Structural dynamics of wind turbines - Wind Power Generation and Wind Turbine Design - page 142

8.1 Modes at stand still

Modes were introduced as the function basis with respect to which the behaviour
of a linear system is fully described. There are three levels of modal analysis: the
purely structural, the aeroelastic and the servo-aeroelastic. The case of a wind
turbine at stand still is convenient for estimating the purely structural modes. At
stand still, the rotor is blocked by the braking system so there is no rotation and
the generator contributes only with its weight. Assuming almost zero infl ow, aero-
dynamic loading can be neglected. One advantage of stand still conditions is that
they can be easily reproduced in full scale. So measurements can be used as a basis
for validating and fi ne tuning structural models. By setting the rotation speed equal
to zero certain inertial terms are eliminated and therefore the stand still modes will
not exactly represent the modal behaviour of wind turbines in operation. Of course
wind turbines rotate slowly and therefore modes will not substantially change as
in other rotor applications [23].
For a well balanced rotor the basic frequency is the rotation frequency p multi-
plied by the number of blades and its multiples. So for a three-bladed turbine the
natural frequencies should be placed away from 3p and 6p in order to avoid reso-
nance. The required margin depends on many factors but one should keep in mind
that large margins are not possible. Besides the natural modes of the different
components, coupled modes will appear as a result of their inter-connections. In
Fig. 9 the natural frequencies of 3 three-bladed commercial machines taken from
the late 1990s, are compared. The lowest two modes are the lateral and longitudi-
nal bending modes of the tower which appear in between 1p and 2p. Such low
values are due to the large mass placed on top of the tower. Next appears the drive
train torsion mode which must be <3p and fi nally the lower blade modes. There are
three fl ap bending modes: the symmetric and two asymmetric. The symmetric

10.00

9.00

8.00

7.00

6.00

500kW stall
1300kW stall
500kW pitch

5.00

4.00

3.00

2.00

1.00

0.00

M1 M2 M3 M4 M5 M6 M7 M8

Eigenfrequencies

Figure 9: The fi rst modes of three wind turbines at stand still.