Page 280 - Wind Energy Handbook

254 DESIGN LOADS FOR HORIZONTAL-AXIS WIND TURBINES

Table 5.3 Extreme Values of Random Component for Different Exposure Times
T 1 min 10 min 1 h 10 h 100 h 1000 h 1 year
T (s) 60 600 3600 36 000 360 000 3 600 000 3 153 600
å 1 T (s) 15 150 900 9000 90 000 900 000 7 884 000
x max =ó x 2.57 3.35 3.84 4.40 4.90 5.35 5.74

of a stall-regulated machine, the linearity assumption breaks down completely,
invalidating the method. With pitch-regulated machines, however, the blade pitch
will respond to wind fluctuations at frequencies below the rotor rotational fre-
quency in order to limit power, causing a parallel reduction in blade loading. This
will modify the spectrum of blade loading dramatically, effectively removing the
frequency components below the pitch system cut-off frequency, and consequently
reducing the magnitude of ó x to be substituted in Equation (5.60).
To illustrate the method, the procedure for calculating the extreme flapwise blade
root bending moment of a pitch-regulated machine operating at rated wind speed
is described below.

(1) Equation (5.48) for the standard deviation of the random component of blade
root bending moment is first modified to eliminate the contribution of frequen-
cies below half the rotational speed to account for the blade pitching response,
and then discretized to give:
ð
2 m X 1
X m
o
2 2
ó 2 ¼ 1 rÙ dC l S (r j , r k , n)dn c(r j )c(r k )r r :(˜r) 2 (5:61)
M 2 dÆ u j k
j¼1 k¼1 Ù
Here the blade is assumed to be divided up into m sections of equal length
˜r ¼ R=m.
(2) After evaluation of the integrals of the m(m þ 1)=2 different curtailed rotational
spectra, the standard deviation of the blade root bending moment is obtained
from Equation (5.61).

(3) The time, T, that the machine spends in a wind speed band centred on the rated
wind speed is estimated using the Weibull curve, and multiplied in turn by the
factor å 1 appropriate to the waveform of the periodic component of blade root
bending moment and by the zero up-crossing frequency of the random root
bending moment fluctuations, to give the effective number of peaks, íå 1 T.

(4) The predicted extreme value of the total moment is calculated by substituting
the standard deviation of the blade root bending moment, ó M (¼ ó x ), the effec-
tive number of peaks, íå 1 T, and the extreme value of the periodic moment into
Equation (5.60).

In the case of a machine with a rated wind speed of 13 m=s operating at 30 r.p.m.
at a site with an annual mean of 7 m=s, the expected proportion of the time spent