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Refraction of PRISM results into components of saved energy
Energy and Buildings, 9 (1986) 169 - 180
169
Refraction of PRISM Results into Components of Saved Fner / MIRIAM L. GOLDBERG*
Statistical Laboratory, University of Wisconsin, Madison, WI 53706 (U.S.A.) MARGARET F. FELS
Center for Energy and Environmental Studies, Princeton University, Princeton, NJ 08544 (U.S.A.) (Received January 1986)
SUMMARY
A simple methodology is developed to augment the physical interpretation o f PRISM results. With this "refraction" method, the estimated energy savings are decomposed into physically meaningful components, indoor temperature changes are inferred, and the effect o f such changes on energy savings is quantified. The method is demonstrated in two test applications. The first, to individual-house billing data for a set o f 243 gas-heated houses, suggests the dominant role o f structural retrofitting in the energy savings achieved by weatherization of the houses. The second application, to utility aggregate data for nearly one million gas-heated houses in one state, points to the importance o f lower thermostat settings in the years immediately following the oil embargo, and, since 1980, to a substantial decline in consumption by appliances including water heaters. More recently, the role o f structural retrofitting seems to be increasing, but a "takeback" effect due to a concomitant increase in indoor temperatures may be eroding the resulting savings. While the refraction results must be interpreted with care, their physical reasonableness, in both test cases, reinforces the potential o f energy billing data to enhance the understanding o f energy conservation trends. INTRODUCTION
Most P R I S M studies to date have emphasized the usefulness of Normalized Annual Consumption (NAC), whose stability makes it a particularly useful monitoring index.
Inferences a b o u t trends from the other PRISM parameters, which are needed to c o m p u t e NAC, are often problematic, particularly at the individual-house level. The base-level and heating-slope parameters, and ~, respectively, are much more sensitive to choice of reference temperature, T, than is NAC, and their relative standard errors tend to be large compared to the 3 - 4 % typical for NAC**. On the other hand, when results for large numbers of houses are averaged in some way, the individual parameters, ~, ~ and T, can offer valuable insight into the nature of conservation activities. In this paper, we describe h o w physical sources of energy savings can be identified, and h o w indoor temperature changes can be inferred, from changes in the individual parameters of the PRISM model. The resulting estimates of savings c o m p o n e n t s must be interpreted with care. Measures of the accuracy of these estimates provide guidance as to h o w precise these interpretations may be; consideration should also be given to the validity of assumptions required for the savings decomposition. The "refraction" approach, to decompose PRISM estimates of energy savings, is tested here on two data bases of gas-heated houses. The first, from a low-income weatherization program in Wisconsin, consists of individualhouse billing data for 243 houses; the second, *Present address: Energy End Use Division, U.S.
Energy Information Administration, Washington, DC 20585, U.S.A. **PRISM, the Princeton Scorekeeping Method, is described in the introductory paper to this issue [ 1 ]. See also the stability analyses reported in this issue [ 2 ]. Elsevier Sequoia/Printed in The Netherlands
170
representing average natural gas consumption for all gas-heated households in New Jersey, consists of aggregate utility sales data. Both are subjects of other papers in this issue [3, 4].
As described in ref. 1, NAC for estimation period k is given by: NAC~ = 365 (~k + {JkHo(rk)
(1)
where Ho(rk) is the long-run heating degreedays c o m p u t e d to base rk. The energy savings, N A C 1 - - N A C 2 , between periods 1 and 2 may be written in terms of changes in the individual parameters ~,/], and r, as follows: -- NAC 2 =
365 (oq - -
-
0/2)
A
+ ~[H0(rl) +
+ (/~I --/~2)/-I0 +
-
-
T
B
H0(r2)] (2)
where /-I0 = [H0(rl) + Ho(r2)]/2
(3a)
and = (~1 + ~2)/2
(~I + a2)/2
(4a)
se(B) =/-70[se2(~l) + se2(fl2)] 1/2
(45)
+ [Fo{r2)se(r2)] 2)1/2
(4c)
In eqn. (4c), Fo{r) is the derivative with respect to r of Ho(r), and corresponds to the length of the heating season to base r. For normalized degree-days H0 determined from integer-valued dally temperature data, this derivative is given by: Fo{r) = H o ( m + 1 ) - - H o ( m )
(5)
where rn is the integer part of r. In a simplified physical model of the heating fuel, it is tempting to associate the T-component of eqn. (2) with lowered thermostat settings, the B-component with structural retrofits or furnace efficiency improvements, and the A-component with decreased appliance usage or increased appliance efficiency for appliances fueled by the heating fuel. To examine the extent to which these associations are valid, we take a closer look at the physical effects likely to induce changes in c~, ~ and, especially, r.
(3b)
For later use, we also define a =
se(A) = 365[se:(0q) + se2((~:)] 1/2
se(T) = ~( [Fo(rl)se(rl)] 2
DECOMPOSITION OF ENERGY SAVINGS
NAC,
To determine the accuracy of this decomposition, we calculate the standard errors {se) of the three components, as follows:
PHYSICAL NENTS
SIGNIFICANCE
OF
THE
COMPO-
(3c)
We use eqn. (2) for the components analysis*. If, indeed, there is a drop in NAC, then the decomposition indicates the sources of observed energy savings, in terms of three physical components. The base-level component (A) represents savings due to reduced base-level consumption; the shell c o m p o n e n t (B), savings due to a decrease in heating slope; and the temperature c o m p o n e n t (T), savings resulting from a decline in reference temperature.
*In earlier w o r k [5], a Taylor's series expansion of eqn. (1) gave two alternate f o r m u l a e similar to eqn. (2), with flk and H0(rk) for k = 1 and k = 2 used instead o f ~ and /70. E q u a t i o n (2), which is exact, is equivalent to the average o f the t w o expansions.
Changes in the reference temperature r are likely to reflect changes in the indoor temperature Tin. However, Tin is not the only factor which affects r. In the PRISM model, r is interpreted as the maximum average daily o u t d o o r temperature at which the furnace is required. This temperature is lower than the indoor temperature, because some of the house's heating requirement is met by intrinsic gains Q, from occupants, appliances, and the sun. The difference between Tin and r depends also on the house's "lossiness" L, which is the product of the heating rate ~ and the furnace efficiency, i.e., r = Tin -- Q / L
(see Appendix 1 of ref. 1).
(6)
171
From eqn. (6), it is possible to derive an expression relating the change in the house's indoor temperature to the observed changes in the model parameters ~, ~ and T. This indoor temperature change can then be translated into an equivalent energy savings or loss. As a first step, we differentiate eqn. (6), then substitute T i n - - r for Q/L in the resulting expression, to obtain the following first-order approximation:
AQIQ, may be approximated by A~/~. If, instead, appliances fueled by the heating fuel contribute only a small fraction of Q, with the dominant sources of Q being sun, people, and unchanged appliances, this approximation overstates AQ/Q. With the above assumptions about AL/L and AQ/Q, eqn. (7) gives: A T i n ~ (7"1 - - T2) - - a [ ( ~ l - - ~2)/~]
+ a[(al - a:)/~]
AT = A T i n + (Tin - - T ) A L / L
-- (Tin -- T)AQ/Q
{7)
(Defining AT= T1--T2, a positive change indicates a drop in T, and thus a change in the direction of conservation.) The first term, ATin, indicates h o w a thermostat setback might translate directly into a reduction in T. The terms in AL and AQ, respectively, indicate h o w interventions such as house tightening and more efficient appliances might affect T. Conversely, eqn. (7) allows us to see what a drop in T implies about a drop in Tin, depending on h o w lossiness L and intrinsic gains Q have changed. For example, a large drop in Q narrows the gap between Tin and T, SO that an observed drop in T will underestimate a drop in Tin. On the other hand, a large drop in L m a y itself induce a drop in T, even w i t h o u t a concomitant change in Tin. Only when there is no significant change in L or Q, or when their changes cancel, will AT track ATin. To estimate ATin from PRISM estimates therefore requires n o t only AT b u t also information a b o u t L and Q. The needed information can be inferred from the parameters ~ and ~, provided some additional assumptions are made. First, assuming no change in the furnace efficiency, the relative change in lossiness, AL/L, is well approximated by Aft/ft. Furnace efficiency improvements and decreased lossiness would both lower {3, so that IA~/~I becomes an overestimate of IAL/L] if furnace efficiency has increased. Second, assuming that appliances represent the main source of intrinsic gains, and that the change in the energy consumed by appliances is essentially uniform across fuels {e.g., for gas and electric appliances in a gas-heated house), the relative change in intrinsic gains,
(8)
where 8, the temperature offset, is defined as:
a = Ti, -- r
(9)
and ~{and ~ are defined in eqn. (3). A final required assumption is the value of 8. The dependence of the temperature offset 5 on L and on Q, as implied by eqn. (6), suggests the importance of exploring the effects of different assumptions a b o u t by applying eqn. (8) over a range of 5-values. As a starting point, we use ~ = 3.9 °C (7 °F)*. The validity of the approximations, AL/L AfJ/fJ and AQ/Q ~ A~/c~, should also be considered, and the effect of varying these assumptions explored. This kind of sensitivity analysis strengthens the conclusions drawn. Equation (8) indicates the extent to which energy savings have been either augmented or diminished by indoor temperature changes. To carry the analysis one step further, the temperature shift ATin can be translated into a quantifiable energy savings or loss. This translation is accomplished by comparing the observed NAC for the second period, NAC2, with the NAC that would have been realized if the indoor temperature had n o t changed. The latter, hypothetical NAC:' is determined by replacing T: with r2 + A T i n in eqn. (1) (with h = 2). Thus, the energy impact of a shift in indoor temperature is given by:
TB = N A C j -- NAC2 = ~:[H0(r2 + ATin) --H0(T:)]
(10)
*This value of ~ is c o n s i s t e n t w i t h the c o n v e n t i o n a l use of 18.3 °C (65 °F) for the reference t e m p e r a t u r e t o g e t h e r w i t h the A S H R A E c o n v e n t i o n of 22.2 °C (72 °F) for the indoor temperature [6 ].
172
Unlike the temperature c o m p o n e n t T in eqn. (2), which incorporates changes in all the factors affecting the reference temperature r, the quantity TB given by eqn. (10) isolates the effect of changing indoor temperature Tin. When the indoor temperature drops between the first and second estimation periods, ATin and TB are positive; in this case, TB represents a "temperature benefit", or the portion of savings attributable to the lowering of indoor temperature. When ATin is negative, TB is negative; the magnitude of TB in this case represents a "takeback effect", or potential energy savings taken back in the form of increased indoor temperature. In either event, the savings that would have occurred in the absence of the change in Tin may be estimated as (NAC1 -- NAC2 -- TB). It is well known that a temperature benefit, or positive savings TB, can be obtained simply by turning down the thermostat, even in the absence of any improvement in the house structure or appliances. On the other hand, economists have conjectured that a takeback (negative TB) might occur after a house has been made more energy efficient, analogous to choosing to drive more after buying a more fuel-efficient car. Equation (10) gives a basis for assessing the extent to which such takeback behavior may be occurring. It is worth noting that changes in indoor temperatures are not necessarily the result of deliberate changes in thermostat settings. Particularly in houses which are initially in poor condition, a side benefit of retrofitting m a y be the reduction of drafts or the equalization of temperature gradients. Eliminating drafts can m a k e a lower temperature comfortable, without a conscious decision to keep a cooler house. Improved heating system balance m a y m a k e previously uncomfortable rooms as warm as the thermostatted room, resulting in a temperature increase on average w i t h o u t a change in thermostat setting, or, conversely, it may eliminate the necessity to overheat some rooms to have others comfortable, resulting in a temperature decrease on average. These possibilities should be considered when interpreting a calculated indoor temperature change A T i n , and the corresponding energy impact TB. The refraction approach, in summary, involves three steps. The first is to separate
the estimated savings for a group of houses into three physically meaningful components, A, B, and T, using eqn. (2). The second step is to estimate the concomitant change in indoor temperature, using eqn. (8), and to convert this temperature change into energy savings (temperature benefit) or loss (takeback), i.e., TB, using eqn. (10). The third step involves interpreting each estimate (A, B, T, and TB) in light of possible conservation actions, including changes affecting the house's appliances, building shell, furnace, and thermostat. For all components, the estimation errors (eqn. (4}), and the sensitivity to a range of possible assumptions, need to be considered.
ACCURACY
MEASURES
When the refraction method is applied to a single pre-post pair of PRISM results for an individual house or an aggregate of houses, the standard error of each component, given by eqn. (4), measures the accuracy of the savings decomposition for that pair. When aggregate PRISM is used [4], the PRISM estimates may be interpreted as the average of the individual-house estimates, and the components breakdown in eqn. (2) as the average of individual-house components. The formulae in eqn. (4) give the measurement errors of this average breakdown, but tell nothing a b o u t the variation in the components across the different houses which comprise the aggregate. If, instead of a single aggregate pre-post PRISM pair, separate pre- and post-retrofit PRISM results are available for each of a sample of houses, the corresponding components breakdown may be c o m p u t e d from eqn. (2) for each house. The house-to-house variation m a y then be measured by either the standard deviation or, more robustly, by the interquartile range of each c o m p o n e n t across the houses in the sample. Taking the mean of each c o m p o n e n t (A, B, T, and TB) across houses will give a result very similar to that which would be found from a single aggregate analysis; if the PRISM model were entirely linear, and all houses in the group had their meters read on the same day, the agreement would be exact. A measure of the accuracy with which each mean or median
173 c o m p o n e n t is determined for N houses is the corresponding standard error of the mean or of the median (see Appendix 3 of ref. 1). These standard errors differ conceptually from the standard error which would be given by eqn. (4) for an aggregate analysis. The latter standard error tells h o w accurately the average (mean) c o m p o n e n t for that particular set of houses has been estimated. The standard error of the mean or median (as given in the next section for the Wisconsin data set} tells h o w accurately the mean or median o f the larger group of houses from which the study group was drawn has been estimated. Wherever possible, we prefer to use measures based on the median rather than the mean. To represent the accuracy of the components estimates in what follows, we use the standard error of the sample median when PRISM has been applied to individual-house data for a sample of houses, and we use the standard errors of the estimates (eqn. (4)) when aggregate PRISM has been applied. Where reference is made to significance of results, the nominal 5% significance level, or 95% confidence level, is used as a standard; however, this significance level should be interpreted as a qualitative indicator rather than as a precise measure.
APPLICATION TO INDIVIDUAL HOUSES The refraction m e t h o d was applied to each house in a group of 243 " G o o d Houses" resulting from the PRISM analysis of Wisconsin's low-income weatherization program [3]. These houses were weatherized in 1982 under a program administered by the Wisconsin Department o f Health and Social Services. While the work done varied considerably across houses, the emphasis was on sealing windows and doors, and installing insulation. The median savings for these houses were 10 % of the pre-retrofitN A C , as compared with 2 % for a set of "Good-House" control houses. Only the treated (weatherized) houses are analyzed here; since the savings in the control group were small, we felt that a decomposition of those savings would not be very meaningful. The refraction results thus represent a decomposition of the total savings, without regard to whether the
savings are attributable to the program or to external events. The Good-House restrictions, that the preand post-weatherization periods each have at least ten actual meter readings and R 2 values from PRISM fits of the data which are greater than 0.90, ensure that the refraction m e t h o d is applied only to houses for which the individual parameters are likely to be physically meaningful. U n e v e n s p a c i n g of meter readings over the year can seriously skew these estimates [2], while low R ~ indicates a poor fit of the data and thus poor determination of the parameters. The results of computing the base-level (A), shell (B), and temperature (T) components for this set of 243 houses are s u m marized in Table 1. For each component, both mean and median measures are shown. Comparing the medians and means to their respective standard errors indicates which changes, averaged over the entire group, are significantly different from zero. For this set of houses, the standard errors of the median and of the mean, the two measures of variability, are quite close for all three variables. The median and mean, the t w o measures of the center of the distribution, are somewhat less consistent, because of the presence of a few extreme outliers, b u t they lead to the same qualitative conclusions. The interquartile ranges plotted in Fig. 1 show clearly the broad distribution of each component's estimates across these 243 houses, as well as the relative contribution of each c o m p o n e n t to the total savings. The median estimate of total savings is 13.1 GJth/year (124 therms/year), which, as mentioned earlier, represents a b o u t 10% of the pre-weatherization consumption level. Shell effects, with a median of 9.8 GJth/year, are by far the dominant contributor to these savings. Changes in base level, with a median of 2.7 GJth/Year, are small b u t still significant, and temperature effects, with a standard error larger than the median of 0.8 GJth/Year, are n o t significant. The dominance of the shell effects is reasonable, since most of the weatherization work done in these houses had to do with shell tightening (see ref. 3). The apparent lack of temperature effects can be explored further using eqns. (8) and (10). The resulting estimates of indoor temperature changes (ATi,) and takeback effects
174 TABLE 1 Summary of refraction results for individual houses in Wisconsin study* Component
Temperature (T) Shell (B) Base level (A) ANAC (total)
Median measures (GJth/year)**
Mean measures (GJth/year) t
Median
IQR
se(median)
Mean
sd
se(mean)
0.8 9.8 2.7
21.1 23.6 10.4
1.4 1.5 0.7
--0.1 13.2 3.2
24.1 23.0 12.8
1.6 1.5 0.8
13.1
20.9
1.3
16.3
18.9
1.2
*Based on 243 Good Houses, from ref. 3. T, B, and A are determined from eqn. (2). For this set of houses, the pre-retrofit NAC had a median of 132 and a mean of 140 GJth/year. **IQR = interquartile range ; se(median) = I Q R / ~ where N is the number of houses. tsd = standard deviation; se(mean) = sd/%/N.
(TB) are s u m m a r i z e d in T a b l e 2. T h e m e d i a n ATin e s t i m a t e is - - 0 . 2 °C, i n d i c a t i n g a slight t e m p e r a t u r e increase. This c h a n g e is small in a b s o l u t e t e r m s , a n d also small c o m p a r e d t o the s t a n d a r d e r r o r o f t h e m e d i a n , 0.3 °C. Overall, t h e n , f o r this g r o u p o f 243 houses, n o significant c h a n g e in i n d o o r t e m p e r a t u r e a p p e a r s t o h a v e o c c u r r e d , a l t h o u g h t h e large i n t e r q u a r t i l e r a n g e ( I Q R ) suggests t h a t s o m e o f t h e h o u s e h o l d s raised o r l o w e r e d t h e i r
25
200
20 150~ (D
15
~. E
ro
iI boo
E
g 5
50
c
gc o
o.e o f-
0
o
-50
-5
-io Component : T
B
A
TOTAL
Fig. 1. Summary of distribution of refraction results across houses in Wisconsin study. For each component [base level (A), shell (B), temperature (T), and ANAC (Total)], the median is indicated by the height of the box, the median value by the number at the top of the box (in GJth/year), and the upper and lower quartiles by the tips of the arrows (the arrow length gives the IQR). For the second and third components, the zero is set at approximately the median of the previous component, to make more evident their summation to the total.
i n d o o r t e m p e r a t u r e s substantially. T h e m e a n ATin e s t i m a t e , - - 0 . 8 °C, is s o m e w h a t larger in m a g n i t u d e , and is n o m i n a l l y significant, b u t this e s t i m a t e is less t r u s t w o r t h y (i.e., less r o b u s t ) t h a n t h e m e d i a n . When t h e t e m p e r a t u r e c h a n g e s are c o n v e r t e d h o u s e b y h o u s e to e n e r g y savings, i.e., t o TB via eqn. (10), n e i t h e r the m e d i a n n o r t h e m e a n indicates a significant t a k e b a c k effect. T h e s e q u a l i t a t i v e results w e r e c o r r o b o r a t e d b y r e - e s t i m a t i n g TB, t h e t a k e b a c k effect, using d i f f e r e n t a s s u m e d t e m p e r a t u r e o f f s e t s 5, a n d b y v a r y i n g a s s u m p t i o n s a b o u t AQ/Q and AL/L in eqn. (8) f o r ATin. T h e o f f s e t 6 was set at 2.2 a n d 5.6 °C as well as the 3.9 °C value used in T a b l e 2. D r o p p i n g t h e A a / ~ t e r m , i.e., a s s u m i n g changes in internal gains to be negligible, was also tried. ( D r o p p i n g t h e Afi/fl t e r m , i.e., a s s u m i n g a n y o b s e r v e d changes in fi t o be a t t r i b u t a b l e n o t to lossiness Changes b u t to h e a t i n g - s y s t e m e f f i c i e n c y i m p r o v e m e n t s , w o u l d n o t be r e a s o n a b l e here, since a l m o s t n o h e a t i n g - s y s t e m w o r k was d o n e in the s t u d y houses.) U n d e r t h e v a r y i n g sets o f a s s u m p t i o n s , the m e d i a n e s t i m a t e s f o r TB r a n g e d f r o m a takeb a c k o f - - 2 . 4 GJ~h/year t o a t e m p e r a t u r e b e n e f i t o f + 0.3 G J t h / y e a r . T h e m e a n s r a n g e d f r o m - - 2 . 2 to - - 0 . 1 G J t h / y e a r . N o n e o f the m e a n s o r m e d i a n s was n o m i n a l l y significant. Thus, even t h o u g h t h e largest m e d i a n takeb a c k e s t i m a t e o f 2.4 G J t h / y e a r is 18% o f t h e t o t a l m e d i a n savings o f 13.1 G J t h / y e a r , a t t e n t i o n t o the u n c e r t a i n t i e s o f t h e e s t i m a t e shows the evidence for a takeback effect to b e w e a k . T h e overall c o n c l u s i o n f r o m this r e f r a c t i o n analysis o f t h e set o f Wisconsin h o u s e s is t h e d o m i n a n c e ' o f shell t i g h t e n i n g
175 TABLE 2 Summary of estimated indoor temperature changes and resulting energy impact for houses in Wisconsin study Number of houses*
Median measures
Change in indoor temp** ATin (°C)
243
--0.16
Energy impact t
241
--0.8
Median
IQR 4.02 23.7
M e a n measures
se(median)
Mean
0.26
--0.77
1.5
--0.7
sd
se(mean)
5.68 22.6
0.36 1.5
TB (GJth/year) *All Good Houses from ref. 3 were used. Equation (10) was not estimated for two extreme outliers, i.e., houses which had T2 + ATin outside the range (--17.7, 37.8) °C ( ( 0 , 1 0 0 ) °F). **ATin is determined from eqn. (8) with ~ = 3.9 °C. A negative value indicates an increase in Tin. "¢TB is determined from eqn. (10). A negative value suggests a takeback effect. To compare with total savings, see ANAC in Table 1.
in the total savings achieved, with very little, if any, of the savings being taken back by an increase in indoor temperatures. Another study, at Oak Ridge National Laboratory, found similar results in a data set o f "clean" electrically heated houses analyzed by PRISM as part of an evaluation of a Bonneville Power Administration (BPA) program [7]. (See related study in this issue [8] .) The estimated mean increase in indoor temperature was 0.2°C for 97 houses receiving retrofits in 1982 and 0.6 °C for 113 houses receiving retrofits in 1983. (A value of 5 = 4 °C was assumed.) Only the latter change was statistically significant; the associated takeback effect amounted to 25% of the total energy saved in the 1983 participant group*. The reason for the different results in the two sets of houses, which received similar retrofits in two successive years, is not evident, particularly since no significant takeback effect was found in either year in the 32-house nonparticipant group. In both the Wisconsin and the BPA studies, the apparent increase in indoor temperatures is tantalizing in view of its possible impact on energy conservation. However, in the Wisconsin study and in the first-year BPA study, the temperature change, if any, is evidently of such small magnitude that it cannot be reliably quantified. The possibility *The O a k Ridge analysis [7] was based on our earlier w o r k [5 ], which predates our formulation of TB. The formula used in ref. 7 for the takeback effect is equivalent to a Taylor-series approximation to our eqn. (10).
of a takeback effect is suggested in the second-year BPA results, but may not be generalizable b e y o n d that specific, fairly small sample of treated houses. With substantially larger data sets, particularly those that span more time, a clearer picture of these trends in temperature settings might emerge. To this end, we turn to a PRISM refraction of a very large set of houses, consisting of all gas-heated houses in the state of New Jersey.
APPLICATION
TO AGGREGATE
CONSUMPTION
For the refraction analysis of aggregate gas consumption in New Jersey, we start with four-year estimates of NAC and of the model's three individual parameters, for 1 9 7 0 - 73 through 1 9 8 2 - 85**. Table 3 contains the PRISM estimates for these periods (see also Fig. 5 of ref. 4, in this issue). Over the entire period, consumption has declined by a total of 47 GJth (440 therms) per customer-year, or by 25% when compared with the pre-embargo (1970 - 73) level. To analyze trends in the post-embargo decade, we choose three non-overlapping four-year periods: 1 9 7 0 - 7 3 (the pre-embargo base period), 1 9 7 5 - 7 8 , and 1 9 7 9 - 8 2 , as periods 1, 2, and 3, respectively; these were the subject of our earlier work [5]. To bring the analysis up to date, we add the most recent nonoverlapping (three-year) period: 1 9 8 3 - 8 5 , as period 4. * * T h e periods are based on August-to-July heating years; 1982 - 85 ends with July 1985.
176 TABLE 3 PRISM per-household estimates by four-year estimation periods for New Jersey aggregate of gas-heating customers Estimation period*
R2
PRISM estimates** Ref. temp. 7" (°C)
H0(7") (°C-days/ year )
Base level ~ (kWth)
Heating slope ~ (Wth/°C)
NAC (GJth/year)
1 9 7 0 - 7 3 (period 1) 1971 -74 1972 - 7 5 1973 - 7 6 1974 -77
0.995 0.992 0.988 0.984 0.991
19.3(0.4) 19.4 (0.4) 19.1 (0.6) 18.8 (0.6) 18.6 (0.4)
2966 2999 2905 2854 2798
1.71(0.08) 1.72 (0.10) 1.75 (0.12) 1.70 (0.13) 1.65 (0.10)
514 503 499 492 475
(11) (13) (15) (18) (13)
185.9(1.3) 184.5 (1.5) 180.4 (1.8) 175.0 (2.0) 166.6 (1.5)
1975 -78 (period 2) 1976-79 1977-80 1978-81
0.993 0.995 0.997 0.993
17.7 (0.4) 17.6 (0.3) 17.3 (0.3) 17.4(0.4)
2595 2569 2505 2523
1.64 1.60 1.56 1.48
(0.09) (0.07) (0.06) (0.08)
488 (11) 488 (9) 490 (7) 484 (11)
161.0 (1.4) 158.6(1.1) 155.5 (0.9) 151.7(1.4)
1 9 7 9 - 8 2 ( p e r i o d 3) 1980-83 1981-84 1982-85
0.990 0.994 0.996 0.994
17.5(0.4) 17.2 (0.3) 17.3 (0.3) 17.6(0.4)
2547 2473 2484 2565
1.39(0.10) 1.34 (0.07) 1.29 (0.05) 1.27(0.07)
475(13) 477 (11) 468 (9) 451 i l l )
148.7(1.6) 144.1 (1.1) 141.3 (0.9) 139.8 (1.1)
1983 - 85 (period 4)
0.995
17.8 (0.4)
2615
1.27 (0.07)
440 (11)
139.0 (1.1)
*Each four-year period starts with August of the previous year and extends through July of the last year indicated. The three-year period, 1983 - 85 (indicated as period 4), is added as a non-overlapping extension of the earlier three main periods for analysis (periods 1, 2 and 3). **Numbers in parentheses are standard errors of the estimates. P O S T - E M B A R G O DECADE
5O - - 450
PC
400
.E
40 100%
350
Q.
A(S2%)
8 3c .c_
300
50%
i,;i~? x'~ii~i o,,
250
g
200 . . . . . . . . . . . .
50: 50%
150 I00 50 O%
(a)
(b)
(c)
Fig. 2. Summary of refraction results for New Jersey aggregate study: post-embargo decade. For each change between periods (1 = 1970 - 73, 2 = 1975 - 78, 3 = 1979 - 82), the base-level (A), shell (B) and temperature iT) components are shown: (a) for period 1 to 2, (b) for period 2 to 3, and (c) for the overall change from period 1 to 3. Both percentage and absolute changes are shown. The number in parentheses is the percentage contribution to the total change in N A C . Arrow from the top of each rectangle represents the standar~l error estimated from eqn. (4) for that component.
177
We start with the results for the postembargo decade. Figure 2 shows the three components CA, B and T) of the energy savings, together with their standard errors (from eqn. (4)), for periods 1 through 3. From 1970 - 73 to 1975 - 78 {Fig. 2(a)), the temperature component (T in eqn. (2)) accounts for about two-thirds of the 13% decline in NAC. From 1 9 7 5 - 7 8 to 197982 {Fig. 2(b)), the base-level component (A) dominates the 8% decline in NAC. For both periods, the shell component (B) contributes only about a quarter of the change in NAC. Over the entire decade, from 1970- 73 to 1979 - 82 (Fig. 2(c)), about 50% of the total energy savings is thus attributed to the temperature component iT), and about 25% each to the base-level (A) and shell (B) components. Extension of the results through 1985 indicates a persistence in the decline of base-level consumption but a shift in the other trends. Figure 3 follows the progression of the three components from the embargo period to the present. The role of the shell component (B) in recent years has dramatically increased, reflecting an accelerated drop in heating slope from 1979- 82 to 1 9 8 3 - 8 5 (see Table 3). On the other hand, the temperature component iT), which
was dominant in the period right after the embargo (Fig. 3(a)), has diminished (Fig. 3(b)), and in the most recent period (Fig. 3(c)) has changed sign due to a slight increase in reference temperature (by 0.3 °C). Between different adjacent periods since the embargo, different components have dominated: first T, then A, and n o w B, as we progress across Figs. 3(a), 3(b), and 3(c). Over the entire period since the embargo, from 1970- 73 to 1 9 8 3 - 8 5 (Fig. 3(d)), the division of the savings among the three components has become fairly even. The standard errors shown in Figs. 2 and 3 allow a rough assessment of the significance of the components. Although the standard errors of the total savings are small (~ 2 GJth for ANAC from one four-year period to another), the standard errors of the individual components are much larger (~ 6 GJth for T, and ~ 4 GJth each for B and A). On a relative scale, the standard error of ANAC between any two periods is in all cases less than 20% of the estimate of ANAC, whereas the relative standard error for an individual component is occasionally larger than the estimate itself. In Figs. 3(a) - (c), only the largest component of the total change between two adjacent periods appears significant by itself: T for period 1 to 2, A for period 2 to 3, and B for
RECENT INDICATIONS A
50--
[
I0(
16
450
,%. ,J=
4OO
._8
350
Q.
M-)
A ( 30 %)
300~
IN
o 3o .c_
g.
250-. ~
I00%
50'
200 $ o
150 ...........
509~
I00 2 50
.o
0
165%),\\\\\\ ...........
(O)
L--o.__------.
0%
(b)
(c)
~,.
)%
(d)
Fig. 3. S u m m a r y o f r e f r a c t i o n results for N e w J e r s e y aggregate s t u d y : r e c e n t i n d i c a t i o n s . F o r e a c h c h a n g e bet w e e n p e r i o d s (1 = 1 9 7 0 - 73, 2 = 1 9 7 5 - 78, 3 = 1 9 7 9 - 82, a n d 4 = 1 9 8 3 - 85), the base-level (A), shell (B) a n d t e m p e r a t u r e (T) c o m p o n e n t s are s h o w n : (a) for p e r i o d 1 t o 2; ( h ) for p e r i o d 2 t o 3; (c) f o r p e r i o d 3 t o 4 ; a n d (d) t h e overall c h a n g e f r o m p e r i o d 1 t o 4. See c a p t i o n t o Fig. 2.
178
period 3 to 4. For the longer intervals--period 1 to 3 in Fig. 2(c), and period 1 to 4 in Fig. 3 ( d ) - - a l l c o m p o n e n t s are sufficiently large to be reasonably well determined. Therefore, while neither the individual parameters ~, ~, and ~ nor the individual c o m p o n e n t s A, B, and T are estimated with great precision, it seems possible to identify, with some degree of certainty, the dominant sources of energy savings from one period to another. The large recent base-level c o m p o n e n t (A) is particularly intriguing. The implied drop in base-level consumption is certainly real, in that actual summer gas consumption (i.e., unadjusted utility sales per customer in July and August) has declined dramatically in recent years, directly mirroring the large 15% drop in ~ between 1975 - 78 and 1979 82. The large shift from oil to gas heating after the major increase in fuel oil prices m a y have contributed (see Fig. 2 in ref. 4), but not necessarily in the direction of reduced c~. A shift from gas to electric appliances is not a likely cause, given the steadiness of perhousehold electricity consumption in the State over the same time period. Much more likely contributors to the gas base-level decline are conservation actions, such as wrapping water heaters, reducing hot-water usage, or purchasing gas appliances with electronic pilot lights. Interestingly, the largest year-to-year drop in ~ (as well as in summer consumption) coincides with the period of a severe water shortage in the area:
1 9 8 0 - 8 1 . Another candidate reason for the base-level drop is reduced household size, by 12% between 1970 and 1980 [9]. Perhaps the most interesting trend is in the temperature c o m p o n e n t T. We use eqns. (8) and (10) to extract the effects of indoor temperature changes. Table 4 summarizes the resulting aggregate estimates for the change in indoor temperature (ATin) and its effect on energy savings (TB), between the main four-year periods. In the earlier period from 1 9 7 0 - 7 3 to 1 9 7 5 - 7 8 (i.e., from period 1 to 2), the aggregate drop in Tin of 1.5 °C is well estimated by the PRISM estimate, AT--1.6 °C. The associated temperature benefit (positive TB) is 15 GJth/year, suggesting that the drop in indoor temperature was responsible for over 60% of the total savings achieved by the aggregate in that period. Not surprisingly, this estimate for TB is similar in magnitude to the temperature c o m p o n e n t T, since ATin ~ At. In the next period, from 1975 78 to 1979 - 82 (period 2 to 3), the decrease in Tin of 0.7 °C is underestimated by AT (=0.2 °C); i.e., due to the concomitant decline in ~, Tin drops by more than just AT would imply. The associated value of TB is 7 GJth/year, again giving a temperature benefit of a b o u t 60% of the aggregate savings. Note that in this period TB is much larger than T, which was only 16% of the total savings. Therefore, over the entire decade from 1 9 7 0 - 7 3 to 1 9 7 9 - 8 2 , a persistent decline in indoor temperature is indicated,
TABLE 4 E s t i m a t e d indoor temperature changes and resulting energy impact for New J e r s e y aggregate s t u d y End p o i n t s o f analysis*
Period 1to2
Period 2to3
Period 3to4
Period 1to3
Period lto4
Change in ref. t e m p . * *
1.55
0.21
--0.30
1.76
1.46
1.52
0.73
--0.24
2.25
2.01
Energy impact tt TB ( G J t h / y e a r )
15.3
7.0
--2.1
22.3
18.5
% o f t o t a l savings (TB/ANAC) x 100
62%
57%
--22%
60%
39%
/xr (°c) Change in i n d o o r t e m p . t
~Tin (°C)
*Period 1 = 1970 - 73, p e r i o d 2 = 1975 - 78, p e r i o d 3 = 1979 - 82, and period 4 = 1983 - 85. * * A positive A r indicates a d r o p in "r, i.e., A r = ~'l - - 7"2 f r o m p e r i o d 1 to 2. l"ATin is determined f r o m e q n . (8) w i t h 5 = 3.9 °C. A positive value indicates a decrease in Tin. **TB is d e t e r m i n e d f r o m e q n . (10). A positive (negative) value suggests a temperature benefit ( t a k e b a c k ) effect.
179
with about 60% of the overall savings attributable to this decline. In Table 4, the only increase in indoor temperature, or negative ATin, is for the most recent period, from 1 9 7 9 - 82 to 1 9 8 3 - 85 (period 3 to 4), suggesting a reversal of this earlier trend. The associated negative estimate for TB indicates a takeback effect of 2.1 GJth/year, and thus that the savings from period 3 to 4 would have been about 20% larger in the absence of the temperature increase. When the entire post-embargo period is considered, from 1 9 7 0 - 73 to 1983 - 85 (period 1 to 4), this reversal has little effect on the overall drop in indoor temperature: the estimates for ATin and TB are quite similar to what t h e y were for the post-embargo decade (period 1 to 3). The results in Table 4 assume 5 = 3.9 °C in eqn. (8). We have also repeated the calculations with values of 5 from 2.2 to 7.8 °C (4 to 14 °F), and, where warranted, without the A~/~ term in eqn. (8) (in order to vary the AQ/Q assumption). The resulting sensitivity analysis confirms the tentative conclusions drawn from Table 4. From period 1 to 2, when the assumptions about both 5 and AQ/Q are varied, the estimates for ATi~ range from 1.1 to 1.5 °C, and the TB estimates range from 11 to 15 GJta/year. For subsequent periods, the decline in base level c~ is sufficiently large that a similarly large change in total intrinsic gains Q seems likely. It therefore seems reasonable to trust eqn. (8), and we examine the sensitivity of the estimates to 5 only. From period 2 to 3, the resulting TB estimates cover a sizeable range, from 5 to 12 GJth/year, but all of them represent more than 40% of the total savings. From period 3 to 4, the TB estimates range from --1.6 to --2.3 GJth/year, and thus bracket fairly tightly the takeback effect identified in Table 4. We are led to an intriguing hypothesis, that structural and furnace retrofitting (through a large positive shell c o m p o n e n t B) is beginning to take hold in New Jersey, but that its potential is being eroded slightly by a takeback effect (through negative TB) resulting from a return to higher indoor temperatures. The overall trend since the embargo m a y be a gradual shifting of the dominating conservation source from a decline in indoor temperatures to shell
tightening. Since this hypothesis makes sense in view of the longer lead times needed for structural retrofitting than for thermostat setbacks, it deserves further testing, both with continued PRISM monitoring and also with independent studies. This aggregate analysis has provided an interesting exploration of how well the PRISM reference-temperature estimate may be expected to t r a c k indoor temperature. With the ~ term in eqn. (8) relatively small, the difference between ATin and Ar is influenced primarily by changes in intrinsic gains, which PRISM can track only through ~. The net result appears to be a consistent post-embargo decline in indoor temperature, viewed through PRISM as a drop in T in the four-year period after the embargo and as a drop in intrinsic gains (via ~) coupled with a smaller change in T in more recent periods. Albeit with large uncertainties, this decomposition of total consumption trends has intriguing policy implications for New Jersey. The possible strong role of lower thermostat settings in post-embargo conservation, and the relatively minor, though growing, role of structural retrofitting, translates into optimism that m u c h greater energy benefits from retrofitting are yet to be achieved. Very recent results, through the summer of 1985, urge caution, in that some of those benefits already achieved are possibly being reversed by a return to higher indoor temperatures. Continued analysis of New Jersey data and similar analyses of data bases in other states are needed to test the validity of these inferences.
IN C O N C L U S I O N
As long as the uncertainties of the estimates are carefully assessed, the PRISM refraction approach seems useful for refining the characterization of conservation in large groups of houses. Two test applications, one to individual-house billing data and one to utility aggregate sales data, demonstrate the added insight available from this closer look at P R I S M savings estimates. In both cases, a dominant role for a single component is suggested, namely, shell tightening in the former and declining indoor temperatures in the latter. A third application, reported
180
elsewhere [7], again found shell effects to be the primary source of savings. Particularly in view of the far-reaching policy implications that may result, more testing is needed. This should be done with the aid of supplemental survey data, with which the assumptions required for the refraction method, and the resulting conclusions, can be validated. If other tests are successful, the refraction approach will allow the scorekeeper to take the information extractable from energy billing data one step further than was hitherto believed possible. Other papers in this issue provide convincing evidence that extremely reliable estimates of energy savings are available from straightforward, but careful, analysis of billing data. The possibility that additional physical insight concerning the sources of these savings may be gleaned from the same data is indeed exciting, and is well worth further attention.
ACKNOWLEDGEMENTS
Funding for the development of this methodology, which was initially provided by a matching grant from the Ford Foundation and the New Jersey Department of Energy (NJDOE), has been continued by the New Jersey gas and electric utilities and NJDOE. The New Jersey data were obtained from the New Jersey Energy Data System of NJDOE. The Wisconsin data were collected under a contract with the Wisconsin Department of Administration, with supplemental funds from Wisconsin Electric Power Co.; data processing was facilitated by access to the University of Wisconsin Statistics Department's research computer. Portions of this work were completed while one author
(MLG) was at the U.S. Environmental Protection Agency. Both authors would like to thank Andrzej Jaworski and Asit Banerjee for assistance in the Wisconsin data analysis, Cathy Reynolds for assiduously updating the New Jersey results, and Robert Socolow for insightful comments throughout the study.
REFERENCES 1 M. Fels, PRISM: an introduction, Energy Build., this issue, pp. 5 - 18. 2 J. Rachlin, M. Fels and R. Socolow, The stability of PRISM estimates, Energy Build., this issue, pp. 149 - 157. 3 M. Goldberg, A Midwest low-income weatherization program seen through PRISM, Energy Build., this issue, pp. 37 - 44. 4 M. Fels and M. Goldberg, Using the scorekeeping approach to monitor aggregate conservation, Energy Build., this issue, pp. 161 - 168. 5 M. Fels and M. Goldberg, Using billing and weather data to separate thermostat from insulation effects, Energy 9 (5) (1984) 439 - 445 (the earlier version of this paper). 6 ASHRAE Handbook 1981 Fundamentals, American Society of Heating, Refrigeration and Air Conditioning Engineers, Inc., Atlanta, GA, 1981, p. 25.3. 7 E. Hirst and D. White, Indoor Temperature
Changes after Retrofit: Inferences Based on Electricity Billing Data for Nonparticipants and Participants in the BPA Residential Weatherization Program, Report No. ORNL/CON-182, Oak Ridge National Laboratory, Oak Ridge, TN, July 1985. See also earlier study: E. Hirst, D. White and R. Goeltz, Indoor temperature changes in retrofit homes, Energy 10 (7) (1985) 861 - 870. 8 E. Hirst, Electricity savings one, two, and three years after participation in the BPA Residential Weatherization Pilot Program, Energy Build., this issue, pp. 45 - 53. 9 Office of Demographic and Economic Analysis,
New Jersey Preliminary Census Counts of Population and Housing: 1 April 1980, New Jersey Department of Labor and Industry, Trenton, NJ, December 1980.
169
Refraction of PRISM Results into Components of Saved Fner / MIRIAM L. GOLDBERG*
Statistical Laboratory, University of Wisconsin, Madison, WI 53706 (U.S.A.) MARGARET F. FELS
Center for Energy and Environmental Studies, Princeton University, Princeton, NJ 08544 (U.S.A.) (Received January 1986)
SUMMARY
A simple methodology is developed to augment the physical interpretation o f PRISM results. With this "refraction" method, the estimated energy savings are decomposed into physically meaningful components, indoor temperature changes are inferred, and the effect o f such changes on energy savings is quantified. The method is demonstrated in two test applications. The first, to individual-house billing data for a set o f 243 gas-heated houses, suggests the dominant role o f structural retrofitting in the energy savings achieved by weatherization of the houses. The second application, to utility aggregate data for nearly one million gas-heated houses in one state, points to the importance o f lower thermostat settings in the years immediately following the oil embargo, and, since 1980, to a substantial decline in consumption by appliances including water heaters. More recently, the role o f structural retrofitting seems to be increasing, but a "takeback" effect due to a concomitant increase in indoor temperatures may be eroding the resulting savings. While the refraction results must be interpreted with care, their physical reasonableness, in both test cases, reinforces the potential o f energy billing data to enhance the understanding o f energy conservation trends. INTRODUCTION
Most P R I S M studies to date have emphasized the usefulness of Normalized Annual Consumption (NAC), whose stability makes it a particularly useful monitoring index.
Inferences a b o u t trends from the other PRISM parameters, which are needed to c o m p u t e NAC, are often problematic, particularly at the individual-house level. The base-level and heating-slope parameters, and ~, respectively, are much more sensitive to choice of reference temperature, T, than is NAC, and their relative standard errors tend to be large compared to the 3 - 4 % typical for NAC**. On the other hand, when results for large numbers of houses are averaged in some way, the individual parameters, ~, ~ and T, can offer valuable insight into the nature of conservation activities. In this paper, we describe h o w physical sources of energy savings can be identified, and h o w indoor temperature changes can be inferred, from changes in the individual parameters of the PRISM model. The resulting estimates of savings c o m p o n e n t s must be interpreted with care. Measures of the accuracy of these estimates provide guidance as to h o w precise these interpretations may be; consideration should also be given to the validity of assumptions required for the savings decomposition. The "refraction" approach, to decompose PRISM estimates of energy savings, is tested here on two data bases of gas-heated houses. The first, from a low-income weatherization program in Wisconsin, consists of individualhouse billing data for 243 houses; the second, *Present address: Energy End Use Division, U.S.
Energy Information Administration, Washington, DC 20585, U.S.A. **PRISM, the Princeton Scorekeeping Method, is described in the introductory paper to this issue [ 1 ]. See also the stability analyses reported in this issue [ 2 ]. Elsevier Sequoia/Printed in The Netherlands
170
representing average natural gas consumption for all gas-heated households in New Jersey, consists of aggregate utility sales data. Both are subjects of other papers in this issue [3, 4].
As described in ref. 1, NAC for estimation period k is given by: NAC~ = 365 (~k + {JkHo(rk)
(1)
where Ho(rk) is the long-run heating degreedays c o m p u t e d to base rk. The energy savings, N A C 1 - - N A C 2 , between periods 1 and 2 may be written in terms of changes in the individual parameters ~,/], and r, as follows: -- NAC 2 =
365 (oq - -
-
0/2)
A
+ ~[H0(rl) +
+ (/~I --/~2)/-I0 +
-
-
T
B
H0(r2)] (2)
where /-I0 = [H0(rl) + Ho(r2)]/2
(3a)
and = (~1 + ~2)/2
(~I + a2)/2
(4a)
se(B) =/-70[se2(~l) + se2(fl2)] 1/2
(45)
+ [Fo{r2)se(r2)] 2)1/2
(4c)
In eqn. (4c), Fo{r) is the derivative with respect to r of Ho(r), and corresponds to the length of the heating season to base r. For normalized degree-days H0 determined from integer-valued dally temperature data, this derivative is given by: Fo{r) = H o ( m + 1 ) - - H o ( m )
(5)
where rn is the integer part of r. In a simplified physical model of the heating fuel, it is tempting to associate the T-component of eqn. (2) with lowered thermostat settings, the B-component with structural retrofits or furnace efficiency improvements, and the A-component with decreased appliance usage or increased appliance efficiency for appliances fueled by the heating fuel. To examine the extent to which these associations are valid, we take a closer look at the physical effects likely to induce changes in c~, ~ and, especially, r.
(3b)
For later use, we also define a =
se(A) = 365[se:(0q) + se2((~:)] 1/2
se(T) = ~( [Fo(rl)se(rl)] 2
DECOMPOSITION OF ENERGY SAVINGS
NAC,
To determine the accuracy of this decomposition, we calculate the standard errors {se) of the three components, as follows:
PHYSICAL NENTS
SIGNIFICANCE
OF
THE
COMPO-
(3c)
We use eqn. (2) for the components analysis*. If, indeed, there is a drop in NAC, then the decomposition indicates the sources of observed energy savings, in terms of three physical components. The base-level component (A) represents savings due to reduced base-level consumption; the shell c o m p o n e n t (B), savings due to a decrease in heating slope; and the temperature c o m p o n e n t (T), savings resulting from a decline in reference temperature.
*In earlier w o r k [5], a Taylor's series expansion of eqn. (1) gave two alternate f o r m u l a e similar to eqn. (2), with flk and H0(rk) for k = 1 and k = 2 used instead o f ~ and /70. E q u a t i o n (2), which is exact, is equivalent to the average o f the t w o expansions.
Changes in the reference temperature r are likely to reflect changes in the indoor temperature Tin. However, Tin is not the only factor which affects r. In the PRISM model, r is interpreted as the maximum average daily o u t d o o r temperature at which the furnace is required. This temperature is lower than the indoor temperature, because some of the house's heating requirement is met by intrinsic gains Q, from occupants, appliances, and the sun. The difference between Tin and r depends also on the house's "lossiness" L, which is the product of the heating rate ~ and the furnace efficiency, i.e., r = Tin -- Q / L
(see Appendix 1 of ref. 1).
(6)
171
From eqn. (6), it is possible to derive an expression relating the change in the house's indoor temperature to the observed changes in the model parameters ~, ~ and T. This indoor temperature change can then be translated into an equivalent energy savings or loss. As a first step, we differentiate eqn. (6), then substitute T i n - - r for Q/L in the resulting expression, to obtain the following first-order approximation:
AQIQ, may be approximated by A~/~. If, instead, appliances fueled by the heating fuel contribute only a small fraction of Q, with the dominant sources of Q being sun, people, and unchanged appliances, this approximation overstates AQ/Q. With the above assumptions about AL/L and AQ/Q, eqn. (7) gives: A T i n ~ (7"1 - - T2) - - a [ ( ~ l - - ~2)/~]
+ a[(al - a:)/~]
AT = A T i n + (Tin - - T ) A L / L
-- (Tin -- T)AQ/Q
{7)
(Defining AT= T1--T2, a positive change indicates a drop in T, and thus a change in the direction of conservation.) The first term, ATin, indicates h o w a thermostat setback might translate directly into a reduction in T. The terms in AL and AQ, respectively, indicate h o w interventions such as house tightening and more efficient appliances might affect T. Conversely, eqn. (7) allows us to see what a drop in T implies about a drop in Tin, depending on h o w lossiness L and intrinsic gains Q have changed. For example, a large drop in Q narrows the gap between Tin and T, SO that an observed drop in T will underestimate a drop in Tin. On the other hand, a large drop in L m a y itself induce a drop in T, even w i t h o u t a concomitant change in Tin. Only when there is no significant change in L or Q, or when their changes cancel, will AT track ATin. To estimate ATin from PRISM estimates therefore requires n o t only AT b u t also information a b o u t L and Q. The needed information can be inferred from the parameters ~ and ~, provided some additional assumptions are made. First, assuming no change in the furnace efficiency, the relative change in lossiness, AL/L, is well approximated by Aft/ft. Furnace efficiency improvements and decreased lossiness would both lower {3, so that IA~/~I becomes an overestimate of IAL/L] if furnace efficiency has increased. Second, assuming that appliances represent the main source of intrinsic gains, and that the change in the energy consumed by appliances is essentially uniform across fuels {e.g., for gas and electric appliances in a gas-heated house), the relative change in intrinsic gains,
(8)
where 8, the temperature offset, is defined as:
a = Ti, -- r
(9)
and ~{and ~ are defined in eqn. (3). A final required assumption is the value of 8. The dependence of the temperature offset 5 on L and on Q, as implied by eqn. (6), suggests the importance of exploring the effects of different assumptions a b o u t by applying eqn. (8) over a range of 5-values. As a starting point, we use ~ = 3.9 °C (7 °F)*. The validity of the approximations, AL/L AfJ/fJ and AQ/Q ~ A~/c~, should also be considered, and the effect of varying these assumptions explored. This kind of sensitivity analysis strengthens the conclusions drawn. Equation (8) indicates the extent to which energy savings have been either augmented or diminished by indoor temperature changes. To carry the analysis one step further, the temperature shift ATin can be translated into a quantifiable energy savings or loss. This translation is accomplished by comparing the observed NAC for the second period, NAC2, with the NAC that would have been realized if the indoor temperature had n o t changed. The latter, hypothetical NAC:' is determined by replacing T: with r2 + A T i n in eqn. (1) (with h = 2). Thus, the energy impact of a shift in indoor temperature is given by:
TB = N A C j -- NAC2 = ~:[H0(r2 + ATin) --H0(T:)]
(10)
*This value of ~ is c o n s i s t e n t w i t h the c o n v e n t i o n a l use of 18.3 °C (65 °F) for the reference t e m p e r a t u r e t o g e t h e r w i t h the A S H R A E c o n v e n t i o n of 22.2 °C (72 °F) for the indoor temperature [6 ].
172
Unlike the temperature c o m p o n e n t T in eqn. (2), which incorporates changes in all the factors affecting the reference temperature r, the quantity TB given by eqn. (10) isolates the effect of changing indoor temperature Tin. When the indoor temperature drops between the first and second estimation periods, ATin and TB are positive; in this case, TB represents a "temperature benefit", or the portion of savings attributable to the lowering of indoor temperature. When ATin is negative, TB is negative; the magnitude of TB in this case represents a "takeback effect", or potential energy savings taken back in the form of increased indoor temperature. In either event, the savings that would have occurred in the absence of the change in Tin may be estimated as (NAC1 -- NAC2 -- TB). It is well known that a temperature benefit, or positive savings TB, can be obtained simply by turning down the thermostat, even in the absence of any improvement in the house structure or appliances. On the other hand, economists have conjectured that a takeback (negative TB) might occur after a house has been made more energy efficient, analogous to choosing to drive more after buying a more fuel-efficient car. Equation (10) gives a basis for assessing the extent to which such takeback behavior may be occurring. It is worth noting that changes in indoor temperatures are not necessarily the result of deliberate changes in thermostat settings. Particularly in houses which are initially in poor condition, a side benefit of retrofitting m a y be the reduction of drafts or the equalization of temperature gradients. Eliminating drafts can m a k e a lower temperature comfortable, without a conscious decision to keep a cooler house. Improved heating system balance m a y m a k e previously uncomfortable rooms as warm as the thermostatted room, resulting in a temperature increase on average w i t h o u t a change in thermostat setting, or, conversely, it may eliminate the necessity to overheat some rooms to have others comfortable, resulting in a temperature decrease on average. These possibilities should be considered when interpreting a calculated indoor temperature change A T i n , and the corresponding energy impact TB. The refraction approach, in summary, involves three steps. The first is to separate
the estimated savings for a group of houses into three physically meaningful components, A, B, and T, using eqn. (2). The second step is to estimate the concomitant change in indoor temperature, using eqn. (8), and to convert this temperature change into energy savings (temperature benefit) or loss (takeback), i.e., TB, using eqn. (10). The third step involves interpreting each estimate (A, B, T, and TB) in light of possible conservation actions, including changes affecting the house's appliances, building shell, furnace, and thermostat. For all components, the estimation errors (eqn. (4}), and the sensitivity to a range of possible assumptions, need to be considered.
ACCURACY
MEASURES
When the refraction method is applied to a single pre-post pair of PRISM results for an individual house or an aggregate of houses, the standard error of each component, given by eqn. (4), measures the accuracy of the savings decomposition for that pair. When aggregate PRISM is used [4], the PRISM estimates may be interpreted as the average of the individual-house estimates, and the components breakdown in eqn. (2) as the average of individual-house components. The formulae in eqn. (4) give the measurement errors of this average breakdown, but tell nothing a b o u t the variation in the components across the different houses which comprise the aggregate. If, instead of a single aggregate pre-post PRISM pair, separate pre- and post-retrofit PRISM results are available for each of a sample of houses, the corresponding components breakdown may be c o m p u t e d from eqn. (2) for each house. The house-to-house variation m a y then be measured by either the standard deviation or, more robustly, by the interquartile range of each c o m p o n e n t across the houses in the sample. Taking the mean of each c o m p o n e n t (A, B, T, and TB) across houses will give a result very similar to that which would be found from a single aggregate analysis; if the PRISM model were entirely linear, and all houses in the group had their meters read on the same day, the agreement would be exact. A measure of the accuracy with which each mean or median
173 c o m p o n e n t is determined for N houses is the corresponding standard error of the mean or of the median (see Appendix 3 of ref. 1). These standard errors differ conceptually from the standard error which would be given by eqn. (4) for an aggregate analysis. The latter standard error tells h o w accurately the average (mean) c o m p o n e n t for that particular set of houses has been estimated. The standard error of the mean or median (as given in the next section for the Wisconsin data set} tells h o w accurately the mean or median o f the larger group of houses from which the study group was drawn has been estimated. Wherever possible, we prefer to use measures based on the median rather than the mean. To represent the accuracy of the components estimates in what follows, we use the standard error of the sample median when PRISM has been applied to individual-house data for a sample of houses, and we use the standard errors of the estimates (eqn. (4)) when aggregate PRISM has been applied. Where reference is made to significance of results, the nominal 5% significance level, or 95% confidence level, is used as a standard; however, this significance level should be interpreted as a qualitative indicator rather than as a precise measure.
APPLICATION TO INDIVIDUAL HOUSES The refraction m e t h o d was applied to each house in a group of 243 " G o o d Houses" resulting from the PRISM analysis of Wisconsin's low-income weatherization program [3]. These houses were weatherized in 1982 under a program administered by the Wisconsin Department o f Health and Social Services. While the work done varied considerably across houses, the emphasis was on sealing windows and doors, and installing insulation. The median savings for these houses were 10 % of the pre-retrofitN A C , as compared with 2 % for a set of "Good-House" control houses. Only the treated (weatherized) houses are analyzed here; since the savings in the control group were small, we felt that a decomposition of those savings would not be very meaningful. The refraction results thus represent a decomposition of the total savings, without regard to whether the
savings are attributable to the program or to external events. The Good-House restrictions, that the preand post-weatherization periods each have at least ten actual meter readings and R 2 values from PRISM fits of the data which are greater than 0.90, ensure that the refraction m e t h o d is applied only to houses for which the individual parameters are likely to be physically meaningful. U n e v e n s p a c i n g of meter readings over the year can seriously skew these estimates [2], while low R ~ indicates a poor fit of the data and thus poor determination of the parameters. The results of computing the base-level (A), shell (B), and temperature (T) components for this set of 243 houses are s u m marized in Table 1. For each component, both mean and median measures are shown. Comparing the medians and means to their respective standard errors indicates which changes, averaged over the entire group, are significantly different from zero. For this set of houses, the standard errors of the median and of the mean, the two measures of variability, are quite close for all three variables. The median and mean, the t w o measures of the center of the distribution, are somewhat less consistent, because of the presence of a few extreme outliers, b u t they lead to the same qualitative conclusions. The interquartile ranges plotted in Fig. 1 show clearly the broad distribution of each component's estimates across these 243 houses, as well as the relative contribution of each c o m p o n e n t to the total savings. The median estimate of total savings is 13.1 GJth/year (124 therms/year), which, as mentioned earlier, represents a b o u t 10% of the pre-weatherization consumption level. Shell effects, with a median of 9.8 GJth/year, are by far the dominant contributor to these savings. Changes in base level, with a median of 2.7 GJth/Year, are small b u t still significant, and temperature effects, with a standard error larger than the median of 0.8 GJth/Year, are n o t significant. The dominance of the shell effects is reasonable, since most of the weatherization work done in these houses had to do with shell tightening (see ref. 3). The apparent lack of temperature effects can be explored further using eqns. (8) and (10). The resulting estimates of indoor temperature changes (ATi,) and takeback effects
174 TABLE 1 Summary of refraction results for individual houses in Wisconsin study* Component
Temperature (T) Shell (B) Base level (A) ANAC (total)
Median measures (GJth/year)**
Mean measures (GJth/year) t
Median
IQR
se(median)
Mean
sd
se(mean)
0.8 9.8 2.7
21.1 23.6 10.4
1.4 1.5 0.7
--0.1 13.2 3.2
24.1 23.0 12.8
1.6 1.5 0.8
13.1
20.9
1.3
16.3
18.9
1.2
*Based on 243 Good Houses, from ref. 3. T, B, and A are determined from eqn. (2). For this set of houses, the pre-retrofit NAC had a median of 132 and a mean of 140 GJth/year. **IQR = interquartile range ; se(median) = I Q R / ~ where N is the number of houses. tsd = standard deviation; se(mean) = sd/%/N.
(TB) are s u m m a r i z e d in T a b l e 2. T h e m e d i a n ATin e s t i m a t e is - - 0 . 2 °C, i n d i c a t i n g a slight t e m p e r a t u r e increase. This c h a n g e is small in a b s o l u t e t e r m s , a n d also small c o m p a r e d t o the s t a n d a r d e r r o r o f t h e m e d i a n , 0.3 °C. Overall, t h e n , f o r this g r o u p o f 243 houses, n o significant c h a n g e in i n d o o r t e m p e r a t u r e a p p e a r s t o h a v e o c c u r r e d , a l t h o u g h t h e large i n t e r q u a r t i l e r a n g e ( I Q R ) suggests t h a t s o m e o f t h e h o u s e h o l d s raised o r l o w e r e d t h e i r
25
200
20 150~ (D
15
~. E
ro
iI boo
E
g 5
50
c
gc o
o.e o f-
0
o
-50
-5
-io Component : T
B
A
TOTAL
Fig. 1. Summary of distribution of refraction results across houses in Wisconsin study. For each component [base level (A), shell (B), temperature (T), and ANAC (Total)], the median is indicated by the height of the box, the median value by the number at the top of the box (in GJth/year), and the upper and lower quartiles by the tips of the arrows (the arrow length gives the IQR). For the second and third components, the zero is set at approximately the median of the previous component, to make more evident their summation to the total.
i n d o o r t e m p e r a t u r e s substantially. T h e m e a n ATin e s t i m a t e , - - 0 . 8 °C, is s o m e w h a t larger in m a g n i t u d e , and is n o m i n a l l y significant, b u t this e s t i m a t e is less t r u s t w o r t h y (i.e., less r o b u s t ) t h a n t h e m e d i a n . When t h e t e m p e r a t u r e c h a n g e s are c o n v e r t e d h o u s e b y h o u s e to e n e r g y savings, i.e., t o TB via eqn. (10), n e i t h e r the m e d i a n n o r t h e m e a n indicates a significant t a k e b a c k effect. T h e s e q u a l i t a t i v e results w e r e c o r r o b o r a t e d b y r e - e s t i m a t i n g TB, t h e t a k e b a c k effect, using d i f f e r e n t a s s u m e d t e m p e r a t u r e o f f s e t s 5, a n d b y v a r y i n g a s s u m p t i o n s a b o u t AQ/Q and AL/L in eqn. (8) f o r ATin. T h e o f f s e t 6 was set at 2.2 a n d 5.6 °C as well as the 3.9 °C value used in T a b l e 2. D r o p p i n g t h e A a / ~ t e r m , i.e., a s s u m i n g changes in internal gains to be negligible, was also tried. ( D r o p p i n g t h e Afi/fl t e r m , i.e., a s s u m i n g a n y o b s e r v e d changes in fi t o be a t t r i b u t a b l e n o t to lossiness Changes b u t to h e a t i n g - s y s t e m e f f i c i e n c y i m p r o v e m e n t s , w o u l d n o t be r e a s o n a b l e here, since a l m o s t n o h e a t i n g - s y s t e m w o r k was d o n e in the s t u d y houses.) U n d e r t h e v a r y i n g sets o f a s s u m p t i o n s , the m e d i a n e s t i m a t e s f o r TB r a n g e d f r o m a takeb a c k o f - - 2 . 4 GJ~h/year t o a t e m p e r a t u r e b e n e f i t o f + 0.3 G J t h / y e a r . T h e m e a n s r a n g e d f r o m - - 2 . 2 to - - 0 . 1 G J t h / y e a r . N o n e o f the m e a n s o r m e d i a n s was n o m i n a l l y significant. Thus, even t h o u g h t h e largest m e d i a n takeb a c k e s t i m a t e o f 2.4 G J t h / y e a r is 18% o f t h e t o t a l m e d i a n savings o f 13.1 G J t h / y e a r , a t t e n t i o n t o the u n c e r t a i n t i e s o f t h e e s t i m a t e shows the evidence for a takeback effect to b e w e a k . T h e overall c o n c l u s i o n f r o m this r e f r a c t i o n analysis o f t h e set o f Wisconsin h o u s e s is t h e d o m i n a n c e ' o f shell t i g h t e n i n g
175 TABLE 2 Summary of estimated indoor temperature changes and resulting energy impact for houses in Wisconsin study Number of houses*
Median measures
Change in indoor temp** ATin (°C)
243
--0.16
Energy impact t
241
--0.8
Median
IQR 4.02 23.7
M e a n measures
se(median)
Mean
0.26
--0.77
1.5
--0.7
sd
se(mean)
5.68 22.6
0.36 1.5
TB (GJth/year) *All Good Houses from ref. 3 were used. Equation (10) was not estimated for two extreme outliers, i.e., houses which had T2 + ATin outside the range (--17.7, 37.8) °C ( ( 0 , 1 0 0 ) °F). **ATin is determined from eqn. (8) with ~ = 3.9 °C. A negative value indicates an increase in Tin. "¢TB is determined from eqn. (10). A negative value suggests a takeback effect. To compare with total savings, see ANAC in Table 1.
in the total savings achieved, with very little, if any, of the savings being taken back by an increase in indoor temperatures. Another study, at Oak Ridge National Laboratory, found similar results in a data set o f "clean" electrically heated houses analyzed by PRISM as part of an evaluation of a Bonneville Power Administration (BPA) program [7]. (See related study in this issue [8] .) The estimated mean increase in indoor temperature was 0.2°C for 97 houses receiving retrofits in 1982 and 0.6 °C for 113 houses receiving retrofits in 1983. (A value of 5 = 4 °C was assumed.) Only the latter change was statistically significant; the associated takeback effect amounted to 25% of the total energy saved in the 1983 participant group*. The reason for the different results in the two sets of houses, which received similar retrofits in two successive years, is not evident, particularly since no significant takeback effect was found in either year in the 32-house nonparticipant group. In both the Wisconsin and the BPA studies, the apparent increase in indoor temperatures is tantalizing in view of its possible impact on energy conservation. However, in the Wisconsin study and in the first-year BPA study, the temperature change, if any, is evidently of such small magnitude that it cannot be reliably quantified. The possibility *The O a k Ridge analysis [7] was based on our earlier w o r k [5 ], which predates our formulation of TB. The formula used in ref. 7 for the takeback effect is equivalent to a Taylor-series approximation to our eqn. (10).
of a takeback effect is suggested in the second-year BPA results, but may not be generalizable b e y o n d that specific, fairly small sample of treated houses. With substantially larger data sets, particularly those that span more time, a clearer picture of these trends in temperature settings might emerge. To this end, we turn to a PRISM refraction of a very large set of houses, consisting of all gas-heated houses in the state of New Jersey.
APPLICATION
TO AGGREGATE
CONSUMPTION
For the refraction analysis of aggregate gas consumption in New Jersey, we start with four-year estimates of NAC and of the model's three individual parameters, for 1 9 7 0 - 73 through 1 9 8 2 - 85**. Table 3 contains the PRISM estimates for these periods (see also Fig. 5 of ref. 4, in this issue). Over the entire period, consumption has declined by a total of 47 GJth (440 therms) per customer-year, or by 25% when compared with the pre-embargo (1970 - 73) level. To analyze trends in the post-embargo decade, we choose three non-overlapping four-year periods: 1 9 7 0 - 7 3 (the pre-embargo base period), 1 9 7 5 - 7 8 , and 1 9 7 9 - 8 2 , as periods 1, 2, and 3, respectively; these were the subject of our earlier work [5]. To bring the analysis up to date, we add the most recent nonoverlapping (three-year) period: 1 9 8 3 - 8 5 , as period 4. * * T h e periods are based on August-to-July heating years; 1982 - 85 ends with July 1985.
176 TABLE 3 PRISM per-household estimates by four-year estimation periods for New Jersey aggregate of gas-heating customers Estimation period*
R2
PRISM estimates** Ref. temp. 7" (°C)
H0(7") (°C-days/ year )
Base level ~ (kWth)
Heating slope ~ (Wth/°C)
NAC (GJth/year)
1 9 7 0 - 7 3 (period 1) 1971 -74 1972 - 7 5 1973 - 7 6 1974 -77
0.995 0.992 0.988 0.984 0.991
19.3(0.4) 19.4 (0.4) 19.1 (0.6) 18.8 (0.6) 18.6 (0.4)
2966 2999 2905 2854 2798
1.71(0.08) 1.72 (0.10) 1.75 (0.12) 1.70 (0.13) 1.65 (0.10)
514 503 499 492 475
(11) (13) (15) (18) (13)
185.9(1.3) 184.5 (1.5) 180.4 (1.8) 175.0 (2.0) 166.6 (1.5)
1975 -78 (period 2) 1976-79 1977-80 1978-81
0.993 0.995 0.997 0.993
17.7 (0.4) 17.6 (0.3) 17.3 (0.3) 17.4(0.4)
2595 2569 2505 2523
1.64 1.60 1.56 1.48
(0.09) (0.07) (0.06) (0.08)
488 (11) 488 (9) 490 (7) 484 (11)
161.0 (1.4) 158.6(1.1) 155.5 (0.9) 151.7(1.4)
1 9 7 9 - 8 2 ( p e r i o d 3) 1980-83 1981-84 1982-85
0.990 0.994 0.996 0.994
17.5(0.4) 17.2 (0.3) 17.3 (0.3) 17.6(0.4)
2547 2473 2484 2565
1.39(0.10) 1.34 (0.07) 1.29 (0.05) 1.27(0.07)
475(13) 477 (11) 468 (9) 451 i l l )
148.7(1.6) 144.1 (1.1) 141.3 (0.9) 139.8 (1.1)
1983 - 85 (period 4)
0.995
17.8 (0.4)
2615
1.27 (0.07)
440 (11)
139.0 (1.1)
*Each four-year period starts with August of the previous year and extends through July of the last year indicated. The three-year period, 1983 - 85 (indicated as period 4), is added as a non-overlapping extension of the earlier three main periods for analysis (periods 1, 2 and 3). **Numbers in parentheses are standard errors of the estimates. P O S T - E M B A R G O DECADE
5O - - 450
PC
400
.E
40 100%
350
Q.
A(S2%)
8 3c .c_
300
50%
i,;i~? x'~ii~i o,,
250
g
200 . . . . . . . . . . . .
50: 50%
150 I00 50 O%
(a)
(b)
(c)
Fig. 2. Summary of refraction results for New Jersey aggregate study: post-embargo decade. For each change between periods (1 = 1970 - 73, 2 = 1975 - 78, 3 = 1979 - 82), the base-level (A), shell (B) and temperature iT) components are shown: (a) for period 1 to 2, (b) for period 2 to 3, and (c) for the overall change from period 1 to 3. Both percentage and absolute changes are shown. The number in parentheses is the percentage contribution to the total change in N A C . Arrow from the top of each rectangle represents the standar~l error estimated from eqn. (4) for that component.
177
We start with the results for the postembargo decade. Figure 2 shows the three components CA, B and T) of the energy savings, together with their standard errors (from eqn. (4)), for periods 1 through 3. From 1970 - 73 to 1975 - 78 {Fig. 2(a)), the temperature component (T in eqn. (2)) accounts for about two-thirds of the 13% decline in NAC. From 1 9 7 5 - 7 8 to 197982 {Fig. 2(b)), the base-level component (A) dominates the 8% decline in NAC. For both periods, the shell component (B) contributes only about a quarter of the change in NAC. Over the entire decade, from 1970- 73 to 1979 - 82 (Fig. 2(c)), about 50% of the total energy savings is thus attributed to the temperature component iT), and about 25% each to the base-level (A) and shell (B) components. Extension of the results through 1985 indicates a persistence in the decline of base-level consumption but a shift in the other trends. Figure 3 follows the progression of the three components from the embargo period to the present. The role of the shell component (B) in recent years has dramatically increased, reflecting an accelerated drop in heating slope from 1979- 82 to 1 9 8 3 - 8 5 (see Table 3). On the other hand, the temperature component iT), which
was dominant in the period right after the embargo (Fig. 3(a)), has diminished (Fig. 3(b)), and in the most recent period (Fig. 3(c)) has changed sign due to a slight increase in reference temperature (by 0.3 °C). Between different adjacent periods since the embargo, different components have dominated: first T, then A, and n o w B, as we progress across Figs. 3(a), 3(b), and 3(c). Over the entire period since the embargo, from 1970- 73 to 1 9 8 3 - 8 5 (Fig. 3(d)), the division of the savings among the three components has become fairly even. The standard errors shown in Figs. 2 and 3 allow a rough assessment of the significance of the components. Although the standard errors of the total savings are small (~ 2 GJth for ANAC from one four-year period to another), the standard errors of the individual components are much larger (~ 6 GJth for T, and ~ 4 GJth each for B and A). On a relative scale, the standard error of ANAC between any two periods is in all cases less than 20% of the estimate of ANAC, whereas the relative standard error for an individual component is occasionally larger than the estimate itself. In Figs. 3(a) - (c), only the largest component of the total change between two adjacent periods appears significant by itself: T for period 1 to 2, A for period 2 to 3, and B for
RECENT INDICATIONS A
50--
[
I0(
16
450
,%. ,J=
4OO
._8
350
Q.
M-)
A ( 30 %)
300~
IN
o 3o .c_
g.
250-. ~
I00%
50'
200 $ o
150 ...........
509~
I00 2 50
.o
0
165%),\\\\\\ ...........
(O)
L--o.__------.
0%
(b)
(c)
~,.
)%
(d)
Fig. 3. S u m m a r y o f r e f r a c t i o n results for N e w J e r s e y aggregate s t u d y : r e c e n t i n d i c a t i o n s . F o r e a c h c h a n g e bet w e e n p e r i o d s (1 = 1 9 7 0 - 73, 2 = 1 9 7 5 - 78, 3 = 1 9 7 9 - 82, a n d 4 = 1 9 8 3 - 85), the base-level (A), shell (B) a n d t e m p e r a t u r e (T) c o m p o n e n t s are s h o w n : (a) for p e r i o d 1 t o 2; ( h ) for p e r i o d 2 t o 3; (c) f o r p e r i o d 3 t o 4 ; a n d (d) t h e overall c h a n g e f r o m p e r i o d 1 t o 4. See c a p t i o n t o Fig. 2.
178
period 3 to 4. For the longer intervals--period 1 to 3 in Fig. 2(c), and period 1 to 4 in Fig. 3 ( d ) - - a l l c o m p o n e n t s are sufficiently large to be reasonably well determined. Therefore, while neither the individual parameters ~, ~, and ~ nor the individual c o m p o n e n t s A, B, and T are estimated with great precision, it seems possible to identify, with some degree of certainty, the dominant sources of energy savings from one period to another. The large recent base-level c o m p o n e n t (A) is particularly intriguing. The implied drop in base-level consumption is certainly real, in that actual summer gas consumption (i.e., unadjusted utility sales per customer in July and August) has declined dramatically in recent years, directly mirroring the large 15% drop in ~ between 1975 - 78 and 1979 82. The large shift from oil to gas heating after the major increase in fuel oil prices m a y have contributed (see Fig. 2 in ref. 4), but not necessarily in the direction of reduced c~. A shift from gas to electric appliances is not a likely cause, given the steadiness of perhousehold electricity consumption in the State over the same time period. Much more likely contributors to the gas base-level decline are conservation actions, such as wrapping water heaters, reducing hot-water usage, or purchasing gas appliances with electronic pilot lights. Interestingly, the largest year-to-year drop in ~ (as well as in summer consumption) coincides with the period of a severe water shortage in the area:
1 9 8 0 - 8 1 . Another candidate reason for the base-level drop is reduced household size, by 12% between 1970 and 1980 [9]. Perhaps the most interesting trend is in the temperature c o m p o n e n t T. We use eqns. (8) and (10) to extract the effects of indoor temperature changes. Table 4 summarizes the resulting aggregate estimates for the change in indoor temperature (ATin) and its effect on energy savings (TB), between the main four-year periods. In the earlier period from 1 9 7 0 - 7 3 to 1 9 7 5 - 7 8 (i.e., from period 1 to 2), the aggregate drop in Tin of 1.5 °C is well estimated by the PRISM estimate, AT--1.6 °C. The associated temperature benefit (positive TB) is 15 GJth/year, suggesting that the drop in indoor temperature was responsible for over 60% of the total savings achieved by the aggregate in that period. Not surprisingly, this estimate for TB is similar in magnitude to the temperature c o m p o n e n t T, since ATin ~ At. In the next period, from 1975 78 to 1979 - 82 (period 2 to 3), the decrease in Tin of 0.7 °C is underestimated by AT (=0.2 °C); i.e., due to the concomitant decline in ~, Tin drops by more than just AT would imply. The associated value of TB is 7 GJth/year, again giving a temperature benefit of a b o u t 60% of the aggregate savings. Note that in this period TB is much larger than T, which was only 16% of the total savings. Therefore, over the entire decade from 1 9 7 0 - 7 3 to 1 9 7 9 - 8 2 , a persistent decline in indoor temperature is indicated,
TABLE 4 E s t i m a t e d indoor temperature changes and resulting energy impact for New J e r s e y aggregate s t u d y End p o i n t s o f analysis*
Period 1to2
Period 2to3
Period 3to4
Period 1to3
Period lto4
Change in ref. t e m p . * *
1.55
0.21
--0.30
1.76
1.46
1.52
0.73
--0.24
2.25
2.01
Energy impact tt TB ( G J t h / y e a r )
15.3
7.0
--2.1
22.3
18.5
% o f t o t a l savings (TB/ANAC) x 100
62%
57%
--22%
60%
39%
/xr (°c) Change in i n d o o r t e m p . t
~Tin (°C)
*Period 1 = 1970 - 73, p e r i o d 2 = 1975 - 78, p e r i o d 3 = 1979 - 82, and period 4 = 1983 - 85. * * A positive A r indicates a d r o p in "r, i.e., A r = ~'l - - 7"2 f r o m p e r i o d 1 to 2. l"ATin is determined f r o m e q n . (8) w i t h 5 = 3.9 °C. A positive value indicates a decrease in Tin. **TB is d e t e r m i n e d f r o m e q n . (10). A positive (negative) value suggests a temperature benefit ( t a k e b a c k ) effect.
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with about 60% of the overall savings attributable to this decline. In Table 4, the only increase in indoor temperature, or negative ATin, is for the most recent period, from 1 9 7 9 - 82 to 1 9 8 3 - 85 (period 3 to 4), suggesting a reversal of this earlier trend. The associated negative estimate for TB indicates a takeback effect of 2.1 GJth/year, and thus that the savings from period 3 to 4 would have been about 20% larger in the absence of the temperature increase. When the entire post-embargo period is considered, from 1 9 7 0 - 73 to 1983 - 85 (period 1 to 4), this reversal has little effect on the overall drop in indoor temperature: the estimates for ATin and TB are quite similar to what t h e y were for the post-embargo decade (period 1 to 3). The results in Table 4 assume 5 = 3.9 °C in eqn. (8). We have also repeated the calculations with values of 5 from 2.2 to 7.8 °C (4 to 14 °F), and, where warranted, without the A~/~ term in eqn. (8) (in order to vary the AQ/Q assumption). The resulting sensitivity analysis confirms the tentative conclusions drawn from Table 4. From period 1 to 2, when the assumptions about both 5 and AQ/Q are varied, the estimates for ATi~ range from 1.1 to 1.5 °C, and the TB estimates range from 11 to 15 GJta/year. For subsequent periods, the decline in base level c~ is sufficiently large that a similarly large change in total intrinsic gains Q seems likely. It therefore seems reasonable to trust eqn. (8), and we examine the sensitivity of the estimates to 5 only. From period 2 to 3, the resulting TB estimates cover a sizeable range, from 5 to 12 GJth/year, but all of them represent more than 40% of the total savings. From period 3 to 4, the TB estimates range from --1.6 to --2.3 GJth/year, and thus bracket fairly tightly the takeback effect identified in Table 4. We are led to an intriguing hypothesis, that structural and furnace retrofitting (through a large positive shell c o m p o n e n t B) is beginning to take hold in New Jersey, but that its potential is being eroded slightly by a takeback effect (through negative TB) resulting from a return to higher indoor temperatures. The overall trend since the embargo m a y be a gradual shifting of the dominating conservation source from a decline in indoor temperatures to shell
tightening. Since this hypothesis makes sense in view of the longer lead times needed for structural retrofitting than for thermostat setbacks, it deserves further testing, both with continued PRISM monitoring and also with independent studies. This aggregate analysis has provided an interesting exploration of how well the PRISM reference-temperature estimate may be expected to t r a c k indoor temperature. With the ~ term in eqn. (8) relatively small, the difference between ATin and Ar is influenced primarily by changes in intrinsic gains, which PRISM can track only through ~. The net result appears to be a consistent post-embargo decline in indoor temperature, viewed through PRISM as a drop in T in the four-year period after the embargo and as a drop in intrinsic gains (via ~) coupled with a smaller change in T in more recent periods. Albeit with large uncertainties, this decomposition of total consumption trends has intriguing policy implications for New Jersey. The possible strong role of lower thermostat settings in post-embargo conservation, and the relatively minor, though growing, role of structural retrofitting, translates into optimism that m u c h greater energy benefits from retrofitting are yet to be achieved. Very recent results, through the summer of 1985, urge caution, in that some of those benefits already achieved are possibly being reversed by a return to higher indoor temperatures. Continued analysis of New Jersey data and similar analyses of data bases in other states are needed to test the validity of these inferences.
IN C O N C L U S I O N
As long as the uncertainties of the estimates are carefully assessed, the PRISM refraction approach seems useful for refining the characterization of conservation in large groups of houses. Two test applications, one to individual-house billing data and one to utility aggregate sales data, demonstrate the added insight available from this closer look at P R I S M savings estimates. In both cases, a dominant role for a single component is suggested, namely, shell tightening in the former and declining indoor temperatures in the latter. A third application, reported
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elsewhere [7], again found shell effects to be the primary source of savings. Particularly in view of the far-reaching policy implications that may result, more testing is needed. This should be done with the aid of supplemental survey data, with which the assumptions required for the refraction method, and the resulting conclusions, can be validated. If other tests are successful, the refraction approach will allow the scorekeeper to take the information extractable from energy billing data one step further than was hitherto believed possible. Other papers in this issue provide convincing evidence that extremely reliable estimates of energy savings are available from straightforward, but careful, analysis of billing data. The possibility that additional physical insight concerning the sources of these savings may be gleaned from the same data is indeed exciting, and is well worth further attention.
ACKNOWLEDGEMENTS
Funding for the development of this methodology, which was initially provided by a matching grant from the Ford Foundation and the New Jersey Department of Energy (NJDOE), has been continued by the New Jersey gas and electric utilities and NJDOE. The New Jersey data were obtained from the New Jersey Energy Data System of NJDOE. The Wisconsin data were collected under a contract with the Wisconsin Department of Administration, with supplemental funds from Wisconsin Electric Power Co.; data processing was facilitated by access to the University of Wisconsin Statistics Department's research computer. Portions of this work were completed while one author
(MLG) was at the U.S. Environmental Protection Agency. Both authors would like to thank Andrzej Jaworski and Asit Banerjee for assistance in the Wisconsin data analysis, Cathy Reynolds for assiduously updating the New Jersey results, and Robert Socolow for insightful comments throughout the study.
REFERENCES 1 M. Fels, PRISM: an introduction, Energy Build., this issue, pp. 5 - 18. 2 J. Rachlin, M. Fels and R. Socolow, The stability of PRISM estimates, Energy Build., this issue, pp. 149 - 157. 3 M. Goldberg, A Midwest low-income weatherization program seen through PRISM, Energy Build., this issue, pp. 37 - 44. 4 M. Fels and M. Goldberg, Using the scorekeeping approach to monitor aggregate conservation, Energy Build., this issue, pp. 161 - 168. 5 M. Fels and M. Goldberg, Using billing and weather data to separate thermostat from insulation effects, Energy 9 (5) (1984) 439 - 445 (the earlier version of this paper). 6 ASHRAE Handbook 1981 Fundamentals, American Society of Heating, Refrigeration and Air Conditioning Engineers, Inc., Atlanta, GA, 1981, p. 25.3. 7 E. Hirst and D. White, Indoor Temperature
Changes after Retrofit: Inferences Based on Electricity Billing Data for Nonparticipants and Participants in the BPA Residential Weatherization Program, Report No. ORNL/CON-182, Oak Ridge National Laboratory, Oak Ridge, TN, July 1985. See also earlier study: E. Hirst, D. White and R. Goeltz, Indoor temperature changes in retrofit homes, Energy 10 (7) (1985) 861 - 870. 8 E. Hirst, Electricity savings one, two, and three years after participation in the BPA Residential Weatherization Pilot Program, Energy Build., this issue, pp. 45 - 53. 9 Office of Demographic and Economic Analysis,
New Jersey Preliminary Census Counts of Population and Housing: 1 April 1980, New Jersey Department of Labor and Industry, Trenton, NJ, December 1980.