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Table of Contents

Acknowledgement ..........................................................................................................................1

Abstract ...........................................................................................................................................2

Chapter 1

Introduction ....................................................................................................................................4

1.1 Introduction ............................................................................................................................4

1.2 Background of Study ..............................................................................................................4

1.3 Problem Statement .................................................................................................................5

1.4 Objective of Project ................................................................................................................5

1.5 Scope of Study .......................................................................................................................5

Chapter 2

Literature Review ..........................................................................................................................7

2.1 Introduction ............................................................................................................................7

2.2 Journal and Research Papers ..................................................................................................7

Chapter 3

Methodology .................................................................................................................................10

3.1 Introduction ..........................................................................................................................10

3.2 Load Analysis .......................................................................................................................10

3.3 System Design ......................................................................................................................16

3.4 Fuzzification .........................................................................................................................17

3.5 Fuzzy Inference Rule ...........................................................................................................20

3.6 Defuzzification .....................................................................................................................23

Chapter 4

Results and Discussions ...............................................................................................................31

Chapter 5

Conclusion ....................................................................................................................................35

References .....................................................................................................................................36

1

ACKNOWLEDGEMENT

First of all, I would like to say Alhamdulillah, praise to our God Allah S.W.T for the

blessings and giving us a good health to finally able to accomplish this report. I would also like

to express our most sincere gratitude to our dedicated lecturer, Datin Prof. Ir. Dr. Shah Rizam

Mohd Shah Baki for all her guidance, patience and also for being very supportive for me to

finish the report perfectly to fit the specifications and requirements to finally able to make this

report almost perfect and flawless. Also being very supportive in all possible ways, my parents

are not to be forgotten as they bless us with unstopped prayers, allowing us to think clearly and

work effectively from the very beginning to the end, without any loose ends. Last but not least, I

would also like to thank all of our friends, especially from the faculty of engineering that spent

their time commenting and contributing brilliant ideas which is vital to the outcome of this

report, and for their outstanding commitment and support.

2

FUZZY LOGIC ELECTRICAL LOAD FORECASTING FOR NEXT DAY

PEAK LOAD

Ahmad Faezi Bin Faizol

Faculty of Electrical Engineering

Universiti Teknologi MARA (UiTM) Malaysia

40450, Shah Alam, Selangor

afaezi.faizol@gmail.com

Abstract

Load forecasting has been always been used by power electrical provider to increase

efficiency as well as to meet demand especially during peak hours. This action can prevent

downtime and power outages in the most demanding hours and several methods have been

practiced to forecast load such as expert system and statistical model-based learning. The fuzzy

logic approach is used in this report to achieve similar result. Past load data ranging from

September to October 1992 is analyzed to develop this system. Peak load of one day is defined at

two times, which are 11 am in the morning and 3 pm in the afternoon. The fuzzy logic system

inputs will be consisting of previous two peak loads and day type. A rule block is used to give

result in the forecasted peak load for next day. The Forecasted load output is expected to contain

less than 2% error when compared to the actual value.

3

CHAPTER 1

4

CHAPTER 1

INTRODUCTION

1.1 BACKGROUND OF STUDY

This study will forecast peak load for the next day based on past peak load values and

type of day. This is a type of short term load forecasting that also includes forecasting in

terms of weekly, daily and hourly. This data is important for electrical provider companies,

to generate enough electricity in peak hours. Peak load of a given day is observed from past

load data. The finding from past load data shows peak load occurred two times in a day,

which is on 11 am and 3 pm on weekdays. Most of Saturdays are half-day working day,

which gives the same load profile as weekdays before noon. After office hours at noon, the

load graph descends similar to holidays. On Sundays, the load profile is low throughout the

day and the peak load on Sundays is observed to be occurred at night at around 8 pm.

This fuzzy logic system will be simulated on FuzzyTech 5.54. The analyzed data from

load curve analysis is used to assign value for fuzzification, which is a process to convert

numerical value to linguistic variable. These inputs in linguistic variable will be used to

assign fuzzy rules that are important to make decision. The final value will be defuzzified

using the best method that gives least error to ensure the reliability and trustworthiness of the

system.

5

1.2 PROBLEM STATEMENT

During generation and distribution process in electrical power provider operation, the

ability to forecast peak load in a day can greatly improve efficiency and save cost. Regular

maintenance and repairs can be done when the electricity demand is low and the provider can

be ready to generate more during peak hours, but accordingly. A system must be developed

to forecast peak load in a day and taking in consideration environmental factors as well as the

type of day.

1.3 OBJECTIVE OF PROJECT

The objective of this project is

1. To develop a fuzzy logic system to forecast peak load of any given day in a week by

using the best fuzzy logic techniques and approaches that gives the least error.

1.4 SCOPE OF STUDY

The study is based on raw electrical load data from September to October 1992, which

the data is used to design a fuzzy logic system to forecast peak load of a given day, based on

the peak load of previous day and peak load of the same day on last week. The accuracy of

forecasted load is determined to determine whether the system is capable or not to be

implemented on the real world.

6

CHAPTER 2

7

CHAPTER 2

LITERATURE REVIEW

1.1 INTRODUCTION

Academicians and electrical engineers around the world have already applied the

artificial intelligence techniques to forecast electrical load. Some of these

accomplishments are already published in IEEE Library Database. A few papers are

found relevant in assisting in the completion of this report. The summary of these papers

are as follows.

1.2 JOURNALS AND RESEARCH PAPERS

Load forecasting with fuzzy logic has been applied worldwide especially in

countries with four seasons, to ensure high efficiency in generation and transmission [1].

Fuzzy logic system in real world application also includes expert system and neural

network to assist in achieving higher accuracy in forecasting. Previous load data is

evidently useful to teach these systems to predict peak load in short term forecasting.

Fuzzy values (linguistic variable) can increase accuracy of a system as numerical method

can largely affected by any value discrepancies. Large or small geographical area also

can contribute to load forecasting as proven by data in Midwest US and the UK [2]. In

[3], type-2 fuzzy logic system is used for load forecasting, which type-2 fuzzy logic

system consist of two steps which is reducer block and then defuzzifier whereas type-1

fuzzy system only has defuzzifier.

It is also woth mentioning that Saleh Ahmadi in [5] presents Iran power

generation and specifically study the Sanandaj Power Network. The case study lists the

factors that is considered during load forecasting including economy and power

disturbance. In [6] Amit Jain in India shows how temperature and humidity can affect

8

load demand in tropical countries. Average day temperature is plotted against average

load, the same is done to average humidity. M.F.I Khamis in [8] shows fuzzy logic

application for a small scale power system. The proposed model can be used to forecast

load one week ahead, every single day in a week is forecasted. The system also

incorporates Data Dynamic Exchange Server to obtain previous load data. In [10] A.R

Koushki simulates that the combination of fuzzy logic and neural network will result in

much more accurate forecasts. The learning algorithm mentioned in this paper is Locally

Linear Model Tree (LoLiMoT) and the results are compared to multilayer perception and

Kohonen Classification and Intervention Analysis.

9

CHAPTER 3

10

CHAPTER 3

METHODOLOGY

3.1 INTRODUCTION

Raw data obtained must be analyzed and interpreted before decision is made in designing

a fuzzy logic system. The fuzzy logic system design will follow a project flow chart and

become a complete system once all the processes are done.

3.2 LOAD ANALYSIS

Load data during September to October is tabulated and analyzed graphically do

determine trends in electrical load as well as pinpointing which day and which hour in a day

a load number represents. The data also contributes to which hour in a day a peak load is

achieved and which day in a week electrical load is low or high. Maximum load in these two

months is observed on Thursday 8th

October 1992 at 11 am which is 4554.8 MW. Minimum

value of load is observed on Tuesday 29th

September 1992 at 4 pm which is only 120 MW.

There was a major blackout throughout Malaysia during that day that contribute to such low

power load.

11

The first week load graph is shown in Figure 1. The load reduces significantly during

Sunday and is also low during Saturday. For the rest of week, the load curve is quite

consistent, except for a drop on Monday at 8 pm.

Figure 1 Load profile first week September 1992

Second week of September load curve shows that the minimum load is also on Sunday as

shown in Figure 2. It is public holiday on Wednesday, so the curve is very similar to

Sundays but with a little bit rise compared to it.

12

Figure 2 Load profile second week September 1992

For the third week of September load curve, the lowest load reading is during Sunday as

illustrated in Figure 3. On Saturday, offices are opened half-day, supporting that the curve is

the same with other weekdays curves before noon and started to fall afterwards.

Figure 3 Load profile third week September 1992

13

A major power outage occurred on 29th

September, causing the load curve to fall greatly

on Tuesday as shown in Figure 4. Recovery process continues in the next day, showing low

load curve (green) similar comparable to Sundays curve (orange). The data collected during

power outage may not be used in actual forecasting system as a reliable system must use

stable, regular load curve on a normal day.

Figure 4 Load profile fourth week September 1992

The pattern goes on for the first week of October. There are no irregular values during the

weekdays which showing normal load curve and the load curve for Sunday is the lowest of

the week as usual. On Saturday which is a half-day work day, the load profile decreases after

noon when offices closed for the day as shown in Figure 5.

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Figure 5 Load profile first week October 1992

On second week of October, the load profile for weekdays follow usual trend, except for

Tuesday which shows significant drop from 11 pm to 12 am but the load recover the next hour as

usual as shown in Figure 6. This occurrence must be caused by typing error in the data input

process or a small and short power outage. The load curve for weekend also follow the usual

trend, low throughout the day on Sunday and half-day working load curve for Saturday.

15

Figure 6 Load profile second week October 1992

For the third week of October, weekdays load plot shows regular pattern except for Friday

that has a slight drop at 3 pm as shown in Figure 7. Sunday load profile shows usual low pattern

and Saturday plot also dropped after office hours ended at noon.

Figure 7 Load profile third week October 1992

16

On the fourth week of October, the load graph suggested that it was public holiday on Monday,

which shows similar load profile to Sunday as shown in Figure 8. Other weekdays show regular

pattern of load plot and plot on Saturday decreases after noon.

Figure 8 Load profile fourth week October 1992

3.3 SYSTEM DESIGN

Figure 9 below shows the flowchart for designing this fuzzy logic system. The system is design

systematically from step by step to increase forecast accuracy as well as tackling problems and

errors wisely in this system.

17

Figure 9 Flowchart for fuzzy logic system

The block diagram of this system is represented in Figure 10. Blocks on the left side

represent input of this sytem and block on the right hand side represents output of the system.

The block in the middle is rule block, where fuzzy rules is located and fuzzy operations are

performed.

Determine input variables and output variable

Input: Day and Previous Load

Output: Forecasted Load

Start

Define linguistic variables for each inputs and outputs

Block diagram of system structure is constructed

Create fuzzy rules for fuzzy logic system

Select fuzzy inference method

Select defuzzification method

Accept system and analyze results

Large error between

forecasted and actual load?

End

No

Yes

18

Figure 10 Block diagram of fuzzy logic system

3.3 FUZZIFICATION

The system consists of 5 inputs which are Day, LastDayPeak1, LastDayPeak2,

LastWeekPeak1 and LastWeekPeak2. These inputs must be converted from numerical values to

linguistic variables. Assignment of fuzzy membership for power values can be equal for all the

inputs. This is to ensure consistent result for all the inputs. Although the memberships have equal

value, the name for each membership function must be different from each other. This is

important to prevent confusion during defining fuzzy rules process.

The first input used is day, numerically written from 1 to 7 where 1 is Monday and 7 is

Sunday. The membership function is as shown below in Figure 11

Figure 11 Membership Function for input Day

19

The next four inputs of the fuzzy logic system are various load, which are LastDayPeak1,

LastDayPeak2, LastWeekPeak1, and LastDayPeak2. LastDayPeak1 is the peak load of previous

day at 11 am, and the membership function is shown in Figure 12.

Figure 12 Membership function of LastDayPeak1

LastDayPeak2 describes peak load from previous day at 3 pm which when second peak occurred

in a day and the membership function is illustrated in Figure 13.

20

Figure 13 Membership function of LastDayPeak2

LastWeekPeak1 is the peak load of same day on previous week at 11 am, and the membership

function is shown in Figure 114.

Figure 14 Membership function of LastWeekPeak1

LastWeekPeak2 describes peak load from same day of previous week at 3 pm which when

second peak occurred in a day and the membership function is illustrated in Figure 15.

21

Figure 15 Membership function of LastWeekPeak2

3.4 FUZZY INFERENCE RULE

Fuzzy rule is then being written to make this system work. IF-THEN statements are used

to define rules. Between inputs, AND, OR and XOR statement can be used. In case of this

project, 512 fuzzy rules are written to satisfy all possibilities of the variables. These 512 rules

can be summarized in FuzzyTECH software in matrix form.

The matrix form can only occupy two axis at a time, Figure 16 shows the rule matrix of

Day versus LastDayPeak1. Figure 17 describes the rule matrix of Day versus LastDayPeak2,

Figure 18 illustrates the relationship between Day and LastWeekPeak1 whereas Figure 19 shows

the rule matrix of Day versus LastWeekPeak2

22

Figure 16 Matrix Fuzzy rule Day versus LastDayPeak1

Figure 17 Matrix Fuzzy rule Day versus LastDayPeak2

23

Figure 18 Matrix Fuzzy rule Day versus LastWeekPeak1

Figure 19 Matrix Fuzzy rule Day versus LastWeekPeak2

24

Fuzzy inference chosen to be used in this system is Max-Min method. For this method,

the membership values in the two or more conditions within IF statement in a fuzzy rule is

compared. Minimum value from these compared value is taken as AND operation is used in IF

statement. For example in Figure 20, the first two membership functions shows the fuzzy value

for two items in the IF statement. The third membership figure shows the resulting fuzzy

inference by using Max-Min method.

Figure 20 Max-Min (Mamdani) fuzzy inference

3.6 DEFUZZIFICATION

The last step in completing this fuzzy logic system defuzzification method. Centre-of-

Maximum (CoM) method uses all maximum values in fuzzy inference membership, and all of

these maximum points are multiplied with its respective crisp value. The summation of all these

terms are then being divided by sums of all membership value of maximum points. This method

of calculation is represented by this formula in Figure 21 where is membership value of all

maximum points and Y is crisp value in x-axis.

Figure 21 Centre-of-Maximum (CoM) defuzzification

= ( )

25

Mean-of-Maximum defuzzification uses the edge value in highest point obtained in Max-Min

fuzzy inference and divide by two to obtain crisp value, as shown in Figure 22.

Figure 22 Mean-of-Maximum (MoM) defuzzification

For Centre of area defuzzification, samples of readings of x axis values are taken for each flat

points in Max-Min fuzzy inference and are multipled by each membership value. In

denominator, the membeship values are multiplied with number of samples taken. CoA

defuzzification is represented by equation shown in Figure 23.

Figure 23 Centre-of-Area (CoA) defuzzification

To demonstrate the system operation, example is taken to forecast peak load on Tuesday

8th

September 1992. The fuzzification for these sets of data are shown below. In Figure 24

Wedenesday is a member of the fuzzy set Weekday to the degree of 1.00

Figure 24 Fuzzy set for Tuesday

( ) = ()

()

() =a + b

2

26

First peak for Monday which is the day before is given as 4362.8 MW is a member of fuzzy set

LDayHigh to the degree of 1.00 as shown in Figure 25.

Figure 25 Fuzzy Set for LastDayPeak1

Second Peak of Monday is given as 4364.3 MW which is a member of fuzzy set LDay2High to

the degree of 1.00 as shown in Figure 26.

Figure 26 Fuzzy Set for LastDayPeak2

27

First peak for Tuesday which is the week before is given as 4175.1 MW is a member of fuzzy set

LWeekMedHigh to the degree of 0.13 and LWeekHigh to the degree of 0.99 as shown in Figure

27.

Figure 27 Fuzzy Set for LastWeekPeak1

First peak for Tuesday which is the week before is given as 4175.1 MW is a member of fuzzy set

LWeek2MedHigh to the degree of 0.04 and LWeek2High to the degree of 1.00 as shown in

Figure 28.

Figure 28 Fuzzy Set for LastWeekPeak2

28

Performing Mamdani Fuzzy Inference (Max-Min Method) will result in a plot as follows in

Figure 29.

Figure 29 Max-min (Mamdani) Fuzzy Inference

Applying the three defuzzification method will result as the foolowing:

(i) Centre-of-Maximum (CoM)

Simulating CoM defuzzification gives the following result as in Figure 30.

Figure 30 CoM defuzzification for 8 September 1992

29

Besides from using software simulation to find defuzzified crisp value, manual

calculations can be performed and compared.

= ( )

=(3208.4 0.21) + (4384.5 0.99)

0.21 + 0.99

= 4178.68

(ii) Mean-of-Maximum (MoM)

Simulating CoM defuzzification gives the following result as in Figure 31.

Figure 31 MoM defuzzification for 8 September 1992

= +

2

=4300 + 4500

2

= 4400

30

(iii) Centre-of-Area (CoA)

Simulating CoA defuzzification gives the following result as in Figure 32

Figure 32 CoA defuzzification for 8 September 1992

= ()

()

=[0.21(2767 + 3000 + 3500) + 0.99(4300 + 4400 + 4500)

(0.21 3) + (0.99 3)

= 4130.6

31

CHAPTER 4

32

CHAPTER 4

RESULTS AND DISCUSSION

4.1 INTRODUCTION

In this chapter, result is collected and represented in table and graph form. Three

defuzzification methods are used in this chapter. The values from actual and forecasted load are

compared and error less than 2% is expected to conclude that the method is the most suitable to

be implemented.

4.2 RESULT AND DISCUSSION

Peak load value is tabulated for a week, the week selected is second week of October as

in Table 1. Three defuzzification methods (Mean of Maximum, Centre of Maximum and Centre

of Area) are performed and compared to the actual values. A graph is also generated in Figure 33

to graphically show differences in simulated and actual values.

Day Actual Peak

Load

Forecasted Peak Load (MW)

MoM CoM CoA

Thursday 4395.2 3976.7 4325.4 4325.9

Friday 4371.2 3976.7 4247.2 4250.1

Saturday 4213.0 3976.7 4172.4 4169.8

Sunday 3209.0 3976.7 3097.3 3102.4

Monday 4443.5 3976.7 4303.0 4411.0

Tuesday 4442.5 3976.7 4315.5 4310.1

Wednesday 4439.0 3976.7 4307.3 4308.1

Table 1 Comparison between Defuzzification Methods

33

Figure 33 Graph comparing Defuzzification methods

Based on Table 1, Relative error is calculated using formula as follows and the results are

tabulated in Table 2.

(%) =| |

100

Day Actual Peak

Load

Forecasted Peak Load (MW)

MoM CoM CoA

Thursday 4395.2 9.5 1.59 1.57

Friday 4371.2 9.02 2.8 2.7

Saturday 4213.0 5.6 0.96 1.02

Sunday 3209.0 23.9 3.5 3.3

Monday 4443.5 10.5 3.1 0.73

Tuesday 4442.5 10.4 2.9 2.9

Wednesday 4439.0 10.4 2.9 2.9

Table 2 Percentage Relative error for three types of defuzzification

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

0 1 2 3 4 5 6 7 8

Elec

tric

al L

oad

(M

W)

Day

Defuzzification Comparison

Actual Load MoM CoM CoA

34

By comparing these graphs of defuzzification methods being used in all of the data, Centre-of-

Area (CoA) and Centre-of-Mass (CoM) method has little difference in result. Between CoA and

CoM methods, CoA methods is more accurate to be used as this method takes more sample in

calculation to come up with crisp defuzzified value contrary to CoM method that take only one

reading per membership value in Max-Min fuzzy inference diagram. Therefore, CoA method is

chosen to be the best method to implement this system.

35

CHAPTER 5

36

CHAPTER 5

CONCLUSION

The system can successfully forecast peak load based on previous peak load data and

type and day. The best implementation is also determined which is using Centre-of-Area (CoA)

defuzzification which takes samples from more points than two other defuzzification method.

The relative error margin is said to be kept under 2% but it cannot be achieved for all instance

despite countless trial and error in modifying the fuzzy rules. The final system managed to

achieve less than 2% error in certain circumstances.

To improve this system in the future, fuzzy logic can be used alongside other artificial

intelligence techniques such as artificial neural network or particle swarm optimization. This

approach can greatly improve the systems accuracy and reliability. Another suggestion is to use

many rule blocks and more inputs that takes into account environmental factors such as weather

and seasons.

37

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