ABSTRACT
Fuzzy Time Series (FTS) plays a great role in fuzzification of data, which is based on certain
membership functions. In this thesis, a 24 weeks load demand data from PHCN was used and
fuzzified based on the Gaussian Membership Functions, after that all fuzzified data are
defuzzified to get normal form. The results obtained using the GMF (Gaussian Membership
Functions) is compared with that of the TMF (Triangular Membership Function), from which
the comparison basis was based on, qualitative performance indicator and statistical error. The
RMSE Values obtained using the GMF and the TMF are 66.5 and 17.1 respectively, while their
correlation factor R is 0.98 for TMF and 0.86 for GMF. From the analysis carried out the TMF
generated the least RMSE and hence, is more suitable in forecasting for electric load.
TABLE OF CONTENTS
TITLE PAGE – – – – – – – – – – .i
DECLARATION – – – – – – – – – ii
CERTIFICATION – – – – – – – – – iii
DEDICATION – – – – – – – – – iv
ACKNOWLEDGEMENTS – – – – – – – – v
ABSTRACT – – – – – – – – – – vi
CHAPTER ONE
INTRODUCTION – – – – – – – – – 1
1.1. BACKGROUND – – – – – – – – – 1
1.2 SIGNIFICANCE OF STUDY – – – – – – – 2
1.3 STATEMENT OF PROBLEM – – – – – – – 3
1.4 PROJECT OUTLINE – – – – – – – – 4
CHAPTER TWO
LITERATURE REVIEW AND THEORETICALBACKGROUND- – – 5
2.1 LITERATURE REVIEW – – – – – – – – 5
2.1.1 INTRODUCTION – – – – – – – – .5
2.2 REVIEW OF PAST WORKS IN THIS AREA – – – – – 7
2.3. FUZZY SET THEORY AND FORCECASTING – – – – 8
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2.3.1 FUZZY TIME SERIES – – – – – – – 8
2.3.2 FUZZY LOGIC OPERATORS – – – – – – – .9
2.4 MEMBERSHIP FUNCTION – – – – – – – 10
2.4.1 MEMBERSHIP FUNCTIONS IN FUZZY LOGIC – – – – 10
2.4.2 MEMERSHIP FUNCTIONS FOR FUZZIFICATION – – – 13
2.4. PERFORMANCE MEASURES – – – – – – – 14
CHAPTER THREE
3.1 INTRODUCTION – – – – – – – 16
3.2 FORECASTING ANALYSIS – – – – – – 16
CHAPTER FOUR
4.1 INTRODUCTION – – – – – – – – 27
4.2 SIGNIFICANCE OF RESULT – – – – – – 31
CHAPTER FIVE
CONCLUSION AND RECOMMENDATIONS FOR FURTHER WORK – – .32
5.1 SUMMARY – – – – – – – – – 32
5.2 LIMITATIONS – – – – – – – – – .32
5.3 CONCLUSION – – – – – – – – – 33
5.4 SUGGESTIONS FOR FURTHER WORK – – – – – 34
REFERENCE – – – – – – – – – – 35
APPENDIX – – – – – – – – – – -44
CHAPTER ONE
INTRODUCTION
1.1 BACKGROUND
Load forecasting is of vital importance in the electricity industry, especially in a deregulated
economy like that of Nigeria. It has many application including energy purchasing and
generation, load switching, contract evaluation, and infrastructural development. A large variety
of mathematical models have been developed and applied in carrying out load forecasting. In
this work, the Fuzzy Time Series (FTS) approach is used for the load forecasting.
There is a planned Government policy towards unbundling the utility (Power Holding Company
of Nigeria (PHCN)) company with the objective of improving efficiency of electricity
generation, transmission, and distribution. This emphasizes proper and effective planning,
management and operations of the network. The operation and planning of a power utility
company requires an adequate model for electric power load forecasting.
Load forecasting plays a key role in helping an electricity utility to make important decisions on
power, load switching, voltage control, network reconfiguration, and infrastructure
development. It is extremely important for an optimal management of generation and
distribution of electric energy to have as precise as possible the load profile prediction.
According to Abbasovand Mamedova (2003), time series represents a consecutive series of
observations taken over equal time intervals. The application of Fuzzy Logic and fuzzy sets to
time series analysis gave rise to Fuzzy Time Series. The method to be applied here is the
method initially used by Abbasovand mamedova (2003), in forecasting population in
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Azerbaijan but adopted by Adeola (2008) and Muazu (2009) in load forecasting. The emphasis
of their works was on determining an optimal interval length and model basis.
AIM AND OBJECTIVES
The aim is to carryout comparative investigation on the effect of triangular and gaussian
membership functions in fuzzy time series (FTS) forecasting.
The objectives are specifically listed as follows:
i. Defining the universe of discourse and interval lengths for the observations;
ii. Partitioning the universe based on the interval length;
iii. Defining the fuzzy set for the observation;
iv. Fuzzification of the observations using the appropriate membership function;
v. Establishing the fuzzy relationships;
vi. Performing the forecast;
vii. Defuzzification of the forecast result
viii. Qualitative and quantitative performance analysis
This study, therefore, is aimed at investigating the effect of triangular and gaussian Membership
Functions on electric load forecasting, building upon the work of Adeola (2008) and Muazu et
al (2009).
1.2 SIGNIFICANCE OF STUDY
In carrying out Fuzzy Time Series (FTS) forecasting, some critical issues include determination
of the interval length and appropriate membership function amongst others. This research will
address the implication of Membership Function in Fuzzy Time Series Forecasting. In Adeola
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(2008) and Muazu et al (2009), investigated load forecasting using the Fuzzy Time Series (FTS)
forecasting technique adopted by Abbasov and Mamdova (2003) and an optimal interval length
of five (5) and model basis of six (6) were determined. It was also observed in their work that
odd number interval lengths performed better than even number interval lengths. The
fuzzification method based on the triangular membership function was used. It then becomes
pertinent to determine the effect of membership functions used for the fuzzification on the
forecasting result.
1.3 STATEMENT OF PROBLEM
It is pertinent to determine the effect of triangular and gaussian Membership Functions
in Fuzzy Time Series Forecasting. This couple with Optimal Interval length in FTS data
analysis offers serious problem in forecasting.
This Research will address the implication associated with Membership Functions in
FTS Forecasting. The Gaussian membership function will be used in the fuzzification
process and the optimal interval length and model basis obtained by Adeola (2008),
Abbasov and Mamedova (2009). The essence then will be to compare and contrast
between the effect of the triangular and Gaussian membership functions (qualitatively
and quantitatively) on the forecasting result.
The following methodology as used by Adeola (2008),Muazu et al (2009) and Abbasov (2003)
is also adopted:
i. Partitioning the data into training data (18-weeks)
and validation data (6 weeks);
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ii. Defining the universal set U containing the interval
between least and greatest variation of load;
iii. Dividing the Universal set U into several interval
lengths (5) containing variation values corresponding to different loads consumed;
iv. Determining the respective value of linguistic
variable or the Fuzzy set (t) i.e. the qualitative description of variation values of
total load as a linguistic variable;
v. Fuzzifying the input data or the conversion of
numerical crisp values into fuzzy values. In this case, the Gaussian membership
function will be used;
vi. Selecting the parameter w>1(model basis) (6)
corresponding to the time period prior to the concerned week;
vii. Calculating the fuzzy matrix pw(T) and forecasting
of the expected load for the preceding week;
viii. Defuzzifying the obtained result or conversion of fuzzy values into quantitative
(crisp) values; and
Tabulating and comparing the results obtained using the Gaussian membership function and
those obtained using the triangular membership function.
1.4 PROJECT OUTLINE
The thesis is divided into five chapters: Chapter One introduces the research work where the
objectives of the research are defined and the methodology applied is explained. The reviews of
literature of similar research work, with the theoretical background are contained in Chapter
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Two. Chapter Three discusses the methodology in achieving the thesis aims, while Chapter
Four deals with the analysis of the results obtained. Chapter Five contains limitations,
conclusion and recommendation. References are provided at the end of the work.
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