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APPENDIX I. INTERPOLATION OF UTILITY AND ENVIRONMENTAL RESULTS 

FROM NEMS-BRS OUTPUT

TABLE OF CONTENTS

TABLES

Table I-1 Set of Multipliers for Each Trial Standard Level . . . . . . . . . . . . . . . . . . . . . . . . . . . I-2

FIGURES

Figure I-1 An Example of the Interpolation of a Trial Standard Level: Difference

 in Coal Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-4

Figure I-2 Example of a Trial Standard Level: Marginal NOx Emissions . . . . . . . . . . . . . I-5
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).

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APPENDIX I. INTERPOLATION OF UTILITY AND ENVIRONMENTAL RESULTS

FROM NEMS-BRS OUTPUT

The effects of proposed water heater energy-efficiency standards on the electricity and natural

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 natural 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 water heater load is

reduced annually according to the energy savings estimated by the National Energy Savings model

(see Chapter 12) for each trial standard level. These energy savings increase over time and are

distinguished by fuel type (electricity, natural gas, LPG, and oil). Differences in fuel 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. 

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 between standards 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

were selected for each of the trial standard levels as shown in Table I-1.
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Table I-1 Set of Multipliers for Each Trial Standard Level

Trial Standard Level 1 4, 6, 8

Trial Standard Level 2 6, 8, 10

Trial Standard Level 3 6, 8, 10

Trial Standard Level 4 2, 3, 4

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). 

Figure I-1 shows an example of the interpolation approach for a water heater 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. 

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 each standard level, 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. 

Figure I-2 shows an example of the extrapolation for NOx emissions rates for trial 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
I-3

calculated by the interpolation method described above). For Trial Standard Levels 2 and 3,

marginal emissions rates for all years are derived by averaging the marginal rates of the three highest

decrement levels (e.g., 6, 8, and 10 times the standard level). For Trial Standard Levels 1 and 4, the

marginal emission rates are derived by averaging the rates of the two highest decrement levels, when

stable numbers are available. In certain years, however, the marginal emission rate is derived from

other methods because the average is obviously unstable. Experience has shown that stable marginal

emissions factors possess a linear trend over time. The presence of noisy, unstable emissions rates,

therefore, raises the need to consider next-best alternatives such as omitting one of the higher

decrement estimates because of instability or opting to use an emission rate from a neighboring year

when an average is not possible.
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-14-12-10

-8-6-4-2

0

0 1 2 3 4 5 6 7 8 9 10

Savings Multiplier

2020 Regression2015 Regression2010 Regression2005 Regression20202015201020052000

No Std. Lvl. 6x Std. Lvl. X1 8x Std. Lvl. X1 10x Std. Lvl. X1

Figure I-1. An Example of the Interpolation of a Trial Standard Level: Difference in Coal Capacity
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-8-6-4-2

02468

S avings Multiplier

g/kWh NOx

Std . Lv l. X1 6x Std. Lv l. X1 8x Std . Lv l. X1

Figure I-2 Example of Trial Standard Level X1: Marginal NOx Emissions
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REFERENCE

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

Consumption Survey: Household Energy Consumption and Expenditures 1997,1999.

<http://www.eia.doe.gov/emeu/recs/recs97/publicusefiles.html>