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RootMyb1 DEL (kNm)
4000
3500
3000
2500
2000
1500
1000
500
m=10
m=3
0
0 200 400 600 800 1000
RootMyb1 standard deviation (kNm)
Figure 135: DEL vs STD values of blade root flapwise bending moment (RootMyb1) from
various simulations of the NREL 5-MW wind turbine. The DEL calculation depends on m,
the slope of the S-N (stress vs. cycles to failure) curve for the particular material. The value
m=3 is typical for welded steel, and m=10 is typical for composite blades.
10.2.3 The Relationship between Variance and Damage Equivalent Loads
Asidefromregulatinggeneratorspeed,theobjectiveofthecontrolinabove-ratedconditionsis
to minimize variations in stress on turbine components because they cause material fatigue,
which over time leads to failure. The damage equivalent load (DEL) (IEC, 2001) is the
standard method of quantifying fatigue damage. However, the DEL is a fairly complicated
nonlinear function of a load on a turbine component, and it is difficult to minimize directly.
Instead, the standard deviation (STD) of a load can be minimized, and this is correlated with
reduction in the DEL, as shown in Fig. 135. Minimizing variance is the same as minimizing
standard deviation because the variance is simply the standard deviation squared.
10.3 Preview Time in Feedforward Control
10.3.1 Ideal Feedforward Controller Preview Time
The ideal feedforward controller (Eq. (216)) is typically non-causal, and therefore not implementableexceptbycausalapproximationorbyusingapreviewmeasurementofthewind.This
non-causality appears whenever TyβFF has more phase delay than Tywt, or in other words,
the blade pitch command takes longer to affect the output of interest than does the wind
disturbance. This happens whenever a blade pitch actuator model is included, and it has also
been observed when blade-flexibilityis modeled. The difference in phase delay between TyβFF
and Tywt determines how much preview time is required to implement the ideal controller. A
smaller-than-ideal amount of preview time is still useful, allowing a better approximation to
the ideal controller than would be possible with no preview time at all.
The pitch actuator for the NREL 5-MW wind turbine is typically modeled as a 2nd-order
low-pass filter with a natural frequency of 1 Hz and a damping ratio of 0.7. This results in a
delay of about 0.225 seconds that appears in TyβFF but not Tywt. Phase delay is converted
to time delay using the equation
time delay = −phase/360 ◦ /frequency.
The time delay is a function of frequency, but remains fairly constant at low frequencies, and
we use this low-frequency value of the time delay.
When blade flexibility is modeled on the NREL 5-MW wind turbine, and when the output
y is chosen to be generator speed error, the delay in TyβFF further increases relative to Tywt.
198 DTU Wind Energy-E-Report-0029(EN)