7/15/00 M. Bikdash 1
Wind Energy Program Wind Energy Program
Modeling and Control of a Bergey-Type furling Wind
Turbine Dr. Marwan Bikdash
Department of Electrical EngineeringNorth Carolina A&T State University
Greensboro, NC 27410
July 14-15 M. Bikdash 2
Wind Energy Program Wind Energy Program
• To study the overspeed-protection furling mechanism of the Bergey Wind Turbine and – Model the furling mechanism (for real-time) – Effect of aerodynamics, generator, electrical side
• Build a simulation package
• To design an active yaw mechanism for larger turbines (and improve performance)– Control Objectives– Control Laws and Algorithms– Actuation mechanism
Objectives
July 14-15 M. Bikdash 3
Wind Energy Program Wind Energy Program
Schedule And Status:
• Completed the Lagrangian derivation of EOM of furling mechanism
• Analyzed YawDyn Output • Approximated YawDyn data using fuzzy models
(real-time; derivatives for linearization)• Analyzed steady-state behavior of turbine• Studying actuation choices for active mechanism • Concurrently writing software in MATLAB and
Simulink• Designing control laws
July 14-15 M. Bikdash 4
Wind Energy Program Wind Energy Program
• Bergey Excel 10KW Turbine
• Operates in the boundary layer of the Earth (turbulence)
• Tail always “points” in the average direction of the wind
• Uses a passive auto-furling mechanism to protect turbine/generator combination from overspeeding in high winds
• Low maintenance/fail safe
• New 40KW turbine envisaged: Is a (still fail-safe) autofurling mechanism desired?
• Use furling to achieve protection AND optimum performance.
Bergey Wind Turbine
July 14-15 M. Bikdash 5
Wind Energy Program Wind Energy Program
Specifications of the 10 KW Bergey Wind
Turbine
Start-up Wind Speed: 3.4 m/s (7.5 mph)Cut-in Wind Speed: 3.1 m/s (7 mph)Rated Wind Speed: 13 m/s (29 mph)Rated Power: 10,000 WattsCut-Out Wind Speed: NoneFurling Wind Speed: 15.6 m/s (35 mph)Max. Design Wind Speed: 53.6 m/s (120 mph)Type: 3 Blade UpwindRotor Diameter: 7 m (23 ft.)Blade Pitch Control: POWERFLEX®Overspeed Protection: AUTOFURLDrive: DirectTemperature Range: -40 to +140 Deg. FGenerator: Permanent Magnet AlternatorOutput Form: 3 Phase AC, Variable Frequency (Regulated 48 - 240 VDC after VCS-10 or 240 VAC, 1Ø, 60 Hz with Powersync® inverter)
July 14-15 M. Bikdash 6
Wind Energy Program Wind Energy Program
αTail Angle between vertical planes
Vie
w fo
r fig
ure
2
θC is c.o.g
α
wθ
wθA-Frame is inertial and pointsin the average direction of wind
North Furling angle between vertical planes
positive CCW
RotorAxis
2av
2bv
1bv1L
2L
3L
Yaw axis offset
1av
OTrv
A
B
4L blades
θ
Wind makes angle with A-Frame
Top View of Turbine Before Tilting
July 14-15 M. Bikdash 7
Wind Energy Program Wind Energy Program
Yaw Axis
β
2bv3b
v
3cv2cv View for fig
ure 3
(furled)
Tail (unfurled)
Hinge Axis about whichthe tail furls
Side view
July 14-15 M. Bikdash 8
Wind Energy Program Wind Energy Program
3dv
Yaw axis
Front View Along Rotor
vc1
3cv
1dv
View for figure 4
γ
Hinge Axis about which the tail furls
rotor
ω
ψ
Top View AlongHinge Axis
Other Views
3dv
2dv
ψ
Padded stops
Tail
July 14-15 M. Bikdash 9
Wind Energy Program Wind Energy Program
Notation
July 14-15 M. Bikdash 10
Wind Energy Program Wind Energy Program
Notation (Continue)
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Wind Energy Program Wind Energy Program
Notation (Continue)
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Wind Energy Program Wind Energy Program
Coordinate Frames
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Wind Energy Program Wind Energy Program
Drag and Lift on Tail
assumption
assumption
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Wind Energy Program Wind Energy Program
Potential and Kinetic Energies
From yaw axis to
aerodynamic center of tail
Rotational speed of tail with respect to inertial A
Frame
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Wind Energy Program Wind Energy Program
Kinetic Energy
July 14-15 M. Bikdash 16
Wind Energy Program Wind Energy Program
Lagrange’s Equation of Motion
July 14-15 M. Bikdash 17
Wind Energy Program Wind Energy Program
Generalized Force for Furling Angle
assumption
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Wind Energy Program Wind Energy Program
Tail Aerodynamic Furling Moment
Depends on the angle between tail and wind
assumption
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Wind Energy Program Wind Energy Program
assumption
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Wind Energy Program Wind Energy Program
Tail Aerodynamic Yaw Moment
Depends on the angle between tail and wind as well as yaw angle
assumption
July 14-15 M. Bikdash 21
Wind Energy Program Wind Energy Program
Tail Aerodynamic Moments
July 14-15 M. Bikdash 22
Wind Energy Program Wind Energy Program
Equations of Motion For Furling Mechanism
assumption
July 14-15 M. Bikdash 23
Wind Energy Program Wind Energy Program
Relative wind direction
θ
wθ−θ∆
ElectricalLoad
Yaw/Furling Dynamics
Wind Speed V
Mechanical Torque
rpm
Moments, Thrusts
Generator
Controller
General Wind Turbine Model
Aerodynamics(YawDyn Fuzzy)⇒
July 14-15 M. Bikdash 24
Wind Energy Program Wind Energy Program
Building the Simulation Software
1. Use the Lagrangian to derive the basic equations of motion of furling mechanism
2. Run YawDyn to characterize the turbine power output and the corresponding aerodynamic forces on turbine (as a function of wind speed, rpm, and angle between wind and rotor
3. Obtain fuzzy approximation4. Add friction and stop terms5. Add generator (Simulink) and electrical load/power
electronics model (Simulink? Sabre?)6. Add/modify dynamics for actuator7. Add model for disturbances (turbulence?)
July 14-15 M. Bikdash 25
Wind Energy Program Wind Energy Program
Generator Model
• Intersection of turbine Torque-Speed characteristics with that of generator yield equilibrium point at onset of furling
• This curve depends on the electrical load seen by the generator• Resistive load (interesting?)• Battery charger (needs work)• General electrical load with power electronics
control • through power electronics
• Assume utility grid interface controlled to always draws rated power at rated speed
July 14-15 M. Bikdash 26
Wind Energy Program Wind Energy Program
0 5 10 15 20 25 30 35 40 450
5
10
15
wind speed(mph)
Out
put p
ower
(KW
)The generator output power vs. wind speed (Bergey data)
Power limiting with synchronous inverter
After furling, Turbine operates at significantly less efficiency.
In this range of wind speeds, Turbine furls and unfurls constantly. This “hunting” behavior, while consistent with the over-speed protection function, is undesirable.
Reduced Efficiency After Furling
July 14-15 M. Bikdash 27
Wind Energy Program Wind Energy Program
0 20 40 60 80 100 120 1400
500
1000
1500
2000
2500
Wind speed in mphTo
wer
th
rust
in L
BS Tower thrust VS. wind speed
Design thrust load
Hunting
We can use tower thrust experimental data to approximate turbine thrust as a function of wind speed or rpm.
Hunting Behavior
July 14-15 M. Bikdash 28
Wind Energy Program Wind Energy Program
• Complexity of HAWT aerodynamics mathematical models
• Once the geometry of the turbine and blades are specified, the aerodynamic forces and moments of the turbine can be computed using YawDyn.
• YawDyn is a software package developed by C. Hansen and his colleagues at the University of Utah.
• Numerical Computations of Aerodynamic forces expensive numerically.
• Example YawDyn calculation for a 40 kW Bergey-type turbine.
YawDyn Software
July 14-15 M. Bikdash 29
Wind Energy Program Wind Energy Program
0 2 4 6 8 10 12 14 16 18 200
0.1
0.2
0.3
0.4
0.5
0.6
Tip Speed Ratio
Pow
er C
oeff
icie
nt
40
60
80
• 40 kW wind turbine
• at 10 degrees wind angle
• different rpms
YawDyn Power Curves
July 14-15 M. Bikdash 30
Wind Energy Program Wind Energy Program
0 5 10 150
0.1
0.2
0.3
0.4
0.5
0.6
Pow
er C
oeff
icie
nt
10
20
30
• 40 KW Turbine
• At 60 rpm • Dtheta =
angle between wind and rotor
Tip Speed Ratio
Different (Yaw -wind) angles
July 14-15 M. Bikdash 31
Wind Energy Program Wind Energy Program
Wind speed m/s0 5 10 15 20 25 30 35 40-50
0
50
100
150
200
250
Pow
er g
ener
ated
in k
W
RPM = 20
RPM = 40
RPM = 60
RPM = 80
RPM = 100
Power Curves at different rpms
• Power levels off for every rpm as wind speed increases
• Power increases with rpm
• Maximum allowable rpm
July 14-15 M. Bikdash 32
Wind Energy Program Wind Energy Program
• YawDyn is computationally expensive for real-time simulations
• Alternative: To generate (learn) a fuzzy inference system (FIS) that approximates YawDyn.
• Gathering a sufficient amount of input/output data to use for the learning process.
• Gathering made possible by a MATLAB interface that allows running several iterations of YawDyn with out user interaction.
Fuzzy Approximation of YawDyn
July 14-15 M. Bikdash 33
Wind Energy Program Wind Energy Program
yawdyn.wnd
YawDynVB.m
Wind Velocity
Wind Angle
RPM
rmp.mWind.m
yawdyn.ipt
YawDyn
yawdyn.pltFixOut.mOUTPUT
MATLAB Interface
July 14-15 M. Bikdash 34
Wind Energy Program Wind Energy Program
• Several FIS architectures can be used to approximate YawDyn.
• Direct approach: Use wind speed, relative wind angle, and rpm as inputs.
• Simplest Approach: Use power coefficient—CPversus the tip speed ratio—TSR.
• Selecting a specific approach includes a trade off between learning time and complexity and approximation quality.
• The next slides will show the implemented FISs.
Architecture of Proposed FIS
July 14-15 M. Bikdash 35
Wind Energy Program Wind Energy Program
Nacelle Yaw Moment
Lateral Hub ForceGeneralYaw
6 MFs / Input 864 Coefficients
9388 Training Points
Wind Speed
Relative Wind Angle
RPM
Rotor Power
Rotor Thrust
Two Fuzzy Inference Systems
Coefficient of PowerCpvsTSRTheta
6 MFs / Input 108 Coefficients
9388 Training Points
Relative Wind Angle
Tip Speed Ratio
July 14-15 M. Bikdash 36
Wind Energy Program Wind Energy Program
YawDyn vs. Sugeno GernalYaw
July 14-15 M. Bikdash 37
Wind Energy Program Wind Energy Program
windV θ∆ rpm rotorP rotorP̂YawDyn
Run Time (sec)
FISRun Time
(sec)
35 31 35 17.95 18.06 4.306 0.110
29 50 21 6.744 6.732 3.185 0.130
17 11 34 9.825 9.848 4.427 0.100
29 18 61 57.33 57.30 7.361 0.110
12 41 48 21.80 22.04 7.691 0.110
23 53 82 83.08 83.37 11.28 0.130
18 17 45 22.88 23.11 6.209 0.130
Using random samples
July 14-15 M. Bikdash 38
Wind Energy Program Wind Energy Program
θ∆ CP CP)
TSRYawDyn
Run Time (sec)
FISRun Time (sec)
13 1.2732 0.0123 0.0129 7.400 0.0710
1 2.7322 0.1196 0.1209 16.35 0.0100
56 3.2620 0.0924 0.0929 11.71 0.0200
48 0.7716 0.0051 0.0053 3.485 0.0100
16 0.9502 0.0062 0.0059 3.905 0.0200
44 4.8564 0.2233 0.2155 7.351 0.0100
27 1.0104 0.0076 0.0076 5.398 0.0100
for random test input samples
Performance of FIS2
July 14-15 M. Bikdash 39
Wind Energy Program Wind Energy Program
• Use the Interpretable Sugeno Approximator (ISA)
• Make its consequent polynomials rule-centered.
• A typical ISA rule has the form:
Rk: If x1 is A1 and x2 is A2 and… xn is An Then
)(...)()( 2221110k
nnkn
kkkkkk rxbrxbrxbbu −++−+−+=
• rk is the rule center (centers of the membership functions of all inputs tested by the kth rule.)
• If the membership functions are chosen properly (local and differentiable everywhere),
• the b coefficients can be interpreted as Taylor series coefficients.
Fuzzy Linearization
July 14-15 M. Bikdash 40
Wind Energy Program Wind Energy Program
Some coefficients of the Sugeno engine can be interpreted as the derivative of the function at rule centers. In this case, these are aerodynamic sensitivity derivatives.
Interpretation of Coefficients
July 14-15 M. Bikdash 41
Wind Energy Program Wind Energy Program
• Fuzzy approximation techniques were used to derive FISs that approximate YawDyn.
• Excellent approximation
• FIS with fewer inputs learns faster• More general FIS approximates better • 1 to 2 orders of magnitude speed up in
computation• Using ISA yields estimates of derivatives as
well to obtain linearized models
Conclusions ANNIE 99
July 14-15 M. Bikdash 42
Wind Energy Program Wind Energy Program
0 5 10 15 20 25 30 35 40-1
0
1
2
3
4
5
Wind Speed
Mo
men
ts
Dtheta = 10 degrees and RPM = 60
Lateral Hub Force
Rotor Thrust
Nacelle Yaw
Moment Curves for 40KW
• Nacelle Moment is dominant!
• Hence specifying furling wind speed is not easy
July 14-15 M. Bikdash 43
Wind Energy Program Wind Energy Program
0 20 40 60 800
50
100
Angle between wind and rotor (degrees)
Power in KW
Vwind = [7 10 13 16 19] m/sec, 80 rpm
0 20 40 60 80-10
0
10
20
Total Aerodynamic Yaw
Starts negative
0 20 40 60 80-10
0
10
20
0 20 40 60 800
2
4
Due to thrust
V
in KNm
Due to Nacelle
Yaw Moment of Nacelle becomes dominant as the rotor moves away from wind.
July 14-15 M. Bikdash 44
Wind Energy Program Wind Energy Program
Equilibrium Conditions
Unknowns
Generator Torque-Speed Characteristics (dependent on electrical load and power electronics)
3 Equations
July 14-15 M. Bikdash 45
Wind Energy Program Wind Energy Program
Onset of Furling
July 14-15 M. Bikdash 46
Wind Energy Program Wind Energy Program
6 8 10 12 14 1620406080
100
Dtheta in deg
Power in kW
4 6 8 10 120
50
100
6 8 10 12 14 168
10
12
14
16
wind speed in m/s
psi=0
6 8 10 12 14 160
5
10
15
Dtheta in deg
Torq
ue in
kNm L1=0.2032
6 8 10 12 14 164
6
8
10
12
Omega in rad/s
2 4 6 8 10 124
6
8
10
12
Om
ega
inra
d/s
Torque in kNm120 150
Omega in rad/s
Po
wer
in k
W
Onset of
Furling. No
control.
Any generator torque-speed Curve
July 14-15 M. Bikdash 47
Wind Energy Program Wind Energy Program
4 6 8 10 12 14 168
10121416
wind speed in m/s
8 10 12 14 162468
10
Dthetain deg
Torque in kNm
6 8 10 12 14 16468
1012
Omega in
rad/s
2 4 6 8 10 12468
1012
Torque in kNm
6 8 10 12 14 1620406080
100120
DthetaIn deg
Power in kW
4 6 8 10 1220406080
100120
Omega in rad/s
Power in kW
Utility grid interface drawing rated power at any wind speed
July 14-15 M. Bikdash 48
Wind Energy Program Wind Energy Program
Design Yaw Control for constant 40 KW at any wind speed
July 14-15 M. Bikdash 49
Wind Energy Program Wind Energy Program
8 10 12 14 16 18 200
20
40
60
80In degrees
L1=0.2032, Lac=4.728
8 10 12 14 16 18 200
10
20
30
40
P(KW); Om(rad/s)
8 10 12 14 16 18 200
5
10
15
V wind in m/s
YawDyn -Tail -Control
Yaw-Furling angle between wind and tail
Yaw = angle between rotor and wind
Furling = angle between tail and rotor
≈
Torque (KNm) Furling Curves obtained under the assumption of constant rated (40KW) power delivered to electrical generator under rated speed.
Yaw Moments in KNm.• Tail Moment essentially constant!• YawDyn: Rotor thrust + Nacelle +
Lateral• Difference must be picked up by Yaw
Control Torque (Acting on nacelle only)
Assuming control moment at the yaw axis only
July 14-15 M. Bikdash 50
Wind Energy Program Wind Energy Program
Design Yaw Control for any desired schedule of Power and rpm
July 14-15 M. Bikdash 51
Wind Energy Program Wind Energy Program
8 10 12 14 16 18 200
20
40
60
80
8 10 12 14 16 18 200.8
1
1.2
1.4
8 10 12 14 16 18 200
5
10
V wind in m/s
P
YawDyn -Control
Torque
-Tail
Yaw-Furling
Yaw
Furling
Maintaining 40KW output but with 10% allowableoverspeed requires 27% less Yaw control
Speed In per unit
Yaw Moments in KNm
10% allowable
Overspeed
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Wind Energy Program Wind Energy Program
Class of Actuators
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Wind Energy Program Wind Energy Program
Linear Motor Geometry
A: the yaw axis
B: the tail hinge
D
FP Q
C
July 14-15 M. Bikdash 54
Wind Energy Program Wind Energy Program
• Simulation software in MATLAB and Simulink
• Equations of motion for furling mechanism derived
• Reliance on YawDyn• Hybrid fuzzy crisp
modeling for real-time simulations
• Nacelle moment dominant in furling behavior. Reshape?
Conclusions • Aerodynamics of tail?• Generator/Load/Power
Electronics? (d-q Simulink model)
• Analysis of equilibrium • onset of furling• scheduled
power/rpm as function of Vwind
• linear motor • Linearization? Stability?
Hopf bifurcation?
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