In this paper, a new calculation procedure to improve the accuracy of the
Jensen wake model for operating wind farms is proposed. In this procedure, the
wake decay constant is updated locally at each wind turbine based on the
turbulence intensity measurement provided by the nacelle anemometer. This
procedure was tested against experimental data at the Sole
du Moulin Vieux (SMV) onshore wind farm in France and the Horns Rev-I offshore wind farm in
Denmark. Results indicate that the wake deficit at each wind turbine is
described more accurately than when using the original model, reducing the
error from 15 % to 20 % to approximately 5 %. Furthermore, this
new model properly calibrated for the SMV wind farm is then used for
coordinated control purposes. Assuming an axial induction control strategy,
and following a model predictive approach, new power settings leading to an
increased overall power production of the farm are derived. Power gains found
are on the order of 2.5 % for a two-wind-turbine case with close spacing
and 1 % to 1.5 % for a row of five wind turbines with a larger
spacing. Finally, the uncertainty of the updated Jensen model is quantified
considering the model inputs. When checked against the predicted power gain,
the uncertainty of the model estimations is seen to be excessive, reaching
approximately 4 %, which indicates the difficulty of field observations
for such a gain. Nevertheless, the optimized settings are to be implemented
during a field test campaign at SMV wind farm in the scope of the national
project SMARTEOLE.
Introduction
Wind turbines are aggregated together in wind farms to take advantage of
economies of scale and reduce overall costs . However,
this creates wake interactions between the turbines which are responsible for
an increase in mechanical loads and a decrease in power production. It is
generally not possible to avoid completely these interactions due to
constraints imposed on the development of wind farms, and moreover in some
cases wake effects are still persistent at significant distances downstream,
up to 10 to 15 diameters .
To reduce these effects and improve wind farm efficiency and sustainability,
wind farm coordinated control strategies are currently investigated. Contrary
to the state-of-the-art control, in which all turbines maximize their own
power production, coordinated control aims at controlling turbines at a wind
farm scale to optimize its overall output. Two different strategies are
mainly considered to achieve this goal: either the upwind turbines are
curtailed to leave more kinetic energy downstream or they are yawed to
deflect the wake away from the downwind turbines.
Results from simulations show that small gains in power production are indeed
possible ; however, they also underline their high
variability with incoming wind conditions . It is
therefore not known to what extent these gains can be reproduced in an
operating wind farm where wind conditions are fluctuating constantly and
significantly. Very few full-scale field tests have been realized to
investigate this question. The concepts of “heat and flux”
and “controlling wind” were
studied some years ago at the Energy research Centre of the Netherlands (ECN) and more
recently the National Renewable Energy Laboratory (NREL) provided in
a field test of their “yaw-based wake steering”
method in an Envision offshore wind farm. They tend to confirm that gains can
be achieved in practice; however, in all cases, uncertainties remain high, and
it is therefore difficult to give a definite conclusion.
Other full-scale field tests are currently being held in France in the scope
of the French national project SMARTEOLE. They are organized in an operating
wind farm owned by ENGIE Green, Sole du Moulin Vieux (SMV), in which
different curtailment and yaw offset strategies are studied. The main
objective of these tests is to investigate the relevance of these strategies
on wind turbine power production and loads, and determine whether they could
prove beneficial when applied on commercial wind farms. A first experiment
campaign was realized between December 2015 and April 2016 and was dedicated
to axial induction control strategy. An intentionally high level of
curtailment was applied on a wind turbine of the farm so that changes in its
emitted wake could be observed from the analysis of downstream active power
data. Even though no increase in aggregated power production was expected, a
first analysis of wind turbine power production in the farm showed that part
of the lost power at the upstream turbine could be retrieved downstream
.
The goal of this paper is to use the knowledge gained during the first
campaign to provide new optimized control commands that could be implemented
in a second field campaign and hopefully lead to an increase in the
aggregated power production of the farm. As SMV is a commercial wind farm,
these commands must be easily applicable without modifying the wind turbine
control system; thus, a model predictive approach is followed to determine the
optimal de-rating to be applied as a function of wind speed and direction. To
limit computational costs and the complexity of the optimization process,
fast and simple models are considered. Hence, simplified engineering models
are to be applied and the main issue when following this kind of approach is
making sure that they are accurately capturing the wake deficit at each wind
turbine. Consequently, the data recorded during the first field test campaign
are analysed further and used to propose a new tuning of the widely used
Jensen model . In this new method, the wake decay
constant is expressed at each wind turbine based on the local measurement of
turbulence intensity provided by the nacelle anemometer. The resulting wake
deficit appears to be more consistent with the observed data at SMV wind farm
than when using a constant value, and this calculation procedure is also
validated considering experimental data from the Horns Rev-I offshore wind
farm.
The rest of this paper is organized as follows. In Sect. ,
the wind farm and the experimental setup used during the first field test
campaign are shortly detailed. Section describes the
principle of the tuned Jensen model, and its performance compared to the
original model is assessed in Sect. . This tuned model
is then used in Sect. alongside a simple
cT estimation procedure to predict in two study cases at SMV wind
farm the optimized settings leading to an increase in overall wind farm
production. Uncertainty of the model estimation is also quantified in this
section and constraints related to field implementation are briefly
discussed. Finally, Sect. provides a summary of the
paper and conclusions.
Experimental setup
Sole du Moulin Vieux is a commercial wind farm owned by ENGIE Green and
located at Ablaincourt-Pressoir in the region Hauts-de-France, approximately
midway between Paris and Lille. Figure shows the layout
of the farm with the interdistances between the turbines and the main
direction angles used in this paper. It consists of seven Senvion REpower MM82
2050 kW wind turbines of 80 m hub height that were commissioned in two steps:
the first five turbines (SMV1 to SMV5) were put in service in 2009, while the
two last ones (SMV6 and SMV7) were installed 4 years later in 2013. The
site is not complex, with a very flat terrain composed mainly of grasslands,
with the exception of a small forest located south of the farm.
Layout of the SMV wind farm and location of wind measurement
devices. Interdistances between
the wind turbines are expressed in rotor diameters (with D=82 m), while
red arrows indicate the main wind direction angles used in this paper.
Long-term wind rose observed at the site of the SMV wind
farm (a) and Senvion MM82 guaranteed power and thrust coefficient
(cT) curves (b).
It can be seen that wind turbines are more or less aligned on a north–south
axis, while the prevailing wind direction is south-west, as seen on the
long-term wind rose of Fig. a. This particular wind
farm was chosen for the field test campaigns of the SMARTEOLE project because
of the proximity with ENGIE Green maintenance centre (located 5 km away from
the farm) and the wake events SMV6–SMV5. Indeed, due to development
constraints, these two turbines were installed very close from each other
(only 305 m, i.e. 3.7 D) and aligned with prevailing wind directions. In
this paper, supervisory control and data acquisition (SCADA) data from the
seven turbines are analysed along
with data from a 80 m met mast and a ground-based lidar (Windcube V1). The
location of these sensors is indicated in Fig. .
Modification of the Jensen modelOriginal model
The Jensen model as it was originally developed by and
is introduced briefly here. In this model, the wake grows
linearly at a rate driven by a coefficient kw called wake decay constant
(WDC) or wake expansion coefficient. The wind speed deficit δw in
the wake is assumed to be uniform, axis-symmetric and depends only on the
downstream distance x and the upstream wind turbine thrust coefficient
cT. It can be computed using mass conservation and can be expressed as
UwU0=1-δw=1-1-1-cT1+kwx/R2,
where U0 is the incoming wind speed at the upstream wind turbine,
Uw the velocity in the wake and R the radius of the upstream rotor.
When summing the wakes from two or more upwind rotors, wind speed deficits
are aggregated via quadratic sum. Therefore, the wake deficit δn at
the nth wind turbine of a row is simply given by
δn=∑i=1n-1δi2,
where δi is the wind speed deficit due to wind turbine i.
As indicated earlier, the Jensen model is probably the most widely used wake
model for wind energy engineering applications, and that is mainly due to its
simplicity and robustness. In particular, its very low computational cost
makes it very suitable for optimization purposes, as a high number of
simulations can be run in a very short time. However, although this model
gives a fairly good estimation of the averaged power deficit in a wind farm
, some studies underline its inaccuracy when it
comes to looking at the individual power production of the wind turbines
. This is a crucial issue for power
optimization using coordinated control, given that the production at the
downstream turbines must be predicted as accurately as possible in order to
choose the optimal settings of the upstream turbine.
There is therefore a need for improvement to be able to use this model for
such purposes. Over the past years, some new models have been derived from the
main equation of the Jensen model. They aim at offering a better
representation of the individual wake deficits by introducing new parameters
and equations, while keeping a low computational cost. For example, in
, the equation of momentum conservation is included to
the model and a Gaussian distribution is assumed for the velocity deficit
profile. The multizone model developed by is also Jensen based
and considers three different areas in the wake, each with its own wake decay
constant. Description of wind turbine wakes is indeed very much improved with
these models; however, they can be relatively difficult to calibrate, as they
consider up to 10 parameters that need to be tuned properly
.
In this paper, a very simple tuning of the original Jensen model is proposed
based on the measure of local turbulence intensity (TI). The idea is to keep
the simplicity of calibration and robustness of the model while improving its
accuracy. As it will be discussed in the next section, and shown later in
Sect. , taking turbulence intensity into account when
tuning the model already significantly improves the performance of the model
and offers a fairly good representation of the velocity deficit along a row
of turbines, both onshore and offshore.
Tuning of the model
As can be seen in Eq. (), there is only one parameter to
be tuned in the Jensen model: the wake decay constant. This empirical
constant is supposed to vary from one wind farm to another but generally the
two recommended values of 0.075 and 0.05 are used for onshore and offshore
wind farms, respectively . In some studies, it is also expressed
more specifically as a function of the particular conditions at the wind
farm, using, for example, the roughness length and the atmospheric stability
or the ambient turbulence intensity
. The link between wake growth and TI was pointed out
by , but more recent studies, based on wind tunnel, large
eddy simulations (LESs), Reynolds-averaged Navier–Stokes (RANS) simulations and
full-scale turbine data, clearly identify TI as one of the most influencing
parameters on the wake growth and magnitude of the wake deficits
.
It is known that TI varies significantly inside a wind farm, as the
wake-added TI from upstream wind turbines is added to the ambient TI
. Keeping the
same wake decay constant for all wind turbines in the farm can therefore lead
to errors in prediction of individual power production. The wake deficit is
underestimated at the first few downstream turbines and overestimated
further down the row , or vice versa
. Consequently, it appears more accurate to assign
a new wake decay constant for each wind turbine that would be directly linked
to the local value of TI rather than considering an averaged value for the
complete wind farm.
This strategy was followed in and an expression between
the wake decay constant and the local TI was proposed on the basis of LES
data:
kw=0.3837(TI)mod+0.003678,
where (TI)mod is the modelled local TI obtained through the
combination of ambient and wake-added TI, the latter being estimated thanks
to the empirical equation developed by . As in this
present paper SCADA data are available, it was rather decided to use the
direct measurement of turbulence intensity provided at each wind turbine
rather than relying on such a generic expression. In the next section,
several methods are presented that can be used to estimate TI from SCADA. A
direct proportionality is considered between kw and the measured
TI, (TI)meas. This was done in order to keep the same
simplicity as in the original Jensen model, i.e. to have only one parameter
to calibrate, the constant c:
kw=c(TI)meas.
It should be noted that the tuning of the wake decay constant is based on TI
only. Although TI is probably the most critical parameter, some studies
underline the link between the variation of cT and kw. Accordingly, in Sect. 4, the tuning
of the Jensen model is evaluated in the constant cT region (see
Fig. 2) in order to isolate the local turbulence effects on the wake
expansion. However, this is no longer true in Sect. ,
where the model is used in an optimization process involving axial induction
control, whose purpose is precisely to change the cT of upstream
turbines.
Estimating TI from SCADA
There are several ways to assess the incoming wind speed from ordinary SCADA
signals, all with their advantages and drawbacks. These different methods are
presented in this section and they can all be used to derive a local
estimation of TI which is a required input for the wake model presented
above. Alternative methods using sensors that are usually not installed on
wind turbines (e.g. lidars or spinner anemometers) are not developed here but
could also fulfill the same purpose.
The first and most obvious way to obtain a wind speed measurement from SCADA
is to consider the nacelle wind speed signal (NWS) emitted by the nacelle
anemometers installed on the wind turbine. However, these sensors are located
behind the rotor and are therefore exposed to a highly distorted flow
. They cannot be relied on to provide an accurate and
instantaneous wind speed measurement, but when it comes to considering local
TI they might be good enough as only 10 min average and standard deviation
values will be involved.
Comparison of wind speed
measurements at SMV5 (for nacelle wind speed, power wind speed and rotor
effective wind speed) and at external sensors (met mast and Windcube). No
sector filtering was applied to the data, explaining the scatter when
comparing sensors at different locations.
Another wind speed measurement can easily be obtained from the active power
production signal and the guaranteed power curve of the wind turbine (or a
measured power curve). This new signal, labelled here as power curve wind
speed (PWS), is generally more reliable than the NWS since the sensor is the
wind turbine itself. Also, due to rotor inertia and the fact that the wind
speed derived using this method is averaged over the whole rotor area, small
fluctuations of the wind flow will be filtered out, resulting in a much
smoother signal. The main issue regarding this method is its limited
applicability: it cannot be used above rated wind speed or during
down-regulation and therefore is unsuitable for wind farm coordinated
control purposes.
In order to solve this problem, a third way was developed in the scope of the
PossPOW project by to calculate the rotor effective
wind speed (REWS) of a wind turbine in these particular situations. In this
method, the REWS is calculated from three SCADA signals (active power, rotor
speed and pitch angle) and a cP model. It must be ensured that the
chosen cP model is fitting as best as possible to the real
cP curve. Alternatively, a cP look-up table can also be
used, when available. In this paper, the cP model and the value of
its parameters are the same as those presented in ,
as they proved to offer a good performance for wind turbines in the same
range (rated power of 2 MW with a diameter of about 80 m) as the ones studied
here.
Overall, 4 months of 1 Hz SCADA data were processed
(1 December 2015–31 March 2016) for the wind turbine SMV5 to compute 10 min
average wind speed and turbulence intensity using these three different
methods. Figure compares these wind speed values
with measurements from reference sensors (met mast and Windcube). No sector
filtering was applied to the data; consequently, a significant scatter can be
found when comparing two sensors at different locations due to wake effects.
It can be observed that these results are very similar to the ones that were
obtained at the Lillgrund offshore wind farm and were presented in
, showing a very nice correlation between the PWS and
the REWS and more scatter when considering the NWS. This is because the wind
speeds calculated through the REWS or PWS methods contain a geometrical
averaging of the wind flow over the whole surface of the rotor which smooths
out wind speed fluctuations . On the other hand, NWS and
met mast are point-wise measurements and therefore are affected by every
single variation of the wind speed.
Comparison of TI measurements at SMV5 (for nacelle wind speed, power
wind speed and rotor effective wind speed) and at external sensors (met mast
and Windcube), represented against wind direction. Error bars shows the
68 % normalized confidence interval (represented for NWS but a same order
of magnitude can be expected for other sensors in the same wind direction
bin). Vertical lines indicate position of wakes for SMV5 sensors and
Windcube.
In Fig. , the turbulence intensity calculated from all
these signals is represented against wind direction (5∘ bins). It can
be seen that outside any wake events, the TI obtained through the NWS signal
is of same order of magnitude than the one measured by external sensors. On
the contrary, TI obtained with either the PWS or the REWS signals is
approximately twice as low. As previously mentioned, this is explained by the
geometrical averaging provided by these two methods.
All wake events are clearly captured by any of the TI signals. At a
particular location of a wake, the TI measured is about twice as high
compared to the free-stream conditions, indicating that wake-added TI is
significant and can be measured reliably with a SCADA signal. Consequently,
any of these TI signals could be used as input for the tuned wake model; it
is simply needed to adjust accordingly the value of the constant c in
Eq. (). However, for the rest of this paper, only the NWS
TI could be considered in practice, given that the PWS signal cannot be used
for down-regulation purposes, while the REWS method requires acquisition and
processing of second-wise data, which were not available for some of the
turbines in the wind farm.
Layout of Horns Rev-I offshore wind farm with turbine spacing and
wind direction angle used in this study (a) and Vestas V80-2MW
guaranteed power and thrust coefficient (cT) curves (b).
Validation of the tuning strategyData filtering and processing
The performance of the tuned Jensen model is now assessed in this section and
compared to the results obtained for the original model. Production data from
two wind farms are considered: the onshore SMV wind farm and the offshore
wind farm of Horns Rev-I (layout of the farm and power and cT
curves for the Vestas V80-2MW wind turbines are shown in
Fig. ). In both cases, the normalized power production
along a row of turbines is analysed. The data are filtered to keep only the
10 min periods when all wind turbines are in operation and the incoming wind
direction is within a ±5∘ interval around the main orientation of
the row. Another filtering is done based on the power production of the most
upstream turbine in order to consider only the 10 min periods when wind
turbines are all in the constant cT region (region II of the
power curve).
For each valid 10 min period, the power production deficit at each wind
turbine is simulated for both the original and the tuned models. When
considering the original Jensen model, the value of kw is
calibrated using the first wake event of the row. In the case of the tuned
wake decay constant, the value of the constant c in
Eq. () is adjusted roughly to limit the individual error
of the model along the row. The value used for (TI)meas is the
10 min TI measurement from the NWS signal. The normalized simulated deficits
are then averaged over all valid 10 min periods and compared with the
normalized measured deficits. The averaged value of the NWS TI signal at each
wind turbine is also drawn to show the variation of the measured TI along the
row of turbine. Error bars in Figs.
and indicate the 68 % normalized confidence
interval.
At SMV wind farm, the power production deficit is studied along row SMV1
to SMV5. The wind direction sector considered is 5±5∘, and
the valid power range for the most upwind wind turbine (SMV1) is fixed to
600–1100 kW to fulfill the constant cT condition. The filtered
data set finally consists of 156 valid 10 min periods recorded between
15 June 2015 and 1 August 2016 (due to small occurrence of northerly winds,
it was needed to consider a longer period than the actual field tests to
gather enough valid data). The wake decay constant for the original Jensen
model was kept as 0.075, the traditional value for onshore wind farm as it
proved to show good performance for the first wake event of the row
SMV1–SMV2.
At Horns Rev-I wind farm, the power production deficit is studied along
row number 5, from HR5 to HR95 (see layout of the farm in
Fig. a). The wind direction sector considered is
270±5∘, and the valid power range for the most upwind wind
turbine (HR5) is fixed to 0–1200 kW to fulfill the constant cT
condition. The filtered data set finally consists of 270 10 min periods
recorded between 16 February 2005 and 25 January 2006. The value for the wake
decay constant of the original Jensen was fixed to 0.09, which is much bigger
than the value of 0.05 traditionally used for offshore wind farms but much
more consistent with the measured deficits. It was already found in other
studies e.g. that using a wake decay constant of 0.05
was clearly overestimating the power deficit for the wind farm of Horns
Rev-I, as it gives narrower wake growth within the wind farm.
Results
The evaluation of the original and the tuned Jensen models on SMV and Horns
Rev-I wind farms is presented in Figs.
and , respectively. In both cases, the normalized deficit
is shown as a function of distance to the most upstream turbine, as well as
the difference between the modelled and the observed deficits at each wind
turbine for different values of wake decay coefficient.
Comparison of the model performance at SMV wind farm. Variation of
experimental and modelled normalized power and turbulence intensity (measured
by the nacelle anemometer) along the row (a) and variation of the
error of the model at each wind turbine for various values of wake decay
constants kw(b). Error bars indicates the 68 %
normalized confidence interval.
Comparison of the model performance at Horns Rev-I wind farm.
Variation of experimental and modelled normalized power and turbulence
intensity (measured by the nacelle anemometer) along the row (a) and
variation of the error of the model at each wind turbine for various values
of wake decay constants kw(b). Error bars indicates the
68 % normalized confidence interval.
It can be seen that the graphs for the two wind farms have a very similar
behavior, with the tuned Jensen model performing better than the original
model. Except for the first wind turbine, the wake deficit calculated with
the original model is always overestimated and the error becomes more
significant towards the downstream direction: from approximately 10 % at the third
turbine of the row, it goes around 15 % to 20 % further downstream.
On the contrary, with the tuned Jensen model, the deficit is captured more
accurately, especially at the wind turbines located in the middle of the row
for which the error is kept at ±5 %. These changes are
consistent with the augmentation of turbulence intensity from the second wind
turbine in the row. Increased TI provides a better mixing between the
disturbed flow in the wake and the undisturbed free flow, which allows a
earlier recovery, both in terms of time and space. This particularity is
taken into account in the tuned Jensen model since the WDC is increased
linearly with TI, while the original Jensen keeping the same WDC all
along the row leads to an overestimation of the deficit.
When analysing the impact of the choice of the constant c linking TI with
the kw in the tuned Jensen model, two observations can be made.
First, it can be seen that the optimal c obtained for each wind farm is
different: 0.75 for SMV wind farm and 0.9 in the case of Horns Rev-I. This
shows the sensitivity of the model to the local conditions and tends to
indicate that a small calibration of the constant will still be needed for
each wind farm to make sure that the wake deficit is correctly modelled. This
site dependency of the Jensen model was already present in its original form;
indeed, in this example, it can be seen that the best WDC obtained for the
offshore wind farm (0.09) is much higher than the recommended values
(0.04–0.05) and the one of the onshore wind farm (0.075).
The second observation is that the modelled wake deficit is varying regularly
when c changes. This ensures that the calibration is as easy and robust as
before, since it is simply needed to tune the value of c until the wake
deficit is described as best as possible. Contrary to the original model, the
accuracy is improved as taking into account the local TI allows a better
representation of the individual wake deficit at each wind turbine.
Consequently, it can be concluded that this tuned Jensen model is providing
an improvement compared with the original model, while keeping the simplicity
of calibration and robustness of the original model. It can thus be used to
define control instructions, as developed in the next section.
Optimization of wind farm power production
After having validated the performance of the tuned Jensen model, it is used
in an optimization process to find the wind turbine settings maximizing their
power performance. Only the axial induction strategy is developed here, due
to its ease of application on a commercial wind turbine. Indeed, it simply
requires to trigger a pre-implemented down-regulated power curve as a
function of incoming wind conditions without modifying the control settings
of the turbine. In practice, only wind speed and direction can be used as
input for triggering a curtailment mode; therefore, power production is
optimized for various wind speed and direction bins.
The hypotheses used during the optimization process are first presented, and
then two study cases at SMV wind farm are analysed. Finally, a study of the
uncertainty of the model outputs is realized based on the data from
Horns-Rev I, and the values obtained are compared with the predicted gains.
cT estimation procedure
Correlation between cP and cT for a Senvion MM82
wind turbine, deduced from the analysis of guaranteed power curve modes for
sound management.
The principle of wind farm power optimization using an axial induction
control strategy is to curtail the upstream wind turbines to gain more energy
on downstream wind turbines. It is hoped that the decrease in the upstream
cT will be high enough to reduce sufficiently the wake deficit so
that the increase in production downstream can compensate for the upstream
cP diminution. Consequently, it is a crucial issue to assess as
accurately as possible how both cP and cT are being
affected by the upstream down-regulation, in order to correctly estimate the
overall production for various curtailment modes.
It is sometimes possible to use look-up tables to link cP and
cT with operational parameters of the wind turbine, such as rotor
speed and pitch angle. However, for this work, no look-up tables were
available, and therefore another method had to be developed. A workaround was
finally found by the analysis of MM82 guaranteed curtailed power curves used
for noise emission reductions. Indeed, when representing cT against
cP, as in Fig. , two different behaviours are
being observed: one below rated wind speed (parabolic relationship) and
another above rated wind speed (linear dependency).
Thus, an empirical relationship could be derived from this analysis, by
fitting a second-order polynomial to the first set of data points and a
first-order polynomial for the second one. The final relationship between
cP and cT used for the optimization process and valid for
an MM82 wind turbine is represented in Eq. () below.
cT=6.1cP2-2.4cP+0.6if6<V<12.5m s-1andcP>0.2cT=1.3cPifV>12.5m s-1
Turbulence intensity distribution
As developed in Sect. , knowing the turbulence intensity is
of primary interest to properly assess the wake deficit. In
Sect. , the TI was calculated in 10 min timescale
resolution to compare the performance of the tuned wake model with the
original one. Here, due to practical constraints, it is not possible to
consider the real-time TI as an input parameter for triggering a curtailment
mode. Instead, it was decided to express the local TI as a function of wind
speed and direction by calculating a TI distribution in the farm.
Consequently, a different WDC is chosen for each wind turbine and each wind
speed and direction bin, so that local TI still has some influence in the
optimization process.
This TI distribution was obtained by averaging the NWS signal of all wind
turbines in the farm in 10∘ direction bins and 1 m s-1 wind
speed bins. The dependency of incoming TI for each wind turbine is
represented for a wind speed of 8 m s-1 on a turbulence intensity rose
in Fig. , alongside with TI measured by the met mast that
can be used for comparison.
TI distribution at each wind turbine used during the optimization
process. This rose is obtained for a wind speed of 8 m s-1 only, but
similar roses were calculated for each wind speed bin. Ambient TI measured at
the met mast is also plotted for comparison.
It can be seen that the TI measured by the wind turbines outside any wake
events is around 9 %–10 %, which is consistent with the met mast
measurements. Some particular terrain effects can nonetheless be observed.
Between 160 and 220∘, the TI measured by SMV7 is increasing up to
12 % to 13 %: this was attributed to the presence of a wood south of
the farm and very close to SMV7 (please refer to the map of the wind farm in
Fig. ). Likewise, an increase of 1 % to 2 % in the
SMV1 TI is observed for wind direction between 340 and 20∘. The
reason for this increase was related the presence of the motorway at the
north of the farm; indeed, the met mast curve shows also a similar increase in
the sector [320∘; 0∘], corresponding to the direction of the
motorway as seen by the met mast location.
Reduction of wake-added TI
In order to describe as accurately as possible the variation of TI in the
farm when optimizing the power production, the influence of the upstream
curtailment on downstream wake-added TI must be taken into account. Indeed,
as the upstream wind turbine is down-regulated, the wake-added TI emitted by
this turbine is reduced. It is expected that this decrease will be more and
more significant as the upwind curtailment increases. Therefore, the TI
distribution presented in the previous section, and calculated for normal
operation conditions, is no longer valid: it must be reduced accordingly with
the percentage of down-regulation applied on the upwind turbine. This is
important especially when considering a row of three turbines (or more),
since the deficit at the third turbine is calculated based on TI at the
second turbine, which is itself dependent on the first turbine curtailment.
To study the impact of upstream down-regulation on downstream wake-added TI,
data from the first field test campaign are considered. Between December 2015
and April 2016, SMV6 was occasionally curtailed of approximately 20 % for
south-western winds (in the direction of alignment SMV6–SMV5). Analysing TI
data provided by the nacelle anemometers, the wake-added TI, TIwa,
can be computed with the following equation:
TIwa=TItot2-TIamb2,
where TItot is the total TI in the wake measured at SMV5 and
TIamb the ambient TI measured at SMV6.
Variation of wake-added TI as a function of wind direction, in
normal operation and during SMV6 curtailment. Error bars indicate the
68 % normalized confidence interval.
Comparison of measured wake-added TI at SMV5 wind turbine between no
curtailment and 20 % curtailment on SMV6, with their 68 % normalized
confidence interval. N/A (not applicable) indicates missing data for some wind direction bins.
Optimization of power production of SMV6 and SMV5. Power curves in
the base and optimized cases (a) and variation of power gain and optimal
SMV6 cP as a function of wind speed for the optimized
case (b).
Ambient and total TI were binned against wind direction (5∘ bin
width) and wake-added TI was deduced for each bin. Results are shown in
Fig. , while numeric values are summarized in
Table . Unfortunately, for the 20 % curtailment case,
only data on the right side of the wake could be exploited. However, it still
provides a very interesting insight of TI reduction with down-regulation as
it covers full wake situation (at 210∘) to partial wake situations
(220–225∘).
It can be observed that the upstream wind turbine curtailment provides a
relatively significant decrease in downstream wake-added TI, as it is reduced
from 14.84 % to 12.50 % for a wind direction of 210∘. As
expected, as wind direction increases and we go from full wake situation to
partial wake situation, reduction of wake-added TI becomes smaller, from
2.34 % to 1.46 %. In this paper, to model the relationship between
percentage reduction of wake-added TI with percentage of upstream
down-regulation, a linear dependency was assumed for a given wake condition:
(%ΔTIwa)=ΔTIwaTIwa=pwake(%DR).
The value of the parameter pwake linking ΔTIwa with %DR is expected to be dependent on the relative
wind direction between the turbines. Consequently, the parameter for full
wake conditions, pfw, will differ from the one for partial wake
conditions, ppw. In this example, where a 20 % down-regulation
was applied, values of pfw≈-0.788 (from the bin
210∘) and ppw≈-1.001 (from the bin 215∘)
could be computed.
In Sect. , dealing with power optimization in a
multiple wake case, reduction of wake-added TI with upstream curtailment is
modelled with the following steps:
First, wake-added TI at each wind turbine in normal operation is calculated
based on the TI distribution presented in Sect. and ambient
TI deduced from the most upstream wind turbine.
Second, as upstream wind turbines are being gradually curtailed in the
optimization process, wake-added TI is adjusted based on
Eq. () above. To simplify the process, only down-regulation
of the closest upstream turbine is considered for the reduction of wake-added
TI. A similar procedure was followed in when modelling
wake-added TI.
Finally, total expected TI at the wind turbine is calculated by inverting
Eq. (). This calculated TI can then be given as input into the local
TI-based wake model to compute the wake deficit at downstream turbines.
Study casesWind turbines SMV5 and SMV6 (single wake case)
The first case to be studied is the SMV6–SMV5 wake event. It is of particular
interest because of the very short spacing between the two wind turbines and
their alignment close to prevailing wind directions. For this study case, a
very simple optimization procedure is used: for each wind speed and relative
wind direction, the cP of SMV6 is gradually decreased up to
20 % of its actual value (and the cT adjusted consequently
based on Eq. ) and the power production of both wind
turbines is computed using the tuned Jensen model. The optimized power curve
for SMV6 is then deduced from all the cP values giving the best
combined production at each wind speed.
Influence of changing relative wind direction. Variation of power
gain (a) and optimal SMV6 cP(b) as a function of
wind speed.
Results are presented in Fig. for full wake
conditions. In Fig. a, power curves for both wind
turbines are plotted, while Fig. b shows the
relative increase in combined power production which is obtained at each wind
speed with the associated amount of curtailment which is applied to SMV6. It
is observed that the maximum gain represents an increase of about 2.5 %
and is found at 7 m s-1 when SMV6 is curtailed by 12 %
(cP decreases from 0.46 to 0.405, while at the same time
cT is reduced from 0.79 to 0.63 according to
Eq. ). More generally, it can be seen that the interest of
coordinated control is limited to the wind speed range 5–11 m s-1,
i.e. when both cP and cT of the upstream turbine are
high. In this range, a small decrease in cP causes a high reduction
of cT, as illustrated on the parabolic cP–cT
relationship of Fig. . As wind speed increases further, the
upstream wind turbine naturally starts to pitch to limit power production to
its nominal value, and therefore axial induction control is no longer
beneficial.
In Fig. , the impact of a changing
relative wind direction on the relevance of applying a coordinated control is studied,
showing the optimal gain that can be expected (Fig. a) and the optimal
amount of curtailment required on SMV6 (Fig. b) as a function of the wind
speed. It is seen that the wind direction sector on which gains can be
observed is particularly narrow. As soon as the full wake condition is no
longer respected, i.e. for relative wind direction above ±5∘, the
benefit of axial induction control drops almost instantly: when wind
direction shifts from 4 to 6∘ at 7 m s-1, gains are reduced
from 2.25 % to approximately 0.6 %. This sensitivity confirms the
very limited applicability of a curtailment strategy for power production
optimization and the difficulty to implement it in a real case situation. As
it is only beneficial on a 10∘ width wind direction sector centred
around full wake conditions, very steady incoming wind conditions are
required to make sure that gains in power production will actually be
observed.
Rows SMV1 to SMV5 (multiple wake case)
The second case to be studied is the row SMV1 to SMV5. The power production
along the row is now studied for full wake conditions and a wind speed of
8 m s-1, for which the coordinated control is expected to give the
highest possible gain. Two different control strategies are being
investigated: in the first one, only the most upstream turbine (SMV1) is being
curtailed, while in the second one each wind turbine is optimally curtailed so
that total power along the row is maximized. In the first case, the optimum
is reached thanks to the same method as in previous section, while for the
second case the following procedure (adapted from ) is used:
Start with no down-regulation applied on the wind turbines: %DRi=0% for i∈{1-5}.
For wind turbine i, from upstream to downstream, find the value %DRi
maximizing power production along the row and considering that all other
%DRj≠i remain constant.
Repeat step 2 until all %DRi values stay constant.
Reduction of wake-added TI was considered as developed in
Sect. . A value pfw≈-0.788 was used for all
wake events in the row except for SMV2 → SMV3, which corresponds to a
partial wake event (the alignment of these two turbines is found for a wind
direction of -2∘). A value of ppw≈-1.001 (deduced
from wind direction bin 215∘ in Table ) was used
instead.
Variation of normalized power at each wind turbine (a),
cumulative relative gain and optimized down-regulation settings (b)
along the row, for full wake conditions (wind direction of 5∘ at
8 m s-1).
Figure shows the result of the process,
with the normalized power production along the row (Fig. a) and the
cumulative relative gain and the percentage of down-regulation at each wind
turbine for the second strategy (Fig. b) (for the first strategy, the same
amount of curtailment is applied to SMV1, while all other wind turbines are
not curtailed). The cumulative relative gain allows following the change of
power provided by the optimization as we move downstream, it is defined at
wind turbine i as
%RGi=100∑j=1iPjopti-∑j=1iPjbase∑j=1iPjbase.
Consequently, the cumulative relative gain at wind turbine SMV5 represents the
total gain obtained thanks to the optimization process.
It can be seen from the figures that both strategies lead to an overall
increase in power production, with the same amount of curtailment imposed on
the most upstream turbine (10 % down-regulation). As seen on the
cumulative relative gain which is positive at the second turbine, the
increase in power at SMV2 is enough to compensate for SMV1 down-regulation.
However, for the first strategy, as downstream wind turbines are not
curtailed, most of the energy released by SMV1 is captured by SMV2 and SMV3
only. The most downstream turbines (SMV4 and SMV5) are only very slightly
benefiting from the down-regulation and total relative increase is limited to
approximately 1 %.
On the contrary, when following the second strategy, the energy made
available by SMV1 down-regulation is more equitably shared between all
downstream turbines. Indeed, SMV3 and SMV4 are also being curtailed so that
high gains can be obtained for SMV5 (as SMV2 is not perfectly aligned with
the rest of the row, it is not beneficial to curtail this turbine). As a
consequence, the cumulative relative gain is decreased at SMV3 and SMV4, but
when considering also SMV5 the total relative increase in power production is
higher than in the first case, reaching almost 1.5 %. This confirms the
idea that the best gains are obtained when each wind turbine is controlled
individually to maximize the overall wind farm output and not their own
power production.
Uncertainty quantification of the calibrated Jensen model
In order to put the optimized wind farm performance into perspective, it is
essential to estimate the uncertainty of the model outputs. Since the
calibration of the model is based on the operational turbine data, the
uncertainty quantification (UQ) is established through the input uncertainty
assessment and its propagation. The uncertainty is defined as the half width
of the 68 % confidence interval, which corresponds to a distance of a
single standard deviation.
Distribution of the uncertainty in the estimated wake velocity by
calibrated Jensen model, (a) the histogram and the boxplot of the
distribution in units (m s-1), (b) the boxplot of the
percentage uncertainty distribution. The median, the boxes, the whiskers and
the outliers are according to Tukey's descriptive statistics
. The red triangles indicate the mean.
In general terms, the uncertainties attached to the SCADA signals are
indicated in the International Electrotechnical Commission (IEC) standards ,
where the main focus is the annual energy production estimates. With the same
focus, investigated the wind direction uncertainty in
particular, which is the most ambivalent input signal to the tuned Jensen
model. Within 10 min intervals, the study showed the uncertainty to be at
the levels of 5∘ for Horns Rev-I wind farm. However, since in this
study the analysis is based on high-frequency data (second-wise data), the
documented value of 3∘ uniform uncertainty in the yaw position signal
is considered for now. For the wind speed input, the dependency
of the uncertainty to the operational range, i.e. regions II and III, is
shown in for effective wind speed and in for
nacelle wind speed. Here, we consider the conservative estimate of
0.3 m s-1 with a Gaussian distribution, where the expected error is
less with 90 % likelihood below the rated region. The uncertainty in wind
speed is propagated through the estimation of TI (see
Sect. ), estimation of kw (see
Eq. ), estimation of cT and finally the
estimation of wake deficit through Eq. . The resulting
uncertainty distributions of the calibrated Jensen model are shown in
Fig. . The uncertainty is propagated in a continuous
time series of 18 h from Horns Rev-I wind farm, using a Monte Carlo analysis
with 1000 realizations per second. The indicators in the boxplots follow
Tukey's descriptive statistics where the boundaries of the
whiskers are the lowest and the highest datum within the 1.5 interquartile
range, IQR, corresponds to ±2.7σ from the mean.
Figure shows that the uncertainty of the calibrated
model output is not normally distributed. This is mainly due to the fact that
along the propagation process, different sources and distributions of
uncertainties are convoluted. It is also seen that there are many outliers in
the distribution, which occur near the rated wind speed, i.e. around the
operational transition between regions II and III as underlined in
. Along that transition region, the assessment of the
cT is highly sensitive to the wind speed (see
Fig. b), causing the propagation of the uncertainty to
diverge. Since for the optimization scenarios discussed above the considered
wind speed are lower, it is concluded that the conservative estimate of the
model uncertainty can be stated as 0.3 m s-1 or, more generally,
4 %.
Towards field implementation
As already mentioned in the introduction of this paper, the optimized control
strategies developed in these case studies are to be tested in a new field
test campaign of the SMARTEOLE project. Through the comparison of the gains
expected via these strategies in Sect. and the
uncertainty quantification of the previous section, it is very important to
note that the tuned Jensen model risks not to provide the reported power
increase in the field tests. In other words, the uncertainty of the model
outputs and control inputs needs to be fully analysed in order to assess the
true performance of the wind farm control approaches. Additionally, in order
to see the full benefit of wind farm control schemes, more “accurate”
sensors/data, more intelligent methods to analyse the data and different
perspectives on how to include the physical complexity of the wind farm flow
into the wake models are also needed.
Furthermore, the tuning of the model in the optimization process was focused
to wind speed and direction only, as in practice these are the only two input
variables that can easily be used for triggering the axial induction control
for a wind farm operator having a limited access to the turbine control
parameters. In reality, because of the highly fluctuating wind conditions
(changes in wind speed, wind direction, turbulence intensity and atmospheric
stability), a more complicated tuning would be required in order to decrease
the risk of implementing innovative control strategies. Ideally, it would be
more suitable to tune the WDC every 10 min (or at even shorter time
periods) based on the latest measurement of wind speed, direction and local
TI and then calculate in real time the optimized settings to be applied at
each wind turbine. Since it would enable to include more dynamics and
complexity of the local flow (both in terms of time and space), model
adequacy would further improve and the resulting uncertainty would be
reduced. However, this kind of scenario would also require much larger
access to the wind turbine control parameters and goes beyond the scope of
this present study.
Finally, it must also be mentioned that while the axial induction strategy
seems to propose a limited benefit in terms of increased combined production
compared to other strategies such as wake steering, its impact on wind
turbine loads should be much more profitable. Indeed, thanks to the
application of a curtailment on the upstream wind turbine, reduction in
thrust and in the tower loads can be expected. Downstream, a decrease in the
fatigue loading of the turbines can be predicted due to the reduction in the
wake-added TI, as illustrated in Fig. above. These
results are interesting and highly relevant since load reduction can be
related to an increased lifetime and therefore a decrease in overall cost of
energy.
Conclusions
Field tests are currently being held on a commercial wind farm in France,
Sole du Moulin Vieux, in the scope of a national project. The objectives of
these tests are to study the potential of wind farm coordinated control
strategies for power optimization and load reduction. In this paper, data
from the first campaign were analysed in detail to propose a new tuning of the
widely used Jensen model. This modification, based on the local measurement
of turbulence intensity given by the nacelle anemometer, proved to be enough
to improve the accuracy of the model and describe more precisely the
individual wake deficit at each wind turbine. The simplicity of calibration
and robustness of the original model is kept since there is still only one
parameter to calibrate. This new tuning strategy was validated with data from
SMV wind farm but also with data from a row of turbines at Horns Rev-I
offshore wind farm.
Using this methodology, power production was optimized in two study cases at
SMV wind farm. An axial induction strategy was considered with a model
predictive approach, and a cT estimation procedure was developed in
order to assess as accurately as possible the combined evolution of
cP and cT during down-regulation of the wind turbines.
Results from the optimization process show that a gain of 1 % to 2 %
in aggregated power production can be expected for full wake conditions and
wind speed between 7 and 9 m s-1. As wind direction changes or wind
speed increases further, gains in power production obtained through the
upstream wind turbine down-regulation quickly drop to zero, underlining the
limited applicability of an axial induction strategy for power production
optimization. Moreover, these gains have to be taken cautiously since some
studies have already underlined discrepancies between model predictions and
actual power productions of wind turbines, especially when variation of the
wake decay constant due to changes in cT was not taken into account
. These results are in line with the performed
uncertainty assessment of the tuned Jensen model, where the uncertainty is
shown to be more than the predicted power increase. This also indicates the
importance of an extensive uncertainty quantification on the simplified flow
models to correctly evaluate the resulting wind farm control strategies.
However, even if the model is not as accurate as it could be, it is hoped
that it is still good enough to give indications about optimal settings where
gains would possibly be found. Based on the results derived in this paper, a
new field campaign was realized between December 2017 and February 2018,
during which a curtailment mode was applied to wind turbine SMV6. Data are
currently being processed to determine whether augmentation in combined power
production could be achieved. Furthermore, data from strain gauges installed
in the blades still have to be analysed to study the impact of axial
induction control on wind turbine fatigue loads. Given the quantified
uncertainty, even though no gains in power production are obtained, a
reduction in loads can be expected.
Future work about wind farm coordinated control realized in the scope of the
SMARTEOLE project will also include the analysis of the potential of the wake
steering strategy and the study of the dynamics involved when a wind turbine
is curtailed or yawed.
Data availability
As the underlying research data were collected on commercial
wind farms, they could not be made publicly available. Please contact the
corresponding author if you have any questions regarding the data used in
this paper.
Author contributions
This work was undertaken by TD as a Master's thesis project
under the supervision of OC, NG, GG and TG. TD developed the tuning of the
model, did the experimental data analysis and the optimization of wind farm
production, and wrote the article. Preprocessing of Horns
Rev-I data and uncertainty
quantification of the model was realized by TG. All authors had a part in
reviewing and editing the manuscript.
Competing interests
The authors declare that they have no conflict of
interest.
Acknowledgements
The authors would like to thank all the engineers and technicians from the
Engie Green O&M centre for their help in setting up the experimental field
tests of the SMARTEOLE project.
Financial support
This research has been supported by the Agence Nationale de
la Recherche in the scope of the project SMARTEOLE (grant no. ANR-14-CE05-0034).
Review statement
This paper was edited by Raúl Bayoán Cal and reviewed by
two anonymous referees.
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