Model of the Correlation between Lidar Systems and Wind Turbines for Lidar-Assisted Control

Abstract

Investigations of lidar-assisted control to optimize the energy yield and to reduce loads of wind turbines have increased significantly in recent years. For this kind of control, it is crucial to know the correlation between the rotor effective wind speed and the wind preview provided by a nacelle- or spinner-based lidar system. If on the one hand, the assumed correlation is overestimated, then the uncorrelated frequencies of the preview will cause unnecessary control action, inducing undesired loads. On the other hand, the benefits of the lidar-assisted controller will not be fully exhausted, if correlated frequencies are filtered out. To avoid these miscalculations, this work presents a method to model the correlation between lidar systems and wind turbines using Kaimal wind spectra. The derived model accounts for different measurement configurations and spatial averaging of the lidar system, different rotor sizes, and wind evolution. The method is compared to real measurement data with promising results. In addition, examples depict how this model can be used to design an optimal controller and how the configuration of a lidar system is optimized for a given turbine to improve the correlation.

Assessing the Severity of Wind Gusts with Lidar

“…This is why some authors prefer a rotor-effective or blade-effective wind speed [13][14][15] instead of the full velocity field. Therefore, in order to make any decision on what action to take in response to an oncoming threat, one requires a method to turn a set of (possibly scattered) measurements into useful information.…”

Optimization of a feed-forward controller using a CW-lidar system on the CART3

“…To avoid this issue, we solved this constrained problem with a brute force optimization based on a spectra-based analytical model [11], shown Figure 2. The main idea is to calculate the correlation directly based on the turbulence spectral properties.…”

“…1 and meet the requirements for using the data for real-time control. SWE investigated the optimal scan distance for the lidar combined with its feed-forward controller by using a spectra-based analytical model [11] of the correlation between the rotor-effective wind speed sensed by the turbine and its lidar estimate. In addition, the SWE controller was optimized by re-tuning the feedback gains in a simulation study.…”

Adaptive Vorsteuerung für Windenergieanlagen

“…Diese Spektren können aus den spektralen Eigenschaften des Windes gewonnen werden [15]. Hier wird exemplarisch (17) für das Ultraschallanemometer modelliert (M → S).…”

“…Mithilfe der Eigenschaften der Fouriertransformation (Normierungen werden weggelassen) kann das Kreuzspektrum berechnet werden: (14)- (16) entsprechend berechnet werden, wobei hier die zeitliche Abfolge und die Windevolution beachtet werden müssen [15]. Bild 10 zeigt eine gute Übereinstimmung mit den Messdaten.…”