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 CASE

............................................................................................................ I -3 I.3 ESTIMATION OF MARGINAL HEAT RATES FOR FINAL RULE ANALYSIS

...... I-4 I.3.1 Sectoral Scope of Marginal Heat Rate

................................................................ I-4 I.3.2 Marginal Heat Rates from the NEMS-BT Simulations

....................................... I-6 I.4 SITE-TO-SOURCE ENERGY C ONVERSION FACTORS

........................................... I-7

LIST OF TABLES

Table I.2.1 Example of Average Heat Rates and Marginal Heat Rates for Beverage Vending Machines in 2014

................................................................... I-3 Table I.4.1 Marginal Heat Rates, 2012–2042

......................................................................... I-7 Table I.5.1 Site-to-Source Conversion F actors for Final Rule Analysis

................................. I-9

LIST OF FIGURES

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

.......................................................................................................... I-6

I-i BVM_FINAL_FR_TSD_AppendixI_08-14-09.docAPPENDIX I. ESTIMATION OF MARGINAL HEAT RATES AND SITE-TO-SOURCE CONVERSION FACTORS

As described in chapter 10 of the technical support document (TSD), site-to-source conversion factors are used to convert energy savi ngs 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 el ectricity at generation plants; and (2) the quantity of electricity lost in the transmission a nd distribution (T&D) of electricity to final customers.

The National Energy Modeling System-Buildi ng Technologies (NEMS-BT) is used by the U.S. Department of Energy (DOE) to translat e end-use electricity savings to source energy savings. The amount of source energy saved as a re sult 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 observi ng the change in the source energy use. For beverage vending machine equipment, the estimated MHR ranges from just over 8,700 British thermal units (Btu)/kWh in 2014 to just under 7,000 Btu/kWh in 2030. This variation occurs as the utility sector to meet the different magnitude and shape of the load compared with the reference case in the April 2009 update to the Annual Energy Outlook (AEO2009-B)

. 1 Over the entire period from 2014, the MHR averages about 7,400 Btu/kWh.

Before turning to a detailed discussion of the MHRs derived from the NEMS-BT for beverage vending machine equipment, it is useful to consider a number of conceptual issues that relate to MHRs (sections I.1 a nd I.2). Section 0 describes more specifically how the MHRs were developed for this overall analysis. Section I .4 discusses how T&D losses were estimated and how the MHRs are translated into site-to-source conve rsion factors.

I.1 COMPETING EFFECTS

On first inspection, an MHR near 7,000 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 the conversion rate does not repres ent a specific marginal generato r or combination of generators but is actually a reflection of several NEMS-B T simulated effects that stem from an energy conservation standard. Thus, the primary reas on the MHR associated with a standard for beverage vending machine equipment is low is because the overall rate of efficiency improvement of the power system (measured as th e 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 ca se will help clarify this situation. As shown in Eqs. I.1 and I.2, the source energy in both the reference and stan dards cases can be expressed as the product of the amount of electricity generated (terawatt-hours [TWh]) times an AHR:

SE  TWh  AHR Eq. I.1

r r r SE

s  TWh

s  AHR

s Eq. I.2

I-1 BVM_FINAL_FR_TSD_AppendixI_08-14-09.docWhere:

SE r , SE s = source energy in the reference and standards cases, respectively (Btu), TWh r , TWh s = terrawatt-hours in the reference a nd standards cases, respectively, and AHR r , AHR s = average heat rates (Btu/kWh) in the refe rence 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:

 SE  SE

s  SE

r  AHR   TWh  TWH   AHR Eq. I.3

Where:

AHR = the average of the AHRs for the reference and standards cases (Btu/kWh),
TWh = the average generation (TWh) for th e reference and standards cases, and Variables preceded by  = the difference between standards and refere nces 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 Eq. I.3 can be thought of as the “displaced generation” effect . The second term can be termed the electric utility “system intensity” effect. This is defi ned in terms of how the AHR changes between the reference and standards cases. No implication is suggested as to whether the utility sector operates different with regard to economic efficien cy between the reference and standards cases.

In prior appliance and equi pment rulemakings, MHR has been employed as convenient means of estimating the amount of source en ergy saved corresponding to a reduction in electricity generation brought a bout by the standard. Based on simulations with the NEMS-BT model, the change in source energy is divided by the change in total gene ration. In terms of Eq. I.3, the MHR is calculated by dividing ∆ SE by ∆ TWh . When both sides of Eq. I.3 are divided by the change in generation, we have:

MHR   SE /  TWh

r  AHR  TWH   AHR /  TWh Eq. I.4

Expressed in this manner, the MHR is shown to be the AHR (averaged between the two cases) plus an adjustment term involving the rela tive sizes of the change s in the AHR and total generation (  AHR /  TWh ). Because an efficiency standard will cause total ge neration to fall, the sign of  TWh is negative. Qualitatively, if the AHR in creases, one can expect to find that the MHR is lower than the AHR. Depending on particular circumstances (as illustrated below), the differences between the MHRs and AHRs emanating from a particular scenario in NEMS-BT can be considerable.

For 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.

I-2 BVM_FINAL_FR_TSD_AppendixI_08-14-09.docIn a rulemaking for residential air conditioners and heat pumps (66 Fe deral Register 7169) TSD, Appendix M noted that the first factor is from slower growth in overall electricity consumption that retards the investment in new, more ef ficient generating capacity. 2 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 generati ng capacity with higher h eat rates than that of the displaced capacity will increase the AHR and, consequently, the lower the MHR.

I.2 EXAMPLE CASE

A numerical illustration of the AHR and MHR relationship for one NEMS-BT case is shown in Table I.2.1. The numbers are extracte d from the NEMS-BT output for a single case for a recent (2008) analysis of energy conservation standards for beverage vending machines.

Table I.2.1 Example of Average Heat Rates and Marginal Heat Rates for Beverage Vending Machines in 2014 Average and Marginal Heat Rates
Case TWh  Avg Heat Rate Total Btu/kWh Btu 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 Chan ge in Source Energy Generation effect Avg of Cases Change Component AHR ∆ TWh Change 10,069.8 -5.2 -51,878 System intensity Avg TWh ∆ Heat Rate 4,238.9 3.8 16,245

AHR Total Change, Btu -35,633

+ Adjustment = MHR 10,069.8 -3153.3 6,917
Table I.2.1 shows generation (in TWh) and AHR (Btu/kWh) for the reference and standards cases. To maintain c onventional units for generation a nd heat rates, the source energy is expressed in bi llion Btu (BBtu).

Comparing the two cases, generation is lowe r by about 5 TWh in the standards case as compared to the reference case in 2030. Howe ver, the AHR is higher by nearly 4 Btu/kWh. Based on the changes in total source energy (35,633 BBtu) and generation, the MHR is 6,917 Btu/kWh, which is 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 Eq. I.2. Using this 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 approximate ly 35,600 BBtu. One possible interpretation of the particular result shown is that the system in tensity effect essentially reduces the impact of displaced generation by about 30 percent (i.e., 16,300/51,900).

I-3 BVM_FINAL_FR_TSD_AppendixI_08-14-09.docI.3 ESTIMATION OF MARGINAL HEAT RATES FOR FINAL RULE ANALYSIS

The estimation of MHRs for use in calculati ng the source energy savi ngs associated with electricity savings shown in TSD chapter 7 are ba sed on a series of simu lations with the NEMS

BT model. As discussed in TSD Appendix K, these simulations employ multiples of the predicted savings in electricity use as a m eans of overcoming model noise in solving the NEMS-BT model. The multiples employed are designated as 20X, 30X, and 40X and are described in TSD Appendix K. For purposes of th e calculating a single se t 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.

I.3.1 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 approaches were c onsidered and are described below.

I.3.1.1 Economy-Wide Measure

Table 1 in the AEO2009-B displays total energy consump tion for eight different major fuel types (petroleum, natural gas, coal, nuclear power, hydro power, 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 under 100 quadrillion Btu (10 15 Btu or quads). The broadest measure of a MHR is to divide the change in economy-wide source energy by the change in total electricity generation.

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 comme rcial customers). As de scribed briefly in TSD Appendix K, 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 small increases in natural gas use by residential and commercial customers (as natural gas becomes relatively le ss expensive than electr icity). This increase contributes to lower MHRs than would be calculated without this effect.

I.3.1.2 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 the Energy Information Administration (EIA) as th e “electric power sector.” Other so urces of electricity generation are the end-use sectors (res idential, commercial, and industrial) . As noted by EIA in the notes to Table A8 of the (2008) AEO , end-use generation “includes comb ined 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 i ndustrial sectors used primarily for own-use generation which may also sell some power to the grid.” In 2012, the effective year of the standards for beverage vending machine equipmen t, end-use generation from the commercial

I-4 BVM_FINAL_FR_TSD_AppendixI_08-14-09.docand industrial sectors is projected in the AEO reference case to account for about 4.1 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 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 NEMS-BT table (as Table A2 in the AEO ) provides fuel inputs, including nucle ar and renewables, for the electric power sector. Unfortunately, NEMS-BT does not re port the fuel consumption used by the enduse sectors for electricity genera tion. This deficiency suggests th at the best approximation to the change in source energy ( ∆ SE) for all electricity genera tion 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 that most of the resulting change in economy-wide source energy is attribut able to the change in generation by the electric power sect or and the industrial sector. 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 MHR will not completely reflect changes due solely to electricity generation. Within the current modeli ng 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 Eq. I.5 yiel ds only an approximate MHR.

I.3.1.3 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. 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 DOE appliance and equipment rulemakings . Second, because MHRs derived from the electric power sector typically show more consistent year-to-y ear changes while having the same general magnitude for all generation, DOE employs 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 3

- year moving averages are used. Because of the co nsiderable uncertainty of whether trends in MHRs would continue past 2030, the post-2030 heat rates have been fixed at 2030 values.

I-5 BVM_FINAL_FR_TSD_AppendixI_08-14-09.docI.3.2 Marginal Heat Rates from the NEMS-BT Simulations

As described in TSD Appendix K, the magnit udes of the energy decrements associated with the actual savings from the proposed st andards are too small for NEMS-BT to produce stable results. This instability is caused by th e numerical noise in the solution process of the model and stems, in part, from a precise bala ncing not always achieve d between the demand and supply sides of NEMS. As a result, DOE estim ated 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 preliminary estimate of savings for the entire set of beverage vending machine equipment under TSL 7 (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 AEO2009-B , these levels of savings correspond to reductions of 0.82, 1.22, a nd 1.63 percent, respectively. Further details on these multipliers are given in section K.2, Choice of Impact Multipliers.

Figure I.3.1 shows MHRs for the electric power sector for three levels of savings associated with 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 applied to the NEMS commercial sector modu le in 2030 ranges between 15 and 30 TWh. The MHRs in Figure I.3.1 are derived from the model-generate d responses by the electri city power sector.

Figure I.3.1 Marginal Heat Rates for 20X, 30 X, and 40X Cases for th e Electric Power Sector

As discussed in TSD chapter 14, the behavior of NEMS in any particular case may be affected by the capacity planni ng aspects of the model that can sometimes unduly influence overall generation in the years ar ound a “shock” to elec tricity demand. As Figure I.3.1 shows, this is particularly evident in the first year of the forecast peri od, in which the 20X case shows a particularly high MHR and the 30X and 40X cases show a particularly low MHR. While these values settle into more similar values therea fter, the 20X case maintains a higher MHR than the

I-6 BVM_FINAL_FR_TSD_AppendixI_08-14-09.docother multipliers throughout the analysis period. For this particular multiplier (20X), the (negative) impact on nuclear gene ration is relatively higher than th e other cases, especially in the earlier years of the analysis.

In developing the response functions for th e utility impacts described in TSD Appendix K, a regression approach was used essentially to average impacts across 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 for selected years 2015–2030 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 seri es by taking a 3-year centered m oving average. For example, the smoothed value for 2020 is the average of the heat rates for years 2019, 2020, and 2021. The values for years 2013 and 2030 are set equal to th e values for years 2014 and 2029, respectively. The resulting MHRs are shown in Table I.3.1.

Table I.3.1 Marginal Heat Rates, 2012–2042
Year Btu/kWh Year Btu/kWh Year Btu/kWh Year Btu/kWh 2012 7,970 2017 7,853 2022 8,068 2027 7,165 2013 8,040 2018 7,950 2023 7,748 2028 6,884 2014 8,759 2019 8,032 2024 7,623 2029 6,807 2015 8,230 2020 8,231 2025 7,578 2030 6,934 2016 8,129 2021 8,204 2026 7,396 2042 6,934

I.4 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 the generation intensity of the u tility sector but also 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 (in TWh):

DE =delivered electricity GG =gross generation NG =net generation T&D = T&D losses

Delivered electricity is the amount electric ity delivered to the building site; energy efficiency standards will reduce DE. Gross generation is the tota l 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 NG and the electri city delivered to final customers.

I-7 BVM_FINAL_FR_TSD_AppendixI_08-14-09.docThe 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 GG and NG, EIA indicates that the electric en ergy used in the operation of power plants is “estimated as 5 percent of gro ss generation.” This simp le 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 Eqs. 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 NG and DE, one can then express DE in terms of NG as follows:

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

To express the change in NG consistent with a one-unit (e.g., TWh) change in DE, both sides of Eq. I.9 are divided by 0.9145:

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 electricity pr oduction. Plant electricity use is thus already reflected in the AHRs reported by NEMS-BT.

All of the discussion in sections I.1 through 0 thus relate s to the heat rates defined in terms of net electricity. As the AHRs define source energy (SE) in te rms of kWh of NG, the incorporation of Eq. I.10 provi des the following relationship:

SE = AHR × NG = AHR × 1.0935 × DE Eq. I.11
For 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 w ith a change in DE use, one obtains:

∆ SE = MHR × 1.0935 × ∆ DE Eq. I.12
Table I.4.1 presents the site-to-source convers ion factors expressed in terms of source Btu per kWh of (displaced) site elec tricity. The values are based on Eq. I.12, where the MHRs in Table I.3.1 have all been multiplied by a constant factor of 1.0935.

I-8 BVM_FINAL_FR_TSD_AppendixI_08-14-09.docTable I.4.1 Site-to-Source Conversion Factors for Final Rule Analysis Year Conversion Factor, Conversion Factor, Year Conversion Factor, Conversion Factor,

source source source source Btu/site kWh Btu/site Btu Btu/site kWh Btu/site Btu 2012 8,715 2.554 2022 8,822 2.586 2013 8,792 2.577 2023 8,472 2.483 2014 9,577 2.807 2024 8,335 2.443 2015 8,999 2.637 2025 8,286 2.429 2016 8,889 2.605 2026 8,088 2.370 2017 8,587 2.517 2027 7,835 2.296 2018 8,693 2.548 2028 7,528 2.206 2019 8,783 2.574 2029 7,443 2.181 2020 9,000 2.638 2030 7,582 2.222 2021 8,971 2.629 2031–2050 7,582 2.222
In some applications (including some prior DOE energy conservation standards rulemakings), the site-to-source co nversion 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 3,412 Btu/kWh. Thus, the values in the last pair of columns are derived from the first two columns by dividi ng all entries by 3,412.

I-9 BVM_FINAL_FR_TSD_AppendixI_08-14-09.docREFERENCES

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2. U.S. Department of Energy. 2001. Cent ral Air Conditioning Supplemental Notice of Proposed Rulemaking (SNOPR) Technical Support Document. Appendix M: Revised Utility Impact Analysis and Environmental Assessment. July 25, 2001. Washington, D.C. (Last accessed April 10, 2009.)

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_ r.html >

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I-10 BVM_FINAL_FR_TSD_AppendixI_08-14-09.doc