Gasch R., Twele J. (Eds.) Wind Power Plants: Fundamentals, Design, Construction and Operation

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4.3 Determination of power, yield and loads

152

value of 8° is easily exceeded. But in most cases, a suitable positioning of the

wind turbines prevents significant energy yield losses.

The measurement of a vertical oblique inflow requires ultrasonic anemometers

which measure all three components of the wind installed at hub height. More-

over, some wind farm planning software, e.g. WAsP Engineering, allow an esti-

mation of the oblique inflow.

Fig. 4-34 Loads due to vertical oblique flow

Influence of wind shear

The wind shear is defined as difference of the horizontal wind speed at the top and

bottom of the rotor. It is either given as the change of wind speed per meter of

height, or as exponent of the power law, equation (4.1). In the certification guide-

lines according to IEC and German Lloyd [20], an exponent of 0.2 is applied in

the load calculations.

v + ǻvv + ǻv

Fig. 4-35 Loads due to the wind profile ( wind shear)

4 The wind

153

The wind shear causes alternating loads on the blades because the blade experi-

ences during every revolution alternating inflow angles, Fig. 4-35. Therefore, the

operational loads and also the bending stress of the rotor shaft increase as well.

On site the wind shear may be influenced by four phenomena:

- Terrain inclination

Strong inclinations of the terrain may cause deviations from the logarithmic

wind profile. For smooth inclinations, the growth of the wind speed with height

may be reduced. In some cases the wind even no longer increases with height,

the gradient reduces to zero. This situation may be advantageous for the eco-

nomic efficiency of the wind farm project since there is no requirement for very

large hub heights for increasing the yield. But if the slopes are too steep and

turbulent flow separation occurs, cf. Fig. 4-11, the wind profile may be de-

formed strongly. Parts of the rotor area may be exposed to a negative gradient.

In other zones of the rotor area there may be very large gradients at the same

time, Fig. 4-36.

Fig. 4-36 Wind profile with strong wind shear due to terrain inclination (steep slope)

- Obstacles

If wind turbines are situated closely behind large obstacles, e.g. a forest, the

wind speed at the bottom of the rotor may be decelerated heavily. The degree

of deceleration depends on the dimensions of the obstacle, its porosity and the

distance between obstacle and wind turbine. The deformation of the logarith-

mic wind profile is shown schematically in Fig. 4-37.

- Small distance between the wind turbines

As mentioned above, the expanding wake flow behind a wind turbine, cf. Fig.

4-29, induces additional turbulence and reduces the wind speed compared to

the ambient free flow since the wind turbine extracts energy from the wind.

This is called the velocity deficit in the wake flow. The continuous line in Fig.

4-38 shows the influence of the wake on the vertical wind profile at a distance

of 5.3 rotor diameters behind the wind turbine. This deformed wind profile

shows areas of a negative gradient, but also some with a strongly positive gra-

dient. For comparison, the dashed line shows the wind profile in front of the

wind turbine.

4.3 Determination of power, yield and loads

154

Fig. 4-37 Wind profile behind obstacles

Fig. 4-38 Wind profile in front of a wind turbine and in the wake behind it at a distance of 5.3

rotor diameters [1]

4 The wind

155

Fig. 4-39 Wind turbines partly shaded by the wake flow of the neighbouring wind turbine

The worst case for the loads on the wind turbine is not the total shading of the

rotor by the wake, but partial shading, Fig. 4-39. Under these circumstances

there is not only a vertical, but also a horizontal gradient, and additionally the

turbulence is increased.

- Atmospheric stability

The different vertical temperature profiles produce different vertical wind pro-

files, as discussed in section 4.2.2. So at different heights there may be layers

with strongly varying wind speeds. Fig. 4-10 showed clearly the vertical gradi-

ent of the wind profile increases with growing stability of the atmosphere

(dashed line).

In the first three cases discussed above (influence of terrain inclination, obsta-

cles and/or distances between the wind turbines), a suitable positioning and/or

hub height of the turbines prevents that the stress due to strong wind shear

exceeds the allowed material strength.

The wind shear at a site may be determined through wind speed measurements

at different heights. But the problem is that the measured gradient is a function

of the height itself, and therefore may not be simply extrapolated to other

heights: The gradient determined from measurements at 10 m and 30 m height

is not identical to the gradient observed between 30 m and 50 m height. Based

on the terrain properties and data of good quality, siting software like the al-

ready mentioned WAsP allows a more precise determination of the gradient.

Furthermore there are other programs like WAsP Engineering for the calcula-

tion of the gradient. But both of the mentioned programs are not able to predict

directly the influence of atmospheric stability.

4.4 Wind measurement and evaluation

The magnitude, time history and direction of the wind are the most important

parameters for the prediction of the expected energy yield – i.e. the quantitative

4.4 Wind measurement and evaluation

156

assessment of a site - as well as the decision which available wind turbine is the

most suitable one.

Since the wind turbine power is approx. proportional to the cube of the wind

speed (until the rated wind speed is reached) the wind regime on a site has to be

determined as exact as possible. An error of 10% in the wind speed measurements

may produce an error in the determined power output of up to 33%. An exact

knowledge of the wind regime is furthermore important for the determination of

the mechanical loads and stress.

There are high requirements on the wind measuring devices, the sensors and

the instrumentation for data recording. Apart from the accuracy of the wind speed

sensor the devices have to be extremely robust in order to record data mainte-

nance-free for long periods.

Moreover, faulty measurements due to wrong installation and sensor icing have

to be prevented. In general, mechanical wind speed sensors like the cup anemome-

ter are well proven and reliable sensors. Their limits of application and possible

sources of errors are mostly known, so among other, they should be calibrated

before and after a measuring campaign.

Sensors without moving parts, like e.g. the ultrasonic anemometer are up to

now seldom applied for long-term measurements since firstly they are more

expensive than the mechanical sensors, and secondly they are more susceptible to

faults because they are generally more complex devices. The ultrasonic anemo-

meter may measure, independent from the current wind direction, instantaneously

all the three components v

, v

und v

of the wind vector

)()()()(

222

Vector

tvtvtvtv

zyx

 . (4.23)

Since a wind turbine is able to extract power only from horizontal wind speed

component v

horiz

which is perpendicular to the rotor swept

)()()(

tvtvtv

yxhoriz

 , (4.24)

a vertical component v

, e.g. due to a slope (cf. Fig. 4-34), is of no use. The cup

anemometer measures directly the horizontal wind speed component v

horiz

but can-

not resolve the vertical component v

Propeller anemometers (also called windmill anemometers) measure as well

only the horizontal wind speed component v

horiz

and have an integrated wind vane.

It is favourable that the wind direction is measured with the same sensor unit,

whereas using a cup anemometer it has to be determined by a separate sensor. But

unfortunately, the integrated wind vane of the propeller anemometer causes a

severe problem: the propeller is wiggling in the wind which distorts the wind

measurement.

4 The wind

157

4.4.1 Cup anemometer

International standards following IEC [4] and IEA [3] refer to the cup anemometer

as the most suitable sensor type for wind speed measurements, Fig. 2-22 and 4-40.

The cup anemometer is a small drag driven wind mill with a vertical axis of rota-

tion. Cup-like drag bodies are fixed with a lever to the vertical shaft. Instead of

hemispherical cups there are more and more conical shells applied since they have

a more distinct edge for defined flow separation.

Anemometers produce either an analogue or a digital signal output. The ana-

logue signal is the voltage, which is proportional to the rotational speed and the

wind speed (cf. equation 2-12), produced by the rotation of a small generator. The

digital signal, a defined number of impulses per revolution produced by reed con-

tacts or an incremental encoder, is counted over in a certain interval and offers this

way a measure proportional to the wind speed.

High quality precision

bearing for minimization

of mechanical losses

Long shaft to minimize

the influence of flow

disturbances of the rotor,

induced by the nacelle

Thoroughly designed rotor

geometry for well defined

vertical sensibility and

dynamic response behaviour

Small and complete sym-

metric housing without sticking

out parts, with a soft outline

to minimize flow disturbances

Fig. 4-40 Cup anemometer [3]

A special attribute of the cup anemometer is the so-called response length (also

called distance constant, [13]) which results from signal delay occurring at rapid

changes of the wind speed due to the inertia of the rotating cup star. If a virtual

wind speed increases with a step function from v

to v

+ 'v , the signal of the

anemometer responds with an exponential curve (i.e. 1

order time delay).

4.4 Wind measurement and evaluation

158

There are several methods to determine the response length [13]. In the wind

tunnel method, a constant wind speed is adjusted, and the acceleration of the

anemometer from standstill to load-free idling is measured. The rotational speed

increases rapidly, therefore, the required measurement instrumentation has to

work fast (i.e. high sampling rate) and with a high resolution. Another method to

determine the response length is the comparison of the cup anemometer with a

high-resolution ultrasonic anemometer.

4.4.2 Ultrasonic anemometer

Ultrasonic anemometers, Fig. 4-41, were developed for the investigation of the

turbulent field in the surface boundary layer. There are up to three pairs of

sonotrodes (speaker-microphone combination) arranged in a way that the three

spatial components of the flow are resolved, equation (4.23). The ultrasonic im-

pulses, emitted at a rate of 100 Hz, travel over the distance s between speaker and

microphone with the speed of sound c. The wind speed component parallel to the

sound travelling direction of the sonotrode superimposes the emitted signal and

leads to different run times for the way with (t

) and against the wind (t

), which

is called the Doppler Effect.



and



(4.25)

Rearranging the equations yields the wind speed component v parallel to the sound

travelling direction of this sonotrode, simply given by the travelling distance and

the two run times.



(4.26)

It is favourable that the wind speed component is determined independently from

the speed of sound which varies with air density and humidity. As mentioned

above, the combination of three sonotrodes gives a sensor which allows the instan-

taneous measurement of all three wind speed components, Fig. 4-41.

A problem inherent of the ultrasonic anemometer is the deflection of the flow

by the sonotrodes heads, and the sensor arms as well. Therefore, the measurement

in the direction of the arms is inaccurate. This is a potential source of measure-

ment uncertainties of long-term measurements with theses sensors. Moreover,

there are effects from the aging of the piezo-electric sonotrodes. At least, the

sensor behaviour is temperature dependent.

4 The wind

159

Fig. 4-41 Ultrasonic anemometer

4.4.3 SODAR

The abbreviation SODAR stands for SOnic Detecting And Ranging. It is a remote

sensing method for the exploration of the atmospheric boundary layer. The principle

is similar to this of Radar and Sonar measurements. The SODAR technique is

mainly applied for recording the vertical wind speed profile. The SODAR device

emits small sharply bundled sound signals in the audible range. These are

reflected at the boundaries between atmospheric layers of different refractive

numbers which comes from differences in temperature and humidity. These

boundaries between atmospheric layers move with the local speed of the wind.

The frequency of the back-scattered signal is shifted with respect to the emitted

signal due to the Doppler Effect. If the sender and the receptor are at the same

location the system is called a monostatic SODAR. The measured Doppler shift is

proportional to the wind speed component parallel to the beam direction of the

sending antenna.

If several antennas or senders are applied which point in different directions the

three-dimensional vector of the wind can be measured. The senders are mostly

arranged in a way to receive a phase-shifted signal (phased array) which allows

simulating the behaviour of several antennas pointing into different directions.

Using the different run times between sender and scattering volume receptor parallel

measurements of the wind speed in different heights are possible to determine the

vertical wind speed profile.

The SODAR measures within a certain air volume, in contrast to the cup anemo-

meter which is limited to the measurement at one single point of the wind field.

4.4 Wind measurement and evaluation

160

In order to measure in heights between 20 and 150 m above ground, so-called

Mini-SODAR systems are applied. They operate in the frequency range between 4

and 6 kHz and reach a resolution of height between 5 and 10 m.

The biggest advantage of the SODAR systems is that they allow measurements

of wind speed and wind profiles in large heights where a measuring mast would be

too expensive. Especially in very complex terrain, e.g. where a forest is found in

the main wind direction, the SODAR systems allow a comparison of measured

and simulated wind profile. But it has to be considered that under stable atmos-

pheric conditions there is only a small scattering, so there will be no valid measur-

ing signals. Moreover, the signal-to-noise ratio decreases with increasing height,

so the allocation of the signals to the related height above ground becomes more

and more difficult. Thus, the installation and adjustment of the SODAR systems as

well as the evaluation and interpretation of the SODAR measurements require

extensive experience and routine.

Fig. 4-42 Scheme of a SODAR measurement

Since the SODAR has a significantly higher power consumption than a cup

anemometer the power supply may by a problem at remote sites. Moreover, the

measurement quality is strongly dependent on measurement disturbances by

obstacles close to the antennas which may disturb and reflect the signals. Since the

emitted signals are in the audible frequency range the measurements are sensitive

to background noise e.g. from cowbell, croaking frogs, the roar of the surf and

more. It should be remembered that the wind profile measured with a SODAR

system in a shorter measuring period is representative only for the specific prevail-

ing atmospheric stratification. All in all, using a SODAR the determination of the

mean wind speed with a desired precision is difficult, therefore it should be

4 The wind

161

applied only in combination with conventional wind sensors installed on a

measuring mast for additional investigations of the wind regime.

4.5 Prediction of the wind regime

4.5.1 Wind Atlas Analysis and Application Programme

The WAsP (Wind Atlas Analysis and Application Programme) was developed for

the energy yield prediction of single wind turbines and wind farms [5].

With the years WAsP became a standard tool for the Micro-siting of wind

farms, but its application has limits which are well known by now.

The software allows to analyze the wind regime at potential sites and to support

the site selection. It is possible to transform the wind speed from one point A to an

arbitrary point B, Fig. 4-43 [5]. For this purpose, in a first step all influences from

orography, roughness and obstacles on the surface wind at point A are removed.

The resulting wind represents the geostrophic wind which is then assumed to be

uniform in a large-scale area. In the second step, the local influences at the point B

are applied which gives the local wind at this site. The energy yield is then deter-

mined using the sectorised wind distributions and the power curve of the chosen

wind turbine (cf. Fig.s 4-22 and 4-25).

The strongly simplified flow model applied in WAsP is based on the Navier-

Stokes equations. The basic assumptions are:

- The atmospheric stratification is approximately neutrally stable.

- Thermal driven winds are neglected.

- The surface inclination is small, so there is no flow separation (inclination be

low approx. 30%, i.e. 17°. But the critical inclination depends in reality e.g.

on the surface roughness and the atmospheric stability).

These basic assumptions allow the linearization and the solution of the Navier-

Stokes equations. This model is relatively simple and requires quite small compu-

tational resources.

The more complex the topography and climatology of a site, the higher are the

uncertainties of this simplified calculation. Furthermore, the radius around point A

in which this method is valid for application depends also on the quality of the

input data. Own wind measurements close to the site are the favoured input data,

so the radius for calculation results is a few hundred meters.