Стохастические модели прогнозирования скорости ветра

• Автор: Гуррера Давиде
• Шифр специальности: 01.04.03
• Научная степень: Кандидатская
• Год защиты: 2012
• Место защиты: Нижний Новгород
• Количество страниц: 107 с. : ил.

Federal State Educational Institution of Higher Professional Education “Lobachevsky State University of Nizhni Novgorod”
A manuscript
t>> Wl
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.. Professor Burlon Riccardo (Italy), Doctor of Physical and Mathematical Sciences, Professor Saichev Alexander Ivanovich
Nizhni Novgorod - 2012
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.

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.

In order to discover or verify the presence of cyclic variation, another useful exploratory tool in the analysis of time series is represented by the sample spectrum, which is the Fourier cosine transform of the sample autocovariance function:
1(f)
' ckcos(2nfk)
(15)
/ being the frequency. The highest frequency (Nyquist frequency) is 0.5 cycle per time interval because the smallest period is 2 intervals. The Nyquist frequency does not depend on the number of observations N, but rather only on the sampling frequency, whereas the lowest frequency l/N&t does depend on N, At being the sampling
interval. Put another way, the lower the frequency we are interested in, the longer the time period over which we need to take measurements, whereas the higher the frequency we are interested in, the most frequently must we take observations.
When a time series has a strong cyclic component at some frequency /, then the spectrum will show a peak at that frequency. It may additionally show related peaks at 2/, 3
generally speaking simply indicate that the main cyclical component is not exactly sinusoidal in character.
However, the sample spectrum usually fluctuates wildly and sometimes it is not capable of any meaningful interpretation. In these cases, it is possible to use a parametric approach called autoregressive spectrum estimation. In fact, many stochastic processes can be adequately approximated by an autoregressive process (see Sec. 2.1.2) of sufficiently high order. Once a suitable model has been estimated, it