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ASSESSMENT OF TURBULENCE MEASUREMENTS FOR OFFSHORE TURBINE TESTING WITH NACELLE-
BASED LIDAR
Rémi Gandoin, Nicolai Gayle Nygaard, Rebeca Rivera, Matthieu Boquet*
DONG Energy Wind Power, Gentofte, Denmark
*Leosphere-Avent, Orsay, France
Summary
In this study, we evaluate different formulations of the turbulence intensity (TI) reconstructed from the radial wind
speed measurements from a two-beam nacelle LiDAR. The LiDAR TI reconstructions are compared with cup
anemometer measurements, and the relative error is quantified and modelled for a range of wind directions,
turbulence and stability conditions. Overall, for small wind direction offsets, the relative error is small, and TI
measurements can be used for filtering power curve verification datasets and carry out statistical load analysis.
1. Introduction
Turbulence Intensity (TI), defined as the ratio between
the 10 minutes standard deviation and mean
horizontal wind speed, is used load validation, and
power curve verification (PCV). In this paper, we rely
on two datasets for validating TI measurements from a
two-beam Wind Iris LiDAR. The campaigns were
carried out during a project focused on validating
mean wind speed and direction measurements for
PCV [1] [2]. A first dataset consists of Wind Iris,
turbine, and cup anemometer data from a met mast (2
rotor diameters upstream) at Avedøre, Denmark [1]. A
second set comes from the LiDAR calibration, and
consists of Wind Iris and met mast data from a cup
anemometer at Høvsøre, Denmark [3] [4], see below.
Figure 1 At Avedøre, the LiDAR was placed on the
nacelle. At Høvsøre, the LiDAR was fixed to the mast.
The mean wind speed vector and its fluctuations
and are given in Figure 2, with the radial wind
speeds and . is the direction misalignment and
the half-opening angle (15 deg.). For each 10
minutes, using as the longitudinal component of
turbulence of , the reference measurement of TI is:
Figure 2 coordinate system and variables description
This is an approximation, as and are slightly
influenced by the transverse component of turbulence
as well, but the literature [5] [6] shows that it does not
greatly affect the accuracy of the measurements.
2. TI formulations and selection
In this section, three formulations of the LiDAR TI
( are investigated: is computed from the
instantaneous reconstructed wind speed, and
from the radial wind speeds.
is compared to using the relative error:
In Figure 3, is plotted against . As expected,
due to volume averaging in the measurement, all
methods underestimate the TI. has the largest
mean relative error (), and gives a slightly
better result than (respectively and ).
Figure 3 relative error between LiDAR and cup at
Avedøre
For the sake of modelling simplicity, and because it
performs the best, method C has been chosen for the
rest of the paper.
3. TI modelling
From Figure 2, the radial fluctuations are:
Assuming that
and
, and
using and where
, we derive:
We define
, and after
remarking that
, the model error
(Eq.1) becomes:
The parameters , and can be computed from the
cup and vane high frequency values. A sanity check
(see Figure 4) shows that when there is no yaw error,
is comparable to standard values [7], and is small
compared to . There is a very weak covariance of
+0.1 between and .
Figure 4 Boxplots of the measured input parameters
(Avedøre)
Figure 5 shows that if the misalignment is small (
deg.), the relative error is small (it would not exceed
5%, which for 7% TI makes 0.3% in absolute term),
positive, and is mostly driven by .
Figure 5 Evolution of the relative error with the wind
direction offset , for different values of and
4. Model validation
4.1 Yaw misalignment
The measurements from [3] offer a wide range of
misalignments (the LiDAR is fixed to the mast). Figure
6a and Figure 6b show comparisons of and for
the two most populated wind sectors during the
campaign.
Figure 6a Evolution of the relative error with . The
dashed line is the 90% confidence interval on the
mean binned value. Høvsøre (LiDAR is fixed). The
peak at 100 degrees is most likely due to the mast
effect.
Figure 6b Evolution of the relative error with . The
dashed line is the 90% confidence interval on the
mean binned value. Høvsøre (LiDAR is fixed).
The model matches the sharp increase in the error
when the wind direction misalignment is large, but
does not capture the negative bias due to the volume
averaging (as expected). The discrepancies between
the model and measurement trends can possibly be
explained either by flow disturbance from the met
mast (the boom of the cup is pointing towards NW),
the small number of data points (2 weeks) and/or
specific atmospheric conditions (see 4.2 and 4.3).
4.2 Stability
As explained in [3], the atmospheric stability affects
the length scale of the eddies (small in stable
conditions), and therefore has an effect on ,
especially in stable conditions where the largest errors
are expected. Very stable conditions can be identified
at Avedøre, as shown in Figure 7 and Figure 8: very
low and very high shear values coincide with
much larger errors compared to unstable conditions
(high low shear).
Figure 7 Scatter plot of the relative error, as a function
of and the shear exponent, for wind directions
between 190-230 deg. Avedøre.
Figure 8 Histograms of the relative error for very
stable (TI<4% and shear>0.2) and unstable (TI>6%
and shear<0.1) conditions, wind sector 120-250 deg.
Avedøre.
4.3 Effect of
The effect of can be highlighted when choosing
either low or high values (<0.4 and >1), selecting only
values of less than 2 degrees, and shear values less
than 0.2, see Figure 9. Despite the negative bias due
to the volume averaging, the difference between the
mean relative error of the two subsets is comparable
with what the model is predicting (we use and
):
The effect of stability and flow homogeneity may be
linked together (i.e. small values in stable
conditions), although no clear correlation could be
established.
Figure 9a Histograms of the relative errors for small
values of (<2 deg.), a<0.4 (top) and a>1.0 (bottom),
Avedøre. Stable conditions are filtered out (shear
<0.2).
4.3 Effect of
The effect of is harder to identify, because it could
only play a role when its value is large () and
when the misalignement is significant (.
Our dataset does not contain such values and the
effect of b has not been demonstrated.
5. Influence on PCV and site assessment
5.1 Power Curve Verification
When comparing two power curves, it is important that
the atmospheric conditions of both datasets match in
terms of shear and TI, as those are factors that affect
the energy content of the wind profile, and possibly
the aerodynamic performance of the airfoil [8]. Profile
measurements are rarely available offshore, and
power curves are typically filtered using TI. The effect
of filtering for TI below 5% and above 18% is
illustrated in Figure 10. Most of the effect comes from
low TI that correspond with higher shear with low
energy content [9]. The result after filtering using the
cup and LiDAR does not change.
5.2 Load validation
Load validation is typically carried out using
concurrent 10 minutes samples of load, wind, wave
and turbine data. Each TI sample need a high level of
accuracy and precision, as it is an input to the aero-
elastic model. Unlike the mean wind speed, the TI has
the biggest impact on fatigue loads (then comes
shear, and veer). Therefore, the large spread shown
in Figure 3 is a limiting factor in the use of the LiDAR
for this purpose, and further work is required on this
topic.
Figure 10 Result after of TI filtering [0.05-018] with
LiDAR and cup is unchanged
6. Conclusions
We have shown that the nacelle LiDAR TI compares
well with a cup anemometer (mean relative error of -
6%). It is dependent on the wind direction offset and
the stability conditions. The largest relative bias is
observed for very stable conditions where the TI is
very low. In unstable conditions the LiDAR seems very
accurate, although not very precise - the lack of
precision being partly due to the inhomogeneity of the
horizontal wind field. Overall the LiDAR performs well
enough for the TI to be used for filtering power curve
verification datasets. Further work is needed regarding
the use of the LiDAR for comparing simulated and
measured loads.
7. References
[1] R. Wagner et al, DTU Wind Energy E-0016, 2013
[2] R. Wagner et al, Wind Energy, 2013 pp1441-1453
[3] A. Mioullet, DTU Wind Energy M-0016, 2012 (MSc)
[4] R. Wagner et al, EWEA 2013
[5] L. Kristensen, Wind Energy pp 59-75, 1995
[6] L. Kristensen, JTECH, pp1139-1148, 2000
[7] IEC 61400-1 Design Requirements, 2005
[8] R. Wagner, Risø-PhD-58, 2010
[9] I. Antoniou, Wind Engineering, pp449-468, 2009
8. Acknowledgments
The authors would like to thank DTU Wind Energy and
Siemens Wind Power for sharing the data, as well as
Samuel Davoust for the invaluable help and support.