Federal State Educational Institution of Higher Professional Education “Lobachevsky State University of Nizhni Novgorod”
A manuscript
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GURRERA Davide
STOCHASTIC MODELS FOR WIND SPEED TIME SERIES
01.04.03 - Radiophysics
DISSERTATION for the degree Candidate of Physical and Mathematical Sciences
Supervisors: Ph.D.. Prolessor Burlon Riccardo (Italy), Doctor of Physical and Mathematical Sciences, Professor Saichev Alexander Ivanovich
Nizhni Novgorod - 2012 2
Abstract
In the last decades many researchers have focussed their attention on wind energy exploitation. One of the main challenges faced in this field is the variation in power output caused by stochastic wind speed fluctuations. In order to compensate them and to take decisions in the context of the electricity market a reliable weather forecast is necessary. Beside the employment of the well-established fluid-dynamical models, there is a growing attention on those predicting methods based on stochastic models and artificial neural networks. Accordingly, the main purpose of this thesis is to provide a general class of stochastic models for hourly average wind speed prediction taking into account all the main features of wind speed data, namely autocorrelation, non-Gaussian distribution, seasonal and diurnal nonstationarity.
The proposed approach, characterized by several novel features respect to previous works, has been applied to the time series recorded during four years in two sites of Sicily, a region of Italy. It comes out that the procedure developed in this study attains valuable results in terms both of modelling and forecasting. Particularly, the 24 hours predictions obtained employing only one-month time series are quite similar to those provided by a feed-forward artificial neural network trained on two years data.
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PACS: Interdisciplinary applications of physics; Probability theory, stochastic processes, and statistics; Computational methods in statistical physics and nonlinear dynamics; Time series analysis in nonlinear dynamics; Computational techniques and simulations.
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Acknowledgements
First of all, I wish to express my gratitude to Prof Riccardo Burlon and to Prof Alexander I. Saichev.
I am also grateful to Prof Bernardo Spagnolo who gave me the opportunity to attend an International Ph.D. Course in Russia. At the Lobachevsky State University of Nizhni Novgorod, I had an opportunity to gain experience, to meet extraordinary professors like Alexander A. Dubkov, to learn Russian, to enjoy some Russian traditions and finally to meet extraordinary colleagues and friends, especially Dr Yuriy V. Ushakov whose support in Russia has been invaluable.
I also wish to thank my family, for the support they provided me through my entire life.
In conclusion, I recognize that this research would not have been possible without the financial assistance of the Italian Ministry of University and Scientific Research and
without the data provided by the Servizio Informativo Agrometeorologico Siciliano (Assessorato Agricoltura e Foreste - Regione Siciliana).
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Table of Contents
Abstract 3
Acknowledgements 5
Table of Contents 7
list of Figures 9
List of Tables 13
Abbreviations 14
1 Introduction 16
1 1 Renewable Energy The Current State 19
1 2 Wind Energy Current Statistics 20
1 S Wind Resource and Power Generation 22
1 4 Providing Balancing Power to Cope with Wind Variability 23
1 5 The Electricity Markets 23
1 6 Wind Speed Probability Distributions a Brief Review 24
17 Wind Speed Forecasting by Stochastic Models the State of the Art 26
2 Theory 29
2 1 Stochastic Models for Time Series 30
2 11 Analysing the Properties of a Time Series 33
2 12 Stationary Models 36
Autoregressive Processes 38
Moving Average Processes 38
Autoregressive Moving Average Processes 39
long-Memory Processes 39
2 13 Non-stationary Models 41
Autoregressive Integrated Moving Average Processes 41
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Seasonal Autoregressive Integrated Moving Average Processes........................42
2.1.4 The Box-Jenkins Procedure....................................................43
Model Identification...............................................................43
Model Estimation...................................................................44
Model Checking.....................................................................45
2.1.5 Forecasting..................................................................46
Measures of Forecasting Accuracy...................................................49
2.2 Artificial Neural Networks '.........................................................50
2.2.1 Introduction.................................................................51
2.2.2 Training a Feed-Forward ANN..................................................53
3 Analysis and Results.....................................................................57
3.1 Data Description................................................................... 57
3.2 The Proposed Approach................................................................68
3.2.1 Data Pre-treatment...........................................................68
3.2.2 The Proposed Class of Models.................................................73
3.3 An Artificial Neural Network Approach................................................74
3.4 Results............................................................................. 76
3.4.1 Modelling Accuracy...........................................................76
3.4.2 Forecasting Accuracy.........................................................82
3.4.3 A Case Study.................................................................89
4 Conclusions............................................................................. 97
Appendix.....................................................................................99
References..................................................................................104
List of Author's Publications................................................................107
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