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10.2514/6.2014-0874
AIAA SciTech Forum
13-17 January 2014, National Harbor, Maryland
32nd ASME Wind Energy Symposium
Sizing and Control of Trailing Edge Flaps on a Smart
Rotor for Maximum Power Generation in Low Fatigue
Wind Regimes
Jeroen Smit∗ and Lars O. Bernhammer
†
Downloaded by UNIVERSITY OF ADELAIDE on October 26, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.2014-0874
Aerospace Engineering, Delft University of Technology, Kluyverweg 1, 2629HS Delft, The Netherlands
Sachin Navalkar
‡
Mechanical Engineering, Delft University of Technology, Mekelweg 2, 2628CD Delft, The Netherlands
Leonardo Bergami§ and Mac Gaunaa¶
DTU Wind Energy, Frederiksborgvej 399, 4000 Roskilde, Denmark
In this paper an extension of the spectrum of applicability of rotors with active aerodynamic devices is presented. Besides the classical purpose of load alleviation, a secondary
objective is established: power capture optimization. As a first step, wind speed regions
that contribute little to fatigue damage have been identified.
For these regions the turbine energy output can be increased by deflecting the trailing
edge (TE) flap as a function of local, instantaneous speed ratios. For this purpose, sizing
of TE flap configuration for maximum power generation is established using blade element
momentum theory.
The investigation then focuses on operation in non-uniform wind field conditions. Firstly,
the deterministic fluctuation in local tip speed ratio due to wind shear was evaluated. The
second effect is associated with delays in adapting the rotor speed to time varying inflow.
The increase of power generation due to wind shear has been demonstrated with an increase
of energy yield of 1%. Finally a control logic based on inflow wind speeds has been devised.
Keywords: wind energy, smart rotor, fatigue, trailing edge flaps, power generation
I.
Introduction
For the last two decades a strong increase in wind turbine size has been observed. One of the main
drivers behind the upscaling is an effort to reduce the cost of energy. A limiting factor in this process are
fatigue loads on rotor blades. Ashuri1 has determined that upscaling of classical wind turbines will not
be cost effective when considering 10 or 20 MW turbines. To enable further growth of rotor diameter the
smart rotor concept has been developed. Smart rotors alleviate fluctuating loads using active aerodynamics
devices mounted on the blades. This results in lower fatigue damage on the turbine, thereby enabling further
upscaling using the same materials.
From previous studies by Bergami2 and Baek3 the hypothesis is formed that fatigue damage at the blade
root in the flapwise direction is mainly caused at and above rated wind speed. Wind turbine operations
below rated speed only contribute to a small extent to the total fatigue damage. This allows the use of
aerodynamic devices on a smart rotor for a secondary purpose: increasing energy capture for wind speeds
below rated.
∗ MSc,
Wind Energy, Delft University of Technology, The Netherlands
Student, Aircraft Structures and Computational Mechanics / Wind Energy, l.o.bernhammer@tudelft.nl
‡ PhD Student, Delft Center for Systems and Control
§ Postdoc, DTU Wind Energy, Denmark
¶ Senior Scientist, DTU Wind Energy, Denmark
† PhD
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American Institute of Aeronautics and Astronautics
Copyright © 2014 by J.
Smit, L.O. Bernhammer, S. Navalkar, L. Bergami, M. Gaunaa. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.
Downloaded by UNIVERSITY OF ADELAIDE on October 26, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.2014-0874
This paper presents an approach for sizing and control of trailing edge flaps for maximum power capture
on a wind turbine with a smart rotor in low fatigue damage wind regimes. Wind turbine control aims
to maximize power generation for below rated wind speeds and control of the aeroelastic loads in region
3. Controllers are designed with the rotor shaft speed and the generated power as input parameter. For
controller region 2, the generator torque is selected such that the rotor operates at optimal tip speed ratio.
Due to the rotor inertia and the time varying inflow, the actual tip speed ratio sees strong fluctuations.
Additionally, local speed ratios along the blade span fluctuate even more due to turbulence in the wind field,
wind shear and tower shadow. Smart rotors, which are traditionally used for load alleviation, are investigated
to harvest these unsteady aerodynamic effects to maximize energy yield.
All analyses and simulations in this study are executed using the NREL 5MW reference turbine.4 In
section II in a first step, fatigue damage is further quantified as a function of wind speed regimes. The loads
on the rotor blade root are found using aeroelastic simulations in GH Bladed.5 From this analysis, wind
speed regions were identified that could be used for power optimization purposes. For the remaining part
of the study an unsteady blade element momentum (BEM) tool has been developed and validated. Using
this BEM tool, it is shown that the possible power increase using flaps consists of a steady part and a cyclic
part. A study on the effects of the sizing and placement of the flaps on (the steady part) of the increase
in power has been conducted. Using the results from this study an optimal flap configuration is proposed.
Through system linearization, the plant for controller design is found with the input being local wind speed
measurements and flap deflections and the output being power generation. In simulation environment, the
reference wind speed at the hub can be exactly known, whereas for the physical implementation this wind
speed needs to be estimated, e.g. through LIght Detection And Ranging (LIDAR) measurements.
II.
Fatigue Damage Quantification
Previous research has shown that fatigue loads in wind turbines can be efficiently alleviated using Smart
rotors.6, 7 The main contribution to the overall fatigue damage is only cased by a fraction of the load
cycles that a turbine encounters. To further quantify the fatigue damage accumulation, a sequence of fatigue
analyses have been carried out. For these fatigue analyses, a set of 10 minute turbulent aeroelastic simulations
are performed in GH Bladed for wind speeds from 3 to 25 m/s. The turbulence intensity varies per wind
speed according to the IEC61400 standards for a wind turbine with turbulence class B.8 The simulations
include tower shadow and wind shear. The blade root moments in flapwise and edgewise direction are
measured. The fatigue damage analysis is done using rainflow counting and the Palmgren-Miner’s rule. This
results in a distribution of the number of load cycles, nj , over a set of load ranges, ∆Mj , for each wind speed
bin, V0,i . Using these cycles per load range the equivalent load Meq,i per wind speed is calculated using
Equation (1). To find the relative fatigue damage per wind speed di Equation (2) is used.
P
m 1/m
j=1 nj,lif e · ∆Mj
(1)
Meq,i =
Tlif e
Ti Meq,i m
(2)
Tlif e Meq,lif e m
With m as the Wöhler exponent for composites equal to 10. The variable Ti represents the time the turbine
operates in the corresponding wind speed bin, according to a Weibull distribution with scale parameter 10.85
and shape parameter 2.15.
In Figure 1(a) the cumulative fatigue damage due to the flapwise bending moment is plotted versus the
wind speed. Wind speeds below 12 m/s contribute less then 2% to the total lifetime fatigue damage due
to flapwise root bending moment, while this region accounts for 60% of the load cycles. This means that
practically all fatigue damage for the blade root bending moment is accumulated above the rated wind speed
of 11.4 m/s. Increasing this envelope to wind speeds up to 15 m/s , the damage increases to 20% of the
total damage, while including 75% of the load cycles. For edgewise loading the fatigue damage is dominated
by the gravity driven fatigue cycles. Figure 1(b) displays the corresponding edgewise damage equivalent
root moments. The gravitational loads can not be alleviated by the use of aerodynamic devices. Unlike the
deterministic gravitational loads, the stochastic part of the blade root flapwise moment can be effectively
addressed by trailing edge flaps, as they have high control authority on the lift coefficient.
Fatigue damage in flapwise and edgewise direction for wind speeds below rated wind speed damage is
negligible compared to damage caused at wind speeds above rated wind speed. Using flaps on a smart rotor
di =
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1
d and n [-] (normalized & cumulative)
d and n [-] (normalized & cumulative)
Downloaded by UNIVERSITY OF ADELAIDE on October 26, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.2014-0874
1
d
0.9
n
0.8
0.7
← d ≤20%
0.6
0.5
← d ≤2%
0.4
0.3
0.2
0.1
0
d
0.9
n
0.8
0.7
← d ≤20%
0.6
0.5
0.4
← d ≤2%
0.3
0.2
0.1
0
5
10
15
20
25
5
10
V0 [m/s]
15
20
25
V0 [m/s]
(a) Flapwise root bending moment
(b) Edgewise root bending moment
Figure 1. Cumulative fatigue damage generation due to equivalent root bending moment and number of load
cycles vs wind speeds
in this wind regime can only have very limited contribution to the reduction of the total fatigue damage.
Using flaps for secondary purposes like maximization of power generation below rated wind speed is therefore
expected to have little impact on the total fatigue damage.
III.
Modeling of unsteady power generation using blade element momentum
theory
To carry out the remaining work presented in this paper an unsteady blade element momentum (BEM)
tool is developed. This tool has been created to perform both, fast steady as well as unsteady analyses with
built-in optimization capabilities.
Blade element momentum theory is widely used in industry and science for wind turbine analyses and
design. The BEM tool used for this work is built according to the framework described by Hansen.9 This
framework allows for time varying inflow conditions resulting in dynamic loading on the turbine blades. In
each time step the following 6 calculation steps are executed.
Step 1 allows for changes in wind velocity over time. However, for the sizing of the flap configuration
presented in the first part of this paper only steady inflow conditions are considered. Step 2 applies a
correction to the wind speed profile to model the wind shear caused by the boundary layer of the earth. The
wind speed V0 can be described as a function of height x and the wind speed at hub height V0 (Hhub ), as
prescribed by the IEC61400 Standards8 see Equation 3. In all simulations a wind shear factor, ν = 0.2, is
used.
ν
x
V0 (x) = V0 (Hhub )
(3)
Hhub
In step 3 the quasi steady axial and tangential inductions factors a and a0 are calculated for each blade
element as described by Hansen10 using Equations 4 and 5 with the normal and tangential coefficients
according to Equations 6, the local solidity, σ = cB/2πr and the Prandtl tip loss factor F according
to Equation 7. In this paper the notationas are used as in the referenced literature. The lift and drag
coefficients in Equation 6 are obtained from static steady airfoil data tables.
For highly loaded blade elements (a > ac with ac = 0.326)) simple momentum theory is not valid and an
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empirical relation is used to calculate axial induction as given in Equations 8.
a=
a0 =
4F sin2 φ
+1
σcn
−1
(4)
−1
4F sin φ cos φ
−1
σct
(5)
cn = cl (φ, θ, β) cos φ + cd (φ, θ, β) sin φ
Downloaded by UNIVERSITY OF ADELAIDE on October 26, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.2014-0874
ct = cl (φ, θ, β) sin φ − cd (φ, θ, β) cos φ
2
B R−r
F = cos−1 exp −
π
2 r sin φ
a=
1
2
2 + K(1 − 2ac ) −
q
(6)
(7)
2
(K(1 − 2ac )) + 4(Kac 2 − 1)
K=
4F sin2 φ
σcn
(8)
In step 3 the induction factors are calculated as if the turbine adapts instantaneously to a new loading
situation (e.g. due to a change in wind speed, change in pitch angle or flap deflection). In reality the induction
does not adapt instantly to new aerodynamics forces hence a time delay is present before Equations (4-6)
do converge. This time delay is modeled using a dynamic wake model proposed by S. Øye11 and is applied
in step 4.
In step 4 steady aerodynamic properties of the 2D airfoils are used. However, with continuous changes in
flow conditions (e.g. due to wind shear, tower shadow) and/or airfoil properties (e.g. blade pitch, flap angle)
steady aerodynamic airfoil properties only give an approximation of the induction properties, depending on
the timescale of these dynamics. In step 5 the dynamic lift, drag and moment coefficients are found using
the ATEFlap model.12 The model combines the effects of shed vorticity and dynamic flow separation by
merging a thin airfoil potential flow model with a dynamic stall model of the Beddoes-Leishmann type.
In step 6 the dynamic aerodynamic load is calculated using unsteady aerodynamic coefficients from step
6 and inductions resulting from step 5. The aerodynamic forces are integrated over the blade assuming linear
variation of the loads between calculation points to obtain aerodynamic thrust and power.
The code has been benchmarked against the aerodynamic module of HAWC213 and found to be in very
good agreement for a range of wind speeds from 5m/s to 11m/s and flap angles from -8 degree to 8 degree.
The maximum occurring error was less than 1.5% as shown in Figure 2.
IV.
Steady state power optimization using flaps and pitch
The starting assumption is that trailing edge flaps on a smart rotor can increase power generation by
altering the aerodynamic properties of the blade. The BEM tool described above was used to simulate
the NREL reference turbine with a single trailing edge flap per blade spanning 10% of the chord length at
0.78 ≤ r/R ≤ 0.98. Deflections have been limited to 10 degrees. The steady aerodynamic data has been
obtained using Xfoil. The sizing simulations are steady state (constant wind fields, no wind shear, no tower
shadow, without dynamic wake model and without ATEFlap model).
For tip speed ratios λ between 4 and 14 the flap angle is varied between -10 and 10 degree. Figure 3(a)
shows the resulting power curves (CP − λ curve). The stars represent the baseline setting with no flap
deflection. The optimal flap setting depends on the tip speed ratio. While the tip speed ratios above
maximum power capture require negative flap deflections, positive flap deflections increase the power capture
when operating below the optimal tip speed ratio. Still the baseline setting achieves the highest overall
power coefficient, when operating at the design tip speed ratio. However, when the turbine is operating at
suboptimal tip speed ratios the power coefficient can be increased by using the trailing edge flap.
The optimal flap angle βopt per tip speed ratio resulting in the highest power coefficient was determined
and is shown in Figure 4 with the corresponding maximal achievable power curve. The same procedure has
been followed to determine the optimal pitch angle θopt of the blade. The results for the optimal pitch angle
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3
0.48
β = -8 deg
2.5
β = 0 deg
2
0.46
β = 8 deg
0.44
1.5
CP [-]
0.5
0
0.4
0.38
HAWC2 β = -8 deg
BEM β = -8 deg
0.36
−0.5
HAWC2 β = 0 deg
0.34
−1
−1.5
0.32
−2
0.3
BEM β = 0 deg
HAWC2 β = 8 deg
BEM β = 8 deg
4
5
6
7
8
9
10
4
11
5
6
7
8
9
10
11
V0 [m/s]
V0 [m/s]
(a) Power coefficient vs wind speed
(b) Difference in power coefficient vs wind speed
Figure 2. Power coefficient below rated wind speed for 3 flap angles and constant, uniform inflow
0.45
0.4
β = -10 deg
β = -8 deg
CP [-]
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∆CP [%]
0.42
1
β = -6 deg
0.35
β = -4 deg
β = -2 deg
0.3
β = 0 deg
β = 2 deg
β = 4 deg
0.25
β = 6 deg
β = 8 deg
0.2
β = 10 deg
4
5
6
7
8
9
10
11
12
13
14
15
λ [-]
Figure 3. Power coefficient vs tip speed ratio for various flap angles and a zero pitch angle and constant,
uniform inflow
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10
θ for optimal pitch
β for optimal flap
θoptimal & βoptimal [deg]
8
0.5
7 m/s
6 m/s
8-10 m/s
11 m/s
0.45
5 m/s
CP [-]
0.4
4 m/s
0.35
0.3
Downloaded by UNIVERSITY OF ADELAIDE on October 26, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.2014-0874
baseline: θ = 0 & β = 0
optimal pitch: θopt & β = 0
0.25
6
7
8
9
10
11
12
13
4
2
0
−2
−4
−8
optimal flap & pitch: θopt & βopt
0.2
5
β for optimal flap & pitch
−6
optimal flap: θ = 0 & βopt
4
θ for optimal flap & pitch
6
4
6
14
10
12
14
λ [-]
λ [-]
(a) Power curves
8
(b) Corrsponding optimal pitch and flap angles
Figure 4. Baseline and improved power curves using flaps and/or blade pitch and corresponding control
settings, with circles representing tip speed ratios for wind speeds below rated and constant, uniform inflow
are also given in Figure 4. The fourth power curve in Figure 4 represents the combined power optimization
using flap deflections and full span pitch. As already concluded from Figure 3(a) the global maximum power
coefficient is not increased with the use of flaps or pitch, however for suboptimal tip speed ratios the use
of flaps is beneficial, and the power coefficient can be increased. A combination of optimal flap and pitch
angle results in the highest power coefficients. When comparing the effectiveness of the flaps and the pitch
mechanism flaps outperform blade pitch for tip speed ratios above 5.
The operation points of the NREL reference turbine as a function of the wind speed at hub height
are displayed by circles in Figure 4(a). The turbine operates at suboptimal tip speed ratios for significant
amounts of time as for wind speeds below 5 m/s a clear increase in power coefficient can be achieved by
flaps. One should also notice that in the entire range of design tip speed ratios up to rated wind speed the
pitch controller power optimization is outperformed by trailing edge flaps. Therefore the trailing edge flaps
are able to increase power production below rated wind speed more than the pitch mechanism. The optimal
flap and pitch angle for maximum power is described as a function of the tip speed ratio and shown in Figure
4(b).
V.
Unsteady state power optimization using flaps
The simulations for Figures 3(a) and 4 were performed with constant wind fields without wind shear
and tower shadow. The local speed ratio λr , defined in Equation 9, on the blade is thus constant during a
rotation.
r
Ω·r
Ω·R
=
=λ
(9)
λr =
V0
V0 (R/r)
R
However a turbine operating in real life conditions experiences time-varying wind velocities on the blade,
resulting in time-varying instantaneous (local) speed ratios.
The time fluctuations in the wind velocity (and correspondingly speed ratio) can be separated into a
stochastic and a deterministic part. The stochastic fluctuations result from the turbulence present in a
wind field. The deterministic fluctuations can be caused by wind shear, tower shadow, tilt angle or yaw
angle. These deterministic variations in velocity and local speed ratio can often be described as a function of
azimuth angle and the radial location. The deterministic nature of these fluctuations makes them particularly
suitable for power maximization.
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2
0.09
excl. shear
incl. shear
1.5
0.08
0.07
∆AEP [%]
∆P [%]
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Steady simulations including wind shear but no tower shadow or turbulence are performed for wind
speeds between 4 and 11 m/s. For each azimuthal position of the blade the flap angle that returns the
highest Cp has been determined in section IV. This information was used to set the flap angles of the blades.
Figure 5(a) shows the average increase in power for a given wind speed bin if the flaps are used as described
above, both for the case where wind shear is included and excluded. Figure 5(b) combines the percentage
increase in Figure 5(a) with the Weibull wind speed distribution and shows the increase of the Annual Energy
Production (AEP) contribution as a function of the wind speed at hub height. To obtain the overall increase
in AEP, one needs to sum all wind speed bins resulting in an increase of AEP of 0.19% excluding wind shear
and 0.27% including wind shear. While the highest increase in terms of power percentage can be reached for
low wind speeds, the contribution to the increase of AEP is higher for wind speeds close to the rated speed
of the wind turbine.
The larger increase in energy capture in the case of shear can be explained by the fact that wind shear
induces changes in the local speed ratio on a blade. These changes lead to more time spent in suboptimal
speed ratio conditions. In these conditions the positive effect of flap-use has already been demonstrated in
Figure 4.
1
0.5
0.06
0.05
0.04
0.03
0.02
0.01
0
4
5
6
7
8
9
10
11
4
5
6
7
8
9
10
11
V0 [m/s]
V0 [m/s]
(a) Increase in power vs wind speed
(b) Increase in annual energy production vs wind speed
Figure 5. Increase in power and annual energy production vs wind speed using optimal flap angle including
and excluding wind shear
VI.
Flap sizing and location
The effects of the sizing of the flap configuration on the possible energy yield increase is investigated.
First the optimum location of the flaps is determined, followed by the span and the number of flaps. During
the optimization, the chordwise length of the flap is fixed at 10%. In this section all analyses are performed
considering steady aerodynamic models and a uniform wind field, with speeds ranging from 4-11 m/s.
The authors are aware that power performance optimization is a secondary purpose of flaps on a smart
rotor. Because of that the actual sizing of the flaps will always be a trade off between possible fatigue
reduction, possible energy yield increase, installation & operational costs and complexity. However the goal
here is to investigate what flap size and location would be beneficial for power optimization. The results
presented here should be incorporated in the design process of flaps on smart rotors.
A.
Effect of spanwise location of flaps
One flap with a length Sf lap = 1 m in spanwise direction and 10% chord c length is placed at 17 different
locations along the blade, between r/R = 0.74 and 0.99. For all combinations of wind speeds and 17 locations,
the optimal flap angle, corresponding to the highest power coefficient, is found with a precision of 0.1 deg.
The increase in power coefficient, expressed as a percentage of its original value, is plotted in Figure 6(a).
The plot shows that the increase in power coefficient is highest at low wind speeds. In Figure 6(b) the curves
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1
0.6
V0 = 4 m/s λ = 11.835
0.9
V0 = 5 m/s λ = 9.895
0.5
0.8
V0 = 6 m/s λ = 8.724
V0 = 8 m/s λ = 7.543
0.4
∆CP [%]
∆CP (normalized) [-]
V0 = 7 m/s λ = 7.974
V0 = 9 m/s λ = 7.54
V0 = 10 m/s λ = 7.535
0.3
V0 = 11 m/s λ = 7.125
0.2
0.7
0.6
0.5
0.4
0.3
0.2
Downloaded by UNIVERSITY OF ADELAIDE on October 26, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.2014-0874
0.1
0.1
0
0
0.75
0.8
0.85
0.9
0.75
0.95
0.8
0.85
0.9
0.95
r/R [-]
r/R [-]
(a) Increase in power coefficient
(b) Increase in power coefficient normalized
Figure 6. Increase in power coefficient due to a 1 meter span flap at various flap locations for various wind
speeds
from Figure 6(a) are divided by their maximum value such that the peaks of the curves reach unity. For
low wind speeds (and high tip speed ratios) the optimum flap position shifts towards the root compared to
its optimum position at higher wind speeds (and near optimal tip speed ratios). To find the location where
the application of flaps is most effective and hence where the largest increase in AEP (∆E) can be achieved,
Equation 10 is used.
P11
CP,i,flap · 12 ρV0,i 3 Arotor Ti
∆E = P11i=4
(10)
3
1
i=4 CP,i,no flap · 2 ρV0,i Arotor Ti
The power (P = CP 12 ρV0 3 A) at each wind speed is multiplied by a probability factor Ti . This probability
factor corresponds to the time of occurrence per wind speed for a Weibull distribution with a scale parameter
10.85 and shape parameter 2.15. The energy yield increase per flap location is shown in Figure 7. The
distinctive peak in Figure 7 results from peaks in Figure 6(b) located at r/R = 0.95 for wind speeds 7-11
m/s. The effect of the high increase in the power coefficient, for flaps closer to the root, at low wind speeds
shown in Figure 6(a) is not visible in Figure 7 because the power produced at those wind speeds is much
lower. Additionally, the Weibull distribution favors outboard flaps as the majority of the probability density
function corresponds to cases where the optimum flap placement is outboard of 95% span.
In order to maximize the energy yield increase the location of the flap should be chosen in such a way
that the area under the curve in Figure 7 is maximized. For a flap with length equal to or larger than 3 m
one can conclude that the flap should be placed from r/R=0.97 extending towards the root of the blade.
The effect of flap length on energy yield is determined in a next step.
B.
Ideal length of flaps
In previous subsection it was concluded that flaps should start from r/R =0.97 and run towards the blade
root. In Figure 8(a) the energy increase was calculated for flap lengths ranging from 1 to 16 m, using
Equation 10. From Figure 8(a) the conclusion can be drawn that a longer flap enlarges the possible energy
increase. However, adding extra flap length becomes less and less effective for larger flap lengths. The local
increase in the curve in Figure 8(b) between 2 and 4 meters can be explained by two peaks for optimal flap
location depending on the wind speed (or tip speed ratio) shown in Figure 6. For flap lengths of 15 meters
an increase in energy yield of 0.5% can be achieved. If the cost of installation of flaps is known a trade off
can be made on the actual size of the flap by determining if the increase in energy production outweighs
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American Institute of Aeronautics and Astronautics
∆E [%]
0.04
0.03
0.02
0.01
0.8
0.85
0.9
0.95
r/R [-]
Figure 7. Increase in yield vs flap location
∆(∆E)/ ∆Sf lap [%/m]
0.5
0.4
∆E [%]
Downloaded by UNIVERSITY OF ADELAIDE on October 26, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.2014-0874
0.75
0.3
0.2
0.1
5
10
0.045
0.04
0.035
0.03
0.025
5
15
10
15
Sf lap [m]
Sf lap [m]
(a) Flap span vs increase in energy yield
(b) Effect of adding 1 m Sf lap at Sf lap
Figure 8. Effect of the size of the flap, Sf lap , on increase in yield, ∆E, with flap located at: 0.73 ≤ r/R = 0.97
the increase in production costs. The energy used for operating the flap is expected to be low for this case
because the flap angle is only changed for a change in average wind speed which is a gradual change.
C.
Number of flap elements
The location and size of the flaps can be determined using Figure 7 and 8. In this section a third design
variable is addressed, namely the number of flap elements that can be individually controlled. In this example
a total flap length of 12m is used to study the effect of the number of flap elements, that can be controlled
separately, on the energy yield. In Figure 9 the energy increase is plotted versus the number of equally
sized flap element. Increasing the number of flap elements from 1 to 4 has a larger effect than increasing
the number of flaps from 4 to 12. However 1 flap element already reaches 95% of the attainable increase in
energy yield of 12 flap elements. Increasing to 2 elements captures 98% of the energy gain.
From these results it is suggested to use one flap to keep the complexity of the system minimal. It is noted
that this suggestion arises from analyses using uniform steady wind fields. In real life operation the turbine
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experiences a variation in local speed ratios along the blade. How to cope with these effects is considered in
a next step.
0.45
∆E [%]
0.445
0.44
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0.435
0.43
2
4
6
8
10
12
nf laps [-]
Figure 9. Effect of number of controllable flaps, nf laps , on yield, E, for a flap with Sf lap = 12 m located at:
0.78 ≤ r/R ≤ 0.97
D.
Final design of flap configuration
In Figure 10(a) the optimal flap angle for a 1-meter flap at various location (as in section A) is plotted. It
can be seen that the variation in optimal flap angle is larger towards the tip than towards the root of the
blade. To obtain more insight into this effect the gradient of the optimal flap angle is calculated for each
location on the blade. This is done for all wind speeds and averaged using the probability factor Ti , described
previously; the results of these calculation are plotted in Figure 10(b). These figures suggest that uniform
flap spacing results in a suboptimal design because the size of the individually controllable flaps should be
relatively small near the tip and large towards the root.
VII.
Controller design
In previous sections, the rotor speed has been prescribed as a function of wind speed according to the
NREL documentation . However to model the rotor speed more realistically in time-varying wind conditions,
a baseline generator torque controller is included as is described in NREL documentation.4 Using this
expanded BEM Tool, two controllers for the flap angles have been created, a Lookup Table Controller (LTC)
and a Model Predictive Controller (MPC), described in the two following subsections.
A.
Lookup Table Controller
The first control input, rotor speed, is a conventional control input for wind turbine controllers. The second
control input, wind speed along the blade, is less standard. In a simulation environment it is easy to ‘measure’
the wind speed on the blade, in real life operation this is less easy.
The control scheme consists of 5 consecutive steps shown in Figure 12. First the local speed ratio is
calculated using the incoming wind speed and predicted rotor speed. Then the local TSR is limited to the
range of the lookup table: if the ratio is below 3 its value is set to 3, if the ratio is above 18 its value is set to
18. Then the table lookup procedure is executed: the optimal flap angle is found using linear interpolation.
The optimal flap angles in the lookup table are found using the same method as described in section IV,
where the optimal flap angle was determined for steady state operation at TSRs between 3 and 18, with a
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βoptimal [deg]
V0 =4 m/s λ =11.835
4
V0 =5 m/s λ =9.895
V0 =6 m/s λ =8.724
2
V0 =7 m/s λ =7.974
0
V0 =8 m/s λ =7.543
−2
V0 =9 m/s λ =7.54
−4
V0 =10 m/s λ =7.535
−6
V0 =11 m/s λ =7.125
0.75
0.8
0.85
0.9
0.95
r/R [-]
(a) Optimal flap angle, βoptimal , for a flap (Sf lap = 1 m) at various location on the blade
0.6
∆β/∆r [deg/m]
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6
0.5
0.4
0.3
0.2
0.75
0.8
0.85
0.9
0.95
r/R [-]
(b) Averaged gradient of optimum flap angle in
spanwise direction
Figure 10. Variations in optimal flap angle for various location and various wind speeds
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B.
1.
Model Predictive Controller
Linearized model
To further investigate the power generation, a more complex controller has been implemented, namely a
Model Predictive Controller, which maximizes aerodynamic torque over a prediction horizon. It has been
assumed that torque can be described as a combination of a static and dynamic response. The static
part depends on the local speed ratio and flap angle. The dynamic part can be seen as a history term
containing the previous states, which influence the current state. A physical interpretation of the latter is
the convection of shed and trailed vorticity. The static part represents the steady state torque corresponding
to the instantaneous conditions on the blade.
The torque is proportional to the product of the square of the wind speed and the torque coefficient:
dyn
Q ∝ CQ
· V02
(11)
dyn
It has been assumed that the torque coefficient, CQ
, is a linear combination of the steady torque coefficient,
st
of previous and current time step, and the torque coefficient of the two preceding time steps according
CQ
to:




dyn
st
C

CQ,i−1 
dyn
CQ,i+1
= A  Q,i−1  + B 

dyn
st
CQ,i
CQ,i
(12)
In a simulation environment it is easy to extract the dynamic torque coefficient, on a real turbine this is
less easy but could be achieved by means of a combination of measurement of wind speed (using LIDAR)
and reconstruction of the torque using strain gauges. During the study on this concept the physical implementation of the controller was of no concern as the goal was in the first place to create a controller capable
of maximizing the power.
15
10
β [deg]
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minimum and maximum flap angle of ±15 degree. The resulting flap angles are shown in Figure 11. In a
final step the flap angle is set for the next time step in the simulation. This procedure is repeated for all
blades in each time step.
The LTC has been implemented in the BEM Tool and tested with a 10 minute simulation with time
varying wind speed. The turbulent wind speed history was created using Turbsim and wind shear was
included. Figure 13 shows the time history for such a simulation. It can be seen that during phases of
increasing wind speed the LTC controller increases the power output, while in cases of decreasing wind
speed, a reduction in generated power is observed. The rotor inertia hereby serves as low-pass filter in the
system such that the aerodynamic power as shown in Figure 13(b) exhibits significantly more vibrations
than the generator power as displayed in Figure 13(a).
In Figure 14 the increase in energy is shown for a square wave in the wind speed signal. The square
marking correspond to step increases in wind speed, while the circles represent step decreases. The diamonds
are the sum of a step increase and a step decrease and therefore represent the effective energy gain. For 1/32
and 1/16 Hz, a very large overshoot in the power response can be seen. This holds true for the decrease in
power when decreasing the wind speed. This loss is more than compensated by the power gain for increasing
wind speeds such that a net gain in generated power is achieved.
5
0
−5
−10
4
6
8
10
12
14
λ [-]
Figure 11. Optimal flap angle vs TSR
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16
18
V̄flap,i+1,j
Ωi+1
calculate
λr,i,j
limit
3 < λr < 18
j≤3
set flap
βi+1,j = βopt
lookup table
βopt = β(λr )
end
Figure 12. Lookup table controller (LTC)
Paero,no flap
Paero,flap
5
Paero [MW]
3.5
3
2.5
2
without flap deflection
with flap deflection
1.5
335
340
345
350
355
360
4
3
2
1
335
365
340
345
350
355
360
t [s]
t [s]
(a) Generator power vs time
(b) Aerodynamic power vs time
Figure 13. Part of time histories for turbulent simulation with average wind speed of 8 m/s
∆E∆V =+1
∆E∆V =−1
∆E
1.2
1
0.8
0.6
∆E [%]
Pgenerator [MW]
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start
0.4
0.2
0
−0.2
−0.4
−0.6
10−2
10−1
100
F∆V [Hz]
Figure 14. Energy gain and loss due to flap use vs frequency of a square wave in wind speed
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365
The steady torque coefficient depends on local speed ratio and the flap angle. This dependency was
determined using steady state analysis in the BEM Tool. For the steady torque coefficient one can write:
st
st
CQ
= CQ
(λr , β)
(13)
A VAF of 100% means that the two compared signals are the same. Figure 15 shows the VAF achieved
for different prediction horizons with the linearized model, as in Equation 12. Especially with a prediction
horizon of 1 time step the model is very capable of predicting the torque coefficient, a VAF> 99% was found.
In the considered prediction horizons of 0.5s and 2.5s, the VAF stays above 80%.
100
95
VAF [%]
Downloaded by UNIVERSITY OF ADELAIDE on October 26, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.2014-0874
Linear regression was applied on the results of a set of simulation to find the vectors A, B. Those
simulations were done for a 1D turbulence spectrum and wind shear combined with a random flap deflection.
If the steady torque coefficient is known the recurrence relation in Equation 12 provides the opportunity
dyn
to predict the torque coefficient, ĈQ
, over an prediction horizon, thoriz . To check the quality of the linear
model, A, B, the variance accounted for, VAF, was determined:


dyn
dyn
var CQ
− ĈQ,i+1
 · 100%
(14)
VAF = 1 −
dyn
var CQ
90
85
80
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
thoriz [s]
Figure 15. Variance accounted for versus the prediction horizon
2.
Optimization procedure
The rotor speed is assumed to be constant and the wind speed can be measured. Consequently the local
speed ratio can be estimated over the prediction horizon. This leaves the flap angle as the only variable in
linear prediction model that is not fixed.
Goal of the MPC is to maximize aerodynamic torque over a time span, the prediction horizon. Using
the linearized model the torque can be expressed as a function of the steady torque coefficient. In order to
achieve maximum torque the following cost function has to minimized:
Cost =
1
ihoriz
P
n=i
=
Qn
1
ihoriz
P
n=i
dyn
CQ,n
(15)
·
2
V0,n
In the MPC this minimization is done through optimization of the steady torque coefficients over the prediction horizon.
The range of possible steady torque coefficients is limited. Therefore, optimization is constrained as
follows. Goal of the MPC is to control the flap angle in such a way that steady state optimum flap deflection
is reached via an optimal path. Because of that the following constraint is introduced: at the prediction
horizon the steady torque coefficient must be the maximum steady torque coefficient possible for the local
speed ratio at that time step. This fixes the flap angle at the prediction horizon, βhoriz . To avoid large flap
commands, the flap angle is only allowed to vary in the range between current flap angle and the flap angle
at the prediction horizon. Combining this range of flap angles with the local speed ratios (known via LIDAR
measurements) over the prediction horizon limits the path that the steady torque coefficient can follow. The
limits of the steady torque coefficients are found using the table described by Equation 13.
This MPC controller has been implemented and first been tested in a series of steps in the wind speed
of 0.5m/s at 0.2Hz and a baseline wind speed of 9m/s. Figure 16 shows a time window of this simulation.
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American Institute of Aeronautics and Astronautics
The baseline case is a simulation without flap activity. For the current simulation a prediction horizon of
2.5 seconds has been chosen. While the LTC controller increases the power during increasing wind speed,
the MPC controller shows a more complicated reaction. Initially, during increasing wind speed, a increase
in power can be seen. However, this increase is quickly turned into a decrease compared to the control free
case. When the wind speed is stepped down, a strong initial dip in the power response is seen, however
this transitions into a significant increase directly after recovering from this dip. The power integral over
one positive and negative step in wind speed is positive such that this controller also yields a higher energy
output.
Downloaded by UNIVERSITY OF ADELAIDE on October 26, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.2014-0874
Qaero [MNm]
2.7
2.6
2.5
2.4
2.3
2.2
72
74
76
78
80
82
84
t [s]
baseline
LTC
MPC thoriz = 2.5s
Figure 16. Aerodynamic torque using the MPC and LTC for a time window between 72 and 92s, with a
prediction horizon of 2.5 s
The performance of the LTC and MPC are compare in Table 1. For the MPC controller two different
prediction horizon were used: 0.5s and 2.5s. One should note that the 2.5s case is purely academic as the
computation time, even when only using a very simple BEM model was much higher than real time and
can therefore not be applied in wind turbine control. The increase in energy capture for the simple LTC
controller is 0.31, while the more complex MPC performs more poorly when considering the low prediction
horizon case. Only when the prediction horizon is significantly increased, the LTC can be outperformed.
Table 1. Increase in energy from LTC and MPC, corresponding to simulations in Figure 16
LTC
∆Eaero [%]
∆Egenerator [%]
3.
0.30
0.31
MPC
thoriz = 0.5s thoriz = 2.5s
0.25
0.40
0.21
0.42
Power production simulations using LTC
As a final step, time domain simulations have also been performed for the LTC controller. This controller was
chosen despite the potentially higher gains of the MPC controller because of the computational requirements
that make an implementation of the MPC in a field test very challenging. Two different turbulence models
have been used, namely the Mann and the Kaimal turbulence spectra to create 1D turbulent wind speed
histories. As before, wind shear was included in the simulations. 10 minutes of turbine operation were
simulated with wind speeds between between 7-11 m/s. Figure 17 shows the energy increase as a function of
wind speeds. One can see that the resulting differences in generator power between the 2 turbulence models
are less than 5% for all wind speeds and will therefore not be decisive for the evaluation of the controller
performance.
As shown in Figures 5(a) and 17, the addition of turbulence to the simulations increases the energy
capture of the LTC from 0.5% to 0.9%. Combining this power performance increase with the Weibull
distribution, an increase in annual energy production of 0.4% is obtained.
VIII.
Conclusions
An approach for the sizing and control of trailing edge flaps for maximum power capture on a wind
turbine with a smart rotor in low fatigue damage wind regimes has been presented.
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American Institute of Aeronautics and Astronautics
0.92
∆Egenerator [%]
0.91
0.9
0.89
0.88
Mann: ∆Egenerator
Kaimal: ∆Egenerator
0.87
0.86
7
8
9
10
11
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V0 [m/s]
Figure 17. Increase in energy vs wind speed: 10 minute simulations with 1D turbulence and wind shear
Wind speeds below rated wind speed contribute less than 2% to the fatigue damage equivalent load
flapwise root bending moment. Therefore, trailing edge flaps can be used for secondary purpose below rated
wind speeds without negative impact on the fatigue damage.
An unsteady BEM tool has been developed and validated against HAWC2Aero. With this tool, it
has been shown that trailing edge flaps cannot increase the maximum power coefficient of the investigated
turbine, when operating at optimal tip speed ratio. However, for suboptimal tip speed ratios, flaps are
able to increase the power coefficient. Although the pitch mechanism is also capable of increasing the power
coefficient, the investigated setup of the flaps outperform the pitch mechanism over the entire range of design
tip speed ratios below rated wind speed.
A turbine operating in a physical wind field experiences great variations of local speed ratios. Part of
these variations are deterministic. The predictability of these variations makes them suitable for power
optimization using trailing edge flaps, as the flap angle for maximum power can be described as a function
of local speed ratio.
Taking into account the possibilities for increasing the energy yield using trailing edge flaps, the size
and location of the flaps has been analysed. A design study aiming for optimal flap location and length
for maximizing power has been carried out. It is concluded that flap elements near the blade tip are most
effective. Accordingly flaps should be placed from 0.97 r/R running towards the blade root. The length of
the flap can be determined after a trade off between the possible power increase and the extra costs and
complexity of installing extra flap length. Multiple flap segments only show a small benefit over a single
flap, therefore it is recommended to only use one element.
An aerodynamic simulation has been performed of the NREL 5MW reference turbine. Two different
control schemes have been studied in a simulation with steps in the wind speed. A look-up table controller
based on the local instantaneous speed ratio increased the energy production of the wind turbine by 0.31%,
while a more complex model predictive controller only increased this value when a sufficiently long prediction
horizon was implemented.
Consequently, the LTC has been used in time domain simulations with a 1D turbulence field and wind
speeds between 7-11 m/s. The controller was able to achieve an increase of 0.4% in annual energy production.
References
1 Ashuri, T. (2012), “Beyond Classical Upscaling: Integrated Aeroservoelastic Design and Optimization of Large Offshore
Wind Turbines,” PhD Thesis, Delft University of Technology, The Netherlands (ISBN: 9789462032101)
2 Bergami, L., Gaunaa, M., “Analysis of aeroelastic loads and their contributions to fatigue damage,” The Science of Making
Torque from Wind, 9.-11. October 2012, Oldenburg, Germany
3 Baek, P. (2011), “Unsteady Flow Modeling and Experimental Verification of Active Flow Control Concepts for Wind
Turbine Blades,” PhD Thesis, Risø-DTU, Denmark
4 Jonkman, J., Butterfield, Musial, Scott (2009), “Definition of a 5MW reference wind turbine for offshore system development,”Technical Report, National Renewable Energy Laboratory, Colorado, USA (NREL/TP-500-38060)
5 Bossanyi, E.A. (2003), “GH bladed theory manual,”Technical Report, Garrad Hassan and Partners Ltd. (282/BR/009)
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American Institute of Aeronautics and Astronautics
Downloaded by UNIVERSITY OF ADELAIDE on October 26, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.2014-0874
6 Bernhammer, L.O., De Breuker, R., van Kuik, G.A.M., Berg, J., van Wingerden, J.-W., “Model Validation and Simulated
Fatigue Load Alleviation of SNL Smart Rotor Experiment,” 51st AIAA Aerospace Sciences Meeting, 7.-10. January 2012,
Grapevine, USA
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using smart rotors,” 9th Phd Seminar on Wind Energy in Europe, 18.-20.September 2013, Visby, Sweden
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9 Hansen, M.O.L. (2008),“Aerodynamics of Wind Turbines - Chapter 9 Unsteady BEM Model,” Earthscan LLC (ISBN:
9781849770408)
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Earthscan LLC (ISBN: 9781849770408)
11 Schepers, J. G., Snel, H., van Bussel, G.J.W., (1995),“Dynamic Inflow: Yawed Conditions and Partial Span Pitch
Control,” Technical Report, ECN Petten, The Netherlands (ECN-C–95-056)
12 Bergami, L., Gaunaa, M. (2012), “ATEFlap Aerodynamic Model, a dynamic stall model including the effects of trailing
edge flap deflection,”Technical Report, Risø-DTU, Denmark (Risø-R-1792(EN))
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