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Characterization and Stochastic Modeling of Wind Speed Sequences
Abstract
Wind energy production is very sensitive to turbulent wind, in particular when wind power variations range from few seconds to 1 hour, are considered. Indeed rapid changes in the local meteorological condition as observed in tropical climate can provoke large variations of wind speed. Consequently the electric grid security can be jeopardized due to these fluctuations. This is particularly the case of island networks as in the Guadeloupean archipelago (French West Indies) where the installed 20 MW wind power already represents 11% of the electrical consumption. From 1 million wind sequences of duration 10 minutes, sampled at 1 Hz during the trade season, we proceed toward two objectives: i) the characterization of the wind speed sequences, ii) the dynamical simulation of the wind sequences using Langevin equation.
... In order to classify and characterize the shape of the wind speed fluctuations PDF, a nonparametric method using Dirichlet distribution mixtures is applied on 1 million wind speed fluctuations distributions . The results presented in [13] [14] have shown the existence of three classes of wind speed distribution: (i) a first class (90% of wind speed sequences) in which PDFs is symmetrical mono-modal. The measurement sequences in this class, correspond to wind regime with a weak turbulent intensity, I u ¼ r=U, around 5%, with r and U represent respectively the standard deviation and the mean of the considered wind speed sequence. ...
Wind energy production is very sensitive to turbulent wind speed. Thus rapid variation of wind speed due to changes in the local meteorological conditions can lead to electrical power variations of the order of the nominal power output, in particular when wind power variations on very short time scales, range at few seconds to 1 h, are considered. In small grid as they exist on islands (Guadeloupean Archipelago: French West Indies) such fluctuations can cause instabilities in case of intermediate power shortages. The developed analysis in [14] reveals three main classes of time series for the wind speed fluctuations. In this work, Probability Density Functions (PDFs) are proposed to fit the wind speed fluctuations distributions in each class. After, to simulate wind speed fluctuations sequences, we use a stochastic differential equation, the Langevin equation considering Gaussian turbulence PDF (class I), Gram–Charlier PDF (class II) and a mixture of gaussian PDF (class III). The statistical and dynamical properties of simulated wind sequences are close to those of measured wind sequences, for each class.
... For these very short time scales less than about 10 min, short term operation analysis need to use PDF whose properties are still under study [53]. In [54], we propose a Gram-Charlier PDF for modeling wind speed distributions for each obtained class with the classification described in this study ...
Wind energy production is very sensitive to instantaneous wind speed fluctuations. Thus rapid variation of wind speed due to changes in the local meteorological conditions can lead to electrical power variations of the order of the nominal power output. The high variability of this renewable energy source can caused a disruptive effect on power quality and reliability, in non-interconnected island networks as in Guadeloupe (French West Indies). To palliate these difficulties, it is essential to identify and characterize the wind speed distribution over very short time intervals. This allows anticipating the eventuality of power shortage or power surge. Therefore, it is of interest to categorize wind speed fluctuations into distinct classes and to estimate the probability of a distribution to belong to a class. This paper presents a method for classifying wind speed distributions by estimating a finite mixture of Dirichlet distributions. The SAEM algorithm that we use provides a fine distinction between three wind speed distribution classes. It is a new nonparametric method for wind speed classification.
Atmospheric wind speeds and their fluctuations at different locations (onshore and offshore) are examined. One of the most striking features is the marked intermittency of probability density functions (PDF) of velocity differences -- no matter what location is considered. The shape of these PDFs is found to be robust over a wide range of scales which seems to contradict the mathematical concept of stability where a Gaussian distribution should be the limiting one. Motivated by the instationarity of atmospheric winds it is shown that the intermittent distributions can be understood as a superposition of different subsets of isotropic turbulence. Thus we suggest a simple stochastic model to reproduce the measured statistics of wind speed fluctuations.
ABSTRACT In order to control and manage,highly aggregated Internet trac,flows eciently, we need to be able to categorize flows into distinct classes and to be knowledgeable about the dif- ferent behavior of flows belonging to these classes. In this paper we consider the problem of classifying BGP level pre- fix flows into a small set of homogeneous,classes. We argue that using the entire distributional properties of flows can have significant benefits in terms of quality in the derived classification. We propose a method,based on modeling flow histograms using Dirichlet Mixture Processes for random distributions. We present an inference procedure based on the Simulated Annealing Expectation Maximization algo- rithm that estimates all the model parameters as well as flow membership,probabilities - the probability that a flow belongs to any given class. One of our key contributions is a new method,for Internet flow classification. We show that our method,is powerful in that it is capable of examining macroscopic flows while simultaneously making fine distinc- tions between dierent,trac,classes. We demonstrate that our scheme can address issues with flows being close to class boundaries and the inherent dynamic behaviour of Internet flows.
The EM algorithm is a widely applicable approach for computing maximum likelihood estimates for incomplete data. We present a stochastic approximation type EM algorithm: SAEM. This algorithm is an adaptation of the stochastic EM algorithm (SEM) that we have previously developed. Like SEM, SAEM overcomes most of the well-known limitations of EM. Moreover, SAEM performs better for small samples. Furthermore, SAEM appears to be more tractable than SEM, since it provides almost sure convergence, while SEM provides convergence in distribution. Here, we restrict attention on the mixture problem. We state a theorem which asserts that each SAEM sequence converges a.s. to a local maximizer of the likelihood function. We close this paper with a comparative study, based on numerical simulations, of these three algorithms.
In order to qualify the fluctuating nature of solar radiation under tropical climate, we classify daily distributions of the clearness index kt by estimating a finite mixture of Dirichlet distributions without assuming any parametric hypothesis on these daily distributions. The method is applied to solar radiation measurements performed in Guadeloupe (16°2 N, 61 W) where important fluctuations can be observed even within a short period of a few minutes. The results put in evidence four distinct classes of distributions corresponding to different types of days. The sequence of such classes can be of interest for prediction.