I-i 

APPENDIX I. ESTIMATION OF MARGINAL HEAT RATES AND 

SITE TO SOURCE CONVERSION FACTORS 

TABLE OF CONTENTS 

I.1 Competing Effects ............................................................................................................I-1

I.2 Example ............................................................................................................................I-3

I.3 ...........................................................................................................................................I-4

I.4 Estimation of Marginal Heat Rates for Final Rule Analysis ............................................I-4

I.4.1 Sectoral Scope of Marginal Heat Rate ................................................................I-4

I.4.2 Marginal Heat Rates from the NEMS-BT Simulations.......................................I-6

I.5 Site-to-Source Energy Conversion Factors.......................................................................I-8

LIST OF TABLES 

Table I.2.1 Example of Average Heat Rates and Marginal Heat Rates for 

Packaged Terminal Heat Pumps in 2014..............................................................I-3 

Table I.4.1 Marginal Heat Rates..................................................................................................I-8 

Table I.5.1 Site-to-Source Conversion Factors for Final Rule Analysis...................................I-10 

LIST OF FIGURES 

Figure I.4.1 Marginal Heat Rates for 20X, 30X, and 40X Cases for the Electric 

Power Sector.........................................................................................................I-7 

EERE-2006-STD-0125 COMMENT 46
 I-ii 

EERE-2006-STD-0125 COMMENT 46
APPENDIX I. ESTIMATION OF MARGINAL HEAT RATES AND 

SITE-TO-SOURCE CONVERSION FACTORS 

As described in chapter 10 of the technical support document, site-to-source conversion 

factors are used to convert energy savings at the site (in kilowatt hours [kWh]) to obtain primary 

or source energy savings. These conversion factors are based on two separate quantities: (1) the 

quantity of source energy needed to produce a kWh of electricity at generation plants and (2) the 

quantity of electricity lost in the transmission and distribution of electricity to final customers. 

The National Energy Modeling System (NEMS-BT) is used to translate end-use 

electricity savings to source energy savings. The amount source energy saved as a result of a 

change in generation is termed the marginal heat rate (MHR), which is calculated by imposing a 

load reduction to the end use of the equipment being analyzed in NEMS-BT and observing the 

change in the source energy use. For BVM equipment, the estimated MHR ranges from just over 

8,500 Btu/kWh in 2015 to about 8,800 Btu/kWh in 2030. This variation has to do with the 

response of the utility sector to meet the different magnitude and shape of the load as compared 

to the reference case in the Annual Energy Outlook (AEO2008).

1

 Over the entire period from 

2014, the MHR averages about 9000 Btu/kWh. 

Before turning to a detailed discussion of the MHRs derived from the NEMS-BT for 

BVM equipment, it is useful to consider a number of conceptual issues that relate to MHRs. 

These issues are discussed in sections I.1 and I.2. Section I.3 describes more specifically how the 

MHRs were developed for this overall analysis. Section I.5 discusses how transmission and 

distribution losses were estimated and how the MHRs are translated into site-to-source 

conversion factors. 

I.1 Competing Effects 

On first inspection, an MHR near 8,500 Btu/kWh is perplexing, as it is lower than that 

most power plants likely to be in existence by 2030. The key to understanding this result is that 

this conversion rate does not represent a specific marginal generator or combination of 

generators but is actually a reflection of several NEMS-BT simulated effects that stem from an 

energy conservation standard. Thus, the primary reason why the MHR associated with a standard 

for BVM equipment is lower than expected is because the overall rate of efficiency 

improvement of the power system (measured as the average heat rate [AHR], Btu/kWh) with the 

standard in place is lower than that of the reference case in the AEO. 

A simple mathematical decomposition of the change in source energy between the 

reference case and the standards case will help clarify this situation. As shown in equations I.1 

and I.2, the source energy in both the reference case and the standards case can be expressed as 

the product of the amount of electricity generated (TWh) times an AHR: 

r r AHRTWhSE r   Eq. I.1

s s AHRTWhSE s   Eq. I.2

 I-1 

EERE-2006-STD-0125 COMMENT 46
Where: 

SEr , SEs, = Source energy in the reference and standards cases, respectively 

TWhr , TWhs = Terrawatt-hours in the reference and standards cases, respectively 

AHRr, AHRs = Average heat rates (Btu/kWh) in the reference and standards cases, 

respectively 

A common decomposition of the difference of two products (e.g., variable X times 

variable Y in two situations) is shown in the following expression: 

rs AHRSESESE TWHTWh  AHR Eq. I.3

Where: 

AHR = the average of the AHRs for the reference and standards cases, 

TWh = the average generation (TWh) for the reference and standards cases; and 

The variables preceded by the delta symbol ( ) represent the difference between the 

standards and references cases (i.e., the difference between the cases for the same year) 

Using this formulation, the first term to the right of the second equal sign in equation I.3 

can be thought of as the “displaced generation” effect. The second term can be termed the 

electric utility “system intensity” effect. The system intensity effect is defined purely in terms of 

how the AHR changes between the reference and standards cases. No implication is suggested as 

to whether the utility sector is operating any differently with regard to economic efficiency

between the reference and standards cases. 

In prior appliance and equipment rulemakings, the concept of a MHR has been 

employed; it is used as convenient means of estimating the amount of source energy that is saved 

corresponding to a reduction in electricity generation brought about by the standard. Based on 

simulations with the NEMS-BT model, it is based on the change in source energy divided by the 

change in total generation. In terms of equation I.3, the MHR is calculated by dividing ∆SE by 

∆TWh. When both sides of equation I.3 are divided by the change in generation, we have: 

TWhSEMHR TWHAHR AHR TWh / r /  Eq. I.4

Expressed in this manner, the MHR is shown to be the AHR (averaged between the two 

cases) plus a adjustment term involving the relative sizes of the change in the AHR and the 

change in total generation ( ). Because an efficiency standard will cause total 

generation to fall, the sign of is negative. Thus at least qualitatively, if the AHR (

AHR /  TWh

TWh AHR ) 

increases, one can expect to find that the MHR is lower than the AHR. Depending on the 

particular circumstances (as will be illustrated below), the differences between the MHRs and 

AHRs emanating from a particular scenario in NEMS-BT can be considerable. 

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EERE-2006-STD-0125 COMMENT 46
For the cases using NEMS-BT to analyze efficiency standards for various types of 

commercial equipment, the long-term (2020 and later) MHRs are consistently lower than the 

AHRs. This reflects an increase in the AHR between the reference and standards cases. This 

increase in the AHRs can be attributed to two factors. 

In the prior rulemakings for residential air conditioners and heat pumps (66 Federal 

Register 7169) the Technical Support Document, Appendix M2

 noted that the first factor is due 

to the slower growth in overall electricity consumption that retards the investment in new, more 

efficient, generating capacity. The second factor involves shifts between different types of 

generating technologies (e.g., gas-to-coal, coal-to-nuclear). These shifts are likely induced by a 

change in the shape in the overall load shape seen by utilities. Any of these shifts that substitute 

generating capacity with higher heat rates than that of the displaced capacity will increase the 

AHR, and consequently, the lower the MHR. 

I.2 Example 

A numerical illustration of the relationship of the AHR and MHR for one of NEMS-BT cases 

is shown in Table I.2.1. The numbers are extracted from the NEMS-BT output for a single case for a 

recent (2008) analysis of energy conservation standards for beverage vending machines (BVMs). 

Table I.2.1 Example of Average Heat Rates and Marginal Heat Rates for Beverage Vending 

Machines in 2014 

Average and Marginal Heat Rates 

 (1) (2) (3) 

TWh 

x Ave. Heat Rate 

(Btu/kWh) = Total BBtu 

Reference case 4,241.5 10,067.9 42,703,098 

Standards case 4,236.3 10,071.8 42,667,465 

 Change -5.2 3.8 -35,633 

MHR = -35,663/-3.8 = 6,917 

Decomposition of Change in Source Energy 

Component 

Ave. of Cases Change Change 

Generation effect (ave. H. Rate) (Chg.in TWh) 

10,069.8 -5.2 -51,878 

System intensity (ave. TWh) (Chg. in H. Rate) 

4,238.9 3.8 16,245 

Total Change 

(Btu) -35,633 

MHR = 

Ave. H. Rate + Adjustment = Marg. H. Rate 

10,069.8 -3153.3 6,917 

 I-3 

EERE-2006-STD-0125 COMMENT 46
I.3

The top two lines of the table show generation (in TWh) and average heat rates 

(Btu/kWh) for the reference and standards cases. To maintain conventional units for generation 

and heat rates, the source energy is expressed in billion Btu (BBtu). 

In comparing the two cases, generation is lower by about 5 TWh in the standards case as 

compared to the reference case in 2030. The AHR in column (2), however, is higher by nearly 

4 Btu/kWh. Based on the change in total source energy (35,600 BBtu) and the change in 

generation, the MHR is computed to be 6,917 Btu/kWh, considerably lower than the AHR. 

The lower portion of the table shows a decomposition of the change in source energy use 

based on the formulation in equation I.2. Using this method, the displaced generation effect is 

calculated to be approximately 51,900 BBtu (of savings). The system intensity effect works in 

the opposite direction, with an estimated increase of nearly 16,300 BBtu. The net effect is the 

observed change in source energy of 35,600 BBtu. One possible interpretation of the particular 

result shown is that the system intensity effect essentially reduces the impact of displaced 

generation by about 30 percent (i.e., 16,300/51,900). 

I.4 Estimation of Marginal Heat Rates for Final Rule Analysis 

The estimation of MHRs for use in calculating the source energy savings associated with 

electricity savings shown in chapter 7 are based on a series of simulations with the NEMS-BT 

model. As discussed in appendix K, these simulations employ multiples of the predicted savings 

in electricity use as a means of overcoming model noise in solving the NEMS-BT model. The 

multiples employed are designated as “20X,” “30X,” and “40X” and are described fully in 

appendix K. For purposes of the calculating a single set of MHRs, an average of the MHRs 

derived from these cases was used. A further adjustment involved smoothing the resulting 

projected values by taking a centered 3-year moving average of the heat rates. The details of the 

methodology will be explained more fully below. 

I.4.1 Sectoral Scope of Marginal Heat Rate 

As discussed in section I.2, the most straightforward calculation of the MHR is to divide 

the change in source energy savings by the change in electricity generation. However, some

consideration as how best to measure these values in terms of the NEMS-BT output may be 

warranted. Three potential approaches were considered: 

a) Economy-wide measure 

Table 1 in the AEO2008 displays total energy consumption for eight different major fuel 

types (petroleum, natural gas, coal, nuclear power, hydropower, biomass, other renewable 

energy, and other). The sum of this consumption is total source energy used in the U.S. 

economy, now estimated to be just over 100 quadrillion Btu. The broadest measure of a MHR is 

to divide the change in economy-wide source energy by the change in total electricity generation. 

 I-4 

EERE-2006-STD-0125 COMMENT 46
In essence, the MHR calculated in this manner incorporates more than just the efficiency 

of the electricity generation sector but also any ancillary changes in direct fossil fuel use by other 

sectors of the economy (e.g., residential or commercial customers). As described briefly in 

appendix U, a typical impact from energy-efficiency standards predicted by the NEMS-BT 

model was to induce a very small increase in retail electricity prices. This small change not only 

magnifies the impact of the initial change in electricity (by further dampening electricity 

consumption), but also leads to very small increases in natural gas use by residential and 

commercial customers (as natural gas becomes relatively less expensive than electricity). This 

increase in natural gas usage contributes to somewhat lower MHRs than what would otherwise 

be calculated without this effect. 

b) All generation 

Electricity in the United States is primarily produced by plants whose primary business is 

to sell electricity, and heat, to the public. These plants are designated by EIA as the “Electric 

Power Sector.” Other sources of electricity generation are the end-use sectors (residential, 

commercial, and industrial). As noted by EIA in the notes to table A8 of the (2008) AEO, enduse generation “includes combined heat and power plants and electricity-only plant in the 

commercial and industrial sectors; and small on-site generating systems in the residential, 

commercial, and industrial sectors used primarily for own-use generation which may also sell 

some power to the grid.” In 2012, the first effective year of the standards for beverage vending 

machine equipment, end-use generation from the commercial and industrial sectors is projected 

in the AEO reference case to account for about 4.5 percent of total generation. 

To calculate a MHR associated with all generators requires both the change in total 

generation (in TWh) and the change in total source energy (expressed in Btu) to produce that 

electricity. NEMS-BT reports total generation, broken out between the electric power sector and 

end-use generation, in a single table (as table A8 in the AEO). Another table produced by 

NEMS-BT (as table A2 in the AEO) provides fuel inputs, including nuclear and renewables, for 

the electric power sector. Unfortunately, NEMS-BT does not report the fuel consumption used 

by the end-use sectors for electricity generation. This deficiency suggests that the best 

approximation to the change in source energy (∆SE) for all electricity generation is likely 

calculated as 

∆ SE (All generators) = ∆ SE (economy-wide) - ∆ Non-electricity (residential) 

∆ Non-electricity (commercial) Eq. I.5

By subtracting the change in non-electricity (fossil fuel) energy use in the residential 

sector, the induced impact of relative fuel prices is excluded from the MHR calculation. For the 

commercial sector, the change in non-electricity energy use is also expected to primarily result 

from a price response, reflected in space and water heating use, and not in the (very small) 

amount of fuel used to generate on-site electricity. Of total commercial and industrial generation 

of electricity in 2005, only about 5 percent was generated in the commercial sector (Annual 

Energy Review 20073

 Table 8.2d). After making these two adjustments, it is reasonable to expect 

 I-5 

EERE-2006-STD-0125 COMMENT 46
that most the resulting change in economy-wide source energy is attributable to the change in 

generation by the electric power sector and the industrial sector.a

 

c) Electric Power Sector 

The third approach is to consider only the MHR that pertains to the electricity produced 

by the electric power sector. NEMS-BT reports both energy inputs and generated electricity by 

major fuel type. This reporting permits calculation of average as well as MHRs for not only for 

the entire sector but also by major type of generating facility. 

The final set of MHRs used in this analysis is based on the third approach (c). First, while 

the economy-wide measures have some utility in showing some the wider energy system effects 

of an energy-efficiency standard, they are less consistent with the definition of MHRs used in 

prior U.S. Department of Energy (DOE) appliance and equipment rulemakings. Second, based 

on the fact that the MHRs derived from the electric power sector typically show more consistent 

year-to-year changes, while having the same general magnitude for all generation, DOE has 

chosen to employ the heat rates from the electric power sector results. As a better indication of 

intermediate trends in the heat rates, the MHRs based on the three-year moving averages are 

used. Because of the considerable uncertainty of whether trends in MHRs would continue past 

2030, the post-2030 heat rates have been fixed at the 2030 values. 

I.4.2 Marginal Heat Rates from the NEMS-BT Simulations 

As described in appendix J, the magnitudes of the energy decrements associated with the 

actual savings from the proposed standards are too small for NEMS-BT to produce stable results. 

This instability is caused by the numerical noise in the solution process of the model and stems, 

in part, from the fact that a precise balancing between the demand and supply sides of NEMS is 

not always achieved. As a result, DOE estimated the various impacts corresponding to different 

trial standard levels (TSLs) using interpolation. The interpolation procedure involved 

implementing reductions to the refrigeration end use at multiples of the proposed standards and 

then linearly interpolating the impacts to correspond to the actual levels of the standards. 

Based upon an estimate of savings for the entire set of BVM equipment under TSL 8 (the 

“max tech” case), a single set of multipliers was selected at 20, 30, and 40 times the predicted 

savings for that particular TSL. In 2030, the actual electricity decrements corresponding to these 

multiples are 15.2, 22.8, and 30.4 TWh. Relative to total projected electricity consumption of the 

commercial sector in the 2008 Annual Energy Outlook, these levels of savings correspond to 

reductions of 0.78, 1.17, and 1.57 percent, respectively. 

Figure I.4.1 shows the MHRs for the electric power sector for the three levels of savings 

associated with the three multipliers. The three levels are labeled “20X,” “30X,” and “40X” for 

consistency with the discussion in appendix K—the actual magnitude of the cooling savings 

 

a

 To the extent that there is some fuel switching for process use in the industrial sector that results from changing 

relative prices due to the standard, the computed marginal heat rate will not completely reflect changes due solely to 

electricity generation. Within the current modeling and reporting structure of NEMS, there is no way to eliminate 

that effect completely; thus, the methodology to calculate the change in source energy expressed in equation (I.5) 

yields only an approximate MHR. 

 I-6 

EERE-2006-STD-0125 COMMENT 46
applied to the NEMS commercial sector module in 2030 ranges between 15 and 30 TWh, as 

mentioned above. The MHRs in Figure I.4.1 are derived from the model-generated responses by 

the electricity power sector [approach (c)]. 

0

2,000

4,000

6,000

8,000

10,000

12,000

2012 2014 2016 2018 2020 2022 2024 2026 2028

Btu/kWh

20X

30X

40X

Figure I.4.1 Marginal Heat Rates for 20X, 30X, and 40X Cases for the Electric Power Sector 

Clearly from Figure I.4.1, the MHRs from the 40X case are generally higher than those 

from the two smaller multipliers, especially toward the end of the forecast period. As discussed 

in chapter 14, the behavior of NEMS in any particular case may be affected by the capacity 

planning aspects of the model that can sometimes unduly influence overall generation in the 

years around a “shock” to electricity demand. For this particular multiplier (40X), the (negative) 

impact on nuclear generation is relatively higher than the other cases. That behavior appears to 

be affecting the MHRs in a different manner than the other cases. 

In developing the response functions for the utility impacts described in the appendix K, 

a regression approach was used to essentially average the impacts across the simulations. The 

estimated coefficients of the linear regression line were then used to interpolate the utility sector 

impacts to correspond to actual savings levels for the various standards. The regressions were 

estimated one for selected years – 2015 through 2030 – at 5-year intervals. 

Because the MHRs are required for each year in the future to calculate source energy 

savings, a more straightforward (two-step) approach was chosen. The first step in the approach 

was to average the simulation results across the all three (20X, 30X, and 40X) simulations. 

Because the simulations appear to still produce year-to-year noise in the results, the second step 

was to smooth the resulting series by taking a 3-year centered moving average. Thus, for 

example, the smoothed value for 2020 is the average of the heat rates for 2019, 2020, and 2021. 

The values for the 2013 and 2030 are set equal to the values for 2014 and 2029, respectively. The 

resulting MHRs are shown in Table I.4.1. 

 I-7 

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Table I.4.1 Marginal Heat Rates 

Year Btu/kWh 

2012 8,939 

2013 8,800 

2014 8,649 

2015 8,508 

2016 8,489 

2017 8,680 

2018 8,905 

2019 9,073 

2020 8,978 

2021 8,950 

2022 8,949 

2023 9,192 

2024 9,270 

2025 9,294 

2026 9,187 

2027 9,024 

2028 8,858 

2029 8,772 

2030 8,818 

2042 8,818 

I.5 Site-to-Source Energy Conversion Factors 

The AHRs and MHRs discussed in the previous sections apply only to electricity 

generation. The factors used to convert electricity savings at building site into source energy 

must not only take into account the generation intensity of the utility sector but also transmission 

and distribution (T&D) losses between power plant and final customers. NEMS-BT does not 

report annual T&D losses in its available set of output tables. Thus, one must rely on other 

information provided by EIA to develop an estimate of these losses. 

An explicit treatment of how DOE estimated T&D losses can be clarified by initially 

defining the following variables: 

DE = Delivered electricity 

GG = Gross generation 

NG = Net generation 

T&D = T&D losses 

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EERE-2006-STD-0125 COMMENT 46
The four variables defined above are expressed in electricity units (for consistency with 

the prior discussion, TWh). Delivered electricity is the amount electricity delivered to the 

building site; energy efficiency standards will reduce delivered electricity. Gross generation is 

the total amount of electricity produced by the electricity sector, including the amount of 

electricity used in the operation of power plant. Net generation is the total generation less the 

electricity used in power plants. T&D losses represent the losses between net generation and the 

electricity delivered to final customers. 

The first two pages of section 8 in the Annual Energy Review 2007 present EIA’s 

estimates as to the approximate relationships of these quantities in the U.S. energy sector. 

Beginning with the gross and net generation, EIA indicates that the electric energy used in the 

operation of power plants is “estimated as 5 percent of gross generation.” This simple 

relationship can be expressed as 

NG = 0.95 × GG Eq. I.6

EIA also indicates that “transmission and distribution losses (electricity losses that occur 

between the point of generation and delivery to the customer) are estimated to as 9 percent of 

total generation.” In formal terms, 

 T&D = 0.09 × GG Eq. I.7

Combining Equations I.6 and I.7 yields 

 T&D = 0.09 × (NG/0.95) = 0.0855 × NG Eq. I.8

Because T&D is the difference between net generation and delivered electricity, one can 

then express delivered electricity (DE) in terms of net generation as follows: 

 DE = NG – T&D = NG – 0.0855 NG = 0.9145 NG Eq. I.9

To express the change in NG that is consistent with a one-unit (e.g., TWh) change in DE, 

both sides of Equation I.9 are divided by 0.9145 to yield 

 NG = (1.0/0.9145) × DE = 1.0935 × DE Eq. I.10

The values for electricity generation in NEMS-BT (and the AEO) are all in terms of net 

electricity generation. In essence, in NEMS-BT, the plant use of electricity is treated as any other 

losses (e.g., thermal losses in fossil fuel plants) in production of electricity. Plant electricity use 

is thus already reflected in the average heat rates reported by NEMS-BT. 

All of the discussion in sections I.1 through I.3 thus relate to the heat rates defined in 

terms of net electricity. As the average heat rates define source energy (SE) in terms of kWh of 

net generation, the incorporation of equation I.10 provides the following relationship: 

SE = AHR × NG = AHR × 1.0935 × DE Eq. I.11

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EERE-2006-STD-0125 COMMENT 46
For the analysis here, it is assumed that the overall T&D losses, on a percentage basis, 

will be the same before and after the imposition of energy efficiency standards. Thus, to evaluate 

the source energy savings associated with a change in delivered electricity use, one obtains: 

∆SE = MHR × 1.0935 × ∆DE Eq. I.12

The first two columns of Table I.5.1 present the site-to-source conversion factors 

expressed in terms of source Btu per kWh of (displaced) site electricity. The values are based on 

equation I.12, where the MHRs in Table I.4.1 have all been multiplied by a constant factor of 

1.0935. 

Table I.5.1 Site-to-Source Conversion Factors for Final Rule Analysis

Conversion 

Factor, source 

Btu/site kWh 

Conversion 

Factor, source 

Btu/site Btu 

2012 9,775 2.865 

2013 9,623 2.820 

2014 9,458 2.772 

2015 9,304 2.727 

2016 9,282 2.721 

2017 9,492 2.782 

2018 9,738 2.854 

2019 9,922 2.908 

2020 9,817 2.877 

2021 9,787 2.868 

2022 9,786 2.868 

2023 10,051 2.946 

2024 10,137 2.971 

2025 10,163 2.979 

2026 10,046 2.944 

2027 9,868 2.892 

2028 9,686 2.839 

2029 9,592 2.811 

2030 9,642 2.826 

2031-2050 9,642 2.826 

In some applications (including some prior DOE efficiency standards rulemakings), the 

site-to-source conversion factors have been expressed in terms of the ratios between source and 

site energy, both measured in Btu. On a site basis, the conversion of electricity from kWh to Btu 

is made with a factor of 3412 Btu/kWh. Thus, the values in the last pair of columns are derived 

from the first two columns by dividing all entries by 3412. 

 I-10 

EERE-2006-STD-0125 COMMENT 46
 I-11 

REFERENCES 

1. EIA (Energy Information Administration). 2008. Annual Energy Outlook 2008. 

DOE/EIA-0383(2008). U.S. Department of Energy, Energy Information Administration, 

Washington D.C. Early Release. 

<http://www.eia.doe.gov/oiaf/archive/earlyrelease08/index.html> (Accessed April 10, 

2009.) 

2. U.S. Department of Energy. 2001. Central Air Conditioning Supplemental Notice of 

Proposed Rulemaking (SNOPR) Technical Support Document, July 25, 2001. Appendix 

M. Revised Utility Impact Analysis and Environmental Assessment. 

<http://www.eere.energy.gov/buildings/appliance_standards/residential/ac_central_1000_

r.html> (Accessed April 10, 2009.) 

3. U.S. Department of Energy, Energy Information Administration. Annual Energy Review 

2007 DOE/EIA-0384(2007). June 2008. 

<http://www.eia.doe.gov/emeu/aer/contents.html> (Accessed April 10, 2009.) 

EERE-2006-STD-0125 COMMENT 46