Tong W. Wind Power Generation and Wind Turbine Design

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Structural Dynamics of Wind Turbines 145

in the measurements is completely absent in the simulation. As already discussed

this is due to mass imbalance.

Blade load results are also shown in Fig. 12 for the same wind turbine now oper-

ated in a ﬂ at terrain site [ 33 ]. In this case the mean wind is 15.4 m/s. However, a 6.0

yaw misalignment is present which explains the pronounced 1p variation on both

diagrams. Again the agreement between predictions and measurements is good.

In this particular case, predictions are shown also from a free wake aerodynamic

code [ 34 ] also showing good correlation to measurements.

The spectral information is the input to fatigue analysis. Fatigue is related to the

frequency content of load amplitudes. The basis of fatigue analysis is to count how

many times a speciﬁ c load change (or range) appears. To this end, the load ranges,

i.e. the difference between a local min and the next max, are sorted in bins and the

number of samples (or cycles) per bin is recorded. In this way the cumulative

fatigue spectrums are produced. In Fig. 13 such spectrums are shown for the loads

Figure 11: PSDs of loads for a 500 kW stall wind turbine operating in complex

terrain at 13 m/s mean wind speed [ 32 ].

Figure 12: Azimuthal variation and PSD of loads of 500 kW stall wind turbine

operated in yaw [ 33 ].

146 Wind Power Generation and Wind Turbine Design

considered in Fig. 10 . Note that the material fatigue data are given similarly and

therefore it is possible to assess the fatigue strength of the design. Of course fatigue

assessment requires the complete load spectrum so that the targeted life time of the

machine is reproduced. The procedure is detailed in the IEC standard [ 35 ] and involves

a long list of 10-min simulations covering the entire range of mean wind speeds.

8.3 Stability assessment

Stability appeared as a problem when wind turbines were ﬁ rst up-scaled to 600 kW.

At that time most wind turbines were stall regulated and research identiﬁ ed

dynamic stall as the main driver of aeroelastic instability [ 21 , 36 ]. In order to ana-

lyze aeroelastic stability, speciﬁ c tools were developed and validated against full-

scale tests measurements; see for example [ 37– 40 ]. The majority of these models

combine the BEM aerodynamic theory with multi-body system dynamics using

beam theory, similarly to the previously described analysis.

For stall regulated machines, the damping of the tower lateral bending mode as

well as the blade lag modes is marginal at high wind speeds where stall is expected

to have its major effect as shown in Fig. 14 . Two sets of results are considered,

both obtained for zero structural damping which in log scale is estimated to add

6–10%. The ﬁ rst set, denoted as “ﬁ xed RPM” corresponds to the modelling of the

drive train as a spring. In this case, the damping of the tower lateral bending mode

and the blade lag modes is negative at all wind speeds. Since there is no other

source of damping except what unsteady aerodynamics contributes, it follows that

this contribution is negative. Fixing the RPM is not realistic and the generator

should be also included. A simple generator dynamics consists of assuming that

the generator torque is proportional to the rotor speed which will add extra damp-

ing. The corresponding results are denoted as “generator”. There is a substantial

increase in the damping of the tower lateral bending mode and the symmetric lag

bending mode of the blade. If structural damping is added the situation will become

Figure 13 : Fatigue loads spectrum for a 500 kW stall wind turbine operating in

complex terrain at 13 m/s mean wind speed [ 32 ].

Structural Dynamics of Wind Turbines 147

only marginally stable which explains why stall regulation has been substituted by

pitch regulation in the design of multi MW machines.

Pitch regulation limits the onset of stall by keeping the mean angles of attack

along the blade up to the level of maximum lift. However light stall will occur

close to maximum lift ﬂ ow conditions which correspond to wind speeds around

rated power production. This is shown in Fig. 15 . Even at ﬁ xed RPM, the range of

wind speeds with negative damping is limited around the rated wind speed. When

the generator is added the damping increases substantially and attains higher positive

values as compared to the stall regulated situation.

So in conclusion, theory indicates that wind turbines are subjected to low damp-

ing in certain modes. In order to assess the validity of this result comparison with

full scale measurements is needed. This is done in Figs 16– 18 in terms of aeroelas-

tic frequency and damping for the most critical modes of a ∼ 3 MW pitch regulated

commercial machine. The measured data were obtained through Operational

Modal Analysis (OMA) [ 41 ] on a collection of normal operation time series of

Wind speed (m/s)

Damping in log decrement (%)

6 8 10 12 14 16 18 20 22 24 26

-20

-10

1st tower lateral (fixed RPM)

1st tower longit. (fixed RPM)

1st tower lateral (generator)

1st tower longit. (generator)

Wind speed (m/s)

Damping in log decrement (%)

6 8 10 12 14 16 18 20 22 24 26

-10

1st progressive lag (fixed RPM)

1st symmetric lag (fixed RPM)

1st regressive lag (fixed RPM)

1st symmetric lag (generator)

1st regressive lag (generator)

1st progressive lag (generator)

Figure 14: Damping variation for the tower bending modes (left) and the blade lag

modes (right) of a commercial 500 kW stall regulated wind turbine [ 38 ].

Wind speed (m/s)

Damping in log decrement (%)

6 8 10 12 14 16 18 20

1st tower lateral (fixed RPM)

1st tower longit. (fixed RPM)

1st tower lateral (generator)

1st tower longit. (generator)

Wind speed (m/s)

Damping in log decrement (%)

6 8 10 12 14 16 18 20

100

1st symmetric lag (fixed RPM)

1st regress. lag (fixed RPM)

1st progress. lag (fixed RPM)

1st symmetric lag (generator)

1st regress. lag (genertor)

1st progress. lag (genertor)

Figure 15: Damping variation for the tower bending modes (left) and the blade lag

modes (right) of a commercial 3 MW pitch regulated wind turbine [ 38 ].

148 Wind Power Generation and Wind Turbine Design

Wind speed (m/s)

Frequency (Hz)

6 8 10 12 14 16 18 20

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Beam1+BEM lin

Beam1+BEM nonlin (tower excit.)

Beam2+FreeWake (tower excit.)

measurements (OMA)

Wind speed (m/s)

Damping in log decrement (%)

6 8 10 12 14 16 18 20

-5

Figure 16 : Frequency and damping variation of the tower lateral bending mode.

damping in log decrement (%)

100

wind speed (m/s)

frequency (Hz)

6 8 101214161820

wind speed (m/s)

6 8 101214161820

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Beam1+BEM lin

Beam1+BEM nonlin (pitch ex.)

Beam1+BEM nonlin (tower excit.)

Beam2+FreeWake (pitch excit.)

measurements (OMA)

Figure 17 : Frequency and damping variation of the tower longitudinal bending mode.

loads with a total duration of several hours. Three sets of simulation results are

shown. The “Beam1+BEM” results were obtained using Euler-Bernoulli beam

theory for the structure and BEM theory for the aerodynamics. Models of this kind

represent the current state of art and can be used either in their linearized form

(denoted as “lin”) or in their original non-linear form (denoted as “nonlin”). The

“Beam2 + FreeWake” results have been obtained using the second order beam

theory outlined in Section 7.2 and the free wake aerodynamic model described in

[ 34 ]. Free wake aerodynamic modelling is a 3D model with signiﬁ cantly higher

computational cost and therefore is regarded as a research tool.

Figures 16 and 17 show the results for the two tower bending modes. Both pre-

dictions and measurements clearly indicate that the lateral bending mode is the

one less damped. However for this particular case predictions signiﬁ cantly under-

estimate the damping. In the speciﬁ c simulations, this underestimation is due to

the fact that the generator dynamics were not included which as already mentioned

improves stability. Another point is that the scatter of the measurements was large

and so of non-negligible uncertainty. Otherwise there is a noticeable mirror effect

between the linear and non-linear results for the lateral mode near the rated wind

speed (13 m/s). Contrary to linear models which give over this range minimum

Structural Dynamics of Wind Turbines 149

damping, non-linear models predict maximum damping. Note that in the longitu-

dinal tower mode the non-linear results resemble to the trends of the test data. The

best correlation was found for the “Beam2 + FreeWake” prediction which indi-

cates that non-linear effects play an important role in terms of accuracy. This point

is further supported by the results for the regressive and progressive lag modes of

the blade shown in Fig. 18 . Both non-linear models provide good damping predic-

tions. In particular the “Beam2 + FreeWake” follows better the trend in the high

wind speed range. So in conclusion the validation procedure indicates that stability

modelling can reproduce the stability characteristics of wind turbines and that

predictions are on the safe side which is very important in design.

References

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wind speed (m/s)

frequency (Hz)

6 8 10 12 14 16 18 20

wind speed (m/s)

6 8 10 12 14 16 18 20

wind speed (m/s)

6 8 10 12 14 16 18 20

wind speed (m/s)

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-5

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150 Wind Power Generation and Wind Turbine Design

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CHAPTER 5

Wind turbine acoustics

Robert Z. Szasz

& Laszlo Fuchs

1,2

Lund University, Lund, Sweden.

Royal Institute of Technology, Stockholm, Sweden.

This chapter presents some of the most important issues related to wind turbine

acoustics. After a short background, an introduction to acoustics follows where we

deﬁ ne the most important parameters that are met in the chapter. Next, the noise

generation mechanisms are discussed from a physical point of view. Some aspects

related to noise propagation and their perception are presented. A major part of the

chapter consists of a review of the prediction models with different level of com-

plexity together with experimental methods that are often used for wind turbine

aeroacoustics. Finally, a short list of noise reduction strategies is also given.

1 What is noise?

Sound is the propagation of low-amplitude pressure waves traveling with the speed

of sound . These pressure waves might be generated in several ways: for example

the vibration of the vocal chords or the membrane of a loudspeaker, periodical vor-

tex shedding in a cavity gives rise to a pure tone (i.e. having a single frequency). In

contrast, turbulent ﬂ ows may generate a broad spectrum sound, containing a wide

range of modes with different amplitudes. Thus, the mechanisms for generating

sound may be quite different resulting in sounds with widely different characters.

Hence, a simple modal characterization of the sound might not be enough to evalu-

ate its perception. When the generated sound is not wanted it is considered to be a

noise . Since the perception of sound as pleasant or annoying is highly individual,

there are no strict limits delimiting noise from acceptable sound.

2 Are wind turbines really noisy?

With the increasing demand of alternative energy sources the number of installed

wind turbines increased exponentially in recent years. Due to the limited amount

154 Wind Power Generation and Wind Turbine Design

of space with favorable wind conditions, there are more and more plants installed

close to residential areas. Together with the ever increasing size of the wind tur-

bines, this reduced distance causes an increasing number of noise related com-

plaints from residents. Even if most wind turbines respect the limits imposed for

industrial noise emissions, the sound emitted is often perceived ‘as a distant pile

driving,’ ‘like a washing machine,’ ‘like a nearby motorway’ or “like a B747 con-

stantly taking off” [ 1 ]. Low-frequency sound (and in particular infra sound with

frequency lower than 20 Hz) is known to have physiological effects (such as nau-

sea and headache). Wind turbine noise is usually continuous and it contains also

low frequencies. These low frequencies decay slowly and may reach to longer

distances (depending on the terrain). In spite of its low level, wind turbine noise

may have negative impact on humans and animals in their neighborhood [ 2 ]. The

overall effects of wind turbines are not yet established through different indepen-

dent studies. However, since there is documented evidence that individuals subject

to wind turbine sound do report undesirable effects, it is deﬁ nitely important to

take into account noise considerations when new wind turbine farms are planned.

3 D eﬁ nitions

Sound is strongly related to the compressibility of the ﬂ uids. When a pressure ﬁ eld

is perturbed, the perturbation is propagating by molecular collisions to the sur-

rounding ﬂ uid. On a macroscopic level this is perceived as a compression wave.

Several physical parameters may be deﬁ ned to quantify different characteristics of

the sound perceived by an observer.

The part of the pressure ﬂ uctuations which is traveling as waves are called the

acoustic pressure and is a function of time and space p ′ = p ′ ( t , x ). The propagation

speed of the sound waves is called the sound speed , which for an ideal gas can be

written as [ 3 ]:

cRTg

⎛⎞

∂

⎜⎟

⎝∂ ⎠

(1)

thus the speed of sound depends on the temperature. For air at atmospheric pres-

sure and 25

C it is approximately 340 m/s.

For a pure tone, the acoustic pressure can be written as:

'( , ) cos 2

ptx A

⎡⎤

⎛⎞

=±

⎜⎟

⎢⎥

⎝⎠

⎣⎦

( 2)

where A is the amplitude in Pa, l the wavelength in m and T the period in s. In eqn

( 2 ) the minus and plus signs denote waves propagating in the positive and negative

directions, respectively.

Since the perceived loudness by the human ear may have a very large range of

intensity one commonly uses a logarithmic scale. Thus, the relative acoustic pressure

is obtained by normalizing the acoustical pressure with a threshold level that equals

to the lowest hearable level ( p

ref

). The acoustic logarithmic scaling is given by