Modeling on Electricity Consumption’s Average of Households
Group in Surabaya with Nonparametric Approach based on Fourier
Estimator
Eko Tjahjono, Sediono, M. Fariz Fadillah Mardianto
and Ajeng Novy Lestari
Department of Mathematics, University of Airlamgga, Surabaya, Indonesia
Keywords: Electricity, Temperature, Nonparametric Regression, Fourier Series.
Abstract: Demand of electrical power increase in line with the number of populations, technological advances, and
information. Household groups are the biggest users of electricity every year. The case study in this research
that be used about electricity usage in Surabaya city. Surabaya is the capital of the province with very high
electrification that equal to 99,79%. This proves that Surabaya can be used as an indicator of electricity. One
factor that influence the high usage of electricity is temperature. The higher the air temperature caused the
use of electrical equipment is increasing so that the used of electricity increases. Prediction of electrical used
is needed to anticipate electricity supply as well as anticipation action against power outage which can disturb
human activities. In this study, electricity consumption of household group in Surabaya was observed
monthly, then predicted using nonparametric regression method based on Fourier series estimator. One of the
advantages of the Fourier series is that it can overcome data that has repeating pattern. This study results a
minimum GCV value when the oscillation parameter reaches 11. The chosen model based on minimum GCV
has met the model goodness criteria. Then, the selected model used to predict the household electricity usage
in Surabaya for some time ahead.
1 INTRODUCTION
Electricity is one of the most important and vital
energy for human life, so it cannot be separated every
day. Nowadays the need for electric energy is
increasing along with the increase of population and
technological progress and information. Currently
electrical energy has been classified as the basic
needs of an area used by five groups of power users.
Household groups are the largest group of electric
energy users in each year. The average population
growth of Surabaya City in 2007 was 0,1172 with a
population of 2.720.156 people and the number of
households was 755.914. The condition of
electrification ratio in 2007 is very high, amounting
to 99,79%. Thus, this is the basic research why use
the city of Surabaya.
Determination of the future of electrical energy is
influenced by various factors. Weather changes cause
changes to consumer comfort and affect the use of
equipment including electrical equipment. The higher
temperature of the air will cause the use of electrical
equipment is greater so that electricity consumption
is increasing.
In this research, electricity consumption’s average
of households group in Surabaya is modeled using
nonparametric regression approach based on Fourier
series estimator. One of the advantages of
nonparametric regression approach using Fourier
series can overcome data having trigonometric
spreading, in this case sine and cosine. The data
patterns corresponding to the Fourier series approach
are repetitive data patterns. Research on the Fourier
series includes Bilodeau (1992), Tripena and
Budiantara (2006).Tjahjono (2009) studied Fourier
series estimators on nonparametric regression, and
Tjahjono et al., (2018) developed an estimated
nonparametric regression model of the Fourier bi-
response series.
2 FOURIER SERIES ESTIMATOR
Fourier series is a trigonometric polynomial function
that has a high flexibility. It is because the pattern of
Tjahjono, E., Sediono, ., Mardianto, M. and Lestari, A.
Modeling on Electricity Consumption’s Average of Households Group in Surabaya with Nonparametric Approach based on Fourier Estimator.
DOI: 10.5220/0008518501470150
In Proceedings of the International Conference on Mathematics and Islam (ICMIs 2018), pages 147-150
ISBN: 978-989-758-407-7
Copyright
c
2020 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
147
data can determine the shape of regression curve
based on estimators in the nonparametric regression,
and it is engaging trigonometric function (Prahutama,
2013). Fourier series estimators are generally used
when the data used are investigated unknown patterns
and there is a tendency of seasonal patterns
(Tripenaand Budiantara, 2006 and Bilodeau, 1992).
Suppose given the observation
data
following the regression model
(1)
and functions
as follows:
(2)
withis an integer, then equation (2) become :
;
(3)
When the observation data is a function of time and
shows periodic phenomena then in estimate m
function used linear model which includes the sine
and cosine functions. This study uses
temperatureas the predictor variable in the time
function
, so
is the temperatureat the
time.
(4)
By taking n paired samples
which fulfill
equation (4) then obtained equation as follows:
(5)
with
,
,
, and
3 RESEARCH METHODOLOGY
The data used in this research is secondary data of
household usage for 2011-2016 in Surabaya, there are
63 observations that be obtained from PT. PLN,
branch of North Surabaya, and temperature data of
Surabaya City obtained from BMKG, station of Perak
Surabaya.
The following steps data analysis used to answer
the purpose of this study as follows:
1. Describe the data of electricity consumption in
Surabaya
a) Entering variable response in the form of data
electricity consumption and predictor variable
of temperature
b) Creating plots for data on electricity
consumption and temperature
c) Calculate and create tables for the mean,
median, mode, and variance values of data on
electricity consumption and temperature
2. Model data of electricity consumption in Surabaya
based on Fourier series estimator using R software
as follows:
a) Defines response variables (Y) and predictor
variables (X). Specifies the function m (x (t
r
))
to use Calculate the value of MSE
b) Calculate the smoothing parameter value (λ)
with GCV
c) Entering the initial smoothing parameter value
(λ) and the final finishing parameter value (λ)
Based on step e selected minimum GCV value
based on looping result.
d) The value of the fining parameter
corresponding to the minimum GCV value is
the optimum parameter value (λ) which will be
used in the next step Input the refined
parameter value (λ) optimal that has been
obtained Calculate the value of a
j
and b
j
e) Calculate the value of
3. Interpret data model of electricity consumption in
Surabaya based on Fourier series estimator
a) Making the results of analysis based on
software output R then make a conclusion
from the analysis results.
b) Creating the table of actual electricity usage
data and estimation data from the model that
has been obtained based on the Fourier series
criteria.
4 RESULT AND DISCUSSION
4.1 Characteristics of Electricity Usage
of Household Group in Surabaya
City
The data analyzed in this study is data of electricity
consumption of household groups in Surabaya area
from April 2011 to June 2016 taken every month in
Kilowatt Hour and monthly temperature data of
Surabaya City during the same period. Overall data
amounted to 63 data, including data from April 2011
to December 2015 as many as 57 data used as in-
sample data while in January 2016 until June 2016 as
much as 6 data used as out-sample data. In-sample
data will be analyzed by Fourier series method to find
out the best model for electricity consumption and
out-sample data used for electricity consumption
ICMIs 2018 - International Conference on Mathematics and Islam
148
forecasting in Surabaya affected by temperature and
time for several periods ahead.
4.2 Relationship between Household
Electricity Usage with Temperature
in Surabaya City
The variable used in this study to identify household
usage in Surabaya is the monthly temperature of that
city. In addition to time or period (months),
temperatures can also affect the size of electricity
consumption, especially in household groups. This
case the temperature effect on the conductor of
electricity so that it can affect the electrical current.
From the results it is known that the relationship or
the influence of heat on the resistance of the wire is
directly proportional. This means that if the
temperature is greater than the resulting resistance the
greater also. This is in accordance with opinion
(Suroso, 2003) that the conductor of electricity is one
important component in the distribution of electric
power.
4.3 Model Data of Electricity Usage of
Household Group in Surabaya City
Data used in this research is secondary data of
electricity usage in Surabaya city on April 2011 up to
June 2015 57 data as observation data (in sample) and
last 6 data as prediction data (out sample). Response
variable in this research is data of electricity usage in
Surabaya City and predictor variable is Surabaya
Kota temperature data and time (month). Here is a
plot between response variables and predictor
variables.
Figure 1: Scatterplot Temperature and Electricity
Consumption in kWh.
Based on Figure 1 which is the average scatterplot of
electricity consumption in Surabaya City against the
monthly temperature of Surabaya City, it can be
assumed that the data plot shows the absence of
certain relationship pattern, the data pattern is
periodic and shows the trigonometric distribution of
sinus and cosine. So, the analysis of the regression
model uses a nonparametric approach based on a
Fourier sequence estimator.
The model of the relationship between the
response variable and the best predictor variable is
obtained by determining the optimal smoothing
parameter (λ) with minimum GCV criterion.
Table 1: GCV minimum.
Lambdas
GCV
MSE
R
2
1
15,45084
13,86724
0,3778355
2
15,59415
12,97832
0,4177173
3
16,20542
12,46954
0,4405442
4
16,12573
11,43542
0,4869407
5
15,9596
10,39413
0,5336593
6
17,18157
10,23808
0,5406606
7
17,60686
9,559401
0,5711099
8
19,28306
9,49612
0,5739491
9
17,91869
7,963864
0,642695
10
10,31607
4,114997
0,8153774
11
9,397186
3,343536
0,8499896
12
10,59919
3,340589
0,8501218
13
10,66285
2,953697
0,86748
14
10,54307
2,544096
0,8858571
Based on Table 1 above which is a table of GCV
values along with MSE and R
2
values on data of
electricity consumption in Surabaya city can be seen
that minimum GCV value is 9,397186 with MSE
value equal to 3,343536 and R2 value equal to
0,8499896 or 85%. The next step is to make a plot
between lambdas with GCV value on the data of
electricity consumption in Surabaya. After obtaining
the minimum GCV value and optimum lambda then
do the estimation model using software R. The
program is made to obtain the value of
as a cosine
function and the value of
as a form of sine function
derived from the Fourier derivative model estimator.
From result of output program in software R obtained
value of β
0
for data of electricity usage that is equal
to 62,43035 and obtained value of λ,
and
as in
Table 2 below:
Table 2: Value of coefficient a
j
and b
j
.
Lambda
1
-0,9814987
-3,984919
2
-0,2589094
-1,307973
3
0,1466272
-0,9980298
4
0,517541
-1,341785
5
-0,6823104
-1,271631
6
0,2800438
-0,4834005
7
-0,03172626
-1,164622
8
0,2975692
-0,1949733
9
1,164072
-1,307459
10
-2,721578
-0,5392087
11
-0.8037324
-0.9470675
Modeling on Electricity Consumption’s Average of Households Group in Surabaya with Nonparametric Approach based on Fourier
Estimator
149
Based on Table 2 which is the table of values of λ,
and
of household electricity consumption data in
Surabaya in 2011 to 2016, it can be found that
household electricity consumption data model based
on nonparametric regression method based on Fourier
series estimator is as follows:
4.4 Interpret Model of Electricity
Usage Data Usage in Surabaya City
based on Fourier Series Estimator
Table 3: Value of coefficient a
j
and b
j.
observations
1
53,02
59,3564
2
55,246
54,7319
3
56,558
54,8453
4
58,317
56,8829
56
70,997
71,4272
57
72,891
66,7502
Based on data of household electrical usage that have
been analyzed using software R obtained optimal
GCV value at 11th lambda that is equal to 9,397186
with value of MSE equal to3,343536 and value of
equal to 0,8499896 or equal to 85% which mean
model have good because can represent data of 85%.
5 CONCLUSIONS
Based on the results of analysis and discussion in this
study it can be concluded that any rise in temperature
can cause changes in the amount of electricity
consumption each month. The model of Fourier
estimator series has been obtained is good with
value of 85% and MSE value of 3,343536 for the
data in sample, while for the data out sample obtained
value of 99% and MSE of0,08893838. This means
the model has been good and in accordance with the
data used in this study.
REFERENCES
Bilodeau, M., (1992), Fourier Smoother and Additive
Models, The Canadian Journal of statistics, 3: 257 –
269
Tripena, A., and Budiantara, I. N., 2006, Fourier Estimator
in Nonparametric Regression, Proceeding
International Conference on Natural Sciences and
Applied Natural Scienes Ahmad Dahlan University,
Yogyakarta.
Tjahjono, E.,Mardianto, M. F. F, Chamidah, N., 2018,
Prediction of Electricity Consumption Using Fourier
Series Estimator in Bi-Response Nonparametric
Regression Model, Far East Journal of Mathematical
Sciences ( FJMS), vol. 103, Number 8, 2018, pp 1251 -
1263.
Tjahjono, E, 2009, weighted Fourier Series Estimator for
Nonparametric Regression, Thesis, ITS, Surabaya.
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