K-i 

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.2.1 Final Implied Multipliers by TSL for All BVM Equipment.................................. K-3

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 BVM Electricity Savings with Different Multipliers with 

Total Generation .............................................................................................. K-3

Table K.2.2 Final Implied Multipliers by TSL–BVMs....................................................... K-4

LIST OF FIGURES 

Figure K.3.1 Example of Regression Smoothing Fits for Fossil-Fired 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 Years 2015, 

2020, 2025, and 2030....................................................................................... K-8

EERE-2006-STD-0125 COMMENT 46
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EERE-2006-STD-0125 COMMENT 46
APPENDIX K. ESTIMATION OF UTILITY AND 

ENVIRONMENTAL RESULTS FROM NEMS-BT OUTPUT

The effects of proposed energy conservation standards for beverage vending machine 

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

model, called NEMS-BT.a

 Because the magnitude of national energy savings as a result of the 

proposed standards is very small relative to total electric generation, the U.S. Department of 

Energy (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 (see chapter 11 of the TSD) for each trial 

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

vending machine (BVM) equipment are replaced with more efficient equipment meeting the 

proposed conservation standards. 

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 BVM 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. 

 

a

 DOE’s Energy Information Administration (EIA) approves of the name NEMS to describe only an official version 

of the model without any modification of the code or data. Because the analysis of BVM energy conservation 

standards entails some minor code modifications and the model is run under policy scenarios that are variations of 

DOE/EIA assumptions, the name NEMS-BT refers to the model as used here. (The Building Technologies [BT] 

program is one of the major program offices within DOE’s Office of Energy Efficiency and Renewable Energy. The 

Building Technologies program is responsible for promulgating energy efficiency standards for the buildings sector 

mandated under the 2005 Energy Policy Act and earlier Federal legislation.) 

K-1 

EERE-2006-STD-0125 COMMENT 46
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) for both 

classes of beverage vending machine equipment considered in this rulemaking (TSL 7 for Class 

A equipment plus 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 through 60 (designated here with a 

suffix X). (Thus, for example, the 2030 BVM savings imposed upon the commercial module in 

NEMS-BT in the 30X case was 30 x 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).b

 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) Annual 

Energy Outlook (AEO 2008) reference case.1 c

 

b

 The numerical noise stems, in part, from the fact that a precise balancing between the demand and supply sides of 

NEMS is not always achieved, given the iterative nature of the solution process. c

 The reader should note that the values of the multipliers used here are solely dependent on the initial (and arbitrary) 

choice of class A and class B vending machine products and a specific trial standard level (TSL) for those products. 

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 a product category in previous sections of the report. 

However, it was judged that the savings decrements (in TWh) tested in NEMS-BT, shown in 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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EERE-2006-STD-0125 COMMENT 46
Table K.2.1 Comparison of BVM Electricity Savings with Different Multipliers with 

Total Generation 

Multiplier 2015 2020 2025 2030 

Savings (TWh) 0.29 0.64 0.76 0.76 1X % of total generation 0.01% 0.01% 0.02% 0.01% 

Savings (TWh) 5.79 12.81 15.20 15.20 20X % of total generation 0.13% 0.27% 0.31% 0.29% 

Savings (TWh) 8.69 19.22 22.79 22.79 30X % of total generation 0.19% 0.41% 0.46% 0.44% 

Savings (TWh) 11.58 25.63 30.39 30.39 40X % of total generation 0.26% 0.54% 0.61% 0.58% 

Based on this testing, 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 the year 2025, 

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

electricity generation. 

K.2.1 Final Implied Multipliers by TSL for All BVM 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 trial standard level) 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 was 5.28 TWh at TSL-5, as compared to the actual value used as the 1X case in 

NEMS-BT of 5.99 TWh. Thus, the scale factor for TSL-5 is 5.28/5.99 = 0.881). 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 first column in Table K.2.2 displays the scale factors for each TSL.d

 The remaining 

columns display 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 BVM equipment were 2.8, 5.7, and 8.5. 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). 

 

d

 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 “2X” case in the original set of simulations was 

interpolated to be a value of, say, 0.10, then the impact for TSL-4 for all refrigeration equipment would be 1⁄2 x 

0.703 x 0.10 = 0.035. 

K-3 

EERE-2006-STD-0125 COMMENT 46
Table K.2.2 Final Implied Multipliers by TSL–BVMs 

Implied Multipliers 

Scale 

Factor 

NEMSBT 

("20X") 

NEMSBT 

("30X") 

NEMSBT 

("40X") 

Class A Equipment

 TSL – 1 0.022 890.4 1,335.6 1,780.7 

 TSL – 2 0.100 200.3 300.5 400.7 

 TSL – 3 0.225 89.0 133.6 178.1 

 TSL – 4 0.352 56.8 85.2 113.7 

 TSL – 5 0.415 48.2 72.3 96.4 

 TSL – 6 0.457 43.8 65.7 87.6 

 TSL – 7 0.553 36.1 54.2 72.3 

Class B Equipment 

 TSL – 1 0.007 2,819.1 4,228.6 5,638.1 

 TSL – 2 0.011 1,882.7 2,824.1 3,765.4 

 TSL – 3 0.053 380.3 570.4 760.6 

 TSL – 4 0.060 332.3 498.5 664.6 

 TSL – 5 0.163 123.1 184.6 246.1 

 TSL – 6 0.181 110.6 165.9 221.1 

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 Annual Energy Outlook (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 x T + a2 x T2

 + 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 implementation of the standard (2012). By 

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EERE-2006-STD-0125 COMMENT 46
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. 

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

the three types of fossil fuel capacity. The particular case shown is for beverage vending machine 

equipment at the “30X” level of savings (or 54.2X relative to TSL-7 for Class A beverage 

vending machine equipment—see Table K.2.2). Clearly, 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.) 

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 combined cycle and combustion turbine technologies. In these 

cases, the model produces significant deviations from trend for periods of up to four years 

throughout the forecast period.e

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. 

Total Generation 

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

2010 2015 2020 2025 2030

Difference (GW)

NEMS-BT

Fitted

Fossil Steam

-2.5

-2

-1.5

-1

-0.5

0

0.5

2010 2015 2020 2025 2030

Difference (GW)

NEMS-BT

Fitted

Combined Cycle

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

2010 2015 2020 2025 2030

Difference (GW)

NEMS-BT

Fitted

Combustion Turbine

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

2010 2015 2020 2025 2030

Difference (GW)

NEMS-BT

Fitted

Figure K.3.1 Example of Regression Smoothing Fits for Fossil-Fired and Total Installed 

Capacity (30X case) 

 

e

 In this particular case, NEMS-BT appears to show some anomalous behavior in the last several years of the 

simulation period, especially for combined cycle and combustion turbines. The regression smoothing approach 

provides a means of generating more plausible predictions in these instances. In some cases, the last year or two of 

the projection was not used in regression fitting procedure. 

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EERE-2006-STD-0125 COMMENT 46
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., coalfired 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 2025. The results shown are based on the three simulations selected for 

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

2025 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. 

Total Generation

-35

-30

-25

-20

-15

-10

-5

0

0 10 20 30 40 50

Savings Multiplier

Difference (TWh)

Coal

-20

-15

-10

-5

0

0 10 20 30 40 50

Saving Multiplier

Difference(TWh)

Natural Gas

-10

-8

-6

-4

-2

0

0 10 20 30 40 50

Savings Multiplier

Difference (TWh)

Renewables

-7

-6

-5

-4

-3

-2

-1

0

0 10 20 30 40 50

Savings Multiplier

Difference (TWh)

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

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EERE-2006-STD-0125 COMMENT 46
Within this range of savings, the graph demonstrates 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 coal, the response at the 30X is proportionately less than either 

the 20X or 40X levels. The approach taken here 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.2.1. Thus, for example, the scale factor associated with Trial Standard Level 

4 for Class A equipment is 0.352. For total electricity generation in 2025, the estimated response 

coefficient is -0.765 (e.g., the slope of regression line in the top left panel Figure K.4.1). Thus, 

the estimated impact on total generation in 2025 from this specific trial standard level would be 

0.352 x -765 = -0.269 TWh. 

K.5 ENVIRONMENTAL IMPACTS 

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

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

emissions for NOx, mercury, and carbon dioxide were extracted from the relevant tables 

produced by NEMS. 

Similar to examples shown in Figure K.3.1, the projections of emissions from 2012 

through 2030 were smoothed using the quadratic function in time discussed above. Response 

functions were then estimated at 5-year intervals between 2015 and 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 smaller response than the 

20X and 40X cases. However, 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 the years 2015 through 2030 reflects the increasing reduction in emissions 

over selected years. There is little change in the slopes between 2025 and 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 the standards. Moreover, reduction in nuclear and renewable generation 

prompted by the conservation standard have the effect of retarding further reductions in carbon 

dioxide emissions toward the end of the period. 

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EERE-2006-STD-0125 COMMENT 46
Carbon Dioxide Emissions (2015)

-30

-25

-20

-15

-10

-5

0

0 10 20 30 40 50

Savings Multiplier

Difference (MMT-CE)

Carbon Dioxide Emissions (2020)

-30

-25

-20

-15

-10

-5

0

0 10 20 30 40 50

Savings Multiplier

Difference (MMT-CE)

Carbon Dioxide Emissions (2025)

-30

-25

-20

-15

-10

-5

0

0 10 20 30 40 50

Savings Multiplier

Difference (MMT-CE)

Carbon Dioxide Emissions (2030)

-30

-25

-20

-15

-10

-5

0

0 10 20 30 40 50

Savings Multiplier

Difference (MMT-CE)

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

2025, and 2030. 

K-8 

EERE-2006-STD-0125 COMMENT 46
K-9 

REFERENCES 

1. U.S. Department of Energy/Energy Information Administration (DOE/EIA), Annual Energy 

Outlook 2008, June 2008. Washington, D.C. DOE/EIA-0383(2008). 

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

Refrigeration Equipment. 

EERE-2006-STD-0125 COMMENT 46