I-i APPENDIX I. ESTIMATION OF MARGINAL HEAT RATES AND SITE TO SO URCE 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 Term inal Heat Pumps in 2014 ..............................................................I-3 Table I.4.1 Marginal Heat Rates ..................................................................................................I-8 Table I.5.1 Site-to-Source Conversi on Factors fo r Final Rule Analysis ...................................I-10

LIST OF FI GURES
Figure I.4.1 Marginal Heat Rates for 20X, 30X, and 40X Cases for the El ectric Power Sector .........................................................................................................I-7I-iiAPPENDIX 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 tw o separate quantities: (1) the quantity of source energy needed to produce a kWh of electricity at genera tion plants and (2) the quantity of electricity lost in th e transmission and distribution of electricity to final customers.
The National Energy Modeling System (NEM S-BT) is used to translate end-use electricity savings to source energy savings. Th e 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 equipmen t being analyzed in NEMS-BT and observing the change in the source energy use. For BVM equipm ent, 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 differe nt 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 numbe r 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 th e 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 repr esent 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 r eason 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 th at of the reference case in the AEO

. A simple mathematical decomposition of th e change in source energy between the reference case and the standards case will help clarify this situ ation. As shown in equations I.1 and I.2, the source energy in both the reference ca se and the standards case can be expressed as the product of the amount of electricity generated (TWh) times an AHR:

r r r AHRTWhSE

  Eq. I.1

s s s AHRTWhSE

  Eq. I.2

I-1Where:

SE r , SE s, = Source energy in the reference and standards cases, respectively TWh r , TWh s = Terrawatt-hours in the reference and standards cases, respectively AHR r , AHR s = 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:

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

Where:

AHR = the average of the AHRs for the reference and standards cases, TWh = the average generation (TWh) for the refere nce 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 generati on” effect. The second term can be termed the electric utility “system intensity” effect. The syst em intensity effect is de fined purely in terms of how the AHR changes between the reference and sta ndards cases. No implic ation is suggested as to whether the utility sector is oper ating any differently with regard to economic efficiency between the reference and standards cases.
In prior appliance and eq uipment rulemakings, the concept of a MHR has been employed; it is used as convenient means of es timating the amount of sour ce 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 base d on the change in source energy divided by the change in total generation. In terms of e quation I.3, the MHR is calculated by dividing ∆ SE by ∆ TWh . When both sides of equation I.3 are divi ded by the change in generation, we have:

TWh AHR TWHAHR TWhSEMHR
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 ( TWh AHR  / AHR TWh   ) 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 di fferences between the MHRs and AHRs emanating from a particular scenario in NEMS-BT can be considerable.

I-2For the cases using NEMS-BT to analyze efficiency standards for various types of commercial equipment, the long-term (2020 and la ter) MHRs are consiste ntly lower than the AHRs. This reflects an increase in the AHR be tween the reference and standards cases. This increase in the AHRs can be attributed to two factors.
In the prior rulemakings for residential ai r conditioners and heat pumps (66 Federal Register 7169) the Technical Support Document, Appendix M 2 noted that the first factor is due to the slower growth in overall electricity consumption that retard s the investment in new, more efficient, generating capacity. Th e 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 he at rates than that of the disp laced capacity will increase the AHR, and consequently, the lower the MHR.

I.2 Example

A numerical illustration of th e 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 NE MS- B T 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 Ma rginal 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-3I.3
The top two lines of the table show gene ration (in TWh) and average heat rates (Btu/kWh) for the reference and standards cases. To maintain c onventional units for generation and heat rates, the source energy is expressed in bi llion Btu (BBtu).
In comparing the two cases, generation is lo wer 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 so urce 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 th is method, the displaced generation effect is calculated to be approximately 51,900 BBtu (of savi ngs). 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 interpretati on of the particular result shown is that the system intensity eff ect essentially reduces the impact of displaced generation by about 30 pe rcent (i.e., 16,300/51,900).

I.4 Estimation of Marginal Heat Rates for Final Ru le Analysis

The estimation of MHRs for use in calculati ng the source energy savi ngs 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 simu lations employ multiples of the predicted savings in electricity use as a means of overcoming model noise in so lving 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 si ngle set of MHRs, an average of the MHRs derived from these cases was used. A furthe r adjustment involved smoothing the resulting projected values by taking a cente red 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 calcula tion of the MHR is to divide the change in source energy savi ngs by the change in electricity generation. However, some consideration as how best to measure these va lues 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 consumpti on for eight different major fuel types (petroleum, natural gas, coal, nuclear power, hydropower, biomass, other renewable energy, and other). The sum of this consumpti on is total source energy used in the U.S. economy, now estimated to be just over 100 quadri llion 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-4In 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 co mmercial customers). As described briefly in appendix U, a typical impact from energy-efficiency standa rds 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 in creases in natural gas use by residential and commercial customers (as natural gas becomes rela tively less expensive than electricity). This increase in natural gas usage contributes to so mewhat 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 de signated by EIA as the “Electric Power Sector.” Other sources of electricity ge neration 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 eff ective 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 pe rcent 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 s ource energy (expressed in Btu) to produce that electricity. NEMS-BT reports total generation, broken out between the el ectric power sector and end-use generation, in a singl e table (as table A8 in the AEO ). Another table produced by NEMS-BT (as table A2 in the AEO ) provides fuel inputs, includi ng nuclear and renewables, for the electric power sector. Unfortunately, NEMS-B T does not report the fuel consumption used by the end-use sectors for electricity generati on. This deficiency s uggests 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 us e in the residential sector, the induced impact of relative fuel pric es is excluded from the MHR calculation. For the commercial sector, the change in non-electricity en ergy 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 co mmercial and industrial generation of electricity in 2005, only about 5 percent was generated in the commercial sector ( Annual Energy Review 2007 3 Table 8.2d). After making these two adju stments, it is reasonable to expect

I-5that most the resulting change in economy-wide s ource energy is attributable to the change in generation by the electric power se ctor and the industrial sector. a
c) Electric Power Sector
The third approach is to cons ider only the MHR that pertai ns to the electricity produced by the electric power sector. NEMS-BT reports bo th energy inputs and generated electricity by major fuel type. This reporting permits calculati on 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 co nsistent with the definition of MHRs used in prior U.S. Department of Energy (DOE) applia nce and equipment rulemakings. Second, based on the fact that the MHRs derived from the electr ic power sector typicall y 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 MH Rs 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 t oo 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 balanci ng between the demand and supply sides of NEMS is not always achieved. As a resu lt, DOE estimated the various im pacts corresponding to different trial standard levels (TSLs) using interpol ation. The interpolati on 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 en tire 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 actu al 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 sa vings 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 associa t ed 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 repo rting structure of NEMS, ther e 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-6applied to the NEMS commercial sector modul e 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 2028Btu/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 ar e generally higher than those f r om the two smaller multipliers, especially toward the end of the forecast period. As discussed in chapter 14, the behavior of NEMS in any pa rticular 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 th is 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 describe d in the appendix K, a regression approach was used to essentially average the impacts acro ss the simulations. The estimated coefficients of the lin ear regression line were then used to interpolate the utility sector impacts to correspond to actual sa vings levels for the various st andards. The regressions were estimated one for selected years – 20 15 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) appro ach 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 re sults, the second step was to smooth the resulting series by taking a 3-year cente red moving average. Thus, for example, the smoothed value for 2020 is the av erage 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-7Table 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 previ ous 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 th e generation intensity of the util ity sector but also transmission and distribution (T&D) losses be tween power plant and final customers. NEMS-BT does not report annual T&D losses in its av ailable set of output tables. T hus, one must rely on other information provided by EIA to devel op 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

I-8The four variables defined above are expressed in electricity units (for consistency with the prior discussion, TWh). Delivered electricit y 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 se ctor, including the amount of electricity used in the operation of power pl ant. Net generation is the total generation less the electricity used in power plants. T&D losses re present the losses betwee n 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 distri bution losses (electricity losses that occur between the point of generation a nd 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 consiste nt with a one-unit (e.g., TWh) change in DE, both sides of Equation I.9 ar e 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 el ectricity is treated as any other losses (e.g., thermal losses in foss il fuel plants) in production of electricity. Plant electricity use is thus already reflected in the aver age heat rates repor ted by NEMS-BT.

All of the discussion in sections I.1 through I.3 thus relate to the heat rates defined in term s of net electricity. As the average heat rates define source energy (SE) in terms of kWh of net generation, the incorpor ation of equation I.10 provide s the following relationship:

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

I-9For the analysis here, it is assumed that th e 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 electri city use, one obtains:

∆ SE = MHR × 1.0935 × ∆ DE Eq. I.12

The first two columns of Table I.5.1 present the site-to-s ource conversion factors expressed in term s of source Btu per kWh of (dis placed) 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 expr essed 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-10I-11 REFERENCES

1. EIA (Energy Inform ation Administration). 2008. Annual Energy Outlook 2008

. DOE/EIA-0383(2008). U.S. Depart ment of Energy, Energy In formation 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. Ce ntral Air Conditioning Supplemental Notice of Proposed Rulemaking (SNOPR) Technical S upport Document, July 25, 2001. Appendix M. Revised Utility Impact Analysis and Environmental Assessment.
< http://www.eere.energy.gov/buildings/applianc e_standa rds/residen tial/ac_central_1000_ r.html > (Accessed April 10, 2009.)

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