I
Table of Contents page I.
Introduction There Is No Substitute for Real Scorekeeping It's Easier Than It May Seem
2
Toward a Standardized Approach
6
II. Summary of the Scorekeeping Method
9
The Physical Basis for the Model
9
Individual-house Analysis
13
The Measurement of Savings
20
Inclusion of Electric Cooling
22
Extension to Utility Aggregates
25
Bibliography of Scorekeeping Publications
29
List of Figures and Table page Figure 1. ,Schematic diagram showing the data requirements for the Princeton scorekeeping method and the estimates that result from it
3
Figure 2,
Daily gas consumption as a function of outside temperature, for a single idealized house
10
Figure 3.
Daily gas consumption as a function of degree-days base \T\, for a single idealized house
12
Figure 4.
Consumption data plotted against heating degree-days base \T\, for sample gas-heated house in New Jersey
14
Figure 5.
Consumption data plotted against heating degree-days base \T\, for sample electrically heated house in New Jersey
17
Table 1.
Example of data base resulting from scorekeeping analysis
19
Figure 6.
Illustration of sliding-month approach
21
Figure 7.
Superposition of degree-day data on consumption data, for sample electrically heated and cooled house in New Jersey
24
Figure 8.
New Jersey aggregate results
26
I. Introduction
There Is No Substitute for Real Scorekeeping To date, a frequent failing of commercial and government conservation enterprises has been a lack of accounting to "keep score" on the value and magnitude of the energy saved by the measures implemented.
At Princeton,
years of related research have convinced.us that serious scorekeeping is essential to the success of all conservation ventures.
Without it, the
importance of conservation cannot be effectively communicated to homeowners, the best programs cannot be distinguished from ineffective ones, and the credibility of conservation is being threatened. Many utilities in the U.S. have undertaken extensive retrofit assistance programs for their customers, not only because of the federal Residential Conservation Service (RCS), which mandates nearly free energy audits for customers, but also because of a growing commitment to energy conservation as a utility investment strategy.
RCS audits have reached
some two million homes •. In addition, the Low-Income Weatherization Program, federally funded but managed at the community level, is reaching many additional homes, not only with an audit but with extensive, often costly, retrofits as well.
With rising fuel prices, one may expect these
retrofit programs to become even more popular. Missing in almost all these programs has been an accurate evaluation of how much energy is actually being saved by specific actions taken.
The
program's yardstick of success is often the number of participants, with no regard for the number of kilowatt-hours of electricity, barrels of oil, or 1
cubic feet of gas saved.
Estimates of savings, if they exist, are based on
engineering models typically without calibration to real-world experience. Such estimates, though useful for planning purposes, are notoriously higher than the actual savings realized, in part because they do not accurately take into account either human behavior or the irregularities in the complex heat flows of real buildings. On the private side, companies which sell conservation services invariably omit feedback to the customer on how much energy money -- the purchase is saving.
and
Furthermore, without records of actual
savings achieved, companies deny themselves a readily available source of information from which they can understand --.and project the services they sell.
the value of
The resulting picture can be one of dissatisfied,
confused customers dealing with a company unable to convey accurate estimates of the value·of its own services, It's Easier Than It May Seem Perhaps surprisingly, it is extremely straightforward to obtain accurate estimates of actual energy savings, and the required data, .utility bills and daily average temperatures, are readily available.
As
depicted in Figure 1(a), the Princeton scorekeeping method, "PRISM", uses utility bills from before and after the retrofit installation, together with average daily temperatures from a nearby weather station for the same periods, to determine a weather-adjusted index of consumption, Normalized Annual Consumption or NAC, for each period.
Analogous to (and, based on
field measurements, clearly more accurate than) the EPA miles-per-gallon rating, the NAC index provides a measure of what energy consumption would
2 ,.,, ,,,,,..
a)
Outputs:
Inputs:
: Monthly billing data : l for each house, 1 pre and post
1-->---
I NAC lor -->--1 each house, I. I pre and post l
l Daily teapera ... :................. >---: :--->--1 I ture data
.l I \ I 1·->·-1 1_____________1_____ ,
----------------
PRISM
: Other physical : :
Long~ter•
--->--1 paraaeters for
1-------->---
l degree-days
b)
I
I each house
Outputs:
Ir.puts:
I NAC for
: "onthly billing data : l for treataent houses,:-->--1 pre tnd post
-->--1 treataent houses, :-->-: pro and post
I
l Control- : 1-->--l adjusted : l savings :
: Monthly billing data : I for control houses,
1-->-.. -l
: pre and post
I NAC lor
I I
I
:--->·-1
PRISK
I
1-->··1··>··1 control houses,
1_____________ 1.••••1
: pro and post
:-->--
I Daily teapera- :-------->---: l ture data
I Other physical : : Long-tero : degree-days
Figure 1.
1-------->-··
--->--1 paraaeters for l
I
I all houses
Schematic diagram showing the data requirements for the Princeton scorekeeping method and the estimates that result from it: a) the basic procedure for a set of houses; b) the procedure when a control group is included. 3
be during a year under typical weather conditions.
The total energy
savings are derived as the difference between the NAC in the pre- and postperiods.
A conservation effect is thus neither masked by.a cold winter nor
exaggerated by a warm one, nor is it obscured if the time covered by billing periods in one "year" is longer than in another. In order to adjust for the influences of occupant behavior and externalities such as energy price changes, and in effect to isolate the savings due to the program from savings that would otherwise have occurred, scorekeeping often requires a set of untreated, "control" houses.
The same
procedure applied to both the treatment and control houses, as shown in Fig. 1(b), gives a measure of control-adjusted savings for the treatment group.
The analysis can then be updated for succeeding years, to track the
durability of the savings.* A more complete evaluation is often desired, to determine the costeffectiveness of various tried approaches to conservation, for example, or the effect of program participation and other explanatory variables.
The
savings estimates, along with other PRISM outputs, provide reliable input to such analyses.
Thus the PRISM analysis depicted in Fig. 1 may be thought
of as a standardized first stage of an evaluation, with subsequent analyses, limited by available data and shaped by the specific needs of the project being evaluated, comprising the second stage. PRISM differs from other weather-normalization procedures in that the house's break-even temperature is treated as a variable, rather than a • Another application of PRISM is for house energy labeling, whereby an actual energy consumption index (based on energy bills) would be attached to any occupied house. Such an index could be extremely valuable to a house purchaser at time of sale, and to the homeowner or billpayer for energy conservation investment choices.
4
constant such as 65°F,
Three physical parameters result from the model
applied to the billing data for the heating fuel of an individual house: base level consumption, corresponding to the amount of fuel used per day (for appliances including water heaters) independent of outside temperature; the reference temperature, approximating the average daily outside temperature above which no fuel is required for heating; and the heating slope, corresponding to the amount of fuel required per degree drop in outside temperature below the reference temperature.
These parameters
can provide indications of the sources of conservation: insulating, turning down thermostats, more efficient appliance usage, etc., and thus define an "energy signature" of the house.
The Normalized Annual
Consumption (NAC) index is derived from these parameters applied to a longterm (say, ten-year) annual average of heating degree-days. It turns out that NAC is extremely well determined (its standard errors are typically 3-4% of the estimate), so that savings of 6% or more may generally be considered significant.
Furthermore, NAC is quite
insensitive to which periods are included, or their length. more reliable index for monitoring conservation.
5
We know of no
Toward
~
Standardized Approach
Among the evaluations of retrofit programs that have been performed, the haphazard array of approaches often makes it impossible to compare savings from one program with another, or to aggregate the effects across programs.
The first "scores" are in from selected RCS and weatherization Nevertheless, the lack of a
programs, and many of them are disappointing.
coordinated approach makes it impossible to learn from our mistakes and plan for more effective programs in the future. The long-range goal of our scorekeeping research at Princeton is to produce a standardized, easy-to-use approach which utilities, communities and others throughout the country may adopt for measuring the savings achieved by their retrofit programs.
Over the past several years,
the PRISM tools have been enormously valuable to our own buildings research program (for example, in the Modular Retrofit Experiment, a collaborative conservation project between Princeton and the natural gas utilities in the New Jersey area (Dutt et al., 1982) and for monitoring statewide conservation trends in New Jersey (Fels and Goldberg, 1984)).
There is now
increasing interest in the scorekeeping method on the part of outsiders. Recently, it was used for the evaluation of Wisconsin's low-income weatherization program (Goldberg et al., 1984).
For their evaluation of
Residential Conservation Service and other utility conservation programs, staff at Oak Ridge National Laboratory are using PRISM as stage one of their two-stage evaluation approach (see, for example, their scorekeeping of Bonneville Power Administration's weatherization pilot program, in Hirst et al., 1985).
The method is being used extensively in Minnesota to
monitor the success of a variety of city and state programs (see, for
6
example, Hewett et al., 1984). There is much more to be learned before PRISM will work equally well for all major fuels, over a wide range of climates and building types. While the initial ·emphasis of the methodology development was on gas-heated single-family houses, we are focusing our current research in three areas: 1) the inclusion of cooling for electrically heated houses-- a nasty problem because the demand for cooling is far more erratic (peopledependent) than it is for heating;
2) the treatment of "bad" houses that
don't respond predictably to weather; and 3) the applicability of the approach to large multi-family buildings, to understand its limitations as well as its strengths.
With the benefit of the wealth of real-world
experiences embodied in ongoing scorekeeping projects such as the above, we are optimistic that these advancements in the methodology are feasible.
7
8
II.
Summary of the Scorekeeping Method
The Princeton scorekeeping method involves a straightforward procedure for calculating energy savings between two time periods.
For each house
being analyzed, the procedure requires meter readings (or for fuel oil, delivery records) for approximately one year in each period•
The
consumption data are then corrected for the effects of weather, which of course is never the same for two different years, and also for differences in the time spanned by the two periods.
From these results the weather-
normalized consumption index, called Normalized Annual Consumption or NAC, is calculated. The Physical Basis for the Model We start by describing the method developed for fuels used for heating but not cooling.
Generally, whether for natural gas, oil or electricity, a
house's heating system is first required when the outside temperature (T) drops below a certain level (the heating reference temperature T), and for each additional degree drop in temperature a constant amount of heating fuel (the heating slope 6) is required. * Thus, the required heating fuel is linearly proportional to
T - T, and the proportional constantS
·represents the house's effective heat-loss rate.
In addition, the house
may use a fixed amount of heating fuel (the base level a) which is independent of outside temperature T.
Formally, the expected fuel
consumption f, as illustrated in Fig. 2 for an idealized house, is given by f :
a + 6 (T - T)+
( 1)
where the term in parentheses is the heating degree-days to base T and the
"+"
* Here
indicates zero if the term is negative. 11
fuel 11 includes electricity as well as natural gas, fuel oil, etc. 9
15
2 0
'
~
1- 0>-
a.
~
::> (/)
2 0
"0 I
0
~
0
10
Cll (I)
;:, 0
u .c (/)
<( C)
~ <(
0
'
(I)
E ....
Cll
s
..:=,
1-
"
"
100
T• AVERAGE DAILY OUTDOOR TEMPERATURE (°F)
Figure 2.
Daily gas consumption (f) as a function of outside temperature (T), for a single idealized house. 10
The physical justification for assuming that both the base level a and the heat-loss rate
e are
constant has been carefully analyzed in previous
work. * The derivation leads to a simple physical interpretation for each of the three parameters.
The reference temperature T represents the
outdoor temperature below which the heating system is required.
The value
of T is influenced primarily by the indoor temperature (thermostat setting) and, in addition, an offsetting contribution from the free heat
(i.e., heat generated by appliances and occupants).
The heat-loss rate B
depends on the conductive and infiltration heat losses, while the base level a represents the fuel requirements of appliances (including lights, for electricity, and the water heater if fueled by the heating fuel). If T is not accurately determined, or if it changes significantly over the time periods studied, the error or change in T will directly affect a, with an opposite sign. as well.
In fact, the slope
B will
be .affected
Fig. 3 illustrates this for the idealized house by plotting f vs.
h for one correct and two incorrect values ofT.
A straight-line fit
through each set of points will have a different slope and intercept. Therefore, an assumed (incorrect) reference temperature, such as the value ·or 65°F so commonly used, is likely to lead to less physically meaningful values of the base level and the heat-loss rate.
As discussed below, it
turns out that estimates of total consumption, over a year, for example, are much less sensitive to choice of ••
• See references given in the Bibliography.
11
z
0 1- >a.. ~
c ::::E "'C ::> I UJ
C1> 10
0
::>
z
"'
0 u ..c: U)
<1:
C)
......
"' E
...
C1> s ~ ..c:
-
<1: 1-
0
4-
--,
-----.--04-----~------r-----~----~------~ 60 50 10 .
20
30
h(T) • DAILY HEATING DEGREE DAYS BASE T (°F-d ay/d ay)
Figur e 3.
'• Daily gas consu mptio n (f) as a funct ion of degre e-day s base curve s for a singl e ideal ized house . In these plots , the three with data, rature tempe and n mptio consu corres pond to the same degre e-day s calcu lated at diffe rent bases T.
12
70
Individual-house Analysis Based on this physical interpretation, the two data requirements for the analysis are actual meter readings, from which consumption is calculated, and daily average temperatures, from which heating degree-days to different reference temperatures are computed in exact correspondence to the consumption periods.
The input to the procedure is then Fi and H1
where:
Fi = average daily consumption (e.g., in kwh/day) in time interval i heating degree days per day to reference temperature T in time interval i, Here Hi(T) is computed from average daily temperatures Tij for the N1 days in interval i, i.e., (2)
where
11
+ 11 indicates that the term in parentheses is set to zero if Tij is
above T.
Fig, 4 shows a plot of Fi against H1 for the 1978-79 heating
year, for a sample house from the Modular Retrofit Experiment (MRE).
A
straight-line relationship is clearly suggested. The set of data points {Fi} and {H 1 J for an approximately year-long period are then fit to a linear model: ( 3)
where ei is the error term.
For a guessed value of reference temperature
<, the base level and heating slope
parameters~
and
S are found by
standard statistical techniques (ordinary least-squares linear regression). The parameters values ofT.
~
and S are calculated in this way for several different
"Best T" is the one for which a plot of Fi vs. Hi (T),
13
House: T 120 PRE, alpha= 0.90, beta= 0.16, R2= 0.9851
1.0
+ ••••••••• 0.3
0
••
.+. 11.0 0
0
•••••••••
0
0
Heating degree-days per
Figure 4.
.+ ...
21.8
day~
0
0
0.
0
0.
0
•••
+ ••
0
•••••
0.
32.6
base tau= 68.1
Consumption data (F 1 ) plotted against heating degree-days base T, i.e., Hi(T), for sample gas-heated house in New Jersey. Heating degree-days to best T (68°F) are shown. The straight line results from fitting the model to Eq. 3.
such as the one shown in Fig. 4, is most nearly a straight line.
Formally,
T is determined as the value for which the mean squared error is minimized, or equivalent!~ for which the R2 statistic is highest.
The
corresponding values of a and 8 are the best estimates of base level and heating slope. In our model, the term a characterizes the temperature-independen t component of consumption (in units/day, where units may be ccf or therms for gas, kwh for electricity or gallons for fuel oil), which is dominated by appliance and water heater usage.
The parameter 8 represents the
incremental amount of gas required for each degree drop in temperature below the reference temperature.
Referring to
B as
the heating slope (in
units/°F-day), the term BlHi(T) gives an estimate of temperaturedependent demand, which is dominated by space-heating.
The reference
temperature T (in °F), which varies from house to house, represents the average outside temperature below which a house's heating system is required. The parameters a, B and T resulting from the model are used to calculate Normalized Annual Consumption, the overall index of consumption which we call NAC.
The NAC index represents consumption which would occur
.in a year with typical weather conditions, and is calculated as follows: NAC : 365 a + 8 H0 (T) where H0 (T) is the heating degree-days (base T) in a "typical" year. The values of H0 used in our recent New Jersey analyses are based on the twelve-year normalization period from 1970 through 1981.*
* Weather
data to compute H1 for each period and H0 , to any reference temperature, were collected from National Oceanic and Atmospheric Administration (NOAA) data for the Newark, NJ, weather station. For example, values of H0 forT = 60 , 65 and 70°F are 3807, 4917 and 6181 °F-days/year respectively.
15
(4)
To illustrate, the model in Eq. 3 applied to the house data in Fig. 4 gives the following results for the best-T approach: T
OF
= =
68.1
(~2.7)
0.90
(~0.26)
ccf/day
s =
0.18
(~0.01)
ccf/°F-day
(~27)
~
NAC
=
1324
R2
=
0.985.
ccf/year
The numbers in parentheses represent the standard errors. small standard error for NAC as compared with is typical of results from this model. represents 63% of the total consumption.
~
The relatively
and S (2% vs. 12% and 6%)
The heating component SH 0 (T) The R2 statistic indicates a very
good straight-line fit, corresponding to the line drawn in Fig. 4. The methodology is directly extendable to electrically heated houses without cooling.
For example, the heating-only model in Eq. 3 applied to
the house data in Fig. 5 gives the following results: T ~
= =
s =
59.5
(~1.6)
OF
29.0
(~1.6)
kwh/day
2.73 (+0.17) kwh/°F-day
NAC
=
20,700
R2
=
0.990.
(~375)
kwh/year
Again, the NAC, with a standard error of 2%, is extremely well determined. In general the NAC estimate provides a reliable conservation index from which energy savings and conservation trends may be accurately estimated.
On the other hand, the three parameters a, S and T
comprising the energy signature of the house, and the estimate of annual heating consumption SH0 (T) derived from them, are less well determined,
F.L~C'
House J44
I
GPU
I
I I I
•••
•
tJO
•I
120
•I
I
...
I
•I
•
I
••• •I
•• :;:
-!••...
I
•
.:1 110 • I
.s:
..
,_. "
a
~
•
ah
= 2.1J
•••
Th
=
JO
NAC
~so
••m
I I
0
u
20
. 0
NO COOL! NG
Results (H03 model)
•
...c 0
.
J44:
I
•
29.0
(+1.6)
kwh/day
(~0.17) kwh/°F- day
.S9.5
(:':1. 6)
oF
= 20,700
(:':375)
kwh/yea r
2 R • 0.990
•I I
•I I • .............. ......... •- ...... •· ......... • ....................... •----- ............ :'1
2
1:1
6
It
10
12
U
o----·· •---- t---- ........................................ •-----•- ----•-- ---•--- .... •-----• -·--·•-- -··
1t.
IR
20
2")
Heating degree- days Hf(Th)
Figur e 5.
211
26
2A
](I
)2
]q
]6
( F-days/ day)
Consumption data plotte d again st heatin g degre e-day s, base T, for sample elect rical ly heate d house in New Jerse y. Estim ates shown are obtain ed from the heatin g-onl y model in Eq. 3. The straig ht line repre sents the best- fit model , whose param eters are indic ated.
lS
U
and their changes over time are often difficult to interpret due to the interference of physical and statistical effects.
While it is tempting to
attribute a change in the base level to water heater wrap or more efficient appliances, for example, or a drop in the heating-consumption estimate to added ceiling insulation or other measures to tighten the structure, such physical inferences are often not statistically valid.
We feel that these
parameters provide physically meaningful indicators, whose changes may not be statistically significant but whose behavior can often suggest the reason for a consumption change. A frequently mentioned shortcut is the use of fixed T, at 65°F. Although
~
and
B are
highly sensitive to the T value used, the NAC results
are not, especially when the best-T values are fairly close to 65°F.
(The
median T value for several samples analyzed by this method has been close to 60°F.)
Nevertheless, our studies indicate that~ and B are
considerably more meaningful when estimated for best T than when estimated at a fixed value.
We strongly recommend that the best-T approach be used
when the results for
~,
B and
T are of interest, as they usually are in a
conservation analysis, or when there is reason to believe that the true T value is quite different from the assumed value. It is generally useful to store the scorekeeping results for subsequent computer analysis, for example as input to stage two of an evaluation.
Table 1 shows a sample summary table from MRE.
Note that the
sixth row of results corresponds to the demonstration house used here. Such examples assume the pre-selection of estimation periods for the model.
When a continuous series of consumption data is available, it is
often enlightening to run a month-sliding analysis, wherein a one-year
18
'f SJGAS
.... "'
WHIT !!IAN· SQOA RE
SAftPL! ONI'l TYPE ID THE PERIOD T 303 c 11/ 2/78- 10/31/79 T 113 c 11/ 2/78 - 10/31/79 T 129 c 11/ 2/78- 10/31/79 T 135 c 11/ 2/78- 10/31/79 T 115 HD 11/ 2/78- 10/31/79 T 120 HD 11/ 2/78 - 10/31/79 T 128 HD 11/ 2/78 - 10/31/79 T 132 80 11/ 2/78- 10/31/79 T 136 80 11/ 2/78- 10/31/79 T 140 80 11/ 2/78 - 10/31/79 T 143 BD 11/ 2/78- 10/31/79 T 150 HD 10/ 3/78 - 10/ 1/79 T 151 80 11/ 2/78 - 10/31/79 T 116 ~R 11/ 2/78 - 10/31/79 T 118 ~R 11/ 2/78 - 10/31/79 T 122 "R 11/ 2/78 - 10/31/79 T 127 ~R 11/ 2/78 - 10/31/79 T 137 ftR 11/ 2/78 - 10/31/79 T 303 c 5/ 2/80 5/26/81 T 113 c 5/ 2/BO 5/26/81 T 129 c 5/ 2/80 5/26/81 T 135 c 5/ 2/80 5/26/81 T 115 80 5/ 2/80 5/26/81 T 120 HD 5/ 2/80 4/24/81 T 128 HD 5/ 2/80 5/26/81 T 132 80 5/ 2/80 5/26/81 T 136 BD 5/ 2/80 5/26/81 T 100 HD 5/ 2/80 4/24/81 T 143 80 5/ 2/80 5/26/81 T 150 8D 5/ 2/80 4/24/81 T 151 HD 5/ 2/80 5/26/81 T 116 "B 5/ 2/80 4/24/81 T 118 ftR 5/ 2/80 4/24/81 T 122 ~R 5/ 2/80 5/26/81 T 127 ftR 5/ 2/80 .5/26/81 T 137 ftR 5/ 2/80 5/26/81
Table 1
FUEL= HG
HD" READS 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 10 10 12 12 10 10 12 12 12 11 11 11 12 11 11 12 12 12
ONn X= CCF
SQ
PRE OR
WATER HEAT
!'PET POST INDEX
PRE PRE PRE PRR 1840 PBE 1800 PR3
2100 PBE 1870 PRE 2110 PRE 1470 PR~
1840 1470 2320 2310 2100 2130 1870
1840 1800 2100 1870
PRE PRE PRE
PRE PRF. PRE PRE PRE POST POST POST POST PCST POST POST POST
8/HW 8/HW H/HW H/BW 8/HW H/HW A/HII H/H• H/R& B/HW H/8& A/Hi H/HW 8/8W 8/HW H/HW
H/HW H/HW H/HW H/HW H/HW H/HW H/HW H/HW H/HW A/HW
2170 POST H/HW
1470 1840 1470 2320 2370 2100 2130 1870
POST PCST POST POST POST POST POST POST POST
A/Hi H/HW H/AW 8/HW 8/AW H/HW H/HW H/RW H/HW
4 4 3 3 3 4 3 2 3 2 3 3 3 3 3 3 3 3 3 5 4 4 4 4 3
3 3 4 5 4 2 3 3 4 2 2
WST.,= NFWARK N OF ITS R X!f 0.9927 0.9S07 0.9935 0.992~
0.9654 0. 9 851 0.9814 0.9700 0.9B90 0.9928 0.9937 0.9893 o.9g04 0.9128 0.9823 0.9874 0.9919 0.9952 0.9958 0.9562 0.9889 0.9E87 0.9786 o. 977 4 0.9901 0.9890 0 .. 992A
0.9965 0.9.09 0.9941 0.9940 0.971;5 0.9848 o.q~ry8
O.H06 0.9786
TRE
68. 5 68.5 63." 67.2 66. 4 68. 1 58.4 62.4 66. 0 62.9 68.8 65.2 60.9 61.5 61.2 68. 0 64.6 65.0 67.9 56.5 64.0 66.0 67.9 65.0 60. 1 64.2 63.0 64.0 67.0 64.0 62.9 63.6 63.6 67.4 62.4 62.5
?
( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (
t
( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (
2. 0) 2.21 1.5) 1. 9) 4. 1) 2.7) 2. 2) 3.0) 2. 2) 1. 5) 1. 8) 1.9) 1.6) 2.8) 3.0) 2. S) 1. 7) 1.4) 1.6) 5.1) 1. 9) 2. 0) 3.8) 3.5) 1. 9) 1.9) 1.6) 1.3) 1 •• , 1 .6) 1.5) 3. 3) 2.6) 1. 8) 1. Q) 2.8)
BEST T
BASE LEVEL X PER DAY 1. 37 ( 0. 229) 0.32 ( 0.161) 1. 22 ( o. 140) 0.49 ( 0.174) 1.14 ( 0.304) 0.90 ( 0.263) 1. 00 ( 0.207) 1. 14 ( 0.222) 1. 23 ( o. 237) o. 60 ( 0.104) 0.69 ( 0.178) 1. 4 5 ( 0. 1 8 8) 0.96 ( 0.194) o. 70 ( o. 256) 1. 37 ( o. 340) o.n 1 o.3E9) 0.99 ( 0.124) 1.00 ( 0.124) 1.45 ( 0.165) o. 47 1 0.169) 1. 19 ( 0.182) o. 52 ( o. 178) 0.89 ( 0.238) o. 94 ( 0.251) 0.95 ( 0.151) 0. AS ( o. 125) 1 .. 7.4 ( 0.153) 0.53 ( 0.070) o. 76 ( 0.196) 1. 14 ( 0.105) 0.79 ( 0.148) o. 58 ( o. 220) 1. 39 ( 0.187) 1 .. 01 ( 0.214) o. 98 ( 0.105) 0. R3 ( o. 2'19)
NRONS=
SET
I. SERIES A
SLOPE
NAC
X PER HOD
X PER YEAll:
0.219 0.136 0.221 0.177 0.155 0.177 0.268 0.174
(
0 .. 219
(
0.165 o. 18 3 0.199 0.310 0.226 0.221 0.270 0.165 0.197 0.185 0.120 0.186 0.160 0.117 0.134 o. 197 0.128 o. 203 0.126 0.174 0.143 0.214 0.152 0.162 o. 201 0.123 1} ..
2
160
( (
(
( ( ( (
( (
( (
( (
( ( ( ( (
( I ( (
( (
(
I ( (
( ( ( ( (
(
0.010) O.Q07) 0.011) 0.009) 0.017) . 0.012) 0.024) 0.01A) o.o 13) 0.009) 0.008) 0.011) 0.019) o. 0 23) o.o 17) 0.016) 0.009) 0.008) 0.007) 0.024) 0.010) 0.009) 0.010) 0.012) 0.012) 0.007) o. 009) 0.005) O.OOA) 0.007) o.o 10) 0.015) 0.013) 0.009) O.On) 0.014)
Exam2le of Data Base resulting from Scorekee2in g Anal~sis. Shown are pre- and post-retrof it houses in a Modular Retrofit Experiment Module.
1755.83 895.88 1457.75 1133.69 1224.00 1323.68 1284.27 1158.99 1568.37 941.18 1310.63 15o e. oo 1575.03 1181.36 1696.88 1AS4.52 1 148.26 1323.30 1560.77 541.27 1293.36 1007.47 979.18 997.86 1093. 12 919.58 1347.25 773.73 1207.70 1079.76 1226.89 902.14 1241.75 111fi2 .. QS E7
99 3. 15
( ( ( (
( ( (
(
( (
( (
( ( (
( (
( (
( ( ( (
( ( ( ( ( ( (
( ( ( ( ( (
32.41) 22 .. 72}
27.4 2) 25.54) 48.2 9) 37 .19) 47.97) 45.13) 37.6 7) 21.06) 25. 1 2) 33.14) 43.01) 54.46) 49.86) 52. 1 €) 23.42) 21.6 2) 25.2 B) 43.18) 33.13) 30.20) 36.5 f) Q1.26) 30.07) 22.76) 28.39) 13. 73) 32.17) 20.27) 27.2 B) 42.9 9) 36.5 S) 35.14) 19.34) 18.57)
estimation "window" is slid forward one month at a time.
In our
experience, this provides a powerful tool not only for the selection of final estimation periods, but also for identification of anomalies in the data, and, more generally, for monitoring gradual changes in consumption. The NAC summary in Fig. 6 illustrates the approach for the MRE demonstration house.
The analogous plots for the individual parameters
(not shown), which are particularly useful for flagging data anomalies in houses less well behaved than this example, demonstrate the temporary instability as the estimation window passes through the retrofit period. The drop in consumption after the retrofit is evident in the NAC plot. ~
Measurement of Savings The NAC index provides the basic parameter for monitoring energy
savings resulting from retrofit programs.
Using billing and weather data
for approximately year-long periods before and after (and not including) the period during which the retrofits were performed, NACpre(T) and NACpost(T) are calculated as averages (medians or means) over houses in the treatment group, for the pre- and post-periods·re spectively.
The
raw, weather-adjuste d change in energy consumption is then given by ( 5)
If a control group is included, analogous control indices NACpre(C) and NACpost(C) are calculated as averages over the control houses, for the same pre- and post-periods.
For an estimate of the savings attributable to the
program of interest, the raw savings can then be adjusted as follows: Sadj
= NACpre(T)
[NACpost(C) I NACpre(C)] - NACpost(T) ,
or, in percentage terms,
20
(6a)
NAC OVER SLIDING 12-MONTH ESTIMATION PERIODS
(Dashed lines are siandard error bounds) 2000
1750
1500
1250
post
N
--- ___
A
c
1000
c
c
............ .......
---
.....
----: ~ ------'·
750
F
500
250
0',-------.--------.--------r -------,--------, 5EF79
JANBO
MAYBO
5EF80
JAN81
MAYBl
ENDING DATE OF E5TIMAT!ON PERIOD
Figure 6.
Illustration of sliding-month approach. Each point represents the NAC estimate resulting from PRISM applied to one year of consumption data, ending on the indicated date. Dotted lines show standard errors of the estimate. MRE demonstration house is used (see Fig. 4). Pre- and post-retrofit periods used for scorekeeping are indicated.
21
The raw savings for the treatment group (Eq. 5), the control savings and the savings adjusted by the control (Eq. 6) are all quantities of interest in scorekeeping.* For the MRE house in Figs. 4 and 6, the raw savings were 325 ccf/year, or 25% of pre-period consumption, with a standard error of 56 ccf/year, or 4% of pre-NAC.
This house belonged to the "House Doctor" group, for which
the median savings may be summarized as follows: raw savings, treatment group: Sraw(T) = 255 ccf/year, or 19% of pre=NAC raw savings, control group:
Sraw(C) = 123 ccf/year, or
= 139
control-adjusted savings:
9%
ccf/year, or 10%.
Thus the savings are highly sensitive to whether they are adjusted by a control, with the net effect of a substantial deflation in this experiment's raw savings due to the control adjustment.** Inclusion of Electric Cooling, The methodology presented thus far has been applied extensively to gas- and oil-heated houses, and electrically heated houses without cooling. For all fuel types, R2-values are typically 0.97 or better, and the accuracy of the estimates corresponding to Figs. 4 and 5 is typical of * Although either median or mean values of NAC may be used in Eqs. 5-6, we prefer medians as the more "robust" (i.e., insensitive to outliers) measure of the center of the group's distribution. Toward the objective of a standardized approach for calculating savings for a group of treated houses, we are currently exploring alternatives to this formulation, to account for different distributions of the pre- and post-period results, and to give meaningful error bars to the group's savings estimates.
**
These MRE results differ from earlier published results (16% for the House Doctor group, 9% for the control, and 7% adjusted savings; Dutt et al., 1982), primarily because means rather than median NAC values were used.
22
the individual houses studied.
Thus, direct extension of the methodology
to electrically heated houses without cooling has been straightforward. If electricity is used for cooling but not heating, a model analogous to Eq. 3 applies, with Hi(1) replaced by cooling degree-days Ci(1 0 ) computed to a cooling reference temperature 1 0 , and with 8 replaced by the cooling rate Sc.
If the house is electrically heated and cooled, the model
becomes:
(7)
Fi =a+ 8hHi(1h) + 8cci(1c) + gi • The corresponding weather-normalized index is given by NAC
=
(8)
3691 + 8h H0 (1h) + 8 0 C0 (1 0 )
where cooling degree-days C0 are computed for the same normalization period establishing H0 • Even in a heating-dominated climate, summer consumption not uncommonly tracks cooling degree-days, as the data in Fig, 7 illustrate.
The results
of applying the heating-plus-cooling model in Eq. 7 to the data are shown with the figure.
Once again, the NAC estimate, with a relative standard
error of 2%, is extremely well determined. Not surprisingly, not all houses behave as predictably as this example does.
In our current project for EPRI, we have been exploring
several modifications of the above equation, such as holding 'c at 70° 0 or estimating summer consumption in excess of base level.
Our experience to
date suggests that the R2-values for houses heated and cooled by electricity will be somewhat lower than they are for a heating-only fuel, but generally high enough for an accurate measurement of savings.
23
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kwh/day kwh{°F-day
Th • 61
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kwh{°F-day
T
oF
• 67
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30
HAC • 35.200 kwh/year
I
I
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.... ..,... .!
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r£FINI1E COOLII«i
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••+••••••--·•+•••••••••••••£••••••• . . ••--•••••+-••••••••. . . -.~. . ---+-•••••••••+--~r•••••+••••••••••+••••••••••tooo~o••••oto ~0 2 J IIi S 6 1 8 9 10 18 B?.
Dec 28
TIRE(meter reading period)
Figure 7. Superposition of degree-day data on consumption data, as a function of meter reading period, for sample electrically heated and cooled house in New Jersey. Estimates shown are obtained from the heating-plus-cooling model. H [---]and C. [ ••• ]are computed respectively 1 to base Th and Tc. Correspondence of degree-day scale on the 1 right with consumption scale on the left was set by eye.
Extension to Utility Aggregates The above methodology is designed to be applied to individual-hous e billing data for large numbers of houses, in utility conservation programs, for example, or retrofit projects such as MRE.
An analogous approach has been
demonstrated to work well for utility aggregate sales of natural gas to gas-heating customers.
To account for the billing lag, a simple function
of this month's and last month's heating degree-day, AH1 , replaces H1 in For example, the very simple form AHi = (Hi+ Hi_ 1)/2 gives reliable results in New Jersey (e.g., R2 > 0.99 for each year since 1970).
Eq. 3.
As for the single-house example in the previous section, the error bars for the aggregate NAC, at approximately ±3% of NAC for single years, are considerably narrower than the bars associated with the individual parameters.
The narrow bounds mean that small changes in typical
consumption can be identified.
Even using a stringent test that the 95%
confidence intervals not overlap, a drop in aggregate NAC of 6% between two years can be judged significant.
This sensitivity to small changes makes
the NAC parameter a valuable conservation index for monitoring purposes. One use of utility aggregates in scorekeeping is as substitutes for control groups, whose selection and monitoring may be costly.
In all of
the MRE locations, very similar estimates of percent savings were obtained from the control samples and from the corresponding utility aggregates for the same time periods.
For our MRE demonstration house, the utility
aggregate savings was 12%, vs. 11% for the corresponding control sample. Another use of the aggregate approach is for monitoring conservation trends.
Figure 8 summarizes the results from using utility sales data from
New Jersey's four natural gas utilities aggregated to the state level
25
1975
1970
a)
1800
-
180
1700
,.
-....,.
"':I0:1500
!:!
a: c "'1600 .....
~ .....
...::r
-... -6
1!50
1400 1-40
1300
b)
1.0
(b)
180
a:
-!1f
~ ~
w
!::
0
,er....
1::1 0.9
j
~
•
w 0.8 t(
r
::E
i=
:::
~
~
~ ? J> c"" u
L.
1-;:'
:e
2!500
1!50
2300
140 PERIOD I 70-73 71-74
rr·r ~
~
u
.. 130
~
-
::E Ql.
35 34 110
3
2 75·78
7~82
TIME PERIOD
Figure 8. New Jersey aggregate results.
r,
In (a), annual per-household results for normalized annual consumption and actual raw data G are compared. In (b), fourNAC, here called r,
year moving composite results, normalized to period 1 (1970-73) 1 are shown for r (--.), and also r(~ the individual parameters a( ••• ), a (--->. and H (T) <·-·> as a meaningful surrogate for T• The arrows on the 0 scale indicate sample standard errors of the estimates, using right-hand 1975-78 results. The circled results are for periods 1, 2 and 3, used in the text.
26
Extension to Utility Aggregates The above methodology is designed to be applied to individual-hous e billing data for large numbers of houses, in utility conservation programs, for example, or retrofit projects such as MRE.
An analogous approach has been
demonstrated to work well for utility aggregate sales of natural gas to gas-heating customers.
To account for the billing lag, a simple function
of this month's and last month's heating degree-day, AH 1 , replaces H1 in For example, the very simple form AH 1· = (Hi+ Hi_ 1 )/2 gives reliable results in New Jersey (e.g., R2 > 0.99 for each year since 1970).
Eq. 3.
As for the single-house example in the previous section, the error bars for the aggregate NAC, at approximately ±3% of NAC for single years, are considerably narrower than the bars associated with the individual parameters.
The narrow bounds mean that small changes in typical
consumption can be identified.
Even using a stringent test that the 95%
confidence intervals not overlap, a drop in aggregate NAC of 6% between two years can be judged significant.
This sensitivity to small changes makes
the NAC parameter a valuable conservation index for monitoring purposes. One use of utility aggregates in scorekeeping is as substitutes for control groups, whose selection and monitoring may be costly.
In all of
the MRE locations, very similar estimates of percent savings were obtained from the control samples and from the corresponding utility aggregates for the same time periods.
For our MRE demonstration house, the utility
aggregate savings was 12%, vs. 11% for the corresponding control sample. Another use of the aggregate approach is for monitoring conservation trends.
Figure 8 summarizes the results from using utility sales data from
New Jersey's four natural gas utilities aggregated to the state level
25
1975
1970
a)
1980
1800
-<
180
1100
-~,..
a:
,.......
1&116()0
....
2
"'2
f51500 :z:
-....
150
1400 140
1300
b)
-8
IDl
1.0
"'
0
!:!
~
0,9
.&.e
j
•
~
j;j
ti :I ~
:::
180
~.....
~ ~
1-.
rr·r z li:' ~
l'i
j
....
~
2500
~0 :I~ 0
;;
u
~
130
·~
Ill.
150
0.8
2300 140
PERIOD 1 70-73 71-74
2
3
75-78
79-82
35 34
TIME PERIOD
Figure 8. New Jersey aggregate results.
In (a), annual per-household results for normalized annual consumption r, NAC, here called r, and actual raw data G are compared. In (b), four-
year moving composite results, normalized to period 1 (1970-73), are shown for r <--->, and also r~~ the individual parameters a ( ••• ), B <--->, and H (T) <·-·> as a meaningful surrogate for T• The arrows on the 0 right-hand scale indicate sample standard errors or the estimates, using 1975-78 results. The circled results are ror periods 1, 2 and 3, used in the text.
26
110
(i.e,, to a total of almost a million customers ).
After weather
normaliza tion, per-custom er consumpti on showed a decline of 26% since the peak level before the oil embargo (Fig, 8a).
Our analysis of the
separatio n between the base-leve l and heating components (Fig. 8b) suggested that most of the conservat ion was due to lowering of thermosta t settings, with perhaps a surprisin gly small fraction due to structura l retrofitti ng of the houses.
Thus, important policy implicatio ns can emerge
from the methodolo gy applied at the aggregate as well as at the house level.
27
28 -',''
Bibliography of Scorekeeping Publications About the Princeton Scorekeeping Method:
puJtl\
(All)
M.F. Fels "The Princeton Scorekeeping Method: An Introduction", PU/CEES /1163, March 1984 (revised January 1985) (a description of the method; this report)
(E,G)
M.F. Fels, J.N. Rachlin and R.H. Socolow "Seasonality of Non-heating Consumption: A Study Based on Submeter Data", PU/CEES /1166, July 1984; Presented at ACEEE Summer Study, Santa Cruz, CA, August 1984 (an analysis of heating vs. non-heating consumption, with an improved understanding of the physical meaning of the model estimates)
(E)
D. Stram, R.H. Socolow and M.F. Fels "The Effect of Burning Wood on Saving Electricity: An Exploratory Analysis", PU/CEES /1165, July 1984; Presented at ACEEE Summer Study, Santa Cruz, CA, August 1984 (an assessment of the reliability of scorekeeping results when wood is supplementing electricity used for heating; the benefits of separating woodusers from non-woodusers for the analysis)
(G,E)
M. Fels, J.N. Rachlin and R.H. Socolow "Stability of the Scorekeeping Model Estimates", draft chapter of research report to the Electric Power Research Institute, October 1984 (an analysis of the data requirements of the scorekeeping model and the effects of different estimation periods)
(E)
M.F. Fels, R.H. Socolow, D.O. Stram and J.N. Rachlin "Monitoring Consumption in Electrically Heated Houses", PU/CEES /1160, Research report to the Electric Power Research Institute, August 1983 (Revised April 1984) (the extension of the scorekeeping approach to electrically heated houses, including an exploration of how cooling might be included in the model)
(0)
M.F. Fels, M.L. Goldberg, M.L. Lavine, R.H. Socolow and P. Abrams "Exploratory Analysis of Oil-Heated Houses", PU/CEES /1139, in collaboration with Petroleum Data Corporation (now Cogito Data Systems) in Princeton, August1981 (revised December 1982) (an assessment of how well the model might be expected to work on oil delivery data)
E=electricity, G=natural gas, O=fuel oil, All=generally applicable to all. 29
BIBLIOGRAPHY (continued) Sample Applications outside Princeton: (E;)
E. Hirst,. H. Goeltz and D. White "l!~e of' Electricity Billing Data to Determine Household Energy' Use 'FingE!!'prints"'• Report ORNLtCON•lli~, Oak Ridge National Laboratory, Oak Ridge, TN, August 1984 (an exploration of different ways to use PRISM estimates to categorize houses)
(E)
E. Hirst, D. White and R. Goeltz "'):'h;ree.Yea!'s after Participation: Eleotl'icity Savings Due t6 ·the BPA Resic!!mtial Weatherization•>•:l'ilot Prog!';l!ll" r Repol"t ORNL/CON.-166', Oak Ridge National Laboratory, Oak Ridge, TN, January 1985 (a complete evaluation, based on NAG's from the scorekeeping approach)
(G)
M. Hewett, T. Dunsworth, T. Miller and M. Koehler nMeaslired vs. P!'edioted Savings from Single Retrofi.ts: A Sample StUdY'IP, Minneapolis Energy Coordination Office, draft report, October 1984 (use of PRISM to assess the accuracy of savings predictions)
(G,E)
M.L. Goldberg, A. Jaworski and I. Tallis ·"EvalUati<>n·.. of'·· Wis
(All)
L.W. Wall, C.A. Goldman, A.H. Rosenfeld and G.S. Dutt nBuil~:t:ng•Enerr1!Jy•C6Dipi::L.a.ticm and Analysis.{BECA} l''al."t B: · Existing lllol."tbiAmei!idan Residell.ti!ll.. ,Bu:J,:l.dings",;v Energy and Buildings, _2, (1983), 151-170 (a standardized data base of scorekeeping results from completed retrofit projects)
31