peak load forecasting on national holiday using …...fuzzifikasi rule base defuzzifikasi inference...

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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


Imam Robandi


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


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


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 Ã 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).




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)



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,




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



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




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



[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


Input Variable “VLD Y”

Figure 7 Membership Function for Variable Input Y T2FIS




-10 -5 0 5 10

1

0

0.5


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



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




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



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%.




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peak load forecasting on national holiday using …...fuzzifikasi rule base defuzzifikasi inference...

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