Conference PaperPDF Available

A Control Scheme to Maximise Power Generation in Off-shore windfarms.

A Control Strategy to Maximise Energy Extraction in
Vahid S. Bokharaieand Johan Meyers
Departmebt of Mechanical Engineering, KU Leuven,
Celestijnenlaan 300A, Heverlee, Belgium
The common practice in existing commercial wind-
farms is to set the control parameters of each indi-
vidual wind turbine such that it extracts as much
energy as possible from the wind, a setting that
we refer to as greedy setting. But since each wind
turbine reduces wind velocity in its wake, down-
stream wind turbines will generate less power. In
this study, using a Large Eddie Simulation (LES)
environment, we show that if the operating points
of some wind turbines are changed to non-greedy
setting, the total energy extracted by windfarm can
be increased. This holds when the control parame-
ters are kept constant for relatively large time peri-
ods. In other words, it is possible to set the control
parameters of some wind turbines in a windfarm
such that the loss in energy extraction caused by
deviating from greedy case is less than the gain in
power generation in the wind turbines which are
located downstream. We also present an optimisa-
tion scheme which is a step towards extending these
results into a more dynamic approach to windfarm
1 Introduction
There are many studies which have considered op-
timisation of windfarm performance, some of them
focussing on optimisation of farm layout both in
small farms [14, 15, 3] and in large arrays [17, 16].
Also different works have been done on windfarm
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sponding author
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control, focussing on various aspects of windfarm
operation such as reduction of structural loads,
power regulation and grid support [23, 10, 13, 5].
Our focus in this study is on increasing energy
extraction in an existing windfarm. Some at-
tempts have been made in this area, for example
in [18, 6, 21]. However, as far as windfarm-flow in-
teractions are included in these studies, they are all
based on fast heuristic models, for example mod-
els for wake interaction and merging such as the
ones presented in [20, 12, 19]. One of the excep-
tions is [9], in which the authors have considered
the optimal control of windfarms using large-eddy
simulations of the windfarm boundary layer as the
state model, allowing for a detailed optimisation
of the dynamic interaction of the windfarm’s tur-
bines with the boundary layer and its large-scale
three-dimensional turbulent structures. Their re-
sults accumulated over one hour of operation shows
16% of increase in energy extraction compared to
greedy case. But the downside of this approach is
that it is computationally intensive and by order of
magnitude too slow for online optimisation.
In this study, we have provided evidence that
shows by an appropriate choice of control param-
eters for the wind turbines (which are the disk-
average thrust coefficients in our study), even when
they are kept constant for a relatively long time
period, an increase in energy extraction can be
achieved. As a step towards adapting these results
to more dynamical windfarm control algorithm, we
present an optimisation scheme which is performed
on the data collected from various simulations. The
simulations are performed using SP-Wind, which
is an in-house Large Eddy Simulation environment
developed in TFSO group in KU Leuven.
The paper is organised as follows: in Section 2,
we present the physical model governing the sys-
tem. In Section 3, we state the mathematical for-
mulation of the optimisation problem. Section 4 in-
cludes description on simulation environment and
simulation setup. Section 5 provides evidence to
demonstrate that the greedy setting is not an opti-
mum setting for a windfarm, even when the control
parameters are set to fixed values. In Section 6, we
presents the results of an optimisation scheme for
the windfarm control problem. In Section 7 we ex-
plain the conclusions and future works.
2 System Model
The governing equations are the filtered incom-
pressible Navier-Stokes equations for neutral flows
and the continuity equation [9]:
5 · ˜u= 0
∂t + ˜u· 5˜u=1
ρ˜p+fe1+5 · τM+f(1)
where ˜u= [˜u1,˜u2,˜u3] is the resolved velocity field, ˜p
the remaining pressure field (after subtracting p),
τMis the subgrid-scale model, and the density ρis
assumed to remain constant. Furthermore, frep-
resents the forces (per unit mass) introduced by
turbines on the flow.
Modern wind turbines are controlled by the gen-
erator torque, and by a blade-pitch controller,
which controls the aerodynamic torque by changing
the angle of attack of the turbine blades. In simu-
lations, two models are widely used for interactions
between wind turbine and the environment: Actua-
tor Line Models and Actuator Disk Models. In the
simulations whose results are reported in the fol-
lowing sections, Actuator Disk Model (ADM) has
been used to calculate the force f. In Actuator Disc
Models, tangential forces are usually neglected. It
is demonstrated that standard ADMs are an accu-
rate representation of the overall wake structure be-
hind turbine except for the near wake, i.e., x/D < 3
with Dbeing the diameter of the turbine [25].
In ADM, the axial force of a turbine on the flow
field is expressed as [9]:
where C0
Tis the disk-based thrust coefficient, b
is the average axial flow velocity at turbine rotor
disk, and A=πD2/4 is the rotor-disk surface.
The disk-based thrust coefficient C0
Tresults from
integrated lift and drag coefficient over the turbine
blade, taking design geometry and flow angles into
account and is considered as the control parameter
in our optimisation scheme. C0
T= 2.0 corresponds
to the case where the wind turbine is set to extract
maximum amount of energy from the wind, and
T= 0.0 represents the case where the wind tur-
bine is shut down and extracts no energy. Hence in
our search to find the optimum setting for a wind-
farm, we limit our feasible region to [0.0,2.0] for all
wind turbines.
3 Problem Description
In existing commercial windfarms, the effects of
turbine wakes and the accumulated local energy ex-
traction from the atmospheric boundary layer leads
to a reduction in farm efficiency, with power gen-
erated by turbines in a farm being lower than that
of a lone-standing turbine by up to 50% [1]. This
effect is shown in [11] with detailed measurements
in the Horn’s Rev windfarm. We will also provide
evidence to this end in the following section.
Since our aim is to maximise the power gener-
ated by a windfarm, the natural choice of objective
function in the optimisation problem is:
F:= ZT
Ptotal(t) (2)
where Trepresents the optimisation horizon and
Ptotal is the total power produce by windfarm. In
the results presented in Section 6, we have assumed
Tto be the whole simulation time period, which is
500 seconds. Therefore, the general form of optimi-
sation problem for maximising energy extraction in
a windfarm can be stated as a PDE-constrained op-
timisation problem whose aim is to maximise Fas
defined in (2), subject to the Navier-Stokes equa-
tions as defined in (1). The following constraint
should also be added to the optimisation setup:
Ti2.0i∈ {1,· · · , n}
where nis the total number of wind turbines in
the windfarm. This is to ensure that the values of
control parameter are physically meaningful.
This is the general setup considered in [9] and
as stated earlier, leads to a computationally inten-
sive optimisation problem. In this study, we have
applied a number of simplifications and approxi-
mations. Firstly, since the simulation results are
sampled every 1 seconds, we have used a discrete-
time formulation for the optimisation problem:
maximise F:=
Pi(t) (3)
where Nsrepresents the total number of available
samples and Pirepresent the electrical power gener-
ated by wind turbine i. Apart from that, instead of
considering velocities in the whole domain, we have
only considered the hub-height velocities and disc-
averaged thrust coefficient of each wind turbine as
state variables. We then use the Extremely Ran-
domised Trees regression method [8] to estimate the
total power produced by the windfarm, instead of
solving Navier-Stokes equations in each iteration.
More on that will be discussed in Section 6.
4 Simulation Environment
and Simulation Setup
Simulations are performed in SP-Wind, which is
developed in TFSO group in KU Leuven and is
based on previous studies on Large Eddie Simula-
tions. SP-Wind uses a pseudo-spectral discretisa-
tion in the horizontal direction. Message Passing
Interface (MPI) is used to run simulations in par-
allel. FFTW library is employed for Fourier Trans-
forms. In the vertical direction, a fourth-order
energy-conservative finite difference discretisation
is used, while time-integration is performed using a
four-stage Runge-Kutta scheme.
The focus has been on aligned windfarms, which
are windfarms whose wind turbines are arranged
in rows aligned with the wind direction. We take
a boundary layer height at H= 1 km, and use a
domain size of Ly×Lx×H= 6.28 ×3.14 ×1 km.
It is assumed that stream-wise direction aligns with
the x-axis. The computational grid corresponds to
Ny×Nx×NZ= 192 ×128 ×160. In simulations,
25 wind turbines are arranged in a 5 ×5 grid with
a diameter of D= 100 meach and hub height
of zh= 100 m. Stream-wise spacing is Sy5D
and span-wise spacing is Sx4D. The simulation
time-steps are set dynamically based on a convec-
tive CFL number of 0.4 in Runge-Kutta method
and is approximately 0.47 seconds in the reported
cases. These parameters are summarised in Table
Domain Size 6.28 ×3.14 ×1 km3
Turbine Diameter 100m
Turbine Height 100m
Turbine Arrangements 5 ×5
Surface Roughness 0.1m
Grid Size 192 ×128 ×160
Cell Size 32.7×24.5×6.25 m3
Time-step 0.47 seconds
Table 1: Simulation Parameters
Simulations are performed using concurrent pre-
cursor method [24], which means an auxiliary do-
main is defined to supply the main domain with a
turbulent inflow. Also, a fringe forcing technique is
used to generate the desired inflow profile [22].
The Thinking node in Flemish Super-Computer
(VSC) is being utilised to run the SP-Wind code.
The simulation time depends on various settings,
but for a typical simulation with the above-
mentioned parameters and in precursor mode, it
takes around 75 minutes to simulate 1000 seconds
of implementation time using 160 processors in pen-
cil decomposition parallel processing mode. Figure
1 shows a snapshot of the hub-height plane in pre-
cursor mode simulation.
Figure 1: Windfarm layout and instantaneous ve-
locity profile at hub-height plane
5 Simulation Results
The results presented in this section provide evi-
dence that even without any dynamical windfarm
control algorithm and by only proper choice of con-
trol parameters of wind turbines, around 1% in-
crease in total power generated in the windfarm
can be achieved. In order to make sure this gain
in generated power is not because of the differ-
ences in inflow velocity profile, all simulations are
started from the exact same initial boundary layer
conditions. The inflow into to the domain which
subsequently specifies the energy transferred into
the domain, depends on the atmospheric boundary
layer conditions. Hence the inflows for two different
simulations are the same if started from the same
atmospheric boundary layer condition. This guar-
antees that the observed differences in generated
powers are caused by changes in control parame-
ters only, not the difference in wind energy injected
into the windfarm. It should be noted that because
of the minute differences caused by round-off errors
for different cases, the inflow profile will have slight
differences at some points. But statistical analysis
showed that these slight changes are insignificant
compared to the reported gains in power.
Table 2 shows some of the cases for which the
total power has been more than the greedy case.
As a reminder, the greedy case corresponds to all
control parameters set at 2.0.
Control Parameters Increase in PT OT AL BASE CASE 0.98% 2.02.0 0.34%
2.01.75 0.13% 0.46% 0.37% 0.12%
Table 2: Comparing Total Power generated by
windfarm for different control settings.
It should be noted that in these simulation, con-
trol parameters for different rows are considered to
be the same. This means that as an example, for
the case, C0
Tfor the second
wind turbine in each row is set to 1.8, and C0
all other wind turbines are set to 2.0. Simulation
results have showed that the wake effects between
rows is negligible compared to wake effects within
each row. Therefore, we have focused our study to
the effects of changing C0
Tin each row to make them
easier to compare the results with other windfarms
with different layouts.
Figure 2 shows the evolution of total power in the
windfarm over 500 seconds, for the greedy case and
for those cases which have performed better than
the greedy case. The changes of control parameters
are applied at time t= 0. It should come as no sur-
prise that greedy case performs better than other
cases at the earliest stages of simulation. This can
be explained considering the fact that it will take
some time for the flow to travel between different
wind turbines in each row.
0 100 200 300 400 500
Figure 2: Instantaneous Power for some of the cases
which have performed better than the greedy case.
The greedy case represented by colour red.
Figure 3 shows the total power produced by each
wind turbine, average over 5 rows, normalised to
corresponding wind turbine in greedy mode. These
diagrams show that in these cases, the loss in power
generation for some wind turbines is compensated
by a larger gain in subsequent wind turbines.
A minute point in reading values in Figure 3 is
that they are normalised to values of the corre-
sponding wind turbines in the greedy case, which
are not the same themselves. Figure 4 shows the
total power produced by wind turbines (averaged
over 5 rows), in greedy setting.
These results are valid for cases where the wind
direction is aligned with the grid’s x-axis. Chang-
ing the wind direction will make the problem qual-
itatively different which is out of the scope of this
study and the subject of future research.
2.00 - 2.00 - 2.00 - 2.00 - 2.00 -
2.00 - 2.00 - 2.00 - 1.90 - 2.00 -
2.00 - 2.00 - 1.90 - 2.00 - 2.00 -
2.00 - 1.80 - 2.00 - 2.00 - 2.00 -
Figure 3: Total Power generated by each wind tur-
bine averaged over 5 rows, normalised to corre-
sponding wind turbines in greedy setting.
1 2 3 4 5
Figure 4: The Total Power generated in each wind
turbine in greedy case, averaged over 5 rows, nor-
malised to the first wind turbine.
6 Optimisation based on
Cross-Entropy method
As we showed in the previous section, by chang-
ing the control setting of certain wind turbines in
a windfarm, we can have an increase in total en-
ergy extraction in the windfarm. In this section, as
a first step towards a more dynamic approach, we
have utilised the Cross Entropy (CE) optimisation
method in order to find the optimum setting based
on the available data obtained from various simu-
lations. Cross Entropy method was originally de-
veloped to estimate probability of rare events and
later on, it was realised that it could be used to
solve difficult optimisation problems [4]. Cross En-
tropy involves two general steps; to generate ran-
dom samples under certain conditions, and to up-
date samples based on the most optimum samples
in each iteration.
One of the advantages of Cross Entropy method
is the limited number of parameters that needs to
be set. They include total number of samples in
each generation, which is set to 1000 in our case,
number of best samples chosen in each generation
to generate the next generation which is set at 50,
and a weight given to previous best samples which
is set at 0.3. Also the mean and standard devi-
ation of the initial population should be specified.
We have considered different values for these initial
values to ensure the optimisation method does not
converge to local minima.
As already explained in the previous section, sim-
ulation results have shown that with the considered
span-wise spacing between the rows, inter-row in-
teractions can be ignored. The objective function is
considered to be the same as defined in (3) with the
difference that the optimisation is performed over a
row of 5 wind turbines, instead of the whole wind-
farm of 5×5. This has become possible by splitting
the simulation results for each 5 ×5 windfarm into
5 sets of one-row windfarms with 5 wind turbines
each. Also, since the last turbine in each row does
not have any other turbine in its wake, its control
value is set at a fixed value of 2.0. Therefore, the
optimisation parameters are C0
Tifor i= 1,· · · ,4.
To evaluate the value of objective function, we
have used the Extremely Randomised Trees regres-
sion method, which is an ensemble of decision trees
[8]. Decision Trees are a non-parametric super-
vised learning method used for classification and
regression. The goal is to create a model that pre-
dicts the value of a target variable by learning sim-
ple decision rules inferred from the data features
[2]. In Extremely Randomised Trees we establish a
collection of decision trees. And while calculating
the splits in the trees, instead of looking for most
discriminative thresholds, thresholds are drawn at
random for each tree and the best of these ran-
domly generated thresholds is picked as the split-
ting rule. In this study, we have used the imple-
mentation of Extremely Randomised Trees as in
[7]. Figure 5 shows the evolution of an optimisa-
tion run, with initial population built around the
mean initial value of [1.0,1.0,1.0,1.0] with a stan-
dard deviation of [0.5,0.5,0.5,0.5]. Figure 6 shows
the estimated calculated power in each iteration.
As can be seen, the algorithm converges to a set
of control parameters with values of approximately
[2.0,1.8,2.0,2.0], which is the optimum solution ob-
served in simulations.
Figure 5: Changes in control parameter in the CE
optimisation scheme.
5 10 15 20 25 30
Figure 6: Changes in power for best case in each
iteration of CE optimisation scheme.
7 Conclusions
In this paper, we showed that the standard practice
in commercial windfarm, in which each wind tur-
bine is set to extract maximum amount of energy
from the wind, is not the optimum setting when the
objective function is the total power generated by
the windfarm. We showed that by suitable changes
in settings, even when these settings are considered
to be fixed for a relatively long period of time, total
energy extracted by the windfarm can be increased.
We then presented an optimisation scheme that
can be considered as a first step towards designing
a more dynamic control methodology to increase
the total gain in power generation. This work can
be extended in a number of ways. It can be ap-
plied to windfarms with different layout, both in
terms of number of wind turbines and in alignment.
More interestingly, the optimisation results can be
adapted to be applied to shorter time-horizons in
order to achieve a more dynamical control scheme
and higher gains in total energy extraction in wind-
8 Acknowledgements
The authors would like to thank Dr. Bert Claessens
from Vito NV, Belgium and Prof. Damien Ernst
from University of Liege, Belgium, for their contri-
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The effect of spacing on the power output of wind turbines in large arrays has been determined theoretically. Following Templin, the effect is assessed by determining the increase in roughness of the earth's boundary layer due to the drag of the turbines. The thickness of the boundary layer is assumed to change in proportion to the square root of the skin friction, which is appropriate for a turbulent Ekman layer, and differs from the assumptions made by Templin. The loss of power for both flat-open country and rough-wooded country is determined as a function of the area density of the turbines, and it is found that quite large spacings are required to avoid a significant loss of power.
A nonlinear optimization problem is formulated to determine the optimal spacing between wind turbines to maximize instantaneous power from a one-line array of machines to be placed in a line parallel to constant wind direction. A specific example is then taken to illustrate the difference between optimal spacing and equidistant spacing.
A computer model for an arbitrary array of wind turbines is presented, in which the power available to each wind turbine in the array is determined for that wind turbine as 'receptor', with each of the other wind turbines acting as a wake generator. The power of the entire array is determined by summing over all the receptors and then determining the average. The discussion covers wake profiles, wake growth and turbulent entrainment (wake development in a nonturbulent and a turbulent infinite medium), effect of ground plane and neighboring wakes, and computer model. The basic equations employ basic fluid mechanical expressions related to drag conservation, wake growth due to turbulent entrainment, and a family of self-similar wake profiles obtained from experiment. This gives full definition of the wake velocity field and helps determine the velocity deficit for a given radius. Power output of selected arrays for all wind conditions is determined. Some typical results for various cases of interest are presented.
The wind turbine operational characteristics, power measurements and meteorological measurements from Horns Rev offshore wind farm have been identified, synchronized, quality screened and stored in a common database as 10 min statistical data. A number of flow cases have been identified to describe the flow inside the wind farm, and the power deficits along rows of wind turbines have been determined for different inflow directions and wind speed intervals. A method to classify the atmospheric stability based on the Bulk-Ri number has been implemented. Long-term stability conditions have been established, which confirms, in line with previous results, that conditions tend towards near neutral as wind speeds increase but that both stable and unstable conditions are present at wind speeds up to 15 m s −1. Moreover, there is a strong stability directional dependence with southerly winds having fewer unstable conditions, whereas northerly winds have fewer observations in the stable classes. Stable conditions also tend to be associated with lower levels of turbulence intensity, and this relationship persists as wind speeds increase. Power deficit is a function of ambient turbulence intensity. The level of power deficit is strongly dependent on the wind turbine spacing; as turbulence intensity increases, the power deficit decreases. The power deficit is determined for four different wind turbine spacing distances and for stability classified as very stable, stable and others (near neutral to very unstable). The more stable the conditions are, the larger the power deficit. Copyright © 2011 John Wiley & Sons, Ltd.