ABSTRACT
Fuzzy Time Series (FTS) forecasting technique is the amalgamation of fuzzy
logic and time series technique. The critical issue in FTS forecasting is the
determination of the interval length. This paper therefore, is a research on
the effect of varying interval length and model basis on electric load
forecasting using Fuzzy Time Series Model. The methodology adopted is
presented and the data used is the load (in MW/MVA) obtained from PHCN
over a 24-week period. The data for 18 weeks is used as the test data while
the remaining 6 weeks is the validation data. It is shown that varying interval
length and model basis give different forecasting results and that interval
length five gives a significantly better result than others based on the
quantitative and qualitative performance test. Furthermore, the results
obtained show that model basis of four gives better forecasting result when
compared to model basis of five and six. The results obtained are presented
and discussed from the standpoint of their degree of consistency exhibited
by the two elements.
TABLE OF CONTENTS
Title page
Title Page i
Declaration ii
Certification iii
Dedication iv
Acknowledgement v
Table of contents vii
List of Figures x
List of Tables xi
List of Symbols xii
Abstract xiii
Chapter One
1.1 Introduction 1
1.2 Project Motivation 2
1.3 Statement of Problem 3
1.4 Methodology 3
1.5 Project Outline 6
ix
Chapter Two: Literature Review and Theoretical Background
2.1 Literature Review 8
2.2 Set theory and Forecasting 11
2.2.1 Introduction to Fuzzy Logic 13
2.2.2 Fuzzy Logic operators 14
2.2.3 Fuzzy Membership Function 15
2.3 Time Series 17
Chapter Three
3.1 Forecasting Methodology 21
3.2 Case A: Five equal length interval 23
3.3 Case B: Six equal length interval 31
3.4 Case C: Seven equal length interval 34
Chapter Four: Result and Analysis
4.1 Introduction 38
4.2 Analysis 40
4.3 Significance of Results 44
Chapter Five: Conclusion and Recommendation
5.1 Introduction 46
5.2 Limitations 47
5.3 Conclusion 48
x
5.4 Recommendation 49
REFERENCE 51
APPENDIX A 54
CHAPTER ONE
INTRODUCTION
The prediction of time series is an important problem in monitoring,
diagnosis, control and decision support for technical and non-technical
systems. While there have been many conventional time series models, one
particular important group of model has been the family of Fuzzy Time
Series. The advent of Fuzzy logic made it possible to tackle a many
problems with Fuzzy input. One of them is the forecasting problem.
Studies have shown that this model seem to be more appropriate in
forecasting, since it could address the problem of time-dependent actuating
variables (e.g. temperature, global solar radiation, etc) which other
traditional models such as statistical, adaptive, smooth dynamic series, auto
regression integration moving average (ARIMA) models could not resolve
without great inaccuracy. Furthermore, the necessary conditions for applying
the conventional time series could be removed in Fuzzy Time Series model.
The Fuzzy Time Series model can be roughly categorized according to how
they formulate the relationships among observations, that is, Fuzzy rules,
Fuzzy function, Fuzzy relationship and others.
Prediction of electric load power consumption can also be resolved using
Fuzzy model. The electricity consumption profile of a power generation and
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distribution company such as Power Holding Company of Nigeria (PHCN)
can after elimination of possible long term trends be regarded as a stationary
time series with seasonal characteristics. It is extremely important for an
optimal management of generation and distribution of electric energy to
have as precise as possible the prediction of the load to be expected.
However, in applying Fuzzy model to forecasting, the determination of the
length of interval is critical. In many previous models, interval length and
models basis were set arbitrarily. No explanations were provided to
determine the length of the interval. However, one recent study [1]
demonstrated that varying interval length and model basis could have great
impact on the forecasting result. This study, therefore, is aimed at
investigating the effect of varying interval length and model basis on electric
load forecasting.
A time series which contains load values for a period of 6 months (24
weeks) is employed to do this.
1.2 PROJECT MOTIVATION
Determination of interval length and model basis in Fuzzy Time Series has
been a critical issue. There has not been any empirical method of
determining an appropriate interval length and as such it becomes very
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important that an investigation be carried out to determine the effect of
varying the interval length on the forecasting result. Because of the critical
nature of electricity in the economic growth and well being of any economy,
any method that can enhance forecasting load demand or load consumption
pattern becomes very important.
1.3 STATEMENT OF PROBLEM
The electricity consumption profile of a power distribution company can,
after elimination of possible long-term trends, be-regarded as a stationary
time series. It is extremely important that for an optimal management of
electric energy, the load prediction should be as precise as possible.
This thesis is aimed at investigating the effect of varying the interval length
and model basis in a bid to improving the forecasting result of electric load
power consumption.
1.4 METHODOLOGY
There are many methods in forecasting time series. They include:
i. Moving average
ii. Auto correlation
iii. Auto Regression Integration Moving Average (ARIMA)
iv. Fuzzy Time Series etc.
4
Moving average (MA): This is one of the statistical methods of forecasting.
It provides a set of very powerful indicator for tracking trend and trend
reversals. Moving average is a lagging indicator, or trend following formula,
that smoothens the volatile swings in a market. It attempts to tone down the
fluctuations of market prices to a smoothed trend, so that distortions are
reduced to a minimum. Essentially, Moving averages is a method for
estimating incidence density when the time period spans several years. The
main drawback to using Moving averages is that broadly speaking markets
spend more time locked in ranges than actually trending.
Autocorrelation: This is the correlation (relationship) between members of
a time series of observations, such as weekly share prices or interest rates,
and the same value at a fixed time interval inter. It is also a statistical
method of forecasting. More technically speaking, autocorrelation occurs
when residual error terms from observation of the same variable at different
times are correlated (related).
Autocorrelation measures the association or mutual dependence between
values of the same time series and different time lags.
Auto Regression Integration Moving Average (ARIMA): This is the
integration of autoregressive process as well as moving average parameters
5
and it explicitly includes differencing in the formulation of the model.
Specifically, the types of parameters in the model are the autoregressive
parameters (P) the number of differencing passes (d) and the moving
average parameter (q).
However, ARIMA is a complex technique, it is not easy to use, as it requires
a great deal of experience, and the method is appropriate only for a true
series that is stationary. That is, its mean, variance, and autocorrelation
should be approximately constant through time [24].
The method applied in this study is Fuzzy Time Series. Different research
work on Fuzzy Time Series proposed different method but the method
adopted by Abbasov et al is used in this study since it allows the prediction
beyond the time available in the test data.
The following is the suggested methodology in carrying out the Fuzzy Time
Series forecasting:
i. Obtaining electric load power consumption data from a PHCN
over a 24 – week period;
ii. Partitioning the data into training data (18-weeks) and
validation data (6 weeks);
iii. Defining the universal set U containing the interval between
least and greatest variation of load;
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iv. Dividing the Universal set U into varying interval lengths (5, 6,
and 7) containing variation values corresponding to different
load consumed;
v. 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;
vi. Fuzzifying the input data or the conversion of numerical value
into Fuzzy value;
vii. Selecting the parameter w>1(model basis) corresponding to the
time period prior to the concerned week;
viii. Calculating the Fuzzy matrix pw(T) and forecasting of the
expected load for the proceeding week;
ix. DeFuzzying the obtained result or conversion of Fuzzy into
quantitative (crisp) value; and
ix. Tabulating the result of different interval and model basis and
comparing the results with the validation data.
1.5. 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
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applied is explained. The review of literature of similar research work with
the theoretical background that forms the bases for the evaluation of the
different available options are contained in chapter 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 this thesis.
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