APPENDIX 10-A. FULL-FUEL-CYCLE MULTIPLIERS

TABLE OF CONTENTS

10-A.1 INTRODUCTION ...............................................................................................10-A-1

10-A.2 METHODOLOGY ..............................................................................................10-A-1

10-A.3 ENERGY MULTIPLIERS FOR THE FULL FUEL CYCLE.............................10-A-3

LIST OF TABLES

Table 10-A.2.1 Dependence of FFC Parameters on AEO Inputs......................................10-A-3

Table 10-A.3.1 Energy Multipliers for the Full Fuel Cycle (Based on AEO2014)...........10-A-3

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APPENDIX 10-A. FULL-FUEL-CYCLE MULTIPLIERS

10-A.1 INTRODUCTION

This appendix summarizes the methods the U.S. Department of Energy (DOE) used to 

calculate the full-fuel-cycle (FFC) energy savings estimated from amended standards for 

commercial clothes washers. The FFC measure includes point-of-use (site) energy; the energy 

losses associated with generation, transmission, and distribution of electricity; and the energy 

consumed in extracting, processing, and transporting or distributing primary fuels. DOE’s 

method of analysis previously encompassed only site energy and the energy lost through

generation, transmission, and distribution of electricity. In 2011 DOE announced its intention, 

based on recommendations from the National Academy of Sciences, to use FFC measures of 

energy use and emissions when analyzing proposed energy conservation standards.1 This 

appendix summarizes the methods DOE used to incorporate impacts of the full fuel cycle into 

the analysis.

This analysis uses several terms to describe aspects of energy use. The physical sources 

of energy are primary fuels such as coal, natural gas, or liquid fuel. Primary energy is equal to 

the heat content (British thermal units [Btu]) of the primary fuel used to produce an end-use 

service. Site energy use is defined as the energy consumed at the point of use in a house or 

establishment. When natural gas or petroleum fuels are consumed at the site (for example in an 

on-site furnace), site energy is identical to primary energy, with both equal to the heat content of 

the primary fuel consumed.

For electricity generated by an off-site power plant, site energy is measured in kilowatthours (kWh). In such a case the primary energy is equal to the quads (quadrillion Btu) of primary 

energy required to generate and deliver electricity to the site. For the FFC analysis, upstream 

energy use is defined as the energy consumed in extracting, processing, and transporting or 

distributing primary fuels. FFC energy use is the sum of primary plus upstream energy use. 

Both primary fuels and electricity are used in upstream activities. The treatment of 

electricity in full-fuel-cycle analysis must distinguish between electricity generated by fossil 

fuels and uranium and electricity generated from renewable sources (wind, solar, and hydro). For 

the former, the upstream fuel cycle relates to the amount of fuel consumed at the power plant. 

There is no upstream component for the latter, because no fuel per se is used.

10-A.2 METHODOLOGY

The mathematical approach to determining FCC is discussed in Coughlin (2012).2 Details 

on analyzing the fuel production chain are presented in Coughlin (2013).3 The methods used to 

calculate FFC energy use are summarized here. When all energy quantities are normalized to the 

same units, FFC energy use can be represented as the product of the primary energy use and an 

FFC multiplier. Mathematically the FFC multiplier is a function of a set of parameters that 

10-A-1
represent the energy intensity and material losses at each stage of energy production. Those 

parameters depend only on physical data, so the calculations require no assumptions about prices 

or other economic factors. Although the parameter values often differ by geographic region, this 

analysis utilizes national averages. 

The fuel cycle parameters are defined as follows.

• ax is the quantity of fuel x burned per unit of electricity produced, on average, for grid 

electricity. The calculation of ax includes a factor to account for losses incurred 

through the transmission and distribution systems. 

• by is the amount of grid electricity used in producing fuel y, in MWh per physical unit 

of fuel y.

• cxy is the amount of fuel x consumed in producing one unit of fuel y.

• qx is the heat content of fuel x (MBtu/physical unit).

• zx(s) is the emissions intensity for fuel x (mass of pollutant s per physical unit of x

produced).

All the parameters are calculated as functions of an annual time step; hence, when 

evaluating the effects of amended standards, a time series of annual values is used to estimate the 

FFC energy and emissions savings in each year of the analysis period and cumulatively. Fossil 

fuel quantities are converted to energy units using the heat content factor qx. To convert 

electricity in kWh to primary energy units, on-site electricity consumption is multiplied by the 

site-to-power-plant energy use factor, described in chapter 10. The site-to-power-plant energy 

use factor is defined as the ratio of the total primary energy consumption by the electric power 

sector (in quads) divided by the total electricity generated each year.

The FFC multiplier is denoted μ (mu). A separate multiplier is calculated for each fuel 

used on site. Also calculated is a multiplier for electricity that reflects the fuel mix used in its 

generation. The multipliers are dimensionless numbers applied to primary energy savings to 

obtain the FFC energy savings. The upstream component of the energy savings is proportional to 

(μ-1). The fuel type is denoted by a subscript on the multiplier μ.

When DOE estimates energy savings attributable to appliance standards, the method for 

performing the full-fuel-cycle analysis utilizes data and projections published in the Annual 

Energy Outlook (AEO); in this case, AEO2014.

4 Table 10-A.2.1 summarizes the AEO2014 data 

used as inputs to the calculation of various parameters. The column titled "AEO Table" gives the 

name of the table that provided the reference data.

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Table 10-A.2.1 Dependence of FFC Parameters on AEO Inputs

Parameter(s) Fuel(s) AEO Table Variables

qx All Conversion factors MMBtu per physical unit

ax All

Electricity supply, disposition, 

prices, and emissions Generation by fuel type

Energy consumption by sector 

and source

Electric energy consumption

by the power sector

bc, cnc, cpc Coal

Coal production by region and 

type

Coal production by type and 

sulfur content

bp, cnp, cpp Petroleum

Refining industry energy 

consumption Refining-only energy use

Liquid fuels supply and 

disposition Crude supply by source

International liquids supply and 

disposition Crude oil imports

Oil and gas supply Domestic crude oil production

cnn Natural gas

Oil and gas supply U.S. dry gas production

Natural gas supply, disposition, 

and prices Pipeline, lease, and plant fuel

zx All

Electricity supply, disposition, 

prices, and emissions Power sector emissions

The AEO2014 does not provide all the information needed to estimate total energy use in 

the fuel production chain. Coughlin (2013) describes the additional data sources needed to 

complete the analysis. The time dependence in the FFC multipliers for dishwashers, however, 

arises exclusively from variables taken from the AEO2014.

10-A.3 ENERGY MULTIPLIERS FOR THE FULL FUEL CYCLE

FFC energy multipliers for selected years are presented in Table 10-A.3.1. The 2040 

value was held constant for the analysis period beyond 2040, which is the last year in the 

AEO2014 projection. The multiplier for electricity reflects the shares of various primary fuels in 

total electricity generation throughout the forecast period. 

Table 10-A.3.1 Energy Multipliers for the Full Fuel Cycle (Based on AEO2014)

2019 2020 2025 2030 2035 2040

Electricity 1.043 1.044 1.045 1.046 1.047 1.047

Natural gas 1.108 1.109 1.111 1.113 1.114 1.114

Petroleum fuels 1.176 1.176 1.176 1.174 1.172 1.170

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REFERENCES

1 U.S. Department of Energy–Office of Energy Efficiency and Renewable Energy. Energy 

Conservation Program for Consumer Products and Certain Commercial and Industrial 

Equipment. Statement of Policy for Adopting Full Fuel Cycle Analyses into Energy 

Conservation Standards Program. Federal Register. August 18, 2011. Vol. 76, no. 160: 

pp. 51281–51289.

2 Coughlin, K. A Mathematical Analysis of Full Fuel Cycle Energy Use. Energy. 2012. 

37(1): pp. 698–708. (Last accessed June 22, 2014.) 

<http://www.sciencedirect.com/science/article/pii/S0360544211006803>

3 Coughlin, K. Projections of Full-Fuel-Cycle Energy and Emissions Metrics. 2013. 

Lawrence Berkeley National Laboratory. Report No. LBNL-6025E. 

4 U.S. Energy Information Administration. Annual Energy Outlook 2014 with Projections 

to 2040. April 2014. DOE/EIA-0383(2014). Washington, D.C. (Last accessed June 22, 

2014.) <http://www.eia.gov/forecasts/aeo/pdf/0383(2014).pdf >

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