a For more information on NEMS, please refer to the U.S. Department of Energy, Energy Information Administration documentation.

A useful summary is National Energy Modeling System: An Overview 2000. DOE/EIA-0581(2000), March 2000. DOE/EIA

approves use of the name NEMS to describe only an official version of the model without any modification to code or data. Because

our analysis entails some minor code modifications and the model is run under policy scenarios that are variations on DOE/EIA

assumptions, the name NEMS-BRS refers to the model as used here (BRS is DOE’s Building Research and Standards office, under

whose aegis this work has been performed).

H-1

APPENDIX H: INTERPOLATION OF UTILITY AND ENVIRONMENTAL RESULTS

FROM NEMS-BRS OUTPUT

The effects of proposed central air conditioner and heat pump energy-efficiency standards

on the electricity and gas industries were analyzed using a variant of U.S. DOE/EIA’s National

Energy Modeling System (NEMS) called NEMS-BRS, together with some exogenous calculations.a

Because the relative size of the energy savings being implemented in NEMS-BRS is too small to be

seen in the context of the whole electricity and gas utility sector, NEMS-BRS is not used directly.

Rather, exploratory runs are conducted to estimate marginal effects, which are then used to calculate

the small effects due to each proposed trial standard level.

To run a simulation in NEMS-BRS, the Residential Demand Module central air conditioner

and heat pump load is reduced annually according to the energy savings estimated by the National

Energy Savings model (see Chapter 7) for each standard level. These electricity energy savings

increase over time and differences in usage among U.S. census divisions come from data derived

from the Residential Energy Consumption Survey (RECS).1

The magnitude of the energy decrement that would be required for NEMS-BRS to produce

stable results safely out of the range of numerical noise is greater than even the most stringent

standard under consideration. Therefore, it has been necessary, in both the utility and environmental

analyses, to estimate results in the range of the standard levels effects using interpolation.

Interpolated values are derived from a series of higher decrement simulations based on the standard

levels. The actual annual savings attributed to each standard level are compared between standard

levels, and those with similar energy savings patterns over time are grouped together. One set of

simulations is run for each of the savings groups. The standard levels for the central air conditioner

and heat pump analysis were divided into four groups:

Standard Level 1: modeled independently

Standard Level 3: used to model Standard Level 2

Standard Level 4: modeled independently

Standard Level 5: modeled independently

To preserve the pattern of energy savings over time for a trial standard level, savings in each

year are multiplied by the same factor. This factor varies for each standard because the magnitude

of the savings changes. An appropriate set of multipliers were chosen to augment the savings to a

magnitude that produces credible results. Using professional judgement, sets of three multipliers

EE-RM-STD-98-440 COMMENT 241ZZ
H-2

were selected for each of the four patterns as shown in Table H.1.

Table H.1 Set of Multipliers for Each Standard Level Pattern

Standard Level 1 5.25, 6.80, 7.64

Standard Level 3 2.77, 3.59, 4.03

Standard Level 4 2.18, 2.82, 3.17

Standard Level 5 1.18, 1.53, 1.71

The output for electricity generation and capacity by fuel type for each of the iterations (e.g.,

6, 8, and 10 times the standard level) is then regressed, with the y-intercept forced through the origin,

and the actual standard level forecast is interpolated along this regression line. The linear regression

is forced through the origin because a zero change must be the case with no standard in place and

because the target points of interpolation are close to the origin (i.e., at low energy decrements).

Other trial standard levels within the same group are interpolated along this regression line by

substituting the x-value in the regression equation with the ratio of energy savings between standard

levels in the peak energy savings year. 

Figure H.1a shows an example of the interpolation approach for a central air conditioner and

heat pump trial standard level X1. The magnitude of the energy savings multiplier is plotted on the

x-axis against the reduction in coal installed generating capacity for each reported year, as shown by

the various plotted lines. In general, results for the various NEMS-BRS runs are reasonably stable

and linear, with the noisy behavior appearing below the first multiplier of the trial standard level

savings decrement. 

 Figure H.1b shows a close-up of the interpolated points for trial standard level X2 from

standard X1. The heavy horizontal lines illustrate the calculated values for the difference in coal

capacity in 2020. These regressions appear stable, so estimating results via interpolation toward zero

seems justified. A similar approach was used to find the drop in installed generating capacity from

other fuels and in generation for each fuel type in each reported year. 

The estimated reduction in total fuel generation that we report at each trial standard level as

determined by interpolation is then used to determine emissions savings. First, annual marginal

emissions rates are calculated for each of the simulations in a savings group, based on the actual

output from NEMS-BRS. Marginal emissions rates incorporate both effects of the standards—the

emissions saved by the reduction in total generation and the slight change in the emissions

characteristics of the whole power sector that result from the slight change in dispatch and capacity

expansion plan. The net effect on the entire system is very small and, typically, the overall effect on

emissions can be fully attributed to the decremental generation. The annual marginal emissions rates

at the trial standard level are then extrapolated from these rates (at multipliers of the trial standard

level savings) by taking a simple average. 

EE-RM-STD-98-440 COMMENT 241ZZ
H-3

Figure H.2 shows an example of the extrapolation for NOx emissions rates for standard level

X1. In this case, marginal rates for NOx emissions are shown for each year. As is evident in the

figure, more stable results are produced at higher levels of demand decrement. At lower decrement

levels (i.e., both on the left-hand side of the figure and in years with small standards impacts), the

emissions rate is quite variable. The dashed plots (years 2003 - 2010) show the earlier years of the

imposed standard—those in which the decrements to demand are smallest (not shown here). In most

cases, these curves are so close to flat that regression of the higher decrement simulation points

produces a curve very close to the simple average of values. The constant emissions rates at higher

decrement levels are therefore assumed to hold in the range of small decrements commensurate with

the various standard levels, and the implied marginal emissions rates are used to estimate emissions

reductions. Total emissions savings in each year are the product of the annual marginal emissions

rate and the reduction in thermal generation for that year (as calculated by the interpolation method

described above). Marginal emissions rates for all years are derived by averaging the marginal rates

of the three highest decrement levels (e.g., 2, 4, and 6 times the standard). Experience has shown

that stable marginal emissions factors possess a linear trend over time. 

EE-RM-STD-98-440 COMMENT 241ZZ
H-4

1 2 3 4 5 6 7 8 9 10

Savings Multiplier

200020052010201520202005 Regression2010 Regression2015 Regression2020 Regression

Lvl. 6x Std. Lvl. X1 8x Std. Lvl. X1 10x Std. Lvl. X1

An Example of the Interpolation of a Trial Standard Level: Difference in Coal Capacity

EE-RM-STD-98-440 COMMENT 241ZZ
H-5

0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

Savings Multiplier

200020052010201520202005 Regression2010 Regression2015 Regression2020 Regression

Std. Lvl. X1 = 1.0 Std. Lvl. X2 = 0.73

2020

2020 

lose-Up of the Interpolation of Trial Standard Level X2 from X1

EE-RM-STD-98-440 COMMENT 241ZZ
H-6

Savings Multiplier

200320042005200620072008200920102011201220132014201520162017201820192020

Std. Lvl. X1 6x Std. Lvl. X1 8x Std. Lvl. X1 10x Std. Lvl.X1

mple of Trial Standard Level X1: Marginal NOx Emissions

EE-RM-STD-98-440 COMMENT 241ZZ
H-7

REFERENCES

1. U.S. Department of Energy-Energy Information Administration, A Look at Residential

Energy Consumption in 1997, 1999. Washington, DC. Report No. DOE/EIA-0632(97).

EIA website: <http://www.eia.doe.gov/pub/pdf/consumption/063297.pdf>

EE-RM-STD-98-440 COMMENT 241ZZ