Subject: Model Documentation for OMEGA 

From: William Charmley/AA/USEPA/US 

To: Chandana_L._Achanta@omb.eop.gov, Amanda_I._Lee@omb.eop.gov 

Cc: Robin Moran/AA/USEPA/US@EPA, Ed Nam/AA/USEPA/US@EPA

Date: 11/07/2011 05:16 PM 

Amanda - 

Here is the web link for OMEGA material; 

http://www.epa.gov/otaq/climate/models.htm 

and here is the model documentation. You can find the discussion on pages 26-30 

OMEGA Model Documentation, 420b10042.pdf 
EPA Optimization Model for Reducing 

Emissions of Greenhouse Gases from 

Automobiles (OMEGA) 

Core Model Version 1.3 Documentation
EPA-420-B-10-042 

October 2010

Assessment and Standards Division 

Office of Transportation and Air Quality 

Office of Air and Radiation 

U.S. Environmental Protection Agency

EPA Optimization Model for Reducing 

Emissions of Greenhouse Gases from 

Automobiles (OMEGA) 

Core Model Version 1.3 Documentation
1

Table of Contents

1. Model Overview ................................................................................................................................. 2

2. Input Files ........................................................................................................................................... 5

A. The Market File: Vehicle Fleet Characterization......................................................................... 5

B. The Technology File: Technology Package Characterization..................................................... 9

C. The Fuels File: Physical Properties and Prices of Fuel and Energy Sources............................. 13

D. The Scenario File: Definition of Regulatory Scenarios and Other Economic Parameters ........ 14

E. The Reference File: Vehicle Survival Rates and Miles Driven................................................. 20

F. Non-editable Input Data............................................................................................................. 21

G. Input Files Currently Distributed with Model ........................................................................... 21

3. Model Operation ............................................................................................................................... 21

A. Determination of Manufacturer-Specific CO2 Emission Standards.......................................... 22

B. Converting Lifetime Refrigerant Emissions to CO2-Equivalent emissions per Mile ............... 22

C. Application of Technology ........................................................................................................ 24

D. Technology Application Ranking Factors ................................................................................. 25

4. Output Files....................................................................................................................................... 31

A. Log of Technology Application Steps – Text Format ............................................................... 32

B. Summary of Cost and Emissions – Excel Format ..................................................................... 36

C. Summary of Technology Pack Distribution – Text format ....................................................... 36

D. VH1 / Final summary of Vehicle Attributes– Excel Format ..................................................... 36

E. VH2 / Stepwise listing of Vehicle Attributes ............................................................................ 36

5. Running the Model ........................................................................................................................... 37

6. Appendix A: Credit Trading Algorithms......................................................................................... 38

7. Appendix B: Calculating Technology Effective Benefits (TEBs) and Cost Effective Benefits

(CEBs)....................................................................................................................................................... 40
2

1. Model Overview

On-road vehicles are the predominant source of greenhouse gas (GHG) emissions from

the transportation sector. Of all on-road vehicles, light-duty vehicles and light-duty trucks

(hereafter referred to as cars and trucks) produce the majority of the GHG emissions. There are

many methods for reducing GHG emissions from cars and trucks due to the myriad technology

options available to improve the efficiency of vehicles. A detailed analysis of the costs and

benefits of various GHG emissions reduction requires a specialized application that optimizes

and accounts for all the promising technologies, going beyond what can be accomplished with

simple spreadsheet tools. Therefore, EPA’s Office of Transportation and Air Quality (OTAQ)

has developed the Optimization Model for reducing Emissions of Greenhouse gases from

Automobiles (hereafter referred to as the “OMEGA” model) to help facilitate the analysis of the

costs and benefits of reducing GHG emissions from cars and trucks.

Broadly speaking, the OMEGA model evaluates the relative cost and effectiveness of

available technologies and applies them to a defined vehicle fleet in order to meet a specified

GHG emission target. Once the target has been met, OMEGA reports out the cost and societal

benefits of doing so. OMEGA models two GHGs; carbon dioxide (CO2) from fuel use and

refrigerant emissions from the air conditioning (A/C) system. The model is written in the C#

programming language, however both inputs to and outputs from the model are provided using

spreadsheet and text files. The spreadsheet output files also facilitate additional manipulation of

the results.

OMEGA is primarily an accounting model. It is not a vehicle simulation model, where

basic information about a vehicle, such as its mass, aerodynamic drag, an engine map, etc. are

used to predict fuel consumption or CO2 emissions over a defined driving cycle. While

OMEGA incorporates functions which generally minimize the cost of meeting a specified CO2

target, it is not an economic simulation model which adjusts vehicle sales in response to the cost

of the technology added to each vehicle. While OMEGA allows vehicle sales to change over

time, the vehicle sales in OMEGA do not dynamically respond to the addition of technology.1

OMEGA can be used to model either a single vehicle model or any number vehicle

models. Vehicles can be those of specific manufacturers or generic fleet-average vehicles.

Because OMEGA is an accounting model, the vehicles can be described using only a relatively

few number of terms. The most important of these terms are the vehicle’s baseline emission

level, the level of CO2 reducing technology already present, and the vehicle’s “type,” which

indicates the technology available for addition to that vehicle. Information required determining

the applicable CO2 emission target for the vehicle must also be provided. This may simply be

vehicle class (car or truck) or it may also include other vehicle attributes, such as footprint.2

GHG emission control technology can be applied individually or in groups, often called

technology “packages.” The user specifies the cost and effectiveness of each technology or

1 OMEGA may be expanded in the future to incorporate such market responses, however, such responses may currently be

addressed “outside of the model” through sequential model runs with market adjustments made between runs.

2 A vehicle’s footprint is the product of its track width and wheelbase, usually specified in terms of square feet.
3

package for a specific “vehicle type,” such as midsize cars with V6 engines or minivans. The

user can limit the application of a specific technology to a specified percentage of each vehicle’s

sales (i.e., a “cap”). The effectiveness, cost, application limits of each technology package can

also vary over time.3 A list of technologies or packages is provided for each vehicle type,

providing the connection to the specific vehicles being modeled.

OMEGA is designed to apply technology in a manner similar to the way that a vehicle

manufacturer might make such decisions. In general, the model considers three factors which

EPA believes are important to the manufacturer: 1) the cost of the technology at the consumer

level, 2) the value which the consumer is likely to place on improved fuel economy and 3) the

degree to which the technology moves the manufacturer towards its CO2 emission target.

Technology can be added to individual vehicles using one of three distinct ranking

approaches. Within a vehicle type, the order of technology packages is set by the user. The

model then applies technology to the vehicle with the lowest Technology Application Ranking

Factor (hereafter referred to as the TARF). OMEGA offers several different options for

calculating TARF values. One TARF equation considers only the cost of the technology and the

value of any reduced fuel consumption considered by the vehicle purchaser. The other two

TARF equations consider these two factors in addition to the mass of GHG emissions reduced

over the life of the vehicle. Fuel prices by calendar year, vehicle survival rates and annual

vehicle miles travelled with age are provided by the user to facilitate these calculations.

For each manufacturer, OMEGA applies technology to vehicles until the sales-weighted

GHG emission average complies with the specified GHG emission standard or until all the

available technologies have been applied. The GHG emission standard can be a flat standard

applicable to all vehicles within a vehicle class (e.g., cars, trucks or both cars and trucks).

Alternatively the GHG standard can also be in the form of a linear or constrained logistic

function, which sets each vehicle’s target as a function of vehicle footprint (vehicle track width

times wheelbase). When the linear form of footprint-based standard is used, the “line” can be

converted to a flat standard for footprints either above or below specified levels. This is referred

to as a piece-wise linear standard.

The GHG emission target can vary over time, but not on an individual model year basis.

One of the fundamental features of the OMEGA model is that it applies technology to a

manufacturer’s fleet over a specified vehicle redesign cycle. OMEGA assumes that a

manufacturer has the capability to redesign any or all of its vehicles within this redesign cycle.

OMEGA does not attempt to determine exactly which vehicles will be redesigned by each

manufacturer in any given model year. Instead, it focuses on a GHG emission goal several

model years in the future, reflecting the manufacturers’ capability to plan several model years in

advance when determining the technical designs of their vehicles. Any need to further restrict

the application of technology can be effected through the caps on the application of technology

to each vehicle type mentioned above.

3

“Learning” is the process whereby the cost of manufacturing a certain item tends to decrease with increased production

volumes or over time due to experience. While OMEGA does not explicitly incorporate “learning” into the technology cost

estimation procedure, the user can currently simulate learning by inputting lower technology costs in each subsequent

redesign cycle based on anticipated production volumes or simply with time.
4

GHG emission standards are specified in terms of CO2 equivalent emissions. These CO2

equivalent emissions can be based on any test procedure. The only requirement is that the base

CO2 emissions specified for each vehicle and the effectiveness of the specified technologies be

based on the same test cycle(s). For example, these emissions can simply be those from the

tailpipe as measured over the current two-cycle CAFE test procedure or they can also include

tailpipe CO2 emissions from air conditioner use, as well as refrigerant emissions from the air

conditioning system. In the case of the latter, the descriptions of vehicle emissions and

technologies must include baseline refrigerant emissions and the effectiveness of each

technology in reducing these emissions. GHG emissions could also be based on the 5-cycle

formulae now used to calculate most vehicles’ fuel economy labels. The user simply needs to

take care to specify CO2 and refrigerant emission and technology effectiveness estimates which

are based on emissions over all five emission tests and as combined according to the five-cycle

formulae. OMEGA bases all of its calculations on a single estimate of test cycle emissions.

Compliance cannot be specified for two distinct test cycles, for example, city and highway test

emissions. Only combined city alone, highway alone or city-highway emissions can be modeled.

Once technology has been added so that every manufacturer meets the specified targets

(or exhausts all of the available technologies), the model produces a variety of output files.

Outputs include specific information about the technology added to each vehicle and the

resulting costs and emissions. Average costs and emissions per vehicle by manufacturer and

industry-wide are also determined for each vehicle class.

EPA has established a webpage for the OMEGA model on the EPA agency website

(http://www.epa.gov/otaq/climate/models.htm). The OMEGA version 1.3 release includes a set

of sample input files; those used to support EPA’s Technical Assessment Report on cars and

light trucks for model years 2017+ are also available on the website. Periodic updates of both

the model and this documentation will be available to be downloaded. Those interested in using

the model are encouraged to periodically check this website for these updates.

The remainder of this document is divided into four sections. The first section describes

the information which can be input to the model. The second section describes the application of

technology in order to comply with the specified standards, what we define as the “core model.”

The third section describes the various output files produced by the model. The fourth section

describes the steps necessary to operate the OMEGA model.
5

2. Input Files

OMEGA is designed to be flexible in a number of ways. Very few numerical values are

hard-coded in the model, and consequently, the model relies heavily on its input files. The

model utilizes five input files: Market, Technology, Fuels, Scenario, and Reference.

All of the input files are Microsoft Excel 2003 spreadsheets and should not be converted

into other formats. The headings of the various types of input data are contained in Row 1 of

each worksheet. It should be noted that these headings cannot be modified by the user. Each

input file also contains two common types of worksheets. One is named “Validation List” and

lists the types of value allowed in each column along with an allowed range of valid values. This

worksheet is typically hidden and can be viewed using the Format/Sheet/Unhide command. The

user can change the range of valid values as desired. The user should not change the type of data

shown as the core model is designed to look for certain types of information in each column and

changing the values entered in an input file does not affect this expectation.

The second common worksheet is named “Errors.” This worksheet contains a button

labeled “Validate Data” which can be selected. When “clicked” this button triggers a macros

which determines if all values in the current workbook fit the expected type of data and fall

within the allowed range of values. Cells that do not fit the criteria are listed and the problem

described. This function can be very useful when developing new input files by reducing the

number of aborted model runs. While useful, please note that some error validation routines are

outdated and may falsely indicate errors.

It is important to note that OMEGA expects all the cells below the last row of required

data to be blank and, more specifically, to have never been written into. If these cells are used

for temporary calculations, the user should go further below to a row which has never been

written into and copy the entire row of blank cells into the row which have been used

temporarily. The error identification process will then recognize these cells as actually being

blank.

A. The Market File: Vehicle Fleet Characterization

The market input file contains much of the required information which describes the

vehicles being modeled. This file consists of four worksheets in addition to the Validation List

and Errors worksheets: Vehicle, Credit, Manufacturer, and Vehicle Type. The “Credit”

worksheet is currently inactive, but is designed to allow the user to input g/mile credits which are

used to alter the stringency of a target. The “Manufacturer” and “Vehicle Type” tabs are lists of

valid values for columns B and D in the Vehicle worksheet. The “Vehicle” worksheet, which is

the substance of the market file, is discussed below.
6

Table 1 shows the various types of data included in the “Vehicle” worksheet.

Table 1 - Input Data in Market Data Worksheet of the Market File*

Column Name Column Name

A Vehicle Index # U Displacement (L)

B Manufacturer V Horsepower

C Model W Max Seating

D Vehicle Type # X Transmission Type

E EPA Vehicle Class Y Drive

F Classic Vehicle Class Z Structure

G Baseline Sales AA Internal Volume

H-O Annual Sales by Cycle AB Primary Fuel Type

P Combined FE (mpg) AC Combined EC (kWh/mi)

Q Tailpipe Co2 (g/mi) AD Refrigerant Type

R Footprint (ft2) AE Refrigerant Lifetime Leakage (g)

S Curb Weight (lb) AF-AY TEB Tech Package 1-20

T No. of Cylinders AZ-BS CEB Tech Package 1-20

* Columns highlighted in gray are not currently used by OMEGA

Column A contains a unique, positive numerical identifier for each vehicle being

modeled. The indices do not need to be in numerical order, just unique and positive. Column B

contains the name of each manufacturer. There are no requirements with respect to the names,

except that the user needs to take care that vehicles intended to be produced by the same

manufacturer are given exactly the same name. Slight differences in spelling or spacing will

cause the model to treat them as separate manufacturers. A list of manufacturers has been

provided in the validation routine to help avoid this issue. Column C contains an alpha-numeric

name for each vehicle. These names do not need to be unique, simply to be as descriptive as the

user desires.

Column D contains the vehicle type number. OMEGA currently allows up to 20 vehicle

types, numbered with integers 1-20. This code provides the connection between the vehicles

listed in the market data worksheet and the available technologies listed in the Technology file.

Column E contains the vehicle class designator. Currently OMEGA can model up to two

vehicle classes: cars indicated with “C” and trucks indicated with “T.” This code provides the

connection between the vehicles listed in the market data worksheet and the standards listed in

the Scenario file. If only one standard applicable to both cars and trucks is being modeled,

vehicles can be labeled as either cars or trucks or both. If both vehicle labels are used,

compliance will still be based on the combination of both vehicle classes, but emissions will be

tracked separately in the model’s outputs. This latter situation is advantageous if cars and trucks

are to have distinct scrappage rates and annual travel estimates.
7

Column F contains the car/truck classification of vehicles under the pre-MY 2011 CAFE

definition. This column is not currently used by the OMEGA model

Column G contains baseline sales. The baseline is the model year prior to the first year

of the first redesign cycle being modeled. Baseline sales are not used in the core model to add

technology to facilitate compliance; instead they are used in order to linearly interpolate annual

vehicle sales during the interim years between the baseline year and the year of the end of the

first redesign cycle. Sales must be positive and may be fractional.

Columns H through O contain sales for the last year of each of up to eight redesign

cycles. Sales must be positive and may be fractional. Currently, the model assumes that a

redesign cycle is five years long. However, the length of the redesign cycle only affects the

interpolation of the model’s outputs between the base year and the end of the first redesign cycle

and between the ends of the subsequent redesign cycles. If a user desires to assume a longer

redesign cycles, this can be easily accommodated, by adjusting the calendar year which

represents the end of each redesign cycle and adjusting the interpolations performed in the

benefits calculation worksheet to include fewer or more calendar years between redesign cycles.

The basic assumption made by the model related to the length of the redesign cycle is quite

simple: that every vehicle sold by the manufacturer is capable of being redesigned within a

redesign cycle (as adjusted by technology application caps of less than 100%).

Sales must be entered for each vehicle, even if the value of sales is zero. Values must

only be entered for redesign cycles actually being modeled. Thus, if only one redesign cycle is

being modeled, then sales must only be entered in Column H. Columns I through O can be blank

in this case. Sales can change in any manner between redesign cycles.

Column P contains each vehicle’s baseline fuel economy value in miles per gallon (mpg).

It is not currently used by the model.

Column Q contains each vehicle’s baseline CO2 emissions in grams per mile (g/mi) over

whichever test cycle or cycles comprise the basis for compliance with the standards described in

the Scenario file. This value should not include the CO2 equivalent emissions related to

refrigerant leakage emissions. Those emissions are described in later columns. The CO2

emissions of Column P could include the CO2 equivalent emissions of GHGs like methane and

nitrous oxide, as long as the effectiveness of the technologies described in the Technology file

and the standards listed in the Scenario file consider these emissions in a consistent manner.

Column R contains each vehicle’s footprint value in square feet. This value is used to

determine each vehicle’s CO2 emission target when the standard is either a constrained logistic

curve or linear function.

Columns S through AA describe several vehicle attributes which are not currently used

by the model. These are included to facilitate future versions of the model which may base

compliance or evaluate model output using one or more of these attributes.
8

Column AB contains a designator for each vehicle’s primary fuel type. Any fuel type is

allowed in the model, so long as its details appear in the Fuels input file. Plug in hybrid vehicles

would be designated by their liquid fuel type, depending on which liquid fuel they used. The

model will consider the electricity used by plug in vehicles based on the value of electricity

consumption per mile described in Column AC, which is described below. Electric vehicles

must be designated with the fuel “EL”.

Column AC contains the vehicle’s baseline electricity consumption in units of kilowatthour per mile (kw-hr/mi). This value is used in calculating the fuel savings component of the

Technology Application Ranking Factor (TARF), in which a comparison must be made between

vehicles and technologies which may consume different types of energy sources, such as liquid

gasoline or diesel, or electricity. Since consumers tend to make decisions on which vehicle to

purchase based on how much the vehicle costs them to drive it, this column helps the model

account for the any energy in the baseline vehicles which is supplied by the electrical grid. This

term only applies to plug in hybrids and battery electric vehicles. In the Fuels input file,

OMEGA allows the user to input a value for the GHG emissions associated with generating a

kw-hr of electricity when determining compliance with the GHG standards. Should a non-zero

value be enetered, the level of electricity usage per mile also affects the vehicle’s baseline CO2

emission level when the model is run.

Column AD designates the type of refrigerant used by the vehicle. This designator must

match one of the types of refrigerant listed on the Refrigerant worksheet of the Reference file

described further below. The primary purpose of this designation is to specify the global

warming potential (GWP) of the refrigerant so that mass emissions of refrigerant leakage can be

converted to their CO2 equivalent emissions. OMEGA allows editable refrigerant data in the

Reference file, such that the user can edit or add additional refrigerant names and GWPs.

Column AE of the market file designates the lifetime leakage of the refrigerant, which the

model uses to calculate the leakage rate in CO2 equivalents. EPA chose to input the lifetime

leakage instead of the leakage rate because the lifetime leakage is easier to quantify. The yearly

distribution of leakage is hard-coded, and OMEGA uses it to convert the refrigerant leakage to

grams of CO2 equivalents per mile.

Columns AF through BS are used to track technology that may be present in the baseline

or reference case. This data is necessary to prevent the model from double counting technology

costs and GHG improvements. Columns AF through AY represent the fraction of the

technology package effectiveness for the different vehicles that is present in the reference case;

for example, a value of 35% for technology package 1 means that 35% of the effectiveness of

technology package 1 on that vehicle type is already present in the baseline vehicle. Similarly,

columns AZ through BS represent the fraction of the technology packages’ cost that is reflected

in the baseline. Likewise, a value of 75% in any of these columns means that 75% of the

technology package’s cost on the particular vehicle has been included in the reference case. A

method for calculating these values is described in Appendix A.
9

B. The Technology File: Technology Package Characterization

i. Background and Major Changes

Since there is large number of technologies which reduce CO2 emissions and a wide array of

different vehicle systems to which they apply, the manufacturers’ design and production processes play

a major role in determining the technology cost associated with lowering fleet-wide CO2 emissions.

Vehicle manufacturers typically develop several unique models based on a limited number of shared

vehicle platforms, allowing for efficient use of design and manufacturing resources. The platform

typically consists of common vehicle architecture and structural components. Given the very large

investment put into designing and producing each vehicle model, manufacturers typically plan on a

major redesign for the models approximately every 5 years. At the redesign stage, the manufacturer will

upgrade or add all of the technology and make all of the other changes needed in order that the vehicle

model will meet the manufacturer’s plans for the next several years. This includes meeting all of the

emissions and other requirements that would apply during the years before the next major redesign of

the vehicle.

This redesign often involves a package of changes, designed to work together to meet the various

requirements and plans for the model for several model years after the redesign. This often involves

significant engineering, development, manufacturing, and marketing resources to create a new product

with multiple new features. In order to leverage this significant upfront investment, manufacturers plan

vehicle redesigns with several model years’ of production in mind. Vehicle models are not completely

static between redesigns as limited changes are often incorporated for each model year. This interim

process is called a refresh of the vehicle and generally does not allow for major technology changes

although more minor ones can be done (e.g., aerodynamic improvements, valve timing improvements).

More major technology upgrades that affect multiple systems of the vehicle thus occur at the vehicle

redesign stage and not in the time period between redesigns.

There are a wide variety of emissions control technologies which involve several different

vehicle systems. Many can involve major changes to the vehicle, such as changes to the engine block

and heads, or redesign of the transmission and its packaging in the vehicle. This calls for tying the

incorporation of the emissions control technology into the periodic redesign process. This approach

reflects manufacturer capability to develop appropriate packages of technology upgrades that combine

technologies in ways that work together and fit with the overall goals of the redesign. It also reflects the

reality that manufacturers fit the process of upgrading emissions control technology into its multi-year

planning process, and it avoids the large increase in resources and costs that would occur if technology

had to be added outside of the redesign process.

The technology input file defines the technology packages which the model can add to

the vehicle fleet. For each vehicle type, the user must add a separate row for each technology

package in the order of how OMEGA should add them to that specific vehicle type. This

approach puts considerable onus on the user to develop a reasonable sequence of technologies.

However, the model also produces output information which can help the user determine if a

particular technology package might be “out of order”. The package approach also simplifies the

model’s calculations and enables synergistic effects among technology packages to be included

to the fullest degree possible.
10

OMEGA version 1.3 contains important changes in the form and function of the technology file.

Previous versions of OMEGA tracked CO2 emissions at the vehicle platform level. OMEGA 1.3 tracks

CO2 emissions by fuel within each vehicle platform. As a result, a vehicle platform can be composed of

sub-vehicles, each with its own fuel, CO2 emission rate and electricity consumption rate. To facilitate

this tracking, every technology package is now encoded with its operating fuel, as well as the fuel of the

vehicles to which it applies. In combination with technology specific caps,4this allows a vehicle

platform to be split so that subsequent technologies can be applied to the specific subsets of the vehicle.

Thus, for example, a certain fraction of a vehicle’s sales can be equipped with a diesel engine.

Subsequent diesel-based technologies can then be applied more simply and directly to this subset of

sales. The model keeps track of the sales and CO2 emission rates of both the gasoline and diesel

versions of the vehicle.

This model feature simplifies the ability to apply technology packages which have caps of less

than 100%. By effectively treating the cap limited packages as including a change in fuels, we simplify

the addition of subsequent technologies to both the subset of vehicle sales with this technology and that

without it. For example, if a certain technology is added to 50% of the sales of those vehicles operating

on gasoline, it may be possible to hybridize both the vehicles with and without the technology, with

differing costs and effectiveness. It is possible to determine the overall impact of hybridizing the nonimproved vehicles first and then the improved vehicles and developing the appropriate OMEGA model

inputs which accomplish both of these steps of technology addition. However, it may be easier to

separate the improved technology vehicles from those without this technology by changing the former

vehicles’ fuel to something other than the vehicle’s baseline fuel (e.g., “E10”) and make the fuel

properties of E10 exactly the same as those for gasoline.

Consider the case of a gasoline vehicle with CO2 emissions of 300 g/mile (described in Table 1).

In this example, there are two sequentially applied diesel packages which are intended to be applied to

the same 50% of the fleet. As shown in Table 1, the first diesel package is applied to 50% of the

gasoline fueled portion of this vehicle’s sales (which is 50% of 100%, since no previous technology

packages have changed fuel type). The second diesel package is applied to 100% of the diesel fueled

portion of this vehicle’s sales, since 50% of the vehicle’s sales are diesel at that point in the technology

application process. The 10% CO2 emission reduction of the second diesel package is only applied to

the 50% of this vehicle’s sales which are already diesel fueled. Thus, OMEGA version 1.3 now more

accurately attributes the reductions to the appropriate subset of sales within the vehicle platform without

the user having to adjust the effectiveness of the second diesel package to account for the model

applying the package to all of the vehicle’s sales.

4

“Cap” is a shorthand term for the maximum penetration rates for certain technologies which define the various technology

paths.
11

Table 1: Tracking CO2

Step Technology

Apply Fuel

Package

Fuel

Maximum

Penetration

Limit

Reduction OMEGA 1.0.2

Applied to

average vehicle.

OMEGA 1.3

Applied to a specific

fuel within a platform.

CO2 Avg CO2

Avg

CO2

Gas

CO2

Diesel

300 300 300 N/A

1 Gasoline Diesel 50% 10% 285 285 300 270

2 Diesel Diesel 100% 10% 270.75 271.5 300 243

ii. Technology File Format

There are four tabs which contain technology packages, each tab keyed to a particular

redesign cycle. Similar to the Market file, the Technology file contains an additional tab entitled

“errors”, which is used for validation purposes.

Table 2, below describes the data in the each redesign cycle tab.

Table 2 - Input Data in Each Worksheet of the Technology File

Column(s) Contents

A Vehicle type number

B Technology package number

C Technology package name

D Abbreviation

E Market penetration caps

F Incremental tailpipe CO2 emission control effectiveness

G Incremental Cost

H Primary fuel of the new technology package

I The fuel to which the technology package applies

J Electrical Conversion %

K Refrigerant emission control effectiveness

L Refrigerant type (NC = no change from previous step)

The data in this file can be categorized in four ways: 1) Information which describes the

individual packages, such as name and vehicle type; 2) Parameters the model uses to calculate

CO2 improvement, such as effectiveness and market penetration cap (the latter being the cap of

sales for each vehicle model of a vehicle type that can receive a technology package); 3)

technology costs 4) Properties of the technology package, such as refrigerant type, fuel type, and

applicable fuel.

Each tab in the Technology input file contains a user-defined list of technology packages

for all of the different vehicle types. This list is organized in ascending order by the vehicle type

to which it applied (Column A), and then by ascending technology package (Column B). The

user need not use the full 20 lines for each vehicle type, but can stop after the last technology

package has been listed. There cannot be any blank lines between technology packages or

vehicle types. The user must record the technology packages within each vehicle type from top
12

to bottom in the order of how the model should add them to the particular vehicle. In typical

OMEGA usage, each package is replaced by the subsequent technology package, so it is critical

that packages improve in aggregate CO2 reduction. The user records a description of the

technology package in Column C, and an abbreviation, if desired, in Column D. The

abbreviation of the last technology package added is displayed in the output files.

Column E contains the maximum market penetration caps for the technology packages.

When technology is sufficiently new, or the leadtime available prior to the end of the redesign

cycle is such that it is not reasonable to project that it could be applied to all vehicle models that

are of the same specific vehicle type, for example, all minivans, the user can limit its application

to minivans through the use of a market cap of less than 100%. When a technology package is

applied to fewer than 100% of the sales of a vehicle model due to the market cap and the

technology does not involve a new fuel, the effectiveness of the technology package is simply

reduced proportionately to reflect the total net effectiveness of applying that technology package

to that vehicle’s sales. OMEGA does not create a new vehicle with the technology package and

retain the previous vehicle which did not receive the technology package, splitting sales between

the old and new vehicles. If subsequent technology packages can be applied to the vehicle, the

user should consider whether in reality the new technology would likely be applied to those

vehicles which received the previous technology or those which did not, or a combination of the

two. The effectiveness of adding the subsequent technology may depend on which vehicles are

receiving it.

Column F contains the Average Incremental Effectiveness (AIE) of the technology

package over the previous package (or over the baseline in the case of technology package 1).

For example, a value of 7.0% in the AIE column would denote a 7.0% tailpipe CO2

improvement beyond any CO2 improvements already realized. (“Tailpipe CO2” refers to the

CO2 emitted over the test cycle assumed to be used to determine compliance- which relates it to

vehicle efficiency.) This value of 7% would include any synergistic effects that components of

the technology package may have with technologies that are remaining on the vehicle type.

Column G contains the incremental technology package cost, which represents the cost

beyond the cost of other technology packages that the model may have added in a previous step.

In the specific case of technology package 1 on each vehicle type, this will be the package cost

over the baseline, since no other technology has been added prior to technology package 1.

Column H and I respectively contain the fuel used by the vehicle after addition of the

technology package, and the fuel of the vehicles to which the technology package applies. These

fuel abbreviations must also appear in the Fuels input file, and are case specific.

Column J contains the electrical conversion percentage. Each technology package potentially

has an “electricity conversion percentage”, which refers to the increase in the grid-supplied electrical

energy consumed by the electric drivetrain relative to reduction in the consumption of energy from

liquid fuel. More specifically, the electricity conversion percentage is the ratio of the increase in gridsupplied electrical energy used by the vehicle (in Btu per mile) divided by the reduction in liquid fuel

use (also in Btu per mile), multiplied by 100%. Electricity is a highly refined form of energy which can

be used quite efficiently to create kinetic energy. Thus, electric motors are much more efficient than
13

liquid fuel engines. Consequently, the electric consumption percentages input in the Technology File

for plug-in hybrid vehicles and battery electric vehicles are generally well below 100%. It may be

possible that this percentage could exceed 100% under certain circumstances, for example when one

type of plug-in vehicle is being converted into another plug-in vehicle and electricity consumption per

mile is increasing due to larger and heavier batteries, etc.

Column K contains the refrigerant effectiveness and is based on the fraction reduction in

direct refrigerant leakage emissions and is separate from tailpipe CO2. Based on a change in

refrigerant included as part of a technology package, noted in Column V, the model will convert

the refrigerant emissions to grams per mile of CO2 equivalent emissions, and add the resultant to

the tailpipe CO2 emissions for the vehicle compliance calculation. A value of “NC” in column

denotes that there is “No Change” in refrigerant from the previous step, or in the case of

technology package 1, no change from the baseline refrigerant.

C. The Fuels File: Physical Properties and Prices of Fuel and Energy Sources

The Fuels input file contains data relevant to liquid fuel and electricity, including energy,

mass, and carbon density, and annual price forecasts for up to 20 years. Similar to the other

input files, the fuels input file is comprised of two worksheets: A worksheet containing data used

by the model and an additional worksheet designed to ensure that the data is within allowable

ranges. There is a third hidden worksheet which contains the range of allowable values. Table 3

describes the layout and content of the “fuel” tab in the fuels input file.

Table 3 - Input Data in Fuel Worksheet of the Fuels File

Column(s) Contents

A Fuel Type

B Energy Density

C* Mass Density*

D Carbon Density

E CAFE Equivalency Factor

F - Y Fuel Price ($/gal)

*The columns highlighted in gray are not used

by the model’s calculations.

Column A describes the fuel type. This value can be any descriptor desired, but EPA

typically specifies gasoline as “G”, diesel fuel as “D,” etcetera. The one exception is that

electricity must be designated as “EL”, in order for the model to connect inputs like the

electricity conversion factor with this fuel. Please note that the fuel names in this file must

match the fuels in the technology and market files at a case specific level.

Column B contains the energy density of the energy source. For the liquid fuels, this

factor has the units of BTU per gallon. Electricity has the units of BTU per kilowatt-hour, which

is essentially a fixed conversion factor. This factor is used when a technology package increases
14

the ability of the vehicle to operate on grid-supplied electricity. It is used in conjunction with the

electrical conversion factors listed in the technology file.

Column C contains the mass density of the liquid fuels in terms of grams per gallon, and

is not used in the model.

Column D describes the carbon density of the energy source, and is used in the

calculation of the fuel savings component of the TARF5as well as in the compliance

calculations. Carbon density is specified in units of grams of carbon per gram per the unit of fuel

which is associated with the fuel price. For liquid fuels, this is grams of carbon per gallon and

for electricity this is grams of carbon per kWh. Since EPA’s current GHG regulations do not

consider the upstream CO2 emissions associated with electricity production, EPA typically runs

the OMEGA model with a zero carbon density for electricity. If a user wishes to incorporate the

upstream emissions of the carbon content of CO2 emissions in the TARF and compliance

calculations, they could enter a positive value in this cell. Please note that these emission values

are in terms of grams carbon, not grams carbon dioxide.

Column E contains the CAFE equivalency factor used in the calculation of manufacturer

fines. The ability to pay fines is not currently active in the model, and so this column does not

affect the technology ranking calculations.

Columns F through Y contain the fuel price either in US Dollars per gallon or US Dollars

per kWh for liquid fuel and electricity, respectively, for 20 calendar years. Fuel prices are to be

input in ascending order by year and are used when calculating the fuel savings over the payback

period in the TARF. The first calendar year listed should be that of the baseline year plus one.

D. The Scenario File: Definition of Regulatory Scenarios and Other Economic

Parameters

The Scenario input file contains data specifying the number and types of model runs.

The Scenarios tab acts as a directory for different model runs, where the user can create an entry

for any number of runs that the model can perform in succession. In the Scenarios tab, the user

must specify the base year, type of compliance target (CO2 or MPG), type of compliance

function, the number of redesign cycles, and the names of the other input files that describe the

vehicle fleet, technology packages, and fuel properties. At present, the model is limited to a CO2

equivalent standard. The elements in the “Scenarios” tab described above are summarized in the

following table:

5 TARFS are discussed on page 29.
15

Table 4 - Input Data in Scenarios Worksheet of the Scenario File

Column(s) Contents

A Scenario ID number

B Scenario name

C Baseline year

D Target Type

E TARF Option

F GHG Target Function Type

G Fleet type (single or combined)

H Number of redesgn cycles

I Fleet trading limit

J Market input file indicator

K Technology input file indicator

L Fuels input file indicator

M Reference input file indicator

*The columns highlighted in gray are not used by the model’s calculations.

Column A in the Scenarios tab indicates the ID number of the model run. From a single

scenario file, the model can run as many different scenarios as the user desires. In Column B,

the user can give each scenario a name, which the model will use in naming the output directory

and files for each scenario. Column C denotes the baseline year for each scenario. This is the

year prior to the first year of the first redesign cycle. Column D indicates the type of standard or

target (CO2 or MPG) the model will use for compliance, and is not currently active in the model.

Column E is where the user designates which of the three Technology Application

Ranking Factors (TARFs) the model should use. The model uses the TARF equations to

determine the order of technology package application on the different vehiclemodels. There are

three TARF equations which are summarized below and are described in detail on page 25.

1. Effective Cost = [Technology package cost minus fuel savings over the payback

period].

2. Cost Effectiveness-Society = [Effective Cost] divided by discounted lifetime CO2

emissions.

3. Cost Effectiveness -Manufacturer = [Effective Cost] Divided by lifetime CO2

emissions.

Column F indicates the user’s preference for type of function for the industry-wide GHG

level. There are three options for compliance targets: 1 = universal; 2 = piecewise linear; 3 =

constrained logistic.

i. Universal Target

The universal target option is a numerical designation which the manufacturers’ average

fleet CO2 cannot exceed. For a universal standard (which could apply to cars, trucks or cars and

trucks combined), only the value listed in the first of each set of the four coefficients is used

(Labeled “A” in the header row of the Target worksheet).
16

ii. Piecewise Linear Target

The attribute-based linear target function is described by up to four coefficients and has

the following piecewise linear mathematical form:

Where

A: Minimum level of CO2 target

B: Maximum level of CO2 target

FPmin: Footprint value where CO2 target

reaches minimum value (i.e.,

intersection of lower asymptote with

slope)

FPmax: Footprint value where CO2

target reaches maximum value (i.e.,

intersection of upper asymptote with

slope)

FP: Vehicle footprint (square feet)

When inputting a piece-wise linear target into the Target worksheet, FPmin and FPmax should be

respectively entered in the C and D coefficient columns.

Example of Footprint-Based CO2 Piecewise Linear Target Function

Footprint (ft2)

CO2 (g/mi)















≥

<≤+−

−

−

<

=

max

min min max

max min

min

;

[ (*] ;)

;

FPFPB

FPFPFPAFPFP

FPFP

AB

FPFPA

y
17

iii. Logistic Curve Target

The footprint-based logistic curve (shown below) is described by four coefficients and has the

mathematical form described below.

( )





















+

−+= −

−

D

CFP

D

CFP

e

e

ABAT

1

Where A, B, and FP have the same definitions

as above

C: Footprint value at equation inflexion

point (i.e., midpoint)

D: The term which controls the rate at

which the CO2 target moves from the

minimum to maximum values. High

values of D cause the curve to move

slowly (in terms of footprint) from the

minimum to maximum target (i.e., a

sort of “inverse slope”)

FP: Vehicle footprint

Column G of the Scenarios tab in the Scenario input file is entitled “fleet type.” There

are two acceptable values for cells in this column: 1 = 1 fleet and 2 = 2 fleets. If 1 is chosen, the

standard defined in the “Standards” tab will be taken from the “Car” standard section and applied

to all of the vehicles listed in the market file, whereas if 2 is chosen, the standards will be defined

by both the “Car” and “Truck” standard sections and applied to cars and trucks separately.

Column H contains the number of redesign cycles the model considers in a given run.

There can be as few as one redesign cycle and as many as eight. The model allows any length to

be assumed for a redesign cycle, as long as the redesign cycle length is the same for all vehicles.

The inputs should be designed appropriately to reflect the user’s assumptions, with the

appropriate modifications made to the benefits post-processor.

Example of Footprint-Based CO2 Logistic Target Function

Footprint (ft2)

CO2 (g/mi)
18

Column I contains the limit (in units of g/mi CO2) imposed on the trading of compliance

credits between cars and trucks. These algorithms are more fully described in an appendix on

page 38.

Columns J-M indicate which files the model will access for the different runs. Column J

contains the name of the market input file; column K contains the name of the technology input

file; column L contains the name of the fuels input file; column M contains the name of the

References file. All files must be in the same directory as the scenario file.

The Scenario input file also contains the economic parameters that the model uses to

calculate the Technology Application Ranking Factors (TARFs). Such economic data is

contained in the “Economics” tab and is organized as illustrated in the following table:

Table 5 - Input Data Contained in the Economics Worksheet of the Scenario File

Column(s) Contents

A Scenario ID number

B Discount rate

C Payback period

D CAFE fine

E Gap

F Threshold cost

G CO2 value increase rate

Column A contains the ID number for the model run, and it must be identical to that in

Column A of the Scenarios tab.

Column B contains the discount rate for future dollar values. The model uses the

discount rate in the TARF calculations when calculating the fuel savings over the payback

period.

Column C designates the payback period over which consumers are believed to consider

fuel savings when purchasing a vehicle.

Column D indicates the value of a fine for non-compliance. Since the Clean Air Act does

not allow EPA to charge a monetary fine for non-compliance, EPA typically records $0 into this

column. The OMEGA model does not currently allow fine payments and a zero should be

entered into this column.

Column E contains the Gap, which is the percentage difference between onroad fuel

economy and test cycle fuel economy. This value is important because compliance is based on

test cycle CO2, whereas the true impact on climate is based on the on-road CO2 and consumer

fuel savings are based on onroad fuel economy. The model uses this difference to convert test

cycle CO2 emissions to onroad fuel economy and calculate fuel savings in the core model’s

TARF equations, as described further on page 25 below.
19

Column F contains the value for the “threshold cost”. This value determines whether the model

will accept some degree of over-compliance when it determines the degree of technology addition

needed for a manufacturer to meet a standard, or if it will reduce the addition of technology so that a

manufacturer just barely complies. Specifically, if the per vehicle cost of the last technology added by

the model in order to reach compliance exceeds the threshold value, the model reduces the percentage of

that vehicle’s sales which receives that technology to just the degree needed to enable compliance. If

the per vehicle cost of the last technology added by the model in order to enable compliance is below the

threshold value, the model leaves the percentage of vehicle sales receiving that technology at the

technology penetration cap for that technology.6

Column G represents the rate of increase in the real value of CO2 emission reductions over time.

This value is included since some studies have predicted that the real value of CO2 emission reductions

will increase over time as the impact of global climate change increase. The units of this term are

percent per annum. This value is used in the Cost Effectiveness-Society TARF described below.

Columns H and I contain the statutory lifetime miles driven by cars and trucks. These values are

used to calculate the credit trading ratio between cars and trucks. Because real VMT tends to grow over

time, but the VMT used in the credit trading equation is determined by regulation, this value can differ

from the VMT in the reference file (described below). For example, the lifetime VMTs per vehicle for

cars and trucks provided in EPA’s current GHG regulations are 195,264 and 225,865, respectively.

The Target tab of the Scenario file contains the parameters describing the GHG compliance targets

required by the universal, segmented linear and constrained logistic functions described above. The first

32 columns describe the car standards for up to eight redesign cycles, if “2” fleets are selected in column

G of the Scenarios worksheet. If “1” fleet is selected, then the standards described in Columns A

through AF apply to both cars and trucks. Similarly, the next 32 columns (AG through BL) describe the

truck standards for up to eight redesign cycles if “1” fleet is selected. This second set of values is not

used if “1” fleet is selected. This is described in Table 6.

6 This flexibility was included in the model to reflect the different ways in which manufacturers apply various technologies.

For example, when adding basic engine technology such as variable valve timing, the manufacturer would generally convert

the entire production volume of a specific engine to this technology. The production of two otherwise identical engines, one

with the technology and one without, would likely not be maintained. However, with more extreme technologies, such as

dieselization or hybridization, the manufacturer often maintains two versions of the vehicle, one with and one without these

technologies. By setting the threshold in between the costs of these two examples, the model will reflect these two

approaches to technology application on the part of a manufacturer.
20

Table 6 - Input Data Contained in the Target Worksheet of the Scenario File

Column(s) Contents Vehicle Class

A - D Coefficients describing the CO2 Standard for Design Cycle 1

Car If “2” fleets

selected

Car and Truck if “1”

fleet selected

E – H Coefficients describing the CO2 Standard for Design Cycle 2

I – L Coefficients describing the CO2 Standard for Design Cycle 3

M – P Coefficients describing the CO2 Standard for Design Cycle 4

Q – T Coefficients describing the CO2 Standard for Design Cycle 5

U – X Coefficients describing the CO2 Standard for Design Cycle 6

Y - AB Coefficients describing the CO2 Standard for Design Cycle 7

AC - AF Coefficients describing the CO2 Standard for Design Cycle 8

AG – AJ Coefficients describing the CO2 Standard for Design Cycle 1

Truck If “2” fleets

selected

Not used if “1” fleet

selected

AK – AN Coefficients describing the CO2 Standard for Design Cycle 2

AO – AR Coefficients describing the CO2 Standard for Design Cycle 3

AS – AV Coefficients describing the CO2 Standard for Design Cycle 4

AW – AZ Coefficients describing the CO2 Standard for Design Cycle 5

BA – BD Coefficients describing the CO2 Standard for Design Cycle 6

BE – BH Coefficients describing the CO2 Standard for Design Cycle 7

BI - BL Coefficients describing the CO2 Standard for Design Cycle 8

As indicated, each CO2 standard is described by up to four coefficients. For a universal standard,

only the value listed in the first of each set of four columns is used (Labeled “A” in the header row of

the Target worksheet). All four columns are required to describe either the segmented linear or

constrained logistic functions described above.

E. The Reference File: Vehicle Survival Rates and Miles Driven

The Reference file contains car and truck annual miles driven and survival rates by year. These

estimates are used in the cost effective TARF (1) and the cost effectiveness-society TARF (2)

calculations when determining fuel savings over the payback period and in the cost effectivenessmanufacturer TARF (3) when determining the lifetime CO2 reduction. TARF 3 uses the statutory VMT

values in the scenario file.

The vehicle survival and VMT estimates are inputted in the tab entitled Vehicle Age. Column A

in this tab contains the vehicle age in years. Columns B and C contain the percentage of cars and trucks

still projected to be on the road of the specified ages, respectively. Columns D and E contain the

average miles driven annually (per vehicle) for cars and trucks, respectively, for vehicles of the specified

ages.

The Refrigerant tab contains data which is only used if refrigerant emissions are included

in the market file. A dynamic list of acceptable refrigerants can be created, and accompanied

with their respective global warming potential. Column A is the refrigerant name, while column

B is the GWP.
21

F. Non-editable Input Data

The only values “hard-coded” into the model which are potentially used in the

application of technology to vehicles are the distribution of leakage rate by vehicle age.

The following table describes the refrigerant leakage rates which are currently hard-coded.

Table 7 – Refrigerant leakage rates

Refrigerant Leakage Fractions

Year % of Total Lifetime

Leakage g/year

Year % of Total Lifetime

Leakage g/year

1 1.1% 19 3.3%

2 1.5% 20 2.7%

3 2.0% 21 2.3%

4 2.4% 22 1.8%

5 2.9% 23 1.4%

6 3.3% 24 1.1%

7 3.6% 25 0.9%

8 4.4% 26 0.7%

9 5.5% 27 0.0%

10 6.9% 28 0.0%

11 8.5% 29 0.0%

12 8.1% 30 0.0%

13 7.5% 31 0.0%

14 7.0% 32 0.0%

15 6.5% 33 0.0%

16 6.0% 34 0.0%

17 4.8% 35 0.0%

18 3.9% 36 0.0%

EPA intends to make this data editable in a future version.

G. Input Files Currently Distributed with Model

The sample files bundled with the installation file contain example or “dummy” data and

are only indicative of realistic values. The files from both the Interim Joint Technical

Assessment Report as well as the 2012-2016 Joint Final rulemaking are available on the EPA

OMEGA webpage.

3. Model Operation

The operation of the “core” model can be described in three steps. The first step

determines the effective CO2 emission standard for each manufacturer and vehicle class. The

second step converts the baseline lifetime refrigerant emissions specified for each vehicle into its

g/mi CO2 equivalent and adds this to the baseline tailpipe CO2 emissions for each vehicle. The
22

third step applies technology until this standard is met or all available technology has been

applied. These steps are described below.

A. Determination of Manufacturer-Specific CO2 Emission Standards

As described above, three types of standards can be evaluated by OMEGA: universal or

flat, piecewise linear, and constrained logistic. Determining each manufacturer’s effective

standard under a flat standard is simple; it equals the flat standard. The second two types of

standards require sales-weighting the CO2 target applicable to each specific vehicle model

produced by that manufacturer. Under these standards, the model calculates each vehicle’s CO2

target by plugging the vehicle’s footprint into the formula describing the standard. Each of the

vehicle-specific targets are then multiplied by the vehicle’s sales in that redesign cycle and the

statutory lifetime VMT for that vehicle class and summed across all vehicles. The sum is then

divided by the sum of the product of vehicle sales by that manufacturer in that redesign cycle and

the lifetime VMT for each vehicle. The result is a sales and lifetime VMT weighted corporate

average CO2 target for each manufacturer’s relevant set of vehicles (i.e., cars, trucks, or cars and

trucks combined).

If one fleet is specified, then the model only performs this calculation once and includes

both cars and trucks in the calculation. If separate standards are specified for cars and trucks,

then the model performs this task twice for each manufacturer for each redesign cycle being

modeled: once for cars and once for trucks. If the same standard is specified for both cars and

trucks and two compliance fleets are specified in the Scenario file, then two separate calculations

are still performed. The result is still two distinct CO2 emission targets, one for cars and one for

trucks.

If a trading limit of “0” is specified, then this stage of the model operation is complete. If

a non-zero trading limit is specified, an additional step is required to ensure that this trading limit

is not exceeded, as described on page 38. Conceptually, we assume that a manufacturer would

prefer to evaluate the application of technology to both its cars and trucks at the same time in

order optimize compliance (via the TARF) over the widest set of vehicles. At the same time, the

manufacturer is assumed to want to avoid generating credits from one of its two vehicle class

fleets which cannot be used by the other fleet due to the limit on trading, since it is incurring cost

with no benefit.

B. Converting Lifetime Refrigerant Emissions to CO2-Equivalent emissions per Mile

Refrigerant leakage emissions are input to the model in terms of lifetime emissions, while

Refrigerant leakage increases with wear and tear of the A/C system. Leakage emissions also

occur during accidents, repairs and vehicle scrappage. Refrigerant emissions per year increase

significantly with age. Since annual mileage decreases with age in general, refrigerant emissions

per mile increase even more significantly with age than emissions per year. In contrast, CO2

tailpipe emissions are input in terms of g/mi and are generally assumed to be constant with age.

Thus, some processing is needed to be the two types of emissions on a comparable basis.
23

OMEGA converts lifetime refrigerant emissions to their equivalent value in terms of CO2

emissions per mile (RCO2) considering the change in societal value of CO2 emissions over time.

The goal is to estimate a level of CO2 emissions per mile, which, if constant over the vehicle’s

life, like tailpipe CO2 emissions are generally assumed to be, would produce the same societal

value of CO2 emissions as the distribution of refrigerant emissions over the life of the vehicle.

This equality is shown in the following equation:

Value of Equivalent Lifetime CO2 Tailpipe Emissions =

Value of Lifetime Refrigerant Emissions

*[*2 *]2 [RefLeakag *e ]2

36

1

36

1

RCO VMT ValueofCO GWP ValueofCO i

i

i

i

i

∑ i ∑ = =

=

Where:

VMTi = the annual miles travelled for the relevant class of vehicle at age i, (i.g., VMTi = Survival Fraction

for a vehicle of age i times the annual vehicle miles driven for a vehicle of age i as input in the Reference

file),

ValueofCO2i = the societal value of CO2 emissions in the calendar year when the vehicle is at age i,

RefLeakagei = the annual rate of refrigerant emissions when the vehicle is at age i, and GWP is the global

warming potential of the refrigerant relative to CO2.

The value of CO2 in a particular year can be described as its base value divided by one

plus the applicable discount rate raised to the power of the age of the vehicle. In this case, the

applicable discount rate is the societal discount rate less the rate of increase in the real value of

CO2 emissions. Since the normal discounting equation assumes that the relevant activity (e.g.,

payment) occurs at the end of the year and emissions occur throughout the year, we multiply by

one plus half of the applicable annual discount rate. The resulting equation is described as

follows:

( ) =

−+

−

+

∑ ×

=

]

1

2

1

*[*)(2 2 *

36

1

/

i

i

i

IRDR

IRDR

RCO mig VMT BaseValueofCO

( ) ]1

2

1

* *e[RefLeakag 2*

36

1

i

i

i

IRDR

IRDR

GWP BaseValueofCO

−+

−

+

∑ ×

=

This equation can be rearranged to solve for the level of CO2 equivalent emissions per mile as

shown in the next equation. (Note that the societal value of CO2 in the base year falls out of the

equation.)
24

( )

( ) ∑

∑

=

=

























−+

−

+

×

×

























−+

−

+

×

=

36

1

36

1

1

2

1

1

2

1

/ )(2

i

i

i

i

i

i

IRDR

IRDR

VMT

GWP

IRDR

IRDR

LeakRate

RCO mig

There are other approaches to converting lifetime refrigerant emissions to their g/mi

equivalent level. Future versions of OMEGA may provide the user with several approaches

from which to select. One approach would be to simply allow the user to specify a baseline

value for g/mi CO2 equivalent refrigerant emissions in the Market file. This way, the user could

use whatever approach was deemed appropriate to estimate this value. Another approach would

be the same as the above, except to base the equivalency on physical emissions and remove the

factors involving discounting. At the present time, the only use of the rate of increase in the

societal value of CO2 emission reductions is in this calculation and as an input to the benefits

calculation spreadsheet. Therefore, if the user desires to perform this equivalency using physical

emissions, they should set the rate of increase in the societal value CO2 emission reductions to

equal the overall societal discount rate being specified. This will cause all of the discount factors

in the above equation to be equal to 1.0. Then, if the user desires to use a different rate of

increase in the societal value CO2 emission reductions in the estimation of benefits, they can

change this value in the benefits calculation spreadsheet.

C. Application of Technology

The portion of the model which applies technology can most easily be described as the multiple

application of three logical steps. The first step is to determine the vehicle in the “best” position to

receive the next technological improvement to enable the manufacturer to meet the specified CO2

emission standard. The second step is to apply this technology, reduce the vehicle’s emissions

accordingly and add the cost of this technology to the manufacturer’s total cost for this redesign cycle.

The third step is to assess the compliance situation and act accordingly. If the standard applies to cars

only, trucks only, cars and trucks combined with a single standard, or cars and trucks combined with two

distinct standards and a zero trading limit (i.e., no trading), the model will:

1) recalculate the manufacturer’s sales and VMT-weighted emissions,

2) compare this new corporate average emission level to the manufacturer’s standard,

3) if the manufacturer is now below the standard, determine if the cost of the last technology is

above or below the threshold cost specified,

3.i) if the cost is below the threshold, the evaluation of this manufacturer is over and the

model moves onto the next manufacturer,
25

3.ii) if the cost is above the threshold, the percentage of sales which receive the

technology is decreased until the standard is just met; the evaluation of this manufacturer

is over and the model moves onto the next manufacturer,

4) if the manufacturer is still above the standard, the model goes back to steps 1 and 2 above and

applies another technology package to further reduce emissions. If no more technology packages

are available, the model moves onto the next manufacturer.

If a non-zero trading limit is specified, the model will follow the largely the same procedure, but

additionally consider the algorithms discussed on page 38.

Once all manufacturers are in compliance or have exhausted the technology available for their

vehicles, the model moves to the next redesign cycle and repeats the above sequence of steps. The

evaluation of the second and any subsequent redesign cycles starts from scratch in that every vehicle

begins with only those technologies present in the Market file. In other words, the model does not start

with the technology added in previous redesign cycles. The assumption behind this aspect of the model

is that manufacturers have the flexibility to reevaluate technology each time a vehicle is being

redesigned. This could involve the evaluation of a technology which was not available in the prior

redesign cycle or a technology which had a maximum penetration cap of less than 100%. Of course,

starting the analysis over each redesign cycle could lead to situations where a manufacturer is projected

to utilize several very different technologies for most of their vehicles in each of several redesign cycles.

The user would have to evaluate the reasons for such an outcome and determine if the inputs were

reasonable or required modification.

The application of technology, described conceptually above, is described in more detail below. In the

following formulae, the subscripts (t-1) and (t) indicate vehicle conditions before and after applying

technology package “t”, respectively.

D. Technology Application Ranking Factors

The Technology Application Ranking Factor (TARF) is used to rank the application of

available technology packages across various vehicles. As described above, the user can choose

between three different TARFs for ranking technology application: 1) Effective Cost, 2) Cost

Effectiveness–Society, and 3) Cost Effectiveness–Manufacturer. The first and third TARFs take

the view of the manufacturer in determining the application of technology. This can be deemed

appropriate since the manufacturer controls the decision making process. Since the manufacturer

must satisfy its customers and regulatory mandates, a manufacturer’s decision making processes

will reflect these needs, as well. More explicitly, the technology cost is assumed to be the full

cost of that technology at the consumer level, including research and development costs,

amortization of capital investment, etc. This cost is generally the same cost as EPA estimates in

its regulatory support analyses when estimating the cost of new standards.7This cost is not

necessarily the increment in price that the manufacturer would charge for that technology, since

price is a function of many factors which can change fairly quickly depending on market

7

See Section III.H of the Draft Regulatory Impact Analysis to the recent EPA NPRM for the control of GHG emissions from

cars and light trucks for a discussion of technology costs at the manufacturer and consumer levels.
26

conditions. The fuel savings of interest are those assumed by a manufacturer to be valued by the

customer, so they are based on fuel prices including taxes and reflect the timeframe which a

customer might consider when purchasing a vehicle. The residual value of the added technology

is not currently reflected in either TARF, but could be added in the future.

The second TARF takes the view of society in deciding which technologies should be

added first. This distinction will be described further below. In all three cases, the vehicle with

the TARF with the most negative value is applied first. Because TARFs 1 and 3 reflect the

manufacturers’ perspective, they are similar conceptually. Therefore, we describe both of these

TARFs before describing TARF 2 below.

i. Effective Cost TARF (TARF No. 1)

The Effective Cost TARF (EffCost) is defined as the cost of the technology (TechCost)

less the discounted fuel savings over a specified payback period of vehicle use. The Effective

Cost TARF was included in the OMEGA model, since it is the equivalent of the technology

ranking process used in NHTSA’s Volpe Model. It allows a user to match this aspect of the

Volpe Model when modeling equivalent standards using both models, if this is desired.

Quantitatively, it is defined as follows:

)1(

1

GAP

EffCost TechCost FS

−

= ×−

TechCost is the cost of technology t per vehicle, as input in the Technology file. Fuel

consumption per mile (over the compliance test cycle used to determine compliance with the

input CO2 emission standards) before (FCt-1) and after technology addition (FCt) is calculated as

follows:













×

=

−

−

−

gC

gCO CD

CO FC

t

t

t

12

244

2

1

1

1













×

=

gC

gCO CD

CO

FC

t

tTARF

t

12

244

2 ,

Where:

CDt-1 and CDt = the carbon density of the liquid fuel (in terms of grams carbon per gallon) before

and after technology application.

CO2t-1 = the level of tailpipe emissions prior to the application of the technology being evaluated

(i.e., after the application of technology t-1), and

CO2TARF,t = the level of tailpipe emissions after application of technology t, without considering

any cap on the level of the penetration of technology t.

44g CO2/12 g C = the mass ratio of CO2 to C, used in converting the carbon density of a fuel to

an emitted mass of carbon dioxide.
27

CO2t-1 is the actual level of CO2 emissions from the particular vehicle which would

occur after the application of all the technologies prior to technology t, considering both the fact

that: 1) some or all of these technology packages may already be present on this vehicle (i.e., the

TEBs), and 2) there may be caps on the application of one or more of these technology packages

which are less than 100%. This level is the appropriate “baseline” CO2 level from which to

evaluate technology t since all previous technologies must be added to the vehicle before

technology t can be added.

Please note, that the current TARFs are essentially defined on a per vehicle basis.

Consequently, OMEGA does not factor in the potential cap on the level of the penetration of

technology t into the TARF calculation.8 Because the calculation of CO2TARF,t does not consider

the impact of any cap on technology penetration, this level of CO2 emissions will differ from the

CO2 emission level of the vehicle should this technology be selected for addition. The equation

for the latter CO2 emission level is described further below. In order to be consistent with the

calculation of CO2TARF,t, the technology cost (TechCost) is also determined without

consideration of the presence of the technology on the vehicle (via the value of CEB) and

without consideration of the cap on the penetration of the technology. Thus, TechCost is simply

the incremental cost of the technology listed in the Technology file.

With these premises, the formulae describing tailpipe CO2 emissions and refrigerant

emissions after the application of this technology package are as follows:

( )

t t

t

t

t

TARF

AIE TEB

CO AIE

CO

− ×

× −

=

−

1

12

2

1

,

( )

1

1

,

1

12

2

−

−

×

×−

× −

=

t

t

t t

t

t

tTARF GWP

GWP

TEBAIE

RCO AIE RCO

It should be noted that both equations include the term (1-AIEt)/((1-AIEt x TEBt). The

effectiveness of adding the technology package (AIE) is determined relative to a vehicle which

does not have that technology package. If a vehicle already has some aspect of the technology

package present, its emissions are lower than they would be without this technology. The term

in the denominator effectively increases the emissions of the vehicle to the level which would

exist without the technology. The full effectiveness of the technology package can then be

applied to this upwardly adjusted CO2 emission level.

Fuel savings without consideration of the gap between onroad and certification fuel

economy (FS) is calculated as follows. Vehicles can have up to two separate energy sources, a

8 Amortized capital costs tend to be higher for technologies which are applicable to lower production volumes. However, the

capital investment of many technologies can be spread across more than one vehicle model. Thus, incorporating the capital

investment associated with technology into the TARF would not be a simple matter. If explicit consideration of capital costs

is added to the model’s operation in the future, both the cap on application of a particular technology and the sales volume of

the vehicle model will likely be relevant and included in the revised TARF. The net result is that the cost of each technology

should represent that for the timeframe and expected production volume for each redesign cycle.
28

liquid fuel (subscript “1” in the equation) and electricity (subscript “2” in the equation ), as

would be the case with plug in hybrids.

[(* *) ( *) ] ,1 1)*5(,11,1 ,2 1)*5(,21,2

1

− −++ − −++

=

= ∑ t − t iRCBY t −+ t iRCBY

PP

FPFCFCVMTi FCFC FP

i

FS

Where:

i = vehicle age,

VMTi = annual vehicle miles travelled for a vehicle of age i,

PP = the payback period, or the length of time the user assume that consumers value fuel savings when

purchasing a new vehicle, stands

FC = fuel consumption per mile of either fuel 1 or 2, which is independent of both vehicle age and calendar

year,

FP = fuel price of either fuel 1 or 2 in the calendar year equivalent to the vehicle age used to determine

annual VMT. For i=1, this calendar year is the base year of the model run plus the redesign cycle times

five years plus the vehicle age less one. For example, for a run with a base year of 2010 and the first

redesign cycle, vehicles with an age of 1 are assumed to be driven in 2015, which is in fact the end of the

first redesign cycle.

As stated previously, we recommend that the CAFE fee be set to zero in the scenario file,

as OMEGA does not currently allow manufacturer fine payment. With the CAFE fee set to zero,

the Effective Cost TARF represents the difference between what it costs the manufacturer to add

the technology to the vehicle and the increase in value from the consumers perspective due to

fuel savings. A positive value for this TARF indicates that the consumer might view the vehicle

less desirably with the technology than without. A negative value for this TARF indicates that

the consumer might view the vehicle more desirably with the technology than without. This

TARF assumes that manufacturers will incrementally add technologies which increase this

desirability to the maximum extent possible.

ii. Cost Effectiveness-Manufacturer TARF (TARF No. 3)

The Cost Effectiveness-Manufacturer TARF (CostEffManuf) incorporates all of the terms

included in the effective cost TARF, but also accounts for the degree that the technology brings

the manufacturer closer to its CO2 standard. It can be described simply as the Effective Cost

TARF divided by the mass of the CO2 equivalent emission reduction over the life of the vehicle

due to addition of the technology. The Cost Effectiveness-Manufacturer TARF can be described

mathematically as follows:

= ௧݂ݑܽ݊ ܯ݂݂ܧݐݏ݋ܥ

்௘௖௛஼௢௦௧ିிௌ௫ భ

భషಸಲುିிாா௫ሺ భ

ಷ಴೟

ି

భ

ಷ಴೟షభ

)

൫ோ஼ைଶ೅ಲೃಷǡ೟ିோ஼ைଶ೟షభ൯ା൫஼ைଶ೅ಲೃಷǡ೟ି஼ைଶ೟షభ൯௫௏ெ ்ೝ೐೒ೠ೗ೌ೟೚ೝ೤

This equation can be rewritten more simply as follows:

= ௧݂ݑܽ݊ ܯ݂݂ܧݐݏ݋ܥ

ா௙௙஼௢௦௧

൫ோ஼ைଶ೅ಲೃಷǡ೟ିோ஼ைଶ೟షభ൯ା൫஼ைଶ೅ಲೃಷǡ೟ି஼ைଶ೟షభ൯௫௏ெ ்ೝ೐೒ೠ೗ೌ೟೚ೝ೤
29

Where,

( )

1

2 . 1 12

−

− ×−×=

t

t

tTARF t GWP

GWP RCO RCO RIE

VMTregulatory = the VMT from the Scenario file

The ratio of GWPs reflects the fact that the technology might change the refrigerant used

and affect the conversion of refrigerant mass emissions to CO2 equivalent emissions.

All of the terms in the above equations have already been defined. The denominator could be

described simply as the reduction in gram per mile tailpipe CO2 and CO2 equivalent refrigerant

emissions times the vehicle’s lifetime VMT. For vehicles of the same class, VMTregulatory is the

same, so the inclusion of VMT in the denominator has no practical impact. However, when cars

and trucks are being modeled together, the inclusion of this term weights has an effect. .

The Cost Effectiveness-Manufacturer TARF represents the degree to which consumer

desirability might change with the technology on a per ton of CO2 controlled basis. The

Effective Cost TARF ignores the degree to which the technology moves the manufacturer closer

to compliance. Thus, a fairly expensive technology which produces a large fuel savings might

have a fairly large negative Effective Cost TARF. The sequence of several less expensive

technologies with smaller fuel savings might all have less negative Effective Cost TARFs and so

would not chosen over the more expensive technology. However, in total, the sequence of

smaller steps might achieve the same overall emission reduction as the more expensive

technology at a lower cost. The Cost Effectiveness–Manufacturer TARF would divide these less

expensive technologies by smaller CO2 emission reductions, thereby increasing their TARF

values relative to the more expensive technology. This would allow the model to choose the

sequence of less expensive technologies over the single expensive technology if their increase in

consumer desirability per ton of CO2 reduced was higher.

iii. Cost Effectiveness-Society TARF (TARF No. 2)

The Cost Effectiveness-Society TARF (CostEffSoc) is identical to the Cost

Effectiveness–Manufacturer TARF with one exception. The Cost Effectiveness-Society TARF

divides the Effective Cost TARF by the discounted lifetime CO2 emission reduction instead of

the lifetime CO2 emission reduction. The discount rate used would be that for the value of CO2

emission reductions over time. The rationale for discounting is simply that society is presumed

to value CO2 reductions in this way. Also, in this case, we would recommend that the user

increase the payback period for fuel savings to cover the life of the vehicle instead of the much

shorter period of time often assumed to be considered by consumers when purchasing a vehicle.

Society values fuel savings over the life of the vehicle and not just for the first few years of use.

The user could also estimate technology costs from a societal point of view if this produced

different cost estimates than those used above. The Cost Effectiveness- Society TARF can be

described mathematically as follows:
30

[( ) ( )]

( ) ∑













































−+

−

+

− + − ×

=

− −

36

, 1 , 1

1

2

1

2 22 *2

i

tTARF t tTARF t i i

t

IRDR

IRDR

RCO RCO CO CO VMT

EffCost CostEffSoc

where all the terms have already been defined.

Applying Technology: As described above, for any individual vehicle, technologies are

applied in the order in which they are listed in the Technology file for the relevant vehicle type.

Thus, at the beginning of the evaluation for a manufacturer, the only technology which is

available to each vehicle is technology package 1 for its vehicle type. Thus, the OMEGA model

compares the TARFs for applying technology package 1 to all of the vehicles in that

manufacturer’s fleet and chooses the vehicle with the most negative TARF. The model then

applies technology package 1 to that vehicle and reduces its GHG emission level. The formulae

for calculating the new tailpipe and refrigerant CO2 emission levels after application of the

technology are shown below:

( )

AIE TEB

CO AIECAP

CO t

t

− ×

× − ×

=

−

1

12

2

1

( )

1

1

1

12

2

−

−

×

×−

× − ×

=

t

t t

t GWP

GWP

TEBAIE

RCO AIECAP

RCO

Here, both the presence of the technology in the baseline configuration of this vehicle and

the cap on technology application are considered. The terms shown in the denominators of both

equations are included due to the definition of the incremental effectiveness of technology.

When calculating the effectiveness of a technology, the user should assume that the vehicle to

which this technology is being applied has all of the previous technology packages applied, but

none of the additional technologies included in the technology of interest. Thus, the incremental

effectiveness of hybridization over an advanced gasoline engine and transmission package might

be 10%. If a specific vehicle or more likely group of vehicles already reflected half of this 10%

hybrid benefit, it would not be correct to simply reduce the effectiveness of the hybrid package

to half of the 10% (i.e., 5%) and multiply base emissions by 0.95. It is more accurate to remove

the effect of the partial hybridization by dividing by 100% minus 5% (i.e., 0.95) and then

multiplying by100% minus 10% (i.e., 0.9). The net effect in this case is to multiply base

emissions by 0.9474, which produces a slightly greater emission reduction than multiplying by

0.95. For modest technologies, the difference is small. However, for technologies which might

reduce emissions by 30% or more, the difference in methodology becomes more significant.

The model also adds the cost to the manufacturer’s running total cost and recalculates the

manufacturer’s corporate average emission level. The formulae used to perform these two

calculations are as follows:

TotalCostt = TotalCostt − 1 + TechCost× × SalesCEB v
31

( )

∑

∑

=

=

×

× ×

= V

v

v v

V

v

v v t

step

Sales LifeVMT

sSale LifeVMT TCO

FleetTCO

1

1

2

2

Where:

v = a vehicle produced by the manufacturer,

V = the total number of vehicles (cars, trucks, or both) produced by that manufacturer,

TCO t = CO t + RCO222 t

, which are the emissions after application of technology t, and

LifeVMTv = the lifetime VMT of the class of vehicle to which vehicle v belongs. Lifetime VMT is the sum

of the product of relevant vehicle survival fractions and annual VMT by vehicle age as input in the

Reference file.

As mentioned above, compliance with the CO2 standards is performed on a sales and VMT

weighted basis, for ease in trading between cars and trucks under the provisions of the proposed

CO2 standards.

At this point, the model checks to see if the manufacturer is in compliance with its CO2

emission standard. If so, it stops and moves on to the next manufacturer. If not, the model then

evaluates the TARF for the next technology package for the vehicle which just received the last

technology package. The model calculates the TARF for this package and compares it to the

TARFs for the technology packages 1 for all of the other vehicles. This sequence of adding one

technology package to one vehicle, reevaluating compliance, and so on, continues until either the

manufacturer complies or until all the available technologies have been applied. When either of

these two endpoints is reached, the model moves to evaluating the next manufacturer or the next

redesign cycle.

The model keeps track of a number of intermediate values throughout the process of

adding technology. These include the order of technology application, the TARFs for each

combination of vehicle and technology, the cumulative cost per vehicle, etc. for use in producing

the various output files.

4. Output Files

The places each scenario output in a separate subfolder. The name of each of these files includes

the name of the scenario listed in Column B of the Scenarios tab of the Scenario file. Each of these

output files and their purpose are summarized in the table below. The main output files are also

discussed in greater detail later in this section.
32

Table 8 – Summary of Model Outputs

File* Summary Description

Main Output Files

X.log Step by step details of the model operation including tech

pack application, cost, CO2, and electricity.

X.xls Summary file that includes manufacturer specific details on

tech pack application, cost, CO2 and electricity.

X-Techpacksales.log Details on the sales of vehicles by tech pack at the

completion of the scenario. Useful in tracking technology

application.

X-vh1.xls Summary of final cost, emissions, and electricity

consumption by vehicle

X-vh2.xls Step by step details of cost by technology pack application,

summarized by vehicle.

Diagnostic Output Files

X.xml Used in loading data into the benefits calculation worksheet.

X-CO2.log Step by step log of sales and emissions by fuel type.

X-CycleResults.log Repeats data that is contained in X.xls.

X-SFX.log Summarizes final sales by fuel type.

X-TARF.log Summarizes the TARF of every technology package vehicle

combination.

X-VehFinal.log Summarizes the data in X-CO2.log

X-VehSteps.log Lists the sales fraction and CO2 emissions for each fuel type

without all of the extra detail in CO2.log

*X is substituted here for scenario name.

A. Log of Technology Application Steps – Text Format

This file depicts the process of technology application to each manufacturer’s fleet and shows the

progress being made towards compliance with the specified standards. Please note that the log has

several different formats which depend upon the user options selected. The example below is

conceptually representative of all log formats. The beginning of the file lists basic information about the

model user, the version of OMEGA being used and the input files. It then presents the technology

application information by redesign cycle and within each redesign cycle by manufacturer and within

each manufacturer by vehicle class (i.e., cars first and then trucks). If a combined car-truck standard is

being evaluated, then only one set of technology application steps is presented which combines both

types of vehicles. At the beginning of each redesign cycle, the file describes the standard or standards

being evaluated. For universal standards, this means the standard itself. For footprint-based standards,

the four coefficients described in the input file are listed. The file then begins a sequence of sections

which apply to a single manufacturer and single vehicle class, as shown below.
33

BMW Baseline Co2avg = 328.74, Target Co2avg = 232.34, Fleet Type = 'C'

Step Index Type Co2pipe Co2tot TP TARF Co2pipe Co2tot Co2avg kWhavg TotCost

1- 5 6 426.5 426.5 1 -0.1276 402.5 402.5 328.22 0 1,414,039

2- 6 6 407.5 407.5 1 -0.1262 385.32 385.32 325.57 0 9,048,127

3- 4 5 334.6 334.6 1 -0.1197 318.52 318.52 322.92 0 18,936,722

4- 3 4 331.5 331.5 1 -0.1193 313.65 313.65 315.17 0 42,826,788

The first line lists the manufacturer, its starting CO2 emission level, its CO2 target or standard

for this scenario and the vehicle class (C for car or combine, and T for Truck). The starting CO2

emission level is simply the base CO2 emission level of each vehicle weighted by vehicle sales in this

redesign cycle. The CO2 standard is either the universal standard listed in the Scenario file, or the footprint based CO2 standard applied to that manufacturer’s vehicles.

The following lines list the step-by-step application of technology packages. Going through the

columns, step is simply a numerical counter following by a hyphen. Index identifies the vehicle

receiving the technology or package and refers to the vehicle number in the Market file. Type shows the

vehicle type for this vehicle. The first column labeled Co2pipe shows the tailpipe CO2 emissions prior

to the application of technology. For the application of technology package 1, this value is the base CO2

emission level shown in the Market file. For subsequent packages, it is the CO2 emission level resulting

from the application of the previous technology package. The first column labeled Co2tot stands for

total CO2 equivalent emissions and is analogous to Co2pipe. Co2tot equals Co2pipe plus refrigerant

emissions in terms of equivalent CO2 emissions. Again, this is either the base refrigerant emission level

or the refrigerant emission level after application of the previous technology package. TP is the

technology package added in this step. TARF is the value of the TARF for this package applied to this

vehicle.

The second column labeled Co2pipe shows the tailpipe CO2 emissions after the application of

the technology package. This value will be consider the efficiency of the technology package, the cap

on the percentage of sales which can receive the package, as well as the percentage of that package

already present on the vehicle (i.e., the TEB). The second column labeled Co2tot shows this value plus

the level of refrigerant emissions existing after any control which have been applied to these.

Co2avg represents the corporate average CO2 emission level for this manufacturer and vehicle

class combination. It will generally decrease after each step of technology application and show

progress towards the manufacturer’s standard. Occasionally, this value will remain constant. This could

be due to round off. Or, the vehicle receiving the technology may have already been completely

equipped with that technology. The OMEGA model still “applies” an applicable technology to each

vehicle when its TARF shows that this is the next best step, even if the cap is less than or equal to the

TEB. In this case, the model simply holds both emissions and costs constant when it applies the

technology.

kWhavg represents the avg kwh/mile of electricity consumed by the fleet. This includes both the

baseline electricity and the additional electricity consumed by plug-in vehicles. To be clear, this is the

average electricity consumed over all miles, not simply the electrically powered miles.
34

TotCost represents the cumulative cost in dollars per model year of the technology added up to

that point. The increment in this value from step to step is the product of three terms: 1) the cost of the

technology package being added, 2) the sales of the vehicle in this redesign cycle, and 3) the cap minus

the percentage of that package already present in terms of cost (i.e., CEB) or zero, whichever is higher.

The very last step of technology addition for each manufacturer and vehicle class combination

may be shown twice, with “OC” following the second listing. In this case, this step does not represent

the addition of technology, but a backwards interpolation between the previous two steps of technology

addition which eliminates the over-compliance which usually results from adding discrete technologies

to specific vehicles. The presence of this interpolation step depends on the value of the threshold cost

input specified in the Scenario file and the cost of the last technology package, as discussed above under

Input files.

This file can be very useful both for diagnostic and analytical purposes. The presence of the

TARF values in the file can be useful in identifying technology packages which have relative poor cost

effectiveness followed by packages with better cost effectiveness. In general, the list of TARF values

should start out negative and become more positive with continued technology application. The only

exception to this should be when the same vehicle receives technology in sequential steps. In this case,

the TARF may become more negative in a successive step, since the OMEGA model could not consider

the more cost effective technology until it applied the previous technology to that vehicle. When the

user observes a series of technologies being applied to the same vehicle in successive modeling steps,

this indicates that separating these technology packages provides little practical purpose in the model

run. Worse, the relatively poor cost effectiveness of the first of the series of technology packages may

be causing the model to add technology to other verhicles which have worse cost effectiveness than the

combination of packages for the vehicle in question. This sequence of technology package additions to

the same vehicle could also be an indication that the order of technologies might not be appropriate (or

there might be an error in one of the technology input values).

From an economic perspective, this file presents the increase in cumulative cost for each

manufacturer as its average CO2 level is reduced. If a sufficiently stringent CO2 standard (e.g., 50

g/mi) is input to the model, manufacturers will not comply with the specified standard. However, the

model will apply all of the technology available to each vehicle. Thus, the file represents a complete

relationship between cost and emissions for each manufacturer. By reading the information contained in

this file into a spreadsheet or other program capable of analysis, the user can quickly determine the cost

for a wide range of CO2 standards without rerunning OMEGA each time. Since the social costs and

benefits of CO2 standards tend to be relatively linear with CO2 level, it is possible to represent these

costs and benefits with simple linear equations. The user can then easily combine the relationship

between manufacturer’s emission levels and technology costs with social costs and benefits at an

industry-wide level. It would then be possible to solve for the industry-wide emission levels which

maximized net societal benefits, produced zero net societal benefit or met some other economic criteria.
35

Example: The following table depicts a portion of the log file from an OMEGA model run.

CYCLE 1 Target Coeffs: (A=204.0, B=275.0, C=41.0, D=56.0) , (A=246.0, B=347.0, C=41.0, D=66.0)

Industry Baseline Co2avg = 287.35, Target Co2avg = 223.31, Fleet Type = 'C'

Step Index Type Co2pipe Co2tot TP TARF Co2pipe Co2tot Co2avg kwhavg TotCost

1- 19 6 405.13 405.13 1 -0.1266 375.33 375.33 286.92 0.0000 33,256,539

2- 14 6 403.17 403.17 1 -0.1264 372.63 372.63 286.61 0.0000 57,241,908

3- 29 13 446.63 446.63 1 -0.1261 412.62 412.62 286.61 0.0000 57,306,310

4- 13 10 392.46 392.46 1 -0.1255 362.57 362.57 286.44 0.0000 70,885,077

5- 18 10 389.46 389.46 1 -0.1253 359.8 359.8 286.28 0.0000 83,589,991

0.0000

33- 28 2 232.56 232.56 1 -0.1106 217.03 217.03 267.17 0.0000 2,117,945,615

34- 14 6 372.63 372.63 2 -0.0904 357.54 357.54 267.01 0.0000 2,158,753,183

35- 14 6 357.54 357.54 3 -0.0973 305.57 305.57 266.49 0.0000 2,238,406,536

36- 19 6 375.33 375.33 2 -0.0901 355.62 355.62 266.21 0.0000 2,297,680,885

0.0000

54- 7 5 325.61 325.61 2 -0.0615 300.75 300.75 244.96 0.0000 6,904,283,762

55- 7 5 300.75 300.75 3 -0.0779 250.06 250.06 243.95 0.0000 7,106,439,868

0.0000

92- 25 4 250.33 250.33 2 -0.0457 212.85 212.85 225.84 0.0000 11,043,478,070

93- 28 2 217.03 217.03 2 -0.0426 203.45 203.45 221.06 0.0000 12,799,723,914

93-OC 28 2 217.03 217.03 2 -0.0426 216.53 216.53 223.31 0.0000 11,973,039,155

The first five technologies added to cars in this model run were all the first technology listed for

each vehicle type (TP = 1). The same is true for steps 6-32 (not shown). Step 33 also adds the first

technology available to vehicle 28. Step 34 adds the second technology available to vehicle 14, while

step 35 adds the third technology available to this vehicle. This sequence demonstrates how the model

evaluates the next available technology for each vehicle when deciding where to add technology next.

In this case, technology number 3 for vehicle 14 was preferred over any of the second technologies for

all the other vehicles. Examination of the TARF values explains why this was the case.

The TARF for the technology number 2 for vehicle 14 was-0.0904, while that for technology 3

was -0.0973. Thus, if -0.0904 was the lowest TARF for step 34, an even lower TARF would have to be

the lowest TARF in step 35. When it is observed that the model adds two technologies in a row to the

same vehicle, the user should question whether the first technology should be modified or the two

technologies should be combined. The reason for this is that, unless step 34 is the very last technology

added to enable compliance, the model will never simply add technology 2 to vehicle 14. Vehicle 14

will always receive either technology 1 or 3. The primary concern is that a relatively high TARF value

for technology package 2 could inappropriately inhibit the application of the combination of technology

packages 2 and 3 to this vehicle relative to the application of technologies to other vehicles.

In this case, the TARFs for technologies 2 and 3 are quite close. Thus, combining them into one

technology package would not produce substantively different results. The same sequence occurs with

vehicle 7 later in the run (steps 54 and 55 in the above table). In this latter case, the difference between

the TARFs is much greater. Combining the two steps may have resulted in the earlier application of the

two technologies than applying them separately.
36

The final three lines of the above table illustrate the interpolation that occurs in the compliance

determination if the cost of the last technology added exceeds the “threshold” input in the Scenario file.

After step 93, the manufacturer’s corporate average CO2 level was 221.06 g/mi, while the standard was

223.31 g/mi. The model adjusted the manufacturer’s corporate average CO2 level to 223.31 g/mi by

only applying technology 2 to a portion of the sales of vehicle 28. This reduced the overall cost of

compliance from $12.8 billion to $12.0 billion. Mathematically, this is equivalent to interpolating

between the average emissions (CO2avg) and cumulative costs of steps 92 and 93.

B. Summary of Cost and Emissions – Excel Format

This file presents a summary of vehicle and manufacturer costs and emission levels resulting

from a model run. The file contains summary information about the run, the model user, the version of

OMEGA being used and the values input on the first tab of the Scenario file. The file then lists five

types of information by manufacturer and vehicle class: 1) vehicle sales, 2) total costs, 3) cost per

vehicle, 4) electricity consumption, and 5) emission level per vehicle.

The file continues by presenting the cost of the technology added to each vehicle and the last

technology package added to each vehicle. The last section of the file presents the series of technologies

added to each vehicle. For each technology, the file shows the step (for each manufacturer-vehicle class

combination) in which the technology was added, the vehicle’s emission levels before and after this

technology and the incremental total cost of adding this technology.

C. Summary of Technology Pack Distribution – Text format

This file lists the final distribution of technology packs applied to each vehicle, and takes the

form of a matrix of vehicles and technology packages, with the sales presented within the matrix. This

is useful information when calculating technology penetrations. As an example, if 40% of vehicle 7

sales receive technology package 6, then 40% of vehicle 7 sales have the technologies in package 6.9

D. VH1 / Final summary of Vehicle Attributes– Excel Format

The “VH1” file lists each vehicle, the final technology package applied to that vehicle, the final

cost, and various attributes about the vehicle. Most of these attributes are carried through from the

market data file, however some such as the CO2 emission rate and electricity consumption are modified

by the model. In many senses, this file is a lower level corollary of the Excel summary file described in

IV.B, and is useful for determining the average cost increase for a class of vehicles.

E. VH2 / Stepwise listing of Vehicle Attributes

The VH2 file provides the cost and CO2 emissions of each vehicle after each technology

package is applied. Similar to the VH1 file, it is organized by vehicle.

9

In rulemaking analyses, EPA typically uses a more detailed methodology to calculate technology penetrations. This method

is documented in Appendix F of the Interim Join Technical Assessment Report.
37

5. Running the Model

Installing the model should add an “OMEGA” icon to the user’s desktop. OMEGA is started by

double clicking on this icon. A graphic user interface (GUI) should appear in a few seconds. The

current GUI is simple and relies on the fact that all of the information needed to run the model is

contained in the input files. The user should then click on “File” in the menu bar and choose “Open”

from the drop down menu. A window will open which displays the files contained in the model’s input

directory. The user should double click on the desired Scenario file and the model will loads the data

contained in this file and that in the Market, Technology, Fuel and Reference files specified in the

Scenario file. The GUI will update and display portions of the Scenario, Market and Technology input

files. The GUI allows the user to partially navigate through these three files in order to confirm that the

correct input files were specified in the Scenario file. When everything is loaded, the car icon will turn

green. The user can also specify an output directory whose filepath will display in the GUI. The user

can now run the cases included in the Scenario file by clicking on the green car button.

As the model is running, the lower left hand corner of the GUI will indicate progress

(e.g., processing Scenario 1 of 5, processing Scenario 2 of 5, etc.). If the Scenario file only

specifies one case to be run, when the model is done with this case, the log (text) file showing

the sequence of technology addition by manufacturer and by redesign cycle appears. This file, as

all of the output files, is automatically named with the case name from the Scenario file, with the

file type “log” added. If more than one case is run, the indicator in the lower left hand corner

will simply say “Done” and no log files are displayed.
38

6. Appendix A: Credit Trading Algorithms

As Clean Air Act allows credit trading between a manufacturer’s car and truck fleets,

OMEGA allows the user to utilize a full range of credit trading scenarios. This trading is

controlled in OMEGA in column I of the scenarios tab of the Scenario input sheet. Entering a

zero into this column prevents credit trading and requires manufacturers to comply with the

relevant emission standards for their cars and its trucks separately. If the user wants to allow

unlimited trading, this is accomplished by inputting a large non-zero number in Column I (e.g.,

1000 g/mi CO2). This effectively allows the model to apply technology across both cars and

trucks and meet the combined standard described above. We say “effectively”, because the

model still checks to ensure that the trading limit is not triggered and this cannot be definitively

determined until compliance is achieved at the end of the evaluation of this manufacturer.10

Thus, in addition to requiring compliance with the fleetwide average CO2 target, the model must

also ensure that each fleet complies with its applicable target plus the trading allowance.

Should a non-zero number be used entered in column I, OMEGA determines the overall salesand vmt-weighted emissions target for the manufacturer with cars and trucks combined:11

= ௥௙ ௠ݐ݃݁ݎܶܽ

+௦஼௔௥ܶ ܯܸݕݎ݋ݐ݈ܽݑܴ݁݃ݔ௦௖௔௥݀ݎܽ݊݀ܽݐܵݔ௦௖௔௥ݏ݈ܵܽ݁

݈ܵܽ݁ݏ௧௥௨௖௞௦ݔܵݐܽ݊݀ܽݎ݀௧௥௨௖௞௦ݔܴ݁݃ݑ݈ܽݕݎ݋ݐܸܯ ܶ௧௥௨௖௞௦

+௦஼௔௥ܶ ܯܸݕݎ݋ݐ݈ܽݑܴ݁݃ݔ௦௖௔௥ݏ݈ܵܽ݁

݈ܵܽ݁ݏ௧௥௨௖௞௦ݔܴ݁݃ݑ݈ܽݕݎ݋ݐܸܯ ܶ௧௥௨௖௞௦

The model also determines the starting point for each manufacturer using the same basic equation

= ௥௙ ௠ݏ݊݋݅ݏݏ݅ ݁݁݉ݏܽܤ

+௦஼௔௥ܶ ܯܸݕݎ݋ݐ݈ܽݑܴ݁݃ݔ௦௖௔௥ݏ݊݋݅ݏݏ݅ ݁݁݉ݏܽܤݔ௦௖௔௥ݏ݈ܵܽ݁

௦௖௞௨௥௧ܶ ܯܸݕݎ݋ݐ݈ܽݑܴ݁݃ݔ௦௖௞௨௥௧ݏ݊݋݅ݏݏ݅ ݁݁݉ݏܽܤݔ௦௖௞௨௥௧ݏ݈ܵܽ݁

+௦஼௔௥ܶ ܯܸݕݎ݋ݐ݈ܽݑܴ݁݃ݔ௦௖௔௥ݏ݈ܵܽ݁

݈ܵܽ݁ݏ௧௥௨௖௞௦ݔܴ݁݃ݑ݈ܽݕݎ݋ݐܸܯ ܶ௧௥௨௖௞௦

Credits are generated when a manufacturer’s fleet of either cars or trucks overcomplies with the

applicable standard. The amount of credits generated equals the difference between the sales weighted

average emission level for that vehicle class and the applicable standard multiplied by the lifetime VMT

per vehicle for that vehicle class. For either vehicle class, in aggregate, the generated credits are

calculated by the equation below.

10 If the trading limit is greater than the emission standard, trading is effectively unlimited.

11 VMT weighting allows the user to account for the difference in miles driven between difference

classes of vehicles and provides for environmentally neutral credit trading:
39

݁݀ݐܽݎ݁݊݁ܩݏݐ݁݀݅ݎܥ

(݀ݎܽ݊݀ܽݐݏ݊݋݅ݏݏ݅ ݁݉ ʹܱܥݔܶ ܯܸݕݎ݋ݐ݈ܽݑܴ݁݃ݔݏ݈ܵܽ݁) =

ሻܽ݃݁ݎ݁ݒ݊ܽ݋݅ݏݏ݅ ݁݉ ʹܱܥݔܶ ܯܸݕݎ݋ݐ݈ܽݑܴ݁݃ݔݏ݈ܵܽ݁ሺ െ

Where

Sales = Sales volume of each car or truck in that redesign cycle,

Regulatory VMT = Lifetime VMT per vehicle according to regulation (from the reference file).

CO2 emission standard = The target set in the scenario file

CO2 emission average = The achieved CO2 level for the vehicles after the application of technology

Credit use is determined by the same formula, except for the substitution of the vehicles

from the other vehicle class, as shown below.

(݀ݎܽ݊݀ܽݐݏ݊݋݅ݏݏ݅ ݁݉ ʹܱܥݔܶ ܯܸݕݎ݋ݐ݈ܽݑܴ݁݃ݔݏ݈ܵܽ݁) ൌ ݁݀ݏݑݏݐ݁݀݅ݎܥ

ሻܽ݃݁ݎ݁ݒ݊ܽ݋݅ݏݏ݅ ݁݉ ʹܱܥݔܶ ܯܸݕݎ݋ݐ݈ܽݑܴ݁݃ݔݏ݈ܵܽ݁ሺ െ

Where

Sales = Sales volume of each car or truck in that redesign cycle,

Regulatory VMT = Lifetime VMT per vehicle according to regulation (from the reference file).

CO2 emission standard = The target set in the scenario file

CO2 emission average = The achieved CO2 level for the vehicles after the application of technology

OMEGA utilizes a simple set of algorithms to determine the correct distribution of

technology between car and truck fleets. OMEGA calculates the level of sales and VMT

weighted emissions of either car and truck emissions which will generate the maximum

allowable use of credits by the other vehicle class (the “lower limit”). It then tracks sales and

VMT weighted car, truck and combined emissions when adding technology. When the sales and

VMT weighted average emissions for either cars or trucks reaches this lower limit, no additional

technology is applied to that vehicle class. Technology is only applied to the other vehicle class,

as this latter class still exceeds the level of its standard plus the allowable trading level.

For example, assume a trading limit of 10 g/mi CO2 is input and the applicable car and

truck standards for a manufacturer are 220 and 300 g/mi CO2, respectively. The model

calculates the combined sales and VMT weighted CO2 emission target using the above equation

for FleetwideCO2Target, which can be simplified as follows:

( )

∑

∑

=

=

×

× ×

= 2

1vc

v v

2

1vc

v v v

Sales LifeVMT

sSale LifeVMT Target

FleetwideCO2Target

Where vc represents the two vehicle classes, cars and trucks.

Once the Fleetwide CO2 Target is known (assumed to be 260 g/mi in this example), this

same equation can be used to determine the level of average car emissions which achieves

compliance when the level of average truck emissions exceed its target by 10 g/mi CO2 (310
40

g/mi in this example). For this example, assume this level is 198 g/mi CO2. Any level of

average car emissions between 198 and 220 g/mi produces credits for trading which can be

effectively utilized towards compliance by trucks. Likewise, the minimum level of average truck

emissions which produces useful credits for use towards compliance by cars is determined which

achieves compliance when the level of average car emissions exceed its target by 10 g/mi CO2

(230 g/mi in this example). Again, for this example, assume this level is 290 g/mi CO2.

The model then proceeds to add technologies to cars and trucks (described in greater

detail below) until one of three criteria is met:

1) combined car and truck emissions reach 260 g/mi CO2,

2) car emissions reach 198 g/mi CO2, or

3) truck emissions reach 290 g/mi CO2.

If combined car and truck emissions reach 260 g/mi CO2 before the other two criteria are

met, the evaluation of this manufacturer is complete. The manufacturer complies with the sales

and VMT weighted standard applicable to cars and trucks combined and any level of trading

implied is less than the maximum allowed. If criterion 2 is reached first, the model continues to

evaluate and apply technology, but only to trucks. In this case, the model continues to

effectively add technology to trucks only until criterion 1 is met (unless insufficient technology

exists to enable overall compliance). Likewise, if criterion 3 is reached first, the model continues

to evaluate and apply technology to cars.

Fleetwide total tailpipe and refrigerant CO2 equivalent emissions are determined in an

analogous fashion. Compliance is achieved when fleetwide total CO2 is equal to or less than the

fleetwide CO2 Target.

7. Appendix B: Calculating Technology Effective Benefits (TEBs) and Cost

Effective Benefits (CEBs)

The market data input file utilized by OMEGA, which characterizes the vehicle fleet, is designed

to account for the fact that the vehicles which comprise the baseline fleet may already be equipped with

one or more of the technologies available in general to reduce CO2 emissions. As described previously,

OMEGA is typically used with technologies in packages, as opposed to one at a time. However, actual

vehicles are equipped with a wide range of technology combinations, many of which cut across the

packages. Thus, EPA developed a method to account for the presence of the combinations of applied

technologies in terms of their proportion of the technology packages. This analysis can be broken down

into four steps

The first step in the process is to break down the available GHG control technologies into five

groups: 1) engine-related, 2) transmission-related, 3) hybridization, 4) weight reduction and 5) other.

Within each group we gave each individual technology a ranking which generally followed the degree

of complexity, cost and effectiveness of the technologies within each group. More specifically, the

ranking is based on the premise that a technology on a baseline vehicle with a lower ranking would be

replaced by one with a higher ranking which was contained in one of the technology packages which we
41

included in our OMEGA modeling. The corollary of this premise is that a technology on a baseline

vehicle with a higher ranking would be not be replaced by one with an equal or lower ranking which

was contained in one of the technology packages which we chose to include in our OMEGA modeling.

In the second step of the process, we use these rankings to estimate the complete list of

technologies which would be present on each baseline vehicle after the application of each technology

package. We then use the EPA lumped parameter model to estimate the total percentage CO2 emission

reduction associated with the technology present on the baseline vehicle (termed package 0), as well as

the total percentage reduction after application of each package, including any baseline technology still

expected to remain present after the application of each package. Similarly, we use a cost estimation

tool to estimate the cost of the CO2 reducing technology present on the baseline vehicle and after the

addition of each package.

The third step in this process is to convert these total levels of emission control effectiveness and

cost to TEB and CEB12 values which can be used when the OMEGA model applies technology packages

on an incremental basis. This is done by comparing each technology package’s incremental

effectiveness and incremental cost on each specific vehicle to those of the package when applied to a

vehicle with no baseline technology. The value of each vehicle’s TEB for each applicable technology

package is determined as follows:

















−

−

−

















−

−

×

















−

−

=

−

−

−

1,

,

1,

,

,

1,

1

1

1

1

1

1

1

ip

ip

ip

ip

iv

iv

i

tTotalEffec

tTotalEffec

tTotalEffec

tTotalEffec

tTotalEffec

tTotalEffec

TEB

Where

TotalEffectv,i = Total effectiveness of all of the technologies present on the baseline vehicle after

application of technology package i

TotalEffectv,i-1 = Total effectiveness of all of the technologies present on the baseline vehicle after

application of technology package i-1

TotalEffectp,i = Total effectiveness of all of the technologies included in technology package i

TotalEffectp,i-1 = Total effectiveness of all of the technologies included in technology package i-1

i = the technology package being evaluated

i-1 = the previous technology package

Equation E-1 – TEB calculation

The value of each vehicle’s CEB for each applicable technology package is determined as

follows:

CEBi = 1 – (TotalCostv,i – TotalCostv,i-1) / (TotalCostp,i – TotalCostp,i-1)

12 As described earlier, the degree to which a technology package’s incremental effectiveness is reduced by technology

already present on the baseline vehicle is termed the technology effectiveness basis, or TEB, in the OMEGA model. The

degree to which a technology package’s incremental cost is reduced by technology already present on the baseline vehicle is

termed the cost effectiveness basis, or CEB, in the OMEGA model.
42

Where

TotalCostv,i = total cost of all of the technology present on the vehicle after addition

of package i to baseline vehicle v

TotalCostv,i-1 = total cost of all of the technology present on the vehicle after addition

of package i-1 to baseline vehicle v

TotalCostp,i = total cost of all of the technology included in package i

TotalCostp,i-1 = total cost of all of the technology included in package i-1

i = the technology package being evaluated

i-1 = the previous technology package

Equation E-2 – CEB calculation

The fourth step is to combine the TEB and CEB values for each individual vehicle

models to match the vehicles being included in the Market file. . The CEB for each vehicle

group is simply the sales-weighted average of the CEB values for each individual vehicle model,

since the cost of each package is the same for each vehicle in a vehicle type. (Only vehicles of

the same vehicle type should be combined.) The TEB for each vehicle group is determined in a

slightly more complex fashion. The individual TEB values are weighted by both sales and base

CO2 emission level. This appropriately weights vehicle models with either higher sales or CO2

emissions within a vehicle type. Once again, this process prevents the model from adding

technology which is already present on vehicles, and thus ensures that the model does not double

count technology effectiveness and cost associated with complying with the reference standards

or the CO2 control scenarios.