction of active material 

η1st first cycle efficiency 

μ fluid viscosity, g/cm s 

Φ1,k metal potential of foil k, V 

ρj density of j, g/cm3 

σj conductivity of j, S/cm 

Section 5.1 

C final cost of lithiated oxide, $/kg 

Ci cost of raw material for component i, $/kg 

Co baseline cost of lithiated oxide, $/kg 

xi molar stoichiometry of component i 

MWi molecular weight of component i, g/mol 

MW molecular weight of lithiated compound, g/mol 

Section 5.4 

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

Co capital cost of an installed equipment for the baseline plant battery, $ 

p power factor 

R designed battery processing rate for specific process step 

Ro baseline plant processing rate for specific process step 

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ACKNOWLEDGEMENTS
 

Support from the Vehicle Technologies Program, Hybrid and Electric Systems, initially under 

Tien Duong and now David Howell, at the U.S. Department of Energy, Office of Energy 

Efficiency and Renewable Energy, is gratefully acknowledged. The submitted manuscript has 

been created by UChicago Argonne, LLC, Operator of Argonne National Laboratory 

(“Argonne”). Argonne, a U.S. Department of Energy Office of Science laboratory, is operated 

under contract no. DE-AC02-06CH11357. The U.S. Government retains for itself, and others 

acting on its behalf, a paid-up nonexclusive, irrevocable worldwide license in said article to 

reproduce, prepare derivative works, distribute copies 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 several 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 several years and made suggestions that resulted 

in improvements. The work was done under the direction of Dennis Dees and Gary Henriksen of 

Electrochemical Energy Storage who provided guidance in carrying out the work and preparing 

this manuscript. 

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EXECUTIVE SUMMARY
 

This report details the Battery Performance and Cost model (BatPaC) developed at Argonne 

National Laboratory for lithium-ion battery packs used in automotive transportation. The model 

designs the battery for a specified power, energy, and type of vehicle battery. 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 directly affects each process step. 

The total cost to the original equipment manufacturer calculated by the model includes the 

materials, manufacturing, and warranty costs for a battery produced 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 equations 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 variable in the calculation may be changed by 

the user to represent a system different from the default values pre-entered into the program. 

The distinct advantage of using a bottom-up cost and design model is that the entire power-toenergy space may be traversed to examine the correlation between performance and cost. The 

BatPaC model accounts for the physical limitations of the electrochemical processes within the 

battery. Thus, unrealistic designs are penalized in energy density and cost, unlike cost models 

based on linear extrapolations. Additionally, the consequences on cost and energy density from 

changes in cell capacity, parallel cell groups, and manufacturing capabilities are easily assessed 

with the model. New proposed materials may also be examined to translate bench-scale values to 

the design of full-scale battery packs providing realistic energy densities and prices to the 

original equipment manufacturer. 

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 provided for use; however, 

the format is admittedly not user-friendly. A parallel development effort has created an alternate 

version based on a graphical user-interface that will be more intuitive to some users. The version 

that is more user-friendly should allow for wider adoption of the model. 

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PREFACE TO THE FINAL REPORT
 

Changes were made to the draft report in direct response to the peer-review report generated by 

ICF International on March 31, 2011 for the U.S. Environmental Protection Agency. Other 

changes were also made in response to additional private peer-reviews. Below is an incomplete 

list of where changes have been made in response to the peer-reviews. Only the most important 

changes are detailed below. 

1. Implemented liquid thermal management on all battery packs. A new section was added to 

explain the thermal management strategy Section 4. Costs of the thermal management are 

addressed in 5.2.3. 

2. Changed the default maximum single-sided electrode thickness to be 100 microns while 

continuing to allow the user to override with any value. A greatly expanded discussion of the 

transport issues, supported with validated physics-based models as well as a sensitivity analysis, 

was placed in Section 3.6.1. Additional instruction on how to change the default value was 

explicitly stated in Section 6.2.2. 

3. Changed allocation of overhead costs based on reviewers comments to more closely represent 

a Tier 1 auto supplier. Exact values with discussion are in Section 5.6. 

4. Added cost estimates for automatic and manual disconnects necessary for safe operation of the 

battery, Section 5.2.3. 

5. Added and increased costs of battery management system to represent the complete 

monitoring and control needs, Section 5.2.2 and 5.2.3. 

6. Increased cost of tabs to account for polymer sealant and use of isolation tape, Section 5.2.2 

7. Changed capital cost of the materials preparation (lower) and coating (higher) in response to a 

more detailed review of the cost inputs from an industrial partner, Section5.3. 

8. Reference and discussion on the validation of the model in Sections 1, 3.4, and 3.6.1. 

9. The definition of the designed fraction of the open-circuit voltage at maximum power and its 

connection to existing vehicle battery systems is discussed in Section 3.2. 

10. Breakdown of the cathode material price into raw materials and baseline costs (processing, 

profit, utilities, other materials) for the oxides based on nickel, manganese, and cobalt is in 

Section 5.2 with some sensitivity to cobalt prices. 

11. Included discussion of what the predicted model price represents and situations where it 

might be conservative or optimistic, Section 1. 

12. Increasing clarity on how to use the spreadsheet, Section 6 & 7. 

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13. Clarification of the production volume scaling methods, Section 5.4. 

14. Discussion of where waste management costs are included in the estimation, Section 5.5 

15. Explanation of approximate method to account for modules, composed of the same cells, 

connected in parallel, Section 3.6.3 

16. Cell thickness changed, moving to thinner values, Section 3.1. 

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1. Introduction
 

The recent penetration of lithium-ion (Li-ion) batteries 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 described here-in is a calculation method that 

was developed at Argonne for estimating the manufacturing cost and performance of Li-ion 

batteries for electric-drive vehicles including hybrid-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.1-11 The cost of a battery will change depending upon the materials 

chemistry, battery design, and manufacturing process.12-14 Therefore, it is necessary to account 

for all three areas with a bottom-up cost model. Other bottom-up cost models exist but are not 

available to the general public and have not been explicitly detailed in an open document. The 

motivation for this work is based on a need for a battery cost model that 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 for the requirements of an application 

4. Accounts for the physical limitations that govern battery performance 

5. Based on a bottom-up calculation approach to account for every cost factor 

The Battery Performance and Cost model (BatPaC) described here-in is the product of long-term 

research and development at Argonne National Laboratory. Over a period of years, Argonne has 

developed methods to design Li-ion batteries for electric-drive vehicles based on modeling with 

Microsoft® Office Excel spreadsheets.12-20 These design models provided all the data needed to 

estimate the annual materials requirements for manufacturing the batteries being designed. This 

facilitated the next step, which was to extend the effort to include modeling of the manufacturing 

costs of the batteries. In the following sections of this document, a model is presented that 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 BatPaC requires some basic knowledge of 

battery 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 

person with reasonable knowledge of batteries may be able to conduct cost comparisons and 

“what if” studies. 

The battery pack design and cost calculated in BatPaC represent projections of a 2020 production 

year and a specified level of annual battery production, 20,000-500,000. As the goal is to predict 

the future cost of manufacturing batteries, a mature manufacturing process is assumed. The 

model designs a manufacturing plant with the sole purpose of producing the battery being 

modeled. The assumed battery design and 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 dense battery. Our proposed solutions do not have to be the same 

methods used in the future by industry. We simply assume the leading battery manufacturers, 

those having successful operations in the year 2020, will reach these ends by some means. 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Establishing the validity of the model calculation is important to justify the conclusion drawn 

from exercising the model. The design methodology used has been previously validated against 

cylindrical wound cell formats.15 The calculated materials quantities agreed with the actual 

values within 3 %. Moving to a prismatic format simplifies the current collection calculation 

while leaving the governing equations unchanged. The new approach developed for calculating 

the cell impedance has been validated against experimental measurements from electrodes up to 

100 μm in thickness.20 The module and battery jacket construction is of lighter construction 

compared to contemporary designs. The battery pack energy density calculated in BatPaC is 

higher than the battery packs used in the first versions of the Nissan Leaf and Chevrolet Volt for 

equivalent cell designs (calculated value of 100 Wh/kg compared to reported value near 84 

Wh/kg for the Volt).21 Significant engineering advances are necessary to minimize current 

inactive material burden in the commercial pack designs thereby reducing the cost, mass and 

dimensions of future automotive battery packs. We have assumed a design that we believe will 

be representative of the engineering progress achieved by successful manufacturers in the year 

2020. 

Validation of the input material and capital costs are more difficult to achieve as few values are 

publically available. We have relied, to a large extent, on private communications amongst 

equipment manufacturers, materials suppliers, cell manufacturers, and original equipment 

manufacturers. Variation does exist amongst the communicated values and we have maintained a 

practical level of skepticism for their accuracy. Experts from all aspects of battery development 

have reviewed the model both privately and as part of a formal peer-review process. While the 

largest uncertainty in calculated values will exist in point cost estimates, the most instructive 

information may be gained by examining ranges in parameter values and relative changes 

between material properties (e.g. the advantage of moving to a manganese spinel cathode from a 

layered-oxide material or from increases in cell capacity, etc). 

The battery pack price to the OEM calculated by the model inherently assumes the existence of 

mature, high-volume manufacturing of Li-ion batteries for transportation applications. Therefore 

the increased costs that current manufacturers face due to low scale of production, higher than 

expected cell failures in the field, and product launch issues are not accounted for in the 

calculation. The model results for year 2020 could be considered very optimistic if the 

transportation Li-ion market fails to develop as a result of insufficient investment in product 

research and development, reduced motivation for lowering petroleum consumption and 

greenhouse gas emissions, and/or a series of high-profile safety incidents. 

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2. Cell and Battery Pack Design Format
 

Various cell and battery design concepts are under development at battery manufacturers. Based 

upon experience gained from extensive previous work, we have found the exact design of the 

battery does not have an important effect on the cost for a set cell chemistry; the amounts of 

electrode materials and the number, capacity and electrode area of the cells, are the determining 

cost factors. The most common cell designs for batteries nearing large-scale 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 winding. For the different cell designs, there are small differences in 

the weights of the terminal extensions and the procedures for connecting these extensions to the 

current collector sheets, with 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. These small differences would have minor effects on the cost of batteries produced in high 

volume in a mature, automated production plant and all of the cell designs can be adequately 

cooled for most applications. We conclude that the BatPaC cost calculations would be relevant 

for batteries differing considerably from the selected design approach. 

To provide a specific design for the calculations, a prismatic cell in a stiff-pouch container was 

selected (Fig. 2.1). For this design, calculations of the current collector and terminal resistances 

are easily done with a one-dimensional model, because the terminals are almost the same width 

as the electrodes. 

Cell with Stiff, MultiLayer Container 

Terminal Seal 

Polymer Seal of 

Cell Container 

to Terminal 

Ultrasonic Welds 

of Terminal to 

Collector Foils 

Cell Cross-Sections 

After Edge Sealing 

After Edge Shaping and 

Addition of Aluminum 

Conduction Channel 

Aluminum 

Conduction 

Channel 

Figure 2.1 Prismatic cell in stiff pouch container with aluminum conduction channel added for 

heat rejection 

3 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

negative

electrode

positive

electrode

The cells are hermetically sealed in module containers, which are then enclosed in an insulated 

jacket. The module enclosure provides added protection of the cell seals from the diffusion of 

moisture from the external environment into the interior of the cells or alternatively loss of 

electrolyte solvent from the cells. The exterior surfaces of the modules are cooled by ethylene 

glycol-water solution. The calculated electrical performance of a battery of this construction is 

near optimum and the configuration is compact and light-weight. We have not likely selected the 

most viable design in this short study; there may be serious flaws in some details. However, the 

calculated overall performance and low cost for the selected design will be challenging to match 

in actual production and will only be met by the most successful manufacturers, those that will 

dominate the market. 

2.1 Cell Design 

The prismatic cell of this design embodies individual positive and negative electrodes consisting 

of current collector foils coated with electrode materials on both sides. The current collectors are 

usually solid copper and aluminum foils for the positive and the negative. An illustration of a 

segment of the cell is detailed in Figure 2.1. Each electrode is made up of active material 

particles held together by a polymeric binder. 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 electrode particles into the electrolyte, across the separator, 

and then insert into the particles composing the opposite 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 

process. In this process, 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 the user desired. 

separator

+ – +

Li+

eseparator 

negative 

electrode 

+ – +

Li+

positive 

electrode 

e -

Figure 2.2 Cell sandwich inside of prismatic pouch cells.
 

4 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The electrodes are easily and efficiently prepared by coating wide sheets of foil (up to 2-meters 

in width) with uncoated strips running the lengths of the foil being coated. The individual 

electrodes can be cut from these sheets with little waste of electrode coating material or foil (Fig. 

2.3). The separator for these cells can be handled as a single sheet that is folded back and forth as 

the electrodes are inserted. The electrodes are inserted so that all of the positive tabs extend 

beyond the separator sheet in one direction and the negative tabs extend in the opposite direction. 

The design model selects the number of electrodes to meet a set cell thickness determined by the 

type of cell: HEV, 6 mm; PHEV, 8 mm; EV, 12 mm. These cell thicknesses are default values 

and may be changed to suit the designer. 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 material is a tri-layer consisting of an outer layer of polyethylene 

terephthalate (PEP) for strength, a middle layer of 0.1-mm aluminum for stiffness and 

impermeability to moisture and electrolyte solvent vapors and an inner layer of polypropylene 

(PP) for sealing by heating.22,23 The two halves of the cell container are pre-shaped to facilitate 

assembly. The aluminum foil in the cell container material provides stiffness and it may be 

increased in thickness to assist in conducting heat to the module container. After sealing the 

edges of the cell, the edges are flattened along the sides of the cell to form a compact shape and 

an aluminum conduction channel is added to assist in heat rejection at the sides of the cells. 

Electrode
 

Coating
 

Uncoated Area 

for CC Tabs 

Lines Showing 

Places to Cut for 

Electrodes 

Figure 2.3 Illustration of coated current collector foil showing four rows of prismatic electrodes 

before slitting or stamping into individual electrodes 

2.2 Module Design 

The module format is based on a casing of 0.5-mm thick aluminum that is sealed by double 

seaming, a process that is well established and inexpensive because it is automated, rapid, and 

uses low-cost equipment that is common in the container industry. The sealing of the module 

provides 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.22 

5 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Heat Transfer Surfaces 

on Top and Bottom of 

Container in Contact 

with Cell Conductors 

Module 

Terminal 

Cell Terminal 

Connections 

Double-Seamed 

Module Closure 

Figure 2.4 Hermetically-sealed module 

The cells are placed on their sides in the module and the terminals of adjacent cells are connected 

either mechanically with small bolts and flat springs to maintain contact or by laser welding. 

Space is provided within the module casing on the left side, as sketched in Fig. 2.4, for an 

electronics package that includes cell monitoring for malfunctions (temperature and voltage) and 

for state-of-charge (SOC) control. The SOC control is activated when ever the battery is at rest 

and it diverts charge from the cells at highest voltage to those at lowest voltage. 

2.3 Battery Pack Design 

The model designs the battery pack (Fig 2.5) in sufficient detail 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 battery jacket either in a single row, with the 

terminals facing the same side of the pack, or in an even number of rows with the terminals in 

one row facing the terminal of an adjacent row. For a pack with a single row of modules, a 

busbar must be provided to carry the current to the front of the battery pack. This feature results 

in an additional cost for the busbar. For batteries with more than one row of modules (Fig. 2.5), 

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, 

negative to positive terminals, by copper connectors. The modules casings are compressed 

together by two steel sheets bound with steel straps at the front and back of the battery pack. The 

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 

structural support to the module casings. 

6 
Figure 2.5 Insulated battery jacket with enclosed modules that are cooled on their upper and 

lower surfaces by ethylene glycol-water solution 

The modules are supported by a tray that provides space for the heat transfer fluid (ethylene 

glycol-water solution) to flow against the top and bottom of each module. All connections to the 

pack terminals that lead to the exterior of the pack and signal wire feedthroughs can be made 

7 
 

 

 

 

 

 

 

 

 

 

 

before inserting the attached modules into the jacket and making the final closure. The bolts 

depicted in the diagram (Fig 2.5) for making this closure are for illustrative purposes only. 

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 thickness of each of the aluminum layers is selected 

by the modeling program to be 1- to 2-mm thick, depending 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 summer weather.16 

Although the main purpose of the battery pack design for the model is to provide a plausible list 

of materials to estimate the manufacturing cost of the battery, the overall design approach 

permits the battery to be shaped by the designer to fit dimensional objectives. If there is a height 

restriction for the battery pack, a high ratio of height-to-width for the positive electrode will 

result in a battery of low height (the cells are placed on their side in the pack). 

8 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3. Modeling of Battery Design and Performance
 

The design portion of the model calculates the physical properties of a battery based on userdefined performance requirements and minimal experimental data. An illustration of the model is 

shown in Figure 3.1. The user is asked to enter a number of design parameters such as the battery 

power, number of cells and modules, and target voltage 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 values will determine the value of the other two. 

An iterative procedure then solves for the user defined 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 materials requirements for the cells, modules, and 

battery pack. 

The model has been designed to allow the user to enter as many customized values as desired. In 

this way, the model allows flexibility in the battery chemistries studies and some of the cell, 

module, and battery design aspects. Hence, the focus of this report is on the method of 

calculation and not the exact values chosen for a specific capacity or cell thickness. However, the 

default cell design parameters as well as experimental data measured at Argonne National 

Laboratory, for a number of different battery chemistries both commercial and developed at 

Argonne, are available for use within the model. There are five governing equations for battery 

performance 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 the 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 user of BatPaC 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 settings as they prefer, we list our suggestions in Table 

3.1. The battery type is defined by the end-use application. Hybrid electric vehicles (HEVs), 

plug-in hybrid electric vehicles (PHEVs), and electric vehicles (EVs) have increasing levels of 

electrical energy storage for use by the vehicle drivetrain. The model will use Table 3.1 or the 

user’s explicit inputs to size the battery correctly for the chosen application. 

Table 3.1 Criteria for designing batteries for a specific end-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 15-95 

Cell Thickness, mm 6 6 8 12 

9 
   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Battery Design Model

Pack Requirements Key Constraints 

• power • max electrode thickness 

• energy or range • target cell potential, V, at 

Iterative Spreadsheet 

Solves for cell capacity 

and designs battery pack 

by varying: 

1. Cell area 

2. Electrode thickness 

3. Internal resistance 

• number of cells 

Cell Chemistry 

Measured Properties 

• pulse power ASI 

• discharge ASI 

• mAh/g, g/cm3 

• electrode porosity 

• SOC window 

• physical properties 

peak power 

• cell/module format 

Calculated Battery 

Pack Properties 

• dimensions 

• volume & mass 

• specific energy, 

power 

• materials required ASI = area specific impedance 

Figure 3.1 Summary flow of the design model 

The microHEV is a micro or mild-hybrid that provides a moderate power level, ~25 kW, for two 

seconds. This design is best suited for cell chemistries capable of very high power-to-energy 

(P/E) ratios. The HEV-HP is a power-assist hybrid that provides the rated power for a full 10 

second pulse. The power for both HEV applications is 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. Therefore, the power rating for the battery is 

10 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

determined at 25 % SOC. PHEV cells should be much larger than HEV cells and thus a cell 

thickness of 8 mm is assumed. Finally, EV batteries use 80 % of their total energy with their 

power rated near the end of discharge. Cell thicknesses are set to 12 mm to accommodate a high 

capacity design. As noted later in the report, selecting a parallel arrangement of cells 

automatically assumes a cell thickness of 6 mm regardless of the end-use application. 

Additionally, the use of negative electrodes operating 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, Li4Ti5O12 (LTO), negative electrode is an example of intercalation electrode with 

almost no risk of plating lithium metal during a charge pulse. On this basis, the available energy 

for LTO-based Li-ion chemistries is suggested to be 75 % for PHEVs and 85 % for EVs. 

In an established factory, the fixed design parameter is most likely the electrode area for a single 

layer rather than a set cell thickness. To make higher capacity cells, more layers of the 

predetermined footprint are stacked, thus increasing the cell thickness. In our model, the plant is 

constructed for the sole purpose of building the battery being designed. Flexibility to produce 

other products is not taken into account. Most importantly, the model calculates very little 

difference in cost whether the cell has large-area layers that are few in number as compared to a 

high number of layers smaller in area. For ease of calculation, we use a set cell thickness to 

determine the number of layers. The area of each layer is set by the cell capacity requirement. 

Accounting for capacity and power fade in the battery requires the user to design the battery with 

the appropriate excess energy and power at the beginning-of-life (BOL). Defining the voltage at 

which maximum power is achieved at BOL is one way to 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 to 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 aspects of materials chemistry, cell design, and 

battery use directly affect the decay of the battery pack. Hence, we allow the user to make 

accommodations for decay as he or she believes is necessary. 

3.2 Voltage at Maximum Power 

The voltage at which a cell reaches the designed maximum power is one of the most important 

factors in the design of a battery. However, this specification is one of the least discussed aspects 

of battery design. The voltage at maximum power, Vcell, 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 demonstrates the maximum achievable power for a battery at BOL is at 

50 % of the open-circuit voltage (OCV). Operating at these 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 increase 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. 

11 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

We design the battery to achieve EOL power capabilities at a specified fraction of the opencircuit voltage, [V/U], at BOL. This approach is unique when compared to current design 

practice of OEMs and cell manufacturers. However, a characteristic value of [V/U] exists for all 

batteries regardless of the battery design process. One may determine this value for an existing 

system in a straightforward manner. The potential at maximum power is measured at the end of a 

10 s pulse at the EOL power rating and the SOC used for the power rating of a specific battery 

type (HEV, PHEV, EV). The designed [V/U] value is the measured potential at the end of the 

pulse divided by the open-circuit potential reached long after the pulse. This design point then 

captures the degree to which the battery has been oversized to enable long-life, cold-start, and 

efficient operation. The remainder of this section presents a discussion for setting the BOL 

voltage at maximum power at no less than 80 % of the open-circuit voltage, [V/U] = 0.8. 

Defining the voltage as a fraction of the OCV, allows for direct calculation of all the necessary 

battery properties (see for example Eq. 3.6 or 3.8 in the section 3.3). 

The allowable increase in battery resistance over the life of the battery is a function of the 

designed voltage for maximum power. In general, designing the battery to achieve maximum 

power at a higher [V/U] allows for larger resistance or impedance increases over the lifetime of 

the battery. Figure 3.2 created from Eq 3.1 displays how the voltage at maximum power will 

change to meet the designed power as the internal resistance of the battery increases. Clearly, 

achieving BOL power at a high fraction of the OCV allows for greater degradation within the 

usable lifetime of a battery. R1 is the initial resistance of the battery at BOL while R2 is the 

resistance as the battery ages. If the minimum voltage is 55 % of the OCV, the allowable 

increase in resistance for batteries designed for BOL max power at 70, 80, and 90 % OCV is 18, 

55, and 175 %. The consequence of achieving the power at lower and lower fractions of the 

open-circuit voltage is that both electric current and heat generation will increase over the 

lifetime of the battery, Figure 3.2b and Figure 3.3. The proper design of a battery will account 

for the changes over the entire lifetime and not just desired behavior at BOL. 

⎧ ⎫ ⎡V ⎤ 1 ⎪ R2 ⎡V ⎤ ⎛ ⎡V ⎤ ⎞⎪ = ⎨1+ 1− 4 ⎜1− ⎟⎬ (3.1) ⎢ ⎥ ⎢ ⎥ ⎜ ⎢ ⎥ ⎟ ⎣U ⎦ 2 2 ⎪ R1 ⎣U ⎦1 ⎝ ⎣U ⎦1 ⎠⎪ ⎩ ⎭

The level of heat production is significantly different at BOL for batteries designed to meet 

maximum power at differing fractions of the open-circuit voltage. We may compare the 

differences in designed [V/U] by assuming the resistive heating (joule heating) is the most 

significant factor in determining the heat generation, Eq. 3.2. This assumption is true for 

moderate to high rate applications. We also reasonably assume the ASI will not change 

significantly in the range of current densities and electrode thicknesses we vary in the 

comparisons. From this point, we can analyze the difference in heat generation from different 

designed [V/U] values, Eq 3.3. 

12 
 

0 25 50 75 100 125 150 175 200

 Increase in Resistance, %

 

 

 

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


95 

90 

85 

80 

75 

70 

65 

60 

55 

50 

80 

70 

60 

50 

40 

30 

20 

10 

0 

Designed 

BOL [V/U] at 

90% 

80% 

70% 

max Power 

Designed 

BOL [V/U] at 

max Power 

90% 

80% 

70% 

0 25 50 75 100 125 150 175 200
 

Increase in Resistance, %
 

Figure 3.2 a) Required change in [V/U] to maintain rated power with increases in internal
 

resistance over the life of the battery. b) Increase in current due to lowered [V/U].
 

13 
 

 

 

 

 

 

⎛ ⎞ 2 

2 ⎡V ⎤ U ⎜1− ⎟ ⎜ ⎢ ⎥ ⎟

2 ⎛ ⎡V ⎤ ⎞ ⎝ ⎣U ⎦ j ⎠ q j = (Apos I ) Rj	 = Itotal U ⎜1− ⎟

⎟ = (3.2) ⎜ ⎢ ⎥ ⎝ ⎣U ⎦ j ⎠ Rj 

⎛ ⎡V ⎤ ⎞

2 

R ⎜1− ⎟ 1 ⎜ ⎢ ⎥ ⎟ q2 ⎝ ⎣U ⎦ 2 ⎠
 =	 2 (3.3) 

q1 ⎛ ⎡V ⎤ ⎞ R2 ⎜1− ⎟ ⎜ ⎢ ⎥ ⎟ ⎝ ⎣U ⎦1 ⎠

0 

50 

100 

150 

200 

250 

300 

350 

400 

450 

500 

Increase in Heat Generation, %

90% 

80% 

70% 

Designed 

BOL [V/U] at 

max Power 

0 25	 50 75 100 125 150 175 200 

Increase in Resistance, % 

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

different designed voltages at maximum power. 

The ratio of resistances may be found by equating the 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
 

14 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

the ratio of heat production at maximum power for the two cases, Eq. 3.5. A battery that achieves 

maximum power at 80 % of OCV will have a heat production 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 %. 

⎡V ⎤ ⎛ ⎡V ⎤ ⎞ ⎜1− ⎟ ⎢ ⎥ ⎜ ⎢ ⎥ ⎟ R 1 ASI A power 1 pos 2 ⎣ ⎦ U U 1 ⎝ ⎣ ⎦1 ⎠ = = (3.4) R ASI A V ⎛ V ⎞ 2 power 2 pos 1 ⎡ ⎤ ⎡ ⎤ ⎜1− ⎟ ⎢ ⎥ ⎜ ⎢ ⎥ ⎟ ⎣U ⎦ 2 ⎝ ⎣U ⎦ 2 ⎠

⎡V ⎤ ⎛ ⎡V ⎤ ⎞ ⎜1− ⎟ ⎢ ⎥ ⎜ ⎢ ⎥ ⎟ q2 ⎣U ⎦1 ⎝ ⎣U ⎦ 2 ⎠ = (3.5) 

q1 ⎡V ⎤ ⎛ ⎡V ⎤ ⎞ ⎜1− ⎟ ⎢ ⎥ ⎜ ⎢ ⎥ ⎟ ⎣U ⎦ 2 ⎝ ⎣U ⎦1 ⎠

Two straightforward design changes will enable operating 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 of 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 as the reduced electrode thickness is above the 

increase in ASI, > 20 microns as discussed in detail below. 

The efficiency of a battery defines the heat rejection 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 the 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 battery 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 cycle. 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 function of the designed potential at which the 

battery reaches maximum power. The figure is created 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/Pmax = 1. In example, a battery 

designed at [V/U] = 0.8 will have 80 % efficiency for 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 battery at power levels below maximum power 

15 
 

 

 

 

 

 

 

(typical driving conditions). Consider two batteries 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/Pmax = 0.45, the battery designed at [V/U] = 0.9 will be 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. 

100% 

90% 

harge

50% 

60% 

70% 

80% 

Efficiency During Disc

0.5 0.6 0.7 0.8 0.9 

0.10 

0.20 

0.30 

0.45 

0.60 

0.80 

1.00 

P/Pmax 

1 

Designed [V/U] at Max Power 

Figure 3.4 Efficiencies for batteries designed to achieve maximum power at different fractions 

of their open-circuit voltage. Comparative efficiency lines are shown for equivalent power 

demands over a period of battery operation. 

16 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3.3 Governing Equations 

The five coupled, algebraic equations that govern the battery design are presented in this section. 

While these equations are perhaps the most important, many other equations are used to fully 

define the battery mass and volume. These other equations will be specified where necessary in 

the following subsections. 

The user of the model specifies the required maximum power, Pbatt, of the battery. This power is 

translated to a current density, I, in Eq 3.6 using the area of the positive electrode, Apos, the 

number of cells, Ncell, the open-circuit voltage at the SOC for power, Uocv,P, and the fraction of 

the open-circuit voltage at which maximum power is achieved, [V/U]. 

Pbatt I = (3.6) ⎡V ⎤ A N U pos cell ocv,P ⎢ ⎥ ⎣U ⎦

The relationship between capacity and battery energy 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, 

Uocv,E. The energy for all batteries designed by the design model is calculated at a C/3 rate and 

the average open-circuit voltage at 50 % SOC. The remaining necessary values are the capacity 

of the cell, C, ASI for energy, ASIenergy, number of cells, and area of positive electrode. Either the 

battery energy or capacity may be specified. The energy may alternatively be determined from a 

stated range, fraction of total energy available, and energy usage rate for the vehicle (Wh/mile). 

⎛ C ASI ⎞ energy E = N C⎜

⎜U − ⎟⎟ (3.7) cell ocv,E 3 A ⎝ pos ⎠

The area of the positive electrode in Eq. 3.8 is determined largely by the area specific impedance 

for power, ASIpower, and resulting voltage drop. The voltage of cell at max power, Vcell,P, is found 

from the product [V/U]Uocv,P, where Uocv,P is the open circuit voltage at the SOC for max power. 

In general, the area of the electrodes 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 lithium plating during charge pulses. The separator area is slightly larger 

than the negative electrode to prevent the electrical shorting of the two electrodes. 

ASI P power batt Apos = (3.8) 

2 ⎡V ⎤⎛ ⎡V ⎤⎞ N cell (U ocv,P ) ⎢ ⎥⎜

⎜1− ⎢ ⎥⎟⎟ ⎣U ⎦⎝ ⎣U ⎦⎠

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

specific capacity of the electrode, Q, volume fraction of active material, εact, bulk density of the 

17 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

active material, ρ, and the positive electrode area. The negative electrode thickness is determined 

by its specific reversible-capacity and the designed excess-capacity to prevent lithium plating 

during charging. We have chosen a ratio of 1.25 negative to positive reversible-capacity (N/P 

ratio) for the default value for the cells with graphite 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 allowable electrode thickness is a user defined 

value. The calculation for the electrode area changes when the designed thickness is greater than 

the maximum allowed (Section 3.6.1). 

C Lpos = (3.9) Qρε act Apos 

Finally, the ASI for power (and for energy to a lesser extent) is calculated using an expression 

that is based on the electrode thicknesses, the current density, and the C-rate. The exact 

expression will be discussed in the next session. The ASI in Eq 3.10 shows the basic 

dependencies with α and β being constant valued parameters. 

α + f (I ) ASI = + β (3.10) L pos 

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 electrode 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 ratios required by automotive applications. 

However, the ASI is not an inherent constant of a specific 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 parameters, etc). The calculation used for the ASI in this 

battery design model has been discussed in detail and validated against experiments elsewhere.20 

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 that originated from 

the change in open-circuit potential with concentration for the intercalation materials. Equation 

3.11 contains the definition of the ASI used in this document. It1 is a positive valued current 

density for a discharge pulse. It2 is equal to zero as it is during the relaxation period after the 

pulse. Time 0, t0, is the time just before a current pulse begins, time 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 with 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. 

18 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

V t 2 −Vt1 ASI = (3.11) I t − I 1 t 2 

The ASI for the electrochemical charge and discharge process is referred here-in as ASIechem. Our 

calculation approach for both the ASI for power and for energy involves adding three 

components together to reach the ASIechem, Eq. 3.12. The first two factors include impedance that 

arises from the interfacial charge transfer and transport. The third factor is a lumped parameter 

used to capture the remaining impedance. 

pos neg ASI = ASI + ASI + ASI (3.12) echem intf intf const 

The interfacial impedance for positive and negative electrodes both contain the charge transfer 

resistance component R T/(ioaLF) as shown in Eq. 3.13 and 3.14. Here, io is the exchange 

current density related to the interfacial area and a is the ratio of interfacial area to electrode 

volume. An approximation often used for a relates the parameter to the volume fraction of the 

active material and the particle radius, a = 3εact/rp. The variables io and a should be specified to 

relate to the same area as they are often not independently determined. 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 ASIechem increases as the electrode thickness is 

reduced. This behavior is typically observed at electrode thicknesses less than 30 microns for 

common Li-ion battery materials. 

RT ASI neg = (3.13) intf i aL F o neg 

⎧ ⎡ ⎤ –0.5 

pos RT ⎪⎛ I ⎞ ⎛ rC ⎞

2 ⎫

⎪ ASI = ⎜1− ⎟⎢1− ⎜ ⎟ ⎥ (3.14) intf ⎨⎜ ionic ⎟ ⎜ ⎟ ⎬ i aL F o pos I ⎢ r ⎥ ⎪⎝ lim ⎠ ⎝ C,lim ⎠ ⎪ ⎩ ⎣ ⎦⎭

The positive electrode interfacial impedance also includes two factors that account for the 

physical limitations that occur from depleting the concentration of the reactants within the 

ionic porous electrode. The Ilim term is the limiting ionic current for lithium cation transport through 

the porous separator. The r term is the limiting C-rate for solid state diffusion of lithium in C,lim 

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, εact, and the 

electrode thickness, L, are used. If either the limiting C-rate or limiting ionic current are 

approached, the ASI will begin to approach an infinite value. This approach assumes the cell and 

material design is such that the transport limitations all occur on the positive electrode. The 

parameters required for the ASI expression are fit to experimental measurements. The ASI 

values are corrected for the interfacial contributions present during measurement so that the 

correct ASI may be determined at different electrode thicknesses. This is termed “ASI correction 

factor” on the System Selection worksheet of the spreadsheet model. 

19 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I = r Qρε L (3.15) C act pos 

The cell ASI for energy, ASIenergy, and power, ASIpower, are determined by adding the ASIechem to 

that of the current collectors, ASIcc, as discussed in the next subsection. The difference between 

ASIenergy and ASIpower is that the limiting currents are not important during the C/3 discharge for 

energy and the ASIconst is a different value for two cases. ASIenergy will always be higher than 

ASIpower if a battery is operated far from the limiting current. The higher impedance is due to the 

formation of significant concentration polarizations during the longer time scale of the energy 

discharge. A reasonable rule-of-thumb is that the ASIconst for energy is 2.2 times the value for 

power in layered oxide materials such as LiNi0.80Co0.15Al0.05O2. 

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. The ASI used to calculate the required cell 

separator area, ASIpower, is larger than the ASI for the electrochemical charge and discharge 

processes, ASIechem,P, as shown in Equation 3.16. The ASIechem value is typically measured from 

experiments and must be added to the external resistances that arise from the materials used to 

conduct the electric current. These resistances come from current collection in the cell and also 

those on the module and battery pack level. 

R A cell cnct pos ASI = ASI + ASI + ASI + (3.16) power echem,P cc term Ncells 

The current collector foil impedance, ASIcc, is determined from an analytical expression, Eq. 

3.17, which accounts for the coated and uncoated region of the foil, labeled act for active and tab 

respectively. The resistance factor, Rf, and the resistance of the current collector foils, Rcc, are 

also shown for clarity in Eq 3.18 and 3.19. The factor of 2 in the Rf 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 current to the foil. An equivalent length for the 

resistance calculation may be determined so that multiplication 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 this 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 constant current density is verified with numerical 

modeling. 

⎛

⎜

⎜

2 (H act ) ⎞

⎟

⎟ tab ASI H W R R
 =
 =
 + H H
 (3.17)
 cc act act cc f act 3
 ⎝ ⎠

⎛

⎜

⎜

⎞

⎟

⎟

2 2
 R
 f = +
 (3.18)
 

σ foil ,neg foil L ,neg foil σ , pos foil L , pos 

20 

⎝ ⎠
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

⎛ H H ⎞ act tab R R
 = ⎜ + (3.19)
 ⎜

⎝

⎟

⎟

⎠ cc f 3Wact W 

The cell terminals are ultrasonically welded to the ends of the current collector foil tabs. While 

the welding removes this contact resistance, the ASI of the terminal must be included in the total 

cell cell resistance. The ASI of the cell terminals, ASI term , is the summation of the positive and 

negative cell terminals as shown in Eq 3.20. The dimensions for these terminals are set by the 

calculated width of the cell and the user defined terminal thickness and height. 

⎛

⎜

⎜

⎞

⎟

⎟

1 1
 H
 cell term ASI
 = + A (3.20) term pos ⎝σ σ term ,neg term , pos ⎠W L term term 

The ASI for connection losses is the last term in the ASI summation stated in Eq. 3.16. This ASI 

value is calculated by multiplying the ratio of cell positive electrode area to number of cells by 

the summation of the resistances, Rcnct, 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 current. The calculation of Rcnct is detailed in Eq. 

3.21 with the individual sources of connection losses shown. The voltage drop resulting from 

cell-to-cell contact resistance, Rcell , is taken to be 10-4Uocv,E in Eq. 3.22, a small fraction of the cntct 

open-circuit voltage. A battery manufacturer would only tolerate a minimal voltage drop from 

cell-to-cell contact. One connection method is to physically 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 value used in the model is left to the choice of the 

user to leave as is or to change to a different value. 

cell mod mod batt R = N R + N R + (N −1)R + R (3.21) cnct cell cntct mod term mod incnt term 

cell 4 cell ocv ,E Rcnct = 10− N U 

(3.22) IA pos 

The module terminal resistance, R mod , calculation in Eq. 3.23 is shown as an example of how the term

terminal and interconnect resistances are calculated for the module and battery pack. The size of 

the terminals and thus their resistance are determined from a calculation based on a predetermined allowable rate of temperature rise for the conductor. This approach is explained in 

more detail in subsection 3.4.3. 

mod Hterm mod R = N (3.23) term term 

σ π (r )

2 

term term 

21 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3.4.2 Potential and Current Distribution in the Current Collection Foils 

The designed current collection system was evaluated using a numerical simulation package. 

Equations 3.24-3.26 were solved for a steady state, isothermal, and 1-D simulation. Here, the 

conductivity, σj, is the effective conductivity of 1⁄2 of the foil (the other half carries the current 

from the opposite side). The bulk conductivity value, σj

0

, is multiplied by the thickness of the 

conductor, Lj/2, to lower the dimension of transport. 

U − (Φ (x)− Φ (x)) ocv 1, pos 1,neg In = (3.24) ASI echem 

∇ ⋅(σ ∇Φ pos ) = −In (3.25) pos 1, 

∇ ⋅(σ ∇Φ neg ) = In (3.26) neg 1, 

The boundary conditions were set for both ends of each foil. The tab ends of the foils were set to 

a specified voltage and the opposite ends of the foils 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 ASIechem was 30 ohm cm2

, and 

the Uocv and Vcell 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 % variation in current density. This verifies the current 

density is uniform along the length of the foil. This is also obvious from the linear relationship of 

current with foil height in Fig. 3.5. The assumption 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 ASIechem is at least twice the value of ASIcc. The simulated resistance of the foils is found 

to raise the ASIechem by 0.7 for an ASIpower of 30.7 ohm cm2

. Additionally, the numerical result 

verified that H/3 is the correct equivalent length to represent the ASIcc for the cell. This may also 

be found analytically, Eq. 3.27-3.29, if you assume an even current distribution. We have shown 

that to be a reasonable assumption. 

In 2 Φ = V + (H − x 2 ) (3.27) 1, pos cell 2σ pos 

I ⎛ x 

2 ⎞ Φ n

1,neg = ⎜ − xL ⎟ (3.28) ⎜ ⎟ σ 2 neg ⎝ ⎠

H 2 1 Φ ⎛ ⎞ 1, pos − Φ1,neg Vcell H 1 1 ASI echem + ASI cc = ∫ dx = + ⎜

⎜ + ⎟⎟ (3.29) H 0 I I 3 ⎝ n σ pos σ neg ⎠

22 
 

 

0 0.2 0.4 0.6 0.8 1

x/H

3.5750 

3.5740 

3.5730 

3.5720 

3.5710 

3.5700
 

Positive foil and cell potential, V
 

Cell 

Positive foil 

Negative foil 

0.0000 

-0.0010 

-0.0020 

-0.0030 

-0.0040 

Negative foil potential, V
 

-0.0050
 

3.5690 -0.0060 

0.00 

0.02 

0.04 

0.06 

0.08 

0.10 

0.12 

Foil current per width, A/cm 

0.00486 

0.00487 

0.00488 

0.00489 

0.00490 

0.00491 

0.00492 

Current density, A/cm2 

Negative foil 

Positive foil 

current density 

0 0.2 0.4 0.6 0.8 1 

x/H 

Figure 3.5 The change in current and potential within the positive and negative foils. The current 

collection design results in a uniform current distribution along the length of the foil. 

23 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

An analogous problem has been solved by Euler and Nonnemacher and then communicated 

24, 25 repeatedly by Newman et al. The analytical solution they presented may be used after a 

slight alteration to dimensionalize the current density 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 of the current collector foil. Thus, this approach 

is a more general solution than the one we use in the design model. 

⎡ ⎛ ⎤ ⎜

⎜

⎞

⎟

⎟

σ σ neg pos + ⎥

⎥

⎥

⎥

⎥

⎦

2
 +
 cosh
 v
 − (Φ ) σ σ
 pos neg 

2 U
ocv 1, pos − Φ1,neg H
 ⎝ ⎠ ASI ASI
 +
 = =
 + (3.30)
 echem cc I
 σ σ+
 v
 sinh
 v
 neg pos 

1 

⎢

⎢

⎢

⎢

⎢

⎣

⎛

⎜

⎜

⎞

⎟

⎟

2 1 1
 2 H 

v =
 + (3.31)
 

σ σ
 ASI echem ⎝ pos neg ⎠

3.4.3 Determination of Module Terminal, Battery Terminal, 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 rise 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 cylindrical terminal radius and mass by assuming 

a length, Hterm. In this way, the size of the module terminal is redesigned during each simulation 

to meet the specified power requirements and allowable temperature rise, Eq. 3.34. The mass of 

the conductor is found to be inversely proportional to the allowable temperature rise. 

dT 

q = mC p (3.32) dt 

H ) term 2

q = (IA pos (3.33) A term term σ

−1/ 2 

pos 

⎡

⎢

⎣

ρ term term σ C
 dT
 ⎤ A (3.34)
 term = IA ⎥

⎦ p dt 

A copper busbar must also be sized for batteries using a single row of modules. We have 

somewhat arbitrarily assumed a ∆Vbb = 30 mV drop across the busbar to be allowable at 

maximum current. This value maybe easily changed by the user. Equation 3.35 is used to 

calculate the mass of the busbar, mbb. The complicated expression for the volume of the busbar is 

24 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

derived from the voltage drop, conductivity, busbar width, wbb, and required busbar crosssectional area. 

I (w )

2 

tot bb m = ρ (3.35) bb bb ΔV bb bb κ

3.5 Calculation of Battery Dimensions 

The goal of the model is to quantify how the various 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 materials requirement to meet this design. 

Summing the mass of the components is relatively straight forward. Determining the total 

volume that contains the components and required free 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 in Eq. 3.36 by accounting for the compression 

factor, Xcomp, and the individual thicknesses of the current collector foils, Lfoil, electrodes, Lpos 

and Lneg, separator, Lsep, and container, Lcont. Xcomp 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 possible changes in electrode volume upon cell 

discharge or charge. 

L − 2L + Lneg 

cell cont foil N = X (3.36) layers comp neg pos L + L + 2(L + L + L ) foil foil sep neg pos 

The Nlayers approximation is necessary as the cell thickness is a user defined parameter. The 

aspect ratio of the cell is also user defined; therefore, solving for the width also determines the 

height of the cell as seen in Eq. 3.37. The width is calculated from the number of layers and the 

aspect ratio, H/W. The factor of 2 enters the denominator as both sides of the foil are assumed to 

be coated. 

A 

W = pos (3.37) pos H 2 Nlayers W 

Having determined the width and height of the electrode, the rest of the cell dimensions are 

relatively straightforward, Eq. 3.38 and 3.39. The width of the cell, Wcell, is 8 mm wider than the 

positive electrode to allow for the larger separator area and pouch seals. The pouch seals are 

folded up, pressing along the inside wall of the module casing. The height of the cell, Hcell, is the 

height of the positive electrode in addition to the distance for the terminals and connections to 

the foil tab, Lterm,cnt. Our assumed design requires 15 mm for this distance. The volume of the cell 

is the product of the three dimensions. 

25 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Wcell = W pos + 8 (3.38) 

H H (3.39) cell = pos + 2Lterm ,cnt 

3.5.2 Module Dimensions 

The module dimensions are defined by Eq. 3.40-3.42. The height and length of the module are 

both just 2 mm wider than the cell dimension. The width of the module is related to the total 

thickness from all of the cells with allowance for a SOC controller at one end. 

H = W + 2 (3.40) mod cell

Lmod = Hcell + 2 (3.41) 

W = L (N +1) +1 (3.42) mod cell cell / mod 

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, Hair, thickness of the module compression plates, Lcomp, and 

the battery pack jacket, Ljack (Eq. 3.43-3.45). Ljack includes a 10 mm thick insulation layer 

sandwiched between two aluminum walls for the container. The thickness of the aluminum wall 

increases from 1 to 1.5 to 2 mm as the battery volume increases from < 20 L to < 40 L to larger 

dimensions. The layout of the modules, number per row, Nmod/row, and number of rows, Nrow, is 

also included. The final volume of the battery is the product of the three dimensions. The space 

left for connections between modules, Lgap, is a function of the number of rows of modules. Lgap 

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 negative 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. 

H = H + 2H + 2L (3.43) batt mod air jack 

Lbatt = N mod/ row Wmod + H air + + 2Lcomp jack 2L (3.44) 

W = N L +L +2L (3.45) batt row mod gap jack 

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 encountered by cell manufactures. 

26 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3.6.1 Maximum Electrode Thickness 

A practical limitation exists for the maximum achievable electrode thickness. This limitation 

may be set by manufacturing capabilities, ionic and electronic current transport within the porous 

electrode, susceptibility to plating lithium on the negative electrode, or aging characteristics 

related to adhesion to the current collector. Some of these challenges are discussed in great detail 

in the following subsection. When the maximum electrode thickness, Lmax, has been reached on 

either the positive or negative electrode, the electrode area equation is modified as shown in Eq 

3.46. The electrode thickness, Ltgt, is the largest electrode thickness, negative or positive, 

calculated at the targeted fraction of the OCV [V/U]. 

L L max tgt A = A (3.46) pos pos L max 

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 maximum 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. 3.47 which is the solution to the quadratic found in Eq. 

3.48. 

⎡ P ASI ⎤ ⎡V ⎤ 1 2 batt power 

⎢ ⎥ = ⎢Ucell + (Ucell ) − 4 ⎥ (3.47) ⎣U ⎦ 2U cell ⎢ N A cells pos ⎥ ⎣ ⎦

P ASI batt power Vcell cell = U − (3.48) Vcell Ncells Apos 

The maximum electrode thickness may have a large impact on the energy density and cost of 

cells designed for high energy and range. Nelson et al. demonstrated this concept in 2009 

assuming a 100 micron maximum electrode thickness.12,19 In 2010, Santini et al. relaxed this 

assumption to 300 micons; although, the thickest electrode discussed in the paper was a 225 

micron graphite electrode in the LMO-Gr EV with 100 mile range. 13 In conversations with 

manufactures, 100 microns appears to be the general electrode thickness used for EV type cells 

at the present time. However, Santini et al. has shown substantial increases in energy density and 

decreases in cost if larger electrode thicknesses may be utilized. The challenges to achieving 

thick electrodes, in addition to those already mentioned, relate to fast charging while avoiding 

lithium metal deposition, utilizing all of the materials reversible capacity, removing gases formed 

during formation cycling, wetting the full porosity of the electrode, achieving defect free 

coatings, and drying the thick electrode at high rates. Our opinion is that the successful cell 

manufacturers will engineer ways to overcome these challenges to increase energy density and 

lower cost. 

3.6.1.1 Challenges of Large Electrode Thicknesses 

Dependent upon the battery chemistry and designed P/E ratio, the maximum achievable 

electrode thickness (loading) may have a significant effect on the end cost and energy density of 

27 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

a battery pack. For batteries designed at low P/E ratios or for cell chemistries with low 

volumetric capacities, the designed electrode thickness based on the target efficiency is often 

larger than what is feasible during operation in a transportation environment. This subsection 

explores some of the challenges that arise in the electrochemistry when larger electrode 

thicknesses are utilized. 

Argonne gained a wealth of experience in the NCA-Gr in 1.2 M LiPF6 3:7 EC:EMC cell during 

the Advanced Technology Development program sponsored by the US Department of Energy 

(DOE). Dees and coworkers developed a world-leading parameter set for a numerical model 

through exhaustive electrochemical measurements, ex-situ characterization techniques, and 

multi-scale modeling activities.26-35 The resulting phenomenological cell model founded on the 

methodology originating from John Newman (UC Berkeley) will be used to evaluate the 

electrochemical behavior of cells using thick electrodes.36 The coupled, non-linear partial 

differential equations are solved with the finite element method using FlexPDE. 

Simulated discharge capacity for the C/1 and C/3 discharge rate is shown in Figure 3.6 as a 

function of electrode thickness. For reference, the target positive electrode thicknesses for this 

cell operating at a 5C-rate and a [V/U] = 0.8 is 142 microns. The line of 100 % capacity 

utilization is also shown as a means to judge the deviation from theoretical capacity. As 

expected, the C/1 rate deviates more strongly than the C/3 rate with increasing electrode 

thickness. The loss in capacity is a result of the cell hitting the discharge voltage cut-off, 3.3 V, 

before all of the lithium has been transported from the negative to the positive electrode. 

Figure 3.7 displays the normalized concentration profile of the electrolyte salt, LiPF6, at the end 

of a C/1 and C/3 discharge for an electrode thickness of 245 microns. The C/1 discharge results 

in a positive electrode starved of electrolyte salt. This transport limitation results in the cell 

prematurely reaching the voltage cutoff. In order to overcome this limitation, the electrode would 

need to be engineered with significantly reduced tortuosity37 or utilize an electrolyte with better 

mass transfer characteristics. This behavior is exacerbated by lower temperatures, such as those 

experienced during winter driving conditions. The fraction of theoretical discharge capacity 

begins to lower significantly at thicknesses greater than 100 microns, 3.4 mAh/cm2

, at the C/1 

rate and 175 microns, 6.4 mAh/cm2

, at the C/3 rate. The electronic transport properties of the 

cathode material also play an important role in determining the current distribution within the 

electrode. While the NCA material has a reasonably high conductivity, other cathode materials 

have lower valued electronic conductivities and, depending on the conductive additive 

properties, may have different current distributions and limitations within the electrode. 

28 
 

 

 

 

 

 

 

 

0 

2 

4 

6 

8 

10 

Discharge Capacity, mAh/cm2 

3-Hour Discharge Capacity 

1-Hour Discharge Capacity 

100 % of capacity 

0 50 100 150 200 250 300 350 

Electrode Thickness, microns 

Figure 3.6 Cell capacity simulated at the C/1 and C/3 rate as a function of electrode thickness 

(loading) for NCA-Gr. 

0.0 

0.5 

1.0 

1.5 

2.0 

2.5 

c/cavg 

1C Discharge 

C/3 Discharge 

Negative 

Positive 

Separator 

0 100 200 300 400 500 

Cell Coordinate, microns 

Figure 3.7 Normalized electrolyte salt concentration at the end of discharge at the C/1 and C/3 

discharge rates. The second half of the positive electrode next to the current collector is starved 

of the LiPF6 salt resulting in a lower utilization of the inherent cell capacity. 

29 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The simulated ASI for a 5C, 10-s discharge pulse at 60 % SOC is shown in Figure 3.8 as a 

function of electrode thickness. The initial decrease in the ASI is a mathematical result of 

diminishing significance of the interfacial impedance as more current is passed in the same 

geometric area. The ASI then remains constant from 75 microns to nearly 400 microns. The 

constant ASI results from ohmic losses that behavior linearly with applied current. The dramatic 

increase in the ASI at the largest electrode thicknesses results from limitations in electrolyte 

transport within the porosity of the positive electrode. This is similar to what is displayed in Fig 

3.7 above during the constant discharge at the C/1 rate for an electrode thickness of 245 microns. 

The most significant issue for pulse power operation with thick electrodes occurs on the negative 

electrode during a charge or regen pulse, Figure 3.9. The potential of the negative electrode may 

drop below that of a hypothetical lithium reference electrode during a charge pulse, inferring an 

undesirable side reaction of lithium plating on graphite.38 This behavior is exacerbated by 

increasing electrode thickness. Operation at higher SOC and lower temperatures will also 

increase the probability of lithium plating. The lithium reference electrode is taken to be in the 

center of the separator layer. The two times shown in the graph, 1-s and 10-s, represent different 

polarization measurements for the electrode. The 1-s value includes all of the interfacial 

impedance and minor contributions from concentration polarization. The longer time value 

includes additional changes in potential due to the concentration gradient in the electrolyte. The 

1-s time is the more accurate valuation of the tendency of the electrode to plate lithium. 

0 

10 

20 

30 

40 

50 

ASI10s, ohm cm2 

Full Cell 

Positive Electrode 

Negative Electrode 

0 100 200 300 400 500 

Electrode Thickness, microns 

Figure 3.8 Calculated ASI from a simulated 10-s, 5C discharge pulse for the NCA-Gr cell 

couple at 60% SOC. Positive and negative electrode thicknesses are similar in value for this cell 

design. Transport within the electrolyte is not limiting until the electrode thickness approaches 

450 microns for these simulation conditions. 

30 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

VNegative vs. VLithium, volts 

0.1 

0.0 

-0.1 

-0.2 

-0.3 

-0.4 

1s Pulse Time
 

10s Pulse Time
 

0 50 100 150 200 250 300 350 

Electrode Thickness, microns 

Figure 3.9 The potential of the negative electrode versus a hypothetical lithium reference 

electrode located in the center of separator during a 5C charge pulse for the NCA-Gr couple. 

The tendency for lithium plating appears to be significant at electrode loadings greater than 3.4 

mAh/cm2 under these specific conditions. Lower continuous and pulse charge rates are most 

likely necessary to ensure the safe operation and long life of this battery. Fast charging of PHEV 

and EV batteries is an oft discussed value-added characteristic necessary to increase the 

attractiveness of electric vehicles to the consumer. However, this fast charge requirement may 

require a lower loading design to prevent lithium plating from occurring. This would not be true 

for batteries based on LTO negative electrodes, or possibly even non-graphitic carbon electrodes 

(e.g. hard carbon). The consequence of a lower loading design is that higher quantities of 

inactive materials are used resulting in a more expensive and less energy dense battery. 

A limit of 100 microns has been chosen for the default maximum electrode thickness. This 

thickness represents a graphite electrode balanced to a positive loading of 3.5 mAh/cm2 and is 

the largest thickness that ASI measurements have been validated at Argonne. However, a low 

volumetric capacity electrode, such as LMO, will result in a lower area-specific capacity as the 

limit will be determined by the positive electrode thickness. One domestic OEM has suggested 

that at the time of this publication, state of the art electrode loadings for PHEV applications are 

less than 2 mAh/cm2

. This low loading level was selected based on cold-start performance, life 

testing, and rate capability studies. We note that different electrolytes will likely have the most 

significant effect on the transport limitations and result in different optimum electrode loadings. 

Gel-based electrolytes or standard carbonate electrolytes mixed with low molecular weight 

polymers are often utilized in pouch cell based batteries. While the ionic conductivity of these 

systems may approach standard carbonate electrolytes used, diffusion of the salt is restricted. 

31 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

This decrease in mass transport will result in large increases in impedance during longer 

discharges (constant speed highway driving). Hence, companies using an electrolyte with 

sluggish mass transport will require thinner electrodes than what the model would normally 

calculate based on pulse power applications. Greater electrode thicknesses may be achievable in 

the future as manufacturers expend significant engineering efforts to minimize the inactive 

material that lowers energy density and raises cost. The concerns over lithium plating may 

remain unless new, less susceptible negative electrodes are developed that still enable high 

energy density. 

Table 3.2 displays a calculated sensitivity analysis for designing the battery at different target 

electrode loadings to achieve 17 kWh of total energy for the NCA-Gr cell couple for two power 

levels, 110 kW and 60 kW of power. The consequence of varying electrode loading at constant 

power and energy is to change the fraction of open circuit voltage at which maximum power is 

achieved at BOL. This quantitative comparison of electrode thickness with [V/U] is only valid 

for the specific battery and cell chemistry designed in the table, while the qualitative results 

would hold for all systems. An alternate but equivalent way to create Table 3.2 is to maintain a 

constant value of [V/U], but vary the designed power level. As mentioned previously, private 

communications suggest that current electrode thicknesses used in PHEV applications are near 

50 microns or 2 mAh/cm2

; however, the exact details of that cell configuration are unknown and 

thus direct comparison should be conducted with caution. For the cell chemistry shown in the 

table, a loading of 2 mAh/cm2 with 110 kW of power correlates to achieving the maximum 

power at BOL at [V/U] = 0.84. Our default suggestion of using 80% of open-circuit voltage 

results in a moderately less expensive battery, albeit similar in value. If a lower P/E ratio battery 

was designed, then the electrode thickness (loading) would be much larger for the same designed 

fraction of open-circuit voltage. The sensitivity to [V/U] decreases with lower [V/U] values 

owing to the inverse proportionality of electrode loading to the P/E ratio. The calculated 

designed electrode loadings for lower P/E ratios will differ the most significantly from those 

used in industrial practice today. This is in part the motivation to limit electrode thicknesses to 

100 microns as well as the transport limitations discussed earlier. While the standard practices of 

today are important, the goal of the calculations is to evaluate the potential cost of Li-ion 

batteries in the future years after improvements have been made resulting from the competitive 

marketplace. Therefore, calculating a range of values will be the most instructive approach to 

determining where future battery costs may fall. 

Table 3.2 The effect of electrode loading on the price of a 17 kWh NCA-Gr PHEV40 battery 

with 96 cells 

17 kWh 110 kW 60 kW 

[V/U] mAh/cm2 microns Price, $ mAh/cm2 microns Price, $ 

68 3.74 96 4305 7.38 188 3954 

72 3.45 88 4358 6.80 174 3977 

76 3.09 79 4442 6.11 156 4014 

80 2.67 68 4572 5.30 135 4091 

84 2.19 56 4780 4.38 112 4188 

88 1.65 42 5163 3.36 86 4364 

92 1.04 27 6045 2.22 57 4749 

32 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3.6.2 Accounting for Parallel Cell Arrangements 

The user of the design model may wish to use a parallel arrangement of cells within the larger 

series arrangement of the battery pack. Several motivations exist for a parallel cell arrangement. 

For example, a battery supplier may wish to only produce 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 the energy requirements while staying within 

battery pack voltage and current requirements. 

When the user chooses to have cells connected in parallel, the design model calculation includes 

the appropriate factors necessary to account for changes in the resistance, volume, and mass of 

the battery. The end result is a lower energy density 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. 

3.6.3 Accounting for Parallel Module Arrangements 

Designing a battery composed of modules in parallel cannot be explicitly simulated in the model. 

However, one may approximate this scenario by simply doubling the number of modules, and 

thus battery pack voltage. The simulated battery pack is nearly the same as if constructed of 

parallel packs. A simple wiring change would lower the pack voltage with a proportional 

increase in capacity. The overall energy and power will be the same. Subtle errors will exist in 

the size of the module terminals and conductors as the calculated total current will be less in the 

series arrangement than that in a parallel configuration. 

33 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4. Thermal Management
 

The power and life of lithium-ion batteries are more drastically affected by the battery 

temperature than they are for most other batteries including those based on lead-acid, nickelcadmium, and nickel-metal hydride systems. It is important that the temperature of a lithium-ion 

battery be controlled at all times, even when the battery is at rest. Developing schemes for 

effectively controlling the pack temperature at minimum cost will certainly be important in the 

success of this technology. The most difficult problem is the removal of heat generated within 

the battery, principally by ohmic heating. Avoiding excessive temperature rise during idle 

periods in hot ambient conditions is also a problem. Either of these conditions might raise the 

temperature to well above 40o

C, which enhances degradation reactions and shortens the battery 

life. Thus, maintaining the battery temperature as near the minimum temperature for adequate 

power will prolong battery life. Because the battery has poor power at low temperatures, heating 

the battery from a very cold condition is necessary and especially difficult for large EV battery 

packs for which no assistance is available from the engine. For electric-drive vehicles to be 

competitive in the market with conventional vehicles, these thermal control problems must be 

solved at moderate costs and by means that do not compromise the safety of the vehicle or 

battery system. 

The BatPaC model has a separate worksheet for estimating the thermal parameters and 

requirements for lithium batteries and for designing the thermal management system. The results 

are transferred to the Battery Design worksheet to calculate the mass, volume and materials 

requirements for the battery pack. 

4.1 Heat Generation Rates in the Battery Pack during Driving 

During driving, the heat generation rate depends on the driving cycle and the power of the 

battery relative to the demands of the cycle for the vehicle being driven. As discussed below, the 

heat capacity of the battery pack smooths out fluctuations in the heat generation rate. The rate 

that the cooling system must handle is the average rate for the most difficult driving conditions to 

which the battery pack will be subjected. 

The best way to determine the maximum cooling rate requirement for the battery pack is by 

vehicle simulation studies. These studies require a battery impedance algorithm that makes 

possible accurate estimates of internal heating and the use of vigorous driving cycles and highspeed driving patterns. The results of vehicle simulation studies of battery heating can be entered 

on line 19 in the Thermal worksheet to override the estimated default values. However, pertinent 

results are not always accessible and therefore we have provided some initial, although 

dramatically simplified, estimations for heat generation. 

For microHEV and HEV-HP battery packs, heat generation is intermittent and substantial 

periods of little or no heat generation exist in the load profile. The model estimates the heat 

generation rate for 25-kW micro-HEV batteries at 100W. For the HEV-HP battery packs, the 

maximum average battery power is derived from the energy requirement, default of E& = 300 

Wh/mile, entered on the Battery Design worksheet (line 157). The energy use requirement for 

HEV-HP batteries is estimated to take place at an average driving speed of 40 mph and involve 

34 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

the battery 50% of the time. These assumptions calculate an average estimated battery power 

level of 6.0 kW. For a 50-kW battery pack, the heat generation is estimated as 5% of the average 

battery power. The heat generation for a HEV-HP battery of different maximum power is 

estimated to be inversely proportional to the battery pack rating as shown in Equation 4.1. 

q HP = E& * 40 *0.5* 0.05* 50 (4.1) HEV − Pbatt

For PHEV battery packs, the maximum heating condition is deemed to occur during the 

declining charge period when essentially all of the vehicle power is supplied by the battery. 

Thus, the factors controlling heating during operation of PHEVs and EVs are similar and may be 

treated in the same way. The highest rate of continuous heat generation will occur on a very 

vigorous driving cycle or when driving at sustained high speed. Continuous discharge of the 

battery at constant power results in increasing impedance and increasing heat generation rate 

because of solid-state diffusion overvoltage. The area-specific impedance (ASI) will reach 2-3 

times the 10-second ASI in about five minutes accompanied by a similar increase in the internal 

heat generation rate. Whether or not steady high speed driving will result in greater internal heat 

generation than a vigorous driving cycle will depend on many factors including vehicle speed, 

& battery power, and electrode thickness. The energy usage requirement, default of E = 300 

Wh/mile, is assumed to occur at a steady discharge of 60 mph in PHEVs and EVs. The vehicle 

speed and energy usage assumptions provide an estimate of the maximum long-term discharge 

rate. The heat generation is calculated from this power requirement and ASI for energy. Finally, 

the maximum heat generation rate is assumed to be 1.3 times the value at 60 mph. The heat 

generated in the battery pack for these conditions is inversely related to the pack power. 

4.2 Heating under Adiabatic Conditions 

A factor to be considered in thermal management is the substantial heat capacity of the battery 

pack. This smoothes out temperature fluctuations resulting from power bursts so that the heat 

dissipation system need only handle the average heat generation rate for the most extreme 

driving profiles the battery is likely to encounter. For large PHEV and EV batteries the heat 

capacity of the battery will limit the temperature rise of the centerline of the cells by distributing 

the heat throughout the battery until steady state is reached. For a large EV battery with power of 

120 kW and energy of 50 kWh, the temperature rise under adiabatic conditions may be only 

15o

C or less for a complete discharge and certainly less with a cooling system even if it is only 

moderately effective. For HEV batteries, which have high power-to-energy ratios, the main 

effect of the heat capacity will be to smooth out temperature fluctuations. 

4.3 Active Cooling Systems 

There are several choices of coolant that have been considered for cooling battery packs 

including air from the cabin, which may be heated or cooled, water-ethylene glycol solutions and 

dielectric liquids such as transformer coolants. Air is the least expensive, but it is less effective 

than the liquids because of its poor conductivity, the need for large flow passages and high 

pumping power. Dielectric liquids are expensive, but have the advantage of being compatible 

35 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

with terminals and other parts at electrical potential. Water-50% glycol solution is inexpensive 

and has good conductivity; we have selected it as the coolant for this study. 

We selected a general cell and battery design that can be adapted to all of the electric-drive 

batteries from micro-HEVs packs to EV packs (section 2). This design incorporates a 

hermetically sealed module closure. Unfortunately, the enclosure does not have sufficient surface 

area to be cooled effectively by air. This design can be effectively cooled by liquids and requires 

that only the module terminals and connectors be protected from contact with a conducting 

coolant, thus accommodating water-glycol coolant. In contrast, cooling individual cells would 

require flow passages between the cells, which would add to the pack volume. That design 

feature would permit air cooling for microHEV and HEV-HP batteries. For larger batteries 

requiring liquid cooling, flow passages between the cells would probably require the use of a 

dielectric coolant because of the difficulty of protecting so many cell terminals from a 

conducting coolant. Alternatively, elaborate flow channels with engineered seals may be used to 

contain an aqueous based heat transfer fluid. 

4.3.1 Heat Transfer from Cell to Module Wall 

As described in section 2, the cells transfer heat to the cooled walls of a hermetically sealed 

module with the aid of an aluminum heat conduction channel. Some of the heat is transferred 

through the sides of the cell to the channel and from there to the module wall. The remainder is 

transferred directly through the seal edge of the cell to the conduction channel flange which is in 

contact with the module wall. Calculation of heat transfer in this two-dimensional array through 

several materials is complex requiring a numerical model. The spreadsheet iterates several 

hundred times in reaching a solution, each resulting in a slightly different cell design. Thus, it 

would be impractical to imbed a numerical model directly, which may increase the total 

calculation time to many minutes. Instead, a software program based on the finite element 

method, FlexPDE 6.15 by PDE Solutions Inc., was employed to calculate heat transfer rates for 

70 cell configurations. The resulting simulations were empirically correlated so that simple 

equations occupying a few cells in the spreadsheet could rapidly calculate the heat transfer rate 

with only a small error. 

An important requirement for calculating heat transfer rates within the cell is to estimate the 

composite conductivities of the cell layers both parallel to the layers and across the layers. The 

resulting conductivities vary considerably with the relative thicknesses of the layers as shown in 

Table 4.1, for which the results are consistent with the literature.39-43 These values for 

conductivities and a range of cell dimensional parameters (Table 4.2) were employed in selected 

arrangements for calculating heat transfer rates with the FlexPDE model for 70 representative 

cells that covered a broader range of variables than is needed for practical cells. For each of these 

cells, the FlexPDE model calculated the temperature difference between the cell center and the 

module housing per unit of heat generation, ΔT/q (o

C/W), and the fraction of the total heat that 

was transferred through the edge of the cell, qe/q. The balance was transferred through the side of 

the cell to the aluminum conductor, qs. The division of the heat transfer into two routes is 

represented by the equation: 

q/ΔT = qe/ΔT + qs/ΔT (4.2) 

36 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Estimated values for qe/ΔT and qs/ΔT were determined by empirical correlation of the results 

obtained for the calculation of the 70 cells by the FlexPDE model with the result shown in Fig. 

4.1. Empirical values of these estimated values resulted in the equations: 

0.58 -0.19 1.2 -0.75 

qe/ΔT = 3.917ky kx Lcell W (4.3) 

0.55 0.58 -0.21 -0.7 0.72 

qS/ΔT = 1628ky kx Lcell W LAl (4.4) 

Table 4.1 Sample calculations of composite thermal conductivities of cell structures across layer 

and parallel to layers 

Cell 1 Cell 2 Cell 3 Cell 4 

Layer Thicknesses, microns 

Positive foil 20 20 20 20 

Negative foil 12 12 12 12 

Positive coating 30 75 150 220 

Negative coating 40 100 200 300 

Separator 20 20 20 20 

Total bicell structure 212 422 772 1112 

Thermal Conductivities, W/cm-K 

Aluminum 2.0 0. 2.0 0. 2.0 0. 2.0 

Copper 3.8 3.8 3.8 3.8 

Positive coating 0.013 0.13 0.13 0.13 

Negative coating 0.013 0.13 0.13 0.13 

Separator 0.0020 0.0020 0.0020 0.0020 

Across layers, kx 0.00689 0.00689 0.01045 0.0.01112 

Parallel to layers, ky 0.4127 0.4127 0.1228 0.0892 

Table 4.2 Range of parameter values for calculating heat transfer rates in FlexPDE model
 

Parameter Levels Evaluated 

1 2 3 4 

Conductivities, W/cm-K 

Across layers, kx (a) 

Parallel to layers, ky 

Cell edge, ke 

0.00689 

0.4127 

0.10 

0.00689 

0.4127 

0.01045 

0.1228 

0.0.01112 

0.0892 

Cell Dimensions, cm 

Cell thickness, Lcell 

Cell width, W 

Cell edge thickness, Le 

Aluminum conductor thickness, LAl 

(b) 

0.6 

8 

0.1 

0.03 

1.0 

12 

0.06 

1.4 

18 

0.10 

(a)The kx and ky values are calculated as in Table 4.1 and were, thus, paired together in the Flex 

PDE model calculations. 

(b)

The total conductor thickness consists of the conductor thickness itself plus twice the thickness 

of the aluminum layer within the pouch material. 

37 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 4.1 Plot comparing the estimated resistance to heat transfer from the cell center to the 

cooled surface of the module to that calculated by the FlexPDE model. 

The average error in the estimated ΔT/q compared to the values calculated by the FlexPDE 

model for the 70 cases studied was 6.0% and the maximum error was 13.0%. This accuracy was 

deemed to be satisfactory in that for all practical battery designs, the error will be only a fraction 

of a degree Celsius. 

4.3.2 Heat Transfer from Module Wall to Flowing Coolant 

Heat may be transferred to and from the modules by flowing fluid directly across the module 

casing. For ease of communication, the focus of this discussion will be on cooling of the module 

rather than heating for cold-climate operation. In theory, both liquid and air may be used as the 

heat transfer fluid. However, the stacked cell design we have selected has minimal exposed area 

relative to the overall volume of the cells. Our calculations have shown that liquid cooling is the 

only feasible option for this particular module design. The superior heat transfer of liquids 

(density and heat capacity) allows for implementation of this compact design without exposure 

of the individual cells to the heat transfer fluid. A design of this kind should result in a lower cost 

and higher energy density battery than a different design that cools individual cells. 

38 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The model directly calculates the temperature drop between the module wall and the heat 

transfer fluid for a set pressure drop, fluid (coolant) temperature rise, and fluid physical 

properties. A 50/50 ethylene glycol, deionized water (EG/H2O) mixture was selected based on 

the low cost and contemporary use in coolant systems. The default pressure drop was taken to be 

10 millibar, but may be changed by the user if desired. The gap in which fluid flows is sized to 

maintain the target pressure drop without going below a minimum gap height of 3 mm. A 

coolant temperature rise of 1 °C was selected to establish a mass flow rate, but also may be 

changed by the user. 

Calculation of the heat transfer coefficient allowed for determination of the temperature 

difference between the module and average coolant temperature. A schematic of the flow 

passageway and change in temperature profile with distance is shown below in Figure 4.2. The 

outer wall of the flow passage is assumed to be perfectly insulated. The inner wall (module 

casing) is assumed to have a constant heat flux perpendicular to the wall. Laminar flow was 

assumed to simplify the calculation of the velocity profile (parabolic). 

Figure 4.2 Heat transfer from the module wall to the laminar flow heat transfer fluid. The 

temperature profile of the fluid is shown at different lengths down the path. 

Frequent use of dimensionless numbers was necessary to adequately correlate the numerical 

results into a generally useable form. We define the Reynolds, Prandlt, Graetzl, and Nusselt 

numbers here for completeness.44 The Reynolds number, Re, is the ratio of inertial to viscous 

forces. The Reynolds numbers were always less than 1000 confirming laminar flow. The Prandlt 

number, Pr, is the ratio of the momentum diffusivity to thermal diffusivity. The Prandlt number 

for the EG/H2O mixture is approximately 38. The Graetz number, Gz, is directly proportional to 

the product of the Reynolds and the Prandlt numbers. Moreover, the Gz value is inversely 

proportional to the distance down the fluid flow path, l, resulting in higher values near the start 

of the flow path. Finally, the Nusselt number, Nu, is the ratio of the convective to conductive 

heat transfer. Here uave is the average fluid velocity, dH is the hydraulic radius (twice the flow 

gap), and μ is the viscosity. The heat capacity, cp, thermal conductivity, k, and heat transfer 

coefficient, h, are the critical heat transfer values. The mass flow rate, G, and the width of the 

channel, W, are the remaining parameters. 

ρu d ave H Re = (4.5) 

μ

c μ Pr = p (4.6) k 

39 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Gc d d Gz = 2 p H = 2 H Re Pr (4.7) kWl l 

hdH Nu = (4.8) k 

Coupled momentum and heat transfer has been solved previously by determining a number of 

the eigenvalues for a series solution of a vast number of various geometrical configurations 

flow.45,46 related to pipe, duct, and parallel plate We have chosen to reach the solution 

numerically and then fit a correlation between the Graetz number and the mean Nusselt number. 

The empirical form provided by Nickolay and Martin provides an accurate means of correlating 

the results over many orders of magnitude.47 The correlation, shown in Equation 4.9, relates the 

Graetz number and the limiting solution, Nu∞ = 5.385, to the mean Nusselt number. Then the 

mean heat transfer coefficient may then be directly calculated from Nu. Here n and C1 are fitting 

parameters. 

n n 1/3 Nu = [(Nu ) + (C Gz ) ]

1 

n (4.9) ∞ 1 

The numerical model was solved with the finite element method using FlexPDE software. We 

note that the bulk or “cup mixing” fluid temperature in Equation 4.10, the average temperature of 

the fluid normalized by the fluid velocity profile, was necessary to reach the proper values. 

Tavg = 1 ∫ T ( y)u( y)∂y (4.10) 2u avg 

The following important assumptions were used to reach a solution. 

1. Flow of incompressible heat transfer fluid is laminar 

2. Thermal diffusion is allowed up and down stream of the heat transfer (for convergence) 

3. Boundary conditions: dT/dy = 0 at insulation; q = constant at module casing 

4. Negligible radiative energy transfer 

5. Steady state conditions reached 

Figure 4.3 displays the temperature profile between the module casing and the insulated wall for 

various distances along the flow channel. The average temperature of the fluid has risen 1 °C at 

the end of the flow path even though the maximum and minimum temperature is separated by 

nearly 5 °C. The simulated change in average temperature down the length of the flow channel 

allows the calculation of the average heat transfer coefficient and thus Nusselt number. The 

correlation, Eq 4.9, determined from various simulations conditions is shown in Figure 4.4. An 

excellent fit is obtained allowing for implementation of the correlation into the design and cost 

model. This correlation now enables efficient and accurate calculations of the heat transfer 

coefficient to be made in the spreadsheet informing the user of the effectiveness of the thermal 

management in the design. 

40 
 

 

 

 

 

 

 

 

24.5 

25.0 

25.5 

26.0 

26.5 

27.0 

27.5 

28.0 

28.5 

29.0 

29.5 

-1 -0.5 0 0.5 1 

Dimensionless distance from centerline 

Fluid temperature, C 

0.00 

0.02 

0.24 

0.46 

0.68 

0.90 

Dimensionless distance 

down fluid path 

Figure 4.3 Temperature profile in the heat transfer fluid for various fractions of the 

dimensionless path length. 

100 

Mean Nusselt number, Num 

10 

1 

Calculations 

Correlation 

Nu∞ = 5.385 

n = 3.592 

C1 = 2.255 

0.1 1.0 10.0 100.0 1000.0 

Graetz number, Gz 

Figure 4.4 Correlation of model simulation results relating the Graetz number and mean Nusselt 

number for laminar flow between an insulated surface and the module casing. 

41 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

In general, the heat transfer from the module is improved by increasing the contact area and 

increasing the fluid flow rate. The contact area may be increased by using cells with a higher 

aspect ratio. This also results in a smaller temperature gradient within the cell as discussed 

previously in section 4.3.1. Increasing the fluid flow rate is accomplished by using a lower 

temperature rise and/or a larger target pressure drop. The gap height may prevent a change in a 

single parameter from having a significant affect on the temperature drop. Physical limitations of 

implementing a cooling system should be considered when moving to higher flow rates and 

pressure drops. The user should note that raising both of these parameters will increase the cost 

of the battery design in ways that the model does not consider (e.g. more expensive pump, 

increasing structural integrity, etc). 

For high speed driving or very aggressive driving cycles, the temperature difference between the 

surface of the cooled module surface and the bulk of the coolant may become fairly large 

(>10o

C). This coupled with the temperature rise within the cells could result in too high cell 

centerline temperatures. This result can be avoided by controlling the inlet coolant temperature 

as a variable that is adjusted in a classic cascade automatic control system to control the module 

wall temperature at the desired value. Thus, the temperature rise at the center of the cells will be 

essentially held to that resulting from conduction within the cell and will not be greatly 

influenced by the temperature rise in the coolant. 

4.4 Cooling and Heating Required to Maintain Pack Temperature 

When parked in the sun for several hours, the internal vehicle temperature and, thus, that of the 

battery may become so hot that the life of the battery is reduced. To avoid this, the vehicle air 

conditioning system may be actuated intermittently to cool the battery. By allowing the 

temperature of the battery to fluctuate by several degrees, it is only necessary to actuate the 

cooling system about once per hour for a few minutes. For a set of target temperatures with a 

difference of 25o

C and with the default insulation thickness (10 mm) and default thermal 

conductivity (0.00027 W/cm-K), BatPaC calculates the average cooling requirement to be about 

60 W for PHEV-40 batteries. The performance coefficient of the vehicle air-conditioning system 

might reduce the actual energy draw to less than half that, but heating of the system outside of 

the battery during the hour-long downtime periods would be a counter-acting factor. The BatPaC 

model calculates the energy required for cooling of all types of electric-drive vehicle batteries. 

However, most HEVs may not have electrically driven air-conditioning units and some other 

method might be needed to avoid very high battery temperatures during parking such as thicker 

insulation and fan cooling. 

If the battery is to deliver full power at startup, it must be at a temperature of at least 5o

C. This 

minimum temperature can be maintained by heaters and circulation of the glycol solution. 

BatPaC calculates the amount of power required to maintain the battery temperature for any set 

of battery and ambient temperatures. PHEV-40 batteries would require about 50 W of heat to 

maintain the battery temperature at 20o

C above that of the ambient under steady-state conditions. 

During recharging this should be easily done for 20 hours at a cost of $0.10 for an energy cost of 

$0.10 per kWh. If the vehicle is not at a source of power for recharging, limited energy (say 1-2 

kWh) can be drawn from the battery (if not blocked by a switch actuated by the driver) and then 

42 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

automatically shut off after maintaining the battery temperature for one to three days, depending 

on the ambient temperature. 

4.5 Heat-up from Cold Ambient Conditions 

All of the batteries for the various types of electric-drive vehicles will occasionally be exposed to 

very cold temperatures, which will require special heat-up procedures. All but the EV batteries 

can be heated with the aid of the engine. This can be done with electric heaters operated from 

power taken from the generator or from glycol solution from the engine cooling system. If the 

latter, it might be prudent to isolate the engine coolant from the battery coolant by means of a 

plastic heat exchanger. 

Another method of heating the battery is by means of the electric heaters that should be available 

for maintaining the battery temperature (section 4.4). BatPaC calculates the amount of heat 

needed and the time required with suitable heater power. For PHEV-40 batteries, about 15 

minutes is required with 2-kW heaters. This method of heating will be slower than with the 

engine coolant and even the latter would result in some delay before the battery is capable of full 

power. 

To avoid delay in starting vehicles from a cold startup, the driver could initiate heating by means 

of a remote device, which in the future may be a telephone. By this means, heating could be 

initiated either from heat drawn from the engine or electric heaters. Remote initiation of heat-up 

would be especially important for an EV away from a charging station in that no engine is 

available to assist heating and the large size of the battery would result in a long heating period 

with electric heaters. The BatPaC model estimates the time under these conditions. 

43 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5. Modeling of Battery Pack Manufacturing Cost
 

5.1 Approach 

The manufactured cost of a battery pack is calculated with input from the design information 

generated in modeling the cell and battery pack performance. The design modeling determines 

the annual materials and purchased items requirements. 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 are scaled from a baseline plant. The baseline 

plant was designed for a battery of intermediate size 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 producing the battery under study. The process 

expenses are summed with the additional costs of operating the manufacturing facility. These 

costs include launch costs, working capital, variable overhead, general, sales, administration 

(GSA), research and development, depreciation, and profit. Additionally, the costs for the 

thermal management, battery management system, and disconnects have been estimated to 

provide the total cost to the OEM for the integrated battery pack. 

In this analysis, all costs are evaluated for 2020 when large battery manufacturing plants are 

built. All dollar values are brought back to 2010 with allowance for inflation. In other words, all 

costs and prices are in 2010 dollars. Some materials and battery manufacturing costs are lower 

than recent values, where we judged that processing improvements for high volume production 

of materials would reduce costs. 

The baseline manufacturing plant was calculated for an annual production rate of 100,000 

batteries. The cost model accounts for different scales of manufacture by recalculating the costs 

of each individual step in the manufacturing process. The changes in capital and operating costs 

will change the calculated unit cost of the battery pack. The parameters were determined to 

provide reasonable estimates for manufacturing rates of 20-500 % of the baseline rate. Thus, for 

a plant that is far different in size from the baseline plant, for instance a pilot plant having an 

annual production of only 5,000 battery packs per year, the estimate from this study would be 

expected to be less accurate than if determined in a study dedicated to that purpose. 

To simplify the cost calculations, it was assumed that all hardware items for the cells, modules 

and battery will be purchased from a vendor specializing in similar products. The costs for these 

items were estimated to be a fixed value plus an additional value proportional to the weight of 

the item, which is calculated during the battery design. In mature manufacturing plants in 2020, 

toward which this study is directed, some items which 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 simulation and thus complicate the cost 

calculations. Assuming that some parts would be purchased if they would actually be produced 

from raw materials would tend to underestimate capital and labor costs and overestimate 

purchased items expenses. However, the net effect would be a very small change to the overall 

unit cost of the battery pack. 

44 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5.2 Materials Costs, Purchased Items, and Pack Integration 

The end battery pack cost depends significantly on the cost of both the active and inactive 

materials that compose the design. In this subsection, the assumed material costs and the 

rationale behind them are presented. We provide for means to scale the materials cost with 

production volume using the same method used for processing rates as discussed in section 5.4. 

In general, the materials costs will be largely insensitive to production volume since we have 

assumed a high volume market already exists. Only the negative and positive electrode active 

materials are assumed to have a minor benefit for larger scales of production. While we state 

suggested materials costs and sensitivity to production scale, the users of the cost model may 

enter any value that he desires. 

5.2.1 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, separator, 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 possible in the Li-ion family of chemistries. 

However, we have chosen to focus on the different available positive electrode materials with 

less attention on the negative electrode. This reflects the current research and manufacturing 

activities. The separator and the electrolyte are also 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 enhanced separators is beyond the scope of this 

work. The user is always able to modify the dimensions, 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 5.1 

compare our suggested costs to those reported recently in the open literature. Our values, as well 

as the others in the table, are derived from conversations with material, cell, and original 

equipment manufacturers. The sources are commonly anonymous 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 for commonly used materials. 

5.2.1.2 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 positive 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 considered a viable choice for use in Li-ion 

batteries for automotive applications. One of the largest drawbacks of LCO, other than safety 

concerns, is the high and volatile cost of the cobalt. While tolerable in the consumer electronics 

market, the cost is too high for use in an automobile battery. Many other materials are in a 

commercially viable state of development and are currently utilized in Li-ion batteries produced 

today (Table 5.1) such as lithium manganese spinel oxide (LMO) and lithium nickel manganese 

cobalt oxide (NMC).3,6 The relative advantages and disadvantages of each material will not be 

discussed here. 

45 
 

 

2007 

Table 5.1 Details of stated costs for cathodes, anodes, electrolyte, and separator.3,6 

ANL TIAX** CARB 

Material Chemistry Abbreviation unit 2010 2010 

Manganese spinel cathode O4 LMO $/kg 10 12 - 16 - 20 8 - 10 Li 1.06Mn1.94-xM'x 

5V spinel cathode* LiNi0.5 Mn1.5 O4 LNMO $/kg 21 - -

Phospholivine cathode LiFePO4 LFP $/kg 20 15 - 20 -25 16 - 20 

Layered oxide cathode* LiNi0.80Co0.15Al0.05O2 NCA $/kg 37 // 33 34 - 40 - 54 28 - 30 Layered oxide cathode* Li 1.05(Ni1/3 Mn1/3 Co1/3 )0.95O2 NMC-333 $/kg 39 // 30 40 - 45 -53 22 - 25 

Layered oxide cathode* Li 1.05(Ni4/9 Mn4/9 Co1/9 )0.95O2 NMC-441 $/kg 29 // 26 - -

Li & Mn rich layered cathode* xLi MnO 2 3 ·(1-x)LiNi Mn y Co z 1-y-zO2 LMR-NMC $/kg 22-29 // 22-25 24 - 31 - 39 ­

Layered oxide cathode LiCoO2 LCO $/kg 60 // 35 - 30 - 40 

Graphite anode C6 Gr $/kg 19 17 - 20 - 23 -

Titanate spinel anode Li 4Ti O5 12 LTO $/kg 12 9 - 10 - 12 ­Electrolyte 1.2 M LiPF6 in EC:EMC $/kg 18 18.5 - 21.5 -24.5 ­

2 Separator PP/PE/PP $/m 2 1 - 2.5 -2.9 ­2 Current collector foil Copper $/m 1.80 - ­2 Current collector foil Aluminum $/m 0.80 - ­

The cost of cathode materials using co-precipitation of Ni, Mn, and/or Co is based off of a correlation. Cobalt $5/mol vs. $2.5/mol separated by "//" *

** Cost represent range of values possible 

46
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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-441 is less expensive than the NMC-333 as 

the cobalt quantity is significantly reduced. The market price for cobalt and nickel metal varies 

dramatically from year to year. Reducing the quantities of these materials in the positive 

electrode will reduce the total price and price volatility. Researchers at TIAX LLC have treated 

this variation and shown the significant effect on end battery cost.10 The average traded 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).48 The metal prices are indicators for how the intercalation material cost will 

relate when compared to one another. The fact these materials are not earth abundant means they 

will not benefit as much as other materials from increased scales of production. 

We employ the relationship in Equation 5.1 to systematically calculate the cost of the transition 

metal based spinel and layered compounds. The final cost, C, of the lithiated oxide depends on 

the baseline cost, C0, and the contributions of the lithium and transition metal raw materials, Ci. 

The molar stoichiometry, xi, is transformed to a mass basis with the molecular weight of the raw 

material, MWi, and the final product, MW. The baseline cost is the sum of the cost for processing, 

additional raw materials, and profit margin associated with the manufacture of the materials. We 

assume a baseline cost of $7/kg for single metal containing oxides (LMO and LCO) and $16/kg 

for the co-precipitated metal oxides such as NMC-333 and NMC-441. NCA is known to have a 

slightly lower yield and requires additional raw materials resulting in an assumed C0 = $20/kg. 

The costs for Li, Ni, Mn, and Co are taken to be 0.22, 0.85, 0.15, and 5.00 $/mol respectively. 

Aluminum is assumed to be similar in cost to manganese for these calculations. One may directly 

translate these numbers to raw materials costs resulting in $6/kg for Li2CO3, $5.5/kg for NiSO4, 

$32/kg for CoSO4, and $1/kg for MnSO4. Calculations are also shown in Table 5.1 using 

$2.5/mol for cobalt as a simple demonstration of the effect of cobalt on the end material cost. 

⎛ $ ⎞ 1 C⎜ ⎟ C + ∑x Ci

MWi (5.1) ⎜ ⎟ = 0 i

⎝ ⎠ kg MW i 

In general, earth abundant elements should be the dominate transition metals used if a low 

positive electrode cost is desired. Both iron and manganese are abundant and inexpensive 

transition metals for intercalation materials. Comparison 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 increased complexity in the manufacturing 

process is realized in the price. However, one could argue that the manufacturing cost will 

decrease with increased knowledge from larger scales of production. 

5.2.1.2 Negative Electrode Active Materials 

While several negative electrode materials exist for 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 hard 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 generic carbon electrode in our model. The price of graphite is 

47 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

much better understood than that of most of the positive electrode materials. However, 

significant differences in cost and performance will exist between synthetic, natural, and coatednatural graphite. The method of production and necessary heat-treatment will control the end 

cost. Graphite, although in different purity grades or microstructure forms, is used in many 

industries. This is in stark contrast to the positive electrode materials. 

The lithium titanate electrode, LTO, offers an interesting option compared to graphite. Unlike 

graphite, LTO operates within the stability window of the electrolyte. The higher electrode 

potential, 1.5 V vs Li, dramatically reduces or eliminates the formation of the solid electrolyte 

interphase (SEI). As a result, nanoparticle-based LTO may be implemented without concerns of 

increased side reactions with the electrolyte. The reduced dimensions increase the available 

surface area for reaction while simultaneously shortening the diffusion length. Both of these 

factors combined with the lack of SEI dramatically reduce the impedance of the electrode. 

5.2.1.3 Electrolyte and Separator 

The electrolyte used in this model is based on a lithium hexafluorophosphate salt, LiPF6, 

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 used to lower the capacity and power fade of 

the battery over time. Polymers may be added to the electrolyte as either a minor or major 

component. This is not discussed in any further detail in this work. The price of 18 $/kg, about 

22 $/L, is only for the base electrolyte (i.e. no additional additives). 

The separator is typically a porous membrane based on polypropylene (PP) and sometimes 

includes a polyethylene (PE) middle layer. PP and PE are very inexpensive raw materials and 

thus the suggested cost of $2/m2 is in large part due to the manufacturing process required to 

form the porous network in the membrane. As competition and scale of manufacture increase, 

the prices of the separator may fall closer to $1/m2

. However, the cost of improved technology 

may offset some of this cost reduction, so we have retained our cost estimate of $2/m2

. 

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 electrodes 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 of the cost model should account for the 

increased technology in the price and dimensions of the separator as needed. 

5.2.1.3 Current Collector Foils 

The current collector foils are based on copper metal for the negative electrode and aluminum for 

the positive electrode. However, the LTO anode material, because of its high voltage relative to 

lithium, enables the use of aluminum as the negative electrode current collector. The price of 

these foils is based on raw materials and manufacturing costs. The aluminum foil is produced by 

rolling of thicker stock foils into thinner and thinner sheets. On the other hand, copper foil is 

48 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

more likely to be produced through an electrodeposition process. The foils are 12 microns and 20 

microns thick for the copper and aluminum current collectors respectively. The foils used in 

batteries have additional requirements beyond the cheapest product available. Surface treatments 

are often necessary to promote adhesion of the electrode to the foil surface. In addition, alloying 

of the foil may be necessary to achieve the required material properties for long life. 

The raw material contributions to the foil price will vary with the volatility of the market price 

for the metals. Figure 5.1 displays the metal ingot price contribution on a $/m2 basis. These 

numbers are based on historical prices for the metals as collected by the USGS.48 

The values for both aluminum and copper tend to vary significantly over the time period 

examined. The price for copper is more volatile and always more expensive than aluminum. 

Analysis of Figure 5.1 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 1.80 and 0.80 $/m2 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 16 % of the aluminum foil 

price and 23 % of the copper foil price. Thus, a doubling of the ingot prices would only 

moderately increase the foil prices. 

1985 1990 1995 2000 2005 2010 

Year 

Figure 5.1 Metal ingot cost contribution to the current collector foils over a 20 year period. The 

average for that period is also shown. All costs are in 2010 US$. 

0.00 

0.10 

0.20 

0.30 

0.40 

0.50 

0.60 

0.70 

0.80 

0.90 

Metal Ingot Cost in 2010 $/m2 

Copper 

Copper 20 yr avg 

Aluminum 

Aluminum 20 yr avg 

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5.2.1.4 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 5.3.3. Only the small amount lost in processing 

need be replaced. No cost is assumed for water used to in the electrode slurry processing. 

5.2.2 Purchased Items Cost 

Table 5.2 lists the purchased items for the cell module and battery jacket. The cost of a SOC 

controller for each cell, or group of parallel cells, is $2.50 plus a small factor for the cell capacity 

(Ah), which allows for higher cell balancing currents for larger cells. The other components cost 

a fixed amount plus an additional factor, which is proportional to their mass, mi. The cell 

negative terminal and parallel cell group connection are both made from nickel plated copper 

sheet and thus have the same cost equation. The costs shown for the terminals include an 

allotment for isolation tape that is necessary to protect the electrical connection. The bus bar is a 

fixed cost and is only charged if a single row of modules is used. A single row of modules 

requires a bus bar in order to locate the positive and negative terminals at the same end of the 

battery. 

Table 5.2 Cost equations for purchased items 

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

SOC controller 2.50 + 0.01C cell or parallel cell group 

Cell positive terminal 0.25 + 4mi cell 

Cell negative terminal 0.25 + 6mi cell 

Cell container 0.20 + 3mi cell 

Aluminum heat conductor 0.10 + 4mi cell 

Parallel cell group connection 0.25 + 6mi parallel cell group 

Module terminals 0.75 + 5mi module 

Balance of module (casing) 1.00 + 3mi module 

Module interconnect 1.00 + 5mi module 

Battery terminals 15.00 + 0.02Itotal battery pack 

Bus bar for one module row 20.00 battery pack 

Battery jacket 30.00 + 7mi battery pack 

5.2.3 Pack Integration Cost 

Various additional components and thus cost are necessary to integrate the battery into the 

electric drive system, which adds cost. While it is not clear what should and should not constitute 

the cost of the “battery pack,” we present these additional items in Table 5.3 in an attempt to be 

complete. The model treats these values as a cost to the OEM for integrating the battery into the 

vehicle. After all, the price of the entire system is of interest to the final consumer of the product. 

50 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The general conclusion is that the pack integration costs have the largest consequence for the 

smallest batteries. The worst case is perhaps that of a small PHEV10 battery. The integration 

costs of a PHEV10 battery carry the burden of charging from the grid, but provide only a modest 

electric drive benefit. The fixed cost of pack integration may amount to 25 % of the battery pack 

total even without considering the costs of additional powertrain components. Clearly, 

understanding the entire cost of the electric drive system is of importance to evaluating the true 

value of the electrified vehicle to a consumer. 

Table 5.3 Costs to integrate battery pack into vehicle drivetrain. $/kW numbers reflect maximum 

kW of cooling or heating required. 

Battery Management System MicroHEV HEV-HP PHEV & EV 

Current and voltage sensing, $ 40 70 100
 

Module controls, $/module 10 10 20
 

Disconnect Units 

Auto. disconnect, $ 50 70 200
 

Manual disconnect, $ 15 15 15
 

Thermal Management System 

Baseline thermal system, $ 30 80 120
 

Additions to AC system, $/kW 40 40 40
 

Heating system, $/kW 20 20 20
 

5.2.3.1 Battery Management System 

The battery management system (BMS), in our assumed battery design, integrates the modules 

and battery into the overall electric drive system. The BMS includes measurement and control 

features such as the following: 

• Measurement of battery pack current and voltage 

• Balancing of the module voltages (cell balancing done within module) 

• Estimation of battery pack state-of-charge (SOC) and state-of-health (SOH) 

• Estimation of module SOC and SOH 

• Monitoring and signaling of battery thermal management 

The cost of the BMS will scale with magnitude of battery current and with the need to charge 

from the electrical grid. Therefore the PHEV and EV batteries will have a higher burden from 

the BMS. The micro-HEV is assumed to have less complicated management and thus less cost 

than the HEV-HP. 

5.2.3.2 Manual and Automatic Disconnects 

The manual and automatic disconnects integrate a high-level of safety and electrical management 

into the electric drive system. The manual disconnect breaks the current flow pathway from the 

high-voltage terminals to the outer system allowing for the safe service of the vehicle and battery 

pack. This disconnect is designed to be operated when the electrical system is de-energized. The 

automatic disconnect is much more complex. This unit contains the connections for the highvoltage system to the rest of the vehicle’s electrical system: drivetrain, grid charging (if 

applicable) and accessories (high and low voltage). Fuses are present as a hard-wired safety 

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device to prevent unusually large current spikes from damaging the battery or drivetrain. 

Multiple contactors are used to appropriately channel electrical current depending upon normal 

operation or grid-charging. Engaging the contactors requires that multiple safety interlocks are 

established including isolation of the high voltage bus from the vehicle chassis and an inertia 

based sensor (crash protection). Finally, a small circuit is provided to prevent arcing of the 

current across the high-voltage contactor when the high-voltage circuit is closed. 

The relative cost of the automatic disconnect amongst the various battery designs is driven by the 

pack voltage, maximum battery current, and the need for charging from the grid. The voltage of 

the pack has a significant effect if a 42 V micro-HEV pack is considered. For this system, 

electrical safety regulations allow a less complicated system to be used. Requiring higher battery 

currents generally increases the cost of electronics and conductors. The additional complications 

arising from grid-charging adds a significant additional cost to the PHEV and EV systems. It is 

unclear to the authors at this time what other factors may enable a lower burden of external 

safety controls. These additional costs in the automatic disconnect unit have the most 

pronounced effect on the cost of smaller batteries, as the burden amounts to a significant fraction 

of the total cost. 

5.2.3.3 Balance of Thermal Management System 

The thermal management of the battery is crucial to meeting the life and safety requirements of 

transportation applications. The complexity of this system must be minimized to reduce the cost 

and size burden on the vehicle. Our assumed design format uses liquid thermal management for 

all vehicle battery types. In practice, current microHEVs and HEV-HPs are more likely to be 

cooled by blowing air. Air-cooling is generally less expensive than liquid cooling, but is less 

effective, requires larger system volume, and may result in substantial background noise. 

Furthermore, directly cooling the pouch cells with air increases the magnitude of oxygen and 

water permeation through the seals resulting in deleterious effects to the fifteen year life of the 

battery. Air cooling is not feasible with our current assumed battery format (stacked cells sealed 

within module). The cells would need to be separated to allow air to flow past at least one side to 

achieve sufficient heat transfer as earlier versions of this model had used.16 Future versions of the 

model may include an option to select either air or liquid cooled. However, the main goal of this 

model is to explore the effect of battery performance and materials chemistry on the price of the 

battery to the OEM. 

A single refrigerant compressor is used for both the cabin air and the battery cooling 

applications. Likewise, the same radiator and fan as the cabin cooling will also be used for the 

battery cooling refrigerant. Most OEMs appear to use an electric compressor for all full-HEVs 

(HEV-HP) and PHEVs/EVs that are liquid cooled. The incremental cost for an electric 

compressor at high volume in year 2020 will likely be $200-300 more than the commonly used 

$100 belt driven compressor. We do not include this incremental cost in our thermal 

management system cost; however, we state it here for completeness. The additional cost to the 

compressor for the battery cooling capacity is insignificant compared to burden of transitioning 

to the electric compressor. Experts in the field have informed us that the electric motor and highvoltage invertor are the largest contribution to the incremental cost of the electric compressor. 

52 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

An expansion valve on the refrigerant line and a heat exchanger (chiller) transfers the thermal 

energy from the heat transfer fluid to the refrigerant loop. A 50/50 DI-water/ethylene-glycol 

solution is selected as the heat transfer fluid. The assumed battery design has the heat transfer 

fluid pumped over the module casing to transfer heat from and to the cells. The battery may be 

heated by either a positive thermal coefficient (PTC) or flexible mat heater. The PTC heater 

would directly raise the temperature of the heat transfer fluid in a reservoir while the matt heater 

would be placed under the battery jacket insulation. 

The PHEV and EV batteries will likely have both active and passive thermal management modes 

requiring some additional monitoring and an electrically actuated valve. We have assumed 

decreasing cooling costs for the HEV-HP and microHEV systems without explicitly dictating 

where the savings originate. In general, one would expect smaller batteries to have a less 

complicated control system, lower flow rates and possibly even direct cooling of the cells with 

the evaporator. 

5.3 Baseline Manufacturing Plant 

The baseline plant is designed to produce 100,000 NCA-Gr baseline battery packs per year. The 

baseline battery pack produced by the plant has sixty, 40-Ah capacity cells, providing a total 

pack power of 50 kW and total energy of 8.7 kWh. The battery will power 20 miles of vehicle 

travel at 70% of the pack energy and 300 Wh/mile. The schematic diagram of the plant (Fig. 5.2) 

is designed to illustrate the flow of materials through the plant and the relative floor areas for the 

processing steps rather than representing a realistic plant layout. The overall manufacturing rate 

of 100,000 battery packs per year is achieved by operating for three shifts at the equivalent of 

300 days per year of fully effective production. There will be more than 300 days of operation, 

but some days will have less than 100% effectiveness. The exceptions to three-shift operation are 

the Receiving and Shipping sections, which are active for only two shifts per day. The cost 

factors for the individual manufacturing steps in the baseline plant are summarized in Table 5.4 

and discussed in detail in the sections that follow. Most of the operations are carried out with 

normal factory atmosphere, but the cell assembly process steps are completed in a dry room 

atmosphere. 

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Shipping 

Cell and 

Scrap 

Recycling 

Receiving 

Control 

Laboratory 

AssemblyRoute 

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 

DryRoom 

Materials 

Handling 

Outdoor dry-roomair 

processingequipment 

The areas in this diagramfor each processing step are approximatelyproportional to 

the estimated plant areas in the baseline plant. 

Figure 5.2 Baseline lithium-ion battery manufacturing plant schematic 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 shifts (two shifts for receiving and shipping) 

5.3.1 Receiving and Shipping 

These operations require the moving equipment and storage facilities common to any such 

factory facilities. The Receiving section handles slightly less than 6,000,000 kg of materials per 

year and also has facilities to handle and store some of the electrode materials in a dry 

atmosphere. The Shipping section is required to enclose the battery packs in crates, which 

requires some automated equipment and more labor than 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 estimated resources needed for the Receiving 

and Shipping sections are shown in the table below. 

Rate Factor Direct Labor Capital Equip.* Plant Area, m2 

Receiving 

Off-loading 

Moving 

Storage 

870,000 kWh/y 3 per shift 3.60 mil$ total 

0.60 

1.20 

1.80 

900 

Shipping 870,000 kWh/y 6 per shift 5.0 mil$ total 900 

*Total cost including installation 

54 
 

Table 5.4 Summary table of the baseline plant
 

100,000 Battery Packs per Year, 50-kW Battery Power, 40-Ah Capacity, 60 Cells per Battery

Operating year: 300 days with three 8-hour shifts (two shifts per day for receiving and shipping)

Direct Labor Cap. Equipment Plant Area 

55
 

Annual Baseline Rate (Ro) 

Receiving (two-shift operation) 869,416 kWh energy 

Materials preparation

Positive electrode 1,712,524 kg active material 

Negative electrode 1,060,374 kg active material 

Electrode coating 

Positive electrode 8,209,039 m2 cell area
 

Negative electrode
 8,209,039 m2 cell area 

Solvent recovery 2,309,021 kg NMP 

Calendering 

Positive electrode 8,209,039 m2 cell area
 Negative electrode
 8,209,039 m2 cell area 

Materials handling# 8,209,039 m2 cell area Electrode slitting 8,209,039 m2 cell area Vacuum drying 8,209,039 m2 cell area Control laboratory 869,416 kWh energy 

Cell Assembly in Dry Room 

Cell stacking 6,315,789 total cells
 

Current collector welding
 6,315,789 total cells
 

Enclosing cell in container
 6,315,789 total cells
 Electrolyte filling, and cell sealing
 6,315,789 total cells
 Dry room control and air locks
 2,000 m2 operating area# 

Formation cycling 6,315,789 total cells 

Final cell sealing 6,315,789 total cells 

Charge retention testing 6,315,789 total cells 

Module assembly 6,000,000 finished cells 

Battery pack assembly and testing 100,000 battery packs 

Rejected cell and scrap recycle 6,315,789 total cells Shipping (two-shift operation) 869,416 kWh energy 

Total 

Workers/
 

Shift
 

3

2

2

4422144245535

28236656

90 

Baseline
 

Hours/yr
 

14,400 

14,400 

14,400 

-

28,800 28,800 14,400 

-

14,400 

7,200 

28,800 28,800 14,400 28,800 

-

36,000 36,000 21,600 36,000 

14,400 57,600 14,400 21,600 43,200 43,200 36,000 28,800 

626,400 

Scale
 

Factor, p
 

0.4 0.5 0.5 

0.5 0.5 0.4 0.5 

0.5 

0.7 0.5 0.5 0.5 0.7 0.7 0.5 0.5 

0.4 0.7 0.5 0.4 0.5 0.5 0.7 0.5 

Baseline 

$millions 

3.60 2.00 2.00 

8.00 8.00 3.00 1.00 1.00 1.50 

2.00 1.60 1.50 4.00 4.00 3.00 5.00 

20.00 30.00 

2.00 4.75 6.00 6.00 2.50 5.00 

127.45 

Scale Baseline Scale 

Area, m2 Factor, p Factor, p 

0.6 900 0.5 0.7 600 0.6 0.7 600 0.6 

(0.2)* 0.8 750 0.8 (0.2)* 0.8 750 0.8 

0.6 225 0.6 0.7 225 0.6 0.7 225 0.6 0.7 900 0.6 0.7 300 0.6 0.7 300 0.6 0.7 300 0.6 

(0.3)** 0.8 600 0.8 

0.8 600 0.8 

0.7 600 0.6 0.7 900 0.6 

0.6 100 0.4 

(0.3)** 0.8 2,200 0.8 

0.7 450 0.6 0.7 900 0.6 0.7 600 0.6 (0.3)*** 0.7 900 0.6 0.7 600 0.6 0.7 900 0.6 

15,425 

#One-third of the space for materials handling is within the dry room.

*The baseline cost for capital equipment for electrode coating, Co, is based on the evaporation of the baseline annual solvent weight (Rso) of 2,309,000 kg for

the positive electrode and 1,527,000 kg for the negative electrode. For batteries requiring different solvent evaporation rates Rs, the cost is multiplied by(annual solvent rate (Rs)/baseline rate (Rso)) 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 cells of 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 to a battery with a different

number of modules (Mod), the cost is multiplied by the ratio of the number of modules, (Mod)/4 raised to the 0.3 power. Cost = Co*(R/Ro)^0.7*(Mod/4)^0.3. 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5.3.2 Electrode Materials Preparation and Delivery to Coating 

The electrode materials, which consist of active material, 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 tanks 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 exceeding 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 tanks 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 Equip.* Plant Area, m2 

Positive 

Materials 

Storage tanks 

Mixing tanks 

Moving equip. 

1,710,000 kg/y 

active material 

2 per shift 2.0 mil$ total 

1.00 mil$ 

0.50 

0.50 

600 

Negative 

Materials 

1,210,000 kg/y 

active material 

2 per shift 2.0 mil$ total 600 

*Total cost including installation 

5.3.3 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 foil, drives off the solvent in a heated oven, and 

turns the foil over while transferring it to a second set of stations. The second set of coating and 

drying stations applies and dries the remaining coating before the coated foil is wound into a 

large roll at the end of the line. An advanced alternative would be to run the foil directly into the 

calendering process. The negative and positive coating lines are very similar. However, some of 

the negative material is coated only on one side to provide the electrodes at the end of the cell 

stacks. For the baseline plant, a total of 8,170,000 m2

/y of coating (annual cell area) is required 

for the positive electrode (slightly more for the negative electrode), which allows for the 5% loss 

of cells expected to fail testing 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 coating capacity must be provided to allow for unscheduled 

downtime. Only one coating line is needed for each electrode type to meet these needs. If one 

coating line breaks down, the other coating 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 require longer ovens at additional capital cost 

which is provided in the adjustment of costs discussed in section 5.4. For the same annual area 

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throughput, a coating line that coats both sides with a 300-micron coating would cost $9,500,000 

rather than the $8,000,000 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 need not be recovered. The estimated resources 

to meet these needs are the following: 

Electrode Coating Rate Factor Direct Labor Capital Equip.* Plant Area, m2 

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 8.0 mil$ total 

18% 

1.5 m 

10 m/min 

One 

13,000,000 m2

/y 

30% 

750 

Negative Electrode 8,170,000 

m 

2

/y cell area 

4 per shift 8.0 mil$ total 750 

Solvent Recovery & 

Oxidation 

1,527,000 kg 

NMP/y 

2 per shift 3.0 mil$ total 225 

*Total cost including installation 

5.3.4 Calendering 

The materials leaving the coating lines may be stored on large rolls (see next section). However, 

typically the materials leaving the coaters would go 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 equipment must match the output of the coating 

equipment producing 8,170,000 m2

/y of cell area with a maximum rate of 13,000,000 m2 of foil 

per year to meet contingencies as in coating. We estimate three workers are necessary to 

collectively operate the two pieces of equipment. The estimated resources to meet these needs 

are the following: 

Calendering Rate Factor Direct Labor Capital Equip.* Plant Area, m2 

Positive Electrode 8,170,000 

m 

2

/y cell area 

2 per shift 1.0 mil$ total 225 

Negative Electrode 8,170,000 

m 

2

/y cell area 

1 per shift 1.0 mil$ total 225 

*Total cost including installation 

5.3.5 Inter-Process Materials Handling 

For all processes (Fig. 5.2), 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 also 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 the 

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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, m2 

8,170,000 

m 

2

/y cell area 

4 per shift 1.5 mil$ total 900 

*Total cost including installation 

5.3.6 Electrode Slitting 

The coated electrode foils are slit into strips between the coated sections and then into individual 

electrodes as shown in Fig. 2.3. The estimated scrap loss of foil for this process is about 8%. The 

estimated resources to meet these needs are the following: 

Electrode Slitting Rate Factor Direct Labor Capital Equip.* Plant Area, m2 

8,170,000 

m 

2

/y cell area 

4 per shift 2.0 mil$ total 300 

*Total cost including installation 

5.3.7 Final Electrode Drying 

In the absence of electrolyte, no harm is done by exposing the electrodes to normal factory air; 

however, the electrodes must be dried by heating under vacuum prior to cell assembly. 

Maintaining extremely low moisture conditions during 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 in the final product. The pertinent processing 

rate in determining the resources necessary for drying is the total amount of active materials 

processed per year (other electrode materials are approximately 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 stacks 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 Equip.* Plant Area, m2 

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 

300 

*Total cost including installation 

5.3.8 Control Laboratory 

The purpose of the control laboratory is to ensure that the raw materials and the electrodes being 

fabricated meet specifications. Laboratory personnel collect or supervise collection of samples 

and carry out analyses. The estimated resources to meet these needs are the following: 

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Rate Factor Direct Labor Capital Equip.* Plant Area, m2 

Control Lab 869,000 kWh/y 4 per shift 1.5 mil$ total 300 

*Total cost including installation 

5.3.9 Cell Stacking 

The cells are assembled in four steps, which are carried out in a dry room. The first of these steps 

is cell stacking. The primary rate factor that determines the cost for all steps in cell assembly is 

the number of cells assembled per year. For cell stacking an additional cost factor is the capacity 

of the cells; large cells usually require more electrodes of larger area and thus a more capable, 

faster cell stacking machine. The method used to determine the extra costs of stacking equipment 

is detailed in Table 5.4. 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 estimated resources to meet these needs for 

the baseline plant are the following: 

Cell Stacking Rate Factor Direct Labor Capital Equip.* Plant Area, m2 

Stacking rate 

Number of units 

Maximum rate 

6,320,000 cells/y 5 per shift 4.0 mil$ total 

5 cells/min 

4 

8,640,000 cells/y 

600 

*Total cost including installation 

5.3.10 Current Collector Welding 

The current collector tabs for the negative and positive electrodes are welded to their respective 

terminals by ultrasonic welding. This procedure achieves a connection of near-zero resistance 

and avoids overheating the electrodes during the welding process. The estimated resources to 

meet these needs are the following: 

Tab Welding Rate Factor Direct Labor Capital Equip.* Plant Area, m2 

Cell rate 

Number of units 

Maximum rate 

6,320,000 cells/y 5 per shift 4.0 mil$ total 

5 cells/min 

4 

8,640,000 cells/y 

600 

*Total cost including installation 

5.3.11 Enclosing Cell in Container 

The aluminum foil in the pouch container is sufficiently thick (100 microns default thickness) to 

permit the use of stiff, pre-shaped pouch halves. The pouches are assumed to be purchased as 

finished parts. Each cell is enclosed in these containers, which are then partially sealed prior to 

injecting electrolyte. The estimated resources to meet these needs are the following: 

59 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Enclosing cells Rate Factor Direct Labor Capital Equip.* Plant Area, m2 

Cell rate 

Number of units 

Maximum rate 

6,320,000 cells/y 3 per shift 3.0 mil$ total 

5 cells/min 

4 

8,640,000 cells/y 

600 

*Total cost including installation 

5.3.12 Electrolyte Filling and Cell Sealing 

At this station, the cells are evacuated, filled with electrolyte and temporarily sealed. The 

estimated resources to meet these needs are the following: 

Filling & 1st Seal Rate Factor Direct Labor Capital Equip.* Plant Area, m2 

Cell rate 

Number of units 

Maximum rate 

6,320,000 cells/y 5 per shift 5.0 mil$ total 

5 cells/min 

4 

8,640,000 cells/y 

900 

*Total cost including installation 

5.3.13 Dry Room Management 

Excellent dry-room atmosphere is required for lithium-ion cell assembly. A maximum dew point 

temperature of –40 °C is maintained in the room. The 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 admit some fresh air to limit the build up of 

contaminants such as electrolyte solvent vapor. These 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 performance. 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, m2 

Dry Room 3,000 m2 2 per shift 20.0 mil$ total 100 

*Total cost including installation 

5.3.14 Formation Cycling, Final Cell Sealing and Charge Retention Testing 

Formation cycling is expensive because it takes considerable 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 improve and thus save cost. We project that the 

entire formation cycling and testing can be done in two shifts. These operations consist of 

charging the cell, discharging to full depth to measure capacity and impedance, followed by fully 

recharging the cells. These tests will be carried out in large temperature controlled cycling units 

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that test 500 cells simultaneously, monitor each cell 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 the cells. 

The short-term testing described above does not detect cells that have self-discharge rates that 

are slightly above normal, which could lead to catastrophic failures later. To detect such defects, 

the cell charge is topped off and the cells are stored for two weeks and then checked for loss of 

charge. Most of the test period is spent in large racks in compact arrays, without electronic 

monitoring. Incidentally, the two-week long self-discharge 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 accumulate in the reservoir space that was created 

during the temporary sealing step. This gas is removed 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 

2200 

Final Cell Sealing 6,320,000 cells/y 2 per shift 2.0 mil$ total 450 

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 

900 

*Total cost including installation 

5.3.15 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 Scrap Recycle section. The accepted cells 

(6,000,000 finished cells per year) are assembled into modules by attaching the terminals 

through laser welding or mechanical joining with spring loaded devices. Electronic circuit packs 

are attached that occupy about the same volume as a cell. An aluminum heat conductor is placed 

around every cell. These operations are carried out at four automated stations each capable of 

handling about 280 cells per hour. For the module design being cost estimated in this model, the 

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module is enclosed 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 packs 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 testing 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 following: 

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 

600 

Battery Pack Assembly 

Modules/pack 

Number of stations 

Packs/h/station 

Capacity 

100,000 packs/y 3 per shift 3.0 mil$ total 

4 

3 

6 

130,000 packs 

450 

Battery Pack Testing 100,000 packs/y 3 per shift 3.0 mil$ total 450 

5.3.16 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 tests. This scrap is gathered and packaged for 

shipment for recycling of the materials having value. No credit is taken for the value of the scrap 

in this model except that the costs of gathering, sorting, 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 recover the scrap, a labor intensive process. The 

yields of materials in the various processing steps are shown in Table 5.5. 

Table 5.5 Materials yields during electrode and cell fabrication 

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 94.0 

The estimated resources needed for scrap recycle are the following: 

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Rate Factor Direct 

Labor 

Capital Equip.* Plant Area, m2 

Scrap Recycle 

Scrap rate 

6,320,000 cells/y 5 per shift 2.5 mil$ total 

441 kg/shift 

600 

5.3.17 Baseline Plant Summary 

The processing rates and the primary cost factors for the baseline plant are summarized in Table 

5.4. The main cost-determining rate of processing for each step is shown in the second column. 

The requirements for direct labor, capital equipment 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 90 

workers per shift, $127,450,000 worth of capital equipment, and 15,425 square meters of plant 

area to manufacture the baseline battery at a rate of 100,000 battery packs per year. 

5.4 Adjustment of Costs for Varying Production Volumes 

Production volume may affect the end price of the battery in two distinct ways. First, the user of 

the model may change the annual production volume and every processing step will be affected. 

Somewhat differently, as the performance requirement and thus design is changed, the 

production of individual steps will change in non-uniform ways. As noted in Table 5.4, there are 

many processing rates that must be considered in addition to the overall number of battery packs 

manufactured per year. Each of these rates affects the costs of one or more steps in the process 

and may have no effect upon the costs of other steps in the process. For instance, when the user 

of the model increases the power of the battery packs without increasing the number of cells or 

their capacity, the model increases the area of the cells and decreases the electrode coatings 

thicknesses. Such changes would result in an increase in the cost of the coating equipment, the 

floor area occupied by the equipment, and in the direct labor for that step in the process. It would 

have no effect on the cost of mixing the materials to be coated because the amounts of these 

materials per battery back are unchanged under the assumed conditions. 

The general approach to cost estimation of multiplying a known cost by the ratio of processing 

rates raised to a power has also been applied to the capital cost of individual items of 

equipment.49 

)

p C = Co(R/Ro (5.2) 

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

rate, Ro. The power factor, p, relates the capital investment cost and the processing rate for the 

manufacturing step. 

If the value of p were 1.0, it would imply that the cost of the equipment item, or the equipment 

items if there are several in parallel, would be directly 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 is larger for the higher processing rates and 

63 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

its cost is less than if it were directly proportional to the processing rate. For process steps 

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 installation, for which there is some savings 

even in installing multiple units of the same processing capacity. The relationship between cost 

and processing rate for two-fold and three-fold rate changes is illustrated in Table 5.6. 

Table 5.6 The effect of processing rate (R) on cost for various scale factors 

C/Co = (R/Ro)

p 

Cost Ratio, C/Co 

Scale Factor, p R/Ro = 2 R/Ro = 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 manufacturing 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 required 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 area were 

estimated for each of the processing steps (Table 5.4). The scale factors selected for the direct 

labor requirement are usually only 0.4 to 0.5, which indicates considerable unit cost reduction for 

increasing the plant throughput. 

For most processing steps, increasing the processing 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 rate would have the opposite effect. Some steps 

in the process such as cell stacking, welding of current collectors, and formation cycling do not 

appear to be easily automated beyond the level intended in the baseline plant and, thus require a 

higher value for the scale factor of 0.8. This higher scale factor results in achieving fewer 

reductions in the cost per battery pack with increasing production volume. Additionally, a higher 

64 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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

process. 

There are five steps for which the cost of the capital equipment is affected by other factors than 

the main processing rate for the process step. These are discussed in the footnotes at the bottom 

of Table 5.4. 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 amount 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 cycling equipment, for which the main cost factor 

in both cases is the number of cells to be fabricated annually, are also adjusted for the capacity of 

the cells; larger cells require more expensive equipment. The cost of the capital equipment for 

battery assembly is primarily a function of the number of cells in the battery, but it is also a 

function of the number of modules that must be interconnected. This dependence is accounted 

for in the model with an additional multiplying factor. 

A breakdown of the baseline plant capital equipment costs listed in Table 5.4 is illustrated in Fig. 

5.3. The largest costs for capital equipment are for formation cycling and testing, cell assembly 

in the dry room and electrode coating. These capital costs are likely to be dominant in any 

lithium-ion battery plant in the near future. 

7% 

3% 

15% 

2% 

1% 

2% 

1% 

1% 

28% 

29% 

9% 

2% 

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 5.3 Breakdown of installed capital equipment costs for the baseline plant
 

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5.5 Plant Investment Costs 

In this model, the calculated investment costs are defined as those directly related with building 

and operating the plant (Table 5.6). Other costs that may require investment, such as research 

and development, are added separately to the unit cost of the battery. The largest investment cost 

is for the installed capital equipment. Each cost item 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 $3,000 

per square meter ($280/sq. ft) including land and utilities. The high cost for land and utilities 

accounts for both the area of the manufacturing facility as well as other land requirements such 

as office buildings and waste water treatment requirements. Launch costs include plant start-up, 

employee training and materials that are lost or recycled in early stages of production, beyond 

the normal amounts. Launch costs are estimated to be 5 % of annual materials costs plus 10 % of 

annual direct labor and variable overhead (Section 5.6). 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 variable costs. 

Table 5.6 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. 

5.6 Unit Costs for Battery Pack 

The unit costs of the battery pack are calculated as summarized in Table 5.7. 

5.6.1 Variable Costs 

The costs of the materials and purchased items are based on the costs discussed in section 5.2, 

and the annual amounts of materials are adjusted for the yields of materials (section 5.3) and 

yield of cells. The direct labor is the sum of the labor cost for each step in the process, which are 

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each calculated for the baseline plant and adjusted for the rate associated with the battery under 

study. Variable overhead is the cost of indirect materials and labor, utilities, and plant 

maintenance. It is estimated to cost 40 % of direct labor costs and 20 % of depreciation. 

5.6.2 Fixed Expenses 

Fixed expenses include General, Sales, and Administration (GSA), research and development, 

and depreciation. The cost of GSA includes the plant office, taxes on income and property, cost 

of sales and insurance. It is estimated by the model as 25 % of direct overhead and depreciation. 

Research and development (R&D) must be 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 price. The greater the investment in the plant and its 

equipment, the greater is the need to be successful in the R&D effort. Thus, the expenditure has 

been set at 40 % of the depreciation expense. Depreciation expense provides funding available 

for future investment in this plant or another venture to replace deteriorating plant and 

equipment. The equipment and plant are depreciated at straight-line rates for 6-year life (16.7 % 

per year) and 20-year life (5 % per year). 

Table 5.7 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 

40% of direct labor cost plus 

20% of depreciation 

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 25% of 

depreciation. 

Research and Development On-going research needed to 

upgrade product and maintain 

competitive position. 

40% of depreciation 

Depreciation Provides funds for new 

investments to replace those in 

current equipment and plant. 

16.7% 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. 

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5.6.3 Profits 

The profit goal for this type of venture varies with 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 average for mature manufacturing as vehicle 

battery production is expected to be in 2020. In general, the chosen cost structure and the 

resulting margin are similar to a Tier 1 supplier in the automotive industry. 

5.6.4 Battery Pack Warranty Costs 

If a battery module or an entire pack fails, the replacement will cost much more than the original 

price paid by the OEM. It is important that such events are rare, but provision must be made to 

reimburse the vehicle owner, especially in the early years of the projected battery life. The extra 

costs of replacing the battery will result from labor 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 increasing share of the cost from between 0 % at 5 

years to 100 % at 10 or more years. With these assumptions, the cost to the battery manufacturer 

will be equal to the present worth of the future costs 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 rate 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 price of the battery before adding the warranty 

cost. 

5.7 Summary of Baseline Battery Cost 

The spreadsheet version of the model, which is discussed in more detail in sections 6 and 7, 

provides a summary sheet which is illustrated in Table 5.8 for the cost of the baseline battery and 

that of two others. This breakdown of the battery costs, 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 voltage would be slightly higher during the 

discharge to determine capacity. The battery with double the capacity has fewer electrodes which 

are longer and wider, because the cell thickness is maintained, resulting in higher resistance in 

the current-collector structure. The higher impedance lowers the voltage during the discharge 

capacity measurements and results in slightly less than twice the energy storage of the baseline 

battery. 

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Table 5.8. Summary of results for cost of baseline battery and that of similar batteries with
 

double the power and double the capacity of the baseline battery 

Baseline Double Power Double Capacity Double Modules 

Calculated Battery Parameters 

Battery energy storage, kWh 8.7 8.8 17.3 17.4 

Battery power at target % OCV, kW 50.0 100.0 86.9 100.0 

Required battery power, kW 50.0 100.0 50.0 100.0 

Capacity, Ah 40 40 80 40 

Number of cells 60 60 60 120 

Battery weight, kg 59.1 72.4 108.2 116.0 

Battery volume, L 31.2 37.1 55.2 59.7 

Weight and Volume of Components Exterior to Battery 

Weight, kg 11.0 9.0 11.0 9.0 

Volume, L 5.6 4.0 5.6 4.0 

Cooling system power requirement, W 1,760 649 857 724 

Vehicle electric range, miles 20.3 20.5 40.5 40.6 

Investment Costs 

Capital equipment cost including installation, mil$ 127 149 161 212 

Building, Land and Utilities 

Area, m2 15,374 18,165 19,204 24,284 

Cost, $/m2 3,000 3,000 3,000 3,000 

Building investment, mil$ 46.1 54.5 57.6 72.9 

Launch Costs 

Rate: 5% of direct annual materials + 10% of other annual costs 

Total, million$ 10.62 13.11 17.05 19.30 

Working capital (30% of annual variable costs), mil$ 28.78 35.80 47.53 53.28 

Total investment, mil$ 212.53 252.58 283.32 357.74 

Unit Cost of Battery Pack, $ 

Variable Cost 

Materials and Purchased Items 

Cell materials 1,302 1,739 2,452 2,547 

Cell purchased Items 63 66 74 110 

Module 202 205 237 399 

Battery pack 148 141 164 187 

Total 1,714 2,151 2,927 3,243 

Direct Labor 

Electrode processing 35 51 47 50 

Cell assembly 26 26 26 39 

Formation cycling, testing and sealing 17 17 17 26 

Module and battery assembly 16 16 16 22 

Cell and materials rejection and recycling 6 6 6 11 

Receiving and shipping 8 8 11 11 

Control laboratory 5 5 7 7 

Total 113 129 130 165 

Variable Overhead 92 107 112 144 

Total Variable Cost 1,919 2,387 3,169 3,552 

Fixed Expenses 

General, Sales, Administration 110 128 135 175 

Research and Development 94 110 119 156 

Depreciation 235 276 297 390 

Total Fixed Expenses 438 514 551 721 

Profits after taxes 106 126 142 179 

Total unit cost per battery not including warranty, $ 2,463 3,027 3,861 4,452 

Summary of Unit Costs, $ 

Materials 1,302 1,739 2,452 2,547 

Purchased Items not including cooling system 412 413 475 696 

Direct Labor 113 129 130 165 

Variable Overhead 92 107 112 144 

General, Sales, Administration 110 128 135 175 

Research and Development 94 110 119 156 

Depreciation 235 276 297 390 

Profit 106 126 142 179 

Warranty (includes battery pack only) 138 170 216 249 

Price to OEM for battery pack, $ 2,601 3,196 4,078 4,701 

Pack integration (BMS & Disconnects), $ 395 395 395 475 

Estimated cost to OEM for thermal management, $ 360 240 280 240 

Total cost to OEM for complete battery system, $ 3,356 3,831 4,753 5,416 

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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 processing. The double power battery requires 

greater labor costs principally for coating the larger electrode area. Capital equipment and 

depreciation costs are higher for both the high power and high capacity battery packs. The 

increases in capital equipment cost for the high-power 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 materials mixing, binder solvent recovery, cell 

stacking and formation cycling steps in the process. 

Overall, doubling the power of the battery increases the price by only 23 %. Doubling the 

capacity of the cells increases the cost by 57 %, considerably more than for doubling the power. 

Alternatively, doubling the number of baseline cells and modules within a larger battery jacket 

(two rows of modules instead of one, twice the voltage, energy, and power) would increase the 

cost by 81 %. 

The summary of unit costs for the baseline battery pack, which is shown at the bottom of Table 

5.8, is illustrated in Fig. 5.4. The materials and purchased items are the largest costs for the 

battery. For larger levels of production, these costs are even more dominant because the scale 

factors for these items are close to one. 

Figure 5.4 Breakdown of unit costs for baseline battery with total price to OEM of $2600. The 

total cost to the OEM, including pack integration components, is $3,360. 

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6 Description of the Spreadsheet Model and Instructions for Use 

6.1 Background 

Historically, the model has been based on Microsoft® Office Excel spreadsheets. The flexibility 

afforded by a spreadsheet approach has been extremely useful to the development of the 

calculations. Until now, the model had been in a constant state of development. Changes to 

parameters and equations were made rapidly and frequently. The publication of this report 

represents the first time a version of the model will 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 the revised model will be made in an orderly 

fashion rather than the continuous improvement approach taken over the last number of years. 

6.2 Instructions 

The following subsections are a brief explanation of how one may operate the spreadsheet based 

model. The user is advised to save the original document separately as a back-up copy. 

Corruption of the calculation is possible and will likely occur during use by someone unfamiliar 

with the model. 

6.2.1 Enabling Calculation 

This Microsoft® Office Excel workbook requires the use of iteration. To enable this feature in 

Office 2003, 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 iterations to 1000 (Figure 

6.1). Perhaps most importantly, 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 

references. If the model is opened while a different Excel spreadsheet is in use, the software will 

also warn of an error. Simply close all Excel windows except for the model; alternatively, one 

could re-enable the iterative function as discussed above. In newer versions of Excel such as the 

Office 2010 edition, the iterative function may be enabled by going to File > Options > 

Formulas. 

71 
 

 

 

Figure 6.1 Automatic iteration must be enabled for the spreadsheet model to function. The top 

screen shot was taken from Microsoft® Office Excel 2003 edition and the lower image is from 

the 2010 edition. 

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6.2.2 System Selection Worksheet 

The cell chemistry is selected by copying the system designated at the top of a column, for 

instance NCA-G in cell F3, pasting it into cell E3 (Figure 6.2). Any of the values in row E can be 

overridden by entering the desired value in column L. For example, the maximum electrode 

thickness may be overridden by placing a new value in cell L53. 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 screen shot of the system selection 

worksheet is in Figure 6.3. An alternative cell couple, NMC333-G, is pasted into column O as an 

example of another commercially relevant battery chemistry. 

Figure 6.2 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. 

6.2.3 Battery Design Worksheet 

The Battery Design worksheet designs five or more batteries for any type of electric-drive 

vehicle (Figure 6.4–6.6). The calculated designs are 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 format is assumed, the exact format 

(prismatic, pouch, can, etc) of the battery does not have a dominant effect on the cost for a set 

cell chemistry system. Our experience teaches us that the amounts of electrode materials and the 

number, capacity and electrode area of the cells, are 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. 

73 
Figure 6.3 System Selection worksheet
 

74
 
Figure 6.4 Top portion of Battery Design worksheet. 

75 
Figure 6.5 Middle portion of Battery Design worksheet 

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The Battery Design worksheet automatically receives input from the System Selection 

worksheet. These values are shown in purple (Figures 6.4 and 6.6) 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 battery design input in the aqua colored cells 

(Figures 6.4 and 6.6). The battery input parameters on lines 54 to 58 (Figure 6.4) and lines 162 

to 164 (Figure 6.6) are the only input values that the operator is required to provide to study a 

group of batteries. The type of vehicle battery (microHEV, HEV-HP, PHEV, or EV) on line 52 

in Figure 6.4, is another important variable to be specified. One performs the selection by typing 

the name of the vehicle battery type in cell F52. While the correct spelling is important, 

capitalization is 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). It is expected that the 

majority of the remaining default values should serve well for most batteries; however, the user 

may also change to their exact specifications. 

The cell capacity (lines 162 to 164 in Figure 6.6) can be set in any of three ways: (1) directly 

specifying the capacity (Ah) on line 162, (2) specifying the total battery energy on line 163 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 follow the directions of the top-most line with 

non-zero values. 

The number of batteries manufactured per year is selected on line 64 in Figure 6.4. Changing this 

value from the default value of 100,000, which is the 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 maintained 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 all other worksheets containing calculations. 

6.2.4 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 6.7). 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. Tables for presentations or for preparing graphs 

of the data can be assembled at the bottom of either 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 chemistries can be copied and pasted (special 

paste, values and numbers formats) to a blank worksheet. On the last worksheets, the cell, 

module, and battery design, as well as the baseline plant are sketched. 

77 
Figure 6.6 Bottom portion of Battery Design worksheet 

78 
 Figure 6.7 Summary of Results worksheet
 

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6.3 Battery Design Format Requirements 

As the battery design is based off an assumed format (Section 2), certain design requirements are 

necessary to ensure the modeled battery is physically realistic. The dimensions of the calculated 

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 for adjustment of the pack dimensions. 

6.4 Troubleshooting and General Advice 

The spreadsheet iterates to find the solution and this 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.). Then the cells may be reset to default values by 

entering a “0” (i.e. zero) in the restart cell, F170 in Figure 6.6. Finally, entering a “1” in F170 

restarts the iteration process leading to a successfully 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 are 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 larger and larger values, which thus demands 

smaller and smaller electrode thicknesses. Eventually, 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 129 for the C-rate and rows 88 and 89 

for the electrode thickness. Therefore, the user may 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 depending 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. 6.1 generally result in 

successful battery designs. Higher P/E ratios are allowable in some situations. Note that selecting 

the microHEV design doubles the allowable C-rate since only two second pulses are used. The 

limiting C-rate, rC,lim, may be found in cell E43 on the System Selection worksheet and is carried 

over to row 76 in the Battery Design worksheet. 

P rC ,lim < (6.1) E 1.35 

6.5 Suggested Number of Cells, Modules, and Performance Inputs 

Table 6.1 presents some suggestions for the required inputs into the design model that might 

change depending on the type of vehicle battery being designed. These values are only 

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suggestions, but tend to be similar to practices used today or projected to be used in the future by 

industry. If the calculated cell capacity is higher than 60 Ah, the user should consider the 

inclusion of parallel cells as an additional parameter to examine. The default energy usage rate in 

BatPaC is 300 Wh/mi. This rate may be used to size the energy requirement based on a desired 

electric range for the vehicle by specifying the distance in row 164 on the Battery Design 

worksheet. 

Table 6.1 General suggestions for range of input parameters that change with battery type 

battery type modules/battery OCV @ 50% SOC Power (kW) Energy (kWh) 

HEV-25 1 - 4 40 - 200 25 0.6 - 1.5 

HEV-HP 2 - 4 160 - 260 25 - 80 1 - 2 

PHEV 4 - 6 290 - 360 40 - 160 4 - 30 

EV 4 - 6 290 - 360 80 - 160 20 - 200 

6.6 Entering a New Material Couple
 

The user of the model may wish to examine an electrochemical couple that is not included as one 

of the options available in the model. We list below a brief explanation on how to properly enter 

new materials into BatPaC. Various properties may be calculated, found in literature or measured 

in the laboratory. The self-consistency of the data used is very important. 

Experimentally measured values required: 

1. Half cell formation cycling data from positive and negative electrode 

2. Half cell cycling data from positive and negative electrode at C/3 rate 

3. Full cell open-circuit voltage measurement at 50 % and 25 % SOC 

4. Full cell ASI measurement for 5C pulse at 50 % and 25 % SOC 

5. Full cell ASI at 50% SOC during a C/3 discharge 

6. Electrode void fractions, active material densities, electrode component weight percent 

7. Estimated interfacial area from surface area (preferred) or particle size measurements 

The ASI calculation includes some additional parameters that become important as the designed 

P/E ratio increases above 10 h-1 or the electrode thicknesses decrease below 30 microns. The user 

is referred to section 3.4 and the supporting manuscript from Gallagher et al.

20 for the parameter 

estimation process. An exchange current of 0.15 mA/cm2, normalized to the surface area 

calculated using the BET method from nitrogen absorption experiments, is used in the model in 

row 77 in the Battery Design worksheet. While the exact value of the exchange current will vary 

from the material to material, the general behavior of the ASI will be preserved with this 

assumption. If lower P/E ratio designs are desired, the exact valuation of the exchange current, 

interfacial area, and limiting C-rate are less important. However, the experimental ASI 

measurement should then come from a cell with similar P/E ratio (electrode loading). Electrode 

thicknesses 40 microns or larger should be used to minimize the contribution of interfacial 

impedance to the ASI measurement. Otherwise the “ASI correction factor” may not accurately 

remove the interfacial component. A reasonable approach for a first approximation of the ASI 

parameters may be to select the same values for a similar material. For example, if the new 

material is based on nano-sized primary particles, then the parameters for LFP or LTO may be 

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close enough. The ASI does depend on a large number of factors and a full determination of the 

parameters is important to capture all of the physical behavior of the cell couple. If the desire of 

user is to reproduce or to reverse engineer an existing cell, then many of the parameters may be 

estimated from the electrochemical characterization of the full cell data. These electrochemical 

results typical require a teardown of the cell to measure the area of the electrodes and their 

loadings/thicknesses, assuming no legal contract has been established prohibiting the analysis of 

the cell. 

The available lithium for cycling in a full cell configuration may be calculated from half cell 

measurements. The calculation method may be found in the Capacity Calculator worksheet in the 

spreadsheet model and is detailed below. Alternatively, the reversible capacity of the full cell in 

the experiment may be normalized to the mass of the positive and negative electrodes while 

carefully accounting for the negative to positive capacity ratio. The first cycle efficiency of a 

positive or negative electrode based half-cell may be defined as the ratio of the first discharge 

capacity divided by the first charge capacity, Equation 6.2. We have assumed the first discharge 

capacity is equivalent to the reversible capacity when measured against lithium foil (half-cell 

arrangement). 

st 

j 

1 η st 

j 

rev 

j 

Q 

Q 

1 = (6.2) 

⎛

⎜

⎜

⎝

The quantity of lithium consumed from the positive electrode in the negative electrode SEI, Qsei , 

may be calculated from Equation 6.3. Here, [N/P] is the negative to positive capacity ratio. 

⎧⎪

⎨

Qrev 

sei P 1st rev mN irrev Q = [N/P ] (Q − Q ) = Q (6.3) QN

rev N N 

mP

N 

After one full cycle, the remaining lithium in the positive electrode available for cycling, QP

act, in 

a full-cell configuration (positive electrode versus non-prelithiated negative electrode) may be 

calculated by choosing the minimum value determined in Equation 6.4 below. Here we see the 

possibility that the positive electrode is unable to accept the full amount of lithium released 

during the first charge cycle. This so called “irreversible capacity” of the positive electrode 

results in lithium residing in the negative electrode. While this excess lithium may require 

additional negative electrode capacity, it also provides some beneficial aspects to cycle and 

calendar life.50 We have chosen to set the [N/P] = 1.25 for layered oxides positive electrodes 

(NCA, NMC441, NMC333) due to their tendency to have a lower first cycle efficiency ~ 88%. 

The lithium manganese spinel and lithium iron phosphate cells have a high first cycle efficency 

and thus we selected a [N/P] = 1.20. For positive electrodes with a high first cycle efficiency, the 

reversible capacity of the cell is reduced by the lithium consumed in the graphite electrode SEI 

during the formation cycle. Conversely, the lithium titanate spinel negative electrode does not 

form an SEI and is significantly safer than the graphite electrode as discussed in Chapter 5. 

Thefore the [N/P] ratio is set to 1.1 for the cells based on lithium titanate spinel. 

Q ⎟ − ] ⎞

⎟

⎟

⎞ ⎞ ⎟

⎠

⎛ ⎛ ⎜

⎜

⎫⎪

⎬
 ⎪⎩ ⎝

⎟

⎟

⎠

⎜

⎜

⎝ ⎪ ⎠ ⎭

η1st η1st 1
 −
 1
 − [N/P
 act rev P N ,
Q
 rev 

P Q
 =
 MIN
 1
 + (6.4)
 P P 

η1 η st 1st 

P N 

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7. Illustrated Results
 

The BatPaC model may be used to study the effects of battery 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, weight and cost. 

7.1 Number of Cells in Series 

For a set battery pack power, the number of cells in the pack has substantial effects on the price 

of the pack, the pack voltage and the maximum current. These effects are illustrated (Figure 7.1) 

for NMC441-Gr PHEV25 batteries (providing 25-mile electric range) with 60-kW power at a 

[V/U] = 0.8. The price of the pack increases by 17% in changing the number of series-connected 

cells in the pack from 32 to 96 and the entire pack integrated cost increases by 15.7%. The 

integrated cost includes additions to the vehicle air-conditioning system to provide for battery 

cooling and the battery management system with disconnects. The change in the maximum 

current, resulting from differing pack voltages, would 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 electric drivetrain, a study is required 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). 

Figure 7.1 The effect of the number of series-connected cells for NMC441-Gr, 60-kW, PHEV25 

packs with 10.7 kWh total energy (70% useable). 

Current PHEV battery technology uses battery packs containing 80-96 series connected cells. 

However, these series connections are often composed of parallel cell groups. For instance, the 

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battery used in the first production model of the Chevrolet Volt is in a 3P-96S configuration.21 

Three low capacity cells are connected in parallel forming a parallel cell group. Then 96 parallel 

cell groups are connected in series. The cost savings from moving to larger format cells with 

only series connections is discussed later in this section. 

7.2 Cathode Materials 

Lithium-ion batteries for PHEVs and EVs do not require a high P/E ratio or low ASI to meet 

their goals. The most important material properties for performance are high specific capacity 

(mAh/g), high cell voltage, and high electrode density. Since the graphite electrode is almost 

universal in commercial cells (although not all graphite is the same), changes in the cathode 

result in dramatically different calculated batteries. To compare the performance of EV battery 

packs made from various Li-ion chemistries, we designed the packs to provide 150 kW at 360 V 

(25% SOC) for a [V/U] = 0.8. Each pack consisted of six modules containing 16, 16, and 18 

cells for the cell chemistries LMO-Gr, NMC441-Gr, and LFP-Gr, respectively. This calculation 

assumes that large capacity cells may be reliably produced. Moving to a parallel connection of 

smaller capacity cells would result in higher cost as discussed later in the section. 

The NMC441-Gr system has excellent energy density and low cost (Fig. 7.2 and 7.3). The LMOGr system is less energy dense than the NMC441-Gr couple, but equivalent in calculated price to 

the OEM. The LFP-Gr system results in a battery that is larger and more expensive than the other 

two chemistries. The mass-specific cathode raw material prices are 29, 20, and 10 $/kg for 

NMC441, LFP and LMO respectively. The differences in initial cost do not directly translate to 

the end cost of the battery. The performance (exhibited by specific capacity and voltage) affect 

the quantity of both active and inactive material required. The NMC441 material achieves 175 

mAh/g at a good cell voltage and is representative of an advanced, although close to 

commercialization, layered oxide cathode.51 The combination in voltage and capacity results in a 

superior energy density compared to the other cathodes. The LMO cathode has similar cell 

voltage to NMC441 and low raw material cost but also a low specific capacity of 100 mAh/g. 

This low capacity results in a positive electrode loading limited by the maximum achievable 

electrode thickness ~100 microns. The LFP electrode has moderate capacity, 150 mAh/g, and 

raw material cost, but exhibits a lower cell voltage and electrode density. These poor 

performance characteristics result in a low energy density battery with a high price. 

7.3 Parallel-Connected Cell Groups and Electrode Thickness Limits 

BatPaC also allows the user to create parallel cell groups and to set a maximum electrode 

thickness. The effect these two unique design factors have on battery price are illustrated below 

in Figure 7.4 for the LMO-Gr and NMC441-Gr systems. In this illustration, the PHEV battery 

pack design parameters are 100 kW of power at a [V/U] = 0.8 and 17 kWh of total energy. The 

nominal battery pack voltage (OCV at 50% SOC) is around 360 V from 96 cell groups connected 

in series. The number of cells in the parallel cell group is varied from a single cell (no parallel 

connections) to four. Two maximum electrode thicknesses of 100 and 200 microns are shown for 

the LMO-Gr chemistry. In contrast to the NMC441-Gr, the LMO-Gr chemistry benefits form 

allowing larger electrode thicknesses. The thickness of the positive electrode is limiting the 

LMO-Gr chemistry while the thickness of the negative electrode limits the NMC441-Gr 

84 
 

 

 

Figure 7.2 Mass and volume of electric vehicle battery packs with lithium iron phosphate (LFP), 

lithium manganese-spinel (LMO) and lithium nickel-manganese-cobalt oxide (NMC441) 

positive electrodes versus graphite designed to deliver 150 kW of power at 360 V (25% SOC). 

Figure 7.3 Battery pack price to OEM for LFP-Gr, LMO-Gr and NMC441-Gr battery packs for 

same designs as in Fig. 7.2. NMC441-Gr and LMO-Gr result in nearly the same price. 

85 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

chemistry. The calculated value for the NMC441-Gr system never exceeds 100 microns for this 

P/E ratio. The LMO-Gr is the least expensive in all cases. However, the difference between the 

two chemistries lessens with smaller limiting electrode thickness. The costs will become even 

closer for lower designed P/E ratios. In general, thicker electrodes reduce the cost of the battery 

pack by lessening the amount of inactive materials used (separator, current collector, etc). 

Moving to 300 microns allows for greater savings in the LMO-Gr design but not the NMC441­

Gr design. However, a lower P/E ratio design for NMC441-Gr would take advantage of electrode 

thicknesses greater than 200 microns. 

The cell capacity is shown for the NMC441-Gr case limited to 100 microns. While the exact 

values will change with cell chemistry, they will all be similar. The cell capacity is reduced by 

one half as a single cell is added in parallel. This approach is commonly used by cell 

manufacturers and OEMs that cannot reliably produce or successfully operate cells of high 

capacity for transportation applications. However, this approach also increases the price of the 

battery pack. In this example, the price is increased by ~ $500 when an additional string of cells 

is incorporated in a parallel arrangement. 

The model calculations show that the lowest cost battery pack will utilize thick electrodes and 

large capacity cells. In current practice, these two approaches have yet to be successfully 

implemented within the entire community. In the challenge of lowering costs, it is useful to point 

out the largest gains come from the initial advances (e.g. moving from 100 to 200 micron limit). 

After that point, the benefits are diminishing. 

7.4 Manufacturing Scale 

The effects of manufacturing scale come into the cost calculation even if the annual number of 

packs produced is unchanged, but the design is altered (e.g. power is increased). For a fixed 

design, the effect of changing the scale of operations 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 decline substantially with increasing production 

rates, especially at low production rates, Fig. 7.5. 

The lines in the graphs are for the best-fit power relationships through the data with power 

factors of -0.076, -0.077, -0.147, and -0.211 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 result 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. 5.2 by adding 1.0 to each power factor. Thus the factors become 0.924, 0.923, 0.853, and 

0.789. These large factors show only a small to moderate effect of scale. When the power curves 

are compared to the points in each of the graphs of Fig. 7.5, it is apparent that the scale factors 

approach one as the scale increases. This is because the model assigns a value of 0.95 for the 

active materials and 1.0 for the balance of the materials. 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 

86 
 

 

 

portion of the total cost for HEV batteries. Increasing the production rate for HEV batteries will 

result in a more dramatic reduction in cost than increasing the production rate for EV batteries. 

Figure 7.4 Battery pack cost as a function of number of parallel cells and for different maximum
 

electrode thicknesses. The electrode thicknesses (100 or 200 μm) represent the limitation not the
 

exact value calculated by the model. The cell capacity is also shown for the NMC441-Gr battery.
 

87 
 

 

Figure 7.5 The effects of manufacturing rate on the price calculated by the model for battery 

packs of various cell chemistries, power capabilities and vehicle types. The EV and PHEV 

batteries are composed of 96 cells and the HEV-25 is composed of 48 cells. 

88 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

8. Future Work
 

8.1 Initial Power Designed at Differing Fractions of the Open-Circuit Voltage 

The objective of this study is to evaluate the various benefits and costs associated with over- or 

under- sizing the initial power of the battery utilizing Argonne National Laboratory’s BatPaC 

(battery performance and cost model) and Autonomie (vehicle model). The fraction of the opencircuit voltage at which initial designed battery power is achieved has a direct impact on heat 

generation during operation, performance under cold conditions, and acceptable power fade. The 

vehicle focus will be on PHEVs for a mid-size vehicle glider and also a small SUV. Coupling the 

vehicle and battery models will allow for a complete study evaluating the benefits and tradeoffs 

associated with this critical design parameter. This work will be carried out in a cooperative 

effort with Argonne’s Transportation Technology R&D Center, which will perform vehicle 

simulation tests to determine the rate of heat generation in the battery pack. 

The end result of this study will be quantitative justification for designing a battery at a set 

fraction of the open-circuit voltage. The justification will likely depend on battery chemistry and 

powertrain type as differing architectures lead to differing benefits. These benefits may lead to 

changes in the system design to maximize net present value. A secondary, but just as important, 

benefit will be extrapolation of thermal management requirements from heat generation and cold 

temperature performance calculated from various levels of sizing the battery. 

8.2 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. 7.1). 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 cells 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 drivetrain is at a minimum. This minimum would 

be for the current at full power for which the slope 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 power 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 model in Section 7, we used an equation (Eq. 

7.1) for selecting the current at full power as a function of the battery pack power. This equation 

is just an estimate and it does not provide for differences in the optimum current that would 

result from differences in cell chemistries, which are known to affect the battery cost versus 

power function. 

89 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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 function of power and maximum current capability. 

Once appropriate cost curves are established, we will 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. 

8.3 Multipurpose Battery Manufacturing Plants 

Our cost modeling is based on the concept that a manufacturing plant is constructed to produce a 

single type of battery pack at a predetermined level of production. In practice, manufacturers will 

have to produce several types of batteries within the 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 example, the cell filling and sealing equipment 

may be required to handle cells of different dimensions. This would most likely increase the 

capital cost for this equipment. Alternatively, additional packaging and sealing lines might be 

needed. We intend to evaluate combinations of vehicle battery packs that are easily integrated 

into the same plant. The manufacturing cost will most likely increase after these considerations 

are built into the model. 

8.4 Stand-Alone Graphical User Interface for Model 

The spreadsheet program described here-in allows versatility in designing the battery and in 

calculating the costs, but like all complex spreadsheet programs it is not user-friendly to those 

unfamiliar with the details of calculation. In addition, 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 with 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 for those interested in batteries regardless of 

the specific material property or manufacturing cost structure the user seeks to analyze. 

90 
 

 

REFERENCES
 

1. M. Anderman, F. Kalhammer, and D. MacArthur. “Advanced Batteries for Electric Vehicles: 

An Assessment of Performance, Cost, and Availability.” California Air Resources Board, June 

(2000). Available from http://www.arb.ca.gov/msprog/zevprog/2000review/btap report.doc 

(accessed on December 17, 2010). 

2. B. Barnett, D. Ofer, C. McCoy, Y. Yang, T. Rhodes, B. Oh, M. Hastbacka, J. Rempel, and S. 

Sririramulu “PHEV Battery Cost Assessment,” 2009 DOE Merit Review, May (2009). Available 

from http://www1.eere.energy.gov/vehiclesandfuels/pdfs/merit_review_2009/energy_storage/ 

es_02_barnett.pdf (accessed on December 11, 2010). 

3. B. Barnett, J. Rempel, D. Ofer, B. Oh, S. Sriramulu, J. Sinha, M. Hastbacka, and C. McCoy, 

“PHEV Battery Cost Assessment,” 2010 DOE Merit Review, June (2010). Available from 

http://www1.eere.energy.gov/vehiclesandfuels/pdfs/merit_review_2010/electrochemical 

_storage/es001_barnett_2010_o.pdf (accessed on December 11, 2010). 

4. A. Dinger, R. Martin, X. Mosquet, M. Rabl, D. Rizoulis, M. Russo, and G. Sticher, “Batteries 

for Electric Vehicles: Challenges, Opportunities, and the Outlook to 2020.” The Boston 

Consulting Group, Available from http://www.bcg.com/documents/file36615.pdf (accessed on 

December 11, 2010). 

5. L. Gaines and R. Cuenca. “Costs of Lithium-Ion Batteries for Vehicles,” Center for 

Transportation Research, Energy Systems Division, Argonne National Laboratory, ANL/ESD42, Argonne, IL May (2000). 

6. F.R. Kalhammer, B.M. Kopf, D.H. Swan, V.P. Roan, M.P. Walsh, “Status and Prospects for 

Zero Emissions Vehicle Technology: Report of the ARB Independent Expert Panel 2007,” 

California Air Resources Board, April (2007). Available from http://www.arb.ca.gov/ 

msprog/zevprog/zevreview/zev_panel_report.pdf (accessed on December 17, 2010). 

7. M. A. Kromer and J. B. Heywood, “Electric Powertrains: Opportunities and Challenges in the 

U.S. Light-Duty Vehicle Fleet,” Sloan Automotive Laboratory, Laboratory for Energy and the 

Environment, Massachusetts Institute of Technology, LFEE 2007-03 RP, Cambridge, MA 

(2007). 

8. P. Mock, “Assessment of Future Li-Ion Battery Production Costs,” presented at Plug-in 2009, 

Long Beach, CA, (2009). 

9. National Research Council of the National Academies, “Transitions to Alternative 

Transportation Technologies – Plug-in Hybrid Electric Vehicles,” The National Academies 

Press, Washington, D.C. (2010). Available from http://www.nap.edu/catalog.php?record_id= 

12826 (accessed on December 17, 2010). 

10. TIAX LLC, “Cost Assessment for Plug-In Hybrid Vehicles (SOW-4656),” Report to US 

DOE Office of Transportation Technology, October (2007). 

91 
 

 

 

 

 

 

 

 

 

 

 

11. M. Anderman “The Plug-In Hybrid and Electric Vehicle Opportunity Report: A critical 

assessment of the emerging market and its key underlying technology: Li-Ion batteries,” 

Advanced Automotive Batteries, May (2010). 

12. P.A. Nelson, D.J. Santini, J. Barnes, “Factors Determining the Manufacturing Costs of 

Lithium-Ion Batteries for PHEVs.” International Electric Vehicles Symposium EVS-24, 

Stavanger, Norway, (2009). 

13. D.J. Santini, K.G. Gallagher, P.A. Nelson, “Modeling the Manufacturing Costs of LithiumIon Batteries for HEVs, PHEVs, and EVs,” International Electric Vehicles Symposium EVS-25, 

Shenzhen, China, (2010). 

14. K.G. Gallagher, P.A. Nelson, D.W. Dees, “PHEV battery cost assessment” 2011 DOE Merit 

Review Presentation Washington, DC May 9-12 (2011). Available from http://www1.eere. 

energy.gov/vehiclesandfuels/pdfs/merit_review_2011/electrochemical_storage/es111_gallagher_ 

2011_o.pdf (Accessed on July 12, 2011). 

15. P. Nelson, I. Bloom, K. Amine, G. Henriksen, “Design modeling of lithium-ion battery 

performance,” Journal of Power Sources, 110, 437 (2002). 

16. P. Nelson, D. Dees, K. Amine, G. Henriksen, “Modeling thermal management of lithium-ion 

PNGV batteries,” Journal of Power Sources, 110, 349 (2002). 

17. G.L. Henriksen, K. Amine, J. Liu, and P.A. Nelson, “Materials Cost Evaluation Report for 

High-Power Li-Ion HEV Batteries,” Electrochemical Technology Program, Chemical 

Technology Division, Argonne National Laboratory, ANL-03/05, Argonne, IL (2002). 

18. P. Nelson, K. Amine, A. Rousseau, H. Yomoto, “Advanced Lithium-Ion Batteries for Plug-in 

Hybrid-Electric Vehicles”, International Electric Vehicles Symposium, EVS-23, Anaheim, Ca 

(2007). 

19. P. Nelson, “Modeling the Manufacturing Costs of Lithium-Ion Batteries for PHEVs,” 

presented at Plug-in 2009, Long Beach, CA, (2009). 

20. K.G. Gallagher, P.A. Nelson, and D.W. Dees, “Simplified Calculation of the Area Specific 

Impedance for Battery Design,” Journal of Power Sources, 196 2289 (2011). 

21. “Chevrolet Volt: Development Story of the Pioneering Electrified Vehicle” ed. Lindsay 

Brooke, SAE International, Warrendale, PA pgs 215 (2011) 

22. A.N. Jansen, K. Amine, and G. L. Henriksen, “Low-Cost Flexible Packaging for High-Power 

Li-Ion HEV Batteries,” Electrochemical Technology Program, Chemical Technology Division, 

Argonne National Laboratory, ANL-04/09, Argonne, IL (2004). 

92 
 

 

 

 

 

23. P.A Nelson and A.N. Jansen, “Comparative Costs of Flexible Package Cells and Rigid Cells 

for Lithium-Ion Hybrid Electric Vehicle Batteries,” Electrochemical Technology Program, 

Chemical Technology Division, Argonne National Laboratory, ANL-06/43, Argonne, IL (2006). 

24. J. Euler and W. Nonnenmacher, “Stromverteilun in Porösen Elektroden,“ Electrochim. Acta, 

2 268 (1960). 

25. J.S. Newman and C.W. Tobias, “Theoretical Analysis of Current Distributions in Porous 

Electrodes,” J. Electrochem. Soc., 109 1183 (1962). 

Electrode thickness limitations 

26. “Diagnostic Examination of Generation 2 Lithium-Ion Cells and Assessment of Performance 

Degradation Mechanisms,” ANL Report, ANL-05/21, July 2005. 

27. D. Dees, E. Gunen, D. Abraham, A. Jansen, and J. Prakash, “Electrochemical Modeling of 

Lithium-Ion Positive Electrodes during Hybrid Pulse Power Characterization Tests” J. 

Electrochem. Soc., 155 (8) A603 (2008). 

28. D. Dees, E. Gunen, D. Abraham, A. Jansen, and J. Prakash, “Alternating current impedance 

electrochemical modeling of lithium-ion positive electrodes,” J. Electrochem. Soc., 152 

(7),A1409 (2005). 

29. D. Abraham, S. Kawauchi, and D. Dees, “Modeling the impedance versus voltage 

characteristics of LiNi0.8Co0.15Al0.05O2,” Electrochim. Acta, 53 2121–2129 (2008). 

30. D. P. Abraham, S. D. Poppen, A. N. Jansen, J. Liu, and D. W. Dees, “Application of a 

lithium-tin reference electrode to determine electrode contributions to impedance rise in highpower lithium-ion cells,” Electrochim. Acta, 49 4763 (2004). 

31. D. P. Abraham, E. M. Reynolds, E. Sammann, A. N. Jansen, and D. W. Dees, “Aging 

characteristics of high-power lithium-ion cells with LiNi0.8Co0.15Al0.05O2 and Li4/3Ti5/3O4 

electrodes,” Electrochim. Acta, 51, 502 (2005). 

32. D.P. Abraham, J. Liu, C.H. Chen, Y.E. Hyung, M. Stoll, N. Elsen, S. MacLaren, R. Twesten, 

R. Haasch, E. Sammann, I. Petrov, K. Amine, G. Henriksen, J. Power Sources, 119-121 511 

(2003). 

33. D. P. Abraham, R. D. Twesten, M. Balasubramanian, J. Kropf, D. Fischer, J. McBreen, I. 

Petrov, and K. Amine, “Microscopy and spectroscopy of lithium nickel oxide-based particles 

used in high power lithium-ion cells,” J. Electrochem. Soc., 150 (11) A1450 (2003). 

34. A.M. Andersson, D.P. Abraham, R. Haasch, S. MacLaren, J. Liu, K. Amine, “Surface 

characterization of electrodes from high power lithium-ion batteries,” J. Electrochem. Soc., 149 

A1358 (2002). 

93 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

35. D. Abraham, J. Knuth, D. Dees, I. Bloom, and J. Christophersen, “Performance degradation 

of high-power lithium-ion cells - Electrochemistry of harvested electrodes,” J. Power Sources, 

170 465 (2007). 

36. J. Newman and K. E. Thomas-Alyea, “Electrochemical Systems,” 3rd ed., Wiley 

Interscience, New York (2004). 

37. Wei Lai, Can K. Erdonmez, Thomas F. Marinis, Caroline K. Bjune, Nancy J. Dudney, Fan 

Xu, Ryan Wartena, and Yet-Ming Chiang, “Ultrahigh-Energy-Density Microbatteries Enabled 

by New Electrode Architecture and Micropackaging Design,” Advanced Materials, 22, E139– 

E144 (2010). 

38. Pankaj Arora, Marc Doyle, and Ralph E. White, “Mathematical Modeling of the Lithium 

Deoposition Overcharge Reaction in Lithium-Ion Batteries Using Carbon-Based Negative 

Electrodes,” J. Electrochem. Soc. 146 (10) 3542-3553 (1999). 

39. Y. Chen and J.W. Evans, “Thermal Analysis of Lithium-Ion Batteries” J. Electrochem. Soc. 

143 (9) 2708-2712 (1996). 

40. S.C. Chen, C.C. Wan, and Y.Y. Wan, “Thermal Analysis of lithium-ion batteries” J. Power 

Sources 140 111-124 (2005). 

41. H. Maleki, S.A. Hallaj, J.R. Selman, R.B. Dinwiddie, and H. Wang, “Thermal Properties of 

Lithium-Ion Battery and Components” J. Electrochem. Soc. 146 (3) 947-954 (1999). 

42. M. Sievers, U. Sievers, and S.S. Mao “Thermal modelling of new Li-ion cell design 

modifications” Forsch Ingenieurwes 74 215-231 (2010). 

43. T.M. Bandhauer, S. Garimella, and T.F. Fuller “A Critical Review of Thermal Issues in 

Lithium-Ion Batteries” J. Electrochem. Soc. 158 (3) R1-R25 (2011). 

44. R. Byron Bird, Warren E. Stewart, and Edwin N. Lightfoot, “Transport Phenomena,” 2nd Ed. 

John Wiley & Sons, Inc, New York, NY (2002). 

45. R.K. Shah and A.L. London, “Laminar Flow Forced Convection in Ducts” Advances in Heat 

Transfer Supplement, Academies Press, New York, NY (1978). 

46. R. Siegel, E.M. Sparrow, and T. M. Hallman, “Steady Laminar Flow Heat Transfer in a 

Circular Tube with Prescribed Wall Heat Flux,” Appl. sci. Res. Section A, 7 386-392 (1958). 

47. M. Nickolay and H. Martin, “Improved approximation for the Nusselt number for 

hydrodynamically developed laminar flow between parallel plates,” Int. J. Heat Mass Tran. 45 

3263-3266 (2002). 

48. United States Geological Survery, Commodity Statistics and Information, Available from 

http://minerals.usgs.gov/minerals/pubs/commodity/ (accessed on December 17, 2010). 

94 
 

 

 

 

49. R.H. Perry, D.W. Green, and J.O. Maloney, Perry’s Chemical Engineers’ Handbook, Sixth 

Edition, pp: 25-68 (1984). 

50. M. Broussely, Ph. Biensan, F. Bonhomme, Ph. Blanchard, S. Herreyre, K. Nechev, and R.J. 

Staniewicz, “Main aging mechanisms in Li ion batteries,” J. Power Sources 146 90-96 (2005). 

51. Sun-Ho Kang, Wenquan Lu, Kevin G. Gallagher, Sang-Ho Park, and Vilas G. Pol, “Study of 

Li1+x(Mn4/9Co1/9Ni4/9)1-xO2 Cathode Materials for Vehicle Battery Applications” J. 

Electrochem. Soc. 158 (8) A936-A941 (2011). 

95