Engineering, 2013, 5, 108-114
doi:10.4236/eng.2013.51b020 Published Online January 2013 (http://www.SciRP.org/journal/eng)
Copyright © 2013 SciRes. ENG
Seasonal Regression Mod els f or Elect ricit y Consumption
Characteristics Analysis
Yusri Syam Akil1,2, Hajime Miyauchi1
1Department of Frontier Technology for Energy and Devices, Kumamoto University, Kumamoto, Japan
2Department of Electrical Engineering, Hasan uddi n Univer s ity, Makassa r, Indo nesi a
Email: yusuri@st.c s.ku mamoto-u.ac.jp , miyauchi@c s.kuma moto -u.ac.jp
Received 2013
Abstract
This paper presents seasonal regression models of demand to investigate electricity consumption characteristics. Elec-
tricity consumption in commercial areas in Japan is analyzed by using meteorological variables, namely temperature
and relative humidity. A dummy variable for holidays is also considered. We have developed models for two levels of
period to analyze demand characteristics, that is, half year models and seasonal models. Some options for each model
are calculated and validated by statistical tests to obtain better models. As r esul t s, hal f year and se asonal models present
explicit information about how the variables affect the demand differently for each period. These specific information
help in analyzing characteristics of studied commercial demand.
Keywords: Commercial Area; Demand Characteristics; Regression Model; Seasons; Relative Humidit y; T e mperature
1. Introduction
In general, electricity consumption analyses such as cha-
racteristics investigation and forecasting can provide
much information related to the time variance of demand.
The result of demand analysis is useful for electric utili-
ties in many aspects, for instanc e, to mana ge and control
their systems more effective. Therefore, it is valuable to
analyze an electricity demand in detail through develop-
ment of demand models. A number of methods can be
used for a demand analysis, and one of them is regres-
sion analysis. As a tool, a regression model needs a
number of data (dependent and explanation variables).
The implementation of proper explanation variables is
req uir ed to ge t a go od model. As an explanation variable,
meteorological parameters such as temperature, humidity,
wind speed, and so on, are commonly used and con-
firmed electricity demand effectively. Prior studies
which employed meteorological parameters and regres-
sion models for electricity demand can be found in ref-
erences such as [1-4]. Reference [1] develops a demand
model using a stepwise procedure to forecast Spanish
daily electricity demand. Reference [2] develops regres-
sion equations to analyze electricity consumption for
residential area in Hong Kong by using climatic and
economic variables. Reference [3] develops the model of
electricity consumption for residential area in Bangkok
Metrop o lis and analyzes e ffect of climatic and economic
factors for demand. Meanwhile, in [4], authors have de-
veloped two statistical models for demand in Greece,
namely dai ly a nd mont hly model s to for ecast d emand up
to 12 months ahead (mid-term demand).
As electricity demand may differ to time [2,3] and
place generally, we have an interest to analyze demand
characteristics for commercial area in a typical city in
Japan by developing demand models. This study also
aims to find the electricity consumption characteristics in
Japan. We analyze demand characteristics based on
seasonal periods for commercial area in Japan. To
achieve the aim, two demand model of two period levels
based on different time length, namely half year models
(CTEChy1, and CTEChy2) and seasonal models
(CTECSM, CTECA, CTECW, and CTECS) are
proposed to reveal further demand characteristics by
regression analysis. They are developed from an initial
model (CTEC) that is derived from all data (whole
period) with the same explanation variables and
statistical validation processes. In the context of this
study, the application of regression approach is effective
enough. Beside simple in composing the models, the
obtained regression coefficients and statistics contain
specific information about the direct relationship
between variables and demand. It may be useful to draw
a seasonal strategy and to meet demands in maintaining
power system performance.
Y. S. AKIL ET AL.
Copyright © 2013 SciRes. ENG
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0
1
2
3
4
5
Normalized hourly demand (Commercial)
-10 010 20 30 40
Temperature (°C)
T max = 36.7 °C; T min = -0.9 °C; T mean = 18.5 °C
Tref tested
1.5
2.0
2.5
3.0
3.5
4.0
30
40
50
60
70
80
90
255075 100 125 150
Com. TRHD (%)
Normalized hourly demand (Commercial)
Relative humidity (%)
Hour (1 Aug 2008 - 7 Aug 2008)
Holidays (2-3 Aug 2008)
2. Data and Initial Demand Model
To compose demand model for characteristics analysis,
three major data are employed, namely a demand in
commercial area (Com. T), meteorological data, and
holidays. The actual demand data of a typical city in Ja-
pan are offered by a utility. It is normalized hourly
data from June 2007 to November 2009. Concerning
meteorological data, we use data of temperature and rel-
ative humidit y of a representative city in the same area in
Japan whe r e the demand data are collected. They are
gathered from Japan Meteorological Agency open web-
site [5].
For characteristics exploration, some figures involved
demand and explanation variables are presented in rela-
tion to construct model. From histogram and scattered
diagram shown in Fig ure 1, it is obtained that relation-
ship between demand in commercial area Com. T and
temperature T (° C) is not linear. B ased on this fact, heat-
ing degree days HDD and cooling degree days CDD va-
riables which defined i n Equations (1) and (2) are used in
the composed model [1,4,6].
)0,
1
max( T
ref
THDD −=
(1)
)0,
2
(max ref
TTCDD −=
(2)
Concerning HDD and CDD, reference value of tem-
perature (Tref) is approximately 18 °C [1]. However, as
electricity demand characteristics may be unique in
places, appropriate Tref for CDD and HDD may lead to
optimum res ul ts. In t his work, fo ur differ ent Tref1 = Tref2 =
Tref values (16 °C, 17 °C, 18 °C, and 19 °C) for models
are calculated and assessed by statistical tests to get bet-
ter result. Moreover, to i nvestigate the effect of te mpera-
ture on the commercial demand, one hour previous tem-
perature values CDD(-1) and HDD(-1) are considered in
models as in [1,4].
Figure 1. Scattered diag ra m betwe en Com. T and temperature.
Figure 2 presents sample values of relative humidity
RHD (%), and demand in one week from 1st (Friday) to
7th (Thursday) August 2008. From the figure, both de-
mand and humidity values fluctuate. However, only the
electricity demand has almost similar daily fluctuation.
The typical demand fluctuation reaches daily maximum
values. Besides, demand in holidays is lower than week-
days.
As an initial demand model, the regression equation
for all period is defined as Equation (3). It expresses the
normalized hourly demand for all data.
t
uDHRHDHDD
HDDCDDCDDCTEC
+++−+
+−++=
6
5
)1(
4
3
)1(
2
10
ααα
αααα
(3)
where CTEC is a demand in commercial area. α0 is
constant, and other α are regression coefficients.
CDD(-1) and HDD(-1) are one hour previous data for
CDD and HDD, respectively. A dummy variable for
holidays DH is added in the model. The value DH=1
expresses holidays, meanwhile the value 0 (zero) is use d
for other days (non-holidays). Here, holidays includes
not only weekends and national holidays but also
non-national holidays such as New Year (2nd and 3rd
Januar y) and Obon F est ival (13th - 16th August).
To avoid serial correlation, an autoregressive compo-
nent in error term is employed in the regression models.
The formula is written in Equation (4) [7]. In this usual
method for regression analysis, current value for error
term is stated as a number of previous errors [4].
tpt
u
pt
u
t
u
t
u
ερρρ
+
++
+
=...
2211 (4)
where ut is error term, ρp are constants, p is the
autoregressive order, and ɛt is a white noise. For the
simplicity of models, second order autoregressive error
term is used for all mode ls in this st udy. Models without
autoregressive, and with one order autoregressive are
also calculated as model options.
Figure 2. Sample of Com. T variation and humidity for one week in
August 2008, and holi days between the peri od.
Y. S. AKIL ET AL.
Copyright © 2013 SciRes. ENG
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0
100
200
300
400
500
600
700
0510 15 20 25 30
(b)
Largely in May
0
1
2
3
4
5
4812 16 20 24 28 32 36 40
Temperature (°C)
Normalized hourly demand (Commercial)
Summer and Autumn season
T max = 36.7 °C; T min = 4.3 °C; T mean = 23.0 °C
0
200
400
600
800
1,000
1,200
468 10 12 14 16 18 20 22 24 26 28 30 32 34 36
Largely i n November
(a)
3. Seasonal Demand Regression Models for
Characteristics Analysis
In this study, to analyze Japanese commercial demand
characteristics, demand regression models for two period
levels are developed from the initial model. From this,
different characteristics for certain periods are inves ti-
gated. Based on this, we focus on exploring characteris-
tics of dema nd under two d ifferent conditio ns of temper-
ature and humidity by a half-year model. Then, by con-
structing seasonal models, we continue to analyze cha-
racteristics more specific for each season. Here, the same
explanation variables as the initial model are applied for
the model of both levels. Similar to [1,4], models are
tested by Akaike Information Criterion (AIC) test and
Schwarz Criterion (SC) test to decide the best model for
each level. The adjusted coefficient of determination R2
is also calculate d.
3.1. Proposed Mod e ls for Ha lf Year Period
Seasonal periods can vary for each place in the world.
Particularly in Japan, the climate condition is relatively
Figure 3. Scat tered diagram between Com. T demand a nd
temperature: (a ) half year 1, and (b) half year 2.
different from each place. However, summer, autumn,
winter, and spring are four seasons occurred in Japan.
The summer season starts from June to August, autumn
from September to November, winter from December to
February, and spring fr om March to Ma y. On t he basis of
these seasons, the initial model is developed into two
types of half year models, CTEChy1 and CTEChy2.
CTEChy1 expresses demand between June and Novem-
ber (summer and autumn), and CTEChy2 expresses de-
mand between December and May (winter and spring).
Basically, the co nd itio ns of su mme r and aut umn ar e sim-
ilar in terms of hot weather in contrast for winter and
spring. Therefore, basic characteristics are observed
through scattered diagram between demand and temper-
ature for each half year as shown in Figure 3. Fro m the
figures, cold temperature in CTEChy1 and hot tempera-
ture in CTEChy2 are mainly appeared in November and
May, respectively. Histograms of temperature are pre-
sented in sub figures in F igure 3. The mean temperature
Tmean in November (14.2 °C) is lower than the minimum
Tref, mea n whi le i n May, the Tmean (19.8 °C) is higher than
the maximum Tref. It underlies to use both CDD and
HDD as appropriate variables in half year models to ex-
plore demand characteristics completely. Other variables
(humidity and holidays) and processes are similar to the
previous one.
The electricity consumption models for CTEChy1 and
CTEChy2 are given in Equations (5) and (6).
t
uDHRHDHDD
HDDCDDCDDCTEChy
+++−+
+−++=
6
ˆ
5
ˆ
)1(
4
ˆ
3
ˆ
)1(
2
ˆ
1
ˆ
0
ˆ
1
ααα
αααα
(5)
t
uDHRHDHDD
HDDCDDCDDCTEChy
+++−+
+−++=
6
ˆ
5
ˆ
)1(
4
ˆ
3
ˆ
)1(
2
ˆ
1
ˆ
0
ˆ
2
ααα
αααα
(6)
where CTEChy1 and CTEChy2 are demand in
commercial area for half year 1 and 2 periods,
respectively.
0
ˆ
α
is constant, and other
α
ˆ
are
regression coefficients. Other variables are the same as
ones in the initial mode l, Equation (3).
However, considering natural variation of the temper-
ature, two other different half year models which ex-
presse d demand between May and October, and between
November and April are calculated as well. It means in
this category, all Tmean (each month) in the period of
CTEChy1 and CTEChy2 become above and below Tref,
resp ective ly (f igure not s hown) . Due to onl y a s mall pa rt
of temperature values remained below or above Tref in
the periods, it is proper to implement only CDD in
CTEChy1, or HDD in CTEChy2. Next, all results are
compared each other to get better result.
Y. S. AKIL ET AL.
Copyright © 2013 SciRes. ENG
111
-10
0
10
20
30
40
1 2 3 4
T maxT meanT min
SM A WS
Time period
Temperature (°C)
Jun - Aug
Sep - Nov Dec - Feb
Mar - May
Tref lines
(2.27)
(1.88)
(2.05)
(1.71)
Notes: ( ) M ean de mand
3.2. Proposed Models for Seasonal Demand
Models
With regard to the eff ort to reveal dem and characteristics,
the preceding models are developed according to the
seasons. Four electricity consumption models, namely
summer (CTECSM), autumn (CTECA), winter
(CTECW), and spring model (CTECS) are composed.
Based on the seasons, November and May are months
in aut u mn and sp ring sea son, re spe ctive ly. The refo re, we
use two temperature variables (CDD and HDD) to com-
pose autumn and spring models (CTECA and CTECS).
For other two models (CTECSM and CTECW), both in
their periods contain a few temperature values below
(Tmin = 13.4 °C) or above (Tmax = 20.8 °C) of Tref range.
Howev e r, we consider only dominant temperature to
compose CTECSM and CTECW models for simplifica-
tion. The range of temperature for each season is shown
in Figure 4.
The regression equations for each seasonal model are
defined in Equations (7)-(10).
t
uDH
RHDCDDCDDCTECSM
++
+−++=
4
ˆ3
ˆ
)1(
2
ˆ
1
ˆ
0
ˆ
β
ββββ
(7)
t
uDHRHDHDD
HDDCDDCDDCTECA
+++−+
+−++=
6
ˆ
5
ˆ
)1(
4
ˆ3
ˆ
)1(
2
ˆ
1
ˆ
0
ˆ
βββ
ββββ
(8)
t
uDH
RHDHDDHDDCTECW
++
+−++=
4
ˆ3
ˆ
)1(
2
ˆ
1
ˆ
0
ˆ
β
ββββ
(9)
t
uDHRHDHDD
HDDCDDCDDCTECS
+++−+
+−++=
6
ˆ
5
ˆ
)1(
4
ˆ3
ˆ
)1(
2
ˆ
1
ˆ
0
ˆ
βββ
ββββ
(10)
where CTECSM, CTECA, CTECW, and CTECS show
demand in summer, autumn, winter, and spring season,
respectively. The
0
ˆ
β
is constant, and other
β
ˆ
values are
Figure 4. Comparison of temperature limits for each season:
SM = summer, A = autumn, W = winter, S = spring.
regression coefficients. The other variables are the same
as ones i n t he previo us mo d el , Equatio n (3).
4. Result and Analysis
4.1. Demand Char a ct erist ics with Al l Period
The regression coefficients and results of the statistical
tests for the initial model of commercial area is listed in
Table 1. From tested Tre f (Tre f 1 = Tref2 = Tref ) in the model,
19 °C gives better result from the assessment by AIC test,
SC test, and R2. The results listed in Tables 1 is the
results for Tre f = 19 °C. In this study, EViews 6 [8] is
used to compute the model eq uations.
As presented in Table 1, R2 and R2 are almost 90%.
It indicates that used variables can explain the
commercial demand well. The application of 5%
significance level for p-value gives that all explanation
variables are significant. The value of 0 for Prob.
(F-Statistics) indicates at least one of the applied
variables influence the demand. Besi de s, Dur b in-Watson
(D-W) statistic implies the initial model doe s not contain
serial correlation because its value is around 2. To
confirm the nonexistence of heteroskedasticity problem,
corrected standard errors regression is performed [7].
The related adjusted standard errors are listed in Table 1
as well.
Among coefficie nt values for meteoro logical variables,
CDD (0.0410) has the highest influence to the demand,
followed by HDD, CDD(-1), HDD(-1), and RHD. As
temperature functions, the coefficient ratio of CDD to
HDD (α1/α3) [9] is around 2.67. The comme rcial de mand
can increase easier under hot temperature than under
cold temperature. Likewise for influence of one hour
previous temperature, CDD(-1) affects the demand
around 4.03 times of HDD(-1). For humidity, it has the
lowest influence to demand. As coefficient for dummy
holidays α6 is ne gative, demand is lower in holida ys than
in non-holidays.
Note: R2 = 0.8988; R2’ = 0.8988; SE Reg. = 0.1814; D-W = 2. 1230;
Prob. (F-Stat.) = 0.0000; AIC = -0.5752; SC = -0.5719
Expl.
Variabl e
All Period Demand Model
CTEC Mo de l (Tref = 19 °C )
Coef. t-statistic
Prob.
(p-value)
Adjs.
standard error
0
α
1.7456 81.93 0 0.0213
CDD 0.0410 30.88 0 0.0013
CDD(-1) 0.0125 13.61 0 0.0009
HDD 0.0153 24.08 0 0.0006
HDD(-1) 0.0031 5.44 0 0.0005
RHD 0.0011 11.96 0 9.7E-05
DH -0.1744 -60.58 0 0.0028
Table 1. Regression results for all period demand model.
Y. S. AKIL ET AL.
Copyright © 2013 SciRes. ENG
112
10
20
30
40
50
60
70
80
90
100
123456 7 8 910 11 12
RHD min
RHD mean
RHD max
Relative humidity (%)
Jun Jul Aug Sep OctNov DecJan Feb Mar Apr May
Month
RHD mean
(June 2007 – May 2008)
RHD mean
(June 2008 – May 2009)
4.2. Demand Char a ct erist ics with Hal f Year
Models
Half year models started from May to October (CTEChy1)
and from November to April (CTEChy2) are obtained.
Naturally, as period of CTEChy1 is hot season, the tem-
perature in CTEChy1 is higher than CTEChy2. Moreover,
all monthl y a verage va lues o f humidit y (RHD mean) i n the
period of CTEChy1 tend to higher than in the period of
CTE Chy2 as shown in F ig ur e 5.
The best results for half year models which are
specified with second order autoregressive error ter m are
presented in Tables 2 and 3. In Table 2, where 19 °C and
16 °C are optimum Tref va lue s for CDD in CTECh y1 , a nd
HDD in CTEChy2 model, respectively. T he statistical
Figure 5. Variation of humidity values for each month from
June 2000 to May 2007
Table 2. Regressi on coeffi cients of the half y ear models.
results in Table 3 and Table 2 show both models
validated well. B y separating the perio d, the value of R2
increases slightly in CTEChy1 (90.88%) and decreases
in CTEChy2 (85.55%) when we compared with R2’ val ue
of CTEC model (89.88%). CTEChy1 has higher degree
of fitne ss t ha n CT E Ch y2 model.
For constant values
0
ˆ
α
, it is obtained larger in
CTEChy2 (1.8137) than in CTEChy1 (1.6260). The
constant value is associated with base demand. Among
meteorological variables in CTEChy1 and CTEChy2
models as in Table 2, CDD (0.0468) and HDD (0.0178)
have the largest effect to the demand, respectively.
However, comparing these coefficient values (CDD in
CTEChy1, and HDD in CTEChy2), the demand
responses higher in hot temperature than in cold
temperature. Concerning humi dity, this variable gives the
lowest influence, and affects the demand only in
CTEChy1 period (high humidity). The elimination of
non-significance variable RHD in CTEChy2 is proper as
it gives almost the same r esults. T he dummy variable DH
shows decrease of the commercial demand in holidays,
but in different amount for both half year models.
4.3. Demand Characteristics with Seasonal
Models
Tables 4 and 5 present best regression results with opti-
mum Tref for each seasonal model. Optimum Tref is 19 °C
for summer and autumn models, meanwhile 16 °C for
other two models. The Tref value tends to high under hot
seasons and vice versa. From the results, the value R2
ranges between 81.34% and 90.19%. The models under
hot seasons (CTECSM and CTECA) have higher R2
values than others under cold seasons (CTECW and
CTE CS ). The hig hest R2’ is in summer, and the lowest is
in winter. However, with R2’values exceed 80% and
three of them above 86%, all models have quite good
fitness degree. Next, among implemented var ia bles in the
seasonal models, CDD(-1) and HDD(-1) in spring
(CTECS) are not significant at 5% significance le vel. As
spring is not so hot or so cold (comfortable season), it
may related to the non-significance of the one hour pre-
vious temperature (CDD(-1) and HDD(-1)) to demand.
For simplification, both CDD(-1) and HDD(-1) in
CTECS model can be eliminated without influence on
regr ession r esults.
Expl.
Variable
Half Y ear Dem and Model
CTEChy1 (Tref = 19 °C) CTEChy2 (Tref = 16 °C)
Coef.
Prob.
(p-value) Coef.
Prob.
(p-value)
0
ˆ
α
1.6260 0 1.8137 0
(48.26) 0.0336* (74.35) 0.0243*
CDD 0.0468 0
(31.75) 0.0014*
CDD(-1) 0.0110 0
(11.84) 0.0009*
HDD 0.0178 0
(24.01) 0.0007*
HDD(-1) 0.0030 0
(4.61) 0.0006*
RHD 0.0030 0 8.00E-05 0.4484
(16.92) 0.0001* (0.75) 0.0001*
DH -0.1870 0 -0.1562 0
(-43.16) 0.0043* (-44.29) 0.0035*
Notes: CTEChy1 = from May to October; CTEChy2 = from November to April;
() t -statistic; *adjs. s tanda rd e rro r; _not significant related to its var iab le
Table 3. Regressi on statistics of the half y ear models.
Half Year
Model
R2 R2
SE
Reg.
D-W AIC
SC
CTEChy1 0.9089
0.9088 0.1978 2.1343 -0.4024 -0.3982
CTEChy2 0.8556
0.8555 0.1524 2.0946 -0.9231 -0.9178
N ote : Prob. (F-Stat.) both C TEChy1 a nd CTEC hy2 = 0. 0000;
Without RHD in CTEChy2 mode l, R2’ = 85.55%
Y. S. AKIL ET AL.
Copyright © 2013 SciRes. ENG
113
Table 4. Regressi on coeffi cients of the seasonal models
with optimum Tref .
From analysis of actual data, the highest normalized
mean demand is found in summer, followed by winter,
autumn, and spring. The use of cooling or heating
equipments can contribute to the sit uation.
The obtained constant values
0
ˆ
β
which represent base
demand are larger in winter (2.0090) than in summer
(1.6009). Meanwhile, base demand for autumn (1.6252)
and spring (1.6157) are between the values in summer
and winter. As lighting equipments may contribute to
base demand, daylight duration is roughly 12 hours in
these periods. For
β
ˆ
coefficients which quantify effect of
variables to demands, they show meteorological va-
riables in summer (CDD, CDD(-1), RHD) have higher
influence to demand than the variables in winter (HDD,
HDD(-1), RHD). In summer, the highest coefficient is
CDD (0.0495), meanwhile in winter is HDD (0.0162).
Next, for sea sons withou t severe temperature, coefficient
value of CDD is found larger than HDD in autumn
(CTECA), and on the contrary in spring (CTECS). It
implies dominant temperature is CDD in autu mn and
HDD in spring. However, compared between the domi-
nant temperature functions, CDD (0.0535) is obtained
higher i n a ut u mn t ha n HD D (0.0194) in spring. As drive r
factors, in su mmer, n ot only temperature (in ter ms of hot)
is high for all months but also humidity. On the other
hand, in winter, only temperature is high (in terms of
cold). Summer and winter peak periods occur in August
and January in Japan, respectively. Humidity RHD may
reduce from the models except for summer. For holidays,
it gives the highest effect on the demand in summer and
on the contrary in spring.
5. Conclusions
This paper presents seasonal regression models to
analyze demand characteristics in com mercial area (Com.
T) in a typical city in Japan. To carry out the analysis,
meteorological and holidays variables are considered as
factors affect the electricity consumption. Two models
are developed depending on the periods, namely half
year (CTEChy1, and CTEChy2) and seasonal models
(CTECSM, CTECA, CTECW, and CTECS). As results,
more specific characteristics can be revealed by the
proposed models by validatin g many statistica l tests. The
obtained optimum Tref for CTEChy1, CTECSM, and
CTECA models are 19 °C, and other three models are
16 °C. I t implies that Tref for the de mand may change b y
periods. They have quite good fitness degree shown by
the adjusted coefficient of determination R2’ which varies
around 85.55% to 90.88% for half year models, and
81.34% to 90.19% for seasonal models. It reflects that
variables affect the demand differently for each period.
The R2 values are relatively high in CTEChy1 for half
Expl.
Variable
Seasonal Demand Model
CTECSM (Tref = 19 °C) CTECA (Tref = 19 °C)
Coef.
Prob.
(p-value )
Coef.
Prob.
(p-value )
0
ˆ
β
1.6009 0 1.6252 0
(27.79) 0.0576* (49.58) 0.0327*
CDD 0.0495 0 0.0535 0
(24.09) 0.0020* (19.69) 0.0027*
CDD(-1) 0.0095 0 0.0190 0
(7.75) 0.0012* (11.15) 0.0017*
HDD 0.0118 0
(10.64) 0.0011*
HDD(-1) 0.0058 0
(5.59) 0.0010*
RHD 0.0044 0 0.0009 0
(13.92) 0.0003* (5.09) 0.0001*
DH -0.2231 0 -0.1515 0
(-34.28) 0.0065* (-31.82) 0.0047*
Expl.
Variable
Seasonal Demand Model
CTECW (Tref = 16 °C) CTECS (Tref = 16 °C)
Coef.
Prob.
(p-value) Co ef .
Prob.
(p-value)
0
ˆ
β
2.0090 0 1.6157 0
(59.03) 0.0340* (49.95) 0.0323*
CDD 0.0090 0
(7.25) 0.0012*
CDD(-1) 0.0010 0.3360
(0.96) 0.0010*
HDD 0.0162 0 0.0194 0
(14.27) 0.0011* (19.80) 0.0009*
HDD(-1) 0.0023 0.0167 0.0008 0.4237
(2.39) 0.0009* (0.80) 0.0010*
RHD -0.0005 0.0032 0.0012 0
(-2.95) 0.0001* (9.48) 0.0001*
DH -0.1813 0 -0.1308 0
(-29.65) 0.0061* (-30.32) 0.0043*
Note s: () t-st a t is tic ; *adjs . s ta nda rd error; _ not significant related to its varia ble
Reg. Statistics Seasonal Model
CTECSM CTECA CTECW CTECS
R2 0.9020 0.8986 0.8136 0.8605
R2’ 0.9019 0.8984 0.8134 0.8602
D-W 2.1626 2.0944 2.0871 2.1188
SE R eg . 0.2133 0.1719 0.1748 0.1237
Prob. (F-Stat.) 0.0000 0.0000 0.0000 0.0000
AIC -0.2507 -0.6813 -0.6476 -1.3390
SC -0.2435 -0.6719 -0.6374 -1.3260
Notes: Without CDD(-1) and HDD(-1) in CTEC S mode l
R2’ = 86.00%; R2’ = 86.09% (2008); R2’ = 85.86% (2009)
Table 5. Regression st ati stics of the four seasonal models.
Y. S. AKIL ET AL.
Copyright © 2013 SciRes. ENG
114
year model, and in CTECSM (summer) and CTECA
(autumn) for seasonal models. Implemented variables
can explain commercial demand o ptimally in ho t weather
rather than in cold weather. The base demand is
relatively higher in the cold than in hot season. Among
meteorological variables, CDD and HDD are the most
significant variables. For non-significance variables,
elimination of them results in simplified models which
may reduce computation burden. Next, in holidays,
demand decreses in a ll period s b ut in difference amount.
The presented results can give more insight especially
when demand characteristics in seasonal levels are
required. It is usefull in quantifying influence of
variables on demand at certain area or period, and in
understanding demand situati on more detail.
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