Document [original]

Wind Energ. Sci., 6, 791–814, 2021

https://doi.org/10.5194/wes-6-791-2021

the Creative Commons Attribution 4.0 License.

Active flap control with the trailing edge

flap hinge moment as a sensor: using it to

estimate local blade inflow conditions and to

reduce extreme blade loads and deflections

Sebastian Perez-Becker, David Marten, and Christian Oliver Paschereit

Chair of Fluid Dynamics, Hermann Föttinger Institute, Technische Universität Berlin, Berlin, Germany

Correspondence: Sebastian Perez-Becker (s.perez-beck[email protected])

Received: 8 January 2021 – Discussion started: 4 February 2021

Revised: 19 April 2021 – Accepted: 20 April 2021 – Published: 2 June 2021

Abstract. Active trailing edge flaps are a promising technology that can potentially enable further increases

in wind turbine sizes without the disproportionate increase in loads, thus reducing the cost of wind energy

even further. Extreme loads and critical deflections of the blade are design-driving issues that can effectively

be reduced by flaps. In this paper, we consider the flap hinge moment as a local input sensor for a simple flap

controller that reduces extreme loads and critical deflections of the DTU 10 MW Reference Wind Turbine blade.

We present a model to calculate the unsteady flap hinge moment that can be used in aeroelastic simulations in

the time domain. This model is used to develop an observer that estimates the local angle of attack and relative

wind velocity of a blade section based on local sensor information including the flap hinge moment of the blade

section. For steady wind conditions that include yawed inflow and wind shear, the observer is able to estimate the

local inflow conditions with errors in the mean angle of attack below 0.2◦and mean relative wind speed errors

below 0.4 %. For fully turbulent wind conditions, the observer is able to estimate the low-frequency content of

the local angle of attack and relative velocity even when it is lacking information on the incoming turbulent wind.

We include this observer as part of a simple flap controller to reduce extreme loads and critical deflections

of the blade. The flap controller’s performance is tested in load simulations of the reference turbine with active

flaps according to the IEC 61400-1 power production with extreme turbulence group. We used the lifting line

free vortex wake method to calculate the aerodynamic loads. Results show a reduction of the maximum out-of-

plane and resulting blade root bending moments of 8 % and 7.6 %, respectively, when compared to a baseline

case without flaps. The critical blade tip deflection is reduced by 7.1 %. Furthermore, a sector load analysis

considering extreme loading in all load directions shows a reduction of the extreme resulting bending moment

in an angular region covering 30◦around the positive out-of-plane blade root bending moment. Further analysis

reveals that a fast reaction time of the flap system proves to be critical for its performance. This is achieved with

the use of local sensors as input for the flap controller. A larger reduction potential of the system is identified

but not reached mainly because of a combination of challenging controller objectives and the simple controller

architecture.

Published by Copernicus Publications on behalf of the European Academy of Wind Energy e.V.

792 S. Perez-Becker et al.: Active flap control with the trailing edge flap hinge moment as a sensor

1 Introduction

Wind turbines have increased dramatically in size over the

past years in an effort to reduce the cost of wind energy and

make it a competitive source of energy. The increased instal-

lation numbers of new wind turbines in Germany over the

years is an example of the success that this strategy has had

(Burger, 2018). Increasing the turbine size also has its draw-

backs. A larger rotor will see increased loads that cannot be

compensated for by a geometric upscaling of the components

alone (Jamieson, 2018, 97–123). In order to withstand these

loads, the structure of turbine components such as the blade

has to be stiffer, which requires more material or stronger

(and more expensive) material. This results in an increase in

cost of energy. Advanced turbine controllers counteract the

increased loads of larger turbines, thereby limiting the need

for additional material and decreasing the cost of energy. The

most widely used actuator for load reduction is the pitch actu-

ator. Its main advantage is its availability because it is already

being used in the power regulation strategy. Yet it has several

drawbacks regarding load control. As wind turbines become

larger, the frequency bandwidth of their pitch actuators is re-

duced mainly due to the increased inertia of the blade. This

reduces the ability of current advanced load-reduction con-

trollers – based on full span pitch control – to react to sud-

den local wind gusts and to fast-changing turbulent inflow,

thereby limiting their effectiveness. Loads arising from non-

uniform wind fields (e.g., wind shear and turbulence) have a

greater effect in larger turbine rotors (Madsen et al., 2020).

Such effects are better countered with spatially distributed

actuation devices than with an actuator for the whole blade,

as is the case for the pitch system.

A promising alternative to conventional full span pitch

control is the concept of the smart rotor with distributed ac-

tive flow control (AFC) devices. Barlas and van Kuik (2010)

give an overview of the different control concepts, actuators

and sensors that are relevant for active load alleviation in

smart rotors. The authors conclude that trailing edge (TE)

flaps and microtabs are the most promising actuation con-

cepts. This comes from their ability to effectively change the

local lift, their high actuation bandwidth and the simplicity

considering their implementation.

1.1 Sensors for active flap control

In addition to AFC actuators, the choice of AFC sensors is

another critical aspect for the load alleviation strategies of

smart rotors. Cooperman and Martinez (2015) give a review

of the possible sensors that can be used in smart rotor con-

trol. Many of these sensors have been used in TE flap control

studies over the past years. We can broadly categorize them

into three groups: strain sensors, inertial sensors and inflow

sensors.

–Strain sensors measure the local strains on a compo-

nent. These can be conventional strain gauges or op-

tical strain sensors. Strain sensors have been widely

used in TE flap control strategies. In particular, strain

sensors measuring the flapwise blade root bending mo-

ment (BRBM) have received much attention. A com-

mon strategy that uses these sensors is called indi-

vidual flap control (IFC). It is based on the individ-

ual pitch control (IPC) strategy (Bossanyi, 2003) and

is often used in combination with the latter (Plumley

et al., 2014b; Lackner and van Kuik, 2010; Plumley

et al., 2014a; Jost et al., 2015; Bernhammer et al., 2016;

Zhang et al., 2016). Other studies have used the flapwise

BRBM sensor in PID-type controllers (Barlas et al.,

2016b; Bartholomay et al., 2018), model-based con-

trollers (Henriksen et al., 2013; Bergami and Poulsen,

2015; Chen et al., 2016; Ng et al., 2016) and adaptive

controllers (Navalkar et al., 2014).

–Inertial sensors are able to measure the motion of a

component resulting from a force. The most common

inertial sensors are accelerometers. They offer the ad-

vantage of sensing the effect of the loads before any de-

flections and strains have occurred. If used for TE flap

control, these sensors give the controller potentially

more time to react to sudden disturbances. Integrating

the acceleration values gives information about the ve-

locity and displacement of the component.

Zhang et al. (2016) compare the performance of IFC

strategies based on acceleration and deflection signals to

the more traditional IFC based on the flapwise BRBM.

In Berg et al. (2009) and Engels et al. (2010), the authors

implement TE flap controllers that use the blade tip de-

flection/deflection rate with a PD or PID feedback loop

to control the flaps. This strategy is also used in Wil-

son et al. (2009), where the combination of IPC and the

aforementioned feedback flap control is explored. In the

INNWIND report (Jost et al., 2015), a similar control

strategy that uses the low-passed blade tip acceleration

as input for a PI feedback loop that sets the flap angle is

implemented. A model predictive controller (MPC) for

TE flaps based on local blade displacement is used in

Barlas et al. (2012).

–Inflow sensors are able to measure the local aerody-

namic conditions of a blade section. They are attractive

because they are able to measure the source of the aero-

dynamic loads on a specific blade section before they

affect the section. This gives the TE flaps more time to

react to aerodynamic disturbances and hence to reduce

the loading. Local inflow sensors on the blade include

pitot tubes and surface pressure sensors. A drawback of

pitot tubes is that they might vibrate during operation

or be affected by rain, ice, dirt or insects. Both factors

diminish the accuracy of the measurements or in ex-

treme cases disrupt them. Surface pressure sensors can

be expensive and fragile and may be clogged during op-

Wind Energ. Sci., 6, 791–814, 2021 https://doi.org/10.5194/wes-6-791-2021

S. Perez-Becker et al.: Active flap control with the trailing edge flap hinge moment as a sensor 793

eration (Cooperman and Martinez, 2015). Other types

of inflow sensor are remote inflow sensors and nacelle-

mounted sensors. An example of the former are lidar

sensors while spinner-mounted anemometers are an ex-

ample of the latter.

Bartholomay et al. (2021) analyze the load reduction ca-

pabilities of feed-forward flap controllers on a 2D airfoil

in a wind tunnel. The controllers estimate the lift acting

on the airfoil by means of either a pitot tube or three

surface pressure ports. Barlas et al. (2018) test an active

flap system on a 2 m blade part mounted on a rotating

test rig. They demonstrate the load alleviation poten-

tial of the system using an open-loop controller based

on local inflow measurements. Andersen (2010) studies

several control strategies based on local inflow measure-

ments and their combination with strain gauges placed

along the blade span. Barlas et al. (2012) also consid-

ered an extension of the MPC strategy that measured the

local inflow of the blade section. Jones et al. (2018) use

a blade-mounted pitot tube in addition to the blade root

strain gauges as an addition to an IPC strategy. The use

of the inflow sensor in a cascaded configuration helps

improve the performance of the controller by bypassing

the limitations of the slow blade dynamics on the con-

troller input.

Manolas et al. (2018) combine an IPC strategy with

a feed-forward TE flap controller based on the inflow

measurements of a spinner-mounted anemometer. Un-

gurán et al. (2018) use a combination of a model-

based feedback individual pitch and flap controller and

a model-inverse-based feed-forward controller that uses

the blade effective wind speed measured with a blade-

mounted lidar system.

1.2 Active flap fatigue control and blade design driving

loads

Strain sensors measuring the flapwise BRBM have been a

popular and effective choice because the main focus of TE

flap control has been fatigue load reduction of the out-of-

plane loads. The frequency content of these fatigue loads is

fairly low (Bergami and Gaunaa, 2014). Therefore, these sen-

sors can be effectively used even if they measure the effect

of the aerodynamic loads with a certain delay (caused by the

blade inertia).

Out-of-plane fatigue loads are design driving for several

turbine components. Yet if we focus on the wind turbine

blade, flapwise fatigue loads are not necessarily the best ob-

jective to use TE flaps or other local AFC devices for.

–Flapwise BRBM fatigue loads have a fairly low-

frequency content. Most of the damage concentrates

around the 1P frequency (Bergami and Gaunaa, 2014)

and can be addressed by the pitch controller using

strategies such as IPC.

–Using TE flaps to mitigate 1P and 2P flapwise BRBM

means that the high bandwidth capabilities of these ac-

tuators are not used effectively.

–Using AFC for fatigue load reduction requires a high

number of duty cycles of the actuator. This is a limit-

ing factor in the choice of the actuator. It is also not in

line with the current philosophy of wind turbine designs

since wind turbines are designed to be low maintenance

machines. Having a high number of duty cycles might

result in high maintenance requirements for the AFC

actuator.

Blade optimization studies that include fatigue-oriented

TE flap control as part of their optimization features did

not show significant additional blade mass reduction com-

pared to an optimized blade design without flaps. Barlas et al.

(2016a) optimize the DTU 10 MW Reference Wind Turbine-

blade (Bak et al., 2013) using a multidisciplinary design,

analysis and optimization tool. They find that the results of

the blade optimization are comparable if the blade is opti-

mized with a fatigue-focused flap controller or if the blade is

optimized without flaps altogether. Chen et al. (2017) use an

optimization algorithm to optimize the blade of the NREL

5 MW Reference Wind Turbine (Jonkman et al., 2009) so

that the levelized cost of energy is minimized. The algorithm

also optimizes a model-based controller used for pitch and

TE flap control (Chen et al., 2016). They conclude that

[t]he blade optimization problems addressed in this

work are primarily driven by flapwise stiffness,

with blade deflection, rotor thrust and flapwise ulti-

mate stresses in the spar forming the design drivers

(Chen et al., 2017, p. 764).

Chaviaropoulos et al. (2014) point out that important load

components for preliminary innovative concepts of multi-

megawatt-scaled turbines include the ultimate loads of the

resulting BRBM, ultimate and fatigue loads of the blade root

torsional moment, fatigue loads of the edgewise BRBM, and

the blade tip-to-tower clearance.

From these findings one can conclude that for modern

large rotor blades, the extreme value of the resulting BRBM

and the blade tip-to-tower clearance will be decisive. In the

edgewise direction, the design-driving loads will be dictated

by the fatigue loads arising from the blade’s mass. In this di-

rection, the blade root has to endure a load fluctuation with

an amplitude equaling the blade’s static moment once per

revolution (1P).

1.3 Active flap control for reducing extreme blade loads

and deflections

Should the objective of an AFC strategy shift to reducing

flapwise extreme loads and critical deflections, it would also

have a positive effect on the design-driving edgewise fatigue

https://doi.org/10.5194/wes-6-791-2021 Wind Energ. Sci., 6, 791–814, 2021

794 S. Perez-Becker et al.: Active flap control with the trailing edge flap hinge moment as a sensor

loads of the blade. When an effective controller reduces ex-

treme loads and deflections, the spar cap of the blade can be

optimized and hence the mass of the blade reduced. This in

turn reduces the edgewise fatigue loads near the blade root.

These loads are mainly caused by gravitational forces. In ad-

ditional optimization loops, the blade mass could be further

reduced, potentially creating a virtuous cycle.

If a TE flap control strategy is used to alleviate loads

with high frequency content (such as design-driving extreme

loads), the choice of a sensor for controller input becomes

much more relevant. Using the flapwise BRBM as an in-

put sensor for the TE flap controller has its advantages in

the implementation and maintenance of the sensor but can

have negative effects on the performance of the controller.

Because sensor and actuator are far apart, aerodynamic loads

and deflections at the blade tip are sensed at the root with

a considerable time lag. This time lag carries through to the

actuation response of the controller, limiting its effectiveness

(Andersen et al., 2010; Fisher and Madsen, 2016; Jones et al.,

2018). Inflow sensors would be an attractive sensor choice

were it not for the practical drawbacks of cost (e.g., lidar) or

susceptibility to the elements (e.g., pitot tubes and pressure

sensors) in their implementation (Cooperman and Martinez,

2015).

A possible sensor that has not received much attention

from the community is the TE flap hinge moment (Behrens

and Zhu, 2011). It has the advantage of providing local load-

ing information of a blade section without the need of ad-

ditional inflow sensors on the blade. The flap actuator is as-

sumed to be enclosed inside the blade section. This protects

the hinge moment sensor (located in the actuator) from the

elements, making it a very robust sensor. The loading infor-

mation from the flap hinge can be used in combination with

the high actuation bandwidth of the flaps to effectively re-

duce extreme loads and critical deflections of the blade. This

idea is attractive because it uses the robust and already avail-

able hinge moment sensor in the flap actuator system as an

input for the controller, thus addressing the aforementioned

drawbacks of cost and susceptibility. It is also advantageous

if the TE flap system is to be designed in a modular layout.

The goal of the present study is to explore and quantify

the potential of TE flaps to mitigate design-driving extreme

loads and deflections. We are also interested in exploring

the possibility of using a local and robust sensor as an input

choice for a controller strategy. This paper presents a novel

method that allows the use of the TE flap hinge moment as

an input sensor. It is a model-based observer that estimates

the effective angle of attack of the blade section given the

hinge moment, the accelerations and the relative wind veloc-

ity of the section (the last quantity is also estimated with our

method). In addition, we use this observer as part of a sim-

ple extreme load controller for flaps and analyze its perfor-

mance in a power production scenario with extreme turbulent

wind. Section 2 summarizes our turbine and flap models as

well as the aeroelastic simulation tools used in this study. In

Sect. 3, we present the model used to calculate the unsteady

flap hinge moment in aeroelastic simulations and our novel

observer that estimates the local aerodynamic information

based on this and other sensors. Section 4 presents the results

of the observer under steady and turbulent wind conditions.

In Sect. 5, we present a simple extreme load controller that

uses this observer. We analyze the controller’s performance

in reducing extreme loads under challenging extreme turbu-

lent wind conditions. The conclusions are drawn in Sect. 6.

2 Methods

The DTU 10 MW RWT was chosen as the turbine model.

It is representative of the new generation of wind turbines

and has been used in several research studies. The complete

description of the turbine can be found in Bak et al. (2013).

2.1 Blade with trailing edge flaps

The blade of the DTU 10 MW RWT was modified to accom-

modate TE flaps. The flaps are modeled via dynamic polar

sets that describe the airfoil with discrete flap angles. For this

study we chose a flap that covers 10 % of the chord and has

maximum deflection angles of δ= ±15◦. Figure 1a shows

the polar data of the FFA-W3-241 airfoil – used in the outer

part of the blade – with the modeled flap at maximum and

minimum deflection. In total 15 polar sets were generated

for different discrete flap positions using a Reynolds number

of 1.5×107. The polars were obtained using the airfoil sim-

ulator XFLR5 integrated into QBlade (Marten et al., 2010).

In the simulation, the polar data between the discrete states

are linearly interpolated.

In total six flaps are integrated into the blade, as can be

seen in Fig. 1b. Each section measures 3 m in the spanwise

direction and is assumed to have one hinge moment sensor

and one accelerometer located at the center of the section.

The six sections are located between 64 and 82 m of the

blade span, which corresponds to a relative location between

74.1 % and 95 % of the blade length. The flap actuators are

modeled as a second-order low-pass filter. In the Laplace do-

main, the filter takes the form

δLP(s)=ω2

s2+2ξω ·s+ω2·δ(s),(1)

where ωis the filter frequency and ξthe damping factor. For

the flap actuators, we chose a frequency of 5 Hz and a damp-

ing factor of 1. The maximum and minimum flap rates are

limited to ±100 ◦s−1.

2.2 Aeroelastic simulation tools

We did the development, testing and simulation of the meth-

ods presented in this study using two aeroelastic simula-

tion tools: the first is NREL’s FAST v8.15 and the second

is TU Berlin’s QBlade.

Wind Energ. Sci., 6, 791–814, 2021 https://doi.org/10.5194/wes-6-791-2021

S. Perez-Becker et al.: Active flap control with the trailing edge flap hinge moment as a sensor 795

Figure 1. Trailing edge flaps on the DTU 10 MW RWT blade. (a) FFA-W3-241 airfoil polars with different flap deflection angles. (b) Position

of the six flaps on the blade.

2.2.1 FAST

FAST uses AeroDyn (Moriarty and Hansen, 2005) as its

aerodynamic model. It is based on the blade element mo-

mentum (BEM) theory and uses several correction models

to account for the unsteady aerodynamic phenomena typi-

cally present in aeroelastic simulations with turbulent condi-

tions. These are the tip- and root-loss model, the turbulent

wake state model, the oblique inflow model, the dynamic

stall model, and the tower shadow model.

The used structural model in FAST is ElastoDyn. It has

a combined multi-body and modal dynamics representation

that is able to model the wind turbine with flexible blades and

tower (Jonkman, 2003).

2.2.2 QBlade

QBlade uses the lifting line free vortex wake (LLFVW)

method as its aerodynamic model (Marten et al., 2015). In

this method, the blade aerodynamic forces are evaluated on a

blade element basis using polar data. The near and far wake

are modeled with vortex line elements. These are shed at the

blade’s trailing edge during every time step and then undergo

free convection behind the rotor. Vortex methods can model

the wake with far fewer assumptions and engineering cor-

rections compared to BEM methods. Especially when the

wind turbine is subjected to unsteady inflow or varying blade

loads, the LLFVW method increases the accuracy compared

to BEM methods (Perez-Becker et al., 2020). To model the

dynamic stall of the blade elements, QBlade uses the ATE-

Flap unsteady aerodynamic model (Bergami and Gaunaa,

2012), modified so that it excludes contribution of the wake

in the attached flow region (Wendler et al., 2016).

QBlade is able to model AFC devices such as TE flaps us-

ing two dynamic polar sets. They are defined for the inner

and outer spanwise locations of the AFC device. It is thereby

possible to model AFC elements that span over two differ-

ent airfoils. The ATEFlap model is also capable of modeling

unsteady aerodynamic effects of flap deflections at high re-

duced frequencies. This allows QBlade to accurately model

the aerodynamics of TE flap actuators with high bandwidths.

This is required if a flap control strategy aims at reducing

extreme loads and deflections.

QBlade has a structural solver based on the open-source

multi-physics library CHRONO (Tasora et al., 2016). It uses

a multi-body representation which includes Euler–Bernoulli

beam elements in a co-rotational formulation. It allows

QBlade to accurately simulate the blade deflections and in-

clude the blade torsion, which has a significant influence on

the blade loads.

A more detailed comparison between QBlade and

(Open)FAST can be found in Perez-Becker et al. (2020).

2.3 Controller

For this study, we used the TUB Controller (Perez-Becker

et al., 2021). It is based on the DTU Wind Energy Controller

(Hansen et al., 2013), which features a baseline pitch and

torque control. It has been extended with a supervisory con-

trol based on the report by Iribas et al. (2015). The supervi-

sory control allows the controller to run a full load analysis.

https://doi.org/10.5194/wes-6-791-2021 Wind Energ. Sci., 6, 791–814, 2021

796 S. Perez-Becker et al.: Active flap control with the trailing edge flap hinge moment as a sensor

Figure 2. Sketch showing the angles and coordinate systems of a 2D airfoil section. The blade section is depicted at a rotor azimuth angle

ϕ=90◦. The colors of the deflected flaps correspond to the polar data of Fig. 1.

The controller baseline pitch and torque control parameters

were taken from the report by Borg et al. (2015). The con-

troller has been extended so that it can control AFC devices

such as TE flaps.

3 Estimation of the aerodynamic information

In this section we present the flap hinge moment model used

in this study and the observer based on this model. The lat-

ter is able to estimate the effective angle of attack and rel-

ative velocity of a flapped blade section by means of local

and global sensors, the former being an accelerometer, a flap

position sensor and the flap hinge moment sensor. These sen-

sors and the hinge are assumed to be positioned at the span-

wise center of the blade section with active flap. The global

sensors are the rotor speed, the rotor azimuth angle and the

blade pitch angle. In this study, we define the sign of the

hinge moment to be the same as for the flap angle, i.e., posi-

tive if the flap moves to the pressure side (see Fig. 2).

The observer comprises two parts: an angle of attack esti-

mator and a relative velocity estimator. The first is a collec-

tion of linear observers that estimate the angles of attack for

different constant relative wind speeds. Together they form a

linear parameter varying (LPV) system which is parameter-

ized by the relative wind velocity. The relative velocity esti-

mator uses simple models to estimate the relative wind speed

and serves as the parameter input for the LPV system.

3.1 Hinge moment model

Because we use polar data to derive the aerodynamic loads

on a blade section, we cannot measure the unsteady hinge

moment directly in the simulations. We therefore need a

model to calculate the hinge moment on a blade section. Ig-

noring friction, the total hinge moment on a blade section

with a TE flap can be determined by the sum of the hinge mo-

ment due to gravity loads, the moment due to the flap inertial

loads and the moment due to aerodynamic loads (Plumley,

2015).

3.1.1 Gravity and inertial loads

The gravity loads can be calculated by taking the fraction of

the flap’s center of mass that has an offset in the out-of-plane

direction relative to the flap hinge. If mflap is the flap’s mass

and dflap the flap’s center of mass measured from the flap

hinge, then the hinge moment due to gravitational loads is

given by

MH-g =mflap ·g·dflap ·sin(ϕ)·sin(δ−(θ+β)).(2)

Here, gis the gravitational acceleration, ϕthe rotor azimuth

angle, θthe aerodynamic twist and βthe pitch angle of the

blade. The reader is referred to the list of symbols (Tables B1

and B2) for the definition of the used symbols in this and the

following equations. Figure 2 shows a sketch of the FFA-W3-

241 airfoil when the turbine is at a rotor azimuth position of

ϕ=90◦to illustrate how the gravity affects the hinge mo-

ment.

The hinge moment due to inertial loads is caused by the

loads due to flap acceleration as well as centrifugal, Corio-

lis and gyroscopic loads. As a first approximation, we chose

to neglect the effect of all inertial loads except those arising

from the flap acceleration. The centrifugal forces will act in

the radial direction (i.e., parallel to the blade span) if we as-

sume a straight, undeflected blade without rotor cone angle.

Hence their contribution to the hinge moment will be zero.

This changes if we introduce a cone angle, a pre-bend and

blade deflection. Since the resulting angle of the deflected

blade to the rotational plane will be small, the contributions

of the centrifugal loads on the hinge moment will be small.

A similar argument can be made for the Coriolis forces. The

gyroscopic loads will only arise if the turbine actively yaws.

In the simulations considered within this study the turbine

did not yaw, so gyroscopic loads were not present and hence

not included.

We can therefore write

MH-I =Iflap ·¨

δ, (3)

where Iflap is the flap’s moment of inertia. In this study,

we approximate mflap as the mass of the blade section with

flap multiplied by the flap’s percentage of the chord length.

Wind Energ. Sci., 6, 791–814, 2021 https://doi.org/10.5194/wes-6-791-2021

S. Perez-Becker et al.: Active flap control with the trailing edge flap hinge moment as a sensor 797

Iflap and dflap are approximated assuming a triangular flap

shape (isosceles triangle) with constant density.

3.1.2 Aerodynamic loads

To model the unsteady aerodynamic hinge moment, we

use a model for thin airfoils in inviscous incompressible

flow presented in Leishman (2006, 492–497). It is based on

Theodorsen’s unsteady aerodynamic theory but re-cast into a

state-space formulation for easier use in simulation and con-

trol applications. The reference gives the complete formu-

lation for unsteady lift, pitch and flap hinge moment coef-

ficients of thin airfoils. In this study we are only interested

in the hinge moment coefficients because the unsteady lift

and pitch coefficients are modeled in QBlade via the LLFVW

method and the ATEFlap model.

It should be noted that the hinge moment model pre-

sented in the reference only models the unsteady aerody-

namic hinge moment due to airfoil and flap motion for a

constant wind speed. A complete model should also include

the unsteady hinge moment contribution of varying gust

fields and changes in the relative wind speed of the airfoil.

Nonetheless, the contribution of both can be neglected for

our application, as discussed in Kanda and Dowell (2005)

and Leishman (2006, p. 457).

We included two minor changes to the model presented

in the aforementioned reference. The first change is the in-

clusion of an offset in the hinge moment coefficient for α=

0◦to model the behavior of cambered airfoils. The second

change is the use of flap effectiveness coefficients (Leish-

man, 2006, p. 500) to model the viscous effects of the air-

foil shape and flap deflection on the hinge moment. For com-

pleteness and for reference in the derivation of the estimator

in Sect. 3.2, the aerodynamic hinge model is briefly presented

here in its state-space formulation.

The unsteady hinge moment coefficient Chfor a thin air-

foil with a TE flap is given by

Chα, ˙α, ¨α,δ, ˙

δ, ¨

δ, ˙

h, ¨

h,Vrel=Cnc

h¨α, ¨

δ, ¨

h,Vrel

+Cqs

h˙α,δ, ˙

δ,Vrel+Cc

hα, ˙α,δ, ˙

δ, ˙

h,Vrel+Cc

h-0,(4)

where Cnc

h,Cqs

hand Cc

hare the non-circulatory, quasi-steady

and circulatory components of the hinge moment coefficient.

αrepresents the angle of attack, hthe section’s displacement

normal to the chord (see Fig. 2), Vrel the relative wind veloc-

ity and Cc

h-0 the constant offset of Chat α=0◦.

If we assume that Vrel is constant, then we can write Eq. (4)

as a canonical state-space system that has the form

x=AHin ·x+BHin ·u,(5)

y=CHin ·x+DHin ·u.(6)

The input vector is given by u=

α˙α¨α δ ˙

δ¨

δ˙

h¨

hTand the output is

y=Ch−Cc

h-0. The internal states of the system are

x=z1z2z3z4Tand describe the circulatory com-

ponents of Ch. The state-space matrices are given by the

following equations.

AHin =Az02×2

02×2Az(7)

BHin =





0 0 0 0 0 0 0 0

1b·(1/2−a)

Vrel 0 0 0 0 1

Vrel 0

0 0 0 0 0 0 0 0

000F10

b·F11

2π·Vrel 000







(8)

CHin =α·Czδ·Cz(9)

DHin =DαD˙αD¨αDδD˙

δD¨

δD˙

hD¨

h(10)

The entries for the Azand Czmatrices are

Az="0 1

−b1·b2·Vrel

b2−(b1+b2)·Vrel

b#,(11)

Cz=F12·b1·b2

4·Vrel

b2F12·(A1b1+A2b2)

2·Vrel

b.(12)

The entries for the feedthrough matrix DHin are given in Ap-

pendix A.

In order to obtain the total hinge moment of a blade section

with flap, we add the individual contributions:

MHin =MH-g +MH-I +MH-A

=MH-g +MH-I +1

2·ρ·V2

rel ·c2·Ch·S. (13)

Figure 3 shows the behavior of the hinge model for vari-

ations of αand δ. The variations of αare obtained by a

pure pitching motion of the airfoil. Figure 3a shows Chvs. α

with a constant flap angle of δ=0◦for a reduced frequency

of 0.01. Analogously, Fig. 3c shows Chvs. δwith a constant

angle of attack of α=0◦for a reduced frequency of 0.01.

We can see that Chis more sensitive to changes in δthan to

changes in α. These subfigures also include the steady val-

ues of Chfor the FFA-W3-241 airfoil for several positions

of αand δ. These are calculated with the XFLR5 module in

QBlade. By adjusting the values of Cc

h-0,αand δ, we can

see that our model captures the general behavior of the hinge

moment coefficient of this airfoil. Figure 3a shows that our

model matches the calculated values of the FFA-W3-241 air-

foil for values of αbetween −5 and 5◦. For values below

and above that range, a nonlinear behavior due to flow sepa-

ration emerges, which our model fails to capture. Regarding

flap deflection, our model captures the behavior of the FFA-

W3-241 airfoil even better (Fig. 3c). It is only for values of

δ≥10◦that our model deviates from the XFLR5 calcula-

tions. The reason for this is again the initial separation of the

flow occurring at the trailing edge of the airfoil due to vis-

cosity effects.

Figure 3b and d show the modeled hinge moment MHin

of a 3 m flapped blade section with 2 m chord length and

a mass mflap of 22.6 g. For these subfigures a relative wind

https://doi.org/10.5194/wes-6-791-2021 Wind Energ. Sci., 6, 791–814, 2021

798 S. Perez-Becker et al.: Active flap control with the trailing edge flap hinge moment as a sensor

Figure 3. (a) Chvs. αwith δ=0◦from XFLR5 results and from quasi-steady model simulations. (b) MHin vs. αfor several reduced freqs.

kand δ=0◦.(c) Chvs. δwith α=0◦from XFLR5 results and from quasi-steady model simulations. (d) MHin vs. δfor several reduced

freqs. kand α=0◦.

speed Vrel of 80 m s−1is used, and it is assumed that the

flapped blade section is at a rotor azimuth angle ϕof 0◦. This

way we have MH-g =0 Nm. In Fig. 3b, MHin is plotted for

oscillations of αat several reduced frequencies kwith a con-

stant flap angle δ=0◦. Figure 3d shows MHin for oscillations

of δand a constant α=0◦. In both cases, the unsteady aero-

dynamics are clearly seen for larger values of k. In Fig. 3d we

can also see the increased effect of MH-I on MHin for larger

values of k.

We note that – although not shown in Fig. 3 – the aerody-

namic hinge model presented in this section is also capable

of calculating the hinge moment due to the section’s normal

displacement h. This includes the implicit calculation of the

effective angle of attack which depends on α,˙α,˙

hand Vrel

(Leishman, 2006, p. 496). A less compact and more readable

form of the aerodynamic hinge moment model can be found

in Leishman (2006, 492–497).

3.2 Estimation of the effective angle of attack

We can use the model presented in the previous section to

estimate the effective angle of attack of the blade section by

means of a linear observer. The idea is to estimate the in-

ternal states of a system based on the measured inputs and

outputs. If we cannot measure the quantities α,˙αand ¨α(be-

cause we would need an inflow sensor), we have to estimate

them using the measured MHin and other available sensors.

In this study, we follow an approach used in Kracht et al.

(2015). The observer model is comprised of three submod-

els: a nonlinear MH-g model, a linear hinge model (that esti-

mates ˆ

MH-A and ˆ

MH-I) and a signal model. The latter is used

to estimate the quantities we cannot measure. All three mod-

els are combined to produce an estimated hinge model ˆ

MHin.

The estimation is then compared to the measured MHin, and

the error is fed back to the states of the linear hinge model

and the signal model using an appropriately chosen gain L.

Figure 4 shows a graphical representation of the observer

structure. The hinge moment model of the observer uses the

same state-space matrices AHin,BHin,CHin and DHin, with

the exception of DHin. The inertial loads given by Eq. (3)

are included in the feedthrough term D¨

δof DHin so that the

linear observer can use the state-space matrices to estimate

MH-A +ˆ

MH-I directly.

The output of the state-space representation does not in-

clude ˆ

MH-A0, the constant value of the hinge moment for α=

0◦. In addition, MH-g cannot be written in state-space form

due to its non-linear nature. It therefore cannot be directly in-

cluded in the observer model. However, it is highly determin-

istic and can be estimated using Eq. (2) with readily avail-

able sensors. The observer uses Eq. (2) to estimate ˆ

MH-g.

As for ˆ

MH-A0, the observer multiplies V2

rel by a constant fac-

tor that includes Cc

h-0 and the dimensions of the blade sec-

tion. Both quantities are subtracted from the measured MHin

so that the error is calculated between (MH-A +MH-I) and

(ˆ

MH-A +ˆ

MH-I).

For this study we use a simple signal model. It basically

assumes that αand its derivatives do not change with time.

The choice of this signal model is based on the fact that the

source of change of α– the incoming wind speed VOP – is

turbulent and therefore difficult to predict. The downside is

Wind Energ. Sci., 6, 791–814, 2021 https://doi.org/10.5194/wes-6-791-2021

S. Perez-Becker et al.: Active flap control with the trailing edge flap hinge moment as a sensor 799

Figure 4. Representation of the linear observer for a constant Vrel. The required sensors and the observer output are marked with a green

and blue background, respectively.

that the estimated signal will always have a lag compared to

the actual signal. The signal model has the following state-

space matrices:

ASig =



010

001

000

,(14)

CSig =I3×3.(15)

We note that other signal models can be used, such as, e.g., a

bank of independent harmonic oscillators (Kracht et al.,

2015), if the wind conditions for a particular site are known

with a certain degree of accuracy.

If we combine the signal and hinge moment mod-

els, we get a state space whose input vector is uS+H=

δ˙

δ¨

δ˙

h¨

hTand its output is yS+H=(ˆ

MH-A +ˆ

MH-I).

The state-space matrices for this combined system are as fol-

lows.

AS+H=ASig 03×4

Bα

Hin AHin(16)

BS+H=03×5

BRes

Hin(17)

CS+H=DαD˙αD¨αCHin(18)

DS+H=DδD˙

δD¨

δD˙

hD¨

h(19)

In these equations, Bα

Hin corresponds to the sub-matrix

of BHin that relates to αand its derivatives. BRes

Hin corresponds

to the rest of BHin. The entries of these matrices are written

out explicitly in Appendix A.

The final state-space representation of our observer has the

form

Aobs =AS+H−LCS+H,(20)

Bobs =(BS+H−LDS+H)L,(21)

Cobs =1000000,(22)

Dobs =01×6.(23)

Its input vector is given by uobs =

δ˙

δ¨

δ˙

h¨

hMHin −ˆ

MH-g −ˆ

MH-A0T

and its

output is yobs = ˆα.

The gain matrix Lis obtained using a standard Kalman

filter design. In order to tune our estimator, we use the co-

variance matrices for process noise QLand for measurement

noise RL.

The derivation of the linear estimator above is only valid

for one fixed value of Vrel. This is not the case for a wind tur-

bine blade in normal operation. In order to extend the estima-

tor so that it can be used for varying Vrel, a linear parameter

varying (LPV) model was built using the observer matrices

for different values of Vrel. This way, the nonlinear aerody-

namic behavior of the flap hinge moment is parameterized

with a set of linear observers, allowing for a fast and opti-

mal estimation for each value of Vrel. If Vrel is used for the

LPV model, it needs to be measured or estimated. The for-

mer option is not available, since we chose not to use inflow

sensors. This leaves us with the estimation option, presented

in the next section.

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800 S. Perez-Becker et al.: Active flap control with the trailing edge flap hinge moment as a sensor

3.3 Estimation of the relative velocity

To estimate Vrel, we decompose the velocity into in-plane

and out-of-plane components. The in-plane component of the

rigid blade can be readily estimated using the rotor speed 

and the distance between the hub center and spanwise center

of the flapped blade section rflap:

VIP =·rflap.(24)

For the out-of-plane component, we use a simple estimator

based on the anemometer wind speed VAne, the rotor azimuth

angle ϕand the normal velocities of the flapped blade sec-

tions of the three blades that share the same spanwise dis-

tance from the rotor hub ( ˙

h1–˙

h3). The latter can be obtained

by integrating the signal of accelerometers measuring the lo-

cal accelerations of the sections of each blade:

VOP =VAne +1Vop ˙

h1,˙

h2,˙

h3,ϕ.(25)

1Vop(˙

h1,˙

h2,˙

h3,ϕ) is a function that accounts for the verti-

cal variation in VOP dependent on the azimuthal position of

the blade due to, e.g., wind shear. It comprises two parts: a

vertical variation part and a tower shadow model.

The vertical variation part uses the once-per-revolution

Coleman transform of the velocities of the blade sections

normal to the chord to get an equivalent amplitude of the

vertically varying velocity normal to the chord of the rotor

annulus at the spanwise position of the flapped blade section.

vsin =2

3·sin(ϕ)·˙

h1+sinϕ+2π

3·˙

+sinϕ+4π

3·˙

h3(26)

We then use a linear transform of this quantity to estimate the

vertical variation in the out-of-plane wind velocity at differ-

ent azimuthal positions of the blade.

1Vop-v =c1·cos(ϕ)·vsin +c2for −π

2≤ϕ≤π

c3·cos(ϕ)·vsin +c4for π

2< ϕ < 3π

(27)

The two cases in the above equation are necessary because of

the non-linear effect of wind shear on the vertical wind veloc-

ity. Because we are approximating the out-of-plane variation

with a simple cosine function, we use two amplitudes to ac-

count for the variation at the lower and upper half planes of

the rotor. The constants c1–c4were obtained by fitting the

results of the values of 1Vop-v and vsin from aeroelastic con-

stant wind simulations of the turbine. In addition, vsin is low-

passed and notch filtered to filter out the higher-frequency

contributions to the normal velocity of the rotor annulus.

The tower shadow variation part uses a simplified approxi-

mation of the tower shadow model from Bak et al. (2001). We

simplified this model by assuming a constant xdistance (out

of plane) between blade and tower. It was taken as the aver-

age distance between the blade section and the tower surface

in constant wind aeroelastic simulations. That is one constant

value that is used for all wind speeds. The tower shadow vari-

ation is added to 1Vop-v to get 1Vop.

Once we have calculated VIP and VOP, we use both quan-

tities to obtain the relative velocity of the flapped blade sec-

tion. In uniform aligned inflow, Vrel would be the resulting

velocity from the previous quantities. This is almost never the

case. To account for the oblique inflow, we use the trigono-

metric correction presented in Damiani et al. (2018):

Vrel =(VOP ·cos(γ)·cos(τ)− ˙x)2+(VIP − ˙y−VOP

·(cos(γ)·sin(τ)·sin(ϕ)+sin(γ)·cos(ϕ)))21

2.(28)

For this correction, we need to know the shaft tilt angle τ

and the current yaw-misalignment angle γ. The latter can be

obtained via the hub-mounted anemometers. In Eq. (28), we

also included the in-plane ( ˙y) and out-of-plane ( ˙x) velocities

of the flapped blade section due to blade elasticity. These can

be obtained by rotating the chordwise and normal velocities

of the section by the current blade pitch angle and the twist

angle (see Fig. 2):

˙x=˙

h·cos(180◦−(β+θ)) +˙

f·sin(180◦−(β+θ)),(29)

˙y= − ˙

h·sin(180◦−(β+θ)) +˙

f·cos(180◦−(β+θ)).(30)

We note that the expression for VOP is a relative simple es-

timation of the out-of-plane velocity. This is not exact since

there is significant variation in VOP along the rotor disc due

to the non-linear wind shear and turbulence. This error can

be tolerated because V2

IP dominates in the right-hand side of

Eq. (28). This is specially so for large rotor blades with high

tip speed ratios, which is the current industry trend. So an

error in VOP will only have a small contribution towards Vrel

and hence towards ˆα. There have been several studies that

include more accurate estimations of the rotor effective wind

speed, Simley and Pao (2016) and Bertelè et al. (2017) be-

ing two examples. Such methods could be used to further

increase the accuracy of the current wind speed estimator.

Additional improvements could also be achieved if we in-

clude the effect of tower top displacements on the estimated

local Vrel.

Combining the Vrel estimator with the estimator for α

gives us the final LPV observer based on the flap hinge mo-

ment sensor.

3.4 Discussion

The derivation of the model and observer presented in this

section is based on several assumptions. The first is the

2D airfoil analysis assumption. It is therefore only correct for

an infinitely thin blade station. Changes in the wind distribu-

tion and angle of attack along the span of the blade section

will have an integrated effect on the hinge moment and po-

tentially deviate from the pure 2D analysis. In this study we

Wind Energ. Sci., 6, 791–814, 2021 https://doi.org/10.5194/wes-6-791-2021

S. Perez-Becker et al.: Active flap control with the trailing edge flap hinge moment as a sensor 801

assume that the aerodynamic conditions do not change sig-

nificantly within a flapped blade section and therefore can be

treated as effective quantities for the section.

To have an idea of the error made with this assumption, we

take the innermost 3 m flapped section with the aforemen-

tioned sensors located at the center of the section span. The

center of this section is situated at a blade radius of 65.5 m.

For turbine operation at rated rotor speed, the difference of

local in-plane wind speeds between the center of the blade

section and the inner part of the section span is about 2 %

of the in-plane velocity at the section center. For the outer

flapped sections, the relative error decreases due to the in-

creased wind speed used for reference. For the out-of-plane

wind speed we can estimate the error by looking at the co-

herence function of the spatial distribution of the turbulence.

Assuming a Kaimal wind model, the spatial coherence func-

tion of two points that are 1.5 m apart is 0.75 for a frequency

corresponding to 1P and an average out-of-plane velocity of

10 m s−1(IEC 61400-1 Ed. 3, 2005).

Ultimately the validity of this assumption is reflected in the

controller performance and has to be assessed experimentally

or in simulations. Jones et al. (2018) also assume a correla-

tion between the lift forces occurring at nearby blade stations

and the lift force of the blade station where a pitot tube is in-

stalled. With this assumption they are able to enhance the

performance of an IPC controller based on the information

of one inflow sensor per blade. In Barlas et al. (2018), the

authors successfully control a 2 m flapped blade section us-

ing a feed-forward controller based on the local information

of one pitot tube. These are encouraging results suggesting

the aforementioned assumption is valid.

The observer presented in this section is based on a thin

airfoil model and does not correspond to physical airfoils

used in wind turbines. As we saw in Sect. 3.1.2, our model

only partially captures the viscous effects of flow separation

that greatly influence the behavior of Chas a function of α.

We approximated this effect with the use of flap effectiveness

coefficients. Nonetheless, the nonlinear behavior for larger

absolute values of αwas not captured. To improve our mod-

eling, we could determine the complete state-space models

of the flap hinge moment at different wind speeds experi-

mentally. This could be done for example in wind tunnel tests

with the help of system identification techniques (Bartholo-

may et al., 2018).

4 Estimator performance

In this section we present the performance of the estimator

using a series of steady and turbulent wind fields in combi-

nation with the turbine model. To illustrate the performance

of our estimator, we simulate one 3 m flapped blade section

at the rotor spanwise position of 74.3 m. The flap angle is

held constant at δ=0◦for all the simulations in this section.

Table 1. Simulation parameters for aeroelastic calculations.

Parameter Steady calculations Turbulent calculations

Mean VHub 4–24 m s−17–17 m s−1(9–17 m s−1)

Wind model steady IEC NTM (ETM)

Wind shear exp. 0.2 0.2

Upflow angle 0◦8◦

Yaw angle −8, 0, 8◦−8, 0, 8◦

Aeroelastic code FAST V8.15 QBlade

4.1 Implementation of model and observer in the

aeroelastic codes

Both the hinge moment model and the observer are included

in the TUB Controller (Perez-Becker et al., 2021). The inputs

for the model (u=α˙α¨α δ ˙

δ¨

δ˙

h¨

hTand Vrel)

and for the observer (uS+H=δ˙

δ¨

δ˙

h¨

hTand the in-

puts for the velocity estimator) are calculated by the aeroe-

lastic code and passed to the controller via an appropriate

interface. For the FAST simulations the interface occurred

within a Simulink environment. For the QBlade simulations,

a special interface was developed between the software and

the controller to be able to pass the required inputs.

As discussed in Sect. 3.4, the hinge moment model and

observer are inherently 2D models that require the input at

one specific location. We chose this location to be the cen-

ter of each flapped blade section and assume that this loca-

tion is representative for the whole section. For the FAST

simulations, the blade is discretized into 46 aerodynamic and

57 structural nodes, with nodes specially chosen at the center

of each flapped blade section. In QBlade, the blade is dis-

cretized into 25 aerodynamic and 20 structural nodes. The

aerodynamic nodes are spaced sinusoidally along the blade

span. The aerodynamic and structural information at the cen-

ter of the flapped blade sections is obtained by linearly inter-

polating the information from neighboring nodes.

The performance of our observer is evaluated by its ability

to estimate the representative aerodynamic quantities at the

center of each flapped blade section.

This modeling approach could be improved if we consider

more aerodynamic blade elements so that several of them lie

within a flapped blade section. These elements would be used

to calculate the lift force acting on the whole section. Using

a representative airfoil polar for the blade section, we could

calculate the effective angle of attack at the center location

of the section and use this as an input for our hinge model.

It would also be this effective angle of attack that would be

estimated by our observer.

4.2 Steady wind conditions

The parameters of the steady wind simulations are listed in

Table 1 under the column “Steady calculations”.

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802 S. Perez-Becker et al.: Active flap control with the trailing edge flap hinge moment as a sensor

Figure 5. Behavior of the estimator for two different wind speeds as a function of the rotor azimuth angle. (a) Flap hinge moment; (b) relative

velocity; (c) angle of attack. E: estimated; R: real.

Figure 5 shows three key variables for our estimator in

simulations with two different hub height wind speeds. One

wind speed around rated wind and one above rated where

the influence of the pitch angle increases. The simulations

were performed with steady wind speeds and a constant na-

celle yaw angle of −8◦. We can see in Fig. 5a the behavior

of MHin as a function of ϕ. In both the 11 and the 17 m s−1

wind speed simulations MHin is mostly determined by MH-A.

The larger azimuthal variation in MHin in the 17 m s−1wind

speed simulations comes from the higher relative wind speed

variations due to wind shear.

Figure 5b and c show the estimated and real values of Vrel

and αas a function of ϕ. We can see that the observer is

able to estimate the relative velocity and angle of attack at

this blade section well. There is a slight delay of ˆαcompared

to α, but it is small at the timescale of one rotor revolution.

For both wind speeds, there is a clear difference at an azimuth

angle of ϕ=180◦. The velocity drop of Vrel is due to the

tower shadow, which was only approximated in our velocity

estimator. This tower shadow effect on αis also not captured

correctly by our estimator (Fig. 5c). We can also see in these

figures the variation due to wind shear of Vrel and α. Our

approximation captures this variation well but there are still

some small differences between the real and the estimated

quantities.

Figure 6 shows the results of steady wind calculations for

all wind speeds relevant to power production and for three

different yaw angles of the nacelle. The markers represent

the mean of the steady simulations, and the error bars repre-

sent the extrema of the simulations. Figure 6a, c and e show

the estimated and real relative velocities at the blade section.

Our velocity estimator is able to capture these differences and

keeps the relative error of the mean velocities at below 0.4 %.

Figure 6b, d and f show the corresponding estimated and

real values of αat the blade section. We see that the observer

manages to estimate the mean angle of attack with an error

below 0.2◦for all simulations. The differences in the extrema

of αare more marked, especially for higher values of Vhub.

The differences in the minima can be explained by the ap-

proximation of the tower shadow, which fails to capture the

dip in αat azimuth values of ϕ=180◦(Fig. 5c). If we look

at the range of Vhub between 8 and 14 m s−1, we can see that

the differences between real and estimated maxima of αare

small. This is of importance if we want to use the observer as

part of a load alleviation controller targeting extreme loads.

This is the wind speed range where the turbine sees the high-

est out-of-plane loading in power production (Barlas et al.,

2016b).

4.3 Turbulent wind conditions

We also analyzed the performance of our estimator in fully

turbulent wind load calculations. These situations are espe-

cially challenging for the observer because our relative ve-

locity estimator does not model turbulent out-of-plane wind

speeds. The setup for the turbulent calculations is shown in

Table 1 in the column “Turbulent calculations”.

Because the observer lacks the turbulent variation in the

out-of-plane wind speed in the relative velocity estimator,

the estimated ˆαwill have a significantly larger variation than

the actual α. This is because the observer will attribute the

changes in MHin to the unmeasured α, since it can only as-

sume a correct parametrization coming from ˆ

Vrel. In order

to limit the variations in ˆα, an additional first-order low-pass

filter was added to the output of the ˆαobserver.

Figure 7 shows time series that illustrate the performance

of the observer in turbulent wind conditions. The simulations

are for mean Vhub values of 7 and 15 m s−1, representing sce-

narios below and above rated wind conditions. The simula-

tions were done using the IEC NTM turbulent wind model.

We can see in Fig. 7 that the estimator is able to capture

the low-frequency variation in αand Vrel well. The differ-

ences arise from the effect of the turbulent wind speed. De-

pending on the wind speed, the magnitude of the differences

between ˆ

Vrel and Vrel can be small or large. Figure 7b shows

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S. Perez-Becker et al.: Active flap control with the trailing edge flap hinge moment as a sensor 803

Figure 6. Observer performance for steady-state calculations. (a) Vrel vs. Vhub for 0◦yaw simulations; (b) αvs. Vhub for 0◦yaw simulations;

(c) Vrel vs. Vhub for 8◦yaw simulations; (d) αvs. Vhub for 8◦yaw simulations; (e) Vrel vs. Vhub for −8◦yaw simulations; (f) αvs. Vhub for

−8◦yaw simulations.

Figure 7. Time series of the estimator performance for two different

turbulent wind speed simulations. (a) αfor Vhub =7 m s−1;(b) Vrel

for Vhub =7 m s−1;(c) αfor Vhub =15 m s−1;(d) Vrel for Vhub =

15 m s−1.

the example of 7 m s−1mean Vhub simulations where the dif-

ferences between ˆ

Vrel and Vrel are small. The differences can

also be more significant, especially for larger wind speeds. In

the 15 m s−1example (Fig. 7d), we can see large differences

in the 1P variation in Vrel in the simulation time between

550 and 600 s. These variations arise from the repeated pass-

ing of the rotating blade through large-scale, slowly varying

turbulent wind gusts and hence are not accounted for in ˆ

Vrel.

Due to the low-pass filtering of ˆα, the abovementioned differ-

ences in Vrel do not lead to large oscillations of the former,

and we can see that ˆαfollows αwell in the low-frequency

regime.

The filtering introduces a time lag which could potentially

be detrimental for a controller. The effects of the filter would

certainly be more marked for an extreme load controller than

for a fatigue load controller. Since we are interested in the

extreme load reduction potential of flaps, we will be analyz-

ing the more critical situation in this study. The description

and performance of such an extreme loads controller are pre-

sented in the next section.

The estimated ˆ

Vrel and ˆαfrom the observer can also be

used for a pitch-based fatigue load controller – such as the

one presented by Jones et al. (2018) – thereby indirectly in-

creasing the use of the flap system beyond extreme load re-

duction.

5 Extreme load reduction under turbulent

conditions

In this section we integrate the estimator presented in Sect. 3

in a simple flap extreme load controller and use it to reduce

extreme blade loads and deflections.

5.1 Extreme load controller

The controller used in this study is based on the extreme load

controller presented by Barlas et al. (2016b). It has an attrac-

tively simple architecture and was shown to work effectively

in the mentioned study. In the original controller, all three

out-of-plane BRBM signals MBR

Y-iare compared to a maxi-

mum threshold Mthr. If

MBR

Y-i≥Mthr,(31)

then all flaps of all blades are deployed to a target angle.

https://doi.org/10.5194/wes-6-791-2021 Wind Energ. Sci., 6, 791–814, 2021

804 S. Perez-Becker et al.: Active flap control with the trailing edge flap hinge moment as a sensor

Figure 8. Graphical representation of the controller logic. The con-

ditions 1 to 4 are given by Eqs. (31) to (34).

We expanded this controller by including additional sen-

sors and criteria to trigger flap action. The controller logic is

shown in Fig. 8. The subscripts of the figure correspond to

the jth flap of the ith blade. Although there are six flaps per

blade, the controller treats them all as a single unit. The in-

put of the individual flaps is averaged per blade (denoted by

the symbol (·)). Combinations of input sensors are compared

against thresholds. If they pass the thresholds, then all flaps

of all blades are set to a target value. The first condition for

triggering the flap action is Eq. (31). This condition is iden-

tical to the one proposed by Barlas et al. (2016b). Here, a

careful selection of Mthr has to be made in order not to influ-

ence the turbine in normal power production. The other three

conditions are

MBR

Y-i≥Mtr1 and ˙xi≥ ˙xtr1or MBR

Y-i≥Mtr2 and ˙xi≥ ˙xtr2,(32)

MBR

Y-i≥Mtr1 and ˆαi≥αtr1 and ˆ

Vrel-i≥Vtr1,(33)

MBR

Y-i≥Mtr1 and MHin-i≤MHin-tr1 and ˆ

Vrel-i≥Vtr1.(34)

Here, Mtr-i,˙xtr-i,αtr1,Vtr1 and MHin-tr1 are threshold values

for the respective input sensors. The idea of these conditions

is to lower the threshold for MBR

Y-ito deploy the flaps for the

cases where extreme bending moments are expected to hap-

pen. It was seen in preliminary simulations that the flap de-

ployment had a delayed effect on the lowering of the blade

root bending moment. Deploying the flaps close to a load

peak would only have a small load reduction effect on MBR

Y-i.

Yet this condition is necessary in order to limit the influence

of the flap controller on the power output of the turbine.

By using the flap hinge sensor in the outer blade span

(Eqs. 33 and 34), the controller has additional aerodynamic

information about the likelihood of a strong wind gust and

is able to deploy the flaps at a lower threshold value of

MBR

Y-i(Mtr1 < Mthr), thus giving the flaps more time to ef-

fectively mitigate the blade root loads. We mentioned in

Sect. 4.3 that our observer includes a low-pass filter for ˆα

which causes a delay in the signal. To enable our controller

to sense sudden increases in α, we also included a condition

based on MHin-idirectly. Assuming that the flap deployment

angle will mostly be δi,j =0◦, the value of MHin-iwill be ap-

proximately proportional to αifor small reduced frequencies

(Fig. 3b).

Preliminary simulations also revealed that blade deflection

dynamics are critical for predicting extreme events of MBR

Y-i

and were not always strongly correlated to the aerodynamic

information. The controller includes Eq. (32) to account for

extreme loads due to large values of ˙x. We include two con-

ditions to also account for very high velocities that occur at

lower values of MBR

Y-i(Mtr2 < Mtr1 and ˙xtr2 >˙xtr1).

If any of the above conditions are met for any blade,

then all flaps of all blades are deployed to the target angle

δtar = −14.5◦. This value is slightly lower than the maxi-

mum modeled value in the polars. This was done to still be

able to model the aerodynamic effect of a flap angle over-

shoot when the flaps are deployed. Additionally, the flaps

were kept deployed for a given time τdep before they were re-

turned to the original position. τdep was chosen to be about a

third of one rotor period. This way if a localized gust triggers

the flap controller of one blade, the following blade will al-

ready have deployed flaps when encountering the local gust.

Finally, the controller also returns the flaps to their 0◦posi-

tion with a reduced rate compared to the maximum flap rate.

This is to have a smooth return to normal conditions and to

avoid excessive oscillations of the blades by frequent on–off

transitions.

The conditions explained so far are valid for cases where

the strategy is used to mitigate the maxima of MBR

Y-i. This is

the case of the considered load cases (Table 1). Equivalent

conditions can be defined for the controller to mitigate the

minima of MBR

Y-i.

We note that this controller treats all flaps in one blade as

a single unit. Why should we make the additional effort to

include multiple flaps per blade? One reason for having sev-

eral flaps per blade instead of one is that a system of multiple

independent flaps will still be able to reduce the loads in the

event of one flap ceasing to function. This makes the sys-

tem more redundant and thus more appropriate for extreme

load reduction. A second reason is that the controller will

have sensorial input from multiple sources. Averaging the

signals of the six flaps smooths out possible local variations

that could arise from using a single set of sensors. Finally,

having multiple sensors and actuators per blade opens up the

possibility of using local distributed control strategies in fu-

ture studies.

5.2 Metrics

The metrics considered in this study are max(MBR

Y) – the

extreme out-of-plane bending moment at the blade root,

max(MBR

XY ) – the extreme resulting bending moment at the

blade root – and max(DT2T

X) – the maximum blade out-of-

plane deflection in the region defined by 5◦before the blade’s

Wind Energ. Sci., 6, 791–814, 2021 https://doi.org/10.5194/wes-6-791-2021

S. Perez-Becker et al.: Active flap control with the trailing edge flap hinge moment as a sensor 805

closest azimuthal position to the tower and 5◦after this po-

sition. For a blade whose rotor azimuth angle is defined as

0◦when the blade is pointing vertically upward, this region

would lie between the azimuth angles of 175 and 185◦. This

metric gives us an estimate of the minimum blade tip-to-

tower surface distance.

Because we are dealing with stochastic wind simulations,

we chose to follow the averaging procedure for extreme val-

ues described in IEC 61400-1 Ed. 3 (2005). The maximum

value of MBR

Y,MBR

XY and DT2T

X(considering all three blades)

is recorded for each simulation. The extreme value is then

taken as the average of the six highest maxima of all simu-

lations. For the case of MBR

XY , we did this averaging analysis

for 72 different angular bins. For each time step, the direction

of the load vector was calculated, and the maximum of MBR

was determined for each angular bin in each simulation. This

gives a more detailed picture of the effect of the flap con-

troller on the extreme resulting bending moments in different

load directions. No safety factors were applied since all the

considered load cases share the same safety factor.

A complete analysis should include other key turbine sen-

sors to measure the overall effect of the controller on the tur-

bine. We chose not to include these sensors in order to limit

the scope of this study.

5.3 Simulation setup

In this study we focused on the load case group that caused

the highest MBR

XY design loads of our selected turbine (Bak

et al., 2013). This is the DLC load case group 1.3 which has

the ETM wind model. We considered a subset of wind speed

bins of this group around the rated wind speed (see Table 1 in

the column “Turbulent calculations”). This is also the region

of maximum rotor thrust and thus the expected maximum

values of MBR

XY and DT2T

X. We considered wind speeds in a

range of mean VHub between 9 and 17 m s−1in 2 m s−1steps.

Six different simulations were done for each wind speed bin,

giving us a total of 30 simulations for each controller config-

uration. We also included the results of simulations from the

DLC load case group 1.1 without flap controller. This way

we have a reference of the load increase due to the increased

turbulence of the DLC 1.3 group.

Although the number of simulations is rather low to de-

termine the overall extreme values of MBR

XY and DT2T

X, our

selection will give us a good estimate of their maxima.

By using QBlade – which has the lifting line free vortex

wake (LLFVW) aerodynamic model and a multi-body based

structural model – we ensure that the results of our load cal-

culations are more accurate than with other codes that use

the more common BEM aerodynamic model (Perez-Becker

et al., 2020). In all simulations we included additional 100 s

simulation time to allow the wake to develop. This time was

discarded in our analysis.

Figure 9. max(MBR

Y) vs. Vhub for the individual simulations with

and without flap controller (AFC in the legend).

5.4 Results

Figure 9 shows an overview of the maxima of MBR

Yfor the

individual simulations of the different DLC groups and con-

troller configurations.

As expected, the highest values of MBR

Yfor the DLC 1.1

power production group occur for wind speed bins around

rated wind. Although some high extreme values are also

recorded for the wind speed bin of Vhub =15 m s−1. This

is because of the turbulent wind conditions. The increased

turbulence of the DLC 1.3 load cases leads to significantly

higher values of max(MBR

Y) when compared to the values

of the DLC 1.1 group. This is for all the considered wind

speeds. Including the TE flap controller in the DLC 1.3 sim-

ulations visibly lowers the maxima of MBR

Y. The extremes

for wind speed bins between 11 and 15 m s−1are compara-

ble to the extremes of the DLC 1.1 group without flap actu-

ation. These wind speed bins also include the highest values

of max(MBR

Y).

A numerical comparison is shown in Fig. 10. Here we

can see the normalized values of max(MBR

Y), max(DT2T

X) and

max(MBR

XY ) for all simulations with and without active flaps

(AFC in the figure). As explained in Sect. 5.2, these values

were obtained by using the averaging procedure of extrema

according to the IEC standard. We can see that by includ-

ing active trailing edge flaps we can reduce the extreme out-

of-plane moment MBR

Yby 8 %, the extreme resulting bend-

ing moment by 7.6 % and the critical deflection of the blade

tip DT2T

Xby 7.1 %. The resulting values are comparable to

the ones obtained by extrema of the DLC 1.1 group.

It is also interesting to see what effect an active flap system

has on the different load directions of max(MBR

XY ) around the

blade root. Figure 11 shows the averaged value of max(MBR

XY )

for different load directions. We can see that the largest val-

ues of max(MBR

XY ) occur for angular bins between 70 and

100◦. These angles are around the value of positive MBR

(90◦). Because we are only considering the DLC 1.1 and 1.3

groups, we will only have a good estimation for the extreme

https://doi.org/10.5194/wes-6-791-2021 Wind Energ. Sci., 6, 791–814, 2021

806 S. Perez-Becker et al.: Active flap control with the trailing edge flap hinge moment as a sensor

Figure 10. Normalized values of max(MBR

Y), max(DT2T

X) and

max(MBR

XY ). Results are shown for all simulations without active

flaps (No AFC), with active flaps (AFC) and for DLC 1.1 only.

resulting bending moments due to the maximum thrust of the

wind turbine, which happens to correspond to this region.

When we look at the effect of the active flap system, we

can see that the reduction of max(MBR

XY ) occurs in this angu-

lar range. In the rest of the angular bins, the maximum result-

ing bending moments are practically identical. This can be

understood if we recall that the controller input only included

strain gauge information in the out-of-plane direction. Ex-

treme resulting bending moments that arise from the combi-

nation of MBR

Yand MBR

Xcannot be captured by the controller

sensors. In addition, the flaps’ control authority is mainly on

the lift, so flap actuation will have little effect on the varia-

tion in MBR

X. Again, the reduction due to flap activity seen in

Fig. 11 reduces the values of MBR

XY to values close to the ones

obtained from considering the loads from DLC 1.1 only.

5.5 Discussion

The results obtained in the previous section show that active

TE flaps are able to reduce extreme loads and critical deflec-

tions of the blade substantially. Given the constraint that the

control strategy should not interfere with the normal power

production (DLC 1.1), a reduction of 7.6 % in max(MBR

XY )

is significant because it almost eliminates the increased ex-

trema in DLC 1.3 due to the extreme turbulence (Fig. 10).

These results are statistical and should be interpreted as an

average performance of the flap system. To better understand

the potentials and limitations of the proposed system, it is

useful to look at some exemplary time series.

Figure 12 shows a selection of the time series for two sim-

ulations from the Vhub =11 m s−1wind speed bin, where

several of the maxima occurred. Each column corresponds

to one simulation. The first column shows a scenario where

the average wind speed (not shown) is increasing and is

rising to values around rated rotor speed (Fig. 12d). The low

value of β(Fig. 12c) leads to high values of rotor thrust and

high values of MBR

Y(Fig. 12a) and to the activation of the

flaps (Fig. 12b). We can see that the flaps are being deployed

Figure 11. Averaged max(MBR

XY ) for different load directions. In

this figure 0◦corresponds to positive MBR

Xand 90◦to positive

MBR

Y. The radial coordinate is given in mega-newton-meters.

even if the values of MBR

Ydo not reach an apparent peak.

This is because Fig. 12a only shows the value of MBR

Yfor

one blade, and all flaps are activated as soon as the deploy-

ment criteria are met by any blade. Let us now consider the

situation around the simulation time of 520 s. Here the blade

passes a local wind gust, and it significantly increases the

value of MBR

Yfor the simulation without flaps. This also ac-

celerates the rotor and activates the pitch system. This does

not happen in the simulation with active flaps. Due to a pre-

vious activation of the flap system, the blade enters the wind

gust with deployed flaps, thereby creating less lift and thus

reducing the load peak by about 16 %. This is one example

showing the large potential that active flap systems have in

reducing the extreme loads of wind turbine blades.

The second column shows a situation where the controller

does not perform as desired. At around 685 s of simulation

time, there is a sudden peak in MBR

Yfor the simulations with

active flaps (Fig. 12e). Just before that event the flaps had just

arrived at their 0◦position, thus allowing the blade to gener-

ate normal lift (Fig. 12f). The flap controller reacts quickly,

but the reaction is not quick enough to mitigate the high load-

ing. Because we are trying to reduce the extreme loads, such

events – although rare – are the ones that lead to the recorded

maxima. In the case of this particular simulation, the extreme

load reduction of the active flap system is only about 1.5 %.

This example also illustrates well the necessity of having fast

reactions from the flap system to sudden changes. This can

only be obtained by including local sensorial information of

the flap system – such as the flap hinge moment and acceler-

ation signals – as part of the controller input.

One challenge in this particular study is that the differ-

ence in extrema between the DLC 1.1 and 1.3 groups is rela-

tively small. Given the fact that the flap system needs a cer-

tain amount of time to have an effect on MBR

Y, we require

the values of the different thresholds to be low. On the other

Wind Energ. Sci., 6, 791–814, 2021 https://doi.org/10.5194/wes-6-791-2021

S. Perez-Becker et al.: Active flap control with the trailing edge flap hinge moment as a sensor 807

Figure 12. Selection of time series for two different simulations with Vhub =11 m s−1. Panels (a–d) correspond to one simulation while

panels (e–h) correspond to the second simulation.

hand they should not be too low in order to avoid influencing

the normal power production of the turbine. The combina-

tion of these two requirements does not leave much room for

threshold selection. Slightly changing the threshold values

helped improve the performance of the flap system in certain

scenarios but lowered the performance in others, thus giving

similar results overall. If the difference in extreme conditions

between the DLC 1.1 group and other DLC groups is higher

(as was reported in Barlas et al., 2016b), then this issue be-

comes less critical.

Another observed issue with the proposed strategy is the

unwanted mutual influence between the pitch and the flap

controllers. We can see an example of this in Fig. 12c. The

deployment of the flaps lowers the lift force but also the

torque produced by the rotor and thus the rotor acceleration.

This results in the pitch controller leaving the pitch angle

longer at 0◦compared to a simulation without active flaps.

While the overall effect on the rotor speed and hence gener-

ator power is small, the effects on MBR

Yare more substantial.

Lower values of βincrease the values of αalong the blade,

leading to higher lift values and higher values of MBR

Y. It

was observed in some simulations that there were values of

max(MBR

Y) with fully deployed flaps comparable to values of

max(MBR

Y) from the same simulations without active flaps.

The difference lay in the respective values of βin each simu-

lation. The influence of the flap controller led to lower values

of βcompared to the simulation without active flaps, indi-

rectly reducing its effectiveness.

A possible solution would be to decrease the value of τdep

or increase the flap rate when returning to the 0◦position,

thus lowering the time that the flaps influence lift production.

Because of the constraints in threshold selection mentioned

before, having a flap deployment cycle that is too fast could

lead to an unstable behavior where the flap system amplifies

the blade oscillation. Another possible solution could be to

adapt the controller so that each blade uses its flap system

independently. While this strategy reduces the interference

between the flap and the pitch controllers, it loses the infor-

mation about the inflow conditions of the preceding blade.

This leads to more false negative scenarios such as the one

described in Fig. 12e–h, again lowering the effectiveness of

the strategy.

All of the limitations discussed above arise mainly from

the chosen controller strategy. While being simple, robust

and able to reduce extreme loads and deflections signifi-

cantly, the proposed architecture shows its limits when used

in such a challenging scenario. Other controller strategy

types, such as, e.g., model-based or adaptive-data-driven

controllers that include combined pitch and flap action, are

possible candidates that could exploit the full potential of ac-

tive flaps while overcoming the observed limitations in this

study.

6 Conclusions

In this paper we explored the potential of active trailing edge

flaps to reduce extreme loads and critical deflections of the

modified DTU 10 MW RWT blade with flaps. We considered

the flap hinge moment as a robust and available sensor that

can deliver valuable local information about the inflow and

enable the flap system to have more time to react to sudden

extreme conditions.

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808 S. Perez-Becker et al.: Active flap control with the trailing edge flap hinge moment as a sensor

In order to use the flap hinge moment as an input sensor for

a controller strategy, we adapted an existing unsteady hinge

moment model for thin airfoils from the literature to use it

in aero-servo-elastic simulations in the time domain. Based

on this model, we developed an observer that estimates the

effective local angle of attack and relative wind velocity of a

blade section from local sensors. The latter include the flap

hinge moment and an accelerometer mounted on the blade

section.

We evaluated the performance of the observer in aeroe-

lastic simulations with steady and turbulent wind conditions.

For steady wind conditions, the error between the estimated

and real values of the mean Vrel was below 0.4 % for all wind

speeds between 4 and 24 m s−1. The error between the esti-

mated and real value of the mean αlay below 0.2◦. We also

tested the observer in more challenging turbulent wind speed

conditions. Although our observer was lacking information

about the incoming turbulent wind, it was able to estimate

the low-frequency content of Vrel and αfairly well. An ex-

ception was seen to be the local turbulent gust slicing of the

blade for higher wind speeds. This leads to increased 1P vari-

ations in Vrel not captured by the observer.

This observer was included in a simple flap controller

strategy to mitigate extreme blade loads and critical blade

deflections. It is based on a series of on-off criteria applied

to several input sensors. The sensors included integrated load

values – such as MBR

Y– and local information of the individ-

ual blade sections – such as MHin,˙x,ˆαand ˆ

Vrel.

We tested the performance of this strategy in aero-servo-

elastic load calculations according to the DLC 1.3 group

from the IEC standard. This group features the extreme tur-

bulent wind model and is responsible for the maxima of MBR

and DT2T

Xof our considered blade. The simulations were per-

formed using the LLFVW aerodynamic model, which has

been shown to calculate aerodynamic loads more accurately

than the conventional BEM aerodynamic models. The pro-

posed flap controller was able to reduce the maxima of MBR

and MBR

XY by 8 % and 7.6 %, respectively. The controller was

also able to reduce the critical blade deflection – i.e., the

blade tip deflection in front of the tower – by 7.1 %. Look-

ing at the maxima of MBR

XY for different load directions, we

found that the flap controller was able to reduce max(MBR

XY )

for angular bins between 70 and 100◦, bringing them down to

values that are comparable to the maxima from normal power

production load cases. These directions correspond to direc-

tions around positive MBR

Y, where the flap control authority

is also highest for a blade with β=0◦.

A more detailed look revealed that active flap systems

in general have the potential to reduce the extreme loads

even further. Yet a combination of challenging conditions –

e.g., constraints in the parameter selection space in order to

reduce extreme loads without interfering with normal power

production – and a simple controller strategy were found to

be the main limitations of the proposed system.

The results of this paper show that active TE flaps have

a large potential to reduce design-driving extreme loads and

critical deflections of wind turbine blades. They can therefore

help create more competitive turbine designs that will reduce

the cost of energy even further. A critical aspect was seen

to be the reaction time of the active flap system, which can

be greatly improved if local sensors – such as the flap hinge

moment – are used as input for the control strategy. More

work needs to be done in order to gain further insight into

this topic and better quantify the aforementioned potential of

flaps.

The model used for the hinge moment calculation could

be improved to increase its accuracy. Further refinements

could include a more detailed state-space representation of

the aerodynamic loads, include other inertial loads such as

centrifugal and gyroscopic loads, and also include friction.

In this study we used identical systems to model the flap

hinge and as input for our observer. This is certainly unreal-

istic, and a robustness study should be done to quantify how

model uncertainty and measurement noise affect the observer

performance. This is especially of relevance due to the lower

sensitivity of the hinge moment coefficient to changes in the

angle of attack. A proof of stability for the LPV observer is

also needed to guarantee that the observer will be stable at all

times.

The model and observer should also be tested experimen-

tally. On the one hand, the proposed model could be com-

pared to experimental data obtained from a 2D airfoil with an

active flap for different reduced frequencies. Alternatively or

complementarily, a system identification could be performed

using experimental data to create an unsteady hinge moment

model from the data to be used in the observer. The observer

and model could also be tested and analyzed experimentally

using an experimental wind turbine in a wind tunnel.

Regarding the controller strategy, a better quantification

of its performance can be obtained by including more DLC

groups that include the load extrema in all directions. Also,

the evaluation of the strategy should be extended to include

more load sensors, such as hub and tower bending moments.

In addition, other control strategies should be considered

as possible candidates for extreme load and deflection con-

trol. In particular, model-based or adaptive-data-driven con-

trollers that are able to control both the pitch and flap actua-

tors are promising candidates to increase the ability of active

flaps to reduce design-driving loads.

Wind Energ. Sci., 6, 791–814, 2021 https://doi.org/10.5194/wes-6-791-2021

S. Perez-Becker et al.: Active flap control with the trailing edge flap hinge moment as a sensor 809

Appendix A: Entries of the hinge model and observer

state-space matrices

This appendix contains the explicit entries of the matrices

used for the hinge model and the hinge model observer. The

entries for the feedthrough matrix of the hinge model DHin

are as follows.

Dα=α·F12

4(A1)

D˙α=α·F12 ·b·(1/2−a)

4Vrel

−b·(−2F9−F1+F4·(a−1/2))

2Vrel

(A2)

D¨α=−F13 ·b2

rel

(A3)

Dδ=δ·F12 ·F10

4π−F5−F4·F10

2π(A4)

D˙

δ=δ·F12 ·b·F11

8π·Vrel

+b·F4·F11

4π·Vrel

(A5)

D¨

δ=F3·b2

2π·V2

rel

(A6)

D˙

h=α·F12

4Vrel

(A7)

D¨

h=F1·b

2V2

rel

(A8)

The geometric constants Fidepend on the flap size relative

to the airfoil chord and are given in Hariharan and Leishman

(1995).

For the hinge observer model, the explicit entries of Bα

Hin

and BRes

Hin are

Bα

Hin =





000

1b·(1/2−a)

Vrel 0

000







,(A9)

BRes

Hin =





0 0 0 0 0

0 0 0 1

Vrel 0

0 0 0 0 0

F10

b·F11

2π·Vrel 0 0 0







.(A10)

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810 S. Perez-Becker et al.: Active flap control with the trailing edge flap hinge moment as a sensor

Appendix B: List of symbols, subscripts and

superscripts

This section contains the list of symbols (Tables B1 and B2)

as well as the list of sub- and superscripts (Table B3) .

Table B1. List of Latin symbols used in this paper.

Symbol Definition

aNormalized position of pitch axis in semi-chords

A1-2 Coefficients 1 and 2 of the indicial functions

bSemi-chord length of airfoil

b1-2 Exponents 1 and 2 of indicial functions

cChord length of airfoil

c1-4 Linear approx. constants between out-of-plane velocities

ChHinge moment coefficient

Ch−0Hinge moment coefficient for α=0◦

dflap Flap’s center of mass measured from hinge point

DT2T

XMaximum blade tip deflection in vicinity of the tower

fChordwise displacement of blade section

F1-13 Geometric flap constants

gGravitational acceleration

hDisplacement of blade section normal to chord

Iflap Flap’s moment of inertia around hinge

kReduced frequency

LGain matrix for αestimator

mflap Flap’s mass

MBR Blade root bending moment

MHin Total flap hinge moment

MH-A Flap hinge moment due to aerodynamic loads

MH-I Flap hinge moment due to inertial loads

MH-g Flap hinge moment due to gravitational loads

QLObserver covariance matrix for process noise

rflap Spanwise position of flapped blade section

RLObserver covariance matrix for measurement noise

SSpanwise length of blade section

VAne Measured anemometer wind speed

Vhub Hub height wind speed

VIP In-plane wind speed

VOP Out-of-plane wind speed

Vrel Relative wind speed

xOut-of-plane displacement of blade section

yIn-plane displacement of blade section

Wind Energ. Sci., 6, 791–814, 2021 https://doi.org/10.5194/wes-6-791-2021

S. Perez-Becker et al.: Active flap control with the trailing edge flap hinge moment as a sensor 811

Table B2. List of Greek symbols used in this paper.

Symbol Definition

αAngle of attack

βBlade pitch angle

γTurbine yaw angle

δFlap angle

1Vop Approximation of vertical variation in out-of-plane velocity

αFlap efficiency coefficient for changes in α

δFlap efficiency coefficient for changes in δ

θTwist angle of blade section

ϕRotor azimuth angle

Rotor rotational speed

ρAir density

τTurbine tilt angle

τdep Minimum time to wait before deployed flaps return

Table B3. List of sub- and superscripts.

Symbol Definition

(·)Hin Corresponding to flap hinge model

(·)Sig Corresponding to signal model

(·)S+HCorresponding to combined signal and hinge model

(·)obs Corresponding to full observer

(·)tar Target value

(·)tr Trigger value

(·)thr Threshold value

(·)XOut-of-plane component

(·)YIn-plane component

(·)XY Resulting component

(·) Estimation of quantity

(·) Mean of quantity

(·) First derivative of quantity

(·) Second derivative of quantity

(·)BR Corresponding to blade root

https://doi.org/10.5194/wes-6-791-2021 Wind Energ. Sci., 6, 791–814, 2021

812 S. Perez-Becker et al.: Active flap control with the trailing edge flap hinge moment as a sensor

Code and data availability. Both FAST and QBlade are open-

source codes available online. The newest version of FAST v8

is available at https://www.nrel.gov/wind/nwtc/fastv8.html (last ac-

cess: 19 May 2021) (NREL, 2021). The latest version of QBlade

is available at https://www.qblade.org/ (last access: 19 May 2021)

(TU Berlin, 2021). The version of QBlade used in this paper that

includes the structural model will be made available soon. The time

series for the turbulent wind calculations used in this paper are

stored in the HAWC2 binary format. They can be made available

upon request.

Author contributions. SPB prepared the manuscript with the

help of all co-authors. DM is the main developer of QBlade.

DM and SPB implemented the interface for flap controllers in

QBlade. SPB developed the hinge model observer and control strat-

egy, performed the calculations, and analyzed the results. COP pro-

vided assistance with the paper review.

Competing interests. The authors declare that they have no con-

flict of interest.

Acknowledgements. Sebastian Perez-Becker wishes to thank

WINDnovation Engineering Solutions GmbH for supporting his re-

search. The authors wish to thank Horst Schulte from HTW Berlin

and Sirko Bartholomay from TU Berlin for their reviews and in-

sightful comments on this paper. We acknowledge the support of

the Open Access Publication Fund of TU Berlin.

Financial support. This open-access publication was funded

by Technische Universität Berlin.

Review statement. This paper was edited by Mingming Zhang

and reviewed by Athanasios Barlas and Vasilis A. Riziotis.

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