APPENDIX K. ESTIMATION OF UTILITY AND ENVIRONMENTAL
 

RESULTS FROM NEMS-BT OUTPUT 

TABLE OF CONTENTS
 

K.1 ALLOCATION OF INPUT ELECTRICITY SAVINGS BY CENSUS DIVISION 

AND END USE .............................................................................................................. K-1 

K.2 CHOICE OF IMPACT MULTIPLIERS ........................................................................ K-2 

K.3 REGRESSION SMOOTHING OF NEMS-BT OUTPUTS ........................................... K-4 

K.4 ESTIMATION OF INTERPOLATING FUNCTIONS FROM SAVINGS 

MULTIPLIERS............................................................................................................... K-6 

K.5 ENVIRONMENTAL IMPACTS.................................................................................... K-7 

LIST OF TABLES 

Table K.1.1 Shares of National Savings by Census Division Used in NEMS-BT .............. K-2 

Table K.2.1 Comparison of Beverage Vending Machine Electricity Savings with 

Different Multipliers with Total Generation by Year ...................................... K-3 

Table K.2.2 Final Implied Multipliers by Trial Standard Level–Beverage Vending 

Machines.......................................................................................................... K-4 

LIST OF FIGURES 

Figure K.3.1 Example of Regression Smoothing Fits for Fossil-Fuel Power Plants and 

Total Installed Capacity (30X case)................................................................. K-5 

Figure K.4.1 Response (Interpolating) Functions for Selected Generation Outputs for 

2025.................................................................................................................. K-6 

Figure K.5.1 Response (Interpolating) Functions for Carbon Dioxide for 2015, 2020, 

2025, and 2030................................................................................................. K-8 

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APPENDIX K. ESTIMATION OF UTILITY AND 

ENVIRONMENTAL RESULTS FROM NEMS-BT OUTPUT
 

The effects of proposed energy conservation standards for beverage vending machine 

equipment was analyzed using a variant of National Energy Modeling System (NEMS) model, 

called NEMS-Building Technology (BT). The U.S. Department of Energy (DOE) Energy 

Information Administration (EIA) approves the name NEMS to describe only an official version 

of the model without any modification of the code or data. Because the analysis of beverage 

vending machine energy conservation standards entails some minor code modifications and the 

model is run under variations of DOE/EIA assumption policy scenarios, the name NEMS-BT 

refers to the model as used here. Because the magnitude of national energy savings as a result of 

the proposed standards is very small relative to total electric generation, the DOE used an 

estimation method involving regression smoothing and interpolation. This appendix describes 

the major elements of this method. 

To run a simulation in NEMS-BT model, the refrigeration load in the commercial 

building module is reduced annually according to the electricity savings estimated by the 

National Energy Savings (NES) spreadsheet model (chapter 11 of the TSD) for each trial 

standard level (TSL). The electricity savings increase over time as various categories of beverage 

vending machine equipment are replaced with more efficient equipment meeting the energy 

conservation standards in today’s final rule. 

The magnitude of the electricity decrement that would be required for NEMS-BT to 

produce stable results out of the range of numerical noise is greater than the highest TSL under 

consideration. Therefore, to estimate results for the TSLs evaluated here, a series of NEMS-BT 

simulations is performed using higher values for the input electricity savings. These simulations 

establish the relationship between the NEMS-BT output variables (electricity generation by fuel, 

installed electricity generation capacity, and emissions) and the electricity savings inputs. For 

each output variable, a regression model is estimated to represent an average response across the 

series of simulations. Impacts are obtained using predicted values from the regression models 

corresponding to the (smaller) levels of savings corresponding to TSLs. 

K.1	 ALLOCATION OF INPUT ELECTRICITY SAVINGS BY CENSUS DIVISION 

AND END USE 

Although the utility and environmental impacts are national in scope, the NEMS-BT 

model operates at a census division level. Lacking sales information for beverage vending 

machine equipment by census division, an allocation of savings was made on the basis of 

population. The shares used to distribute the savings across census divisions are shown in 

Table K.1.1. The shares are held constant for the forecast period through 2030. 

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Table K.1.1 Shares of National Savings by Census Division Used in NEMS-BT 

Census Division Share 

% 

New England 11.2 

Middle Atlantic 14.1 

East North Central 16.0 

West North Central 6.8 

South Atlantic 18.4 

East South Central 6.0 

West South Central 11.2 

Mountain 6.5 

Pacific 16.0 

K.2 CHOICE OF IMPACT MULTIPLIERS 

To gain some understanding of the how NEMS-BT would respond to various magnitudes 

of savings, a “reference” time series of savings was initially selected from a preliminary version 

of the NES spreadsheet model. This reference series was selected as the savings that would result 

from the most stringent TSL (maximum technologically feasible efficiency level or max tech) for 

both classes of beverage vending machine equipment considered in this rulemaking. Max tech is 

TSL 7 for Class A equipment and TSL 6 for Class B equipment. 

The preliminary estimated savings from these two equipment types in 2030 was 0.76 

terawatt-hours (TWh) or 2.59 trillion British thermal units (Btu) in site energy terms. Based upon 

a previous rulemaking that also affected electricity use for refrigeration (DOE 2008), NEMS-BT 

was run using the projected time series of savings that were multiplied by a series of factors that 

ranged from 10–60 (designated here with a suffix X). Thus, for example, the 2030 beverage 

vending machine savings imposed upon the commercial module in NEMS-BT in the 30X case 

was 30  2.59 TWh = 22.8 TWh. 

Based on the graphical output and a comparison of trends among the output variables, the 

numerical noise from the model appeared to overwhelm the impact of the savings decrement for 

the smaller multiplier factors (i.e., less than 20X). The numerical noise stems in part from a 

precise balancing between the demand and supply sides of NEMS that is not always achieved, 

given the iterative nature of the solution process. Table K.2.1 compares the savings decrement 

applied to the model under various multipliers and how the magnitude of the savings compares 

with total electricity generation in the Energy Information Administration’s (EIA’s) Updated 

Annual Energy Outlook 2009 (AEO2009) reference case.1 

The values of the multipliers used are solely dependent on the initial (and arbitrary) 

choice of Class A and Class B vending machines and a specific TSL for those machines. The 

NEMS-BT simulations were performed prior to the final engineering analysis and selection of 

TSLs and so the 1X multiplier does not correspond to any specific TSL for in previous sections 

of the report. However, it was judged that the savings decrements (in TWh) tested in NEMS-BT 

(lower portion of Table K.2.1) were in the relevant range of magnitudes to yield stable and 

robust predictions by the model and so additional runs using different multipliers were deemed 

unnecessary. For use in the predicting the impacts from the set of final TSLs, the savings 

decrement from any TSL was converted into an appropriate multiplier by scaling in proportion to 

the values shown in the first row of Table K.2.1. 

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Table K.2.1 Comparison of Beverage Vending Machine Electricity Savings with Different 

Multipliers with Total Generation by Year 

Multiplier Electricity Savings 2015 2020 2025 2030 

1X Savings, TWh 0.29

% of total generation 0.01 

20X Savings, TWh 5.79 

% of total generation 0.13 

30X Savings, TWh 8.69 

% of total generation 0.20 

40X Savings, TWh 11.58 

% of total generation 0.27 

 0.64

0.01 

12.81 

0.28 

19.22 

0.42 

25.63 

0.56 

 0.76 

0.02 

15.20 

0.31 

22.79 

0.47 

30.39 

0.63 

0.76 

0.02 

15.20 

0.30 

22.79 

0.45 

30.39 

0.60 

Based on this analysis, a decision was made to use the multipliers in the range of 20X 

through 40X. While these multipliers are greater than 1, they still do not yield large perturbations 

to the base case simulation. For example, as Table K.2.1 indicates, even at 40X in 2025, the total 

savings decrement applied to the model represents only about 0.6 percent of total electricity 

generation. 

Final Implied Multipliers by TSL for All Beverage Vending Machine Equipment 

Subsequent to the production of the NEMS simulations described earlier, some revisions 

were made to the final set of energy savings estimates for the final rule. In addition, for purposes 

of reporting utility and environmental impacts for beverage vending machines, Class A and Class 

B equipment are distinguished. To adjust for these changes, the difference between the final 

savings estimate (by TSL) and the savings from the initial “reference” time series was 

represented as a scale factor. For example, the energy savings for the final version of the energy 

standard was2.06 TWh at TSL 5 for Class A equipment, as compared to the actual value used as 

the 1X case in NEMS-BT of 2.59 TWh. Thus, the scale factor for TSL 5 is 2.06/2.59 = 0.796. 

The scale factor essentially adjusts the savings from all refrigeration equipment for a specific 

TSL to be consistent with the reference series and, thus, be consistent with the interpolation 

procedure described above. 

The final implied multipliers by TSL are presented in Table K.2.2. The first column in 

Table K.2.2 displays the scale factors for each TSL. The scale factors can also be viewed as 

interpolating values relative to the set of NEMS-BT impact runs. Thus, for example, if an impact 

upon a particular variable from the “20X” case in the original set of simulations were 

interpolated to be a value of 4, then the impact for TSL 5 for all refrigeration equipment would 

be (1/20)  1.16  4 = 0.232. The remaining columns in Table K.2.2 show the implied 

multipliers from the three simulations performed with NEMS-BT (using their designations of 

20X, 30X, and 40X). For example, the actual final multipliers used for TSL 4 for Class A 

beverage vending machine equipment were 29.7, 44.5, and 59.4. Because the savings for TSL 1 

through TSL 3 are smaller than those for TSL 4, the implied multipliers are larger than those for 

TSL 4 (and vice versa for TSL 5). 

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Table K.2.2 Final Implied Multipliers by Trial Standard Level–Beverage Vending 

Machines 

Equipment Type Scale NEMS-BT Implied Multipliers 

Factor 20X 30X 40X 

Class A Equipment 

TSL 1 0.041 484.6 726.9 969.2 

TSL 2 0.197 101.3 152.0 202.6 

TSL 3 0.437 45.8 68.7 91.5 

TSL 4 0.674 29.7 44.5 59.4 

TSL 5 0.796 25.1 37.7 50.2 

TSL 6 0.878 22.8 34.2 45.6 

TSL 7 1.068 18.7 28.1 37.5 

Class B Equipment 

TSL 1 0.017 1,199.9 1,799.9 2,399.8 

TSL 2 0.025 808.6 1,212.8 1,617.1 

TSL 3 0.124 161.0 241.6 322.1 

TSL 4 0.142 140.8 211.2 281.6

 TSL 5 0.382 52.3 78.5 104.6 

TSL 6 0.426 47.0 70.5 93.9 

K.3 REGRESSION SMOOTHING OF NEMS-BT OUTPUTS 

Even at the selected multiplier levels shown in Table K.2.2, the simulations with 

NEMS-BT produces considerable year-to-year variation that appears to be caused by numerical 

noise from the model solution. This variation appears to affect the outputs related to specific 

generation fuel and technologies more so than total generation or total installed capacity. For the 

utility impact assessment, it is more important to identify distinct trends in the utility sector 

adjustment process rather than year-to-year variation that may be spurious results from the model 

solution process. 

To reduce the potential effect of numerical noise from NEMS-BT simulation, a 

smoothing regression was estimated for each of the model output variables. The output variables 

are measured as the differences between the AEO reference case and the energy efficiency 

standards case. The formulation of the smoothing regression was a simple quadratic function of 

time (in years) with the following form: 

Y(T) = a1  T + a2  T 2

 + u Eq. K.1 

Where: 

Y = output variable for time period T (difference from reference case),
 

T = time in years, T = 0 in 2012, T = 1 in 2013, etc. 

a1, a2 = estimated regression coefficients, and 

u = random disturbance term. 

The regression specification is such that the fitted (predicted) value of the variable is 

forced through the origin in the year prior to the year the standard goes into effect (2012). By 

forcing the impact to be zero in 2011, this procedure generates estimated impacts that typically 

could be expected to change in a systematic fashion beginning in 2012. 

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Figure K.3.1 illustrates this procedure for the differences in total installed capacity and 

the three types of fossil fuel-fired generating plant capacity. The particular case shown is for 

beverage vending machine equipment at the “30X” level of savings (or 28.1X relative to TSL-7 

for Class A beverage vending machine equipment). NEMS-BT indicates a very smooth path of 

differences in total generation capacity as shown in the top left panel of the figure. (In this case, 

the regression smoothing would not be necessary.) 

Total Generation Fossil Steam 

2010 2015 2020 2025 2030 2010 2015 2020 2025 2030

0.5 0.8

0.6

0

NEMS-BT

Fitted

NEMS-BT

Fitted

0.4

0.2

Difference (GW) Difference (GW) 

Difference (GW) Difference (GW) 

-0.5

-1

-1.5

-2

-2.5

0

-0.2

-0.4

-0.6

-0.8

-1

Combined Cycle Combustion Turbine 

2010 2015 2020 2025 2030 2010 2015 2020 2025 2030

1 5

0 4

NEMS-BT

Fitted

NEMS-BT

Fitted

-1

-2

-3

-4

3

2

1

0

-5 -1

-6 -2

Figure K.3.1 Example of Regression Smoothing Fits for Fossil-Fuel Power Plants and 

Total Installed Capacity (30X case) 

For plants using specific fuels or technologies, the differences in particular years from a 

smooth trend line are more substantial. The deviations from the fitted trend line are most 

pronounced for facilities using fossil steam technologies. In these cases, the model produces 

significant deviations from trend for up to 5 years throughout the forecast period. In this 

particular case, NEMS-BT appears to show some anomalous behavior in the last year or two of 

the simulation period, especially for fossil steam. The regression smoothing approach provides a 

means of generating more plausible predictions in these instances. In some cases, a single 

particularly anomalous year was not used in regression fitting procedure. 

Nevertheless, over the entire forecast period, the long-term trends in the capacity of all of 

these types of plants are apparent from the graphs. The approach in this analysis is to abstract 

these short-term deviations from what appear to be long-term trends. 

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0 10 20 30 40

K.4	 ESTIMATION OF INTERPOLATING FUNCTIONS FROM SAVINGS 

MULTIPLIERS 

The development of utility and environmental impacts focused on specific years from the 

NEMS-BT simulations: 2015, 2020, 2025, and 2030. For each output variable (e.g., coal-fired 

electricity generation), the predicted values from the trend regression were extracted for each 

savings multiplier level (20X, 30X, and 40X). A subsequent linear regression was performed 

using these values for the dependent variable and the values of the saving multiplier as the 

independent or explanatory variable. The y-intercept of this regression is forced through the 

origin. This restriction ensures that the predicted value of a NEMS-BT output variable is zero 

when the savings multiplier is zero. Predicted values for non-zero multipliers are calculated by 

taking the estimated regression coefficient (slope) times the value of the savings multiplier. 

Figure K.4.1 shows several examples of this estimation approach. The magnitude of 

the energy savings multiplier is plotted on the x-axis against the total reduction in generation 

capacity for the year 2030. The results shown are based on the three simulations selected for 

beverage vending machine equipment (20X, 30X, and 40X as described above). The fitted 

2030 values from the smoothing regression of the NEMS-BT output are shown in the large solid 

(black) diamonds. In the case of total generation capacity, the linear regression line is closely 

aligned to the three points corresponding to the 20X, 30X, and 40X savings multipliers. 

-30

-25

-20

-15

-10

-5

0

0 10 20 30 40 50

Difference (TWh) 

Savings Multiplier 

Total Generation 

-14

-12

-10

-8

-6

-4

-2

0

0 10 20 30 40 50

Difference (TWh) 

Savings Multiplier 

Natural Gas 

Difference (TWh) 

-16

-14

-12

-10

-8

-6

-4

-2

0

0 10 20 30 40 50

Difference(TWh) 

Saving Multiplier 

Coal 

Renewables 

2

1

0

-1

-2

-3

-4

-5

-6

Savings Multiplier 

50

Figure K.4.1 Response (Interpolating) Functions for Selected Generation Outputs for 2025 

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Within this range of savings, the graph demonstrates that the impact on total capacity predicted 

by the model is proportional to the magnitude of the refrigeration electricity savings. 

For the other generation types shown in Figure K.4.1, the responses deviate from strict 

proportionality. For example, for renewables, the response at the 20X is proportionately greater 

than either the 30X or 40X levels. The approach essentially produces a weighted average of the 

responses across these various savings multipliers. 

The predicted value of a NEMS-BT output variable for a given standards level is 

interpolated along the regression line estimated for that variable. The computation of savings 

from a particular standards case first takes into account the scale factors shown in the first 

column in Table K.2.2. Thus, for example, the scale factor associated with TSL 4 for Class A 

equipment is 0.674. For total electricity generation in 2030, the estimated response coefficient is 

-0.260 (e.g., the slope of regression line in the top left panel of Figure K.4.1). Thus, the estimated 

impact on total generation in 2030 from this specific TSL would be 0.674  -0.260 = 

-0.269 TWh. 

K.5 ENVIRONMENTAL IMPACTS 

The general approach for estimating the impacts on the utility sector was used to develop 

an environmental assessment in terms of changes in emissions. Annual values of the emissions 

for oxides of nitrogen (NOx), mercury (Hg), and carbon dioxide (CO2) were extracted from the 

relevant tables produced by NEMS. Similar to examples shown in Figure K.3.1, the projections 

of emissions 2012–2030 were smoothed using the quadratic function in time discussed above. 

Response functions were then estimated at 5-year intervals between 2015–2030. 

Figure K.5.1 shows the estimated response (or interpolating) functions for carbon dioxide 

emissions. There is very little disparity in the magnitudes of carbon dioxide emissions across the 

three multipliers selected. However, the 30X case shows a somewhat greater response than the 

20X and 40X cases in 2030. But the regression-based average takes all three cases into account, 

leading to strong indication of a reduction in carbon dioxide emissions. 

The scale of the y-axis is held constant for each of the plots and so the clockwise rotation 

of the slopes across 2015–2030 reflects the increasing reduction in emissions over selected years. 

There is little change in the slopes from 2025–2030, reflecting a distinct slowdown in the rate of 

increase of savings. By the middle part of the next decade, most beverage vending machine 

equipment will have already been replaced by more efficient equipment mandated by today’s 

standards. Moreover, reduction in nuclear and renewable generation prompted by today’s 

standards have the effect of retarding further reductions in CO2 emissions toward the end of the 

period. 

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-30

-25

-20

-15

-10

-5

0

0 10 20 30 40 50

Difference (MMT-CE) 

Savings Multiplier 

Carbon Dioxide Emissions (2015) 

-30

-25

-20

-15

-10

-5

0

0 10 20 30 40 50

Difference (MMT-CE) 

Savings Multiplier 

Carbon Dioxide Emissions (2020) 

-30

-25

-20

-15

-10

-5

0

0 10 20 30 40 50

Difference (MMT-CE) 

Savings Multiplier 

Carbon Dioxide Emissions (2025) 

-30

-25

-20

-15

-10

-5

0

0 10 20 30 40 50

Difference (MMT-CE) 

Savings Multiplier 

Carbon Dioxide Emissions (2030) 

Figure K.5.1 Response (Interpolating) Functions for Carbon Dioxide for 2015, 2020, 2025, 

and 2030 

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REFERENCES 

1. U.S. Department of Energy–Energy Information Administration. An Updated Annual Energy 

Outlook 2009 Reference Case Reflecting Provisions of the American Recovery and 

Reinvestment Act and Recent Changes in the Economic Outlook. April 2009. Washington, 

D.C. SR/OIAF/2009-03. 

2. U.S. Department of Energy. 2008. Technical Support Document for Commercial 

Refrigeration Equipment. 

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