Surrogate modelling of wind fields from point-wise atmospheric turbulence measurements

Friedrich, Jan; Moreno, Daniela; Sinhuber, Michael; Wächter, Matthias; Peinke, Joachim

doi:10.1088/1742-6596/2265/2/022026

Cited by 6 publications

(4 citation statements)

References 17 publications

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“…In superstatistics, a system changes from one state to another while we treat all observations as if they originated from the same state. In terms of the energy system, these diferent states of the system could be related to diferent generation mixes and demand patterns or due to drivers such as superstatistical behavior in the wind [42]. Note that superstatistics has been discussed on power-grid frequency recordings before [11], and there are further hints that the dynamics of power-grid recordings get more complex on shorter time scales.…”

Section: Multifractality and Correlationsmentioning

confidence: 99%

Microscopic Fluctuations in Power-Grid Frequency Recordings at the Subsecond Scale

et al. 2023

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Complex systems, such as the power grid, are essential for our daily lives. Many complex systems display multifractal behavior, correlated fluctuations and power laws. Whether the power-grid frequency, an indicator of the balance of supply and demand in the electricity grid, also displays such complexity remains a mostly open question. Within the present article, we utilize highly resolved measurements to quantify the properties of the power-grid frequency, making three key contributions: First, we demonstrate the existence of power laws in power-grid frequency measurements. Second, we show that below one second, the dynamics may fundamentally change, including a suddenly increasing power spectral density, emergence of multifractality and a change of correlation behavior. Third, we provide a simplified stochastic model involving positively correlated noise to reproduce the observed dynamics, possibly linked to frequency-dependent loads. Finally, we stress the need for high-quality measurements and discuss how we obtained the data analyzed here.

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Section: Multifractality and Correlationsmentioning

confidence: 99%

Microscopic Fluctuations in Power-Grid Frequency Recordings at the Subsecond Scale

et al. 2023

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“…For further review of superstatistics and non-Gaussian diffusion, we also refer the reader to [25]. For the methodology employed in this paper, we refined the idea first proposed in [26] and recently applied to the reconstruction of wind fields from point-wise atmospheric turbulence measurements [27,28]. This approach essentially constitutes a n-point generalization of classical superstatistics.…”

Section: Introductionmentioning

confidence: 99%

Stochastic interpolation of sparsely sampled time series by a superstatistical random process and its synthesis in Fourier and wavelet space

2023

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We present a novel method for stochastic interpolation of sparsely sampled time signals based on a superstatistical random process generated from a multivariate Gaussian scale mixture. In comparison to other stochastic interpolation methods such as Gaussian process regression, our method possesses strong multifractal properties and is thus applicable to a broad range of real-world time series, e.g.~from solar wind or atmospheric turbulence. Furthermore, we provide a sampling algorithm in terms of a mixing procedure that consists of generating a~$1+1$-dimensional field~$u(t,\xi)$, where each Gaussian component~$u_\xi(t)$ is synthesized with identical underlying noise but different covariance function~$C_\xi(t,s)$ parameterized by a log-normally distributed parameter~$\xi$. Due to the Gaussianity of each component~$u_\xi(t)$, we can exploit standard sampling alogrithms such as Fourier or wavelet methods and, most importantly, methods to constrain the process on the sparse measurement points. The scale mixture~$u(t)$ is then initialized by assigning each point in time~$t$ a~$\xi(t)$ and therefore a specific value from~$u(t,\xi)$, where the time-dependent parameter~$\xi(t)$ follows a log-normal process with a large correlation time scale compared to the correlation time of~$u(t,\xi)$. We juxtapose Fourier and wavelet methods and show that a multiwavelet-based hierarchical approximation of the interpolating paths, which produce a sparse covariance structure, provide an adequate method to locally interpolate large and sparse datasets.

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“…In this contribution, we discuss current and potential future applications of this wind field model at the example of meteorological mast array measurements [13,14], LIDAR measurements, and the modeling of turbine wakes. The paper is organized as follows, Section 2 and 3 give an account of the modeling framework, Section 4 describes potential future applications, whereas concluding remarks are given in Section 5.…”

Section: Introductionmentioning

confidence: 99%

Wind fields from atmospheric turbulence measurements

Friedrich

Peinke

2023

J. Phys.: Conf. Ser.

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We present recent advances in the modeling of wind fields and their reconstruction from real-world atmospheric turbulence measurements. The proposed wind field model provides a statistically coherent framework for modeling the empirically observed occurrence of extreme atmospheric events. Furthermore, we demonstrate that the model is general enough to enmesh real-world measurement points, e.g., from meteorological masts or LIDAR, and thus provides a rather convenient method for the reconstruction of highly resolved, three-dimensional wind fields. Our methodology is based on the so-called superstatistics of Gaussian-distributed (or Mann-type) velocity fields with fluctuating covariances and exactly reproduces higher-order statistics due to extreme small-scale wind fluctuations. Therefore, it could lead to more realistic inflow conditions and might potentially enhance the current design standard of wind turbines. We further discuss potential applications of the wind field model in the context of LIDAR measurements as well as for wake situations.

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Surrogate modelling of wind fields from point-wise atmospheric turbulence measurements

Cited by 6 publications

References 17 publications

Microscopic Fluctuations in Power-Grid Frequency Recordings at the Subsecond Scale

Microscopic Fluctuations in Power-Grid Frequency Recordings at the Subsecond Scale

Stochastic interpolation of sparsely sampled time series by a superstatistical random process and its synthesis in Fourier and wavelet space

Wind fields from atmospheric turbulence measurements

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