Publishers version - DTU Orbit

PSD (m 2 /s)
10 3
10 2
10 1
10 0
10 −1
10 −2
Blade and Rotor Effective Wind Speed Spectra
Rotor Effective Wind Speed (Entire Disk)
Blade Effective Wind Speed
Collective Component, u hh
Shear components, Δ h , Δ v
10 −2
10 −1
Frequency (Hz)
Figure 145: Power spectra of rotating blade effective wind speed as well as collective and
shear components due to three rotating blades. The rotor effective wind speed, calculated
by integrating wind speeds weighted according to their contribution to power over the entire
rotor disk, is shown for comparison. Spectra are generated for the IEC von Karman wind field
model using the NREL 5-MW turbine at mean wind speed 13 m/s.
Simley and Pao (2013a) can be extended to calculate the spectra of the collective and
shear components due to three rotating blades, using Eq. (239). Using the IEC von Karman
wind field and the NREL 5-MW model, the rotating blade effective wind speed and rotating
collectiveandsheartermsareplottedinFig.145fortheratedrotorspeed12.1rpm(0.202Hz)
and above-rated wind speed 13 m/s. The blade effective wind speed spectrum contains peaks
at the 1P frequency (0.202 Hz) and its harmonics, due to the blade passing through turbulent
structures once per revolution. The collective and shear component spectra contain peaks at
the 3P (three times per revolution) frequency (0.606 Hz) and its harmonics because each of
the three blades passes through structures once per revolution. Also shown in Fig. 145 is the
rotor effective wind speed averaged across the entire rotor disk, calculated using Eq. (229),
to highlight the difference between modeling rotor effective wind speed as the wind felt by
the rotor disk and the wind felt by three rotating blades.
Forwindturbinecontrols,itispopulartouselinearmodelsoftheturbineinthenon-rotating
frame because the resulting transfer functions do not vary with azimuth angle as much as
in the rotating frame. Rotating variables at each of the three blades are instead represented
as a collective component y0, a vertical component yv, and a horizontal component yh. For
example, the flapwise bending moment experienced by each blade can be represented as the
average bendingmomentoverall blades(y0), the netbendingmomentoftherotoraroundthe
y axis (yv), and the net bending moment around the vertical z axis (yh). Transfer functions
are calculated in the non-rotating frame using the multiblade coordinate (MBC) transform
(Bir, 2008),which is used as the basis forEqs. (237) and (239). The response of the collective
component of a turbine variable is dominated by the collective wind component uhh, and the
vertical and horizontal components are dominated by the vertical ∆v and horizontal ∆h shear
components of the wind, respectively. Figure 146 contains the magnitude squared frequency
response of the transfer functions from hub height wind speed to the collective component of
flapwise blade root bending moment as well as the transfer functions from horizontal shear
and vertical shear to the horizontal component and vertical component of blade root bending
moment generated using FAST (Jonkman and Buhl, 2005) with the 5-MW model at the
above-rated wind speed 13 m/s. These transfer functions include blade pitch and generator
208 DTU Wind Energy-E-Report-0029(EN)
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