WESWind Energy ScienceWESWind Energ. Sci.2366-7451Copernicus PublicationsGöttingen, Germany10.5194/wes-3-243-2018A simulation study demonstrating the importance of large-scale trailing vortices in wake steeringA simulation study demonstrating the importance of large-scale trailing vorticesFlemingPaulpaul.fleming@nrel.govhttps://orcid.org/0000-0001-8249-2544AnnoniJenniferChurchfieldMatthewMartinez-TossasLuis A.https://orcid.org/0000-0003-2353-4999GruchallaKennyLawsonMichaelMoriartyPatrickhttps://orcid.org/0000-0001-7122-5993National Wind Technology Center, National Renewable Energy Laboratory, Golden, CO 80401, USAPaul Fleming (paul.fleming@nrel.gov)14May20183124325516November201722November201725January201811April2018This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/This article is available from https://wes.copernicus.org/articles/3/243/2018/wes-3-243-2018.htmlThe full text article is available as a PDF file from https://wes.copernicus.org/articles/3/243/2018/wes-3-243-2018.pdf
In this paper, we investigate the role of flow structures generated in wind
farm control through yaw misalignment. A pair of counter-rotating vortices is
shown to be important in deforming the shape of the wake and in explaining
the asymmetry of wake steering in oppositely signed yaw angles. We also
demonstrate that vortices generated by an upstream turbine that is performing
wake steering can deflect wakes of downstream turbines, even if they are
themselves aligned.
We encourage the development of improvements to control-oriented engineering
models of wind farm control, to include the effects of these large-scale flow
structures. Such a new model would improve the predictability of
control-oriented models. Further, we demonstrate that the vortex structures
created in wake steering can lead to greater impact on power generation than
currently modeled in control-oriented models. We propose that wind farm
controllers can be made more effective if designed to take advantage of
these effects.
The author's copyright for this publication is
transferred to Alliance for Sustainable Energy, LLC. Alliance for Sustainable
Energy, LLC, is the manager and operator of the National Renewable Energy
Laboratory. Employees of the Alliance for Sustainable Energy, LLC, under
contract no. DE-AC36-08GO28308 with the US Dept. of Energy, have authored
this work. The United States Government retains and the publisher, by
accepting the article for publication, acknowledges that the United States
Government retains a non-exclusive, paid-up, irrevocable, worldwide license
to publish or reproduce the published form of this work, or allow others to
do so, for United States Government purposes.
Introduction
Wake steering is a wind farm control concept in which the upstream turbines are
intentionally misaligned to deflect its wake away from a downstream turbine
(). For certain arrangements of turbines, it
can be shown that the power of the downstream turbine is increased by more
than is lost by misaligning the upstream, yielding a net increase in power.
Early research in this field used wind tunnel experiments to demonstrate the
possibility of wake steering. Experiments presented in
showed that, for example, wake steering implemented in a two-turbine row could
yield a total relative power gain of 10 %. In
, the wake of a model wind turbine in a tunnel
was measured. When the turbine was yawed, the wake was deflected and,
additionally, vortex shedding was observed which was similar in behavior to
what would be expected from solid discs. In ,
wake steering is studied at a scaled wind farm.
Later work in wake steering made assessments of the technique using
computational fluid dynamic (CFD) simulations of small arrays of wind
turbines. For example, examined wake-steering
performance for an offshore array of two turbines separated by 7 diameters (hereafter D)
and observed an increase in total power.
In order to design controllers to implement wake-steering control strategies,
it is necessary to build engineering models that contain the relevant physics
but are described in a computationally efficient way such that the model can
be used in large-scale optimizations or used as an internal model within a
real-time controller. A first model of wake steering, based on CFD analysis,
was provided by . The model predicts wake
deflection as a function of yaw angle and thrust coefficient.
In , an engineering wake model, known as FLORIS (FLow
Redirection and Induction in Steady State) was introduced. The model combined
the wake-steering model of with the wake-recovery model of . In addition, this model separates
the wake into zones that recover at different rates. The model was shown to
predict the behavior of wake steering for a given set of CFD simulations
(focused largely on two-turbine and fully waked scenarios) and, given its
execution speed, can be used to design controllers as well as look at coupled
wind farm layout and control optimizations (see
). In this model, the wake appears as a
deficit of energy that flows downstream and is characterized as (i) an
initial deficit determined by the turbine thrust, (ii) a rate of recovery
determined by topology (i.e., FLORIS inherits wake-recovery parameters from
the Jensen model whose values are set by rules of thumb for onshore or offshore),
and (iii) a wake deflection caused by wake steering. This version of FLORIS
was used to design a strategy for wake steering that was tested at a
commercial offshore wind farm in , with an improved
wind farm power performance under waked conditions.
More recently, the FLORIS model has been improved by incorporating the
theoretical models of wake behavior and steering presented in
and
. One of the improvements was the inclusion of
turbulence to describe the wake recovery. Turbulence in turbine wakes is
generated by ambient wind conditions as well as turbine operating conditions.
These critical changes greatly improve the general applicability of models
such as FLORIS. For example, wake expansion and the recovery are now
dependent on ambient and induced turbulence intensity, which can resolve the
modeling discrepancies observed in .
To date, engineering models are beginning to include modeling of the main
atmospheric components (turbulence intensity, veer, and shear) needed to
accurately predict and control wakes via wake steering. The basic conception
of wake steering remains that a rotor operating in misaligned conditions
creates a force perpendicular to the flow that generates the deflection in
wake direction and decreases the thrust and overall velocity deficit in the
wake. Further, based on
and , the change in thrust also impacts recovery rate.
Wind tunnel tests in and
show good agreement overall with these latest
models.
However, recent research has underlined that in addition to changing the
deficit and location of a wake, yaw misalignment changes other properties in
the flow, which can be observed as impacting the shape of the wake. In
, large-eddy simulations (LES) are used to study
the behavior of wake steering under varying atmospheric conditions. The
authors note that the shape of the wake under yawed conditions is curled
rather than circular. This curvature is shown to impact the estimate of the
wake center. Further, the authors explain the change in shape by showing that
the cross-flow wind of an aligned turbine is largely due to counter-rotating
vortices that appear in the flow behind a yawed turbine and generate this
distortion. This is consistent with the results of
.
Diagram of the method used in the paper. In this example, showing
the flow as viewed from above, a single turbine is included in a SOWFA
simulation. A period of 1600 s of the flow is averaged and then the
hypothetical turbine rotor is scanned across this averaged flow to compute
the power that would have been produced by a turbine at a given
location.
studied the curled wake phenomenon experimentally
using a porous actuator disk and with LES using an actuator disk and an
actuator line model. The curled wake is observed in experiments and
simulations. The mechanism behind the curled wake is again explained as a
pair of counter-rotating vortices which are shed from the top and bottom of
the rotor due to yaw misalignment. This mechanism was confirmed by
.
In , a rear-facing nacelle-mounted lidar is used to
scan the wake of a turbine in aligned and yawed conditions at five locations
downstream ranging from 1 D to approximately 3 D. The
deflection predicted by earlier simulation models is clearly observed as well
as the curling of the wake shape.
The current state of control-oriented models supposes that the change in wake
“location” and strength can be well modeled as a deflection of a wake
generated with a lower thrust. In other words, the effect of the
counter-rotating vortices on the flow is assumed to be captured in the
engineering models that modify only the deflection, deficit, and recovery of
the wake. A curled wake of some deflection amount might be well-enough
described by a circular wake of larger deflection.
In this paper, a CFD-based analysis is used to examine how the consideration
of the counter-rotating vortices can impact wind farm control analysis and
design. This paper undertakes an investigation of the impact of these
vortices on yaw-based wake control. The contributions of this paper are first
a demonstration that a deflection-only control-oriented model of wind farm
control cannot reconcile all observed effects, even, to some extent, for a
single turbine wake case. A second contribution is the demonstration that the
influence of the vortices is especially critical when arrays of multiple
turbines are considered. A steered wake of an upstream turbine is shown to
deflect the wake of an aligned turbine downstream, and combinations of
steered turbines are shown to involve merging of generated cross flows. The
discussion section considers how wind farm control, based on the generation
of specific large-scale structures and not on geometrical deflection, could
be different and more effective than current methods. The future work
recommendations conclude that incorporating the shed vortices into
engineering models used to design wind farm controllers can improve wind farm
control performance and should be undertaken.
Models
This paper focuses on two specific wind farm models. First, FLORIS is a
low-fidelity, control-oriented tool for wind farm control, which includes
several possible wake models developed by National
Renewable Energy Laboratory (NREL) and TU Delft
. FLORIS is python-based, open source, and available
for download on github (https://github.com/WISDEM/FLORIS, last access:
8 May 2018). The overall approach of FLORIS
is to provide an engineering model of wakes that predicts the important
average behaviors of wakes in a computationally efficient way such that it
can be used to derive control strategies through optimization or function as
an internal controller model. A recent report compares predictions of the
latest FLORIS model to lidar data from a utility-scale wind turbine operating
in yaw and provides good agreement ().
In this work, the wake model used in this paper assumes a Gaussian wake that
is derived from self-similar turbulence theory (). The wake expands linearly and
the parameters of this Gaussian wake are a function of ambient turbulence
intensity and turbine operation. Overlapping wakes are combined using a
sum-of-squares approach that has been used previously in literature
(). It is important to note that there are
alternative methods to combine wakes as wake superposition is an ongoing
research topic ().
Wake deflection is also included in this model based on the yaw misalignment
of a turbine. It is modeled using a budget analysis of the Reynolds-averaged
Navier–Stokes equations. For further details, the reader is referred to
.
Second, the Simulator fOr Wind Farm Applications (SOWFA) is a high-fidelity
framework used to perform LES of wind farm flows,
developed by NREL (). In LES, the filtered
Navier–Stokes equations are solved numerically, providing a time-evolving
three-dimensional flow field in the wind farm. Within SOWFA, wind turbines
are modeled using an actuator disk/line model with torque, blade pitch, and
yaw controllers. SOWFA is based on the OpenFOAM libraries and has been used
in past research of wind farm controls for design and analysis
().
In past research, the SOWFA and FLORIS have been used together. In a typical
workflow, SOWFA simulations of a small farm are run to provide tuning inputs
to FLORIS, which is then used to predict optimal controllers that are then
tested in SOWFA. Successful iterations of this process yield controllers that
can be used in field testing (see for example
)
One constraint of this approach is that, given the computational requirements
of running SOWFA, tuning cases are typically limited to approximately 10–20
runs, and these are focused on high-loss scenarios such as one turbine
directly waking another. For example, simulations of two turbines aligned in
the flow, with and without yaw, for different distances downstream are a
typical focus.
Power output in SOWFA (solid) and FLORIS (dashed) for a hypothetical
turbine directly downstream of a baseline or yawed turbine at different
distances.
An example of the approach used in this paper is now described. In one
scenario, a SOWFA simulation including one turbine modeled as an actuator
disk with rotation is simulated (see Fig. ).
Figure illustrates a turbine in positive yaw in the
convention used of positive being a counter-clockwise rotation when viewed
from above. Note that for all figures, horizontal planes (such as
Fig. ) are viewed from above, while cross-stream planes
(such as Fig. ) are viewed from upstream. The
simulation is run for 2000 s, and the flow is averaged over the last 1600 s
to allow for transients to dissipate. The averaged flow is provided directly
via OpenFOAM output functions. From the averaged flow, a power is computed,
which would have been produced by an additional hypothetical turbine at some
point downstream. This way, rather than results from a handful of turbine
positions, a continuum of turbine locations can be considered. This approach
was adapted from power calculations used in
This power is computed by averaging the cubed wind speed over a hypothetical
rotor disk from the averaged flow. The cubed average is then converted to
power through
P=0.5ρACpU3,
where ρ is the density, A is the rotor area, Cp is the
coefficient of power (which is derived from a look-up table based on wind
speed precomputed from the aero-elastic turbine simulator FAST;
), and U is the rotor averaged wind speed. The
hypothetical turbine can be swept across the area behind the turbine in the
averaged flow to compute the effect on power for turbines across a wide range
of locations. This method allows for inspection of change in power for a wide
variety of turbine array configurations. For comparison, this process can be
repeated directly in FLORIS to compute the power of a downstream turbine for
a range of locations.
One advantage of using this method to compare wake predictions between models
is that it focuses on the comparison on the quantity of interest, which is
the power production of turbines at a given location. Rather than trying to
identify a wake center, focus is shifted from how far the centroid of deficit
is shifted to how much expected power production is possible at a given
location. This will be important if, for example, focus were to shift from wake
deflection to energy entrainment.
Cut-through of SOWFA flow (viewed from upstream), minus the
background flow, at a distance of 7 diameters behind the turbine for baseline
and yawed 25 and -25∘. Deficit in axial flow is shown in blue,
saturating at a deficit of 2 m s-1 to broadly show the wake area. For
the SOWFA cases, the in-plane flow is visualized by arrows whose relative
size indicates the strength of the flow. Red circles indicate a rotor located
directly downstream of the turbine.
All simulations in this paper are of a neutral atmospheric boundary layer,
with a mean wind speed at hub height of 8 m s-1, similar to what has been used in past studies
(). This simulation had at hub height 6 %
turbulence intensity with a shear exponent of 0.085. The domain size is
5 km × 1.8 km × 1 km. The simulations include the NREL 5-MW reference turbines from
, modeled as an actuator disk with rotation for
computational efficiency. In previous work, the actuator disk model with
rotation has been shown to be comparable to an actuator line model in predicting
power (see )
One-turbine case
The one-turbine case shown in Fig. is the first case to be
analyzed where a single NREL 5-MW turbine is placed in the flow. In one case,
it is has no yaw offset (denoted as “baseline”), and then ±25∘
of yaw. In the first case, the hypothetical turbine is swept downstream with
no lateral offset. The results are shown in Fig. .
In both SOWFA and FLORIS, power is improved by misaligning the upstream
turbine. In addition, more power is generated in the positive (CCW) yawed
case than in the negative (CW) yawed case (see Fig. ).
This asymmetry of wake steering, which has been documented previously, is an
important result. For example, in the simulation study in
, where two 5MW turbines are aligned directly in
the flow, after deducting the power lost because of yaw on the first turbine,
only positive yaw produces an overall gain in power for a case of two
turbines separated by 7 D (note this would not be true for example in
certain partial overlap cases, but it demonstrates the important of this
asymmetry in wake steering).
Power output of hypothetical downstream turbine for various
downstream distances and lateral offsets (a). Solid lines are SOWFA results, and dashed are
from FLORIS. (b) The percent gain (of the total power of the actual
and hypothetical turbine) is shown relative to the baseline of the two yaw
angles.
Layout of SOWFA simulation as in Fig. , now with
two turbines. Note that only the first turbine is yawed in controlled cases.
In the original FLORIS model (), this asymmetry is
captured by assuming that a wake has a certain natural deflection, even when
operating in non-yawed conditions. This offset was previously used to
describe the asymmetry between positive and negative wake-steering angles.
Conventionally, this natural offset angle was 0.13∘. This paper
further reconsiders the source of this asymmetric behavior of the wake and
its impact on the wind farm control strategy.
One way we can investigate the impact of the generated vortices on the wake
is to look at cut-through slices of the flow at a distance downstream of the
turbine. This is shown in Fig. . These
cut-through slices are cut cross-wise through the flow direction and include
the average value of all velocity components. In these plots, the
time-averaged flow with no turbines is first subtracted and so only the
change from the background is plotted. These cut-throughs are plotted for
both FLORIS and SOWFA.
Comparing the plots in the figure, we can note that FLORIS shows the impact
of positive yaw as primarily impacting the location of the wake and the depth
of the deficit. SOWFA, however, includes a large impact on wake shape, which
is caused by the two counter-rotating vortices seen in
Fig. . This is in line with the analysis of
and .
Horizontal cut-through of two-turbine flow in FLORIS and SOWFA. Gray
lines pass through edges of rotor to help distinguish flow location relative
to rotor.
As a first qualitative observation of the baseline cases, there does not
appear to be any natural deflection (this will be further examined later).
The natural deflection angle appears to be absent in this case and similar
cases where the amount of veer in the simulation is kept to a minimum.
Second, observing the in-plane flow, shown by arrows in the SOWFA plots in
Fig. , the asymmetry in wake behavior likely
comes from the interaction of the counter-rotating vortices with the wake (as
seen in the SOWFA baseline case of Fig. ) and
the wind shear. More specifically, in the positive yaw case, the top vortex
rotates constructively with the deflection of the wake and rotation of the
wake (generated by the rotation of the turbine). In the negative yaw case,
the lower vortex interacts more substantially with the rotation of the wake.
The top vortex is also stronger because the wind speed is stronger at the top
of the rotor as compared to the bottom of the rotor due to the shear layer
and the interaction with the ground. This difference in vortex interaction
may explain the asymmetry in the wake based on yaw misalignment. A third
observation is that, in the positive yaw case
(Fig. ), the left side of the wake has been
moved further to the right than FLORIS estimates, which computes deflection
based on the center alone.
Figure shows the power of the hypothetical turbine that is
swept laterally across the wake at different distances downstream. The left
column of figures show the wake “profile” (measured in MW), and we see very
good agreement between SOWFA and FLORIS. Note that the largest impact in gain
in power (right column) is offset from turbine directly downstream. This
percent gain includes the loss of the upstream turbine.
Under positively offset yawed conditions, the power improvements for turbines
negatively offset from the wake center line are greater than what FLORIS
estimates for distances greater of 7 D and more.
Cut-through visualizations of FLORIS and SOWFA 2 diameters (D) in front of
second turbine (top row) and behind the second turbine (remaining rows).
We note here that this effect cannot be modeled through a retuning of
FLORIS. The main parameter available for implementing deflection asymmetry is
a natural deflection angle. However, observing the “profile” of the
baseline SOWFA case, it is not deflected but instead is centered about zero.
Increasing the natural deflection angle in FLORIS would raise the error
observed in the baseline (as well as the negatively yawed case).
Power of a hypothetical turbine behind the second turbine in SOWFA
(solid) and FLORIS (dashed) (a) and percent increase relative to
baseline (b). FLORIS has good agreement in the baseline case but
misses the change in wake behavior obtained in the yawed case in SOWFA.
Further, we cannot simply assume the wake recovers more quickly in positively
yawed cases, because we note that in all cases the depth of the trough of
the deficit is predicted accurately by FLORIS. Therefore, the shape of the
wake is a factor in being able to more accurately predict the power gain due
to yaw misalignment, especially in cases of turbines offset from exactly
downstream.
A first result of the paper is the suggestion that the asymmetry in wake
steering, where positive yaw is superior to negative yaw, is better explained
by vortex–wake interactions than a natural deflection angle. This is more
important for a two-turbine interaction when the downstream turbine is not
directly downstream.
Two-turbine case
The impact of the counter-rotating vortices becomes even more clear when the
simulation includes multiple turbines. In a second simulation, a case is
considered where two turbines are in the flow 7 D apart. The first
turbine is either operating with no yaw misalignment or operating with
25∘ yaw misalignment while the second turbine is always aligned. The
layout is shown in Fig. .
Power of a hypothetical turbine in baseline, yawed (+25∘),
and partial wake. Panels (a) and (c)
shows the power profile 2 diameters (D) before the second turbine, while panels (b) and (d) is
14 D behind.
Horizontal cut-throughs of the flow at hub height in SOWFA and FLORIS are
compared in Fig. . The most striking observation is
that in the SOWFA case, the second turbine's wake appears to be deflected,
even though that turbine is aligned to the flow. In other words, the second
wake appears to also be steered. We will refer to this phenomena as
“secondary steering”. This is not predicted by FLORIS. If we observe a
cut-through at 7 D downstream of the second turbine, we see that
there is a deflection of the wake of the second non-yawed turbine (see
Fig. ).
Combining observations from Figs. and
, we observe that FLORIS expects the wake
of the second turbine to be impacted by the first wake primarily through
reduced inflow velocity and increased turbulence. Both of these effects do
not lead to the deflection of the second wake. In this case, the second wake
is significantly deflected in SOWFA. This deflection appears to be explained
as a combination of the rotating wake of the second turbine, with the top
vortex generated by the first yawed turbine. Considering the impact on power
of a hypothetical third turbine defined 7 D downstream of the second,
the difference between FLORIS and SOWFA is substantial. As seen in
Fig. , FLORIS expects a maximum gain for the
three-turbine total of approximately 7 %, where SOWFA predicts a total
power gain of 17 %. Also, SOWFA finds some locations where the three-turbine
array loses power, while FLORIS does not.
Layout and numbering of turbines in a turbine array case for both
SOWFA and FLORIS.
Discussion of secondary steering
In the previous section, the concept of “secondary steering” is introduced,
wherein a steered wake causes a deflection of the wake of a downstream
turbine that is itself not yawed. This has important implications for wind
farm controller design, and it is critical to understand the driving
mechanisms.
Change in turbine power relative to baseline for each turbine across
the various scenarios in both SOWFA and FLORIS.
Change in total power for SOWFA and FLORIS across the cases.
In this section, we consider an alternative explanation for the observed
phenomena and discrepancy with the FLORIS engineering model. In the previous
section, the vortices generated by wake steering are suggested as the cause
of the “secondary steering” phenomena, because they can be seen in flow
analysis to generate persistent cross flows that continue after the
combination of wake with the second turbine.
Cut-through visualizations of SOWFA following each row in the
turbine array scenario “yawAll”.
However, a possible alternative explanation is that the first deflected wake
is producing a partial wake scenario. FLORIS' wake combination model, as
described earlier, is based on sum of squares. Given that
show that sum-of-squares superposition, as is used in
FLORIS, has an error in prediction relative to newer methods, this could be
the explanation for the discrepancy; i.e., partial wake overlap leads to an
apparent secondary steering and improved wake combination models in FLORIS
would resolve the discrepancy.
To test this, a new SOWFA simulation is run, similar to the two-turbine cases
described in the previous section and shown in Fig. .
However, in this case, the front turbine is moved down 0.25 D. In this
configuration the wake of the upstream turbine overlaps the downstream
turbine in a similar location as the steered wake of the originally located
turbine. However, in this case the generated vortices are not produced.
Figure shows the results of this new comparison. In the
left column, the wake “profile” 2 D upstream of the downstream turbine is
shown in both FLORIS and SOWFA. The “partial” wake case shows a deficit in
a similar location to the yawed case. In the right column are the
“profiles” from FLORIS and SOWFA 14 D after the downstream turbine. In the
upper FLORIS figure, you can see that FLORIS assumes that both yawing and
translating the front turbines will cause the power deficit far downstream to
be both shifted a little bit, and in a similar way. However, SOWFA shows that
while the FLORIS prediction of the combined partial wake is not as accurate
as its prediction of the incoming single wake (as could be expected from
), the substantial change in the yawed case is much
more different than FLORIS' prediction. Note for example the minimum of the
“profile” of the yawed wake far downstream is further deflected than the
incoming steered wake. This is the “secondary steering” and probably cannot
be modeled as combination of partial overlap only, as in that case the
minimum should appear in between the minimum of the two wakes to be combined.
Multiple-turbine case
Building on the results from the three-turbine case, a final case simulates a
tightly spaced wind farm and is used to further explore the importance of
these counter-rotating vortices generated under yawed conditions. A
12-turbine wind farm, shown in Fig. , is modeled in
both SOWFA and FLORIS. The case uses the same inflow, as well as runtime
(2000 s) and averaging time (1600 s) of all previous cases.
This layout affords the opportunity to assess how the consideration of
vortices impacts previous assumptions of wake steering. If wake steering only
deflects wakes to the right or the left of a downstream turbine, then it is
possible to incidentally steer a wake into a different turbine operating
nearby. This description suggests that wake steering will be difficult in
situations where a turbine's wake cannot be directed easily into empty space.
However, noting that vortices and wakes combine in a profitable manner when
wakes interacted going downstream, we can speculate that vortices can provide
a constructive mechanism for wakes located near to each other laterally as
well.
Additionally, in FLORIS as currently modeled, it is expected that although
the three horizontal rows of turbines are tightly spaced, the effect of
simultaneously applying wake steering to turbines 0, 1, and 2 would be
equivalent to the super-position of applying wake steering to each row
individually. However, in SOWFA, the generation of these large-scale
structures, i.e., counter-rotating vortices, influence each other and can
combine in ways that are not captured in the current engineering model.
We ran five simulations of the scenario in Fig. , one
in which all turbines operate aligned (“baseline”), three where only one of
the upstream turbines is yawed (“yaw0,” “yaw1,” and “yaw2”), and a
final where all three are yawed (“yawAll”). Then in the analysis, we can
compare the results of summing the effects of individually yawed turbines
from separate simulations (“sumInd”) in post-processing to the case of
simultaneously yawing all turbines within the simulation (“yawAll”).
Figure shows the change in power from baseline, for
each turbine, for SOWFA and FLORIS. We note that the power predicted for the
baseline case is 13.05 MW for FLORIS and 13.107 MW for SOWFA, which
indicates good agreement.
For the first row, which is the upstream turbines implementing the yaw
misalignment, the losses between SOWFA and FLORIS are similar, and small
differences between individual and simultaneous yawing are observed. However,
in the second row, while FLORIS continues to show no difference between
individually and simultaneously yawed conditions, SOWFA shows a consistent
gain when yawing is simultaneously applied versus summing of individual yaw
misalignment effect (“yawInd”).
In the third row, as indicated in the earlier three-turbine analysis, FLORIS
sees no impact on turbine power, whereas SOWFA observes an increase and a
difference between individual and simultaneous yawing. This continues to a
lesser extent in the fourth row, now a full 21 D behind the yawed
turbines.
The summed turbine power is shown in Fig. . Again, FLORIS
underestimates the power increase from the later rows and assumes that
individually applied yaw offsets can be summed to the whole, while SOWFA
shows an increase from simultaneous application. Figure
shows cut-throughs following each of the rows in the “yawAll” simulation.
Most notably, it appears that the counter-rotating vortices that are
generated from the three upstream turbines are combining to have a larger
impact on the downstream turbines. Just by operating the upstream turbines
under misaligned conditions, these large-scale structures are generated and
propagate throughout the farm.
Conclusions
In this paper, the role of flow structures, particularly a pair of
counter-rotating vortices, generated in wind farm control through yaw
misalignment was investigated. These vortices were shown to be important in
(1) deforming the shape of the wake, (2) explaining the asymmetry of
efficacy in wake steering of oppositely signed yaw angles (rather than the
currently used natural deflection angle), and (3) understanding how a
“steered” wake interacts with a downstream wake and with laterally adjacent
wakes. These findings are critical for developing an effective, robust
strategy for wind farm control.
One important finding of the paper was that, because of the presence of these
vortices, a steered wake can deflect the wake of a downstream turbine, even
if that turbine is not yawed, a process called “secondary steering”. A
second finding was that combinations of wakes from yawed turbines are shown
to involve merging of generated cross flows. These combinations can lead to
changes in power generation that are different then adding the changes of
yawing individual turbines.
In ongoing research at NREL, new engineering wake models which contain these
behaviors due to the generated vortices are under development to be
incorporated into FLORIS. Once completed these new models will be compared to
similar SOWFA data sets to determine whether they can resolve all
discrepancies. Such new models can then be used to develop new wind farm
controllers. These new wind farm controllers can be optimized to take
advantage of the controllability afforded by the vortices ability to
manipulate the flow and will yield a more powerful form of wake steering than
currently exists.
Data can be shared on request but are not available on a public repository.
The authors declare that they have no conflict of
interest.
Acknowledgements
The Alliance for Sustainable Energy, LLC (Alliance) is the manager and
operator of the National Renewable Energy Laboratory (NREL). NREL is a
national laboratory of the US Department of Energy, Office of Energy
Efficiency and Renewable Energy. This work was authored by the Alliance and
supported by the US Department of Energy under contract no.
DE-AC36-08GO28308. Funding was provided by the US Department of Energy Wind
Energy Technologies Office. The views expressed in the article do not
necessarily represent the views of the US Department of Energy or the US
government. The US government retains and the publisher, by accepting the
article for publication, acknowledges that the US government retains a
nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce
the published form of this work, or allow others to do so, for US
government purposes. Edited by: Carlo L.
Bottasso Reviewed by: two anonymous referees
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