4.3 Determination of power, yield and loads
4.3.5 Effects of wind and site on the wind turbine loading
Extreme wind speeds
As mentioned in section 4.2.4, the Weibull distribution function shows mostly a good agreement with the frequency distribution of the measured wind speed. In contrast to that, the distribution of extreme wind speeds follows other statistical laws and is not represented by the Weibull function. Extreme wind speeds are of- ten expressed as n-year wind speed, i.e. the 10-min mean wind speed which is exceeded in the average once in the period of n years. In course of the wind turbine design, the 50-year wind is of interest. It is found that for a description of these extreme wind speeds the twice exponential Gumbel distribution is very suitable
exp( Į(V ȕ)) )
(V e
F (4.21)
where F(V) is the cumulated probability that the mean wind speed V is exceeded.
More details on this topic are found in the literature [1].
In practice, the extreme meteorological limiting conditions of a site are very important for the determination of the loads on the wind turbine and for the classifi- cation of the site, see table 9-2 (cf. IEC 61400-1).
There is a close relationship between the maximum gust wind speed and the maximum 10-min mean wind speed in the observed period: they are linked by the standard deviation Vv, as shown in Fig. 4-30a. The measurement of 10-min aver- ages on the Danish west coast in a height of 20 m comprised approx 1,500 values [33].
4.3 Determination of power, yield and loads 148
a)
Mean wind speed in m/s
Actual wind speed in m/ s
Minimum Maximum
Standard deviation
Mean wind speed in m/s
Actual wind speed in m/ s
Minimum Maximum
Standard deviation
b)
Fig. 4-30 a) Minima, maxima and standard deviations of the wind speed versus the 10-min aver- age values [33]; b) Gust factor versus wind speed for different measuring heights [1]
The 3-sec-50-year extreme gust Ve50 is therefore calculated from the maximum 10-min mean value Vm50, given in table 9-2 (cf. IEC 61400-1), and the estimated turbulence intensity Iv
Ve50 = Vm50(1 + 2,8 Iv) . (4.22) Remember in this context the equation (4.9) where Iv = Vv / v . The factor 2.8 in equation (4.22) is called gust factor and was confirmed by measurements for dif- ferent heights, Fig. 4-30b. In the German guidelines of the German Lloyd dated 2003 [20] and the DIBt dated 2004 [21] the recommendations for the considera- tion of gusts are identical or similar.
Consequences of the turbulence
In section 4.2.3 the description of turbulence using the turbulence intensity Iv was already introduced, it is the ratio of standard deviation to the mean wind speed in the averaging period (mostly 10 minutes), equation (4.9). As discussed with Fig.
4-15, its value depends on the wind speed. This dependency is respected in the standards of IEC 61400 [19] and the guidelines of German Lloyd [20], table 9-2.
Apart from the blade weight, turbulence is a main cause of material fatigue.
Producing alternating loads it stresses the whole blade, but above all the blade root, shown schematically in Fig. 4-31. Moreover, the turbulent wind field causes alternating torsion of the drive train, and furthermore the alternating thrust stresses the tower.
Fig. 4-32 shows exemplarily for two different turbulence intensities the opera- tional loads at the blade root (flapwise bending) versus the wind speed.
High natural turbulence intensities Iv may be caused among other by obstacles (e.g. a near building), surface roughness (e.g. strong vegetation) and terrain incli- nation, according its origin named ambient turbulence (or environmental or natural turbulence.
Fig. 4-31 Turbulences provoking dynamic loads and vibrations
4.3 Determination of power, yield and loads 150
Amplitude of thedamage equivalent Rectangular load collective Mxb in kNm
Wind speed in m/s 2500
2000
1500
1000
500
0
0 5 10 15 20 25
20%
10%
Fig. 4-32 Operational loads at the blade root of a 1,25 MW wind turbine for two different turbu- lence intensities [22]
But additionally, increased high turbulence intensity is caused in the wind turbine wake, named induced turbulence intensity IW. It is problematic when there is a disadvantageous wind farm layout with too small distances between the wind tur- bines. Therefore, in course of the wind farm siting it has to be assured that the sum of natural turbulence Iv and turbulence IW induced by the wake flow of neighbour- ing wind turbines does not exceed the limiting values applied in the design certifi- cation. Else, the service life may be reduced significantly (worst case: some months instead of 20 years). Fig. 4-33 shows the additionally induced turbulence intensity IW in the wake depending on the distance from the wind turbine, ex- pressed in multitude of the rotor diameter. The results are based on measurements at four different sites. The Fig. shows that, e.g., the limiting value of 20% turbu- lence intensity given in the German construction guideline of DIBt [21] is already exceeded by the induced turbulence intensity alone for a distance of less than 4 rotor diameters! Of course, for a certain site, the wind direction frequencies have to be included in a closer consideration as well.
It has to be mentioned in this context that the natural turbulence and the wake induced turbulence have a different length scale and therefore different effects on the wind turbine. The longitudinal length scale of the natural turbulence is in the range of 600 to 1.000 m, whereas the length scales for the wake flow turbulence are in the range of 1 to 2 rotor diameters. And at least it has to be considered that on one hand the turbulence intensity in the wake is increased, but the wind speed, and therefore the wind energy, is significantly reduced.
0.0 0.1 0.2 0.3 0.4 0.5
0 2 4 6 8 10
Abstand in Rotordurchmessern Iw
I_w_mod Andros Taff Ely AlsVik Vindeby
Distance in rotor diameters 0.0
0.1 0.2 0.3 0.4 0.5
0 2 4 6 8 10
Abstand in Rotordurchmessern Iw
I_w_mod Andros Taff Ely AlsVik Vindeby
Distance in rotor diameters
Fig. 4-33 Additionally induced turbulence intensity Iw in the wake behind wind turbines [23]
While the mean wind speed at the site is decisive for the occurring loads, the tur- bulence intensity is a measure for the frequency of the load cycles. Therefore, both have to be considered in course of the planning and the wind farm layout. For the load calculations, the standard deviation ıv is of a higher importance than the turbulence intensity.
The data for wind speed and turbulence intensity are at best determined from measurements at the planning site. But apart from that, there are also planning tools, e.g. WAsP Engineering (Wind Atlas Analysis and Application Program) [14], which allow a consideration of the topography and the surface roughness in the siting calculations.
Consequences of oblique inflow
At sites on hills there is not only a deviation of the vertical wind profile from the logarithmic profile, but also a deviation of the inflow from the horizontal direction (i.e. an oblique inflow). Therefore, the blades are exposed permanently to an alter- nating inflow angle of the relative velocity leading to increased operational loads at the blade root. Additionally, the rotor shaft is stressed by bending, shown sche- matically in Fig. 4-34.
In course of the calculation of the loads for certification according to the guide- lines of IEC and German Lloyd [20], a mean flow inclination angle of up to 8° is assumed. This deviation from a horizontal inflow is caused by an inclination of the terrain. The influence of the terrain decreases with increasing height above ground. Especially in very complex terrain, e.g. scarps and cliffs, the limiting
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 + ǻv v + ǻv
Fig. 4-35 Loads due to the wind profile ( wind shear)
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]
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.