Load Alleviation on Wind Turbine Blades using Variable Airfoil Geometry

111 Pages·2005·3.1 MB·English

Load Alleviation on Wind Turbine Blades using
Variable Airfoil Geometry (2D and 3D study)
M.Sc. Thesis
Technical University of Denmark
Department of Mechanical Engineering
Section of Fluid Mechanics
Peter B. Andersen
June 2005
Preface
This report is the result of the work carried out by Peter B. Andersen, stu-
dent at the Technical University of Denmark (DTU), in the fulfillment of
the requirements forobtainingthedegreeMasterofScience inWindEnergy
at DTU.
The project has been developed during the period February, 2005 to June,
2005 at Risø National Laboratory and the Fluid Mechanics Section of the
Mechanical Engineering Department (MEK) at DTU.
The supervision has been undertaken by Christian Bak, Mac Gaunaa and
Thomas Buhl from Risø and Niels K. Paulsen from IMM at DTU and Jens
N. Sørensen from MEK at DTU.
Abstract
The operating conditions of wind turbines make them subject to fluctuating
loads that create fatigue damage. Alleviating these loads would reduce the
needed materials or increase the lifespan of the blades.
2D model
An aerodynamic model coupled with a rigid spring/damper model is used.
A PID and a LQR control is implemented and investigated for a 2D airfoil
section in order to formulate a control strategy. Turbulent wind of 60 sec-
onds is used. The standard deviation of the normal load was reduced by
74% for the PID regulation when the flapwise deflection was used as state
varible for the control. For the LQR reduction was 82%. The PID control
was chosen over the LQR because of simplicty and computational speed.
3D model
Flexible trailing edge (TE) flaps have been modeled on a 33 meter long
V66 blade from Vestas. The structural blade model comprises a cantilever
beam with modal expansion of blade and camberline deformations. The
aerodynamic model includes a BEM model with various 3D corrections and
a flap model which include effects of the wake history. The PID control
is implemented to control the flaps. Effects of system time lag, flap power
consumption and signal noise is included. The equivalent flapwise blade
root moment is reduced 61% using 7 meter TE flaps with infinite power
available for the flap actuators. TE flaps with 1% cross sectional blade mass
gives a reduction of 60% when flap actuators consume 100W/m maximum.
The potential drops to 41% when signal noise is added to the control. An
algoritmhasbeenproposedforcollectingdatawhichislesssensitivetonoise.
Keywords: Wind Turbine, Load Alleviation, Fatigue Loads, Trailing Edge
Flaps, PID control, LQR control, Signal Noise.
.
De betingelser som vindmøller udsættes for gør dem s˚arbare for udmat-
telses laster. Ved at fjerne disse udmattelseslaster ville det være muligt at
reducere materiale forbruget eller forøge en vinges levetid.
2D model
En aerodynamisk model er kombineret med et stivlegemet fjeder system.
En PID og LQR regulator er udviklet og undersøgt for et 2D vingeprofil
for at formulere en kontrol strategi. En turbulent vindserie p˚a 60 sekunder
er brugt. Standard afvigelsen p˚a normal kraften er reduceret 74% for PID
kontrollen n˚ar den flapvise udbøjning er brugt som tilstandsvariablen for
kontrol systemet. For LQR kontrollen er reduktionen 82%. PID kontrollen
blev valgt fremfor LQR da den er simplere at bruge og kræver færre bereg-
ninger.
3D model
Fleksiblebagkantflapperermodelleretp˚aen33meterV66vingefraVestas.
Denstrukturellemodelbyggerp˚aenfastindspændtbjælkehvorudbøjningerne
er beskrevet ved modal former for bjælken og bagkant flappen. Den aerody-
namiskemodelinkludererenBEMmodelmedforskellige3Dkorrektionerog
enflapmodelmedkølvandshistorikindbygget. PIDkontrollenerindbygget
til at styre bagkant flapperne. Tidsforsinkelser, effekt forbrug til flappen og
signal støj er inkluderet i modellen. Det ækvivalente flapvise rod moment
er reduceret 61% ved brug af 7 meter flapper, hvor der ikke er begrænsning
p˚a den effekt aktuatorene kan bruge. Bagkants flapper som vejer 1% af det
sektionerne vejer giver en reduktion p˚a 60% n˚ar flap aktuatorene maksi-
malt m˚a bruge 100W/m. Potentialet falder til 41% n˚ar støj signalet bliver
inkluderet. En algoritme er foresl˚aet til opsamling af data, som er mindre
støj følsom.
Contents
1 Introduction 1
I 2D modelling 3
2 Method 3
3 Load considerations 7
4 Control 9
4.1 PID . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
4.2 LQR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
5 Result and discussion, part I 15
5.1 Determining state variable candidates . . . . . . . . . . . . . 17
5.2 PID . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
5.3 LQR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
5.4 Choosing state variable, control and what to optimize for . . 22
5.5 Effects of changing the duration of the turbulent wind signal 22
6 Conclusion, part I 24
II 3D modelling 25
7 Method overview 25
7.1 Aerodynamic model . . . . . . . . . . . . . . . . . . . . . . . 26
7.2 Structural model . . . . . . . . . . . . . . . . . . . . . . . . . 30
7.3 Servo model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
7.4 Numerical considerations . . . . . . . . . . . . . . . . . . . . 38
8 Defining fatigue 39
9 PID control 40
9.1 Signal noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
9.2 Tuning methods . . . . . . . . . . . . . . . . . . . . . . . . . 45
10 Results, part II 48
10.1 Model inspection . . . . . . . . . . . . . . . . . . . . . . . . . 49
10.2 Systems of flaps . . . . . . . . . . . . . . . . . . . . . . . . . . 52
10.3 Effects of damping, gravity, wind shear and tower effect . . . 56
10.4 Servo modeling, time delays and limited power . . . . . . . . 58
10.5 PID versus PI . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
10.6 Signal noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
10.7 Combining all effects . . . . . . . . . . . . . . . . . . . . . . . 64
11 Conclusion, Part II 66
12 References 70
A Appendix part I 72
A.1 Calculating stiffness . . . . . . . . . . . . . . . . . . . . . . . 72
A.2 Aerodynamic equations for flaps . . . . . . . . . . . . . . . . 73
A.3 Defining 2D load reductions . . . . . . . . . . . . . . . . . . . 75
A.4 Laplace transformations . . . . . . . . . . . . . . . . . . . . . 76
A.5 Linearizing equations for LQR . . . . . . . . . . . . . . . . . 77
A.6 Potter’s algorithm for solving Riccati’s equation . . . . . . . . 86
A.7 Flap deflection series . . . . . . . . . . . . . . . . . . . . . . . 87
B Appendix part II - 3D modeling 89
B.1 Deriving mode shapes and eigenfrequencies for torsion . . . . 89
B.2 Turbulent wind field at 15 stations . . . . . . . . . . . . . . . 91
B.3 Calculating blade root moments. . . . . . . . . . . . . . . . . 92
B.4 Aerodynamic power . . . . . . . . . . . . . . . . . . . . . . . 93
B.5 Technical sensor data. . . . . . . . . . . . . . . . . . . . . . . 94
B.6 Verifying MTM using Kp/Kd-sweep . . . . . . . . . . . . . . 96
B.7 PSD percent reduction of flapwise root moment . . . . . . . . 97
B.8 Final result in table form . . . . . . . . . . . . . . . . . . . . 98
C Appendix - Runge-Kutta algoritm 99
C.1 Firstorder Runge-Kutta . . . . . . . . . . . . . . . . . . . . . 99
C.2 Second order Runge-Kutta. . . . . . . . . . . . . . . . . . . . 100
Nomenclature
Roman symbols
A˜,A˜ Helping variables used in the state space formulation of the
2
governing equation for the LQR control method.
a A non-dim. position of the point where the 2D section is
fastened. [2·EA −1]
c
ACC Abbreviation for Accelerometer.
A ,b Flat plate expression coefficients for the aerodynamic re-
i i
sponse functions.
b Half sectional chord length (c/2). [m]
B˜,C˜ Helping variables used in the state space formulation of the
governing equation for the LQR control method.
c Sectional chord length. [m]
c determinestheratioofasignalcomingfromeitherthestrain
tune
gauge or the accelerometer.
CG Center (of) gravity, the vectorial point of attack for gravity
on an airfoil section. [m]
C ,C ,C ,C Damping coefficients for the 2D case [log%]
n x y θ
D˜ Helping variables used in the state space formulation of the
governing equation for the LQR control method.
D The damping matrix used for the 3D model. [8x8 matrix
Ns/m]
D Drag force. [N]
Defl The degree of which a camberline mode shape is deflected.
DOF Degrees Of Freedom.
E˜ Helping variables used in the state space formulation of the
governing equation for the LQR control method.
E Error, what the control algorithm seeks to minimize.
EAx Point (of) elasticity (elastic axis). point where a normal
force (out of the plane) will not give rise to a bending of the
section. [m] (measured the LE in 2D and the c/4 in the 3D
model).
EI Bending stiffness about first principle axis [Nm2]
1
EI Bending stiffness about second principle axis [Nm2]
2
EMP External Modeling Principle
E TheerrortobeminimizedinthePDregulatorforestimating
pwr
the needed power consumption for the flap. [deg]
EQ Equivalent flapwise root moment, found using a 60 second
F
turbulent wind series. [kNm]
EQ Equivalent edgewise root moment, found using a 60 second
E
turbulent wind series. [kNm]
F˜ Helping variables used in the state space formulation of the
governing equation for the LQR control method.
flap−masses A percentage of the cross sectional mass than is used for
building the flap at that section. The mass for the servo
actuator system is not included in this percentage. [%]
flap chordwise length of flap [m]
l
flap mass of flap [m]
m
f ,f ,f ,f Stiffness eigenfrequencies for the 2D case [Hz].
n x y θ
G˜ Helping variables used in the state space formulation of the
governing equation for the LQR control method.
GI Torsional stiffness [Nm2]
t
G Transfer function.
s
GX The generalized coordinates used in the 3D model.
h Height above ground, used to calculate the wind shear. [m]
H ,.. Aerodynamic constant for deformable airfoils
dydx
H Height of tower. [m]
tower
Imm Mass moment of inertia around CG [Kgm2]
Imm Mass moment of inertia of the flap. [Kgm2]
flap
IMP Internal Modeling Principle
K The stiffness matrix used for the 3D model. [8x8 matrix
N/m]
Kd Differential gain. [any]
Ki Integral gain. [any]
K ,K ,K ,K Stiffness coefficients for the 2D case [N/m].
n x y θ
Kp Proportional gain. [any]
L Lift force. [N]
LE Leading edge
M The mass matrix used for the 3D model. [8x8 matrix Kg]
M Torsional moment of a section. [Nm/m]
M Torsional moment using no flap. [Nm]
reference
MTM Multilayer Tuning Method, a gain tuning method used for
the 3D PID flap control.
m ,m(z) Discrete and distributed mass along the V66 blade. [Kg/m]
i
mf(x) Non.dim. flap mass distribution.
ms (x) Mode shape of flap in y direction at the chordwise position
f
x.
ms (z) Mode shape i for the blade in x direction at radial position
i,x
z.
ms (z) Mode shape i for the blade in y direction at radial position
i,y
z.
ms (z) Torsional mode shape j for the blade at radial position z.
j,Θ
N Normal force for a section [N/m]
N Normal force using no flap [N/m]
reference
n Gaussian noise (used when simulating measuring data from
i
a strain gauge or an accelerometer).
P The power supplied to the flap. [W]
P Effect gain/loss due to the work performed by the aerody-
aero
namic forces on the flap. [W]
P Effect needed to balance the work done by inertial forces
inertia
while flapping. [W]
PC Pressure center (the vectorial point of attack for the aero-
dynamic forces) [m]
PI Constants used to model flap inertia forces.
i
P x,i) Sectional external force aligned with radial axis. [N]
(
P y,i) Sectional external force in the rotor plane. [N]
(
P Sectional external force perpendicular to the rotor plane.
z,i
[N]
Q The three-quarter equivalent quasi steady upwash.
QC Effective equivalent three-quarter upwash.
r Radial position of section on blade. [m]
i
R Length of V66 blade. [m]
RHS Right Hand Side
R Percent reduction in RMS torsional moment compared to
M
reference (no control)[%]
R Percent reduction in RMS normal force compared to refer-
N
ence (no control)[%]
R Percent reduction in RMS transverse force compared to ref-
T
erence (no control)[%]
s Non.dim. time used to model dynamics of finite thickness
airfoils. [2 RrU dt]
c 0 rel
SC Shear center. the point on the section where an in-plane
force will not rotate the section. [m] (measured from the
c/4 in the 3D model).
SG Abbreviation for Strain Gauge.
SNR Signal-to-noise ratio [dB]
T Transverse force of a section [N/m]
TE Trailing Edge
T Transverse force using no flap [N]
reference
u Real deflection. [m]
u A mode shape vector at the eigenfrequency ω . [m]
ev,j r
V Adjustment factor for the free wind speed, used when cal-
f
culating wind shear.
V Relative wind velocity seen by airfoil section. [m/s]
rel
V Rotational velocity Ωr . [m/s]
rot i
V Free wind velocity. [m/s]
wind
x Edgewise deformation for 2D model. [m]
X Distance from PE to c/4. [m]
E
x State variables. [any]
i
x Reference state variables, an optimum state that is desired.
i,ref
[any]
X Distance from CG to c/4. [m]
m
X Distance from SC to c/4. [m]
s
y Flapwise deformation for 2D model. [m]
y Discrete flapwise deformation at iteration number i. [m]
i
z Aerodynamic state variable.
i
Nomenclature
Greek symbols
α Inflow angle for airfoil section also referred to as angle of
attack. [deg]
β Deflection angle for flap, angle between camberline of flap
and undeformed section. [deg]
δ Logarithmic decrement for mode shape j.
j
Ω Rotational speed of blade. [rad/s]
ω Eigenvalue for dynamic system of equations. [rad/s]
r
ω Eigenvalue for dynamic system of equations. [Hz]
f
φ Angle between relative wind seen by the blade and the ro-
tational plane. [deg]
ϕ Angle between a line parallel to the rotor plane and the
chordline going through the EAx point. [deg]
Θ Torsional twist of section due to the aerodynamic moment.
[deg]
Θ Totaltorsionaltwistofsection. (Θ +Θ +Θ )[deg]
Σ twist pitch defl
Θ The degree the whole blade is rotated (pitched), it is con-
pitch
stant for the entire blade. [deg]
Θ Thedesignedandproducedtwistoftheairfoilsection,varies
twist
section to section. [deg]
Θ Θ +Θ
0 twist pitch
τ Duration of a time window (e.g. used for the reference vari-
able defining E). [s]