10-B-i

APPENDIX 10-B. FULL FUEL CYCLE MULTIPLIERS

TABLE OF CONTENTS

10-B.1 METHODOLOGY .............................................................................................. 10-B-1

LIST OF TABLES

Table 10-B.1.1 Full Fuel Cycle Multipliers for the AEO2011 Forecast Period ............... 10-B-3
10-B-1

APPENDIX 10-B. FULL FUEL CYCLE MULTIPLIERS

10-B.1 METHODOLOGY

To provide one unit of energy to the final consumer, for example, in buildings, vehicles 

or industrial processes, a variety of fuels are used in upstream activities. Thus, if the point-of-use 

(site) energy demand is reduced by one unit, the economy-wide demand for energy will be 

reduced by an additional amount corresponding to this upstream fuel use. The sum of site energy 

and upstream energy is called the full-fuel cycle (FFC) energy. This appendix provides a brief 

description of the methodology used to calculate FFC savings from the site energy savings that 

result from a candidate standard level. The mathematical approach is discussed in the paper “A 

Mathematical Analysis of Full Fuel Cycle Energy Use”,

1 and details on the fuel production chain 

analysis are presented in the paper “Calculation of Full Fuel Cycle Multipliers for Energy Use in 

Buildings”).

2 This appendix outlines the steps involved in the calculation, defines the data that 

are taken from the AEO and used in the calculation, and presents the results of the calculations 

for electricity, natural gas and fuel oil.

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

as the product of the site energy and an FFC multiplier. The 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, i.e. the calculations do not 

require any assumptions about prices or other economic data. Most generally, these parameter 

values may vary by geographic region, time, etc. For the calculations used in this analysis, the 

parameters represent national averages. 

Schematically, the steps in the calculation of FFC energy associated with electricity 

savings are:

1. Assume the site energy savings, denoted S0 (mWh), are known.

2. Site electricity savings are converted to electricity savings at the power plant, taking into 

account the transmission and distribution loss factors. The power plant electricity savings 

are given by S1 = tdloss*S0, where 

• S1 is the power plant electricity savings (mWh)

• tdloss is the transmission & distribution loss factora

3. Power plant electricity savings are converted to fuel savings. This conversion depends on 

a set of parameters ax where

• x is an index used to indicate fuel type, with x=c for coal, x=g for natural gas, and 

x=p for petroleum fuels

• ax is the amount of fuel x consumed per MWh of electricity produced at the power 

plant

• The fuel savings are S2x = ax S1 , for each fuel type x 

 

a The values for tdloss are taken from NEMS. The value depends on region and changes slightly over the forecast 

period. The range of tdloss is 1.07 to 1.09.
10-B-2

The value of ax over the analysis period is calculated from NEMS output. It depends on 

the capacity mix by fuel type, and on individual power plant efficiencies or heat rates, 

and so varies with region and with time. The higher the penetration of renewables, the 

lower the value of ax. 

4. For each fuel type x, an analysis of the fuel production chain determines the amount of 

energy required to produce one unit of fuel for site consumption. This analysis accounts 

for all energy sources, including electricity, that are used in fuel production. The 

consumption of fuel y required to provide one unit of fuel x for site consumption is 

denoted by the matrix element Vxy .

5. The matrix elements Vxy, which represent the incremental use of fuel y in the production 

chain for fuel x, are converted to the matrix elements Mxy, which represent the economy 

wide reduction in demand for fuel y resulting from a one unit reduction in demand for 

fuel x. 

6. The equation S3y = ∑x Mxy S2x gives the full fuel cycle savings of fuel y.

7. The fuel savings are converted to energy units by multiplying S3y by the heat content of 

fuel y, denoted qy. The total FFC energy savings are given by the sum over the index y, 

so the total is equal to ∑x qy S3y.

In addition to electricity, natural gas and petroleum-based fuels (primarily fuel oil) are used 

in buildings. The steps required to calculate the full fuel cycle energy use associated with 

production of gas or fuel oil are essentially identical to the scheme outlined above. The only 

difference is that the analysis begins at step 3, with the site fuel savings substituted for S2x. 

For simplicity in applications, the FFC energy use is summarized as a multiplier μ (mu). This 

is a dimensionless number that can be applied to the site energy savings to obtain the FFC energy 

savings. The upstream component of the energy savings is proportional to (1-μ).

This methodology is completely general and is based on the mathematical definition of the 

quantity the FFC energy is meant to represent. The supporting numerical calculations of the 

parameters can be implemented in a variety of ways. As the data required are incomplete, some 

simplifying assumptions or approximations need to be made (these are explained in detail in the 

paper “Calculation of Full Fuel Cycle Multipliers for Energy Use in Buildings”)

2

. These will 

generally have a limited quantitative impact, but may lead to small differences in the fuel cycle 

energy use parameters calculated by different authors. The GREET model developed by 

Argonne National Laboratory3 is one example of a spreadsheet tool that calculates full fuel cycle 

energy use, with a focus on vehicle-fuel systems. For the Department's appliance standards 

energy savings estimates, the implementation of the FFC calculations has been designed 

specifically to make use of energy forecast data published in the AEO. These data include time 

series of:

1. Domestic production of natural gas by source type, imports of natural gas, and natural gas 

use by the oil and gas industry

2. Domestic production and imports of petroleum fuels by source type; total refinery inputs, 

outputs and refinery fuel use

3. Electric generating capacity by fuel type and fuel consumption for power generation
10-B-3

4. Coal use for power generation, by source type and coal quality

5. Fuel heat content for each fuel type

These quantities vary with each year in the AEO forecast period, leading to a corresponding 

variation in estimates of the full fuel cycle energy multipliers. Multipliers are presented in Table 

10-B.1.1 for the AEO forecast years 2012 to 2035. To extend the analysis period beyond 2035, 

the years 2020 to 2035 are used to define a linear trend, which is then extrapolated to the final 

year of the analysis period.

For electricity, the site-to-source conversion factors are not included in the multiplier 

shown in Table 10-B.1.1. Hence, this multiplier is applied to the source energy savings. Site-tosource conversion factors are given in chapter 10.

Table 10-B.1.1 Full Fuel Cycle Multipliers for the AEO2011 Forecast Period

Forecast year

Source 

Energy 

Savings For 

Electricity

Site Fuel Oil 

Savings

Site Natural 

Gas Savings

2008 1.056 1.123 1.135

2009 1.058 1.120 1.129

2010 1.061 1.120 1.139

2011 1.060 1.118 1.139

2012 1.060 1.131 1.136

2013 1.059 1.130 1.133

2014 1.059 1.130 1.131

2015 1.059 1.129 1.129

2016 1.058 1.129 1.128

2017 1.058 1.130 1.127

2018 1.057 1.129 1.126

2019 1.057 1.128 1.125

2020 1.056 1.127 1.126

2021 1.055 1.127 1.125

2022 1.055 1.127 1.125

2023 1.055 1.127 1.125

2024 1.054 1.127 1.124

2025 1.054 1.127 1.123

2026 1.053 1.127 1.123

2027 1.053 1.127 1.122

2028 1.054 1.128 1.122

2029 1.054 1.128 1.121

2030 1.055 1.130 1.121

2031 1.055 1.131 1.120

2032 1.055 1.131 1.120

2033 1.055 1.131 1.120

2034 1.055 1.132 1.121

2035 on 1.055 1.132 1.121
10-B-4

REFERENCES

1. 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>

2. Coughlin, K., Calculation of Full Fuel Cycle Multipliers for Energy Use in Buildings.

LBNL Paper, 2012

3. Argonne National Laboratory, The Greenhouse Gases, Regulated Emissions, and Energy 

Use in Transportation Model. <http://greet.es.anl.gov/>