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Advanced characterization of atmospheric turbulence by high-order statistics.

Advanced characterization of atmospheric turbulence by high-order statistics. Allan Morales, PhD. Student. M. Wächter and J. Peinke Warsaw, April 22, 2009. “Turbulence is a challenge for WECs ..... “ Cheng-Hu Hu, Vestas Wind Systems, Denmark.

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Advanced characterization of atmospheric turbulence by high-order statistics.

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  1. Advanced characterization of atmospheric turbulence by high-order statistics. Allan Morales, PhD. Student. M. Wächter and J. Peinke Warsaw, April 22, 2009

  2. “Turbulence is a challenge for WECs ..... “ Cheng-Hu Hu, Vestas Wind Systems, Denmark.

  3. More statistical parameters are necessary to describe wind turbulence. Wind Turbulence ≠ Turbulence Intensity!!! Neccessity and modelling of ONE-point Higher-order statistics. Neccessity and modelling of TWO-point Higher-order statistics. Example with FINO I (Cup anemometer at 100m) data and Turbsim.

  4. Turbulent Fluctuations from the Mean Wind Speed. • From the original wind • time series we obtain • the high-frequency • fluctuating part. Typically T=10min

  5. What is actually inside our turbulent signal?? One-point statistics / Two-point Fluctuation‘s Distribution Turbulence Intensity = Second order statistics Distribution of fluctuations is not Gaussian for measured data Probability of extreme events is heavily underestimated Higher moments of u‘ are needed

  6. Modelling of p(u‘) One-point statistics • Look at windows of T=10 minutes • and calculate fluctuations. • In T=10min. Distributions are • closely Gaussian! • Real distribution of u’ is just a superposition • of Gaussian distributions with different σT. • We only need to know how to superimpose • them! We need a model!

  7. σTAre themselves • log-normal distributed • Hansen et. al. • Wind Engineering 2005 Modelling of p(u‘) One-point statistics • We only need to know how to superimpose • them! We need a model! • let‘s take a look at the population of σT

  8. Moddelling of the u‘ distributions One-point statistics / Two-point Now we can apply the super-statistics approach. Beck et. al The key parameter is: It can be directed computed either from high frequency data or even from the information of the turbulence intensities!!

  9. Moddelling of the u‘ distributions One-point statistics / Two-point With this model we achieve a correct estimation of all the population of u´. Even extreme events! The key parameter can be either estimated from high frequency data or from 10 minutes averaged values (Turbulence Intensity, Mean Wind Speed) Possible site dependency of will lead to a more general description of u´

  10. What is actually inside of our turbulent signal?? One-point statistics / Two-point Turbulence Intensity = Second order statistics Distribution of fluctuations (Higher Order) P(u´) modelled via

  11. What is actually inside of our turbulent signal?? One-point statistics / Two-point IEC Standard Turbulence Intensity = Second order statistics Distribution of fluctuations (Higher Order) P(u´) modelled via Two-point statistics: Distribution of increments (Higher Order) Power Spectral Density = Simple correlation

  12. Simulation example with TurbSim Based on the concept of super-statistics we run wind time series simulations. One-point statistics are well reproduced. Two-point statistics up to second order are also included in TurbSim, Via the Kaimal spectral density.

  13. Simulation example with TurbSim However higher-order two point statistics are not reproduced!

  14. Conclusions and outlook: • PDFs are in general no Gaussian for both One-point Two-point • PDFs can be modelled by similar approaches (but not equall!!). • A better assessment of turbulence probably requires a systematic • measurement of and or similar higher-order parameters.

  15. Thank You! Contact: allan.morales@uni-oldenburg.de http://www.forwind.de/forwind/ Poster 426 Today at 14:00

  16. Application example. Both data sets share the same mean wind speed. Fino and Growian TIs= 6.36% and 5.75% Power spectrum are very similar (high frequency). And still different in higher-order two-point statistics!!

  17. How all this affects the Wind Energy Converters? Mücke et. al. TurbSim (Wind Field) FAST (Dynamics of the machine )

  18. Probability Density Functions are not Gaussian! Two-point statistics (Increments)

  19. Two-point statistics (Increments) Higher moments.

  20. Two-point statistics (Increments) The 2nd-order moment of Is already grasped by the Autocorrelation or the power Spectrum. However again the increment PDFs are in general not Gaussian, Similarly to p(u‘). Tau

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