Page 318 - Wind Energy Handbook

292 DESIGN LOADS FOR HORIZONTAL-AXIS WIND TURBINES

substituting half the maximum range of the periodic signal, including harmonics, for
the amplitude of the sinusoid. A fuller summary is given in Hoskin, Warren and
Draper (1989). They concluded, along with Morgan and Tindal (1990), that the
Madsen method yielded slightly less accurate fatigue damage values than the Dirlik
method for the MS1 monitored data for flapwise bending referred to above.

5.9.4 Wind simulation

Wind simulation, which was introduced in Section 5.7.6, has two significant
advantages over the methods described above for fatigue damage evaluation. First,
it can handle non-linear relationships between wind speed fluctuations and blade
loadings in the calculation of stochastic loads, and second, it avoids the difficulty of
deriving the fatigue stress ranges arising from combined periodic and stochastic
load components. It is therefore currently the favoured method for detailed fatigue
design. The procedure is essentially as follows.

(1) Generate a three-dimensional ‘run of wind’ for the chosen mean wind speed,
with the desired shear profile and tower shadow correction.

(2) Perform a step-by-step dynamic analysis on the turbine operating in this wind
field, to obtain in-plane and out-of-plane bending moment time histories at
different radii.

(3) Convert these bending moment time histories to time histories of bending
moments about the principal axes.

(4) Compute stress–time histories at chosen points on each cross section.

(5) Derive the number of cycles in each stress range ‘bin’ by Rainflow Cycle
Counting (see Section 5.9.5 below).

(6) Scale up the cycle numbers in line with the predicted number of hours of
operation at the chosen mean wind speed.

(7) Calculate corresponding fatigue damage numbers based on the applicable S=N
curve.

(8) Repeat above steps for different mean wind speeds, and total the resulting
fatigue damages at each point.

A computationally simpler alternative is to generate a one-dimensional ‘run of
wind’ (in which only the longitudinal component of turbulence is modelled), and
run a number of simulations at different, fixed yaw angles.
The duration of wind simulations is limited by available computer power, with a
time history length of 600 s being frequently chosen. A consequence of this is that a
single simulation will not provide an accurate picture of the infrequent high-stress