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Stochastic methods for the characterization and simulation of wind energy production
Publication . Scholz, Teresa, 1986-; Lopes, Vitor; Lind, Pedro Gonçalves, 1976-; Gama, Margarida Telo da, 1956-
The aim of this PhD thesis is to apply tools from stochastic modeling to wind power, speed and direction data, in order to reproduce their empirically observed statistical features. In particular, the wind energy conversion process is modeled as a Langevin process, which allows to describe its dynamics with only two coefficients, namely the drift and the diffusion coefficients. Both coefficients can be directly derived from collected time-series and this so-called Langevin method has proved to be successful in several cases. However, the application to empirical data subjected to measurement noise sources in general and the case of wind turbines in particular poses several challenges and this thesis proposes methods to tackle them. To apply the Langevin method it is necessary to have data that is both stationary and Markovian, which is typically not the case. Moreover, the available time-series are often short and have missing data points, which affects the estimation of the coefficients. This thesis proposes a new methodology to overcome these issues by modeling the original data with a Markov chain prior to the Langevin analysis. The latter is then performed on data synthesized from the Markov chain model of wind data. Moreover, it is shown that the Langevin method can be applied to low sample rate wind data, namely 10-minute average data. The method is then extended in two different directions. First, to tackle non-stationary data sets. Wind data often exhibits daily patterns due to the solar cycle and this thesis proposes a method to consider these daily patterns in the analysis of the timeseries. For that, a cyclic Markov model is developed for the data synthesis step and subsequently, for each time of the day, a separate Langevin analysis of the wind energy conversion system is performed. Second, to resolve the dynamical stochastic process in the case it is spoiled by measurement noise. When working with measurement data a challenge can be posed by the quality of the data in itself. Often measurement devices add noise to the time-series that is different from the intrinsic noise of the underlying stochastic process and can even be time-correlated. This spoiled data, analyzed with the Langevin method leads to distorted drift and diffusion coefficients. This thesis proposes a direct, parameter-free way to extract the Langevin coefficients as well as the parameters of the measurement noise from spoiled data. Put in a more general context, the method allows to disentangle two superposed independent stochastic processes. Finally, since a characteristic of wind energy that motivates this stochastic modeling framework is the fluctuating nature of wind itself, several issues raise when it comes to reserve commitment or bidding on the liberalized energy market. This thesis proposes a measure to quantify the risk-returnratio that is associated to wind power production conditioned to a wind park state. The proposed state of the wind park takes into account data from all wind turbines constituting the park and also their correlations at different time lags.
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Fundação para a Ciência e a Tecnologia
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SFRH
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SFRH/BD/86934/2012