Structural dynamics of wind turbines - Wind Power Generation and Wind Turbine Design - page 144

Figure 10: Azimuthal variation of loads for a 500 kW stall wind turbine operating
in complex terrain at 13 m/s mean wind speed [32].

against full scale measurements. The model used is described in [31]. It consists of
combining a BEM aerodynamic model with a multi-body structural model of the
type described in the previous paragraphs.
In the fl apwise direction the blade is expected to respond to its natural frequency
which is 4p in accordance with our previous discussion. There is also a small 1p

variation which is due to wind shear. At 180 o the blade passes in front of the tower
which constitutes an extra excitation which explains the higher load amplitude
between 180 o and 270 o . The overall agreement is good although the effect of the
tower is slightly more pronounced in the simulation. Going on to the shaft, a clear
3p dominance is found. On top of the 3p variation there is also a 6p variation in the
simulation. This is because the rotor has three blades contributing to the shaft bend-
ing loading and therefore multiples of 3p are excited. A 1p is not expected unless
there is a mass imbalance on the rotor which is apparently the case for the specifi c
machine as indicated in the measurements. Again the overall agreement between the
predicted and the measured responses is good in terms of amplitudes. There is a
level difference which could be due to many reasons. Quite often level differences
originate from measuring errors which are not easy to detect before hand.
Azimuthal averaging produces deterministic information on the loads in the
sense that the loading will undergo the same load variation for any full rotation.
Therefore it is necessary to also add the stochastic part corresponding to non-
periodic variations. Information of this kind is given by the load spectrum.
Figure 11 depicts the power spectral densities (PSDs) of the two loads considered
previously in log scale. It is expected to have high spectral energy at 1p (=0.5 Hz
for this particular machine) and its multiples. The spectrum of the fl apwise bend-
ing moment at blade root, shows high activity at 1p and in between 3p and 4p. 1p
excitation is due to wind shear, tower blade passing and the rotational sampling of
the wind spectrum, while the activity between 3p and 4p corresponds to the blade
modal excitations. It is in this frequency range that the blade fl ap modes appear: the
symmetric at

∼

4p as well as the two asymmetric. On the other hand the spectrum
of the shaft tilt moment is dominated by the 3p excitation. The 1p excitation seen

∼