APPENDIX 10-B. FULL-FUEL-CYCLE MULTIPLIERS

TABLE OF CONTENTS

10-B.1 INTRODUCTION ............................................................................................... 10-B-2

10-B.2 METHODOLOGY .............................................................................................. 10-B-2

10-B.3 FULL-FUEL-CYCLE ENERGY MULTIPLIERS ............................................. 10-B-4

LIST OF TABLES

Table 10-B.2.1 Dependence of Full-Fuel-Cycle Parameters on Annual Energy Outlook

Inputs........................................................................................................ 10-B-4

Table 10-B.3.1 Upstream Energy Multipliers (Based on Annual Energy Outlook 2014) 10-B-4

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APPENDIX 10-B. FULL-FUEL-CYCLE MULTIPLIERS

10-B.1 INTRODUCTION

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

savings expected to result from amended 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 encompasses only 

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

electricity. However, 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.1 This appendix summarizes the methods used to incorporate the FFC impacts 

into the analysis.

This analysis uses several different terms for “energy use.” The physical sources of 

energy are primary fuels such as coal, natural gas, liquid fuels, and the like. Primary energy is 

equal to the heat content, in British thermal units (Btu), of a primary fuel that is used to provide 

an end-use service, such as, water heating.

a Site energy use is the energy consumed at the pointof-use in a building or industrial process. Where natural gas or petroleum fuels are consumed at a

site, such as in a boiler, site energy is identical to primary energy ‒ both are equal to the heat 

content of the primary fuel consumed. Electricity is considered site energy and measured in 

kilowatt hours (kWh).

b In this case, the primary energy is equal to the amount of primary energy

required to generate and deliver the site electricity.c This primary energy is calculated by 

multiplying the site kWh times the site-to-power plant energy-use factor, addressed in chapter 

10. For the FFC analysis, the upstream energy use is defined as the energy consumed in 

extracting, processing, and transporting or distributing a primary fuel. FFC energy use is the 

sum of primary energy at the site or power plant plus upstream energy use. 

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

electricity in FFC analysis must distinguish between electricity generated by fossil fuels and 

uranium, and electricity generated from renewable fluxes (e.g., wind, solar and hydropower). For 

the former, the upstream fuel cycle impacts are derived based on 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-B.2 METHODOLOGY

The mathematical approach to FFC is addressed in the paper A Mathematical Analysis of 

Full Fuel Cycle Energy Use and details about the fuel production chain analysis are presented in 

a A British thermal unit is the amount of energy needed to cool or heat one pound of water by one degree 

Fahrenheit.

b

A kilowatt-hour is a unit of energy equivalent to one kilowatt (1 kW) of power expended for one hour. A kilowatt 

hour is a unit of energy equal to 1,000 watt-hours. The total energy in kilowatt-hours is the product of the power in 

kilowatts and the time in hours. 1 kWh = 3412 Btu. c Quad is a unit of energy, short for quadrillion, where 1 quad = 1015Btu or 293.1 billion kWh.

10-B-2

 
the paper Projections of Full-Fuel-Cycle Energy and Emissions Metrics.

2,

.

3 The text below 

provides a brief summary of the methods used to calculate FFC energy.

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 power sector primary energy use factor indicated in chapter 10. 

The power sector primary 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 generation in 

each year.

The FFC multiplier is a dimensionless number denoted μ (mu). The upstream component 

of the energy savings is proportional to (μ-1). A separate multiplier is calculated for each fuel 

used on site. The fuel type is denoted by a subscript on the multiplier μ. A multiplier is also 

calculated for electricity reflecting the fuel mix used in its generation. 

For DOE’s appliance standards energy savings estimates, the FFC analysis methodology 

is designed to make use of data and projections published in the Annual Energy Outlook (AEO). 

Table 10-B.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. The Projections of Full-Fuel-Cycle Energy and Emissions Metrics

paper describes the additional data sources used to complete the analysis.3 However, the time 

10-B-3
dependence in the FFC multipliers arises exclusively from variables taken from the AEO. The 

FFC analysis for commercial packaged boilers used data from AEO 2014.

4

Table 10-B.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-B.3 FULL-FUEL-CYCLE ENERGY MULTIPLIERS

Upstream energy multipliers are presented in Table 10-B.3.1 for selected years. For years 

after 2040 (the last year in the AEO), DOE maintained the 2040 value. The multipliers are 

applied to site energy. The multiplier for electricity reflects the shares of various primary fuels in 

total electricity generation over the forecast period.

Table 10-B.3.1 Upstream Energy Multipliers (Based on AEO 2014)

2019 2025 2030 2035 2040 2045 2050

Electricity 0.044 0.045 0.046 0.047 0.047 0.047 0.047

Natural Gas 0.109 0.111 0.113 0.114 0.114 0.114 0.114

Petroleum Fuels 0.176 0.176 0.174 0.172 0.170 0.170 0.170

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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. U.S. Department of Energy-Energy Information Administration, Annual Energy Outlook 

2014 with Projections to 2040, 2014. Washington, DC. 

<http://www.eia.gov/forecasts/aeo/>

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