forecasting of electricity demand by end-use characteristics
TRANSCRIPT
Electric Power Systems Research, 6 (1983) 177 - 183 177
Forecasting of Electricity Demand by End-Use Characteristics
T. N. GOH
Industrial and Systems Engineering Department, National University of Singapore, Singapore 0511 (Republic of Singapore)
S. S. CHOI and S. B. CHEN
Electrical Engineering Department, National University of Singapore, Singapore 0511 (Republic of Singapore)
(Received April 7, 1983)
SUMMARY
Effective forecasting requires that efficient use be made o f the information contained in the available data so that essential data prop- erties can be extracted and projected into the future. As an alternative to econometric methods for electricity demand forecasting, which are subject to errors and uncertainties in model specification and knowledge o f causal variables, time series analysis has the advantage o f being statistically adaptive to data characteristics. Through a comparative study with data f rom more than six years, it is demonstrated that good forecasting results can be obtained with an approach based on stochastic time series modelling o f homoge- neous sectors o f electricity end users. This refined approach outperforms both conven- tional data smoothing techniques and time series modelling o f aggregate demands.
methods of forecasting, ranging from simple data extrapolation techniques to complex econometric models. The choice of a specific approach depends upon considerations such as the required quality of forecasts, availabil- ity of input information, ease of application, and cost of adoption. These factors are not necessarily compatible, calling for a search of cost-effective compromises or variations in many cases.
From the point of view of information utilization, forecasting efficiency is enhanced if the model-building process is based only on routinely available information, and models are structured in such a way that the existing data format can be exploited for model refinement. This aspect of forecasting, in addition to the general principles set out in the previous paragraph, is featured in the study described in this paper.
1. INTRODUCTION
Forecasting of electricity demand is a recurrent, yet by no means routine, require- ment in the management of utilities. Usually difficulties in forecasting stem primarily from complexities in patterns of electricity con- sumption and the variability of such patterns over different periods of time. Most forecast- ing efforts entail the characterization of patterns and variabilities through mathemat- ical models, which in turn project the essen- tial information into the future. Various degrees of sophistication exist in available
2. STUDY BACKGROUND
The electricity supply of the Republic of Singapore, a city-state in Asia with a popula- tion of about 2.3 million, is the responsibility of a single authority, namely the Public Util- ities Board (PUB). In the past decade, short- term forecasting has been carried out by both the Corporate Planning Department as well as the Electricity Department of the Board. The methods used were mostly fitting of causal (regression) models to data on factors such as the gross domestic product (GDP), popula- tion, output of the manufacturing industry, and number of units of public housing [1, 2].
0378-7796/83/$3.00 © Elsevier Sequoia/Printed in The Netherlands
178
This approach faces the difficulty of model specification and unreliability in the knowl- edge of the variables involved. It was pain- fully noted that forecasting of economic indicators is a major exercise in itself, and un- certainties associated with future values of these variables in a given model will contrib- ute to further errors in electricity demand forecasts.
An alternative to the econometric approach is time series analysis. The only information required in time series analysis is historical data on electricity demand, which are readily available. The stress is on data characteriza- tion rather than on cause-and-effect investiga- tions, and errors in time series forecasting are affected only by methods of projection of data characteristics, not the lack of knowl- edge of factors in a model or errors in model specification. A comparative s tudy of the effectiveness of several time series fore- casting techniques has been conducted with PUB data [3], leading to the conclusion that the Box-Jenkins method of stochastic modelling is superior to conventional methods such as moving average and exponential smoothing, at least in the particular study. As a further phase of the forecasting effort, a more sophisticated data t reatment is now employed with the objective of improving modelling and forecasting accuracy.
3. DATA DESCRIPTION
It is noted that data on national electricity consumption are actually the aggregate of several recorded components, since various tariffs are set by the PUB for different categories of users of electricity. Instead of modelling and forecasting a single aggregate time series, as has often been done in past studies, it would be more logical to examine the consumption patterns of each of the homogeneous sectors of end users. An added advantage is that the forecasting results not only can be aggregated for load management, but will also serve as inputs to financial analysis and marketing projections.
Altogether six mutually exclusive categories of users are defined by the PUB: domestic, non-domestic, entertainment, public lighting, industrial, and non-industrial; the first four use low-tension supplies and the
last two high-tension. Data on monthly demand by these users from January 1975 to June 1981, a total of 78 months, are avail- able. The data reflect the 'post oil-crisis' economy and cover sufficient time for meaningful modelling studies. To eliminate the effect of unequal number of days in a month, the data are 'normalized' by means of division of each value by the appropriate number of days in the month, so that what- ever seasonality properties found to be present in the data are solely due to demand fluctuations. Subsequently, the forecast values are reverted to their untransformed values through the appropriate multipliers.
The electricity demand data of two well- defined end uses, domestic and industrial, are shown in Figs. 1 and 2 respectively. The time series are based on daily demands averaged over each month. An increasing trend and a discernable seasonality are noted in both series. Since Singapore is situated some 70 km from the Equator, the climate is relatively uniform throughout the year and has negli- gible effects on electricity consumption. How- ever, it is interesting to note that during February, in which the Lunar New Year falls and many festivities take place, domestic consumption sharply increases; on the other hand, a dip in industrial consumption is evi- dent during the January-February period, when most plants shut down for days on end for the holiday season. Data characteristics such as these will invariably be lost if the analysis is based on aggregate consumptions. The other sectors are relatively free from effects of the long holiday period and seasonality is less marked. Together with the aggregate data, a total of seven time series are available for analysis.
4. FORECASTING METHODS
In this study, the last 12 points of each of the time series are not used for the modelling process so that they serve to check the accuracy of forecasts based on information contained in the first 66 points. Accuracy of forecasts is expressed through the common criterion of mean squared error:
1 N = - Y , , ( x t - ~ t ) ~ (1) MSE N ~= 1
@ February
Xt
3.5
2-5
2.0
1.5
1.0
05
GWhr/day
179
i i i
0 10 20 30
Fig. 1. Monthly electricity demand of domestic users.
I I i i
40 50 60 70 |
Xt
7.(
6.0
5-0
4-0
3-0
2.0
GWhr/day
Fig. 2. Monthly electricity demand of industrial users.
i 5 ~ , 7 ~ - 40 0 60 0 t
180
where x t and 0e t are the actual and forecast value, respectively, at time t ( t = 1 , 2 , . . . , N), and N is the total number of forecasts. A collection of forecasting techniques of varying degree of sophistication is at tempted so as to answer the following questions:
(1) Do the specific data characteristics asso- ciated with different end users call for differ- ent forecasting techniques ?
(2) Is forecasting by sectors of users a demonstrably better approach than aggregate forecasting ?
The techniques, chosen for their suitability for short-term forecasting, are conventional smoothing methods (single and double mov- ing averages, single and double exponential smoothing) and stochastic modelling. Their principles or theoretical foundations are well established [4, 5] and need not be elaborated here. For stochastic modelling, the notat ion as set out by Box and Jenkins [6] is followed: for a time series Xl, x2 . . . . . B is a backward shift operator such that
B m x t = x t m, B " B m x t = B n ( B m x t )
where m and n are positive integers. Thus, for example, a model of the form
(1 --B)(1 -- )~IBS)(1 -- ~blB -- ~ 2 B 2 ) x t
= (1 -- 71B8)(1 - - O 1 B ) a t (2)
reflects a linear trend and S-period seasonality in the observed xt series, and kl , ~bl, ~b2, 71, and 01 are model parameters estimated by the method of least squares. The model is a statis- tically adequate representation of the x t series if values of the at series are normally and in- dependently distributed with zero mean and constant variance, i.e. no further statistical properties of x t are left unmodelled. Model identification, parameter estimation and statistical checking for model adequacy constitute a complete modelling routine, which is followed by derivation of the fore- casting equation by simple algebraic manipulations [5, 6]. Some typical adapta- tions of the Box-Jenkins approach are re- ported [ 7 - 9 ].
5. COMPARISON OF TECHNIQUES
The results of analysis and forecasting of seven time series are summarized in Table 1. The relative importance of each sectorial
series is reflected by its percentage contribu- tion to the total series, and the MSE values for 66 months of forecasts obtained by various techniques are exhibited and ranked in reversed order of magnitude. Thus the best and worst forecasts for the domestic series are given by Box-Jenkins methodology and double moving averages respectively. This is also found to be true for all the six sectorial time series. In fact, the MSE rankings may be combined so that, for a given technique, a weighted ranking index is given by
6
= ~ , p i r i (3) i= l
where, for series i, Pi and r i are the percentage contribution and technique ranking respec- tively. The computed indices are shown in the last row of Table 1. It is noted that for fore- casting the total series, Box-Jenkins meth- odology and double exponential smoothing remain the best and second best respectively.
It is evident from the results that various forecasting techniques do perform differently for different time series, indicating that sec- torial data characteristics could dictate the suitability of a particular technique: for example, although single exponential smooth- ing is a poor technique for handling the domestic and industrial series which, as noted earlier, have high seasonality patterns, it can be used to forecast entertainment and public lighting demands, which are not seasonal. Another significant observation is that Box- Jenkins methodology consistently outper- forms other techniques, a conclusion also reached in an earlier study [ 3 ].
6. COMPARISON OF MODELS
The superiority of Box-Jenkins methodol- ogy stems from the fact that each stochastic time series model is built specifically with reference to the distinct statistical properties of the data, and model adequacy must be verified by formal statistical tests before fore- casts are made. In contrast, other techniques are based on pre-set rules for data extrapola- t ion and do not possess any adaptive capabil- ity: for example, once the smoothing con- stant is fixed, no flexibility is possible in an exponential smoothing process.
TA
BL
E 1
Co
mp
aris
on
of
fore
cast
ing
tec
hn
iqu
es
Use
r S
ecto
rial
co
nsu
mp
tio
n
(~)
MS
E f
or 6
6-m
on
th f
ore
cast
s an
d r
ank
ing
SM
A
DM
A
SE
S
DE
S
BJM
Mu
ltip
lier
fo
r M
SE
1. D
om
esti
c 1
7.0
1
.72
(3)
2.2
2(5
) 1
.85
(4)
1.6
5(2
) 0
.44
(1)
x 10
-2
2. N
on
-do
mes
tic
38
.2
4.3
1(4
) 4
.46
(5)
4.2
9(3
) 3
.93
(2)
3.0
8(1
) x
10 -2
3.
En
tert
ain
men
t 0.
5 0
.71
(3)
0.9
8(5
) 0
.70
(2)
0.7
2(4
) 0
.70
(1)
x 10
-4
4. P
ub
lic
lig
hti
ng
1.
0 0
.21
(4)
0.2
2(5
) 0
.19
(2)
0.2
0(3
) •
0.1
9(1
) x
10 -4
5.
In
du
stri
al
34
.4
6.5
7(3
) 8
.76
(5)
7.4
1(4
) 6
.49
(2)
3.8
9(1
) x
10 -2
6.
No
n-i
nd
ust
rial
8.
9 0
.53
(2)
0.6
8(5
) 0
.63
(4)
0.5
6(3
) 0
.53
(1)
x 10
-2
7. T
ota
l (s
ingl
e fo
reca
st)
10
0.0
2
7.9
6(4
) 2
7.2
3(3
) 2
9.3
1(5
) 2
7.0
8(2
) 1
9.2
6(1
) x
10 -2
Wei
gh
ted
tec
hn
iqu
e ra
nk
ing
in
dex
(se
ries
1 -
6)
(3.3
) (5
.0)
(3.6
) (2
.1)
(1.0
)
SM
A:
sing
le m
ov
ing
ave
rage
; D
MA
: d
ou
ble
mo
vin
g a
vera
ge;
SE
S:
sing
le e
xp
on
enti
al s
mo
oth
ing
; D
ES
: d
ou
ble
ex
po
nen
tial
sm
oo
thin
g;
BJM
: B
ox
-Jen
kin
s m
eth
- o
do
log
y.
TA
BL
E 2
Co
mp
aris
on
of
tim
e se
ries
mo
del
s
Use
r M
od
el
MS
E f
or
66 m
on
ths
MS
E f
or 7
8 m
on
ths
1.
Do
mes
tic
(1 -
-B)(
1
--B
12
)(1
+ 0
.49
7B
)x
t =
(1 -
- 0
.93
0B
12
)(1
+
0.7
89
B)a
t
0.4
4 X
10
-2
0.5
0 X
10
-2
2.
No
n-d
om
esti
c (1
--B
)(1
--
0.6
50
B1
2)(
1
+ 0
.61
1B
+ 0
.50
0B
2)x
t =
a t
3.0
8 x
10
-2
3.1
4 x
10
-2
3.
En
tert
ain
men
t (1
--B
)x
t =
(1 -
- 0
.75
0B
)a t
0
.70
x 1
0 -4
0
.62
x 1
0 -4
4.
P
ub
lic
lig
hti
ng
(1
--B
)x
t =
(1
-- 0
.45
0B
)a t
0
.19
X 1
0 -4
0
.18
x 1
0 -4
5.
In
du
stri
al
(1 -
-B)(
1
-- 0
.67
5B
12
)(1
+
0.8
05
B +
0.6
10
B2
)xt
= a
t 3
.89
x 1
0 -2
4~
90 x
10
-2
6.
No
n-i
nd
ust
rial
(1
--B
)(1
+
0.7
31
B +
0.3
33
B2
)xt
= a
t 0
.53
x 1
0 -2
0
.75
x 1
0 -2
7a
. T
ota
l (s
ingl
e fo
reca
st)
(1 -
-B)(
1
-- 0
.67
5B
12
)(1
+
0.8
03
B +
0.5
35
B2
)xt
= a
t 1
9.2
6 x
10
-2
21
.95
x 1
0 -2
7b
. T
ota
l (c
om
bin
ed f
ore
cast
) S
um
of
valu
es f
rom
6 s
ecto
rs
14
.43
× 1
0 -2
1
8.0
7 ×
10
-2
b~
182
Xt
15.0
10.0
GWhr/doy
/
t / \
~,/~ ,¢~/~t ~ / , , . ~ . . _ . _ . / , , . ~x " - - . . . . Forecost
Actual
5.0
~ , i * * I I a
0 1 10 20 30 40 50
Fig. 3. Monthly total demand and combined forecast.
50 70
For further examination of the results, the time series models are exhibited in Table 2. It is seen from the Table that all the time series are brought to stationarity by the difference operator 1 - - B . The strong seasonality of demands of domestic, non-domestic and indus- trial users is reflected by 12-month seasonal parameters in the respective models. In fact, domestic and non<lomestic consumptions are described by the same model form; inasmuch as together they constitute 72.6% of the total consumption, the same model form has been found adequate for characterizing the total consumption as well. Entertainment and public lighting, having no seasonality, share another common model form. These results vividly point to the need for separate charac- terization of demand patterns according to end users.
As for performance in forecasting, the capability of a given model in describing data from 66 months is reflected by the MSE, and forecasting capability may be judged by the MSE for forecasting values of the subsequent 12 months. The data in Table 2 suggest that industrial use of electricity is the most dif- ficult to characterize and forecast, which may not be surprising in view of the fact that the level of industrial activities was often subject to sudden shifts during the period of fast
economic growth in Singapore after the 1973 - 74 oil crisis.
It may be noted that there are two ways to forecast aggregate electricity demand. The usual approach is to model the total demand time series and obtain single forecasts from the resulting model. An alternative is to ob- tain separate models and forecasts for differ- ent users first, then combine the individual forecasts together. It is seen from Table 2 that the second method, which in this particular study entails forecasting of six components, is clearly a superior one, yielding 66-month and 78-month MSE values (0.1443 and 0.1807} that are 25% and 18%, respectively, lower than the corresponding values (0.1926 and 0.2195) associated with single forecasts. A plot of the combined forecasts is shown in Fig. 3. The reduction in MSE is so significant that the extra effort in modelling six time series instead of one can be well justified.
7. C O N C L U S I O N S
Results of this study lead to two useful conclusions. First, stochastic time series modelling and forecasting is shown to yield better results in electricity demand forecast- ing in comparison with conventional methods
of da ta ex t r apo la t i on . This is because these mode l s specif ical ly t ake into a c c o u n t the pre- sence o f a n y t r end , seasonal i ty , and s tochas t ic d e p e n d e n c e exis t ing in t he pas t da ta , whereas in m e t h o d s such as exponen t i a l s m o o t h i n g , da ta weigh tage schemes are arb i t rar i ly im- posed on the da ta r a the r t h a n derived f r o m them, and are hence devoid o f any adapt ive capab i l i ty to suit da ta pa t t e rn changes. Second ly , the adap t ive p r o p e r t y o f s tochas t ic mode l s should be fu r t he r exp lo i t ed b y its app l ica t ion to c o m p o n e n t series f r o m differ- en t end uses. C o m b i n a t i o n o f forecas ts for sectors o f h o m o g e n e o u s end users wou ld yield a m o r e accura te f u t u r e value o f to ta l electric- i ty d e m a n d than forecas t ing wi th a single aggregate mode l . A forecas t ing s t ra tegy based on s tochas t ic mode l l ing o f end-use charac te r - istics, a d m i t t e d l y requir ing m o r e e f fo r t a t the mode l -bu i ld ing stage, should p rove cost- ef fec t ive in the long run in view o f the vast ly i m p r o v e d accuracy a t ta inable .
ACKNOWLEDGEMENT
The authors are indebted to the Public Utilities Board, Republic of Singapore, for supplying the data used in this work and are grateful for the cooperation extended by its staff during the course of the study.
183
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