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TECHNICAL BRIEF

Symmetry Considerations When Using Proper Orthogonal Decomposition for Predicting Wind Turbine Yaw Loads

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

Department of Civil, Architectural, and Environmental Engineering,University of Texas at Austin

J. Sol. Energy Eng 128(4), 574-579 (Jul 18, 2006) (6 pages) doi:10.1115/1.2349541 History: Received February 19, 2006; Revised July 18, 2006

In an earlier study, the authors discussed the efficiency of low-dimensional representations of inflow turbulence random fields in predicting statistics of wind turbine loads that included blade and tower bending moments. Both root-mean-square and 10-min extreme statistics for these loads were approximated very well when time-domain simulations were carried out on a 600kW two-bladed turbine and only a limited number of inflow “modes” were employed using proper orthogonal decomposition (POD). Here, turbine yaw loads are considered and the conventional ordering of POD modes is seen to be not as efficient in predicting full-field load statistics for the same turbine. Based on symmetry arguments, reasons for a different treatment of yaw loads are presented and reasons for observed deviation from the expected monotonic convergence to full-field load statistics with increasing POD mode number are illustrated.

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Copyright © 2006 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

(a) ART machine, (b) spatial grid for simulations of turbulence on the 42m×42m rotor plane

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Figure 2

Eigenvalues λi of the sample covariance matrix of the simulated along-wind turbulence field

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Figure 3

First 9 (out of 36) eigenmodes of the simulated along-wind turbulence field over the 42m×42m rotor plane of the ART machine with the corresponding fraction of total energy

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Figure 4

(a). The first through ninth eigenmodes of the simulated along-wind turbulence field over the 42m×42m rotor plane of the ART machine with the corresponding fraction of total energy; (b) the 10th–18th eigenmodes of the simulated along-wind turbulence field over the 42m×42m rotor plane of the ART machine with the corresponding fraction of total energy

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Figure 5

Ratio of variance of turbine load measures based on 1, 5, 10, and 20 POD modes to that based on full-field inflow simulation

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Figure 6

Ratio of 10-min extreme of turbine load measures based on 1, 5, 10, and 20 POD modes to that based on full-field inflow simulation

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Figure 7

The variance of the yaw bending moment (YBM) process contributed by each inflow POD mode (additional to that caused by the mean wind profile)

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Figure 8

The first four most important inflow mode shapes for yaw load based on the results from Fig. 7 together with the positions of the blades where imbalance of internal forces on the two blades brings about large yaw loads. The amount of field inflow energy from each mode is also shown.

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Figure 9

Ratio of variance of yaw bending moment for two different POD mode orderings to that based on full-field inflow simulation

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Figure 10

Ratio of the mean 10-min extreme of yaw bending moment for two different POD mode orderings to that based on full-field inflow simulation

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