Matthias Wächter

Short term fluctuations of wind and solar power systems

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 {\it 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

The turbulent nature of the atmospheric boundary layer and its impact on the wind energy conversion process

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Stochastic modeling and performance monitoring of wind farm power production

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.

Stochastic method for in-situ damage analysis

Wind turbines operate in the atmospheric boundary layer, where they are exposed to turbulent atmospheric flows. As the response time of wind turbines is typically in the range of seconds, they are affected by the small-scale intermittent properties of turbulent wind. Consequently, basic features that are known for small-scale homogeneous isotropic turbulence, in particular the well-known intermittency problem, have an important impact on the wind energy conversion process. We report on basic research results concerning the small-scale intermittent properties of atmospheric flows and their impact on the wind energy conversion process. The analysis of wind data shows strong intermittent statistics of wind fluctuations. To achieve numerical modeling, a data-driven superposition model is proposed. For the experimental reproduction and adjustment of intermittent flows, the so-called active grid setup is presented. Its ability to generate reproducible properties of atmospheric flows on the smaller scales of lab...

Wind velocity measurements using a pulsed LIDAR system: first results

We present a new stochastic approach to describe and remodel the conversion process of a wind farm at a sampling frequency of 1Hz. When conditioning on various wind direction sectors, the dynamics of the conversion process appear as a fluctuating trajectory around an average IEC-like power curve, see section II. Our approach is to consider the wind farm as a dynamical system that can be described as a stochastic drift/diffusion model, where a drift coefficient describes the attraction towards the power curve and a diffusion coefficient quantifies additional turbulent fluctuations. These stochastic coefficients are inserted into a Langevin equation that, once properly adapted to our particular system, models a synthetic signal of power output for any given wind speed/direction signals, see section III. When combined with a pre-model for turbulent wind fluctuations, the stochastic approach models the power output of the wind farm at a sampling frequency of 1Hz using only ten-minute average values of wind speed and directions. The stochastic signals generated are compared to the measured signal, and show a good statistical agreement, including a proper reproduction of the intermittent, gusty features measured. In parallel, a second application for performance monitoring is introduced in section IV. The drift coefficient can be used as a sensitive measure of the global wind farm performance. When monitoring the wind farm as a whole, the drift coefficient registers some significant deviation from normal operation if one of twelve wind turbines is shut down during less than 4% of the time. Also, intermittent anomalies can be detected more rapidly than when using ten-minute averaging methods. Finally, a probabilistic description of the conversion process is proposed and modeled in appendix A, that can in turn be used to further improve the estimation of the stochastic coefficients.

Towards a Simplified DynamicWake Model Using POD Analysis

Based on the physics of stochastic processes we present a new approach for structural health monitoring. We show that the new method allows for an in-situ analysis of the elastic features of a mechanical structure even for realistic excitations with correlated noise as it appears in real-world situations. In particular an experimental set-up of undamaged and damaged beam structures was exposed to a noisy excitation under turbulent wind conditions. The method of reconstructing stochastic equations from measured data has been extended to realistic noisy excitations like those given here. In our analysis the deterministic part is separated from the stochastic dynamics of the system and we show that the slope of the deterministic part, which is linked to mechanical features of the material, changes sensitively with increasing damage. The results are more significant than corresponding changes in eigenfrequencies, as commonly used for structural health monitoring.

Principal axes for stochastic dynamics

Wind velocity measurements were taken using a Leosphere Windcube LIDAR system, which operates as a pulsed laser Doppler anemometer. Here we report on first results, which show typical characteristics of atmospheric wind velocities.

Markov properties in presence of measurement noise

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.

Langevin power curve analysis for numerical wind energy converter models with new insights on high frequency power performance

We introduce a general procedure for directly ascertaining how many independent stochastic sources exist in a complex system modeled through a set of coupled Langevin equations of arbitrary dimension. The procedure is based on the computation of the eigenvalues and the corresponding eigenvectors of local diffusion matrices. We demonstrate our algorithm by applying it to two examples of systems showing Hopf bifurcation. We argue that computing the eigenvectors associated to the eigenvalues of the diffusion matrix at local mesh points in the phase space enables one to define vector fields of stochastic eigendirections. In particular, the eigenvector associated to the lowest eigenvalue defines the path of minimum stochastic forcing in phase space, and a transform to a new coordinate system aligned with the eigenvectors can increase the predictability of the system.

Characterizing Wake Turbulence with Staring Lidar Measurements

Recently, several powerful tools for the reconstruction of stochastic differential equations from measured data sets have been proposed [e.g., Siegert, Phys. Lett. A 243, 275 (1998); Hurn, J. Time Series Anal. 24, 45 (2003)]. Efficient application of the methods, however, generally requires Markov properties to be fulfilled. This constraint typically seems to be violated on small scales, which frequently is attributed to physical effects. On the other hand, measurement noise such as uncorrelated measurement and discretization errors has large impacts on the statistics of measurements on small scales. We demonstrate that the presence of measurement noise, likewise, spoils Markov properties of an underlying Markov process. This fact is promising for the further development of techniques for the reconstruction of stochastic processes from measured data, since limitations at small scales might stem from artificial noise sources rather than from intrinsic properties of the dynamics of the underlying process. Measurement noise, however, can be controlled much better than the intrinsic dynamics of the underlying process.