1

Memo 

To: Docket EPA-HQ-OAR-2010-0799

From: Joseph McDonald, U.S. EPA-OTAQ-ASD 

CC: Ed Nam, U.S. EPA-OTAQ-ASD 

Date: Tuesday, November 29, 2011 

Re: Initial BatPaC Variation Study 

The attached document contains a cost sensitivity analysis conducted by Argonne National Laboratory 

using the BatPaC model. The analysis varied cost and design input variables and estimated a 

confidence interval for the cost of various Li-ion cathode types and for different vehicle applications. 
An Initial BatPaC Variation Study

Kevin G. Gallagher and Paul A. Nelson

September 13, 2011

Summary

The following ranges are suggested as an initial approximation to account for variation that will 

occur in the cost inputs and possible design limitations in BatPaC. The larger uncertainty for 

LMO in PHEV and EV batteries is due to an interaction with the electrode thickness limitation.

These values do not account for any uncertainty that results from advanced Li-ion chemistries 

successfully entering the market place. If one considers the likely entry of less expensive and 

more energy dense materials, and the potential for significant improvements in manufacturing 

processes, the uncertainty towards lower costs will certainly increase. If a simpler approach is 

desired for EVs and PHEVs, using +/- 20 % for every EV and PHEV battery modeled is a 

reasonable alternative that considers some probability of advanced technologies entering the 

market in the 2020 timeframe. Future versions of BatPaC will include error estimation within the 

model.

Summary Table 1. Suggested confidence bounds as a percentage of the calculated point estimate 

for a graphite based Li-ion battery using the default inputs in BatPaC.

Discussion

The general approach in this variation study is to produce a distribution of cost inputs and 

analyze a range of battery designs to capture the spread in calculated battery price if the default 

cost inputs or design parameters are in error. The eight largest cost contributions comprising the 

battery price to the OEM, shown in Table 1, were evaluated to determine the range of possible 

values and the likely form of the distribution, normal or log-normal. For normal distributions, the 

standard deviation was approximated as 1⁄4 of the range of values. The parameters for log-normal 

distributions were hand-fit to set the minimum and maximum at the outer range of the 95 % 

confidence interval. Equations 1 and 2 were used to create the distribution for each cost input, 

Cij, from independent sets of 3000 normally distributed random numbers, rij. Here, Ci is the mean 

and σi is the standard deviation for the normal distribution of cost input i. Additionally, μi is the 

location parameter and αi is the scale parameter for the log-normal distribution. Each collection 

of cost inputs was used to produce an end battery price to the OEM. The battery designs used in 

this study are detailed in Table 2. 

 normal (1)

Battery type Cathodes lower upper

HEV LMO, LFP, NCA, NMC -10% 10%

PHEV, EV NMC, NCA -10% 20%

PHEV, EV LMO, LFP -20% 35%

Confidence Interval
 ( ) log-normal (2)

Table 1. Cost input ranges and distributions used in variation study

Table 2. Battery designs considered in variation study

The variation in calculated price solely due to cost input estimates results in a near-normal 

distribution of values. The results may be adequately summarized by the calculated mean and 

standard deviation. Only the cases of the default design limitations are shown in Table 3 (100 

micron limit, 1 cell in cell group). A value of +/- 10 % would adequately capture the 95% 

confidence interval of the calculated price distributions for all battery chemistries and battery 

types.

Table 3. Distribution in calculated price from cost input variation

Item low medium high distribution mean std dev location scale

Separator 0.75 2 4 log-normal 0.75 0.3

Copper foil 1 1.8 2.6 normal 1.8 0.4

Electrolyte 18 21.6 25.2 normal 21.6 1.8

Graphite anode 12 19 25 normal 19 3.25

LMO cathode 8 10 16 log-normal 2.35 0.15

NMC cathode 22 29 34 normal 29 3

NCA cathode 22 37 42 normal 37 5

LFP cathode 10 20 30 normal 20 5

SOC controller 1.5 2.5 3.5 normal 2.5 0.5

Coating capital 5 8 12 normal 8 1.75

Formation capital 20 30 50 log-normal 3.45 0.2

Battery type HEV-HP PHEV25 EV100

Power (kW) 40 65 115

Energy (kWh) 1.5 10.7 30

Range @ 300 Wh/mi 1 25 80

Number of cells 72 96 96

Number of modules 4 6 6

Cells in parallel group 1 1 1, 2

Electrode thickness limit (micron) 100 50, 100, 150 70, 100, 200

Cathode chemistries LMO, LFP LMO, NMC441, NCA LMO, NMC441, NCA

battery cathode mean std deviation 2s/mean

HEV LMO 1268 49 0.08

HEV LFP 1475 65 0.09

PHEV25 LMO 2995 134 0.09

PHEV25 NMC441 3087 128 0.08

PHEV25 NCA 3325 153 0.09

EV100 LMO 6051 339 0.11

EV100 NMC441 5927 279 0.09

EV100 NCA 6648 364 0.11
Quantifying the error in calculated price due to the relative success or failure of certain design 

criteria is more difficult. We have chosen to vary the electrode thickness limitation for the PHEV 

and EV calculations. In addition, the EV battery was also calculated in a 2P-96S configuration (2 

cells in parallel) to capture the possibility of smaller capacity cells while maintaining the 100 

micron thickness limit. No design changes were analyzed for the HEVs. Treating each of the 

battery design occurrences as equally probable, the calculated population of each of the 

chemistries becomes a skewed distribution. Capturing the skewed and sometime bi-modal 

distribution in a simple statistical fashion is not straightforward. We suggest the use of a 

distribution parameter, ε, to establish the outer limits of a 95 % confidence interval from the 

point estimate, Po, created from the default values. This parameter is used in an empirical fashion 

in Equation 3 and 4. The factor of 1.05 is used to capture the increase in the mean of the 

population as compared to a spot estimate using the default inputs. The distribution parameters 

used in this study are twice the value of the standard deviation divided by the mean.

 

( ) (3)

 ( ) (4)

The NMC441 and NCA cathodes for PHEV and EV data sets may be captured using a 

distribution parameter of 0.15. The LMO cathode requires distribution parameter of 0.28. The 

larger variation of the LMO cathode results from interaction with the limiting electrode 

thickness. A similar behavior is expected for LFP in energy batteries as this cathode also has a 

low volumetric capacity. The NMC441 and NCA cathodes have a significantly higher 

volumetric capacity and thus are less sensitive to this limitation. Figures 1-3 present the variation 

of the PHEV and EV trials with the suggested confidence bounds highlighted by red lines.
Figure 1. PHEV25 price distributions for NMC441 / Gr batteries. Red lines denote suggested 

upper and lower bounds for confidence interval. Black line represents price calculated from 

default values.

2600 2800 3000 3200 3400 3600 3800 4000 4200 4400

0

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2000 Count

Battery Price to OEM, US$

 NMC441 / Gr

2600 2800 3000 3200 3400 3600 3800 4000 4200 4400

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1000 Count

Battery Price to OEM, US$

 150 micron limit

 100 micron limit

 50 micron limit
Figure 2. PHEV25 price distributions for LMO / Gr batteries. Red lines denote suggested upper 

and lower bounds for confidence interval. Black line represents price calculated from default 

values.

2500 3000 3500 4000 4500 5000

0

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2500 Count

Battery Price to the OEM, US$

 LMO / Gr

2500 3000 3500 4000 4500 5000

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Battery Price to the OEM, US$

 150 micron limit

 100 micron limit

 50 micron limit
Figure 3. EV100 distributions for LMO / Gr and NMC441 / Gr batteries. Red lines denote 

suggested upper and lower bounds for confidence interval. Black line represents price calculated 

from default values.

5000 6000 7000 8000 9000

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Battery Price to OEM, S

 LMO / Gr

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Battery Price to the OEM, US$

 NMC441 / Gr