Page 281 - Wind Energy Handbook

BLADE DYNAMIC RESPONSE 255

operating within a 2 m/s wide band centred on the rated wind speed is 5.6 percent.
Taking the machine lifetime as 20 years and a zero up-crossing frequency of 1.2 Hz,
this results in a peak factor, g 1 , of 5.8. For the 40 m diameter machine considered in
Section 5.7.2 and a turbulence intensity of 20 percent, this translates to a peak value
of the random component of blade root bending moment of about 230 kNm,
compared to the extreme value of the periodic component, including wind shear, of
about 300 kNm. It should be emphasized that the peak value of the random
component quoted is a theoretical one, i.e., it assumes the linearity assumptions are
maintained even for the large wind speed fluctuation needed to generate this
moment. In practice, a machine operating in a steady wind speed equal to rated is
usually not all that far from stall, so the larger fluctuations may induce stall. In this
example, the square root of the weighted mean of the integrals of all the curtailed
rotational spectra is about 0.5ó u , so the idealized uniform wind speed fluctuation
equivalent to the extreme root moment is about 0:20 3 13 3 0:5 3 5:8 ¼ 7:5m=s.
The method outlined above has more validity at higher wind speeds, when the
blades are pitched back, and are operating further away from stall. However, it is
important to note that the other linearity assumption used in deriving Equation
(5.25), namely that ö is small, becomes increasingly in error.
It will be now be evident that the calculation of stochastic extreme loads is
fraught with difficulties because non-linearities are likely to arise as the extremes
are approached. In so far as lift forces ‘saturate’ due to stall, or even drop back, as
wind speed increases, a crude and simple approach to extreme out-of-plane
operational loads is to calculate an upper-bound based on the maximum lift coeffi-
cient for the local aerofoil section and the relative air velocity, W. The induction
factors will be small, and can be ignored.
The most sophisticated approach, however, is to analyse the loads generated by a
simulated wind field. As computing costs normally restrict the length of simulated
‘campaigns’ to a few hundred seconds or less, statistical methods have to be used to
extrapolate from the extreme values of loadings calculated during the campaign to
the extreme values to be expected over the machine design life.
One method, which is discussed by Thomsen and Madsen (1997), is to use
Equation (5.60) with T set equal to the appropriate exposure period over the
machine design life, and values of z max and ó x abstracted from the simulation time
history with the aid of azimuthal binning to separate the periodic and stochastic
components. The danger of this approach with simulations of short duration is that
the azimuthal binning process treats some load fluctuations due to the slicing of
low frequency gusts as periodic rather than stochastic, so that the standard
deviation of the stochastic component, ó x , is underestimated.

5.8 Blade Dynamic Response

5.8.1 Modal analysis

Although dynamic loads on the blades will, in general, also excite the tower
dynamics, tower head motion will initially be excluded from consideration in order