WESWind Energy ScienceWESWind Energ. Sci.2366-7451Copernicus PublicationsGöttingen, Germany10.5194/wes-1-143-2016An innovative method to calibrate a spinner anemometer without the use of yaw position sensorDemurtasGiorgiogiod@dtu.dkCornelis JanssenNick GerardusDTU Wind Energy, Frederiksborvej 399, 4000 Roskilde, DenmarkRomo Wind A/S, Olof Palmes Alle 47, 8200 Aarhus N, DenmarkGiorgio Demurtas (giod@dtu.dk)27September20161214315212April201619April201618July20167September2016This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://wes.copernicus.org/articles/1/143/2016/wes-1-143-2016.htmlThe full text article is available as a PDF file from https://wes.copernicus.org/articles/1/143/2016/wes-1-143-2016.pdf
A spinner anemometer can be used to measure the yaw misalignment and flow
inclination experienced by a wind turbine. Previous calibration methods used
to calibrate a spinner anemometer for flow angle measurements were based on
measurements of a spinner anemometer with default settings (arbitrary values,
generally k1,d= 1 and k2,d= 1) and a reference
yaw misalignment signal measured with a yaw position sensor. The yaw position
sensor is normally present in wind turbines for control purposes; however,
such a signal is not always available for a spinner anemometer calibration.
Therefore, an additional yaw position sensor was installed prior to the
spinner anemometer calibration. An innovative method to calibrate the spinner
anemometer without a yaw positions sensor was then developed. It was noted
that a non-calibrated spinner anemometer that overestimates (underestimates)
the inflow angle will also overestimate (underestimate) the wind speed when
there is a yaw misalignment. The new method leverages the non-linearity of
the spinner anemometer algorithm to find the calibration factor Fα
by an optimization process that minimizes the dependency of the wind speed on
the yaw misalignment. The new calibration method was found to be rather
robust, with Fα values within ±2.7 % of the mean value for
four successive tests at the same rotor position.
Coordinate systems and definition of angles: rotating spinner
coordinate system xs′ , ys′ and zs′; non-rotating shaft coordinate system xs, ys
and zs; fixed nacelle coordinate system xn, yn and zn; yaw
direction θyaw; yaw misalignment γ; flow inclination
angle β; tilt angle δ; azimuth position of flow stagnation point
on spinner θ (relative to sonic sensor 1) and rotor azimuth
position ϕ (position of sonic sensor 1 relative to vertical). From
.
Introduction
The spinner anemometer measures the horizontal wind
speed Uhor, yaw misalignment γ and flow inclination β
experienced by a wind turbine by measuring the flow on the spinner by using
three 1-D sonic sensors. The three 1-D sonic sensors are mounted on the
spinner and connected to a so-called “conversion box”. Each sonic sensor
arm also contains a 1-D accelerometer, the measurements of which are used in the
conversion box to calculate the rotor position. The main purpose of the
conversion box is to execute the conversion algorithm that transforms the 1-D
sonic sensor readings, which are in a rotating coordinate reference system
(Fig. ), to the fixed nacelle coordinate reference
system as Uhor, γ and β. The conversion algorithm
takes into consideration the wind turbine tilt angle δ, which is set in
the conversion box as a constant. The shape of the spinner is accounted for
by two calibration coefficients: k1 and k2. The first coefficient
mainly relates to wind speed measurements, while the ratio of the two
coefficients kα=k2/k1 mainly relates to flow angle
measurements. The relations between the wind speed U, flow angle α
and azimuth position of the stagnation point θ producing V1,
V2 and V3 measured by the three 1-D sonic sensors are
V1=Uk1cos(α)-k2sin(α)cos(θ)=U⋅k1cos(α)-kαsin(α)cos(θ),V2=Uk1cos(α)-k2sin(α)cosθ-2π3=U⋅k1cos(α)-kαsin(α)cosθ-2π3,V3=Uk1cos(α)-k2sin(α)cosθ-4π3=U⋅k1cos(α)-kαsin(α)cosθ-4π3.
The conversion algorithm (Eqs. to )
was derived from Eqs. () to (). The values of k1 and k2 constants are generally not
know when the spinner anemometer is installed on a wind turbine for the first
time; they are therefore set to an arbitrary value, generally k1,d= 1 and
k2,d= 1. The calibration procedure will then provide the correction
factors F1 and Fα to correct the default values to calibrated
values (Eq. ). The output values relative to a spinner
anemometer which measures with default calibration settings has the
subscript “d” (Uhor,d, γd, βd).
k1=F1⋅k1,dk2=F2⋅k2,d=kα⋅k1=kα,d⋅Fα⋅k1α=arctank13V1-Vave2+V2-V323k2VaveVave=13V1+V2+V3U=Vavek1cosαV1<Vave:θ=arctanV2-V33V1-VaveV1≥Vave:θ=arctanV2-V33V1-Vave+πUx,s=Ucos(α)Uα=Usin(α)Uy,s=-Uαsin(ϕ+θ)Uz,s=-Uαcos(ϕ+θ)Ux=Ux,scos(δ)+Uz,ssin(δ)Uy=Uy,sUz=Uz,scos(δ)-Ux,ssin(δ)Uhor=Ux2+Uy2γ=arctanUyUxβ=arctanUzUhor
Existing calibration methods for flow angle measurements
Two methods based on measurements to calibrate a spinner anemometer for flow
angle measurements proposed in consist of yawing the wind
turbine by ±60∘ several times under manual control (as indicated
by the turbine yaw position sensor, with respect to the mean wind direction).
During this test, the output parameters of the spinner anemometer
(Uhor, γ, β) are recorded at a high sampling frequency
(10 Hz). The analysis of the measurements provides the correction factor Fα
that, multiplied by the default kα,d, gives the correct
kα calibration value.
The methods are based on the assumption that the wind direction is constant
during the test. Due to this requirement, recommended doing the test at wind speeds above 6 m s-1. Both methods need the yaw position to be
measured in order to calculate the reference yaw misalignment γref,
defined as the mean wind direction minus the
instantaneous yaw position during the test (see for details). In
the first method (abbreviated as GGref), Fα was calculated by
calibrating the measurements iteratively, until the linear fit of γ as
a function of γref was giving a line of slope equal to 1.
In the second method (abbreviated as TanTan), only one linear fitting was
made to tan(γ) as a function of tan(γref). In this
case, the slope coefficient of the fit was exactly Fα. The two
calibration methods were found to be sensitive to the width of the yawing
span. In fact, different Fα values were obtained, subsetting the
data set to a variable span of γref.
A new method to find the Fα value that does not require a yaw
position measurement and to use the non-linearity of the spinner anemometer
conversion algorithm is proposed.
The wind speed response method
The wind speed response method (abbreviated WSR) is based on the assumption that the wind speed
is constant during the test. The turbulence of the real wind will add some
scatter in the measurements which will reduce the repeatability of the
result. While in principle a single yawing movement is sufficient, in
practice the wind speed fluctuations need to be averaged by yawing the wind
turbine several times. The spinner anemometer is able to measure inflow
angles (yaw misalignment γ and flow inclination β) and wind
speed U. A wrong kα value will result in a wrong value of the
angle γ, which will turn into a wrong value of the horizontal wind
speed Uhor. In other words, a wrong kα makes the wind
speed measurement dependent on the yaw misalignment. This property of the
spinner anemometer model (Eqs. –) was
verified with a data set consisting of constant wind speed Uhor and
13 values of yaw misalignment going from -60 to 60∘ in steps
of 10∘. The tilt angle and the flow inclination were set to arbitrary
values (equal to zero for Fig. ). In the real world the
tilt angle of the wind turbine is typically between 3 and 6∘, while the flow inclination varies within approximately ±10∘. The
conversion algorithm takes into consideration both the tilt angle δ
and the measured flow inclination βd when calculating the yaw
misalignment γd; therefore, they have no influence on the result of
this method. V1, V2 and V3 were calculated with
Eqs. ()–() with kα= 1 and k2= 1.
Equations () to () (which are the direct
conversion algorithm presented in ) were used with new values
of kα equal to 0.5, 1 and 2, with the calculated V1, V2
and V3 to calculate Uhor,d and αd. k1 was kept
equal to 1.
When the conversion was made with kα= 1, Uhor,d
and αd matched the (correct) initial values of Uhor
and α (black line in Fig. ). On the other hand, when
the conversion was made with kα,d= 0.5, the wind speed and angle were
overestimated (blue curve in Fig. ) because
kα,d is too small compared to the correct kα value equal
to 1 in this example. Similarly, with kα,d= 2, the angles and the
wind speed were underestimated (red curve in Fig. ).
From the experience of calibration on several turbines, the default settings of
kα,d= 1 is too small. Therefore, the wind speed response looks like a
happy smile, and an Fα> 1 is required to correct the default
calibration value. Note that the wind speed is still measured correctly for a small inflow angle (where the three curves of Fig. are
close to each other).
Effect of three kα values on yaw misalignment and wind
speed measurements. Black line shows data where the kα is correct
(equal to 1 for our theoretical spinner model). Blue curve shows
kα set to 0.5. To correct the blue curve to the black curve, the
correction should be made with Fα> 1 (Fα= 2 in
this case). Red line shows kα set to twice the correct value; therefore, we need Fα< 1 to correct the measurements to the
black line.
The method to optimize Fα consists of minimizing the RMSE (root
mean square error) of a horizontal linear fit made to the measurements
of Uhor,d for varying Fα. Uhor is obtained
applying the Fα calibration to the measurements of
Uhor,d, γd and βd acquired with default values
k1,d and k2,d. For this reason Uhor is a function of
Uhor,d, γd, βd, k1,d, k2,d and Fα.
The function object of the optimization is
RMSE=fUhor,d,γd,βd,k1,d,k2,d,Fα=1n∑1nUhor‾-Uhor2,
where the first three variables come from the measurements, the fourth and fifth
are the settings of the spinner anemometer at the time of acquisition of the
measurements, and the last one (Fα) is the independent variable
used in the optimization. The function of Eq. () was optimized to
its minimum using a combination of golden section search and successive
parabolic interpolation .
Application of the method
The measurements were acquired in February 2016 on a NEG Micon 2 MW wind
turbine installed in Denmark. The wind turbine was yawed in and out of the
wind several times with the rotor stopped with one blade pointing downwards.
Figures and show the 10 Hz data
recorded during the calibration procedure. Figure a–c
show non-calibrated measurements, while Fig. a–c
show calibrated measurements. In both Figs.
and , the sub-figure (a) shows the time series of the yaw
misalignment and yaw misalignment reference (measured with a yaw position
sensor). Sub-figure (b) shows the time series of the wind speed.
Sub-figure (c) shows the wind speed response as a function of yaw misalignment.
Before calibration, test 6. (a) Time series of yaw
misalignment as measured by the spinner anemometer and by the yaw position
sensor. (b) Wind speed time series as measured by the spinner
anemometer before F1 calibration. (c) Wind speed as a function of
yaw misalignment measured by spinner anemometer.
(d) Calibration correction factor Fα calculated in three
different methods as a function of yawing span ranging from ±10 to
±90∘ in steps of ±5∘.
After calibration, test 6. (a) Time series of yaw
misalignment as measured by the spinner anemometer and by the yaw position
sensor. (b) Wind speed time series as measured by the spinner
anemometer before F1 calibration and after Fα calibration.
(c) Wind speed as a function of yaw misalignment both measured by
spinner anemometer and calibrated with Fα. (d) Root mean
square error of the horizontal fit (red line in c) as a function
of Fα.
Figure d shows the value of Fα calculated with
the three different methods (GGref and TanTan from and the
present method, WSR), for varying ranges of yawing the wind turbine out of the
wind (data were filtered according to γref in steps of
5∘ span per side). The Fα value was calculated with the WSR
method only if there were at least 30 s of measurements in the outmost
5∘ of the considered range (which justifies the fact that the scatter
plot of Fig. c appears wider than the maximum range shown
in Fig. d by the green line).
Discussion
As seen also in tests performed on other wind turbine models, the GGref and
TanTan methods tend to give a higher Fα for increasing yawing span
than the WSR method. This is especially true for the TanTan method because
of the tangent function properties, which tend to increase rapidly when
approaching a 90∘ angle.
As seen in Fig. d, the value of Fα is dependent
on the chosen width of yawing the turbine in and out of the wind. For the
TanTan and GGref methods, suggested limiting the span to
±45∘. The value of Fα calculated with the WSR method tends
to stabilize and be comparable with the previous two methods for a yawing
span within 50 and 70∘.
Above a certain large inflow angle (depending on the spinner shape) the air
flow would separate from the spinner surface with the consequence of the
downwind sensor measuring in a separated flow region. In this condition the
spinner anemometer cannot measure correctly, since the relation between the
sensor path velocities does not follow the spinner anemometer mathematical
model (Eqs. to ).
The Fα value calculated for a yawing span of ±60∘ was 1.619.
This value was used to calibrate the measurements, which are show in
Fig. a–c. In Fig. c, the red
line shows the mean wind speed for the measurements where the yawing span is
in the range ±60∘. Figure d shows how the RMSE
varies as a function of Fα, and it also shows the optimum Fα as a dot
at the minimum RMSE.
The method is based on the assumption of a constant wind speed. When applying
the method to a spinner anemometer exposed to natural wind the wind speed
will naturally vary in the time frame of about 1 h needed to complete
the six yawing cycles (Fig. a). The wind speed variations
are clearly visible in the wide scatter of Fig. c, which
are averaged when calculating the RMSE (Eq. ). The turbulence
reduces the repeatability of the result (Fα) since it introduces
some randomness into the measurements. The result can be improved by a large
number of tests or by using a stable wind source. The worst case is that the
increase (and decrease) in wind speed is synchronized with the yaw position
of the turbine, which is basically impossible when the turbine is
yawed several times.
Sensitivity analysis
The calibration test was performed several times on the exact same turbine.
The rotor was stopped with one blade pointing downwards (the so-called bunny
position), and the nacelle was yawed six times for each test: by ±90∘ (test 7 to 10) or ±60∘ (test 1 to 6) by operating it manually from
the turbine control panel. The yaw moves with a speed of about
0.5∘ s-1; therefore, one test of six sweeps takes approximately 1 h.
Tests 7 to 10 were made on the same day, one after the other, for the exact
same rotor position. The WSR method was used to calculate Fα for
each test and several yawing spans (Fig. ); this is also reported in
Table for the case of ±60∘ yawing span. Test 3 and 5
faced some data acquisition problems and were discarded.
Fα values for eight calibration tests made on the same
wind turbine. Tests 7 to 10 were made with exact same rotor position relative
to a wind turbine yawing span of ±60∘.
Regarding the ability of the method to give reproducible results, the
variation of Fα for tests 7 to 10 is within ±2.7 % of the mean
value 1.52. Since the rotor position is the same for the four tests, the only
possible factor responsible for the variations is the wind turbulence. The eight results are within ±8.5 % of the mean value 1.59. It seems that the
Fα value relative to the first four tests (about 1.67) is higher than
the last four tests (1.50), which could be due to a different rotor position, which plays a role if the rotational symmetry of the spinner and sensor
mounting positions is not accurate. The accuracy of the mounting position of
the sonic sensors on this spinner was not investigated.
Root mean square error as a function of Fα. Markers locate
the minimum value of RMSE and the corresponding Fα value. Bold coloured lines are tests performed for the exact same rotor
position.
Sensitivity of the Fα to the yawing span. Bold coloured lines are tests performed for the exact same rotor position. For test 2 the
wind turbine was yawed by ±60∘, but an initial offset of the turbine
with respect to the wind direction and a wind direction change during the
test determined measurements up to 80∘. The values in the legend show the mean wind speed during the test.
Goodness of a calibration and benchmark on 17 wind turbine models
The variations encountered in the estimation of Fα call for the
definition of a variable to judge the quality of the calibration. One
indicator could be related to the shape of the curves of Fig. .
The flatter and shallower the minimum, the larger the uncertainty on Fα.
The indicator was called the quality score (QSC, see Eq. ), calculated
as the slope to the left of the minimum point.
QSC=RMSEFα-0.1-RMSEFα0.1
Figure shows QSC as a function of the span of yawing.
What minimum quality score should a test have to give meaningful Fα?
To answer this question, the wind speed response method was
applied to a database of yawing tests consisting of 29 calibration tests made
on 17 turbine models. Results are shown in Figs. and .
The quality score (QSC) is a measure of how much the RMSE as a
function of Fα peaks at the minimum. A wide yawing span gives a clearer peak. The values in the legend show the mean wind speed during
the test.
Figure can help to identify which conditions of wind
speed and turbulence lead to a more precise estimate of Fα, which
means a more steep RMSE(Fα) curve or, in other words, a high QSC.
Average wind speed and turbulence intensity were calculated from the
measurements calibrated with Fα for a range of yaw misalignments
included in the interval -30 to 30∘. This is to ensure that
there is no flow separation from the spinner surface and therefore ensure
the spinner anemometer model validity (the spinner anemometer model is
expressed by Eqs. ()–()). Figure
shows an inverse relation between the quality score
and the turbulence intensity of the wind speed as measured by the spinner
anemometer during the yawing test. Figure shows that
the QSC increases with the wind speed Uhor.
Application of the method to a large database of wind turbines.
Colour-coded according to the mean wind speed.
Fα calculated with three methods over a large database of
wind turbines. Colour-coded according to the mean wind
speed.
The most pronounced correlation in Fig. is between QSC
and TI, where the QSC increases for decreasing turbulence intensity. This
suggests that the ideal condition to perform the test is at low turbulence.
The initial statement (in Sect. ) that the wind speed
turbulence would reduce the accuracy of the method is also confirmed by a QSC
that reduces as the TI increases. A condition of low-turbulent wind can be found by night, when the atmosphere is stable, at a site that
is flat with low roughness. It seems also that the QSC increases for
increasing Uhor; however, the scatter of QSC also increases and
there are several points with a low QSC despite the high wind speed. This
means that to achieve a high QSC, a low TI is more important than a high wind speed.
Comparison with previous methods
The Fα was calculated with the three methods GGref, TanTan, and WSR
for a range of yawing (γref), i.e. ±45,
±45 and ±60∘, respectively.
Figure shows a comparison of Fα values for 29
tests made on 17 wind turbine models. All the spinner anemometer were
initially set with the same default calibration values (k1,d= 1,
k2,d= 1); therefore, it is possible to compare the
Fα values directly. Most of the turbines present an Fα between 1 and 2, values
which are attributable to a pointed spinner shape (like a Vestas V52) or a
rounded spinner (like a NEG Micon NM80). The four tests with an Fα
between 2.5 and 3.5 belong to a flat spinner like the one of a Siemens SWT-6.0-154.
The two methods which agrees the most are the GGref and the TanTan methods.
This good agreement, however, does not imply that the Fα estimate
is accurate but rather that the two methods are similar (in fact, they are
both based on a linear fitting of the measurements, as described in the
section “Existing calibration methods for flow angle measurements”).
The value of Fα calculated with the WSR method shows a lower level
of agreement with the other two methods, being based on a completely
different principle.
Conclusions
The article presented a new method to calibrate spinner anemometer flow angle
measurements (yaw misalignment). The advantage of the method is that it does
not need the yaw position of the nacelle to be measured.
The robustness of the method was investigated by repeating the calibration
test on the same turbine several times, with the rotor locked in the exact
same rotor position to avoid sensor mounting deviations playing a role. The
Fα values found for four tests for the exact same rotor position were
within ±2.7 % of the mean value.
The quality score parameter (QSC) was introduced to quantify the goodness of the
Fα estimate. The QSC was found inversely dependent on the
turbulence intensity. To have a precise estimate of Fα, it is
therefore better to perform the test in low-turbulence wind conditions. The
relation found between the QSC and the width of yawing suggests yawing the
turbine further than by ±60 and up to ±80∘ (these values
might be different for other spinner shapes). Another issue to consider is
that the test could start with an offset and end up being -90 to
70∘ instead of -80 to 80∘. This is easily avoidable by yawing the wind turbine a bit further than the desired yawing span.
The sensitivity of the method to the width of yawing the turbine in and out
of the wind was investigated by applying the calibration method to a subset
of the original database. The subset was obtained filtering for
γref∈ [-s, s], where s was the span ranging from
10 to 90∘ in steps of 5∘. Significant variations of the
Fα value were found for yawing span s below approximately 60∘.
The Fα calculated with the wind speed response method was compared
with the Fα calculated with previous methods (GGref, TanTan) using
29 calibration tests performed by Romo Wind A/S on 17 wind turbine models.
The sensitivity to the span of yawing showed that the WSR method tends to
stabilize to the same values as GGref for a yawing span larger than approximately
50∘. Both the GGref and TanTan methods gave similar values of up to
±40∘; then, the TanTan method gave a higher Fα and diverged from GGref for
a yawing span larger than 70∘.
A recommended yawing span to use to calculate Fα seems to be
±60∘ for the WSR method and ±40∘ for the TanTan and GGref
methods; however, the turbine should be yawed further than this angle
(±90∘ recommended) to compensate for initial offset error in the yaw
position and wind speed direction change during the test.
It is best to perform the test at the lowest possible turbulence intensity,
which might be found in stable atmospheric conditions (typically by night) at a flat site with low roughness.
It is recommended to verify the variation of Fα as a function of
the span of yawing (using the calibrated yaw misalignment if the yaw sensor is
not available), since substantially different spinner shapes might give a
stable Fα at different yawing spans.
Nomenclature
V1Speed along the sensor path of probe 1V2Speed along the sensor path of probe 2V3Speed along the sensor path of probe 3VaveMean value of V1, V2, V3UWind speed vector modulusUhorHorizontal wind speed componentUhor,dHorizontal wind speed (non-calibrated)Uhor,d,cHorizontal wind speed component (calibrated with correct kα but not yet with k1)k1Calibration constant mainly related to wind speed calibrationkαCalibration constant mainly related to angle calibrationk2Calibration constant (equal to kα⋅k1)RMSERoot mean square errorQSCQuality scoreGGrefGamma–gamma reference methodαInflow angle with respect to the shaft axisδShaft tilt angleβFlow inclination angleγYaw misalignmentγrefReference yaw misalignmentϕRotor positionUhor‾Mean horizontal wind speedθAzimuth position of flow stagnation point on spinner (relative to sonic sensor 1)F1Calibration correction factor mainly related to wind speed calibrationFαCalibration correction factor mainly related to angle calibrationF2Calibration correction factor (Fα⋅F1)TITurbulence intensityWSRWind speed response methodTanTanTangent–tangent method
Acknowledgements
We thank Romo wind A/S for financing one third of the PhD project that this article is part of.
Edited by: H. Hangan
Reviewed by: three anonymous referees
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