The prospects of active wake deflection control to mitigate wake-induced power losses in wind farms have been demonstrated by large eddy simulations, wind tunnel experiments, and recent field tests. However, it has not yet been fully understood how the yaw control of wind farms should take into account the variability in current environmental conditions in the field and the uncertainty in their measurements. This research investigated the influence of dynamic wind direction changes on active wake deflection by intended yaw misalignment. For this purpose the wake model FLORIS was used together with wind direction measurements recorded at an onshore meteorological mast in flat terrain. The analysis showed that active wake deflection has a high sensitivity towards short-term wind directional changes. This can lead to an increased yaw activity of the turbines. Fluctuations and uncertainties can cause the attempt to increase the power output to fail. Therefore a methodology to optimize the yaw control algorithm for active wake deflection was introduced, which considers dynamic wind direction changes and inaccuracies in the determination of the wind direction. The evaluation based on real wind direction time series confirmed that the robust control algorithm can be tailored to specific meteorological and wind farm conditions and that it can indeed achieve an overall power increase in realistic inflow conditions. Furthermore recommendations for the implementation are given which could combine the robust behaviour with reduced yaw activity.

In recent years, more and more wind turbines have been installed in ever
larger wind farms. On the one hand, this has advantages in logistics, network
connection, maintenance, and the utilization of the limited suitable
locations. On the other hand, this leads to situations where turbines are
considerably more affected by harmful wake conditions. Downstream turbines
are experiencing higher turbulence, which is generally associated with larger
fatigue loads, and lower wind speeds, which results in a lower energy yield.
In order to counteract this, different strategies are being investigated that
try to reduce these negative wake effects. One approach to achieve this is
active wake deflection by intended yaw misalignment, which was already
investigated by

The contribution of this article continues the investigations of

The objectives of this paper are (1) to analyse the impact of dynamical wind direction changes on active wake deflection strategies, (2) to introduce a methodology to optimize the yaw angle adjustment in a wind farm by taking these fluctuations and measurement uncertainties into account and (3) to propose open-loop control algorithms for active wake deflection in a wind farm.

In this paper, a quantitative analysis of wind direction variability and its
effect on active wake deflection is carried out. Therefore, first the
employed model for wake deflection (Sect.

The investigation in this article is based on the FLOw Redirection and
Induction in Steady state (FLORIS) model

FLORIS extends the popular Jensen wake model

A schematic visualization of the wake model in FLORIS, containing
three discrete wake zones. Furthermore, active wake deflection by purposely
misaligning the turbine rotor with the flow is shown (cf. Fig. 4a in

These three wake zones each contain their own set of parameters for wake
recovery and expansion, increasing the model's flexibility and fidelity.
Furthermore, FLORIS uses the simplified analytical model from

In short, FLORIS predicts the time-averaged steady-state conditions of the
flow and each turbine's power capture as a function of each turbine's axial
induction (i.e. a parameterization of the generator torque and blade pitch
angles), yaw angle, and atmospheric conditions inside a given farm. The
applicability of the model has been demonstrated in high-fidelity simulations
(e.g.

The analyses in this article were carried out on the basis of measurements at
a meteorological mast (referred to as a met. mast hereafter). In

The wind direction angle can be expressed in radians

The wind direction

Exemplary 5 min time series of wind direction measurements recorded
at an onshore test site in northern Germany sampled at

The turbulent changes in the wind direction are in contrast to the slowly
reacting yaw mechanism of utility-scale wind turbines. The deviation between the
wind direction and the yaw angle of the turbine is usually averaged over
several minutes and a threshold for the deviation is used to keep the turbine
from constantly yawing

For the exemplary time series, both representations demonstrate the
similarity to the normal distribution reasonably well, which agrees with the
findings of

In order to optimize the yaw settings of the turbines in a wind farm, we
assume that the total power output of a wind farm consisting of

Next we introduce two different optimizations of the yaw angles which
differ in the description of the wind direction variability. Firstly, we are
neglecting wind direction changes within the investigated time period. The
optimization problem formulated in Eq. (

To solve the integral in Eq. (

A number of algorithms can be used for the computation of these kinds of
optimization problems, including the intuitive game theoretic approach
presented in

In order to evaluate the control strategies derived from the conventional and
the robust optimization, a case study is performed for a reference test wind
farm. It consists of nine NREL 5-MW turbines

Layout of the reference wind farm. The reference turbine (T32) is marked in red.

With this layout the distances between adjacent turbines are 3D
horizontally, 4D vertically, and 5D diagonally. These values are comparable
to the dense spacing in the offshore wind farm Lillgrund

The focus of the investigation is to determine the sensitivity of the control
strategies with regard to wind direction variability and uncertainty. In
order to perform this investigation with realistic data, wind direction
measurements from a met. mast at

Wind rose of 1

In this section, the method for investigating the statistical properties of
wind direction changes using measurement data is examined
(Sect.

As mentioned in Sect.

However, the dynamics of the wind direction are not the only uncertainty
factor in rotor alignment. In addition, there are inaccuracies in the
determination of the wind direction and the alignment of the turbine. Such
types of measurement errors are commonly assumed to be independent and
normally distributed

For these reasons, a normal distribution is chosen for the probability
density function of the measured wind direction in the robust optimization,
which represents the assumed uncertainty and variability in the wind
direction. This is in accordance with

Since the support of the normal distribution is unrestricted, we limit the
range to

The solutions of the conventional and the robust optimization
are the optimal yaw angles of all the turbines for all wind directions. In
Fig.

Optimized yaw angles of the centre turbine in the southernmost row
(T32) for three different robustness parameters

In Fig.

In the blue plot (

In the red plot (

We elaborate an exemplary case to better understand the impact of wind
directional variation and uncertainty on active wake deflection for the
different robustness parameters. For this purpose, we select an arbitrary
wind direction that is assumed to predominate at the moment and to which the
turbines adjust according to the respective optimization. We call this wind
direction the estimated wind direction

Illustration of the yaw angles of the reference wind farm for an
estimated wind direction

For a better comparison of the optimized yaw angles to the baseline, the yaw
angles according to the baseline are depicted in each of the four
illustrations in Fig.

Again, it can be seen that the deviation becomes smaller with increasing
robustness parameters. However, the results of the robust optimization with

Firstly, the yaw angles of the northernmost turbines (T11, T12, T13) slightly deviate from the inflow direction, although there are no downstream turbines to consider. The observed small positive offset is opposite to the negative yaw misalignment of the other turbines. The reason for this is that the robust optimization considers all inflow directions around the estimated wind direction in its objective function. The turbines in the northernmost row align themselves towards inflow directions from where less wake effects occur, so they can produce more power in these situations. Consequently, the power output is reduced for inflow direction in the opposite direction. However, the relative power loss is smaller, since in this case the turbines already produce less power due to the stronger wake effects.

Secondly, the optimized yaw angle of the T31 differs slightly from the optimized yaw angle of the turbines T32 and T33. This is due to the location of this turbine at the edge of the wind farm. If the wind would turn anticlockwise, the wakes of the turbines T32 and T33 affect the rest of the wind farm, e.g. T12. This is not the case with T31, so this turbine does not have to take this into account and applies a larger yaw misalignment.

In order to further analyse the results of the optimizations, we look
in detail at the reference turbine T32. The set points for the yaw angle of
the reference turbine (T32) are displayed in Fig.

Optimized yaw angles of the reference wind turbine for

The yaw angle of the reference turbine according to the conventional
optimization (

For these settings, we can now calculate the power output of the reference
wind farm for different wind directions with the help of FLORIS. The
normalized power difference

Normalized power gain of the conventional optimization (black) and
of the robust optimization (blue and red) compared to the baseline (grey) for

The graph illustrates the power gain of the robust optimizations and how it
is affected if the wind direction

For wind directions above roughly

In this section, the following four time-dependent yaw control algorithms are
introduced and evaluated with the help of FLORIS on the basis of wind
direction measurements.

Greedy yaw control: this reference control is derived from the baseline, it refers to the situation
that every individual turbine tries to locally maximize its power output by yawing directly into the wind direction without
any intentional yaw misalignment. The term greedy control was introduced by

Conventional wake deflection: this active wake deflection control scheme applies the yaw angles
calculated by the conventional optimization (

Robust wake deflection (

Robust wake deflection (

In the next step we are extending our evaluation of the four abovementioned
control strategies based on the actual time series from the wind direction
measurements. Two test cases, A and B, are each analysed for three different
robustness parameters (

Evaluation process of the control schemes with wind direction measurements. Red boxes mark the steps in which the measured data are used as input.

First, the 1

Test case A: evaluation of the relative power gain over the
estimated wind direction

Finally, the power output for the optimized wake deflection

Figures

Test case B: evaluation of the relative power gain over the
estimated wind direction

Starting with test case A, the upper graph of
Fig.

In the middle graph the result of the robust wake deflection for

Figure

The introduction of additional uncertainties also affects the robust wake
deflection, but the effects are not as strong as with the conventional wake
deflection. The robust wake deflection with

The achieved results of the robust control algorithms for the different
robustness parameters are summarized for test cases A and B in
Table

Summarized power gains for test cases A and B and the different robustness parameters.

The evaluation of the yaw angle optimization and of the associated yaw
control algorithms are based on real dynamic wind direction measurements, but
for the calculation of the wake losses and the power output, a simplified
steady-state wake model is used, which approximates the average wake flow. In
addition, we have limited our investigation to the partial load range, which
we consider to be the most important. In this case, we assumed a constant
thrust coefficient of the turbines for the analysis. Furthermore, we have
assumed that all uncertainties that occur can be estimated by a normal
distribution. This assumption proved to be sufficient in the evaluation, but
individual sources of uncertainty can still be further investigated. The
deviations of the mean values from successive wind direction time series
denoted by

Histogram of the changes of the mean values of successive wind
direction time series

Hence the work here is intended to serve as a proof of concept and as the basis for further investigations. Following this research, qualitative investigations based on LESs and free field experiments are proposed. When LESs are used one should take care that they properly reproduce real wind direction dynamics.

The relative power gain used here as a key performance indication must not be confused with a pure increase in the annual energy production (AEP). For a reliable estimation of the AEP, a time series of both wind speed and direction of an average entire year together with the wind turbine power curve and availability as well the wind farm layout have to be available. The direct use of the commonly applied Weibull distribution of the mean wind speed would be insufficient. Since in this paper we wanted to focus on comparing the efficiency of the different control strategies in the partial load range, we used the relative power increase instead of the AEP.

Exemplary illustration of the yaw angle set points of the reference turbine T32 according to the passive wake deflection.

In this study, the robustness parameter was deliberately set to a fixed value
for the entire evaluation period in order to demonstrate its influence and
effects. A meaningful refinement of the algorithm would be to utilize a
variable robustness parameter and adapt it to the ambient conditions, e.g.
the mean wind speed, turbulence intensity, and atmospheric stability.
Observations and LESs

The histogram shows two pronounced maxima. One by approx.

The presented results are potentially of significant importance for implementing active wake deflection in the field. The simplicity of the presented open-loop robust control algorithm makes it easy to integrate it into a real yaw control system, which offers the possibility to obtain further insights with the assistance of field campaigns. For this purpose, the wind farm layout and the turbine characteristics must be known for the calculations with the wake model; in addition, the global alignment of the turbines should be as correct as possible and the wind measurements must be relatively reliable. If these requirements are met, the optimized yaw schedules can be calculated for the individual turbines and the robust wake deflection can be used. In principle, the robust wake deflection is even a decentralized control system, since each turbine follows its own optimized yaw set points independently of the others. However, in practice a wind farm regularly undergoes topology changes. This means that turbines change their status and are switched off if necessary. In such a case, the optimized wake deflection of at least the adjacent turbines should be deactivated for the corresponding wind direction sector and the greedy control should be used. A straightforward adjustment would be, for example, the switch to the greedy control for these turbines in the respective wind sector.

Given the industry's interest in easy and robust solutions, a particular
implementation could be the so-called passive wake deflection. This means
that the yaw angle of an upstream turbine is set to a constant value for
certain wind direction sectors. “Passive” in this context refers to the
strongly reduced yaw activity in comparison to the large yaw amplitude in the
case of the conventional yaw angle optimization discussed in
Sect.

In this case, according to the robust optimization with

The consideration of the aerodynamic interactions in wind farm control has
some critical requirements that must be met as best as possible. This
includes the absolute orientation of the wind turbine and a bias in the
measurements. While the absolute orientation of the wind turbine is not
important for turbine control, it plays a decisive role in wind farm control,
as it is required to derive the aerodynamic interactions of the turbines. A
bias in wind direction measurement has negative implications for both wind
turbine and wind farm control. For this reason, the risk of a significant
bias needs to be minimized. Therefore, great care must be taken during
installation and alignment of the wind vane. If possible, additional
measuring instruments for determining the wind direction should be
considered, such as nacelle-mounted lidar or the consideration of blade loads
for the determination of the inflow as described in

The aim of this research was to demonstrate the influence of dynamic wind direction changes on active wake deflection and to present its potential to increase the energy yield of a wind farm in a realistic environment if wind direction dynamics and associated measurement uncertainties are considered properly. Therefore, we first examined the stochastic properties of wind direction measurements and confirmed that a normal distribution is a useful approximation. Next, we demonstrated that the high sensitivity towards wind direction changes poses a risk for the successful application of active wake deflection. To cope with these fluctuations and uncertainties, a robust optimization approach for the yaw angles of all wind turbines in a wind farm as a function of the wind direction and the wind direction variability was introduced. The method takes dynamic wind direction changes and imprecision in the determination of the wind direction into account within a statistical framework in the optimization.

The results indicate that, in an evaluation of different open-loop control algorithms with real wind direction time series, the robust optimization can successfully increase the performance of a reference wind farm, while the conventional optimization neglecting wind directional dynamics and uncertainties can lead to a decrease in power output compared to greedy control without any attempt of wake steering.

The introduced robustness parameter

The underlying measurements were collected as part of a project funded by the German Federal Ministry for Economic Affairs and Energy (BMWi) to investigate active wake control. Please contact the corresponding author for questions regarding the data used in the paper.

AR developed the underlying method and carried out the examination in this paper. JKS supported the examination, particularly in the initial phase, by carrying out preliminary tests and intensive consultation. BD gave important advice on the study and provided the FLORIS model for the investigation. JWvW and MK helped with additional advice and intensive reviews.

The authors declare that they have no conflict of interest.

This work was partially funded by the German Federal Ministry for Economic Affairs and Energy (BMWi) in the scope of the projects CompactWind (FKZ 0325492B) and OWP Control (FKZ 0324131A). The research was partly supported by the German Academic Exchange Service (DAAD) with funds from the Federal Ministry of Education and Research (BMBF). Contributions of the authors affiliated to TU Delft received a partial grant by the European Union's Horizon 2020 research and innovation programme under grant agreement no. 727477. Edited by: Jakob Mann Reviewed by: Dominique Philipp Held and one anonymous referee