Indices of energy consumption: An exploratory analysis of a utility's monthly billing data

Enrrq> Vol. 5. pp. I I I7- I I30 Pergamon Press Ltd.. 1980. Printed tn Great Britain

INDICES OF ENERGY CONSUMPTION: AN EXPLORATORY ANALYSIS OF A UTILITY’S MONTHLY BILLING DATA-t MARGARET F. FELS Center for Energy and Environmental Studies, Princeton University, Princeton, NJ 08544, U.S.A.

and THOMAS H. WOTPKI Office of Consumption

Data Studies, U.S. Energy Information Administration, Washington, DC 20461, U.S.A. (Received

1 November

1979)

Abstract-Simple weather-sensitive models are derived and applied to monthly energy billing data for a large utility region in New Jersey. Natural gas demand in the residential sector is explored in depth, and the method is applied to other gas and electricity sectors. The results are related to an earlier empirical study of single-family residences. Our findings and hypotheses fall into two classes, those which are specific to the utility’s customers and those which pertain to utility data in general. As for the specific utility’s residential gas customers, the findings suggest that they reduced their use of gas during the oil embargo of 1973-74 and the New Jersey natural gas shortage of 197677, and, most likely, the consumption reduction was due to lowered thermostats and reduced use of appliances rather than to retrofitting of dwellings. The more general findings are that utility data can be very valuable for monitoring changes in consumption patterns, and that there is a potential for extracting consumption indices from the data; these indices would not only signal whether consumption patterns are changing but also why. The first of our conclusions needs to be examined for other sample data sets and other regions. The second, our most important hypothesis, merits systematic investieation.

1. INTRODUCTION

AND

SYNOPSIS

As awareness of possible fuel shortages and resulting high energy prices has increased, so has the need for information on how and where energy is used, how patterns of use have changed, when these changes occurred relative to economic and political events, and what changes can be expected in the future. Federal and state officials, and many consumers as well, need data for describing, monitoring and forecasting energy consumption practices. In particular, there is a keen interest among policy makers and analysts in the changes in energy consumption associated with the embargo of 1973-74 or with the various appeals of national and state leaders to conserve energy. In addition, questions of how to determine whether and how much conservation has taken place in the recent past and how responsive the population might be to conservation policies will loom large as such policies receive greater attention. In this paper, we explore the potential usefulness of monthly billing data from electric and gas utilities for describing and monitoring energy consumption. Our analyses indicate that a great deal can be learned from these data about the aggregate physical and statistical characteristics of residential and commercial energy consumption, and that there is a large potential for developing important indices of consumption for these sectors. tThe research for this report was begun during 1978 while both authors were members of the Center for Energy and Environmental Studies, Princeton University. The opinions expressed here are solely those of the authors. 1117

1118

MARGARET F. FELS and THOMASH. WOTEKI

Our findings are based on a series of exploratory data analyses of a variety of data generously supplied by the Public Service Electric and Gas Company (PSEG), New Jersey’s largest utility. One of these analyses, which is based on billing data for the utility’s residential gas customers, is presented in some detail. Three other analyses, of electricity demand in the residential sector and gas demand in two other sectors, are reviewed briefly to explore their similarities to the residential gas analysis.? Many utilities make extensive use of their own billing data to forecast demand for their utility regions. PSEG is an excellent example, with sophisticated forecasting capabilities. We do not intend to duplicate or pretend to improve on their methodologies. Rather, our interest is in relatively simple analytic techniques which might be applied to data from several utilities to provide tools for monitoring energy use at the state or national levels. Analyses of a large utility’s accurate billing data provide an excellent starting point. In Section 2, we take a wide-angle view of the data to obtain a picture of historical trends in gas consumption and growth in the number of customers. We conclude the section by closing in on the data from 1970 to 1978 and fitting a simple linear model to associate the variation in the gas billing data with climatic variations. In the third section we review an earlier, empirical model for energy flows in individual residences, use it to suggest how the parameters of the present model might be used as indices of energy consumption, and discuss the implications of interpreting the coefficients in this way. In Section 4 we review some of our other analyses thereby reinforcing the findings based on the residential gas data. All of the findings resulting from this research are in the form of hypotheses flowing from a series of exploratory data analyses of a utility’s billing data, and in this spirit we make no claims to have developed the “best” model of energy consumption. We may define exploratory data analysis as a body of techniques for summarizing and exposing data and ferreting out hypotheses and likely fruitful lines of investigation. Or, as Tukey’ says, exploratory data analysis is “looking at data to see what it seems to say” while recognizing that “[it] can never be the whole story, but nothing else can serve as a foundation stone”.

I I960

I I%5

I 1970

I 1975

1978

Fig. 1. Yearly variation of average residential gas demand per month compared with the total number of customers served by the utility. 2. EXPLORING

GAS

BILLING

DATA

(a) A wide-angle view The monthly billing data supplied by PSEG include the number of residential customers billed and their total monthly demand for natural gas, from January 1960 tAl1 of the results summarized here are described in considerable detail in a technical report’ available through the Princeton University Center for Energy and Environmental Studies.

Indices of energy consumption

?5:

70-

“E ;

65-

: E

60-

2 t -

0

o 55-

9 ; cr

0

o

0

50-

45-

I

0 1

I960 Fig. 2.

I

1965

I

1970

I

1975

1978

Yearly variation of average residential gas demand per customer per month (RESGAS).

through February 1978. To begin our exploratory analysis, these data were averaged over months within years, as plotted in Fig. 1.t It is immediately apparent that average monthly demand and the number of customers billed both rose steadily until about 1970 at which point some flattening in both trends occurred. To examine whether per-customer demand similarly increased over this period, we turn to Fig. 2, where we display the values of RESGAS, or average demand per customer, averaged over months within years. Explicitly, we define RESGAS as the average demand, in therms per customer (T/cust), computed from the total amount of gas for which customers were billed during a month divided by the number of residential gas customers billed during that month.$ As can be seen, average demand rose steadily from 1960 to 1970, indicating that the increase in total demand was due not only to an increase in the number of customers but also to a marked change in consumption habits or the stock of gas-consuming appliances: an increase in the proportion of gas-heated homes is an example. At first sight, the flattening in RESGAS beyond 1970 is not surprising: since the number of billed customers stabilized, we would expect average demand to exhibit stability. However, demand fluctuations in recent years are evident from Fig. 2, and additional information is required to explain to what extent these fluctuations are caused by variations in the severity of cold weather or changes in consumption habits within the fixed-customer base. As portrayed in Fig. 2, the latter effects would tend to be obscured if they were small relative to weather-related changes in demand. (b) Zooming in: the seasonal component We turn now from average yearly to average monthly values for RESGASG, as shown in Fig. 3. A large seasonal component in average demand is evident, with typical values ranging from 25 T/cust in August and July to about 130 T/cust in January. Also displayed in Fig. 3 are typical values for monthly degree-days from January 1960 to February 1978 for the New Jersey weather station to be used in this study (Newark)./ There is tWe have adopted the convention that a year runs from August to July so that it contains a complete heating season, and that years are dated by the January they include, so that 1970 refers to the period from August 1969 to July 1970. The “averages” as computed include some weighting of outlying values, and differ a small amount from simple arithmetic mean values. tl therm = 10’ Btu and corresponds to _ lo2 SCF of natural gas. $The January average value, for example, represents the mean of all January values in the ninteen-year sample. l/The number of (heating) degree-days in a month is a crude but standard measure of the coldness of a month. If T is the average temperature in “F for the ith day in a month, then (65 - I;) is the number of degree-days for that day, provided the difference is positive, and is zero otherwise. The sum 2(65-‘1;) over the days in a month is the number of degree-days in the month. The degree-day data used in this report are taken from NOAA publications.3 The use of a single location’s weather data is justified in the earlier report.’

MARGARETF. FELSand THOMASH. WOTEKI

I120

f - 1000

E I:

-800

-600 -400 -200

I

I

AUG

1

NOV

I

zP 8

zi g P ‘Z P

I

1

FEB

i?

MAY

JUL

Fig. 3. Comparison of monthly variation of per-customer residential gas demand (RESGAS) with heating degree-days (HD). Data for each month are averaged over all years, from 1960 to the present.

a strong indication that the seasonal variation in average demand is closely associated with the variation in monthly degree-days, so that removing this component of variation might reveal other currently obscured variations in demand. This weather-related component of demand is not surprising of course: one of the primary uses for gas is space heating and the colder it is the more gas we would expect the utility’s customers to use. In addition to indicating that we might profit from removing the seasonal variation in demand, these data also suggest what form the adjustment might take. Figure 3 shows that the gas demand lags degree-days by approximately half a month. This can be explained from the fact that our data originate from meter readings. A meter read on the first of the month is for consumption during the previous month; a meter read on the last day of the month is for consumption during that month. Very crudely put, if demand is related to the coldness of a month then about half the gas demand billed in a month is related to the weather in the previous month and half is related to the current month. This explains the lag behavior in Fig. 3 and suggests that we should adjust the variation in RESGAS for variations in a lagged heating degree-day variable, AHD, where AHD is the average of the degree-day values for a month and the month previous. From this point on, we restrict our attention to the monthly data from August 1969 to February 1978, in order to focus on a time period exhibiting relative stability in gas demand. During this period, not only did the total number of customers and their total demand stabilize (Fig. l), but the fraction of residential customers with space heating (vs those without) and the number of customers with gas water heating also leveled off.? Although the significant demand increase prior to 1970 is of historical interest, we will not explore that segment of the data here. Our goal will be to explore the fluctuations in recent average demand and, in particular, the variation in demand which cannot be attributed to changes in degree-days. Consistent with our discussion concerning Fig. 3, we fit the coefficients o! and /I in the equation RESGAS = a and /.IAHD + RESIDUAL

(1)

tin the 1960s the fraction of gas residential customers with space heating increased by 66% while the corresponding increase between 1970 and 1977 was.only 14%, with a leveling off to only 1% in the last year. The follow-up study to this one will analyze the PSEG residential heating customers separately from these without heating. In addition, the study will apply a similar analysis to billing data from other, smaller utilities, in order to assess the reliability of utility data in general. (Long experience with PSEG, a large utility with sophisticated computerized data bases, attests to the accuracy of the data upon which the present analyses are based.)

Indices of energy consumption

1121

Table 1. Results of fitting eqn (l)* to monthly billing data.** Meall

Variable AHD

AHD = 410.8

(‘F-day)

Intercept 4 -

44.9

a = 27.6

Standard

Error

from

0.119

Standard

Error

of

R2 = n.988;

*RESGAS

= a + 6

**Billing Electric

data and

Deviation

376.1

RESGAS = 76.3

RESGAS(T/cust/mo)

Slope

Standard

ReRression

6 = 1.3

number

of

x 10

months

-3

5.0+ .

~103

ARD + RESIDUAL. from August Gas Company

1969 to February in New Jersey.

t ‘he

standard error from a regression squared residual and thereby measures

1978

are

from

is the square the averaRe

Public

Service

root of the average size of the residual.

by using ordinary least-squares regression analysis. The results are displayed in Table 1. Judging by the value R2 = 0.988, we have secured an excellent fit to the data. The results indicate that, in a month with no degree-days, RESGAS was typically 27.6 therms per customer, and that, for each 100 degree-day difference in a pair of months, average demand tended to differ by 11.9 T/cust. In Section 3, we will attribute a physical meaning to the coefficients a and B. For analyses of this type, the R2 value is only one measure of the goodness of fit and even well fitting models may not explain all of the structure in the data. We turn our attention now to a critical evaluation of the goodness of fit of eqn (1) to the data. (c) A look at the residuals

An examination of the values of the RESIDUAL component from eqn (1) is enlightening. These are displayed in Fig. 4 where they are plotted against time; they are summarized in Fig. 5 by averaging over months within years to give average residual vs year. The

15

0

t

cl0

IO

OO 0

0

0

00

0

t 0

5

0 00

o

00

0

Oo”

0

0

O0

0

0

0 0

0 00

0~~--0-_00

@O

8

0

0 _

0

0 og=

0@

“,_

OO O0 -5

dD0

0

0

0

i

00

0

o~*:oo

0

0 0

0

0

00 0 0

OQ)

-20 AUG. I969

AUG.1971

AUG.1973

AUG.1975

AUGl977

Fig. 4. RESIDUAL results from a fit of residential gas demand (RESGAS) to eqn (I). Em 5/t t-c

MARGARET F. FELS and THOMAS H. WOTEKI

1122

Fig. 5. Average

values

of TREND

by year

for a fit of residential eqn (1).

gas demand

(RESGAS)

to

residuals are not scattered randomly about the value zero and both plots indicate a distinct time trend in this degree-day independent component of demand. The striking feature in Fig. 5 is the smooth increase in the residuals from 1970 to 1973, followed by a sharp drop in 1974 and another after 1976. The latter drop contrasts with the increase in total demand per customer observed in Fig. 2. Only when the extremely cold winter of 1977 is accounted for can one notice an effective decrease in demand from what would otherwise have occurred. In relative terms, the weather-independent percentage decline between 1973 and 1974 may be estimated by comparing the actual total for RESGAS during 1974 with the value we would expect for that year knowing the total number of degree-days and assuming that 1974 would duplicate 1973 in all other respects (see Ref. 1). Thus residential gas consumption in 1974 represents approximately a 4.8% drop from what would have occurred without some change in the trend; a similar decline for 1977 is computed to be 5.0%. This pattern of change in the residuals suggests some interesting hypotheses concerning changes in consumption habits among the utility’s residential customers. We return to a discussion of these changes when we examine conservation effects (Section 3b). In spite of the high R2 value, therefore, the residual plots suggest some systematic behavior not explained by the degree-day dependent component alone. This systematic variation can be eliminated by fitting a separate intercept term (a) for each year of data. As we shall see, such an adjustment to the fitted equation has important implications in terms of the hypotheses suggested by the data. Therefore, we make some effort to assess the stability of the fitted coefficients. The technique we use is the jack-knife, described in Mosteller and Tukey4 as a general-purpose method for assessing the instability or variability of a statistic, i.e. the “direct assessment” of instability. (d) Closer still: yearly intercepts Our data have a natural hierarchy: we can group months into years (from August to July inclusive, as before). The idea of the jack-knife applied to eqn (1) is to assess the effect of each year of data on the stability of the fitted coefficients, not by using the data for that year alone, but by examining the effect upon the entire set of data that results from omitting that year. The results, with explanation, are displayed in Table 2. Included in Table 2 aie relative standard errors as estimated from the jack-knife. The relative standard error of a statistic is a measure of its year-to-year variability, independent of the units of the coefficients. As can be seen from the ratios of relative errors

1123

Indices of energy consumption Table 2. Jack-knife statistics for Value from Table 1

Coefficient (a)

Jackknifed’ Value

27.58

6

(+a:

0.5518

0.1184

7.2U1.99

HelaCiVe Variability

(S;7 )

27.66

0.1186 Rati0s:

and /I in eqn (1).

Jackknifed“ Variability

(2,)

a

a

2.794 x 10 -6

= 3.62,

2.68611.412

Relative Standard E?XClr (S*/Z*)

)

7.21 x 1O-4

2.686

x 1O-2

1.99 x 10 -4

1.412

x 1O-2

= 1.90

.-Given data yij which are organized into n groups (1 < i < n1 of k values (1 < I < k). which in our analvsis corresuonds to monthi\; values oraanized bv heating ye.&, we compute the jeckknife v&e as follows:. Let 2 be ;he v lueof a statistic, such as E, computed using the complete data .set and let g ? i, be the same statistic computed using all data except the ith group, 12 I 5. n. Then let Zi = ng - (n-1)2(i) and g* = Z Zi/n. The latter is the jackknifed value of g and Sg = I: (gi - 2*)2/n(n-1) is the jackknife estimate of variability. Thus Sg estimates the variability in ;J* which is inherent in grouping the data into n groups.

presented in the table, the relative standard error of a is nearly twice that of B indicating that the year-to-year variability of a is greater than that of j?. With this strong indication that p is relatively stable, the patterns in Figs. 4 and 5 suggest that a separate value of a should be obtained for each year of data. Table 3 shows the results of fitting the equation RESGAS,, = a + ai + fi AHDij + RESIDUAL,,, to the data. The subscripting

Zai = 0

(2)

denotes the jth month of the ith year. The coefficient

(a + ai) corresponds to fitting a separate intercept for the ith year, and the constraint Zai = 0 simply expresses tli as a deviation from an overall intercept term a. As expected the values of a, duplicate the pattern of residuals in Fig. 5.

Figure 6 displays the residuals from eqn (2) plotted against time. In contrast to Fig. 4 there are no obvious systematic trends in the plot, the residuals appearing to be randomly scattered around zero. Some remaining systematic structure might yet be revealed through a much closer examination of the data, but such an examination is beyond the scope of the present exploratory analysis. With the results summarized in Tables 1 and 3, we have exposed and summarized the obvious systematic structure in the data, and thereby conclude the statistical portion of our exploratory analysis of these billing data. We turn now to interpreting the fitted coefficients and the implications this has in terms of what hypotheses are suggested by the data and how such data might be used for developing indices of consumption. 3. INTERPRETATION

OF

THE

RESULTS

(a) Interpreting the coeficients In an ongoing empirical study of energy consumption in occupied homes in Twin Rivers, New Jersey,5 the amount of heating fuel (F) needed on a daily basis to maintain a Table 3. Yearly intercepts resulting from fitting eqn (2)’ to monthly billing data. Yearly

a

Coefficient: Fitted

Value:

Residual

*

RESGAQ

cr7o %

27.0

=

-2.4

1.2

?2

a73

a74

m75 ?6

?7

3.5

5.6

2.2

0.6 -0.6

-4.5

Sum of Squares - 1375.2

a+ai

+BAHD ij

+

deviations

;

R2 = 0.993

RESIDUALi,,

Z Oi - 0

“78 -5.6

5 0.119

1124

MARGARETF. FELSand THOMASH. WOTEKI

Fig. 6. RESIDUAL

results from the jack-knife analysis applied to eqn (2) for residential gas demand (RESGAS).

house at a derived fixed temperature

has been described by F = /?(TR - TA)+

(3)

where 7” is the average outside temperature, TR is a reference temperature for the house and fl is an overall performance index for the house which characterizes its response to cold weather. The quantity (TR - TA)+ is equal to (TR - TA) if the difference is positive, and is zero otherwise. According to the theory underlying the model, the reference temperature TR carries information about factors under the control of residents, such as thermostat setting and the added heat load from the use of appliances (electric and gas), and some information about the thermal properties of the housee6 A lowered thermostat setting or increased use of appliances should result in a lowered value of TR. The overall interpretation of TR is that it indicates the warmest outdoor temperature at which the heating system must supply heat to the house, or the effective temperature it must maintain. Although not independent of the physical properties of the house, it is dominated by the actions of the residents. The value of p, in this theory, is independent of the outside temperature and internal and solar heat gains, and indexes the house’s average rate of heat loss and heating system efficiency, factors determined primarily by the design, construction and maintenance of the house.6 Adding insulation or weather-stripping or overhauling the heating system should decrease the value of /?. The empirical analyses carried out in the Twin Rivers program generally support these interpretations of TR and /3.6-” Differences in /I-values among houses were observed to correspond in a way consistent with theory to differences in design and construction characteristics, such as number of bedrooms, presence of double-pane windows and compass orientation of the house, while reductions in j? were observed to coincide with improvements in insulation. ‘-* Also confirming the theory, variations in TR were associated with changes in the behavior of occupants: in one-owner homes, the value of TR changed considerably less than it did in homes that changed owners.6 Additionally, the value of TR was lower among two-bedroom houses than among those with more bedrooms, possibly because the smaller houses tend to be occupied by people without children and are therefore more frequently unoccupied, with the result being lower average interior temperatures.’ The possibility of extending these single-house observations to our findings for a utility’s customers in the aggregate is appealing. To explore this, we extrapolate the single-house theory embodied in eqn (3) to the utility billing data by expressing the equation in a form similar to eqn (1). First, if the heating fuel is gas and a0 is the daily average amount of gas used to fire other appliances such as the water heater, then eqn (3) becomes : F + a0 = a0 + fi(TR - TA)+ .

(4)

Indices of energy consumption

1125

Thus, if the average temperature for a day is less than TR, we may sum eqn (4) over the days in a cold month (when TA < TR) to obtain RESGAS = m{a0 + /?(TR - 65)} + pZ(65 - TA)+ or

RESGAS = u + /? HD

(5)

where m is the number of days in the month and HD is the number of heating degreedays in the month (in “F-day).? Equation (5) is eqn (I) for a single house, that is, eqn (1) can be thought of as having been derived by averaging eqn (5) (for each customer) over all of the utility’s customers. Our approach in this study differs from that taken at Twin Rivers in two major ways. First, the Twin Rivers analysis was designed to identify TR, then find the coefficient p for the variable (TR - TA)+. Our heating coefficient /? is for the variable (65 - T’)+, and a correction term for TR is included in a with the non-heating gas consumption term. Second, the Twin Rivers observations were taken on individual houses with similar structure and occupant characteristics, while each of our observations is aggregated over many thousand different residences. The possible biases introduced by aggregation and by specification of the temperature base for the variable HD need to be explored further in order to allow a more direct comparison of the results of this analysis with those from the earlier single-house studies. Nevertheless, consideration of eqn (1) as an extension of the single-house model provides a valuable framework for interpreting the results presented in the previous section. In summary then, the working hypothesis derived from this physical interpretation of the coefficients in eqn (1) is that b is an average performance index for the dwellings represented in the utility data, and a comprises a combination of the average rate of use of appliances and average reference temperature. Deferring the investigation of the reference temperature component of a to a future study, we will refer here to Q as the baseload consumption and p as the heating coefficient. Two important investigations stem from the working hypothesis. The first is whether and how the utility customers changed their consumption habits in response to apparent fuel shortages. The other, treated later in the section, is the extent to which utility billing data can be used to help develop consumption indices for monitoring changes in factors affecting energy consumption. (b) A conservation hypothesis Let us re-examine Fig. 5 and Tables 2 and 3. The data suggest that the heating coefficient (p) of the dwellings represented in the data remained relatively constant throughough 1970-1978 but that baseload consumption (a) rose steadily from 1970 to 1973$ and then changed abruptly. From 1973 to 1974, the latter heating season being the one which marked the beginning of the Arab oil embargo, there was an evident drop in baseload consumption, and our hypothesis suggests that these residential customers reacted to the oil embargo by turning down their thermostats or by reducing their use of appliances. This drop was followed by a general trend towards lower baseload consumption including another relatively large drop from 1976 to 1977. It was during the heating season of 1977 that New Jersey residents faced a natural gas shortage, which resulted in appeals from the Governor to the residents to turn down their thermostats. The data suggest that they did so. These data alone, of course, cannot provide incontrovertible evidence that these customers actually turned down their thermostats or reduced appliance usage as opposed to retrofitting their houses. This hypothesis is only as tenable as our physical interpretations of the coefficients a and B. Only with supplementary data on the behavior of individual TStrictly speaking, the formal calculations described here apply only when the condition TA < TR 5 65°F (18.3”C) holds daily. In the empirical studies cited above TR = 62°F (16.7”C) on the averar ‘.-he condition TA < TR will almost certainly be achieved in all but the summer and marginal months. $Note that the 1973 data include the 1972-73 heating season, etc.

1126

MARGARETF. FELSand

THOMAS H.

WOTEKI

customers can the hypothesis be verified. However, the hypothesis appeals to reason: assuming customers did reduce their energy consumption on the average, it is more realistic in the short run to expect them to turn down their thermostats than to weatherstrip or insulate. If we accept the conservation hypothesis as given, namely that these customers reacted to the Arab oil embargo and the New Jersey natural gas shortage by turning down their thermostats or curtailing the use of appliances, it is problematic at best to identify to what they were reacting: appeals by state and national officials to reduce energy consumption, for example, or higher energy prices. The possibility that conservation resulted from official public appeals is very attractive but no doubt unverifiable. As for higher prices, a preliminary analysis that we carried out using the dollar value of the utility’s bills (corrected for inflation) indicates that the sharp increase in the average prices paid for natural gas in the residential sector lagged the sharp drop in 1973-74 baseload by about a year and that the relationship between the sharp drop in baseload from 1976 to 1977 and the changes in price over that period are obscure. We can only conclude that the dependence of demand on price, as represented in these data, is very complex and cannot be resolved here with these data alone. (c) Consumption indices

The desirability of being able to monitor and understand changes in consumption patterns brings us to the second major implication of our basic hypothesis: the use of billing data to provide consumption indices. Our analysis indicates that monthly utility billing data could be the basis for a data system to monitor changes in energy consumption among residential customers. Coordinated with field experiments or periodic surveys of individual customers for the purposes of verifying changes in factors affecting energy consumption, billing data could be used to estimate the energy savings from various policies such as increased prices or tax incentives for retrofitting or public conservation appeals. A. national system of this type could help monitor progress towards energy conservation goals or alert officials to abrupt changes in energy consumption patterns. Although many factors need to be considered before this suggestion could be implemented (including, to say the least, gaining the cooperation of the utilities and organizing the data system), the potential benefits appear to be significant. Alternatively, or in coordination with a national system, state-level systems for the same purpose might be developed. Currently, most state governments have access, at best, only to scattered information on energy consumption in their states. Furthermore, the time and dollar cost of collecting detailed data on energy consumption is apt to be prohibitive. Some monthly electricity sales data are published at the state level (by the U.S. Energy Information Administration), but through the lack of federal regulation natural gas utilities do not supply analogous data.? Our analysis indicates that monthly sales data from both the natural gas and electricity utilities operating in a state could be of enormous value to the state’s energy planners. In reality, state-level systems may offer advantages over a single national system not only because of the difficulties of organizing a large-scale national system, but because, in most if not all states, the public utility commissions have set a precedent for regular data submission from all the utilities in the state to the state government.

4. BORROWING

STRENGTH:

OTHER

CUSTOMER

CLASSES

Continuing our analysis of PSEG billing data, we have extended the analysis applied to residential gas demand to several other natural gas sectors, and to residential and tCurrently several states (Minnesota; New Jersey, Wisconsin and others) are successfully obtaining data from their natural gas as well as electric utilities. New Jersey is currently developing an energy data system which will emphasize monthly energy use data for the purposes of seasonal monitoring through analyses such as those described here.’ Through excellent cooperation with all utilities in the state, discrepancies in rate category definitions among utilities have been resolved so that all NJ utilities report sales data in a set of detailed but consistent categories.

Indices of energy consumption

1127

other sectors for another fuel type, electricity. In this section, we briefly review the results of three of these exploratory analyses.? Even if the conclusions drawn from the residential gas analysis applied to that data alone, we feel that the data would be worthy of further attention. The fact that similar results can be seen in the data for other customers then reinforces our conclusion that the potential usefulness of monthly billing data merits extensive investigation. The three classes of customers we consider are: general service commercial gas customers (GSGC), gas heating service (non-residential) customers (HSGS) and residential electricity customers (RESEL). Customers in the first class tend to be small commercial establishments that use gas for space heating, water heating, and cooking. The second class applies to commercial and industrial establishments with a special rate category for building heating. Table 4 displays the results of fitting the analog of eqn (1) to data for the two commercial gas categories, as compared with RESGAS. Also shown is a comparison of relative magnitudes of the heating degree-day coefficients (/3r) in terms of the energy required, as compared with the baseload a, for each increment of 100 heating degree-days. The resulting heating degree-day effect varies from a large value for HSGS to a value two orders of magnitude lower for the GSGC category. In exploring the residential electricity data (RESEL), we observed two seasonal components in the data, one corresponding to the heating season and one for the cooling season. As Fig. 7 indicates, a sharp summer peak due to air-conditioning demand is evident in the monthly variation. We expect that, unlike the model of gas demand, cooling degree-days will be an essential component of our electricity analysis. Note that the billing data for RESEL apparently lag cooling degree-days (CD) by less than 1 month, similar to the observed lag for RESGAS and HD in Fig. 3. Accordingly, the following equation was fit to the data: RESEL = CI+ BIAHD + &ACD

+ RESIDUAL,

(6)

where ACD is the average of the cooling degree-days for a month and the month previous. Since the summer component of demand in residential electricity was seen to dominate the winter component, the electricity data were organized by calendar year rather than August through July. The results of this fit are added to Table 4. Note the relatively high value of the cooling degree-day coefficient &), indicating that for each 100 degree-day difference in a pair of summer months, average demand tended to differ by 74 kWh per customer compared with the baseload of about 320 kWh per customer. In Fig. 8 we have displayed the analog of Fig. 5 for the four customer classes. In the present figure, however, the average values of the RESIDUAL components have been normalized by the appropriate standard error for regression1 displayed in Table 4. The normalization therefore adjusts the scale of the residuals to make the plots readily comparable across customer classes. Explicitly, each normalized value in the plots is of the form: average value of residual within a year + standard error from the regression. Figure 8 shows that all of the year-to-year changes in the normalized residuals are of the same order of magnitude across all classes. In addition, the abrupt change in the patterns of the residuals from 1973 to 1974 is evident. In the classes RESGAS, RESEL, and HSGS, this takes the form of a sharp drop which amounts to a 48% conservation effect (see discussion in Section 2 as well as Table 4), while in GSGC there is a leveling off of an otherwise upward climb. Table 4 shows that the latter sector has the smallest heating degree-day effect, suggesting a much lower opportunity for conservation of heating fuel. In terms of our conservation hypothesis developed earlier for RESGAS, the data suggest that the residential and heating-service customers reacted to the onset of the oil embargo most likely by adjusting thermostats and reducing the use of various appliances. (The jack-knife analysis applied to each customer class would ascertain the extent to which the variation is contained in the a-coefficient.) tThese results, in addition to the results for several additional sectors, are discussed in detail in the technical report,’ along with the results from extensive validity checks and accuracy assessments. $See footnote in Table 1.

category

Heating service (a)

HSGC:

452.7

234.6

64.3

74.1

204.2

13.9

44.9

Results B or 81 13 2

49.6

--

0.0357 --

27.6 0.119

-__._______-i

a

AHD + RESIDUAL

0.04

3.81

0.07

103 96

'lberms/cust/month

376.1 386.8

410.8 403.2

St.Dev.

101.8

--

ACD

0.23

-_

--

-_

0.43

Number of months AHD

kwhlcustlmonth

Units of DEMAND

3.6

5.0

a

a

Degree-day effects B or 61(100) 62(100)

Units of AHD and ACD are 'F-day, giving coefficients B,rCland figin units of DEllANDper 'F-day.

(b) DEMAND = n + BJ AHD + B2 ACD + RESIDUAL

(a) DEMAND = a + B

Model used

0.934

0.988

2Measures of Errox R -Value St. Error

*lhe following models were used as indicated above by (a) or (b):

RESEL: Residential electric (b)

General service commercial (a)

GSGC:

76.3

(Mean Demand) St. Dev

RESGAS: Residential gas(a)

Rate

DEMAND

Table 4. Degree-day analysis for selected customer classes.*

132.7

_-

st.Dev.

-3.9%

-8.1%

__

-4.8%

Estimated conservation effect 1973-4

Indices of energy consumption

1129

HO

RESEL

co

-JAN

Fig. 7. Comparison

APR

-7-v

JUL

DEC

of the monthly variation of per-customer residential electricity demand (RESEL) with heating (HD) and cooling degree-days (CD).

Fig. 8. Comparison of yearly average RESIDUAL values for four customer classes (see Table 4 for a summary of results).

Beyond 1974, the classes diverge. In the RESGAS and HSGS classes there is a noticeable drop in the residuals from 1976 to 1977 coincident with the natural gas shortage. Thus, the pattern of the HSGS residuals is consistent with that of the residential gas data and suggests a conservation hypothesis here also. However, the general service commercial customers (GSGC), the other class of customers presumably directly affected by the gas shortage, show an effective increase from 1976 to 1977. Explaining this contrast in the residual patterns could indicate where attention should be directed in the event of future gas shortages. Finally, the residual pattern for residential electricity (RESEL) customers suggests no particular response to the gas shortage, but the absence of a strong return to the preembargo pattern of increasing residual (degree-day independent) demand. Depending on the validity of the conservation hypothesis, this pattern might be interpreted to suggest a learned conservation behavior. It will be interesting in the next stage of this analysis to monitor whether this trend toward leveled-off consumption is a continuing one. Total electricity demand per residential customer showed a gradual increase from 1974 through 1977 (see Ref. 1). The tapering off of residuals in Fig. 8, in contrast to the increase in total demand, suggests that the increase is due solely to more severe weather conditions. No leveling-off or conservation effect can be seen from the demand-percustomer data alone. As we saw in Section 2 for RESGAS, behavior not evident in the

1130

MARGARETF. FELTand Tno~lls H. WOTEKI

original RESEL billing data becomes apparent ponent is extracted.

when the degree-day

dependent

com-

5. RECOMMENDATIONS

At a time when information on energy consumption is at a premium, it appears that valuable quantitative assessments of energy conservation can be built on basic utility monthly billing data. Our findings indicate that these data can be a rich source both for developing consumption indices and for monitoring changes in consumption patterns across classes of customers. In order to verify the conservation hypotheses posed here, the available utility data must be coordinated with carefully developed surveys or field experiments to form the basis of useful, highly informative and relatively inexpensive energy consumption data systems at the state or national level. The enormous value of utility billing data is realizable once the data are collected on an ongoing, systematic basis as part of a coordinated data system program. Acknowledgements-The authors gratefully acknowledge the generous cooperation of New Jersey Public Service Electric and Gas Company, and thank Miriam Goldberg, who is continuing these analyses as part of her graduate research, for invaluable assistance throughout this work. The work reported here was partially supported by the National Science Foundation’s International Decade for Oceanic Exploration and Climate Dynamics Research Programs, as part of an ongoing project entitled “Seasonal Climate Forecasts of Energy Management” (Principal Investigator, Prof. Edith Brown Weiss, Georgetown University Law Center).

REFERENCES 1. T. H. Woteki and M. F. Fels, “Weather-Sensitive Analysis of Energy Demand: A Case Study in New Jersey”. Princeton University Center for Environmental Studies, Rep. No. 68, Princeton, NJ 08544 (June 1978). 2. J. W. Tukey, Exploratory Data Analysis, pp. V and 3. Addison-Wesley, Reading Mass. (1977). 3. National ,Oceanic and Atmospheric Administration, “Local Climatological Data: Annual Summary with Comparative Data”, and July issue of “Climatological Data: New Jersey” (summary for all stations), National Climatic Center, Ashville, NC 28801. 4. F. Mosteller and J. W. Tukey, Data Analysis and Regression. Addison-Wesley, Reading, Mass. (1977). 5. Energy and Buildings 1 (April 1978; the entire issue is devoted to reports of Princeton University’s energy analysis of Twin Rivers, New Jersey housing). 6. T. F. Shrader, “A Two-Parameter Model for Assessing the Determinants of Residential Space Heating”, Princeton University Center for Environmental Studies, Rep. No. 69, Princeton, NJ 08544 (June 1978). 7. L. S. Mayer and Y. Benjamini, Energy and Buildings 1, 30 (1978). 8. T. H. Woteki, “The Princeton Omnibus Experiment: Some Effects of Retrofits on Space Heating Requirements”, Princeton University Center for Environmental Studies, Rep. No. 43, Princeton, NJ 08544 (Dec. 1976). 9. M. F. Fels, ‘Choosing Data for an Energy Data System: New Jersey as a Case Study”, Princeton University Center for hvironmental Studies, Rep. No. 84, Princeton, NJ 08544 (May 1979); presented at ORSA/ TIMS Joint Nat. Meeting, New Orleans, May 1979.