Nacelle power curve measurement with spinner anemometer and uncertainty evaluation

. The objective of this investigation was to verify the feasibility of using the spinner anemometer calibration and nacelle transfer function determined on one reference turbine, to assess the power performance of a second identical turbine. An experiment was set up with a met-mast in a position suitable to measure the power curve of the two wind turbines, both equipped with a spinner anemometer. An IEC 61400-12-1 compliant power curve was then measured for both turbines using the met-mast. The NTF (Nacelle Transfer Function) was measured on the reference turbine and then applied to both turbines 5 to calculate the free wind speed. For each of the two wind turbines, the power curve (PC) was measured with the met-mast and the nacelle power curve (NPC) with the spinner anemometer. Four power curves (two PC and two NPC) were compared in terms of AEP (Annual Energy Production) for a Rayleigh wind speed probability distribution. For each turbine, the NPC agreed with the corresponding PC within 0.10% of AEP for the reference turbine and within 0,38% for the second turbine, for a mean wind speed of 8 m/s. 10


Introduction
Measuring the performance of a wind turbine means establishing the relation between wind speed (input) and electric power (output). While the measurement of the electric power is straight forward (because it is already in electrical form), the challenge 15 is to measure the wind speed. The IEC61400-12-1 standard describes the instrumentation requirements and the calculation procedures to determine the power curve with the method of bins, measuring the wind at hub height upstream of the wind turbine with a cup anemometer installed on a meteorological mast. A met-mast is costly, therefore the IEC61400-12-2 standard was developed to define requirements and procedures to measure the wind speed on the wind turbine. While the use of the nacelle anemometer (mounted on the nacelle roof) for performance measurements is a well established procedure, the spinner 20 anemometer is a less experienced option to measure the wind turbine performance. A spinner anemometer (Pedersen (2007)) consist of three one dimensional sonic wind speed sensors mounted on the spinner of the wind turbine. The advantage of a spinner anemometer over a nacelle anemometer is that it is measuring in front of the rotor rather than behind, where the flow is influenced by the wake of the blades and other elements present on the nacelle as described by Frandsen et al. (2009).
The spinner anemometer must be traceable calibrated using a met-mast in order to measure the wind speed accurately and to obtain an absolute power curve, according to the standard IEC61400-12-2 (2013) and as reported by Demurtas (2014).
Installation of a met-mast for each wind turbine is obviously not viable. Therefore the possibility of using the calibration found on a first -reference-turbine with a spinner anemometer to another one of same type was investigated in this work.
The objectives of the investigation were to: 5 -Install a met-mast to measure the power curve (PC) on two wind turbines next to each other.
-Install spinner anemometer on both wind turbines.
-Calibrate the spinner anemometer on the reference wind turbine.
-Measure the nacelle transfer function (NTF) on the reference wind turbine.
-Compute the NPC and PC for the reference turbine 10 -Apply the calibration values and NTF measured on the reference turbine to the second turbine.
-Compute the NPC and PC for the second turbine -Compare the NPC with PC for both turbines.

Site description
The measurements were taken at the Nørrekaer Enge wind farm, located in the north of Denmark. This wind farm consist of a row of 13 Siemens 2.3 MW wind turbines (Fig. 1) in a very flat site, 80 m hub height and 93 m in rotor diameter. Every wind turbine was equipped with a spinner anemometer, but only the data from turbine T4 and T5 were used in this work. For this experiment, an IEC61400-12-1 (2005) compliant met-mast was erected near turbine T4 and T5 (Fig. 2).

k α calibration
The calibration for inflow angle measurements was made with the wind speed response method (WSR) described in Demurtas and Janssen (2016). The turbine was yawed several times of plus minus 60 • in good wind conditions. The resulting calibration value k α = 1.442 was used to correct the measurements with the procedure described in Pedersen et al. (2015). The uncertainty on the k α value could be calculated by repeating the test several times (as was done in Demurtas and Janssen (2016), which 5 found a repeatability of the result within 8.5% of the mean value, for a different wind turbine model). In this case the calibration test was performed only once, and the uncertainty was estimated to u kα = 10% • k α .

k 1 calibration
The objective of this calibration is to find the value of the k 1 calibration constant that makes U hor to match the free wind speed U mm when the turbine is stopped and is facing the wind. During operation of the wind turbine the rotor induction is accounted for with the nacelle transfer function (NTF) as described in the IEC61400-12-2 standard. To acquire the measurements needed for the calibration the wind turbine should be stopped, so that the wind seen by the spinner anemometer is not influenced by 5 the induction. However, stopping the wind turbine would cause an energy loss, therefore the calibration was performed with the wind turbine in operation at high wind speed as proposed by .
The k 1 calibration procedure was based on measurements acquired during operation of the wind turbine where k 1 was set to the default value k 1,d = 1 in the spinner anemometer conversion box. The correction factor F 1 was calculated as the ratio where U hor,d,c is the horizontal wind speed measured with default k 1,d and calibrated k α .
Since T4 is pitch regulated, F 1 should tend to an asymptote as the wind speed increase (Fig. 4) because the induction decreases for high wind speed. The value of F 1 = 0.6019 was calculated as the average of the values for free wind speed greater than 15 m/s. Since the default value was k 1,d = 1, the calibration value is: 15 k 1 is not subject to uncertainty because it is compensated with the uncertainty estimation of the NTF. This is further explained in section 9.

Measurement database, data filtering and corrections
The measurement data-base consists of 237 hours of measurements acquired in a free wind direction sector between 101 • and 229 • as measured by the wind vane on the met-mast. The spinner anemometer measurements from both turbine 4 and 5 were calibrated with the k α and k 1 values found for T4. Ten minute data sets where the minimum wind turbine rotor rotational speed was lower than 40 rpm were filtered out in order to keep data where the turbine is continuously in operation. Data sets where 5 the ten minute mean power coefficient (measured with the met-mast) were higher than 16/27 (the Betz limit) were filtered out to remove four outliers (this is a deviation to the requirements of the IEC61400-12-1 (2005) standard). There was no need to filter for freezing temperature, since the temperature was between 6 and 14 • C.
The sonic sensors wind tunnel calibration values were not set in the spinner anemometer conversion box as required in Demurtas (2014). However a correction was made on the measurements to take into account the results of the wind tunnel 10 calibration. From the calibration certificates the sensors on turbine 5 has smaller slope coefficient (m 5 ) and smaller offset (q 5 ) than those on T4 (m 4 and q 4 ), which means that the sensors on T5 are reading a bit higher wind speed than sensors on T4.
Measurements of T5 were reduced with the ratio of the mean slope and the difference in mean offset.
(3) Figure 5 shows the ten minute mean values of power and calibrated wind speed. The wind speed was normalized with a value 15 between 10 and 14 m/s for confidentiality reasons.
The traceability of the measurements of the spinner anemometer on T4 was ensured by the calibrated met-mast instruments and the NTF, while the traceability of the spinner anemometer on T5 was ensured by the NTF and wind tunnel calibration of the sonic sensors.
Measured air density was between 1.2 and 1.27 kg/m 3 .

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Wind Energ. Sci. Discuss., doi:10.5194/wes-2016-29, 2016 Manuscript under review for journal Wind Energ. Sci. Published: 2 September 2016 c Author(s) 2016. CC-BY 3.0 License. Figure 5. Scatter plot of power as a function of spinner anemometer normalized wind speed (n.w.s.) and met-mast normalized wind speed measurements, for turbines T4 and T5, before application of the NTF and before air density correction. Met-mast measurements to the left, and spinner anemometer measurements to the right. Turbine T4 measurements upper and turbine T5 measurements lower. Data refers to the same measurement period.

Nacelle transfer function measurement
The purpose of the NTF is to correct the spinner anemometer measurements to be representative of the free wind speed.
U mm is the free wind speed measured by the met-mast, and U f ree is the free wind speed calculated by correcting the spinner anemometer measurements (U hor ) with the NTF.
The IEC61400-12-2 (2013) standard defines the NTF as the met-mast wind speed binned as a function of the nacelle wind 5 speed. Krishna et al. (2014) investigated the root cause for high deviations in the self consistency check with the IEC61400-12-2 (2013) method and proposed an improved method, which consist of binning the spinner anemometer wind speed as a function of the met-mast wind speed. This procedure is used here. If a wind speed bin has less than 3 measurements, the value of the NTF is calculated by linear interpolation from the adjacent bins if they both have at least 3 measurements each. No air density correction was made for the measurement of the NTF. The measured NTF for the spinner anemometer installed on turbine T4 is shown in Fig. 6 .
As expected the NTF is approximately 1:1 at high wind speed (around 11-15 m/s, thanks to the k 1 calibration), and is lower than 1:1 for the range of wind speeds where the turbine is operating with high Cp (high induction, which makes the wind speed 5 by the spinner anemometer lower than the free wind speed).

NTF self consistency check
The black line in Fig. 7 shows the power difference between the PC and the NPC of turbine 4. The blue and red curves shows the pass/fail boundaries defined in IEC61400-12-2 (2013) for the NTF. Both power curves were interpolated to the center of the bin with a cubic spline 1 , so that the power values for the two power curves correspond to the same wind speed. Krishna is identical to the PC (and therefore the self consistency check should return zero power difference for any wind speed bin).
However in the present calculations the power difference was not zero. The PC was binned according to the met-mast wind speed (U mm ), and the NPC was binned according to the corrected nacelle wind speed (U f ree ). Krishna et al. (2014) suggested to bin both PC and NPC according to U mm to keep uniformity in the binning process, but doing so would mean binning the  As mentioned, Krishna et al. (2014) suggest to bin the NTF corrected nacelle wind speed according to the met-mast wind speed U mm to check the validity of the NTF. In the normal use of the NTF the met-mast is not available, and the power curve would be binned according to U f ree . The procedure to calculate a NPC shall be the same on the reference turbine (where the NTF was measured and verified with the self consistency check) and on other turbines. Therefore it makes make more sense always to calculate the bin averaged power curve binning according to U f ree . In the procedure used in the present analysis, the 5 bin average of the NTF corrected nacelle wind speed U f ree are different from the bin average of the measured free wind speed U mm (binning both according to U mm ). The cause is explained as follows.
The bin averages are computed by binning according to the same U mm , therefore the binning itself should not make a difference. The spinner anemometer measurements that fall outside the range of definition of the NTF are lost during the application of the NTF. Therefore the bin average of those utmost bins will most likely be different from the original bin 10 average value. One more reason for the bin average values to be different is that the correction applied with the NTF is applied the NTF is applied to the time series, the slopes of the linear interpolation segments are different on the two sides of the NTF definition point in a certain bin i. In fact in Fig. 9 top-right the red line is not a horizontal straight line.

Application of the nacelle transfer function
The NTF measured on turbine 4 was applied on spinner anemometer measurements of turbine 4 and then on turbine 5. Linear interpolation was used between the points that defines the NTF as described in the IEC61400-12-2 (2013) standard. The mea-5 surements that fall outside the range of the definition of the NTF are lost, since the NTF is undefined for these measurements.
With the application of the NTF, part of the measurements were lost because the NTF was not defined above a certain wind speed (in Fig. 6 the red line does not extend as much as the black points, therefore about 2.5 hours of measurements are lost out of 237 hours).
The relation between free wind speed measured from the met-mast U mm and free wind speed calculated from spinner 10 anemometer measurements U f ree is shown in the scatter plot of Fig. 8 for turbines 4 and 5.
Since the spinner anemometer was calibrated following the method described in section 3, the spinner anemometer wind speed measurements are already matching the met-mast wind speed at high wind speeds (U > 1.2 times rated wind speed), that is when the rotor induction is low. From Fig. 9 we can see that the correction applied by the NTF is mostly localized below rated wind speed.

Power curves and AEP
The calculated free wind speed and measured free wind speed were corrected to standard air density of 1.225 kg/m 3 with Eq.
5 after the application of the NTF. This is in accordance with IEC61400-12-2 (2013) for a pitch regulated turbine.
The met-mast power curve was also corrected to standard air density of 1.225 kg/m 3 with Eq. 6 in accordance with IEC61400-   A measure of the difference between the curves was evaluated by calculating the annual energy production (AEP) for a Rayleigh wind speed distribution with annual average wind speed between 4 m/s and 11 m/s. Table 2 shows the difference in AEP estimated for the four power curves. The AEP was calculated for the extrapolated power curve up to 25 m/s. The nacelle power curve compared with the met-mast power curve within 0.10 % of AEP (at 8 m/s average wind speed) on the reference turbine, and within 0.38 % on the other turbine (see Tab. 2). The NPC is not identical to the PC, as well as the 5 binned values of U f ree are not equal to the binned values of U mm even when binning both according to U mm .
As expected, PC4 with NPC4 compares better than PC5 with NPC5, since the NTF was measured on T4. The uncertainty on AEP calculated for PC4 in the DTU report I-0440 Demurtas (2015) (with the same turbine and same measurement set-up, but not public for confidentiality of the data presented) was found to be 14.2% for V avg = 4 m/s, 5.7% for V avg = 8 m/s and 4.2% for V avg = 11 m/s. The AEP difference is more than ten times smaller than the AEP uncertainty.  give the uncertainty of the horizontal wind speed.
The uncertainty of spinner anemometer on T4 due to differences in mounting of the three sonic sensors is zero, since this spinner anemometer was used to measure the NTF. The mounting of the second spinner anemometer (on T5) was compared with the mounting of the reference spinner anemometer (on T4) and an additional uncertainty due to mounting differences with respect to T4 was added to the measurements of the spinner anemometer on T5.

Uncertainty related to wind tunnel calibration of sonic sensors
The relation between the wind tunnel speed and the velocity component in the sensor path is: If the angle φ s of the sonic sensor path with respect to the horizontal mounting plate was not measured, one should assume that φ s is within the manufacturing tolerance, φ s = 35 • ± 1.5 • . The standard uncertainty on φ s can therefore be expressed by 15 the tolerance divided by the square root of three as: In this case the angle φ s was measured as part of the wind tunnel calibration (see Tab. 1). The uncertainty on φ s depends on the accuracy of the protractor (the instrument to measure angles). In this case, a digital protractor with an accuracy of 0.2 • was used, and therefore u φs = 0.2 • was used instead of 0.866 • .
The uncertainty on the wind tunnel calibration was expressed in the calibration certificates for a coverage factor k c = 2 as a binned value as a function of wind tunnel speed. While the uncertainty is typically almost constant for a cup anemometer, the 5 sonic sensor uncertainty showed increase with wind speed. The standard uncertainty (k c = 1) was calculated by dividing the value reported in the certificates by two. The calibration standard uncertainty (function of wind speed) was fitted to a line as shown in Eq. 9.
The uncertainty on the sonic sensor velocity V 1 is obtained combining the uncertainty u t with the uncertainty u φs , using 10 the equation for combination of uncertainty of independent variables as expressed in Eq. 10 (according to section 5.1.2 of the GUM, JCGM/WG1 (2008)) and also shown in IECRE (2015) clarification sheet.
Equation 10 applied to Eq. 7 results in Eq. 11: With u t (Eq. 9) as the uncertainty of the wind tunnel wind speed and u φs as the uncertainty on the sensor path angle (Eq. 8 or uncertainty of the protractor). The combined uncertainty on V 1 due to wind tunnel calibration is: The same applies to each of the sensors (u 2 , u 3 ).

Evaluation of spinner anemometer mounting 20
The three sonic sensors should be mounted on the spinner with the best possible rotational symmetry and equal distance from the spinner center of rotation. A visualization method for documentation of the sonic sensors installations was developed by Demurtas and Pedersen with the use of photography, Demurtas (2015). The initial mounting of the sensors was used for the first power curve measurements reported in Demurtas (2015). The accuracy of sensor mounting was then improved and the power curve measurement repeated and reported in this work. The mounting position was evaluated with photography method 25 described in . Due to the challenge of photographing a feature of size in the order of centimeters (the sonic sensor) from a long distance (80 meters from ground to spinner) we used a 400 mm optic zoom and a high resolution digital camera (24 megapixel).
Several photos of the spinner were taken from the ground during rotation of the wind turbine and three photos selected each time a sonic sensor is visible on the side of the spinner, with the sky in the background.
Each of the six photos (three for each turbine, Fig. 11) was post processed making it semi-transparent. The photos were overlayed, scaled and rotated in order to make the spinner contour to match. The sky was made transparent and a contrasting red background added (Fig. 12).

5
The photo overlay was scaled to make the sonic sensor path 16.7 cm long, like it is in reality. The positions of the sonic sensors on the spinner were measured in the plane of the photos as the angle between a plane perpendicular to the spinner axis and the sensors of extreme forward and backwards positions. The position of the sensor paths were measured on the photo with a vector graphic software (inkscape).
The improved mounting of the sensors showed a mounting accuracy in the order of ±2 cm. This was an improvement of 10 the initial mounting whose accuracy was ±6 cm.

Uncertainty in wind speed measurements due to mounting imperfections
The uncertainty connected to the error in mounting position of the sonic sensor was investigated approximating the spinner as a sphere and using potential flow theory to calculate the flow around a sphere. The mean air velocity along the sensor path was calculated averaging the wind velocity component along the sensor path in three points along the path (points shown with a black or red dots in Fig. 13).

5
The flow field was calculated for a mesh of 0.01 in x and y direction. The coordinates of each point were converted from cartesian coordinates (x p , y p ) to polar coordinates (r, θ) with Eq. 13 and Eq. 14. An angle of π/2 was added to the θ p coordinate (Eq. 14) to rotate the result in order to have the flow coming from the left parallel to the x axis. This also rotated the origin of the angles to the vertical axis, which is convenient to measure the position of the mounting angles of the sonic sensors.
θ p = arctan (y p /x p ) + π/2 (14)  The potential flow model is oriented such that the inflow is in axis with the pinner axis of rotation, therefore U = U hor = U 0 .
The flow field was calculated in polar coordinates with Eq. 15 (along radius) and Eq. 16 (perpendicular to radius) with the equations by Faith and Morrison (2013).
The modulus of the wind speed was calculated with Eq. 17 and shown with the color scale in Fig. 13.
The air velocity along the sensor path at the point p(r, θ) was calculated with Eq. 18, where 35 • is the default angle between the sensor path and the sensor root (tangent to the spinner surface). Equation 18 was used to calculate the wind velocity along the sensor path in each of the black points shown in Fig. 13. Then, the mean wind speed along each sensor path was calculated as average value of the velocity along the sensor path in the three points related to each sensor path (Eq. 19).
The sensor path wind speed was calculated for each of the four sensor mounting positions measured with the photographic 5 method of Fig. 12, and is presented in Tab. 3. The sensor path wind speed was normalized to the wind speed upstream of the spinner (U 0 ). The uncertainty due to mounting imperfections is a type B uncertainty ("Guide to the expression of uncertainty in measurements" (JCGM/WG1 (2008), chapters 4.3.1 and 4.3.7). The probability of the sonic sensor wind velocity to be within the interval a − to a + calculated from the positions identified with the photographic method is equal to one and the probability that it lies outside the interval is zero. There is no particular reason for the sensor path wind velocity to fall into the interval in 10 a particular position. Therefore we can assume that the probability that the sensor path wind speed is within the interval is a rectangular distribution. This means that the standard uncertainty is: The uncertainty is a value relative to the wind speed upstream of the spinner anemometer (U hor ). This uncertainty does not apply to the wind turbine 4 which was used to measure the NTF. 15

Combination of uncertainties through the spinner anemometer conversion algorithm
This section will explain how to combine the uncertainty on the input quantities to obtain the uncertainty on the output of the spinner anemometer: the horizontal wind speed. The uncertainty on U hor is the combination of the following uncertainty components: 20 u 1 Sensor 1 wind tunnel calibration (which includes u t and u φs ).
u 2 Sensor 2 wind tunnel calibration (which includes u t and u φs ).
u 3 Sensor 3 wind tunnel calibration (which includes u t and u φs ).
u m Sensors mounting. u kα Angular calibration.
The uncertainty on k 1 is u k1 = 0 because all the uncertainty related to wind speed is included in the uncertainty of the NTF (u N T F , see section 9.7). The uncertainties on the sonic sensor speeds (u 1 , u 2 and u 3 ) are substantially equal but we keep them separated with different names for clarity. U is not measured directly, but is determined from the quantities V ave and α through a functional relationship g: α is also not measured directly but is determined from the quantities V 1 , V 2 , V 3 and k α through a functional relationship f : V ave is the average between V 1 , V 2 , V 3 calculated with the relationship h: To calculate the uncertainty on U we need first to calculate the uncertainty on V ave and on α.
The uncertainty on V ave is calculated applying the rule for combination of uncertainties of uncorrelated input quantities (Eq. 10) to the function h (Eq. 23), resulting in Eq. 24 assuming that u 1 = u 2 = u 3 .
The uncertainty on the inflow angle α can be calculated combining the uncertainty of V 1 , V 2 , V 3 , and k α applying Eq. 10 to 15 the function f (Eq. 22), resulting in Eq. 25.
Given the complexity of the function f (Eq. 22) the derivative was computed numerically with the help of a computer.
V 1 , V 2 , V 3 were calculated for a wind speed U in a range 0-25 m/s with Eq. 27 to 29, for six arbitrary values of α, and used to compute the partial derivatives of Eq. 25. The uncertainty on k a was set to u kα = 0.1 • k α as found by Pedersen et al. (2015).
The uncertainty on U calculated for six arbitrary values of α with Eq. 26. V ave was calculated with Eq. 23 and V 1 , V 2 and V 3 with Eq. 27, 28 and 29. The results are shown in Fig. 15. As seen in Fig. 15, the uncertainty on U is function of the flow angle α. For inflow angles below 5 • Fig. 15 shows that the u U is basically only function of U . A typical average inflow angle to a wind turbine is smaller than 5 • , as presented in Pedersen et al. (2014). The uncertainty of the wind speed is typically function of the wind speed only. In order to keep the calculation simple (especially in the calculatio of power curve uncertainty), a simple model (Eq. 30, red crosses in Fig. 15) was fitted to the line corresponding to an inflow angle of 6 • , which is unlikely to be exceeded on average during normal operation of most 5 wind turbines in a range of wind speeds 4 to 20 m/s.
Now that the uncertainty on the wind speed modulus U is known, it is possible to calculate the uncertainty on its horizontal component U hor . By combining the equations of the conversion algorithm (which can be found in ), U hor is expressed as: The position of the flow stagnation point θ in Eq. 31 is a function of V 1 , V 2 , V 3 . The rotor position φ is calculated based on the accelerometers located in each sonic sensor root. To be absolutely correct, one should apply the method for combination of uncertainty to Eq. 31. However, it is reasonable to assume that U hor ∼ U due to the small inflow angle α and that u U hor ∼ u U because the uncertainty on the turbine tilt angle δ and rotor position φ is likely to be smaller than the other uncertainty components. Moreover, the improved accuracy in the estimation of u U hor would be wiped out by the simplification made with Eq. 30. Therefore, the uncertainty on the horizontal wind speed U hor is reasonably equal to the uncertainty on U :

Uncertainty of spinner anemometer output
The uncertainty of the spinner anemometer wind speed measurements of turbine 4 (Eq. 33) is the combination of the uncertainty 5 on the spinner anemometer output (u U hor ) with the uncertainty due to the discrepancies between different MEASNET wind The uncertainty on the measurements of the second spinner anemometer (on T5) shall also include the uncertainty due to mounting imperfections to account for the dissimilarity with the reference spinner anemometer (on T4): Figure 16 shows the combination of each uncertainty term to the final uncertainty budgets. As it can be seen in Fig. 16, the uncertainty of the sensor path speed (pink crosses) is very close to the wind tunnel speed (black line), due to the small contribution to the uncertainty coming from the uncertainty of the sensor path angle φ s . what matters is that the mounting position of the sonic sensors and the shape of the other spinner anemometers (on T5 in this case) are similar to the reference one (on T4 in this case). All the sonic sensors were calibrated in the same wind tunnel. The MEASNET uncertainty was added to u U instead of to u 1 , u 2 and u 3 to avoid counting it three times.

10
The uncertainty of the met-mast wind speed measurement (Eq. 35, Fig. 17) is (according to IEC61400-12-2 (2013)) the combination of the wind tunnel uncertainty u t , the MEASNET uncertainty to account the discrepancies between different wind tunnels u M E , the uncertainty due to the cup anemometer class u a.class (that takes into account the response of the cup anemometer to turbulence and flow inclination), and u s.cal. = 2%V i because there was no site calibration.

Uncertainty of NTF
The uncertainty on the NTF (u N T F ) is the combination of the various uncertainty components as: where u mm is the uncertainty on the measured free wind speed. 5 u sa is the uncertainty of the spinner anemometer measurements.
u M is the uncertainty due to the NTF method, considered 2% of the wind speed due to seasonal variations (u M = 0.02V i ) in the standard IEC61400-12-2.
s N T F is the statistical uncertainty of the captured data-set (

Uncertainty on calculated free wind speed
To measure the absolute power curve of a wind turbine the spinner anemometer output must be corrected to free wind speed by use of the nacelle transfer function (NTF). The uncertainty on the free wind speed is therefore a combination of u s.a. with For the case of the reference wind turbine (T4, used to measure the NTF) the uncertainty is calculated differently. u N T F already contains the uncertainty of the reference spinner anemometer (T4) and the uncertainty of the met-mast measurements.
Therefore the uncertainty of the free wind speed calculated with the NTF is just the uncertainty of the NTF (Eq. 38).
The mounting accuracy was investigated by overlaying six photos of the spinner taken from ground level during rotation, each showing the corresponding sensor when it is at the side of the spinner. The photos unveil deviations in the order of ±2 cm between some of the sensors. It was expected that the mounting imperfections played a major role in the total uncertainty of the second spinner anemometer. However, the contribution of other uncertainty sources combined (the 1/ √ 3% MEASNET 5 traceability of wind tunnel calibrations for cup-anemometer on the met-mast and spinner anemometers sensors, the 2% for lack of site calibration) was much larger than the uncertainty due to the mounting of the sensors (which was 1.2%). Figure 18. Uncertainty on wind speed. The met-mast wind speed includes 2% additional uncertainty due to lack of site calibration.
As shown in Fig. 18, the uncertainty of the NTF is larger than the met-mast uncertainty, as expected. The met-mast uncertainty is larger than the spinner anemometer uncertainties (dashed lines) because of the 2% added due to missing site calibration, which does not apply to the spinner anemometer output (but applies to the NTF later to calculate the free wind 10 speed). The turbine T5 has a larger uncertainty than the reference turbine, as expected, due to the mounting imperfections.
Note that the distance between the two dashed lines is due to the mounting imperfections, but the impact of such imperfections is significantly reduced once the uncertainties on the spinner anemometer output are combined with the NTF uncertainty.
The main goal of this study was to measure the power performance of a wind turbine using a spinner anemometer which was calibrated with the calibration determined on a "reference" spinner anemometer on an identical wind turbine. The calibration (k α and k 1 values) determined on the reference spinner anemometer can be moved to a second spinner anemometer estimating an additional uncertainty due to the mounting differences. This is only possible if the two spinners have the same outer shape.

5
The mounting differences (and associated uncertainty) could be completely avoided if the positioning of the sonic sensors was exactly equal between the reference spinner, and another spinner. This geometric perfection could be achieved with the collaboration of the manufacturer of the spinner, by integrating the sensor mounting fittings in the mould, so that all the spinners comes out identical.
The spinner anemometer was calibrated for wind speed measurement, so that it reads the wind speed correctly in a condition 10 of zero induction (stopped rotor, or operation at high wind speed ). While this step is not essential because this correction can be included in the NTF, it is convenient to use the NTF to only correct the induction. When the spinner is calibrated for wind speed measurements, a change in the spinner anemometer configuration (for example move the sensors to another point on the spinner) can be accounted with a new k 1 , and the NTF stays unvaried.
Apply the same NTF on another turbine is reasonable only if the wind turbine control strategy and the rotor are identical to 15 the reference turbine. This requirement however could be removed if further research can demonstrate that the induction at the rotor centre (what matters for the spinner anemometer) is unvaried for changing rotor diameter or control strategy.
The uncertainty due to discrepancies between MEASNET wind tunnels (u M E = 1%/ √ 3) was combined with the uncertainty of the spinner anemometer output wind speed (u U ), while a more correct approach would have been to include u M E in the wind tunnel uncertainty u t . The first approach was used to keep the analysis of propagation of uncertainties (through the 20 spinner anemometer conversion algorithm) free from contributions of constant terms (such as u M E ), which would otherwise have masked the contribution attributable to the sole spinner anemometer conversion algorithm.
Adding the MEASNET uncertainty to the spinner anemometer output instead of to the input does not lead to a significant error in the total uncertainty, since the effect of the conversion algorithm on the uncertainties is small (as shown in Fig. 16 by the small distance between the pink crosses and the blue line, which is basically all due to the 10% uncertainty on k α ).
If the spinner anemometer of the reference turbine (T4) is replaced, the uncertainty of the new spinner anemometer should be added to the NTF uncertainty (u f ree4 = u 2 N EW sa4 + u 2 N T F ). If the data set used to calculate NPC on T4 is different to the one used to measure the NTF, the type A uncertainty of the new data set shall be added to the NTF uncertainty (u f ree4 = u 2 N T F + s 2 N EW sa4 ). Each sonic sensor (three for each spinner anemometer) should be calibrated in the wind tunnel and the results of the cali-30 bration set in the spinner anemometer conversion box (the procedure is explained in Demurtas (2014)). If a sensor fails and is replaced, the new wind tunnel calibration values should be set in the conversion box. If the sensors are not calibrated, a new (more difficult) calibration of k 1 should be made every time a sonic sensor is replaced.
The reference spinner anemometer should be calibrated in flat terrain. The calibration of the spinner anemometer for wind speed measurements and the measurement of the NTF can, in practice, be done with any free wind speed measurement device (met-mast, nacelle lidar or ground based lidar). In complex terrain, a spinner anemometer should be assigned the calibration and NTF measured on a identical wind turbine in a flat terrain. The free wind speed calculated applying the NTF to the spinner anemometer measurements in complex terrain will provide a free wind equivalent to the one of a flat site, with no need for site 5 calibration.
A large flow inclination can also be expected in a wind farm environment. The spinner anemometer is well suited to measure in the wake of other turbines (turbulent flow with large flow inclination angles). However it has to be kept in mind that the spinner anemometer is a point measurement, compared to the rotor swept area. If the rotor is partially operating in the wake of another turbine there will be a reduced power output, but the spinner anemometer measurement (which is not interested by the 10 wake) would not be representative of the average wind condition over the swept area.

Conclusions
The study investigated the methods to evaluate the power performance of two wind turbines using spinner anemometers.
The power curves of two adjacent wind turbines (T4, T5) were measured by means of a common traceable calibrated metmast and spinner anemometers on each turbine. All sonic sensors were calibrated in a traceable wind tunnel. T4 was the 15 reference turbine. The reference spinner anemometer installed on T4 was calibrated with respect to angular and wind speed measurements to take into account the shape of the spinner and the mounting position of the sensors. The spinner anemometer on T5 instead, was assigned the calibration constants of the reference spinner anemometer. Similarly, the NTF (Nacelle Transfer Function) was measured on the reference turbine T4 and applied to both turbines. The four power curves of the two turbines (two met-mast power curves and two spinner anemometer power curves) were compared in terms of AEP (Annual Energy 20 Production). The nacelle power curves compared very well with the met-mast power curves for a range of annual average wind speeds. The uncertainty of the spinner anemometer wind speed measurements was analyzed in detail, taking account of the propagation of the uncertainty trough the spinner anemometer conversion algorithm. Some small approximations were made.
The sonic sensor mountings were verified with photos taken from the ground and a method for estimation of uncertainty related to mounting imperfections was proposed. The uncertainty on the free wind speed calculated with the NTF was mostly 25 due to the uncertainty of MEASNET traceability and lack of site calibration. In less significant part the uncertainty was due to the spinner anemometer sensor calibration and mounting imperfections.
In summary, under the condition that the mounting of the sonic sensors are very similar to the reference mounting, power performance measurements with use of spinner anemometer can be made within 0.38% difference in AEP for an annual average wind speed of 8 m/s.     U hor,d,c Horizontal wind speed (calibrated with correct k α but not correct k 1 ).
U mm Horizontal wind speed measured by the met-mast at hub height.
U mm,n Horizontal wind speed measured by the met-mast at hub height, corrected to standard air density.
U f ree4 Free wind speed calculated with the nacelle transfer function from spinner anemometer measurements (turbine 4).
U f ree5 Free wind speed calculated with the nacelle transfer function from spinner anemometer measurements (turbine 5).
U 0 Free stream inlet wind speed used in the potential flow analysis.
u 1 Uncertainty on V 1 .
u t Uncertainty on V t . 5 u m Uncertainty on wind speed due to mounting imperfections.
u M Uncertainty due to the NTF method (seasonal variations equal to 0.02 V i ).
u M E Uncertainty to account for the discrepancies between different MEASNET wind tunnels.
u mm Uncertainty on U mm . u sa4 Uncertainty on wind speed measurements of the spinner anemometer mounted on turbine T4. 10 u sa5 Uncertainty on wind speed measurements of the spinner anemometer mounted on turbine T5.
V 1 is the wind speed in the sensor path 1.
V 2 is the wind speed in the sensor path 2.
V 3 is the wind speed in the sensor path 3.
V ave Average wind speed of sonic sensors.

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V avg Annual average wind speed used to calculate the wind speed probability distribution.