APPENDIX J. ESTIMATION OF UTILITY AND ENVIRONMENTAL 

RESULTS FROM NEMS-BT OUTPUT 

TABLE OF CONTENTS 

J.1 Allocation of Input Electricity Savings by Census Division and End Use ...................... J-2

J.2 Choice of Impact Multipliers ........................................................................................... J-2

J.3 Regression Smoothing of NEMS-BT Outputs ................................................................. J-5

J.4 Estimation of Interpolating Functions from Savings Multipliers .................................... J-7

J.5 Environmental Impacts .................................................................................................... J-9

LIST OF TABLES 

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

Table J.1.2 Heating and Cooling Share for PTHP Equipment by Census Division .................... J-2

Table J.2.1 Comparison of Savings with Different Multipliers with Total 

Generation ............................................................................................................. J-3

Table J.2.2 Final Implied Multipliers by Equipment Class and Trial Standard 

Level ..................................................................................................................... J-4

LIST OF FIGURES 

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

Installed Capacity (200X case for PTHP). ............................................................ J-7

Figure J.4.1 Response (Interpolating) Functions for Selected Generation 

Outputs, PTHP Case for 2025 ............................................................................... J-8

Figure J.5.1 Response (Interpolating) Functions for Carbon Dioxide, PTHP 

Case, for Years 2015, 2020, 2025 and 2030. ...................................................... J-10

 J-i 

 EERE-2007-BT-STD-0012 COMMENT 32
APPENDIX J. ESTIMATION OF UTILITY AND ENVIRONMENTAL 

RESULTS FROM NEMS-BT OUTPUT

The effects of proposed energy conservation standards for packaged terminal air 

conditioners (PTACs) and packaged terminal heat pumps (PTHPs) was analyzed using a variant 

of National Energy Modeling System (NEMS) model, called NEMS-BT.1 a Because the size of 

national energy savings as a result of the proposed standards for PTACs and PTHPs are so small 

relative to the size of the entire electric utility sector, 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 space-cooling 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 PTAC and PTHP 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.

As discussed in Chapter 14, the utility and environmental impacts from an amended 

energy conservation standard on PTAC equipment can be expected to be different from a 

standard on PTHP equipment. Separate sets of runs with the NEMS-BT model were made for 

each type of equipment to distinguish these effects. 

a

 DOE’s 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 PTAC and PTHP energy efficiency standard 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. 

 J-1 

 EERE-2007-BT-STD-0012 COMMENT 32
J.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 PTAC/PTHP 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 J.1.1. The shares are 

held constant for the forecast period through 2030. 

Table J.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% 

For PTHP equipment, energy efficiency standards will yield electricity savings for both 

heating and cooling. Based on the building energy use simulations described in Chapter 7 of this 

TSD, an estimate of savings between heating and cooling was developed for each census 

division. The simulation results were weighted by state population estimates corresponding the 

locations employed in the analysis. The relative shares between heating and cooling vary 

slightly across trial standard levels for PTHP. As the shares for two of the trial standard levels 

were very close to each other (TSL 2 and TSL 6), the shares for TSL 6 were used develop 

heating and cooling savings inputs for NEMS-BT. The heating and cooling shares by census 

division are shown in Table J.1.2.

Table J.1.2 Heating and Cooling Share for PTHP Equipment by Census Division 

Census Division Cooling Heating 

 New England 35% 65%

 Middle Atlantic 42% 58%

 East North Central 41% 59%

 West North Central 51% 49%

 South Atlantic 73% 27%

 East South Central 69% 31%

 West South Central 80% 20%

 Mountain 59% 41%

 Pacific 59% 41%

J.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 the NES spreadsheet 

model. This reference series was selected as the savings that would result from highest level of 

TSLs for PTHP equipment with cooling capacity great than 10,000 Btu/h (i.e., representative 

cooling capacity of 12,000 Btu/h for standard sizes PTHPs as shown in Chapter 11). As 

described in Chapter 7, the energy savings for this equipment category are estimated 

 J-2 

 EERE-2007-BT-STD-0012 COMMENT 32
approximately 25 percent higher than the equivalent-sized PTAC equipment. NEMS-BT was 

run for this stream of savings, as well as for higher multipliers (designated here with a suffix X), 

including 2X, 5X, 10X, 20X, 100X, 200X, and 300X. It was judged on the basis of graphical 

output and comparison of trends among the output variables, that the numerical noise from the 

model was overwhelming the impact of the savings decrement for the smaller multiplier factors 

up to 20X.b Table J.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 

EIA’s Annual Energy Outlook (AEO2008) reference case.2 c

Table J.2.1 Comparison of Savings with Different Multipliers with Total Generation 

2015 2020 2025 2030 

 Multiplier 

Total Generation 

(TWh) 4,483 4,723 4,972 5,231 

1X Savings (TWh) 0.039 0.076 0.103 0.125 

% of total generation 0.001% 0.002% 0.002% 0.002% 

100X Savings (TWh) 3.9 7.6 10.3 12.5 

% of total generation 0.09% 0.16% 0.21% 0.24% 

200X Savings (TWh) 7.8 15.2 20.6 25 

% of total generation 0.17% 0.32% 0.41% 0.48% 

300X Savings (TWh) 11.7 22.8 30.9 37.5 

% of total generation 0.26% 0.48% 0.62% 0.72% 

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 a particular PTAC/PTHP product and a specific trial standard level (TSL) for that product. The NEMSBT simulations were performed prior to the final selection of TSL’s and so the 1X multiplier does not correspond to 

any specific TSL for a product category in previous sections of the report. (The final estimate of energy savings for 

standard size (small + large capacity) PTHP equipment at TSL 6 is very close to the 1X value, having an actual 

multiplier of 1.032) However, it was judged that the savings decrements (in TWh) tested in NEMS-BT, shown in 

lower portion of , 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 . This procedure is explained 

more fully below. This same scaling was used for both PTHP and PTAC equipment, with the savings for PTHP 

equipment allocated to cooling and heating. 

Table J.2.1

Table J.2.1

 J-3 

 EERE-2007-BT-STD-0012 COMMENT 32
Based on this testing, a decision was made to use the higher multipliers in the range of 

100X through 300X. While these multipliers are large, they still do not yield large perturbations 

to the base case simulation. For example, as Table J.1.1 indicates, even at 100X in the year 2025 

the total savings decrement applied to the model represents only about 0.5 percent of total 

electricity generation. 

Final Implied Multipliers by Equipment Class and Trial Standard Level 

Subsequent to the production of the NEMS simulations described in the previous section, 

some revisions were made to the final set of energy savings estimates for the NOPR. In addition, 

for purposes of estimating utility and environmental impacts for standard-size equipment, the 

two size equipment classes (equal or less than 10,000 Btu/h and greater than 10,000 Btu/h) were 

combined. To adjust for these changes, the difference between the final savings estimate (by 

equipment class and trial standard level) and the savings from a preliminary “reference” time 

series (PTHP, >10,000 Btu/h, at the largest TSL) was represented as a scale factor. The scale 

factor essentially adjusts the savings from particular equipment class and TSL to be consistent 

with the reference series and thus consistent with the interpolation procedure described above.

The first column in Table K.2.2 displays the scale factors for each equipment class and 

TSL.d

 The remaining columns display the implied multipliers from the three simulations 

performed with NEMS-BT for either PTACs or PTHPs (using their designations of 100X, 200X, 

and 300X). For example, after combining the size categories for PTHP equipment, the actual 

multipliers for TSL-7 were 52, 104, and 156. Because the savings for TSL 1 through 6 are 

smaller than those for TSL 7, the implied multipliers are larger than those for TSL 7. 

Table J.2.2 Final Implied Multipliers by Equipment Class and Trial Standard Level 

 Implied Multipliers 

Scale

Factor

NEMSBT

("100X") 

NEMSBT

("200X") 

NEMSBT

("300X") 

Equipment Class 

PTAC - Std. Size 

 TSL - 1,2,4 0.137 729 1,457 2,186 

 TSL - 3 0.307 326 652 977 

 TSL - A 0.728 137 275 412 

 TSL - 5 0.543 184 368 552 

 TSL - 6 0.834 120 240 360 

PTAC - Non-Std. Size 

 TSL - 1,2,4 0.042 2,359 4,718 7,077 

 TSL - 3 0.070 1,436 2,872 4,308 

 TSL - 5 0.107 936 1,872 2,809 

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 “1X” case in the original set of simulations was 

interpolated to be a value of, say, 0.10, then the impact for TSL-3 for standard size PTAC equipment would be 

0.224 x 0.10 = 0.022. 

 J-4 

 EERE-2007-BT-STD-0012 COMMENT 32
PTHP - Std. Size 

 TSL - 1 0.267 375 750 1,125 

 TSL - 2,3 0.558 179 359 538 

 TSL - A 0.666 150 300 450 

 TSL - 4,5 0.898 111 223 334 

 TSL - 6 1.032 97 194 291 

PTHP - Non-Std. Size 

 TSL - 1 0.055 1,804 3,609 5,413 

 TSL - 2,3 0.076 1,317 2,634 3,951 

 TSL - 4,5 0.128 781 1,562 2,343 

 Implied Multipliers 

Scale

Factor

NEMSBT

("100X") 

NEMSBT

("200X") 

NEMSBT

("300X") 

Equipment Class 

PTAC - Std. Size 

 TSL - 1,2,4 0.137 729 1,457 2,186 

 TSL - 3 0.307 326 652 977 

 TSL - A 0.728 137 275 412 

 TSL - 5 0.543 184 368 552 

 TSL - 6 0.834 120 240 360 

PTAC - Non-Std. Size 

 TSL - 1,2,4 0.042 2,359 4,718 7,077 

 TSL - 3 0.070 1,436 2,872 4,308 

 TSL - 5 0.107 936 1,872 2,809 

PTHP - Std. Size 

 TSL - 1 0.267 375 750 1,125 

 TSL - 2,3 0.558 179 359 538 

 TSL - A 0.666 150 300 450 

 TSL - 4,5 0.898 111 223 334 

 TSL - 6 1.032 97 194 291 

PTHP - Non-Std. Size 

 TSL - 1 0.055 1,804 3,609 5,413 

 TSL - 2,3 0.076 1,317 2,634 3,951 

 TSL - 4,5 0.128 781 1,562 2,343 

J.3 Regression Smoothing of NEMS-BT Outputs 

Even at the selected multiplier levels shown in Table J.1.1, 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 or may not be spurious results 

from the model solution process. 

 J-5 

 EERE-2007-BT-STD-0012 COMMENT 32
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 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 2011, T = 1 in 2012, etc. 

a1,a2 = estimated regression coefficients 

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 the prior to the implementation of the standard (2011). 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. 

Figure J.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 the PTHP equipment at the 

200X level of savings. 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 fossil steam plants,the simulation reveals a u-shaped 

curve that shows a reduction in capacity until around 2025 and then rising sharply after that. 

The deviations from the fitted trend line are more pronounced for combined cycle plants. 

Nevertheless, over the entire forecast period, the downward trend in the capacity of these plants 

is very apparent from the graph. The approach in this analysis is to abstract these very shortterm deviations from what appears to be a long-term trend. Finally, for combustion turbines, the 

deviations from a smooth downward trend are relatively small. The use of the quadratic 

specification is most apparent here as the decline in capacity accelerates during the latter portion 

of the forecast period. 

 J-6 

 EERE-2007-BT-STD-0012 COMMENT 32
Total Generation 

-14

-12

-10

-8

-6

-4

-2

0

2

2010 2015 2020 2025 2030

Difference (GW)

NEMS-BT

Fitted

Fossil Steam

-5

-4

-3

-2

-1

0

1

2

3

2010 2015 2020 2025 2030

Difference (GW)

NEMS-BT

Fitted

Combined Cycle

-2

-1.5

-1

-0.5

0

0.5

2010 2015 2020 2025 2030

Difference (GW)

NEMS-BT

Fitted

Combustion Turbine

-7

-6

-5

-4

-3

-2

-1

0

1

2010 2015 2020 2025 2030

Difference (GW)

NEMS-BT

Fitted

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

Capacity (200X case for PTHP). 

J.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 (100X, 200X, and 300X). 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 J.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 three simulations for PTHP 

equipment. 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 100X, 200X, 300X

 J-7 

 EERE-2007-BT-STD-0012 COMMENT 32
 J-8 

Total Generation

-35

-30

-25

-20

-15

-10

-5

0

0 50 100 150 200 250 300 350

Savings Multiplier

Difference (TWh)

Coal

-25

-20

-15

-10

-5

0

0 50 100 150 200 250 300 350

Saving Multiplier

Difference(TWh)

Natural Gas

-2

0

2

4

6

8

10

0 50 100 150 200 250 300 350

Savings Multiplier

Difference (TWh)

Nuclear

-20

-15

-10

-5

0

5

0 100 200 300 400

Savings Multiplier

Difference (TWh)

Figure J.4.1 Response (Interpolating) Functions for Selected Generation Outputs, PTHP 

Case for 2025 

savings multipliers. Within this range of savings, the plot demonstrates the impact on total 

capacity predicted by the model is basically proportional to the magnitude of the savings. 

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

proportionality. For example, for natural gas, the response at the 300X is greater than either the 

100X or 300X 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 savings from a 

particular standards case is first converted into a savings multiplier using the relationships shown 

in Table J.2.1. Thus, for example, if the trial standard level for a particular product were to yield 

a decrement of 0.052 TWh in 2025, the savings multiplier would be calculated as 

0.5 (= 0.052/0.103, where 0.103 is 1X in 2025 from Table J.2.1). For total generation, the 

estimated response coefficient is -0.10 (e.g., the slope of regression line in the top left panel 

Figure J.4.1). Thus, the estimated impact on total generation in 2020 from this specific trial 

standard level would be 0.5 x -0.10 = -0.05 TWh.

 EERE-2007-BT-STD-0012 COMMENT 32
The entire estimation process was performed separately for PTAC and PTHP equipment. 

As described in Chapter 14, the response coefficients for total generation, for the same total 

savings decrement, was somewhat different for PTAC versus PTHP equipment. The impact on 

installed generation capacity is significantly higher for PTAC equipment as compared to PTHP 

equipment. 

J.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 J.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 five-year intervals between 2015 and 2030.

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

emissions for PTHP equipment. In general, total carbon emissions are approximately 

proportional to the level of the saving decrement (for the savings decrements shown in 

Table J.2.1 corresponding to 100X, 200X, and 300X). 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 

2020 reflects the increasing reduction in emissions over these years. The slope is somewhat 

smaller in the latter years for this particular series of simulations. This behavior likely reflects a 

sharp reduction in nuclear capacity by 2030, particularly in the 200X and 300X cases, which 

tends to offset some of the reductions in carbon emissions from fossil fuel generation (see 

Chapter 14 for impacts on particular generation technologies). 

 J-9 

 EERE-2007-BT-STD-0012 COMMENT 32
Carbon Dioxide Emissions (2015)

-50

-40

-30

-20

-10

0

0 50 100 150 200 250 300 350

Savings Multiplier

Difference (MMT-CE)

Carbon Dioxide Emissions (2020)

-50

-40

-30

-20

-10

0

0 50 100 150 200 250 300 350

Savings Multiplier

Difference (MMT-CE)

Carbon Dioxide Emissions (2025)

-50

-40

-30

-20

-10

0

0 50 100 150 200 250 300 350

Savings Multiplier

Difference (MMT-CE)

Carbon Dioxide Emissions (2030)

-50

-40

-30

-20

-10

0

0 50 100 150 200 250 300 350

Savings Multiplier

Difference (MMT-CE)

Figure J.5.1 Response (Interpolating) Functions for Carbon Dioxide, PTHP Case, for Years 

2015, 2020, 2025 and 2030. 

 J-10 

 EERE-2007-BT-STD-0012 COMMENT 32
 J-11 

REFERENCES 

1. U.S. Department of Energy. Energy Information Administration. National Energy Modeling 

System: An Overview 2003. (DOE/EIA-0581(2003), March 2003. 

http://tonto.eia.doe.gov/reports/reports_kindD.asp?type=model%20documentation.

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

Outlook 2008, April 2008. Washington, D.C. DOE/EIA-0383(2007). 

 EERE-2007-BT-STD-0012 COMMENT 32