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Figure 136: Estimated preview required to cancel the delay of the prefilter, as a function of
wind speed. The prefilter is assumed to be a 2nd order low-pass Butterworth filter with cutoff
frequency corresponding to 0.04 rad/m.
The physical reason for this blade-flexibility delay is not understood, but it does conincide
with non-minimum phase zeros in the linearized turbine model. The resulting delay ranges
from 0.05 to 0.3 seconds depending on average wind speed. Additional or different delay in
TyβFF relative to Tywt may appear when a different output of interest is chosen.
10.3.2 Prefilter Preview Time
In additionto the previewtime required to implementthe ideal feedforwardcontroller,preview
timeisneededtoimplementtheminimummeansquareerrorprefilter(Eq.(226)).Theprefilter
generally takes the form of a low-pass filter, where the better the wind measurements are,
the higher the cutoff frequency of the low-pass filter is. Every low-pass filter introduces delay
(or requires equivalent advance knowledge of the incoming signal). The higher the cutoff
frequency of the low-pass filter, the less delay is introduced at any given frequency. Therefore
better measurements mean less delay introduced in the prefilter and less required preview
time.
A typical nacelle-mounted lidar, designed for control, yields good measurements up to a
wavenumber of about 0.04 rad/m. For a wind speed of 13 m/s for example, this frequency is
0.04 rad/m×13 m/s/(2π rad) ≈ 0.08 Hz.
Figure 136 shows the preview time required (the time delay introduced at low frequencies)
by the prefilter, assuming it is a 2nd-order low-pass Butterworth filter with a cutoff frequency
corresponding to 0.04 rad/m. (The amount of delay introduced depends on the order of the
filter in addition to the cutoff frequency. A higher-order means a steeper cutoff and more
delay introduced.) We see that the preview time needed for the prefilter is much greater
than the preview time needed for the ideal feedforward controller, and it decreases with
increasing wind speed, ranging from about 1.5 to 3 seconds. Preview time available from
the lidar measurement also decreases with increasing wind speed because it is determined by
the preview distance divided by the average wind speed. More detail on required preview time
due to pitch actuators, blade flexibility, and imperfect wind measurements can be found in
Dunne et al. (2012).
10.3.3 Pitch Actuation Preview Time
The ideal model-inverse feedforward controllerdesign method assumes we want to minimize a
single output or set of outputs, such as generator speed error or blade root bending moments,
DTU Wind Energy-E-Report-0029(EN) 199