Measurement of rotor centre flow direction and turbulence in wind farm environment

The measurement of inflow to a wind turbine rotor was made with a spinner anemometer on a 2 MW wind turbine in a wind farm of eight wind turbines. The wind speed, yaw misalignment and flow inclination angle was measured during a five months measurement campaign. Angular measurements were calibrated by yawing the wind turbine in and out of the wind in stopped conditions. Wind speed was calibrated relative to a met mast in a wake-free wind sector during operation. The calibration measurements were used to determine the basic k1 and k2 constants of the spinner anemometer and a four parameter induction factor function. Yaw measurements and turbulence measurements, where the average wind speed was corrected to the far field with the induction function, showed good correlation with mast measurements. The yaw misalignment measurements showed a significant yaw misalignment for most of the wind speed range, and also a minor symmetric yaw misalignment pattern. The flow inclination angle showed slight variation of inflow angle with wind speed and clear wake swirl patterns in the wakes of the other wind turbines. Turbulence intensity measurements showed clear variations from low turbulence in the wake-free wind sector to high turbulence in the wakes of the other wind turbines.


Introduction
The measurement of inow to the wind turbine rotor is of relevance for control purposes and for performance and loads assessment. Yaw misalignment of turbines is traditionally made with reference to a met mast, but newer instruments are being applied. Yaw misalignment and ow inclination angle measurements with a spinner anemometer was made from 2007 [1,2,3]. Yaw measurements with a spinner based lidar was compared with mast measurements in [4], and shortcomings were discussed in [5]. Yaw measurements with a spinner anemometer were compared with nacelle based lidars [6]. Turbulence measurements with nacelle based lidars show some deviation from mast measurements due to long measurement volume [7]. Turbulence measurements with a spinner anemometer is new. Appropriate calibration of a spinner anemometer show that with correction for induction, turbulence measurements can be made with high condence. Thus qualitative measurements in a wind farm of these measurement parameters can reveal new insight into the wind inow to wind turbine rotors.

Wind farm environment
The measurements were made on wind turbine no. 5 in Tjaereborg wind farm, see gure 1. The wind turbine is a V80 2 MW wind turbine with hub height 60 m and rotor diameter 80 m. The other wind turbines in the wind farm are Vestas and NEG Micon types with a nominal power of 2-2.75 MW and rotor diameters of 54-80 m. The reference met mast was located 120 m southwest (213 • ) of the no. 5 turbine. Cup anemometers and wind vanes were mounted on booms at hub height. A spinner anemometer was mounted on the spinner, see gure 2. Directions and relative distances are shown in table 1. The wake-free sector (212 • − 252 • ) with the mast in front of wind turbine no. 5 was used for calibration purposes. The terrain in the sector was at and without obstacles, with 1 km to the North sea. Another wake-free sector (297

Calibration
The spinner anemometer algorithm utilizes two constants k 1 and k 2 to convert the measured wind speeds of the three sonic sensors to horizontal wind speed, yaw misalignment and ow inclination angle. The default values of the constants before calibration were set to k 1,d = k 2,d = 1. The calibration of angular measurements is dependent on the constant k α = k 2 /k 1 , the ratio between the two basic constants. For calibration of angular measurements one has to nd a correction factor F α to correct the default ratio to the corrected ratio k α = F α k α,d . k 1 may then be kept constant and k 2 be corrected to k 2 = F α k 2,d . The calibration for angular measurements is made by yawing the wind turbine in and out of the wind in stopped condition while measuring yaw misalignment and the nacelle direction with a yaw direction sensor. Figure 3 shows a plot of yaw direction data versus yaw misalignment data obtained during yawing. Figure 4 shows the time series after applying the correction to the yaw misalignment data. The correction factor F α = 1.023 is close to 1, and then the angular measurement data can be corrected proportionally, while otherwise the correction would have to take the non-linear conversion algorithm into account: Here α is the calibrated inow angle to the rotor shaft and α d the measured inow angle with the default constants k 1,d = k 2,d = 1. The tilt angle of the wind turbine was for this calibration case neglected and the yaw misalignment was equalled the inow angle to the rotor shaft.    The yaw misalignment measured with the spinner anemometer were compared to yaw misalignment measurements with the mast wind vane and yaw direction sensor, see gure 5. Except for a large 42 • oset error of the yaw direction sensor seen in the gure, the slope shows good agreement between the two measurement methods. Calibration for wind speed measurements was made by relating spinner anemometer wind speed to a mast cup wind speed. Calibration could be made in stopped condition but this would imply high production losses. The measurements were instead made during operation. However, the mast distance was only 1.5D instead of the minimum required 2D, so the far eld wind speed might be considered about 2% too low due to induction of the rotor.
The correction factor F 1 = 0.743 was determined to correct the spinner anemometer constants to measurement of the free wind speed in stopped condition, Due to the fact that the angular correction factor F α was very close to 1, the measured wind speed by the spinner anemometer U can with a good approximation be linearly related with the default measured wind speed U d : Spinner and mast wind speed measurements during operation are shown in gure 6. The correction factor F 1 = 0.743 was determined by tting data to very low and very high wind speeds, where the induced wind speed due to the operating rotor is insignicant. Figure 7 shows the data after application of the wind speed calibration correction factor according to equation 2.    The non-linearity of the curve in gure 7 is due to the rotor induced wind speed in the centre of the rotor during operation. The induction factor a = (U cup − U )/U cup , extracted from gure 7, is shown in gure 8. The induction factor data were tted to an appropriate induction factor function with four parameters: The induction factor function with the parameters A = 5.6, B = 0.25, C = 3 and D = 1.8 is shown in blue in gure 8. Spinner anemometer wind speed data, corrected with the induction factor function, see gure 9, shows that corrected spinner anemometer wind speed comply well with free mast cup wind speed.
The standard deviation of the measured wind speeds with the spinner anemometer and the mast cup anemometer are plotted in gure 10 (without corrections for induction). The gure shows good compliance between the spinner anemometer and mast measurements. However, the turbulence intensity measured by the spinner anemometer, see gure 11, is overestimated compared to the mast measurements. If we, meanwhile, correct the measured average wind speeds by the spinner anemometer to the far eld average wind speed with the induction factor function, then the turbulence intensity measurements comply quite well with the mast cup measurements, see gure 12. This will be further commented in the discussion chapter. For all turbulence intensity measurements by the spinner anemometer, which are presented in the following, the average wind speed is corrected in this way to the far eld while the standard deviation is not.

Inow measurements from all wind directions
Inow measurements from all wind directions are shown in gures 13 to 15. The yaw misalignment measurements, gure 13, show a rather scattered pattern, averaged at about 10 • . Some scattered points go to negative yaw misalignments, and in the sector 300 • − 330 • a smaller cloud of data are centred around −10 • . The ow inclination angle in gure 14 shows inow angles scattered around 0 • , which should be expected for at terrain, but with signicant up and down  the data is increased, but additionally some ow inclination angles at about −8 • is seen at 10-14 m/s wind speed. The turbulence intensity in the wake-free sector, gure 20, is seen to be below 8% in the wind speed range 6-18 m/s and is increased at lower wind speeds. The minimum turbulence intensities are close to 2%. For all wind directions the turbulence intensity, gure 21, is increased and for high wind speeds is averaged about 15%. Below 10 m/s the turbulence gradually increases up to 30%.

Discussion
The calibration of the spinner anemometer was made in a wake-free sector with low turbulence, and the calibration was shown to result in measurements that correspond quite well with the mast measurements. This was the case for angular measurements, gure 5, as well as for wind speed, gure 9, and turbulence measurements, gure 12. The preconditions for this qualitatively good result should be found in the low ow distortion on the sonic sensors in front of the rotor and in the fact that the turbulence intensity is only disturbed by the overall induction due to the rotor. In dening the wind speed measured by the spinner anemometer as the free wind speed in stopped condition the induction becomes a clean correction that only depend on rotor parameters such as rotational speed, pitch angle and rotor thrust. Local distortion eects that nacelle based instruments are very dependent on can be neglected even though the spinner anemometer sonic sensors are inuenced by the blade root vicinity. As long as the spinner anemometer conguration applies to the spinner anemometer conversion algorithm the calibration should lead to adequate calibration results. Measurement of free wind speed requires the induction function to be applied, and this can be made with a simple function with four constants. Applying the induction function, turbulence measurements can also be made with good accuracy. The standard deviation measured by the mast and the spinner anemometer, gure 10, seems to correlate quite well. However, the average wind speed has to be adjusted to the free wind. The reason for this must be that the smaller vortices that dominates the standard deviation, measured by the spinner anemometer, are not aected by the rotor induced wind speed, while the average speed of the overall ow is reduced due to the induction. The question is whether this will always be the case independent of the structure of the turbulence. The measurements of rotor centre inow shown in gures 13 to 21 show features that need to be commented. The clear up and down slope of ow inclination angles in the sector 180 • to 215 • in gure 14 is very distinct. This wind sector is the wake sector of the nearest wind turbine no. 6 3.2 rotor diameters away. The ow inclination pattern is well explained by the swirl of the wake of the upfront wind turbine. The direction of rotation of its rotor is CW (seen from the front). This causes a wake swirl in the opposite CCW direction, and this gives the peak tip ow inclination angles of −13 • and 15 • , based on 10 min averages. Minor wake swirls are seen behind the other wind turbines. The wake swirl based on 30 sec averages is shown in gure 22. The shorter time average data show a more robust cluster of data for the wake swirl where the slope on the up-going inclination angles seem to be quite much the opposite of the down-going angles.
The yaw misalignment, gure 13, shows a smaller amount of data at about −10 • in the sector 300 • to 330 • . This sector is a wake-free sector but with high turbulence due to the nearby village Tjaereborg about 1 km away. Figure 17 reveals that the −10 • yaw misalignment actually occurs at quite high wind speeds, 10-14 m/s. The gure also shows that a symmetric yaw misalignment pattern exists for a smaller amount of data. The cause of this might be due to the control system making alternating use of the two 2D sonics that are symmetrically mounted on either side of the nacelle of the wind turbine. The log on the wind turbine might conrm this assumption as irregularities on the yaw control were identied during the measurement campaign.
The yaw misalignment of −10 • in the sector 300 • to 330 • is observed to occur at the same time as a −10 • ow inclination angle at 10-14 m/s, see gures 17, 19 and 14. A closer look at the wind inow from the 300 • to 330 • sector with 30 sec averaging data, see gure 23, shows that the yaw misalignment and ow inclination angle are not correlated, but are divided into two distinct scattered groups. It is surprising to see the high scatter in ow inclination angles, especially the very low downwards values. The explanation to these very low values may be due to the high terrain roughness from the village very close to the wind turbine. The drag of the village reduces the wind speeds at lower levels which might give room for air with higher wind speeds from above to enter lower levels.
Evidence of faulty measurements of the spinner anemometer have been considered but there have not been found reasons for rejecting unexpected inow angular measurements. Measurements of inow angles in the centre of a wind turbine rotor in wind farm environment was never measured before, so hopefully physical explanations for the explored phenomena will be found by other means to support the measurements.

Conclusions
Application of a spinner anemometer for inow measurements to a wind turbine rotor in wind farm environment was demonstrated. Calibration for angular measurements was made by yawing the wind turbine in and out of the wind in stopped condition, and calibration for wind speed measurements was made during operation by referencing a met mast in a free wind sector. Apart from calibration of the basic k 1,d and k 2 constants an induction function with four constants was determined. The measurements of yaw misalignment showed good compliance with mast related wind measurements. This also conrms the ow inclination angle measurements which are equivalent to the yaw misalignment measurements. Standard deviation of measured wind speed showed good compliance with mast measurements. Turbulence measurements were overestimated by the spinner anemometer. However, correction of the measured wind speed at the spinner with the use of the induction factor correction function gave good compliance with mast turbulence measurements. This indicates that the smaller vortices in the air are not inuenced by the overall reduced wind speed due to induction.
Yaw misalignment measurements showed an average yaw misalignment of about 10 • and with a high scatter. A symmetric yaw misalignment pattern was found with yaw misalignments at about −10 • . The cause of this might be due to the control system using the two symmetrically mounted sonic sensors on the nacelle in an alternating way. Flow inclination angle measurements were scattered around 0 • , which should be expected for at terrain, but with signicant up and down ow in wakes of other wind turbines due to wake swirl. The largest wake swirl showed an upow of about 15 • and a downow of about −13 • in the wake of the nearest wind turbine at 3.2D distance. Some ow inclination angles of −10 • were seen in other sectors at high wind speeds, especially with ow from the close high terrain roughness village Tjaereborg. The turbulence measurements showed signicant changes behind the wakes of the dierent wind turbines in the wind farm. Maximum turbulence of 0.25 was seen behind the nearest wind turbine at distance 3.2D, being reduced to 0.22 for a turbine at 4.3D and to 0.20 for turbines at 5.4-7.0D.