Wind and solar power are known to be highly influenced by weather events and may ramp up or down abruptly. Such events in the power production influence not only the availability of energy, but also the stability of the entire power grid. By analysing significant amounts of data from several regions around the world with resolutions of seconds to minutes, we provide strong evidence that renewable wind and solar sources exhibit multiple types of variability and nonlinearity in the time scale of seconds and characterise their stochastic properties. In contrast to previous findings, we show that only the jumpy characteristic of renewable sources decreases when increasing the spatial size over which the renewable energies are harvested. Otherwise, the strong non-Gaussian, intermittent behaviour in the cumulative power of the total field survives even for a country-wide distribution of the systems. The strong fluctuating behaviour of renewable wind and solar sources can be well characterised by Kolmogorov-like power spectra and q-exponential probability density functions. Using the estimated potential shape of power time series, we quantify the jumpy or diffusive dynamic of the power. Finally we propose a time delayed feedback technique as a control algorithm to suppress the observed short term non-Gaussian statistics in spatially strong correlated and intermittent renewable sources.
Wind turbines generate electricity from turbulent wind. Large fluctuations, and, more importantly, frequent wind gusts cause a highly fluctuating electrical power feed into the grid. Such effects are the hallmark of high-frequency turbulence. Here we show evidence that it is the complex structure of turbulence that dominates the power output for one single wind turbine as well as for an entire wind farm. We illustrate the highly intermittent, peaked nature of wind power fed into the grid. Multifractal scaling is observed, as described initially by Kolmogorov's 1962 theory of turbulence. In parallel, we propose a stochastic model that converts wind speed signals into power output signals with appropriate multifractal statistics. As more and more wind turbines become integrated into our electric grids, a proper understanding of this intermittent power source must be worked out to ensure grid stability in future networks. Thus, our results stress the need for a profound understanding of the physics of turbulence and its impact on wind energy.
A general hierarchical statistical framework for the characterization of wind turbulence is proposed. This framework should ease the understanding of different existing statistical approaches and enable a clear path for refined methods of characterization. Low-order statistical descriptions were extended by higher-order statistics with respect to one-point and two-point statistics. In particular, we showed that proper analysis leads to a superstatistics approach for the probability of velocity fluctuations. To demonstrate the importance of our considerations, we analysed wind time series of the research platform FINO 1. On one side, we showed how different statistical aspects can be reproduced quite accurately, whereas on the other, the necessity of more profound approaches was worked out. The analysis of the measured data provides some deep insights into the nature of wind turbulence. Most interestingly, for conditioned data subsets, we found higher-order statistical behavior well known for idealized turbulence. Finally, we give an outlook on how to achieve a general n-point statistical description. * The wind speed in the perpendicular plane to the axis of rotation of the cup anemometer. * This approach can also been understood under the context of the so called superstatistics. 20 Wind Energ. 2012; 15:391-406
We describe an R package developed by the research group Turbulence, Wind energy and Stochastics (TWiSt) at the Carl von Ossietzky University of Oldenburg, which extracts the (stochastic) evolution equation underlying a set of data or measure ments. The method can be directly applied to data sets with one or two stochastic variables. Examples for the one-dimensional and two-dimensional cases are provided. This framework is valid under a small set of conditions which are explicitly presented and which imply simple preliminary test procedures to the data. For Markovian processes involving Gaussian white noise, a stochastic differential equa tion is derived straightforwardly from the time series and captures the full dynamical properties of the underlying process. Still, even in the case such conditions are not fulfilled, there are alternative versions of this method which we discuss briefly and provide the user with the necessary bibliography.
We apply a modified proper orthogonal decomposition (POD) to large eddy simulation data of a wind turbine wake in a turbulent atmospheric boundary layer. The turbine is modeled as an actuator disk. Our analysis mainly focuses on the pragmatic identification of spatial modes, which yields a low order description of the wake flow. This reduction to a few degrees of freedom is a crucial first step for the development of simplified dynamic wake models based on modal decompositions. It is shown that only a few modes are necessary to capture the basic dynamical aspects of quantities that are relevant to a turbine in the wake flow. Furthermore, we show that the importance of the individual modes depends on the relevant quantity chosen. Therefore, the optimal choice of modes for a possible model could in principle depend on the application of interest. We additionally present a possible interpretation of the extracted modes by relating them to the specific properties of the wake. For example, the first mode is related to the horizontal large-scale movement.
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