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International Journal of Civil Engineering and Technology (IJCIET)
Volume 9, Issue 6, June 2018, pp. 1001–1015, Article ID: IJCIET_09_06_114
Available online at http://www.iaeme.com/ijciet/issues.asp?JType=IJCIET&VType=9&IType=6
ISSN Print: 0976-6308 and ISSN Online: 0976-6316
© IAEME Publication Scopus Indexed
PEAK LOAD FORECASTING ON NATIONAL
HOLIDAY USING FUZZY-FIREFLY
ALGORITHM AT JAWA-BALI ELECTRICITY
SYSTEM IN INDONESIA
Andi Imran
Department of Electrical Engineering, Institut Teknologi Sepuluh November, Indonesia
I Made Yulistya Negara
Department of Electrical Engineering, Institut Teknologi Sepuluh November, Indonesia
Imam Robandi
Department of Electrical Engineering, Institut Teknologi Sepuluh November, Indonesia
ABSTRACT
This paper discusses the short-term load forecasting of peak load on national
holiday. The peak load is forecasted using Fuzzy Inference System Type 2, in which is
combined with the firefly algorithm. Firefly algorithm is used to optimize the footprint
of uncertainty (FOU) on fuzzy logic that consists of antecedent (X, Y) and consequent
(Z). This method is applied for short-term load forecasting by utilizing data from the
daily peak loads during a holiday in the electrical system of Jawa-Bali, Indonesia.
Then focused on peak load data from four days before the holiday (h-4) and on
holidays (h). The tests showed that the method of Fuzzy Inference System Type-2
Firefly provide accurate forecasting, showing by its significant lower absolute error.
The peak load national holidays forecasting error using Interval Fuzzy Logic Type 2-
firefly amounted to 0.453167666%, using IT1FL of 1.272449841%, using IT2FL of
1.265763% and using IT2FL-BBBC of 0.974277222%.
Key words: Interval Type-2 Fuzzy Logic, Firefly, MAPE.
Cite this Article: Andi Imran, I Made Yulistya Negara and Imam Robandi, Peak Load
Forecasting on National Holiday using Fuzzy-Firefly Algorithm at Jawa-Bali
Electricity System in Indonesia, International Journal of Civil Engineering and
Technology, 9(6), 2018, pp. 1001–1015
http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=9&IType=6
1. INTRODUCTION
Electric load forecasting is an important part on power system operation in order to achieve
optimal planning in operation of the systems [1]. Load forecasting is covering short-term,
medium-term and long-term load forecasting [2-4]. Short-term load forecasting is required for
Peak Load Forecasting on National Holiday using Fuzzy-Firefly Algorithm at Jawa-Bali
Electricity System in Indonesia
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controlling and scheduling the operation of power systems [2]. Medium and long-term load
forecasting is required for maintenance, fuel purchases, plant development and planning of
future distributions. Accurate load forecasting has a significant impact on the operation and
production costs of electric utilities [3]. Research on load forecasting has spawned numerous
papers and journals [5-7]. These publications have led to the development of various methods
of forecasting. This method is classified into two categories: classical approach (conventional
method) and artificial intelligence method. The classical approach is based on statistical
methods, which cannot be accurately represent complex nonlinear relationship between the
load and a series of factors such as daily and weekly rhythms of time that can lead to high
error in load forecasting [6]. Artificial intelligence method has an ability to provide better
performance when dealing with nonlinear data [6]. The advantages of artificial intelligence
method compared to conventional method are computational technique and simple algorithm,
structural simplicity and high accuracy performance without having to solve any nonlinear
equations into mathematical equations. Therefore, the author in this research discusses hybrid
method in the load forecasting, which is a suggestion of earlier researchers [5]. Thus the
hybrid method of interval type 2 fuzzy inference system-firefly is used in this research.
Interval type-2 fuzzy inference system (IT2FIS) becomes a concern for short-term load
forecasting because it has a simple concept and high-performance identification. IT2FIS is the
formulation and mapping process from input to output using interval type 2 fuzzy logic [8-
13]. One of the advantage of fuzzy logic [14] is the knowledge and experience of experts can
be easily used and applied. Firefly algorithm is an algorithm based on swarm for
optimization; this algorithm is inspired by the social behavior of firefly. There are two
important things in the firefly algorithm that is light intensity variations and formulation of
appeal [15]. General formulation of this algorithm is presented with a model of mathematical
analysis to solve problem with a single objective function. The result obtained with the
proposed alternative technique shows that it is able to produce good optimal solution [16].
Hybrid method of interval type 2 fuzzy inference system-firefly is used in this research on
the Jawa-Bali load forecasting, especially on national holiday. In the proposed method, we do
not take environmental factors as variable. This work is motivated by Kim, who stressed that
the load profile during the holiday is really an anomaly than normal working day in a year
[17]
2. INTERVAL TYPE-2 FUZZY LOGIC
Type-2 fuzzy set is a development of fuzzy type-1 which is re-defuzzy. Fuzzy type-1 based-
knowledge logic system is used to build the rules in an uncertainty fuzzy logic system (FLS).
There are three reasons of uncertainty rules [7]:
Rules of antecedents and consequents can have different perception in different people.
Polling of group of experts on consequents is often different to the same rules as most experts
do not agree on the rule.
The training data contains a lot of noise.
Rankings on type-2 fuzzy set can be on subset of secondary membership. Similiar to FLS
Type-1, FLS Type-2 is also include fuzzy inference system (FIS) membership functions and
defuzzification. The difference is that before defuzzification process there is type reduction
process which has several methods; one of them are Kernik Mendel Algorithm (KMA).
Interval Type-2 Fuzzy Logic System (IT2FLS) structure can be seen in Figure 1. Figure 1
shows the process of IT2FLS from input value of crisp x set into the output value of Y=f(x)
equation.
Andi Imran, I Made Yulistya Negara and Imam Robandi
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FuzzifikasiRule Base
Defuzzifikasi
Inference
Engine
Input Crisp
X
IT2 FSs
Output Crisp
Y
IT2 FSs
Type-Reducer
T1FS
Figure 1 Type-2 Fuzzy Logic System (T2FLS) Structure
2.1. Interval Type-2 Fuzzy Set
Interval type-2 fuzzy set (IT2FS) is denoted à by the membership function with [ ], its characteristic can be recognized on the following equation:
,0.1
,xx X x J
x uAA Jx
x u
(1)
x is a primary variable which has domain X; , secondary variable, have domain
for each is called primary membership of . Uncertainty of is expressed with the
combination of all primary membership ( ) which is called the footprint of uncertainty
(FOU) of . The equation can be seen as follows:
( {( , ); [0,1]})x X
FOU Jx x u u JA x
(2)
Jx is interval with the following equation:
( , ); ( ), ( )AAJx x u u x x
(3)
From equation 2.5 FOU ( ) can be expressed by the equation:
( ( ), ( ))x
A
XA
FOU xA x
(4)
= Primary membership of
= Lower Membership Function (LMF) af
= Upper Membership Function (UMF)of
( )UMF A
( )FOU A
u
I
( )FOU A
( )UMF A
Embedded FS
x( )LMF A
Figure 2 FOU (dark color), LMF (dotted line), UMF (solid line) and Embedded FS (wavy line).
Peak Load Forecasting on National Holiday using Fuzzy-Firefly Algorithm at Jawa-Bali
Electricity System in Indonesia
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2.2. Interval Type-2 Fuzzy Membership Function Operations
Operation on fuzzy interval type-2 set is almost the same as fuzzy type-1 set; but on IT2FL
logic system, the operation is performed on two intervals that are UMF (top) and LMF
(below) at once. Operation on fuzzy interval type-2 membership function can be seen in
Figure 3.
10.90.80.7
0 1 2 3 4 N (x)Input 1
Max-
Min
Max-
Min
10.90.80.7
0 1 2 3 4 N (x)Output 1
Figure 3 Operation fuzzy set interval type-2 (IT2FLS)
2.3. Karnik Mendel Algorithm
The searching of centroid on fuzzy interval type-2 is done by using Upper Membership
Function (UMF) and Lower Membership Function (LMF). Kernik Mendel formulates this
method as follows [11, 15]:
'
1
( )
1
( ') [ , ]nn
n n
Nn n
nCos N
nf F x
y Yn
f y
Y x yl yr
f
(5)
1 1 1 1[1, 1]
1 1 1 1
1 1 1 1[1, 1]
1 1 1 1
min
max
n nk N L Nn n n n n n
n n k n n Ll k N n nk N L Nn n
n n k n n L
n n n n n nk N R Nn n
n n k n n Rr k N n nk N R Nn n
n n k n n R
f y f y f y f yy
f f f f
f y f y f y f yy
f f f f
(6)
switch point of L and R are as follows:
1
1
L L
R R
y yl y
y yr y
(7)
After getting the value of yl and yr, then look for the value of the centroid by the equation:
( )
2
yl yrCentroid
(8)
Andi Imran, I Made Yulistya Negara and Imam Robandi
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3. FIREFLY ALGORITHM
For simplicity in describing the firefly algorithm, three ideal regulations are used as follows
[20]:
All fireflies are unisex so that one firefly will be attracted to other fireflies regardless of their
gender.
The appeal is proportional to its level of their brightness, therefore when every firefly is
flashing, one of them will move to the brightest. The brightness of both of them is declined
due to their distance increases. If there is no brightest firefly, the firefly moves randomly.
The brightness of a firefly is affected or determined by the objective function place of each
firefly.
Figure 4 show flow chart of the fireflies algorithm.
Random Fireflies
Sending / Receiving
Information
Isn.t the best location
Find the best
location
(Attractiveness)
Find Location
Fitness Function
Identification
Start
End
No
Yes
No
Yes
Figure 4 Flow chart fireflies algorithm
3.1. Light Intensity and Attractiveness
In the firefly algorithm, there are two important things which are the light intensity variation
and the attractiveness formulation. For convenience, we assume that the attractiveness of a
firefly is determined by its brightness associated with the encoding of objective function. In
the simplest case for maximum optimization problem, the first brightness of a firefly at a
location of x can be selected as I(x) f(x). However, the appeal of β is relative; it can be seen
in view of fireflies or judged by other fireflies. Thus, it will vary with the distance between
firefly i and firefly j. In addition, the light intensity decreases with distance from the source,
Peak Load Forecasting on National Holiday using Fuzzy-Firefly Algorithm at Jawa-Bali
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and the light is also absorbed about environment, so we can follow the appeal in order to vary
the degree of absorption.
The simple form of the light intensity I(r) of firefly varies according to the inverse of
square law.
0
2( )
II r
r (9)
I0 is the original light intensity. In order to prevent a single form at r = 0 expression Is/r2,
the combined effect of both the inverse square law and absorption can be estimated as a legal
form of Gaussian.
( ) r
oI r I e (10)
The appeal of firefly is proportional to the light intensity which seen by closed fireflies, it
can be determined by the attractiveness of β of a firefly:
2r
oe (11)
The distance between i and j fireflies on xi and xj, respectively the Cartesian distance:
‖ ‖ √∑ ( )
(12)
The movement of an i firefly which is attracted to j firefly which is brighter is defined as:
( )
is the coordination of spatial fireflies to- , is the coordination of spatial fireflies to ,
is randomization parameter and i is a vector value from random value between 0-1.
4. PEAK LOAD FORECASTING ON NATIONAL HOLIDAY USING
IT2FL-FIREFLY ALGORITHM
The implementation of it2fuzzy-firefly for peak load forecasting on national holiday is done
by using three stages, namely preparation stage (pre-processing), processing stage and final
stage (post-processing) [7].
4.1. Pre-Processing
Preparation stage is preparation of peak load data on 14 national holidays to look for load
difference (LD), typical load difference (TLD), maximum weekdays (max WD) and variation
load difference (VLD). Load difference (LD) for maximum load is a load difference within 4
days before the national holiday which is given by:
( ) ( )( ) 100
( )MAX
MaxSD i MaxWD iLD i x
MaxWD i
(14)
( ) 4 ( ) 3 ( ) 2 ( ) 1
( ) 4
WD WD WD WDi d i d i d i d
MaxWDi
(15)
MaxSD (i) is the peak load on special day and maxWD is the average of maximum load 4
days before holiday. Then, looking for a distinctive characteristic of a typical peak load or
typical load difference (TLDMAX (i)) by averaging the peak load of similar LDMAX (i) in
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previous years. After that, calculating the variation load difference, which is the difference
between Load Difference (LD) and Typical Load Difference (TLDMAX (i)) which can be seen
by the following equation:
max max max( ) ( ) ( )VLD i LD i TLD i (16)
max max maxmax
( 1) ( 2) ( 3)( )
3
LD i LD i LD iTLD i
(17)
Peak load data which is used to calculate Max WD and LD max is based on (10) and (11)
equations respectively and the results are presented in Table 1 and 2.
Table 1 Peak Load in 2010
National Holidays Peak Load in 2010 (MW)
WD(i)d-4 WD(i)d-3 WD(i)d-2 WD(i)d-1 MaxSD(i)
16036.00 15861.00 15791.00 14740.00 13562.00
17590.00 16897.00 16312.00 16796.00 15259.00
16642.00 16320.00 17885.00 16973.00 15192.00
17526.00 16539.00 15829.00 16918.00 15960.00
17041.00 17084.00 16963.00 16584.00 15542.00
17491.00 17618.00 17251.00 17220.00 15498.00
15721.00 14882.00 13254.00 12051.00 11494.00
14882.00 13254.00 12051.00 11494.00 11700.00
17025.00 16727.00 16862.00 16632.00 15598.00
15934.00 17522.00 17700.00 17522.00 16076.00
17481.00 17250.00 17047.00 16605.00 15302.00
17209.00 16438.00 15809.00 16556.00 15620.00
17144.00 17157.00 16812.00 15590.00 14901.00
17695.00 17722.00 17638.00 17482.00 16040.00
Table 2 VLD max for Idul Fitri 2009 and 2010
Year Max WD LD Max TLD max VLD max
2010 12920.3 -9.4445 -9.3503 -0.0942
2009 13318.5 -12.332 -7.8592 -4.4733
4.2. Processing
Interval Type-2 FLS fuzzy set operation is identical with the operation on type-1 fuzzy sets,
but Interval Type-2 FLS has FOU. FOU is a membership function generated from two type-1
logic fuzzy set which is bounded by upper membership function (UMF) and lower
membership function (LMF).
( )x
1.0
Upper MF
Foot Print of
Uncertainty (FOU)
Lower MF
x
Figure 5 FOU fuzzy type 2
Peak Load Forecasting on National Holiday using Fuzzy-Firefly Algorithm at Jawa-Bali
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Generally, IF-THEN fuzzy rules is used in this method for predicting the maximum load
which is expressed as follows :
IF X is Ai AND Y is Bi THEN Z is Ci
Fuzzyfication design of X and Y input is using IT2MF Editor. There are 11 membership
functions is used [7], namely :
Negative Very Big (UNVB and LNVB)
Negative Big (UNB and LNB)
Negative Medium (UNM and LNM)
Negative Small (UNS and LNS)
Negative Very Small (UNVS and LNVS)
Zero (UZE and LZE)
Positive Very Small (UPVS and LPVS)
Positive Small (UPS and LPS)
Positive Medium (UPM and LPM)
Positive Big (UPB and LPB)
Positive Very Big (UPVB and LPVB)
Examples of fuzzy rules can be seen in Table 3.
Tabel 3 Fuzzy Rules
No. Antecendent Consequent
Rules X Y Z
1 PVS PS NS
2 PS NS PS
3 PVS ZE ZE
4 ZE ZE PS
5 PS PS PVS
6 ZE PVS NS
7 NM NS NVS
8 NS NVS ZE
9 ZE NVS PVS
10 ZE PVS ZE
11 NS ZE NVS
12 PVS NVS PS
13 NVS PS NVS
14 NM NVS NVS
Rules in Table 3 can be seen in the rule editor as follows:
[R1] IF X is PVS AND Y is PS THEN Z is NS
[R2] IF X is PS AND Y is NS THEN Z is PS
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[R14] IF X is NM AND Y is NVS THEN Z is NVS
One of the example in selecting fuzzy set is using max rule by taking the largest value of
which is in accordance with the degree of membership (μ) of the input (X, Y) and output (Z)
variables in the Tahun Baru Masehi which can be seen in Table 4. The input value of X, Y
and Z variables are VLDmax of the holiday data. X is VLDmax(i) on similar holidays in the
year before the forecasting year. Y is VLDmax(i) on previous holidays (adjacent) in
forecasting year. Z is VLDmax(i) forecasting. LMF and UMF parameters are limited by the
value of X, Y and Z variables. LMF and UMF parameters on FOU are optimized by using
firefly algorithm. X, Y and Z variables are represented as a starting position of firefly. X, Y
and Z variables are shown in figure 6, 7 and 8.
Table 4 Establishment of Rule Base For Input X In 2010
Holida
ys
Name
Variab
el
VLD
max
Degree of membership (μ) Set
of
NV
B NB
N
M
N
S
NV
S ZE PVS PS PM
P
B
PV
B X
Tahun
Baru
Masehi
X 2,9984
88
0,50
1
0,4992
4 PVS
Y 4,8004
52
0,08
8
0,9116
2 PS
Z
-
3,2783
8
1
PVS
Antecedent (X, Y) and consequent (Z) T2FIS figures as follows:
-10 -5 0 5 10
1
0
0.5
Interval Type-2 Membership Function Plots
Input Variable “VLD X”
Figure 6 Membership Function for Variable Input X T2FIS
-10 -5 0 5 10
1
0
0.5
Interval Type-2 Membership Function Plots
Input Variable “VLD Y”
Figure 7 Membership Function for Variable Input Y T2FIS
Peak Load Forecasting on National Holiday using Fuzzy-Firefly Algorithm at Jawa-Bali
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-10 -5 0 5 10
1
0
0.5
Interval Type-2 Membership Function Plots
Input Variable “VLD Z”
NVB NB NS NVS ZE PVSNM PS PM PB PVB
Figure 8 Membership Function for Variable Input Z T2FIS
4.3. Post-Processing
After getting VLDMAX forecasting value, then forecast load difference can be expressed as
follows:
MAX MAX MAXForecast LD i Forecast VLD i TLD i (18)
Peak load forecasting on national holiday can be calculated as follows:
' ( ( ))( ) ( )
100
MAXMAX
ForecastLD xMaxWD iP i MaxWD i
(19)
To measure the performance of the proposed method then used absolute error equation;
the smaller error obtained show the accuracy of the proposed method is higher. Absolute error
can be expressed as follows:
100%forecast actual
actual
P PError x
P
(20)
' ( ) ( )100%
( )
MAXP i MaxSD iError x
MaxSD i
(21)
5. RESULTS AND DISCUSSION
The data used is the peak load data of Jawa-Bali electricity system started in 2007-2010 by
using Interval Type-2 Fuzzy Inference System - Firefly Algorithm (IT2FISFA) method and
several methods such as the Interval Type-1 Fuzzy Logic (IT1FL), Interval Type-2 Fuzzy
Logic (IT2FL), Interval Type-2 Fuzzy Logic-Big Bang Big Crunch (IT2FL-BBBC) as a
comparison. Then, the data is devoted to four days before and during holidays. The result of
the calculation of peak load forecasting on national holiday in 2010 can be seen in Table 5
and 6.
The test results by using IT2FISFA method as a proposed method for load forecasting
showed excellent results, in which the Mean Absolute Percentage Error (MAPE) of VLDMAX
is 0.140721009%. By using IT1FL, MAPE is 0.492639977%. By using IT2FL, MAPE is
0.453680469%. By using IT2FLBBBC, MAPE is 0.201490746%. For complete results can be
seen in table 5 and 6, as well as figure 9-12. Table 5 is the results of VLDmax and table 6 is the
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results of load forecasting with four methods as comparison. Figure 9-12 show the results of
the plotting.
Table 5 Results of VLD Forecast on National Holidays in 2010.
N
o Holidays Name
VLD
Targ
et
IT1FLS IT2FLS IT2FLS-BBBC IT2FIS-FA
VL
D
Error(
%)
VL
D
Error(
%) VLD
Error(
%) VLD
Error(
%)
1 Tahun Baru
Masehi
-
3.278
38
-
0.99
98
-
2.27855
-
1.00
23
-
2.27603 -1.08
-
2.19838
-
2.29147
6473
-
0.98690
0901
2 Proklamasi
Kemerdekaan RI
4.800
452
3.99
65
0.80396
4
3.99
78 0.80262
3.81915
0256
0.98130
2
4.57246
4325
0.22798
8054
3 Idul Adha
-
0.721
91
0 -
0.72191
-
1.92
1.19808
6 -1.44
0.71808
6 -1.8
1.07808
5984
4 Tahun Baru
Hijriyah
4.110
907
2.44
91
1.66183
1
2.65
42
1.45668
6
2.23757
9726
1.87332
7
3.99560
3782
0.11530
3202
5 Maulid Nabi
Muhammad SAW
2.111
261
-
0.28
37
2.39496
3
-
0.04
7
2.15827
8
0.17547
0724 1.93579
1.06647
021
1.04479
1013
6 Isra Mi'raj
-
4.341
49
-
3.84
72
-
0.49431
-
2.73
4
-
1.60747
-
2.91584
0345
-
1.42565
-
4.18052
6377
-
0.16096
1879
7 Idul Fitri I
-
2.176
05
-
2.00
32
-0.1729
-
1.90
65
-
0.26959
-
1.75528
5525
-
0.42077
-
2.06207
2181
-
0.11398
1591
8 Idul Fitri II
-
0.094
18
-
0.55
28
0.45859
1
-
0.40
44
0.31025
2
-
0.53800
6271
0.44382
5
-
0.09497
8398
0.00079
7545
9 Wafatnya Yesus
Kristus
1.913
659
2.87
79 -0.9642
2.58
29
-
0.66923
2.91600
0822
-
1.00234 2.52
-
0.60634
1042
1
0
Kenaikan Yesus
Kristus
0.962
723
-
3.00
98
3.97252
2
-
2.19
06
3.15333
9
-8.88E-
16
0.96272
3 0.72
0.24272
2575
1
1 Natal
-
2.063
65
-
2.00
39
-
0.05971
-
2.00
31
-0.0606 -1.44 -
0.62365
-
2.06412
5619
0.00047
4617
1
2 Nyepi
3.278
635
2.45
41
0.82451
9
2.65
07
0.62793
8
2.86312
851
0.41550
7
3.28064
5464
-
0.00201
0186
1
3 Tahun Baru Imlek
-
1.351
21
-
2.82
84
1.47713
7
-
2.75
64
1.40520
1
-
2.33713
0868
0.98591
7
-
2.48224
8776
1.13103
4751
1
4 Waisak
-
1.330
38
-
1.32
54
-
0.00498
-
1.45
24
0.12203
6
-
1.50556
1569
0.17517
9
-
1.32947
4168
-
0.00090
802
Mean Average Percentage Error
(MAPE)
0.49263
9977
0.45368
0469
0.20149
0746
0.14072
1009
Peak Load Forecasting on National Holiday using Fuzzy-Firefly Algorithm at Jawa-Bali
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Tabel 6 Results of Peak Load forecasting on National Holidays in 2010.
N
o Holidays Name
Act
ual
(M
W)
IT1FLS IT2FLS IT2FLS-BBBC IT2FIS-FA
Foreca
st
(MW)
Error(
%)
Forec
ast
(MW
)
Error
(%)
Foreca
st
(MW)
Absolu
te
Error(
%)
Foreca
st
(MW)
Error(
%)
1 Tahun Baru
Masehi
135
62
13917.
61757
2.6221
6
13917
.227
2.619
285
13905.
10076
2.5298
68433
13716.
02562
1.1357
14671
2 Proklamasi
Kemerdekaan RI
152
59
15123.
1421
0.8903
5
15123
.362
0.888
906
15093.
17221
1.0867
53998
15220.
47287
0.2524
87917
3 Idul Adha 151
92
15314.
40052
0.8056
9
14988
.865
1.337
121
15070.
24852
-
0.8014
18369
15009.
21052
1.2031
9562
4 Tahun Baru
Hijriyah
159
60
15682.
42838
1.7391
7
15716
.686
1.524
522
15647.
09815
1.9605
3792
15940.
74091
0.1206
71014
5 Maulid Nabi
Muhammad SAW
155
42
15136.
82046 2.607
15176
.865
2.349
341
15214.
50296
2.1071
74344
15365.
24226
1.1372
90848
6 Isra Mi'raj 154
98
15583.
98144
0.5547
9
15777
.623
1.804
249
15745.
99145
1.6001
51336
15525.
99932
0.1806
64078
7 Idul Fitri I 114
94
11518.
15977
0.2101
9
11531
.676
0.327
784
11552.
81078
0.5116
65024
11509.
93121
0.1386
0455
8 Idul Fitri II 117
00
11640.
74526
0.5064
5
11659
.919
0.342
573
11642.
65665
0.4901
14132
11699.
89696
0.0008
80724
9 Wafatnya Yesus
Kristus
155
98
15760.
10338
1.0392
6
15710
.509
0.721
307
15766.
5087
1.0803
22493
15699.
93502
0.6535
13426
1
0
Kenaikan Yesus
Kristus
160
76
15393.
93774
4.2427
4
15534
.59
3.367
814
15910.
70535
1.0282
07592
16034.
32575
0.2592
32723
1
1 Natal
153
02
15312.
21488
0.0667
6
15312
.352
0.067
649
15408.
61782
0.6967
57392
15301.
91886
-
0.0005
30254
1
2 Nyepi
156
20
15483.
92694
0.8711
5
15516
.372
0.663
433
15551.
42892
0.4389
95402
15620.
33174
-
0.0021
23822
1
3 Tahun Baru Imlek
149
01
14654.
66816
1.6531
2
14666
.675
1.572
547
14736.
59097
1.1033
42244
14712.
39147
1.2657
44094
1
4 Waisak
160
40
16040.
87857
0.0054
8
16018
.483
0.134
145
16009.
10843
-
0.1925
90835
16040.
16012
-
0.0009
9827
Mean Average Percentage
Error (MAPE)
1.2724
49841
1.265
763
0.9742
77222
0.4531
67666
Figure 9 Results of VLD Forecasting on National Holidays in 2010
Andi Imran, I Made Yulistya Negara and Imam Robandi
http://www.iaeme.com/IJCIET/index.asp 1013 [email protected]
Figure 10 Results of VLD Error Forecasting on National Holidays in 2010
Figure 11 Results of Load Forecast for National Holidays in 2010
Figure 12 Results of Load Forecasting Error on National Holidays in 2010
6. CONCLUSIONS
Interval Fuzzy Inference System Type-2 method, which is optimized by using Firefly for peak
load forecasting on national holidays in Jawa-Bali 500kV electrical system showed excellent
results, where the average of load forecasting error is 0.453167666%, while using IT1FL, the
average of load forecasting error is 1.272449841%, using IT2FL is 1.265763% and using
IT2FL-BBBC is 0.974277222%.
Peak Load Forecasting on National Holiday using Fuzzy-Firefly Algorithm at Jawa-Bali
Electricity System in Indonesia
http://www.iaeme.com/IJCIET/index.asp 1014 [email protected]
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