APPENDIX H. ESTIMATION OF MARGINAL HEAT RATES AND
 

SITE TO SOURCE CONVERSION FACTORS
 

TABLE OF CONTENTS
 

H.1 Competing Effects .......................................................................................................... H­1
 

H.2 PTHP Example................................................................................................................ H­3
 

H.3 Estimation of Marginal Heat Rates for Final Rule Analysis .......................................... H­4
 

H.3.1 Sectoral Scope of Marginal Heat Rate .............................................................. H­4
 

H.3.2 Marginal Heat Rates from the NEMS­BT Simulations..................................... H­6
 

H.4 Site­to­Source Energy Conversion Factors..................................................................... H­8
 

LIST OF TABLES

Table H.2.1 Example of Average and Marginal Heat Rates for PTHPs in 2014 ...................... H­4
 

Table H.4.1 Marginal Heat Rates ............................................................................................ H­11
 

Table H.4.2 Site­to­Source Conversion Factors for Final Rule Analysis................................ H­11
 

LIST OF FIGURES

Figure H.3.1 Marginal Heat Rates for 100X, 200X, and 300X Cases, PTAC,

Electric Power Sector.......................................................................................... H­7

Figure H.3.2 Marginal Heat Rates for 100X, 200X, and 300X Cases, PTHP,

Electric Power Sector.......................................................................................... H­7
 

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APPENDIX H. ESTIMATION OF MARGINAL HEAT RATES AND
 

SITE­TO­SOURCE CONVERSION FACTORS
 

As described in Chapter 10 of the TSD, site­to­source conversion factors are used to

convert energy savings at the site (in 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 kilowatt­hour of electricity at generation plants and 2) the quantity of electricity that

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

The NEMS­BT model is used to translate end­use electricity savings to source energy

savings. The amount source energy that is saved as a result of a change in generation is termed

the marginal heat rate (MHR). The MHR is calculated by imposing a load reduction to the end

use of the equipment being analyzed in NEMS­BT and observing the change in the source

energy use. For packaged terminal air conditioner (PTAC) and packaged terminal heat pump

(PTHP) equipment, the MHR varies from just under 8,000 Btu/kWh in 2012 to more 12,000

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).

Before turning to a detailed discussion of the marginal heat rates derived from the

NEMS­BT for PTAC and PTHP equipment, it is useful to consider a number of conceptual

issues that relate to marginal heat rates. These issues are discussed in sections H.1 and H.2.

Section H.3 describes more specifically how the marginal heat rates were developed for this

overall analysis. Section H.4 discusses how transmission and distribution losses were estimated

and how the marginal heat rates are translated into site­to­source conversion factors.

H.1 Competing Effects

On first inspection, an MHR less than 8,000 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 NEMS­BT simulated effects that stem from an

energy efficiency standard. Thus, the primary reason why the PTACs and PTHPs MHR is lower

than expected is because the overall rate of efficiency improvement of the power system

(measured as the average heat rate, 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 H.1

and H.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 average heat rate (AHR):

SE = TWh ⋅ AHR (H.1) r r r

SEs = TWhs ⋅ AHRs (H.2)

H­1

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where

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

TWhr , TWhs = Terrawatt­hours 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:

ΔSE = SEs − SEr = AHR ⋅ ΔTWh + TWH ⋅ ΔAHR (H.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 ( Δ ) 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 H.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 average heat rate 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 marginal heat rate

(MHR) has been employed. The MHR 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 NEMS­BT model, it is based on the change in

source energy divided by the change in total generation. In terms of Equation H.3, the MHR is

calculated by dividing �SE by �TWh. When both sides of Equation H.3 are divided by the

change in generation, we have:

MHR = ΔSE / ΔTWhr = AHR + TWH ⋅ ΔAHR / ΔTWh (H.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 (ΔAHR / ΔTWh ). Because an efficiency standard will cause total

generation to fall, the sign of ΔTWh is negative. Thus, at least qualitatively, if the average heat

rate ( ΔAHR ) 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

marginal and average heat rates emanating from a particular scenario in NEMS­BT can be

considerable.

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For the cases using NEMS­BT to analyze efficiency standards for PTAC/PTHP

equipment, the long­term (2020 and later) MHRs are consistently lower than the average heat

rates. This reflects an increase in the average heat rate between the reference and standards

cases. This increase in the average heat rates can be attributed to two factors.

The first factor, as noted in the prior rulemakings for residential air conditioners and heat

pumps (66 FR 7169) 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., gas­to­coal, coal­to­nuclear). 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, lower the MHR.

H.2 PTHP Example

A numerical illustration of the relationship of the AHR and MHR for one of NEMS­BT

cases is shown in Table H.2.1. The numbers are extracted from the NEMS­BT output for the

middle multiplier case for PTHPs.1

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 H.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).

1 The specific case is for the “200X” multiplier for PTHP. See appendix U for explanation.

H­3

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Table H.2.1 Example of Average and Marginal Heat Rates for PTHPs in 2014
 

Average and Marginal Heat Rates

(1) (2) (3)

x Ave. Heat Rate

TWh (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

Marginal Heat Rate = ­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

Marginal Heat Rate =

ave. H. Rate + Adjustment = Marg. H. Rate

10,069.8 ­3153.3 6,917

H.3 Estimation of Marginal Heat Rates for Final Rule Analysis

The estimation of marginal heat rates 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 NEMS­BT model. As discussed in appendix U, these simulations employ multiples of the

predicted savings in electricity use as a means of overcoming model noise in solving the

NEMS­BT model. The multiples employed are designated as “100X”, “200X”, and “300X” and

are described fully in appendix U. For purposes of the calculating a single set of marginal heat

rates, an average of the marginal heat rates derived from these cases was used. A further

adjustment involved smoothing the resulting projected values by taking a centered three­year

moving average of the heat rates. The details of the methodology will be explained more fully

below.

H.3.1 Sectoral Scope of Marginal Heat Rate

As discussed in section H.2, the most straightforward calculation of the marginal heat

rate is to divide the change in source energy savings by the change in electricity generation.

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However, some consideration as how best to measure these values in terms of the NEMS­BT

output may be warranted. Three potential approaches were considered:

a) Economy­wide measure

Table 1 in the Annual Energy Outlook 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

marginal heat rate is to divide the change in economy­wide source energy by the change in total

electricity generation.

In essence, the marginal heat rate 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 energy­efficiency standards predicted by

the NEMS­BT 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 marginal heat rates 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 end­use 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 electricity­only plant in the

commercial and industrial sectors,; and small on­site generating systems in the residential,

commercial, and industrial sectors used primarily for own­use generation which may also sell

some power to the grid.” In 2012, the first effective year of the standards for PTAC/PTHP

equipment, end­use generation is projected in the AEO reference case to account for about 4.5

percent of total generation.

To calculate a marginal heat rate 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. NEMS­BT reports total generation, broken out between the electric power sector

and end­use generation, in a single table (as Table A8 in the AEO). Another table produced by

NEMS­BT (as Table A2 in the AEO) provides fuel inputs, including nuclear and renewables, for

the electric power sector. Unfortunately, NEMS­BT does not report the fuel consumption used

by the end­use 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

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� SE (All generators) = � SE (economy­wide) ­ � Non­electricity (residential)

� Non­electricity (commercial) (H.5)

By subtracting the change in non­electricity (fossil fuel) energy use in the residential

sector, the induced impact of relative fuel prices is excluded from the marginal heat rate

calculation. For the commercial sector, the change in non­electricity 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 on­site electricity. Of total commercial and

industrial generation of electricity in 2005, only about 5 percent was generated in the commercial

sector (Annual Energy Review 2005, Table 8.2d). After making these two adjustments, it is

reasonable to expect that most the resulting change in economy­wide source energy is

attributable to the change in generation by the electric power sector and the industrial sector.1

c) Electric Power Sector

The third approach is to consider only the marginal heat rate that pertains to the

electricity produced by the electric power sector. NEMS­BT reports both energy inputs and

generated electricity by major fuel type. This reporting permits calculation of average as well as

marginal heat rates for not only for the entire sector, but also by major type of generating facility.

In the discussion to follow, marginal heat rates will be compared only between

approaches (b) and (c). While the economy­wide measures have some utility in showing some

the wider energy system effects of an energy­efficiency standard, they are less consistent with

the definition of marginal heat rates used in prior DOE appliance and equipment rulemakings.2

H.3.2 Marginal Heat Rates from the NEMS­BT Simulations

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

actual savings from the proposed standards are too small for NEMS­BT 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 cooling end use at multiples of the proposed standards and then

linearly interpolating the impacts to correspond to the actual levels of the standards. Based on a

preliminary estimate of savings for one of the products (TSL 6 for standard size PTHPs), a single

set of multipliers was selected at 100, 200, and 300 times the predicted savings for that particular

1 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 completely

eliminate that effect and thus the methodology to calculate the change in source energy expressed in Equation (H.5)

yields only an approximate marginal heat rate. 2 The differences between the marginal heat rates derived in approach (a) and (b) are not large. For PTHP

equipment, the marginal heat rates in 2030 from approach (a) range between 2 and 10 percent lower than those

based on approach (b). The range depends on the magnitude of the electricity savings imposed on the model. The

lower heat rates in (a) stem from a very slight increase in fuel use (primarily natural gas) for space and water heating

that deduct from the fuel savings from lower electricity generation. This small increase in space and water heating

is due to cross­price elasticity effects in the building models in NEMS.

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0

5,000

10,000

15,000

20,000

25,000

2012 2014 2016 2018 2020 2022 2024 2026 2028 2030

Btu/kWh

100x case

200x case

300x case

standard and product. In 2030, the actual electricity decrements corresponding to these multiples

are 12.5, 25.0 and 37.5 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 0.6, 1.2, and 1.8 percent, respectively.

Figure H.3.1 and Figure H.3.2 show the marginal heat rates for PTAC and PTHP

equipment for the three levels of savings. The three levels are labeled “100X”, “200X” and

“300X” for consistency with the discussion in appendix U—the actual magnitude of the cooling

savings applied to the NEMS commercial sector module in 2030 ranges between 12.5 and

Figure H.3.1 Marginal Heat Rates for 100X, 200X, and 300X Cases, PTAC, Electric

Power Sector Btu/kWh

14,000
 

12,000
 

10,000
 

8,000
 

6,000
 

100x case 4,000 200x case

2,000 300x case
 

0
 

2012 2014 2016 2018 2020 2022 2024 2026 2028 2030

Figure H.3.2 Marginal Heat Rates for 100X, 200X, and 300X Cases, PTHP, Electric Power

Sector

H­7

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37.5 TWh, as mentioned above. The marginal heat rates in Figure H.3.1 and Figure H.3.2 are

derived from the model­generated responses by the electricity power sector [approach (c)].

Using the NEMS­BT model consistent with the AEO 2008, the marginal heat rates

generally tend to increase over time. This behavior reflects the proportionately greater reductions

in the coal and nuclear generation over the forecast period (as discussed in Chapter 14). As

explained in sections H.1 and H.2, a decrease in the average heat rate (stemming from reduced

share of coal and nuclear generation) is consistent with an increase in the marginal heat rate

when total generation declines.

While these simulations display the impacts of the NEMS at varying savings decrements,

there is still considerable uncertainty as to whether this specific behavior can be reliably

interpolated to the much lower levels of savings associated with the actual standards. As

discussed in appendix U, different levels of savings decrements were tested in order to determine

an approximate level of savings that would yield less noise in the year­to­year results.

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

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 5­year intervals.

Because the marginal heat rates are required for each year in the future to calculate

source energy savings, a more straightforward (two­step) approach was chosen. The first step in

the approach was to average the simulation results across the three simulations.. Because the

simulations appear to still produce year­to­year noise in the results, the second step was to

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

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

values for the 2012 and 2030 are set equal to the values for 2013 and 2029, respectively. The

resulting marginal heat rates are shown in Table H.4.1.

Based on the fact that the marginal heat rates derived from the electric power sector show

more consistent year­to­year 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 marginal heat rates based on the

three­year moving averages are used. Because of the considerable uncertainty as to whether the

trends in marginal heat rates would continue past 2030, the post­2030 heat rates have been fixed

at the 2030 values.

H.4 Site­to­Source Energy Conversion Factors

The average and marginal heat rates 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.

H­8

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NEMS­BT 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
 

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 2006 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 (H.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 (H.7)

Combining Equations H.6 and H.7 yields

T&D = 0.09 * (NG/0.95) = 0.0855 * NG (H.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 (H.9)

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

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

NG = (1.0/0.9145) * DE = 1.0935 * DE (H.10)

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

electricity generation. In essence, in NEMS­BT, 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 NEMS­BT.

All of the discussion in sections H.1 through H.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 H.10 provides the following relationship:

SE = AHR * NG = AHR * 1.0935 * DE (H.11)

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 (H.12)

The first two columns of Table H.4.2 present the site­to­source conversion factors

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

Equation H.12, where the marginal heat rates in Table H.4.1 have all been multiplied by a

constant factor of 1.0935.

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

site­to­source 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 3,412 Btu/kWh. Thus, the values in the last pair of columns are derived

from the first two columns by dividing all entries by 3,412.

H­10

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Table H.4.1 Marginal Heat Rates
 

Year PTACs Year PTHPs

2012 8,405 2012 7,418

2013 8,405 2013 7,418

2014 8,297 2014 7,653

2015 8,922 2015 8,304

2016 9,156 2016 8,400

2017 9,594 2017 8,559

2018 9,413 2018 8,767

2019 9,239 2019 9,062

2020 10,024 2020 9,582

2021 10,651 2021 9,669

2022 11,525 2022 9,837

2023 10,981 2023 9,430

2024 10,919 2024 9,506

2025 10,788 2025 9,762

2026 11,410 2026 10,339

2027 12,082 2027 10,610

2028 12,487 2028 10,735

2029 12,783 2029 10,869

2030­2042 12783 2030­2042 10,869

Table H.4.2 Site­to­Source Conversion Factors for Final Rule Analysis
 

Conversion Factor, source

Btu/site kWh

Conversion Factor, source

Btu/site Btu

PTAC PTHP PTAC PTHP

2012 9,191 8,111 2.694 2.377

2013 9,191 8,111 2.694 2.377

2014 9,073 8,368 2.659 2.453

2015 9,756 9,080 2.859 2.661

2016 10,012 9,186 2.934 2.692

2017 10,491 9,359 3.075 2.743

2018 10,293 9,587 3.017 2.810

2019 10,103 9,909 2.961 2.904

2020 10,961 10,478 3.213 3.071

2021 11,647 10,573 3.414 3.099

2022 12,602 10,756 3.693 3.152

2023 12,007 10,312 3.519 3.022

2024 11,940 10,394 3.499 3.046

2025 11,797 10,674 3.458 3.128

2026 12,477 11,306 3.657 3.313

2027 13,212 11,602 3.872 3.400

2028 13,654 11,739 4.002 3.440

2029 13,978 11,885 4.097 3.483

2030 13,978 11,885 4.097 3.483

2031­2050 13,978 11,885 4.097 3.483

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REFERENCES
 

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

2006 (DOE/EIA­0384(2006), June 2007.
 

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

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

Website:
 

http://www.eere.energy.gov/buildings/appliance_standards/residential/ac_central_1000_r.html
 

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