0
RESEARCH PAPERS

Low-Dimensional Representations of Inflow Turbulence and Wind Turbine Response Using Proper Orthogonal Decomposition

[+] Author and Article Information
Korn Saranyasoontorn, Lance Manuel

Department of Civil Engineering, University of Texas at Austin, Austin, TX 78712

J. Sol. Energy Eng 127(4), 553-562 (Jul 07, 2005) (10 pages) doi:10.1115/1.2037108 History: Received March 27, 2005; Revised July 07, 2005

A demonstration of the use of Proper Orthogonal Decomposition (POD) is presented for the identification of energetic modes that characterize the spatial random field describing the inflow turbulence experienced by a wind turbine. POD techniques are efficient because a limited number of such modes can often describe the preferred turbulence spatial patterns and they can be empirically developed using data from spatial arrays of sensed input/excitation. In this study, for demonstration purposes, rather than use field data, POD modes are derived by employing the covariance matrix estimated from simulations of the spatial inflow turbulence field based on standard spectral models. The efficiency of the method in deriving reduced-order representations of the along-wind turbulence field is investigated by studying the rate of convergence (to total energy in the turbulence field) that results from the use of different numbers of POD modes, and by comparing the frequency content of reconstructed fields derived from the modes. The National Wind Technology Center’s Advanced Research Turbine (ART) is employed in the examples presented, where both inflow turbulence and turbine response are studied with low-order representations based on a limited number of inflow POD modes. Results suggest that a small number of energetic modes can recover the low-frequency energy in the inflow turbulence field as well as in the turbine response measures studied. At higher frequencies, a larger number of modes are required to accurately describe the inflow turbulence. Blade turbine response variance and extremes, however, can be approximated by a comparably smaller number of modes due to diminished influence of higher frequencies.

Copyright © 2005 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

The National Wind Technology Center’s Advanced Research Turbine (ART) used in the numerical studies

Grahic Jump Location
Figure 2

Thirty-six spatial locations on the 42m×42m rotor plane of the ART machine used in the POD analyses

Grahic Jump Location
Figure 3

Eigenvalues of the covariance matrix of the along-wind turbulence for each POD mode

Grahic Jump Location
Figure 4

Cumulative fraction of energy in low-order representations of along-wind turbulence

Grahic Jump Location
Figure 5

First nine eigenmodes and corresponding fractions of eigenvalues of the covariance matrix of the along-wind turbulence field

Grahic Jump Location
Figure 6

Fraction of the target variance of the along-wind turbulence component at the 36 grid points on the rotor plane (see Fig. 2) based on 1 and 10 POD modes

Grahic Jump Location
Figure 7

Reconstructed time series of the along-wind turbulence at grid point 15 (see Fig. 2) based on 1, 5, and 10 POD modes (compared with the target)

Grahic Jump Location
Figure 8

PSDs of the reconstructed along-wind turbulence at grid point 15 (see Fig. 2) using 1, 5, and 10 POD modes compared with the full-field simulation and the target Kaimal spectral model

Grahic Jump Location
Figure 9

Median, 5th percentile, and 95th percentile PSD estimates of along-wind turbulence at grid point 15 (see Fig. 2) using 5 POD modes compared with similar estimates from full-field simulations

Grahic Jump Location
Figure 10

Coherence spectra of the reconstructed along-wind turbulence components at a lateral separation of 8.4m (between grid points 15 and 16) using 1, 5, and 10 POD modes compared with the full-field simulation and the target IEC exponential coherence model

Grahic Jump Location
Figure 11

Coherence spectra of the reconstructed along-wind turbulence components at a lateral separation of 25.2m (between grid points 14 and 17) using 1, 5, and 10 POD modes compared with the full-field simulation and the target IEC exponential coherence model

Grahic Jump Location
Figure 12

Plots of (a) flapwise bending moment at the blade root, (b) edgewise bending moment at the blade root, and (c) fore-aft tower base bending moment derived from 1, 5, and 10 POD inflow modes compared with full-field simulations

Grahic Jump Location
Figure 13

Zoomed-in 10s plots of (a) flapwise bending moment at the blade root, (b) edgewise bending moment at the blade root, and (c) fore-aft tower base bending moment derived from 1, 5, and 10 POD inflow modes compared with full-field simulations

Grahic Jump Location
Figure 14

Contribution of 1, 5, and 10 inflow POD modes to the PSD of the flapwise bending moment at the blade root compared with the target PSD based on full-field inflow simulations

Grahic Jump Location
Figure 15

Contribution of 1, 5, and 10 inflow POD modes to the PSD of the edgewise bending moment at the blade root compared with the target PSD based on full-field inflow simulations

Grahic Jump Location
Figure 16

Contribution of 1, 5, and 10 inflow POD modes to the PSD of the fore-aft tower bending moment at the base compared with the target PSD based on full-field inflow simulations

Grahic Jump Location
Figure 17

Median, 5th percentile, and 95th percentile PSD estimates of flapwise bending moment at the blade root using 5 POD modes compared with full-field inflow simulations

Grahic Jump Location
Figure 18

Ratio of variance of turbine response measures based on 1, 5, 10, 20, and 36 POD modes to the target variance

Grahic Jump Location
Figure 19

Ratio of ten minute mean extreme turbine response measures based on 1, 5, 10, 20, and 36 POD modes to the target mean extreme

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In