Introduction
A wind turbine wake is the volume downwind of a wind turbine, affected by the
fact that the wind turbine removes momentum from the flow, thus reducing the
downwind speed. Also, in the wake, the flow is more turbulent than in the
inflow because of the rotation of turbine blades and the presence of the
wind turbine itself as an obstacle to the incoming wind flow
.
Wind turbine wakes impact the layout optimization and energy production of
large wind farms . In fact, the reduced wind speed in
the wake region has a direct effect on the power extracted by downwind
turbines .
Moreover, the increased turbulence in wakes enhances turbulent loads for
downwind turbines, possibly inducing premature failure
.
Therefore, wakes need to be studied and understood in order to maximize the
efficiency of wind energy production. In particular, wake models are applied
in several steps of the design and lifetime management of wind farms, whose
layout is studied in detail to maximize the amount of energy generated by the
turbines . Moreover, the overall
wind resource assessment process needs to take into account the effect of
wakes to have a reliable prediction of future power production
. Lastly, wind farm control techniques
incorporate detailed studies of wake characteristics while periodically
changing some features of the turbines (such as yaw angle and pitch angle) in
order to maximize the overall power production from the whole wind farm
(; ; ).
Typically, all these processes are computationally intensive and apply
low-order models of turbine wakes
, such as the Jensen
model . In this way, several scenarios
can be tested, but these lower-cost models oversimplify reality and may not
be capable to fully represent wake characteristics in a detailed and
realistic way .
Atmospheric stability has been shown to have a major impact on wind turbine
wake evolution and wind farm performance in both observational
and modeling studies
:
wakes in stable conditions persist for long distances downwind, while during
unstable conditions the enhanced turbulent mixing erodes the wakes more
quickly.
Wake characterization from field data can validate and improve the quality of
numerical models. Data from field campaigns avoid possible limitations of
wind tunnel simulations, such as down-scaled geometric dimensions and low
Reynolds numbers . Lidars and radars have been widely
used recently to characterize wind turbine wakes. These instruments can
measure wind characteristics above the heights of most traditional
meteorological towers, and they can be deployed and moved rather easily,
allowing measurements at several different locations. Many wake validation
studies from remote sensing measurements focus on individual isolated
turbines
,
with some studies that aim to reconstruct the three-dimensional structure of
wind turbine wakes . The interactions
between multiple wakes must be captured in studies of large wind farms, as
done by , ,
, ,
, and .
In this paper, we analyze scanning lidar and profiling lidar measurements
from the CWEX-13 field campaign in a large wind farm in Iowa, and we extend
the individual wake detection algorithm proposed by
to characterize multiple wakes. The
three-dimensional structure of wakes from a row of four turbines is assessed
in terms of velocity deficit, width of the wakes, and wake centerlines.
Section 2 describes the CWEX-13 field campaign and how we use measurements
from the instruments deployed at the site. In Sect. 3 we present the wake
characterization algorithm for multiple wakes, an expansion of the algorithm
proposed by . Section 4 highlights how wake
characteristics (velocity deficit, wake width, and wake centerline) change in
three-dimensional space, and for the first time we quantify the effect of
ambient wind veer on the vertical stretching of the structure of wakes. In
Sect. 5 we compare the present results with those obtained in previous
studies, and we suggest possible future work to improve wake simulations and
models.
Data and methods
This study analyzes the scanning lidar and profiling lidar measurements from
the CWEX-13 observational campaign, summarized in
and .
Schematic view of the part of the wind farm in central Iowa where
the CWEX-13 field campaign took place. The row of four turbines whose wakes
are detected by the scanning lidar is highlighted in a purple ellipse.
CWEX-13 observational dataset
CWEX-13 campaign took place between late June and
early September 2013 in a wind farm in central Iowa, the same wind farm
studied in previous CWEX campaigns; however, CWEX-13 focused on a part of the
wind farm that is different from what is discussed in
, ,
, and . The region
exhibits strong diurnal cycles of atmospheric stability and frequent
nocturnal low-level jets . The area has a
flat topography, with large fields of corn (height 1–2 m) and soybeans
(height 0.3–0.8 m). The region also has four small villages, some riparian
regions and a few trees and buildings (some photos of the site are included in the
Supplement).
Figure shows a schematic diagram of the area of the wind
farm of interest in CWEX-13. The yellow dots represent the wind turbines,
whose main technical specifications are reported in Table .
For the purpose of this work, we focus on the characterization, using
scanning lidar data, of the wakes from the row of four turbines enclosed in
the purple ellipse in Fig. .
Lidar measurements
Three WINDCUBE v1 vertical profiling lidars (blue diamonds in Fig. ) were deployed at the site during the field campaign, and
they were located south of the studied row of four turbines, 8.5D north of
the above-mentioned turbines, and 5.7D north of a second row of turbines.
These instruments provided vertical profiles of wind speed and direction from
40 to 220 m above the surface, with measurements
collected every 20 m. At CWEX-13, southerly wind conditions
dominated the campaign. So, we used data from the WC-1 profiling lidar to
measure upwind conditions for the studied row of turbines, and calculate the
ambient wind veer.
Technical specifications of the studied wind turbines in CWEX-13
field campaign.
Rotor diameter (D)
80 m
Hub height
80 m
Rated power
1.5MW
Cut-in wind speed
3.5 m s-1
Rated power at
11 m s-1
Cut-out wind speed
20 m s-1
Description of the 30 min cycle of scanning lidar scans in CWEX-13
field campaign. The characteristic fixed angle refers to the elevation angle
for PPI and VAD scans and the azimuth angle for RHI scans.
Number
Type
Characteristic fixed angle
Duration of
Cumulative
of scans
of scan
each scan
time
2
VAD
75∘, 60∘
132 s
00:00–04:24
6
PPI
2.8∘, 2.5∘, 2.2∘, 2.1∘, 1.8∘, 1.5∘
104 s
04:24–14:48
3
RHI
160∘, 170∘, 180∘
32 s
14:48–16:24
6
PPI
2.8∘, 2.5∘, 2.2∘, 2.1∘, 1.8∘, 1.5∘
104 s
16:24–26:48
6
RHI
160∘, 170∘, 180∘, 180∘, 170∘, 160∘
32 s
26:48–30:00
From 31 July to 6 September 2013, a LEOSPHERE WINDCUBE 200S scanning lidar
was deployed with the northernmost WINDCUBE v1 profiling lidar (WC-3 in
Fig. ). demonstrated
good agreement between the co-located scanning and WC-3 profiling lidars
measurements at the altitudes where measurements overlapped. Scanning lidars
can operate sweeping the azimuth angle with a constant elevation angle, the
so-called plan position indicator (PPI) mode (velocity
azimuth display – VAD – mode when a full conical scan is conducted), or
sweeping the elevation angle while holding the azimuth angle fixed, in the
so-called range-height indicator (RHI), mode
. In CWEX-13, the scanning lidar used a combination
of PPI, VAD and RHI scans, with a 30 min cycle (each PPI scan lasted
approximately 100 s, spanning an azimuth range of 50∘ with a
speed of 0.5∘ s-1, while a RHI had a duration of about 30 s; see Table ).
Measurements were collected with slant range gates of 50 m at
ranges up to 5000 m from the instrument, with an angular
resolution of 0.5∘. Line-of-sight (radial) velocity was measured
with an accuracy better than 0.5 m s-1.
Given the dominant southerly wind conditions, the WINDCUBE 200S scanning
lidar can use horizontal (PPI) scans to observe wakes propagating from the
row of four turbines of interest. The horizontal scans were performed at six
different elevation angles, giving a range of different vertical positions
depending on the distance from the lidar. Approximately 10 min were
required to collect the series of six elevation tilts; elevation angles
varied from 1.5 to 2.8∘, which allow measurements at a
variety of vertical positions between the bottom and top of the rotor disk of
the turbines, as shown in Fig. .
We select for a detailed analysis 2 days (23 and 26 August 2013) displaying
wind conditions representative of the typical southerly wind pattern for the
site. The first case, 23 August, had predominant southeasterly wind
conditions, with relatively low wind speed, which never exceeded
10 m s-1 at 220 m a.g.l. During 23 August 2013, 438 PPI scans were
performed, 73 for each of the six elevation angles. In contrast, 26 August
showed southwesterly wind, which is the most common situation for the site,
with greater wind speed (up to 20 m s-1 at 220 m a.g.l.). During
26 August 2013, 576 PPI scans were performed, 96 for each elevation angle. By
comparing the results from these two different days, the effect of wind
direction on some wake characteristics can be assessed. Figure
shows examples of maps of line-of-sight velocity measured by the scanning
lidar during two PPI scans performed at night on the selected days. The wind
turbine wakes can clearly be detected in terms of reduced wind speed downwind
of the four wind turbines.
Schematic representation of the position where measurements from PPI
scans are available, at six different elevation angles, as a function of the
distance from the scanning lidar. The horizontal dashed lines show the
vertical limits of the rotor disk of the turbines and hub height. The
position of the four turbines is represented by the vertical dashed lines,
with red lines for outer turbines and blue lines for inner turbines. From the
westernmost to the easternmost turbine, the distances from the scanning lidar
are 2136, 2102, 2171, and 2286 m. The change in elevation between the
turbine location and the lidar location (7 m) is taken into account.
Color maps of line-of-sight velocity measured by the scanning lidar
during two PPI scans performed at 11:57 UTC (06:57 LDT) on 23 August
2013 (a) and at 02:33 UTC (21:33 LDT) on 26 August
2013 (b). The scanning lidar is located in the origin of the
coordinate system. The two arrows show wind direction as measured by the
profiling lidars WC-1 and WC-2 at 80 m a.g.l.
Surface flux measurements for quantifying atmospheric stability
Several surface flux stations (provided by Iowa State University) were
deployed at the CWEX-13 site (orange squares in Fig. ). We
used measurements from the surface flux station ISU_3 to assess
atmospheric stability conditions, with the calculation of Obukhov length L,
defined as
L=-θv‾⋅u∗3k⋅g⋅w′θv′‾,
where θv is the virtual potential temperature (K),
calculated from the sonic anemometer virtual temperature data Tv and the
measured pressure p as θv=Tvp0pR/cp, with p0=1000 hPa and R/cp≈0.286;
k=0.4 is the von Kármán constant; g=9.81 m s-2 is
the acceleration due to gravity;
u∗=(u′w′‾2+v′w′‾2)1/4 is the friction velocity
(m s-1); and w′θv′‾ is the kinematic
sensible heat flux (W m-2).
Reynolds decomposition for turbulent flows is applied to separate the average
and fluctuating parts of the relevant quantities. The average time period
used to compute the Reynolds decomposition must be much longer than any
turbulence timescale, but much shorter than the timescale for mean flow
unsteadiness. For this purpose, it has been fixed to 30 min, a typical
time range used to compute turbulent averages for atmospheric boundary layer
phenomena .
As to atmospheric stability, we consider neutral atmosphere for L≤-500 m and L>500 m; unstable conditions for -500 m <L≤0 m;
and stable conditions for 0 m <L≤500 m .
Wake characterization algorithm for multiple wakes
The line-of-sight velocity (uLOS) measured by the WINDCUBE 200S scanning
lidar (Fig. ) during the horizontal (PPI) scans can be analyzed to
determine wake characteristics and how they evolve in space as the wakes
propagate. proposed a wake detection
algorithm and applied it to characterize the wake from a single turbine,
later expanding it to treat nacelle-based lidar measurements
. Here we expand the same algorithm to
characterize wakes from a row of four turbines.
(a) Plan view of the coordinate system for scanning lidar
PPI scans; (b) 3-D sketch of the main geometric quantities relevant
in a lidar scan.
Data pre-processing
First, a threshold is imposed to the carrier-to-noise ratio (CNR), which
represents the strength of the backscattered signal compared to background
noise (values closer to 0 dB indicate a stronger signal relative to the
noise): all measurements with carrier-to-noise ratio <-27 dB are
discarded from further analysis .
Measurements with a lower CNR often had unrealistically high (>15 m s-1) values of radial velocity; this threshold value is
comparable with choices in other studies
.
Moreover, in each scan, line-of-sight velocity data which are not included in
the interval (μ-3σ^, μ+3σ^), where μ
is the average of the data, are removed from the analysis. The standard
deviation σ^ is evaluated according to the median absolute
deviation (MAD), assuming normally distributed data: σ^=1.4826 MAD, where MAD = median (|uLOS,i-median(uLOS)|). In
the remaining part of the wake detection algorithm, measurements will be
weighted according to the inverse of the square of the radial wind speed
dispersion, which is a measurement of the standard deviation of the
backscattered signal of the lidar and thus an indicator of the uncertainty of
values .
Wake detection
To implement the wake detection, measurements of line-of-sight velocity
uLOS at each range gate in each PPI scan are fitted to two different
models: the first is for ambient flow conditions without wakes, the second
represents each of the four wakes as a Gaussian function subtracted from
uniform ambient flow
.
Ambient wind speed is modeled with uniform speed u and direction ϕ, as
shown in Fig. . At a fixed elevation angle, the line-of-sight
velocity uLOS can be related to the assumed uniform ambient wind speed
u with a simple geometric transformation involving horizontal wind
direction ϕ and the lidar azimuth angle α, namely
uLOS=u⋅cos(α-ϕ),
where both α and ϕ are >0 for clockwise rotations from north.
The azimuth angle α can be related to the range gate r and the
transverse coordinate y=r⋅cos(θ)⋅sin(α),
yielding
uLOS(y,r)=u⋅r2-y2rcosϕ+yrsinϕ,
which represents the first model for uLOS applied in the wake detection
algorithm. In this case, the ambient flow wind speed u and the ambient wind
direction ϕ are the fitting parameters of the model. This “no wake” fit
is the same as in .
The second implemented model represents each wake from the four turbines in
the row as a Gaussian function subtracted from
uniform ambient flow u:
uLOS(y,r)=u-∑i=14aiexp-(y-yi)22swi2⋅⋅r2-y2rcosϕ+yrsinϕ.
This second model has 14 fitting parameters: the ambient wind direction
(ϕ), the ambient wind speed (u), the amplitudes of the Gaussian functions
(ai; i.e., the wake velocity deficit amplitudes), the four transverse
coordinates of wake centers (yi), and four parameters controlling the widths
of the wakes (swi). Note that each of the four wakes is modeled with its
own parameters, permitting variable characteristics between the wakes. The
amplitude ai can be 0, for the trivial case of no wake.
Nonlinear regression (least squares) is applied with the two different models
specified above. In the fitting procedure, the transverse coordinate y is
used as the independent variable, while the measured line-of-sight velocity
uLOS is the dependent variable; moreover, the dispersion of measured
uLOS is used as weights for the data. In setting the first-guess values
for the parameters, physical limits are set: the velocity deficit amplitudes
must be ≥0 but lower than the uniform ambient flow wind speed u, the
locations of the centers of the wakes must be included in the range of
transverse coordinates y in each scan, and the width of the wakes must be >0.
The best estimates for the parameters of the two models are found. An extra
sum-of-squares F test is applied to determine whether the second model, which is
naturally suited to better fit data considering its higher number of
parameters, is significantly better than first model in fitting the
data. A threshold p value is set to 0.05; if the calculated p value is
less than this threshold, then the second model is considered capable to
significantly better represent the data, and thus it is selected
.
Figure shows an example of line-of-sight velocity measurements at a
single range gate in a PPI scan (with error bars representing the dispersion
of the measurements). The red continuous line is the fit performed by the
wake characterization algorithm.
Model acceptance criteria
The quality controls implemented in the first steps of the wake detection
algorithm (limits to CNR, MAD method to discard outliers, physical limits to
the values of the fit parameters) assure a very good quality of the fits,
measured in terms of Pearson correlation coefficient and mean squared error.
However, some other quality-control steps are applied to solve possible
issues related with the complexity of the expansion of the algorithm to
detect multiple wakes.
At the smallest range gates, depending on a given wind direction, not all the
four wakes from the studied row of four turbines may be included in the lidar
scan because of the limited range of azimuths of each scan. In these
situations, the application of the second model, which aims to fit
uLOS with four wakes, may result in the detection of some spurious wakes
besides the actual (but less than four) real wakes seen in the PPI scan.
These spurious wakes are typically detected where sudden – but very limited –
natural changes in the line-of-sight velocity occur. To solve this false
detection, fitted wakes with nonrealistic velocity deficits (smaller than
half of the minimum velocity deficits of the other wakes detected at the same
range gate) and/or widths (smaller than 0.1D or bigger than one quarter of the
whole transverse range) are excluded from the results.
Example of line-of-sight velocity data measured by the scanning
lidar at a specific range gate during a PPI scan. Error bars are the
dispersion of line-of-sight velocity measurements. The red line represents
the fit performed by the wake characterization algorithm.
Another issue is related to the possibility of the algorithm detecting wakes
with a double-peaked shape – typical of near-wake
or arising from the interference of an obstacle with the laser beam of the
lidar – as two separate wakes. The algorithm detects a double-peaked wake
when the transverse positions of the centers of two adjacent wakes are closer
than half of the width of the largest wake. When these double-peaked wakes
are detected, the algorithm can instead consider a single-peaked wake with a
velocity deficit amplitude which is the average of the two detected velocity
deficit amplitudes, a wake center located at the average y between the two
detected peaks, and a wake width determined adding a half-width (2swi) to each external edge of the two detected peaks.
Besides these quality-control steps, the algorithm can re-order the remaining
wake parameters to associate them to the correct physical wake from the
considered row of four turbines. This procedure is dependent on wind
direction, which determines in which order the four wakes are excluded from
the scan area of the lidar at lower range gates.
The wake characteristics database, which is the output of the application of
the wake detection algorithm (which is publicly available at
https://github.com/nicolabodini/CWEX13), is then used to study how wake
characteristics evolve in three-dimensional space.
For each detected wake, the velocity deficit is calculated as the ratio
between the velocity deficit amplitude ai and the ambient flow wind speed
u (estimated from our algorithm at each performed fit at each range gate
and elevation) :
VDi=u-uwakeu⋅100=aiu⋅100.
The wake width has been defined in different ways in the literature; here we
calculate it as in :
wi=4⋅swi,
which is equivalent to the 95 % confidence interval of the Gaussian velocity deficit profile.
The wake centerline will be studied considering the temporal evolution of the planar coordinates of the center of each wake, i.e., the peak of the velocity deficit.
As final quality-control steps, the MAD method is applied again to discard
wake characteristics which do not lie within 3 standard deviations of the
mean characteristic at each range gate for each whole night
; moreover, only fits with Pearson correlation
coefficient
(corr(uLOS,u^LOS;g)=cov(uLOS,u^LOS;g)/cov(uLOS,uLOS;g)cov(u^LOS,u^LOS;g),
where g represents the data weights) larger than 0.9 and mean squared error
(MSE=1∑i=1ngi∑i=1ngi(u^LOS,i-uLOS,i)2) lower than 0.5 are included
in the final analysis of the results.
Results
Once all the fits are completed, and the wakes fully characterized, it is
possible to study how the wake characteristics vary in space for the four
studied turbines.
Frequency of wake detection and atmospheric stability
Atmospheric stability has a major impact
on wind turbine wake
evolution and wind farm performance: wakes in stable conditions persist for
long distances downwind, while during unstable conditions the enhanced
turbulent mixing erodes the wakes more quickly.
To get a quantitative measurement of this effect, Fig. shows
the percentage of scans where wakes were detected by the algorithm, at each
range gate, for different stability conditions of the atmosphere (measured in
terms of the Obukhov length) during all the 438 and 576 scans (at all the
considered elevation angles) performed on 23 and 26 August 2013,
respectively. The plot clearly shows how wakes can
easily be detected in stable conditions, while during unstable conditions the
algorithm is not capable of properly detecting wakes at least 40 % of the
time. Moreover, wakes erode more quickly during unstable conditions, with the
degradation becoming more intense approximately at 700 m (∼8.5D)
downwind of the wind turbines, while under stable conditions wakes are
detected in most of the scans up to approximately 1000 m (∼12D)
downwind of the turbines.
All the results presented in the next paragraphs focus on stable conditions
of the atmosphere.
Velocity deficit results
Wind speed reduction in the wake region, measured in terms of velocity
deficit, is the most distinct wake effect.
Percentage of wakes detected by the characterization
algorithm vs. downwind distance, for stable and unstable conditions of the
atmosphere (neutral conditions were detected only for very short periods and
are not included here). Results from PPI scans performed on 23 and 26 August
2013.
Velocity deficit vs. downwind distance, at different vertical
positions, for wakes from (a) an outer turbine and (b) an
inner turbine. Gray horizontal dashed lines represent the vertical limits of
the rotor disk of the turbines; the horizontal continuous gray line shows the
hub height of the turbines. Data collected from 05:31 to 05:42 UTC (from
00:31 to 00:42 LDT), 26 August 2013, from a succession of six PPI scans
performed at six different elevation angles.
Velocity deficit vs. downwind distance, for the four wakes of the
studied row of turbines. Continuous lines represent the median values
calculated from the PPI scans performed at all the considered elevation
angles during the night (stable conditions) of 26 (a) and
23 (b) August 2013; shaded areas show ± 1 standard deviation
of the data.
Figure shows contour plots of velocity deficits for a wake from an
outer turbine (panel a) and a wake from an inner turbine (panel b),
computed using the results of the wake detection algorithm from PPI scans
performed at six different elevation angles from 05:31 to 05:42 UTC (from
00:31 to 00:42 LDT) on 26 August 2013. The horizontal axis shows the downwind
distance from the turbines, expressed in terms of rotor diameters D, with
D=80 m. The plot clearly shows that the velocity deficit
decreases with downwind distance, and the wake of the outer turbine exhibits
smaller velocity deficits compared to the wake of the inner turbine.
To understand if the results are systematic, Fig. shows
velocity deficit versus downwind distance from the turbines, calculated from
the 276 (242) PPI scans, at all the elevation angles, performed during the
whole night – stable conditions – of 26 (23) August 2013. The continuous
lines show the median values of velocity deficit, and the shaded area
represents the standard deviation of the data.
Wake width vs. downwind distance from the turbines, for the wakes of
the four turbines in the studied row, from PPI scans performed at all the six
considered elevation angles. Continuous lines represent median values; shaded
areas show ± 1 standard deviation of the data. (a) Data from
the night (stable conditions) of 26 August 2013, with southwesterly wind
conditions. (b) Data from the night (stable conditions) of 23 August
2013, with southeasterly wind conditions. (c) Aggregated plot,
average of data from the nights of 26 and 23 August, considering the single
turbines with reference to their relative distance from the scanning lidar.
As expected, velocity deficit decreases with downwind distance, since the
speed reduction in the wake tends to become smaller due to the entrainment of
free-stream surrounding air. The plot also confirms that wakes from outer
turbines (number 1 and number 4) have lower velocity deficits than the wakes
from inner turbines (number 2 and number 3) for relatively small downwind
distances, with a difference up to 15 %. The presence of outer turbines seems
to reduce the effectiveness of lateral entrainment of faster air to recover
wind conditions in the inner wake regions of the wind farm. These results are
comparable for both the considered nights: different wind directions do not
seem to affect them.
Wake width results
The widths of the wakes also change with downwind distance (expressed in
terms of rotor diameters D, Fig. ).
Panel (a) shows results from the stable conditions of the night of 26 August
2013, while panel (b) shows results for the stable conditions of the night
of 23 August 2013. In both cases, for all the four turbines, the wake widths
increase moving away from the turbine, exceeding 2D after a downwind
distance of 8–10D.
However, if we focus on the single wakes, we can see how different wind
directions (southwesterly during 26 August, southeasterly during 23 August)
can affect the ability of the scanning lidar to measure line-of-sight
velocity and, thus, detect this characteristic of the wakes. By comparing the
two plots in panels (a) and (b), it is clear that the scanning lidar
systematically identifies as the widest the wake which, at a given downwind
distance, is the most perpendicular to the laser beam (i.e., the last one the
laser beam meets: turbine 4, at the right edge of the row, for southwesterly
wind; turbine 1, at the left edge of the row, for southeasterly wind). Then
the detected width of the wakes progressively decreases moving to the wakes
from adjacent turbines.
Qualitative sketch of the dependence of detected wake width on the
orientation of the coordinate grid used by a scanning lidar (purple triangle)
as a function of the wind direction. Panel (a) shows the case of a
wake aligned with the line of sight from the scanning lidar (wind direction
shown by the blue arrow), while panel (b) shows the case of a wake
not aligned with the line of sight from the lidar. The dashed arrow
highlights the difference in the detected wake width for the two cases, at
fixed downwind distance from the turbine (yellow ellipse).
Figure c aggregates results from 23 and 26 August, and it shows
how wake width changes with downwind distance considering the single turbines
from the closest to the furthest from the scanning lidar, depending on the
particular wind direction, as shown in the right schemes in the panel. The
plot confirms the systematic dependence of the detected wake widths on the
relative position between the wake and the scanning lidar.
(a) Wake centerlines for an outer (on the left) and inner
(on the right) turbine, from the PPI scans measurements during the
02:30–03:30 UTC (21:30–22:30 LDT) time period, 26 August 2013.
(b) Wake centerlines for an inner (on the left) and outer (on the
right) turbine; data from the 09:30–10:30 UTC (04:30–05:30 LDT) time
period, 23 August 2013. Dashed lines represent the median values of wake
centerlines, while the continuous lines show results at different vertical
levels: for each wake, light colors refer to measurements between 35 m and
55 m a.g.l., while darker colors represent data points with a vertical
height greater than 75 m. Yellow dots show the position of wind turbines.
This result is due to the relationship between the viewing angle and the
aspect ratio of the lidar retrieval “pixels”, which are related to the
relatively long range gate (50 m) and relatively narrow azimuthal
resolution (0.5∘). As qualitatively shown in the schematic of
Fig. , the scanning lidar measures the line-of-sight velocity
in narrow pencil-shaped “pixels”. With this geometry, if the wind direction
– and thus the wake – is aligned with the line of sight from the lidar, the
wake width can be assessed with high precision due to the high azimuthal
resolution in each pencil-shaped area (panel a). However, if the wind
direction – and thus the wake – is not aligned with the line of sight from
the lidar (panel b), then the same wake will be measured as generally wider,
since the retrieval of the wake width is now affected by the relatively
coarse radial resolution of the lidar coordinate grid. In the schematic
diagram shown in Fig. , at an arbitrary fixed downwind
distance from the turbine, the (same) wake would be detected as 19 %
larger when it is not aligned with the line of sight from the scanning lidar.
This result becomes more evident when the laser beam is more perpendicular to
the wake. This result is due to the aspect ratio of the lidar “pixels” and
thus would affect other wake characterization approaches relying on
instruments not co-located with the turbine – such as in
and – but would not affect nacelle-mounted
wake measurements, such as in and
, as nacelle-mounted wake measurements are
usually aligned with the wake unless the wake is intentionally yawed
.
Wake centerline results
PPI scans at multiple elevation angles provide insight into the three-dimensional
structure of wind turbine wakes. Different conditions at different vertical
levels have a considerable impact on the wake centerline, i.e., the change of
the position of the wake center downwind of the turbine.
Qualitative cross-stream slices of stream-wise velocity deficit. The
perspective is looking downwind. (a) A graphic representation of the
classical Gaussian shape of the magnitude of wake velocity deficit.
(b) An ellipsoid which represents the vertical stretching of the 3-D
structure of a turbine wake as a consequence of wind veer.
Figure shows a plot of the median position of the centers for the
wakes of the two turbines located at the west edge of the considered row of
four turbines for the 02:30–03:30 UTC (21:30–22:30 LDT) time period during
the night of 26 August 2013 (southwesterly wind, panel a) and for the two
turbines located at the east edge of the considered row of four turbines for
the 09:30–10:30 UTC (04:30–05:30 LDT) time period during the night of 23 August 2013 (southeasterly wind, panel b). Dashed lines represent the
median value for the wake centerlines; continuous lines show the results for
data points with different vertical heights: light colors show results for
points with a vertical height between 35 and 55 m, while dark colors refer to measurements taken above 75 m a.g.l. (these levels were chosen to create bins at low and high heights
compared to the vertical dimension of the turbines, with approximately the
same number of vertical positions where the lidar measurements were taken, as
shown in Fig. ). A clear change in the position of the
wake centers is detected between low and high vertical levels. This
stretching is independent of wind direction: the change can be seen for both
southwesterly (panel a, 26 August) and southeasterly (panel b, 23 August)
wind conditions.
This change of the wake centerline with vertical height causes a stretching
of the vertical structure of the wakes: the velocity deficit structure of a
turbine wake, whose stream-wise velocity deficit is traditionally considered
as a 3-D Gaussian in a cross-stream plan (Fig. a), should instead
be represented – when this vertical stretching occurs – by a rotated
ellipsoid (Fig. b), as already observed in both field
measurements and large-eddy
simulations .
Relationship between ambient veer and wake centerline
The vertical stretching of wake structure occurs because of the wind veer,
the clockwise change of wind direction with height that often occurs in
stable conditions, like those of 23 and 26 August 2013. To get a deeper
insight on the relationship between ambient wind veer and vertical changes of
the wake centerlines, we analyze several 30 min periods (each corresponding
to two subsequent sequences of six PPI scans at the six different elevation
angles) during the nights of 23 August 2013 (southeasterly wind) and
26 August 2013 (southwesterly wind). For each considered time frame, the wind
veer is calculated as the average difference between the wind direction at
100 and 40 m, as measured by the vertical profiling lidar located to measure
upwind conditions (WC-1 in Fig. ). The two vertical heights
are chosen as representative of the two different vertical levels considered
when assessing the changes of wake centerlines (35 m <z< 55 m and
z>75 m). Moreover, the wake centerlines at different vertical
levels have been fitted with straight lines, and the angle between the lines
which approximate the wake centerlines at 35 m <z<55 m and z>75 m is calculated and then considered as the
angular difference between the wake centerlines at different vertical levels.
Figure shows how angular difference between wake centerlines at
different vertical levels compares to ambient wind veer between 100 and 40 m, for all the available time frames during the
nights of 23 and 26 August 2013, for wakes from an inner and an outer turbine
in the considered row.
Angular difference between wake centerlines at different vertical
heights (35 m <z<55 m and z>75 m) vs. wind veer between 100
and 40 m. Data for an inner and an outer wake in the considered row of
four turbines, for several 30 min time frames during the nights of 23 and
26 August 2013. Continuous lines are the linear regressions from the data
(red best fit: 2.04 + 0.23x; blue best fit: 1.23 + 0.25x), for
the outer and the inner wake. Dashed line highlights the
unreached
equality between ambient veer and wake centerlines angular difference.
The results show that, although the angular change in the wake centerline at
different vertical levels is systematically detected, the wind veer is always
much larger than the actual angular difference between the wake centerlines
at the different vertical levels: the change of the positions of the wake
centers is related to, but not completely determined by, the wind veer.
Moreover, as suggested by the linear regression fits, wakes from outer
turbines often present a larger angular difference in wake centerlines
compared to wakes from inner turbines, though with variability for different
veer values that motivates further study.
A possible physical explanation for this phenomenon can be detected in the
interaction between wake rotation due to rotating blades and wind veer. The
blades of the wind turbines in CWEX-13 wind farm rotate clockwise and so the
downwind wakes rotates counterclockwise . The wake can
thus be considered as a sort of plume with its own momentum and rotation that
interacts with the ambient veer, which in turn tends to rotate the wake in
the opposite direction (in the Northern Hemisphere), thus causing a
larger reduction in the
global wake vertical stretching than would be present had only the ambient
veer affected the wake. Inner wakes seem to be less subject to the effect of
ambient wind veer, as if the presence of outer turbines reduces the ability
of ambient wind characteristics to reach and impact inner regions of the wind
farms.
Conclusions
Wakes from a row of four turbines have been characterized using line-of-sight
wind speed measurements from PPI scans performed by a scanning lidar. Data
were collected in late summer 2013 during the CWEX-13 field campaign
, in a wind farm in a flat region in central Iowa.
The wake characterization algorithm proposed by
has been extended to assess wakes from
multiple turbines.
Wakes erode quickly during unstable conditions of the atmosphere, and they
can in fact be detected here primarily in stable conditions in this dataset.
The velocity deficit in the wakes decreases with downwind distance from the
turbines, and it is lower for wakes from outer turbines in the studied row.
The width of the wakes increases with downwind distance, with systematic
differences in the ability of the scanning lidar to detect the width of the
wake according to the component of the direction the wakes perpendicular to
the direction of laser beam of the scanning lidar. Wake centerlines change at
different vertical levels as a consequence of the ambient wind veer, causing
a stretching of the vertical structure of the wakes. Although the field
measurements of and
demonstrated that turbine wakes stretch into ellipses during stable
conditions, for the first time we have quantified the effect of ambient wind
veer on the stretching of wakes. In fact, the angular change in the wake
centerlines at different heights is systematically much lower (a half or
less) than the wind veer registered at the same heights. Moreover, this
angular change of the wake centerlines at different vertical levels is found
to be usually greater for wakes from outer turbines. This wake stretching,
due to wind veer, not only is seen in these field measurements but also
emerges in the stably stratified simulations of ,
, ,
, and . As more
three-dimensional measurements of wakes become available due to the use of
scanning lidar and scanning radar, a more solid representation of wind
turbine wakes can be assessed.
These results can become critically important to assess and improve
large-eddy simulations of wakes as well as to suggest improvements to
mesoscale parametrizations
to account for subgrid-scale wake interactions. Moreover, wind energy
companies can also benefit from our results in trying to enhance the quality
of low-order wake models currently used for wind resource assessment, wind
farm layout optimization, and wind farm control techniques, with the final
goal of an improvement of wind energy production efficiency.