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 FULL-FUEL-CYCLE ENERGY MULTIPLIERS .............................................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 Full-Fuel-Cycle Energy Multipliers (Based on AEO 2013)....................10-A-3

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APPENDIX 10-A. FULL-FUEL-CYCLE MULTIPLIERS

10-A.1 INTRODUCTION

This appendix summarizes the methods used to calculate full-fuel-cycle (FFC) energy 

savings expected to result from potential standards. 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. The U.S. Department of Energy’s (DOE’s) traditional approach encompassed only site 

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

electricity.1 Per DOE’s 2011 Statement of Policy for Adopting Full Fuel Cycle Analyses, DOE 

now uses FFC measures of energy use and emissions in its energy conservation standards 

analyses. This appendix summarizes the methods used to incorporate the full-fuel-cycle impacts 

into the analysis.

This analysis uses several different terms to reference energy use. The physical sources of 

energy are the primary fuels such as coal, natural gas, liquid fuels, etc. Primary energy is equal to 

the heat content (Btu) of the primary fuels used to provide an end-use service. Site energy use is 

defined as the energy consumed at the point-of-use in a building or industrial process. Where 

natural gas and petroleum fuels are consumed at the site (for example in a furnace), site energy is 

identical to primary energy, with both equal to the heat content of the primary fuel consumed. 

For electricity, site energy is measured in kWh. In this case the primary energy is equal to the 

quads of primary energy required to generate and deliver the site electricity. This primary energy 

is calculated by multiplying the site kWh times the site-to-power plant energy use factor, given 

in Chapter 10. For the FFC analysis, the 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 fuel cycle analysis must distinguish between electricity generated by fossil fuels 

and uranium, and electricity generated from renewable fluxes (wind, solar and hydro). For the 

former, the upstream fuel cycle impacts are derived from the amount of fuel consumed at the 

power plant. For the latter, no fuel per se is used, so there is no upstream component.

10-A.2 METHODOLOGY

The mathematical approach is discussed in the paper A Mathematical Analysis of Full 

Fuel Cycle Energy Use,

2 and details on the fuel production chain analysis are presented in the 

paper Projections of Full Fuel Cycle Energy and Emissions Metrics.

3 The text below provides a 

brief summary of the methods used to calculate FFC energy.

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When all energy quantities are normalized to the same units, the FFC energy use can be 

represented as the product of the primary energy use and an FFC multiplier. The FFC multiplier 

is defined mathematically as a function of a set of parameters representing the energy intensity 

and material losses at each production stage. These parameters depend only on physical data, so

the calculations do not require any assumptions about prices or other economic data. While in 

general these parameter values may vary by geographic region, for this analysis national 

averages are used. 

In the notation below, the indices x and y are used to indicate fuel type, with x=c for coal, 

x=g for natural gas, x=p for petroleum fuels, x=u for uranium and x=r for renewable fluxes. The 

fuel cycle parameters are:

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

electricity. The calculation of ax includes a factor to account for transmission and 

distribution system losses. 

• by is the amount of grid electricity used in production of 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)

The parameters are calculated as a function of time with an annual time step; hence, a 

time series of annual values is used to estimate the FFC energy and emissions savings in each 

year of the analysis period. Fossil fuel quantities are converted to energy units using the heat 

content factors 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. 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 quadrillion Btu’s) divided by the total electricity generation in each year.

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

used on site. A multiplier is also calculated for electricity reflecting the fuel mix used in its 

generation. The multipliers are dimensionless numbers that are 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.

For DOE’s appliance standards energy savings estimates, the fuel cycle analysis 

methodology is designed to make use of data and projections published in the Annual Energy 

Outlook (AEO). Table 10-A.2.1 provides a summary of the AEO data used as inputs to the 

different parameter calculations. The AEO does not provide all the information needed to 

estimate total energy use in the fuel production chain. Reference three describes the additional 

data sources used to complete the analysis. However, the time dependence in the FFC multipliers 

arises exclusively from variables taken from the AEO. The FFC analysis for PTAC and PTHP

equipment used data from AEO 2013.

4

10-A-2
Table 10-A.2.1 Dependence of FFC Parameters on AEO Inputs

Parameter Fuel 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 power sector energy 

consumption

bc, cnc, cpc coal Coal Production by Region and 

Type

Production by coal 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 Crude oil domestic production

cnn

natural 

gas

Oil and Gas Supply US 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

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

FFC energy multipliers are presented in Table 10-A.3.1 for selected years. For the

analysis period beyond 2040, the last year in the AEO 2013 projection, the 2040 value was held 

constant. The multiplier for electricity reflects the shares of various primary fuels in total 

electricity generation over the forecast period.

Table 10-A.3.1 Full-Fuel-Cycle Energy Multipliers (Based on AEO 2013)

2019 2020 2025 2030 2035 2040

Electricity 1.041 1.041 1.040 1.040 1.041 1.040

Natural Gas 1.101 1.101 1.100 1.098 1.099 1.100

Petroleum Fuels 1.139 1.140 1.148 1.158 1.166 1.168

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REFERENCES

1. United States - Office of the Federal Register, Federal Register, Volume 76, Number 160, 

August 18, 2011. UNT Digital Library. Washington D.C.

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

37(1): pp. 698-708 

<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. Energy Information Administration, Annual Energy Outlook 2013 with Projections to 

2040, 2013. Washington, DC. <http://www.eia.gov/forecasts/aeo/pdf/0383(2013).pdf>

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