64
Wind Turbine Control W. E. Leithead University of Strathclyde, Glasgow Supergen Student Workshop 24th September 2010 1
Wind Turbine Control
W. E. Leithead
University of Strathclyde, Glasgow
Supergen Student Workshop24th September 2010 1
Outline
1. Introduction
2. Control Basics
3. General Control Objectives
4. Constant Speed Pitch Regulated WT’s
5. Variable Speed Stall Regulated WT’s
6. Variable Speed Pitch Regulated WT’s
7. Conclusion
2Supergen Student Workshop
Reproduced with permission of EWEA
24th September 2010
Introduction
3Supergen Student Workshop
Oversees total operation of wind turbine including
– start-up/shutdown
– safety of turbine operation
– fault handling
– data collection
Supervisory control
Continuously adjusts dynamic state of wind turbine
– cause the operating point to track the on-design trajectory
– minimise the off-design fluctuations
Operational control
Focus
24th September 2010
• Stall regulated constant speed
• Pitch regulated constant speed
• Stall regulated variable speed
• Pitch regulated variable speed
Wind Turbine Types
Supergen Student Workshop 4
Introduction
24th September 2010
Constant wind speed curves
Supergen Student Workshop 5
Introduction
24th September 2010
6
0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8-0.5
0
0.5
1
1.5
2
2.5
3x 10
6
99%
99%
98%
98%
97%
97%
96%
96%
Beginning of Stall
4 m/s5 m/s
6 m/s7 m/s
8 m/s
9 m/s
10 m/s
11 m/s
12 m/s
Torque [Nm]
Rotor Speed [rad/s]
Rated power
Supergen Student Workshop
Stall regulated constant speed
Introduction
24th September 2010
7
0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8-0.5
0
0.5
1
1.5
2
2.5
3x 10
6
99%
99%
98%
98%
97%
97%
96%
96%
Beginning of Stall
4 m/s5 m/s
6 m/s7 m/s
8 m/s
9 m/s
10 m/s
11 m/s
12 m/s
Torque [Nm]
Rotor Speed [rad/s]
Rated power
Pitch regulated constant speed
Supergen Student Workshop
Introduction
24th September 2010
0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8-0.5
0
0.5
1
1.5
2
2.5
3x 10
6
99%
99%
98%
98%
97%
97%
96%
96%
Beginning of Stall
4 m/s5 m/s
6 m/s7 m/s
8 m/s
9 m/s
10 m/s
11 m/s
12 m/s
8
Torque [Nm]
Rotor Speed [rad/s]
Rated power
Stall regulated variable speed
Supergen Student Workshop
Introduction
24th September 2010
0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8-0.5
0
0.5
1
1.5
2
2.5
3x 10
6
99%
99%
98%
98%
97%
97%
96%
96%
Beginning of Stall
4 m/s5 m/s
6 m/s7 m/s
8 m/s
9 m/s
10 m/s
11 m/s
12 m/s
9
Torque [Nm]
Rotor Speed [rad/s]
Stall regulated variable speed
Rated power
Supergen Student Workshop
Introduction
24th September 2010
10
Pitch regulated variable speed
Supergen Student Workshop
Introduction
pitchingTorque [Nm]
Rotor Speed [rad/s]
24th September 2010
Control Design Task:
– Changed with the technology
Related Activities
– Model development and validation
– Dynamic analysis
Introduction
Supergen Student Workshop 11
Reproduced with permission of BWEA
24th September 2010
Define operational strategy– different control modes
Ensure smooth switching– between control modes– controller start-up and shut-down
Within each mode cater for– aerodynamic nonlinearity
– actuator constraints
Design linear control law for each mode
Introduction
Control design task
Supergen Student Workshop 12
Implementation issues
24th September 2010
Feedback systems
Linear Control Basics
SystemController+
-
Closed loop system stability is required
Output will asymptotically converge to setpoint
Setpoint
(e.g. Desired Rotor speed)
Output
(e.g. Rotor Speed)
transfer functions
Supergen Student Workshop 1324th September 2010
Transfer functions model the dynamics
( )1
0 1 11
0 1 1
... ;
...
m mm m
n nn n
b s b s b s bG s m na s a s a s a
−−
−−
+ + + += ≤
+ + + +
Roots of the denominator are the poles.
Unstable poles have negative real parts.
Roots of the numerator are the zeros.
Non-minimum phase zeros have negative real parts.
Transfer functions
1( )1
G ss
=−
unstable non-minimum phase2
( 1)( )2 3 1
sG ss s− −
=+ +
Supergen Student Workshop 14
Linear Control Basics
24th September 2010
15
1( )1
G ss
=+
1( )1
G jj
ωω
=+
s=jω
Horizontal axis: log10(frequency in rad/s)
Vertical axis (top): 20log10(|G(jω)|)
Vertical axis (bottom): Arg(G(jω))
10-2
10-1
100
101
102
-40
-20
0
mag
nitu
de [d
B]
10-2
10-1
100
101
102
-100
-50
0
frequency [rad/s]
phas
e [d
eg]
• Dynamics represented by transfer function G(s)
gain
phase
Supergen Student Workshop
Linear Control Basics
24th September 2010
Bode Diagram
Frequency (rad/sec)10
-210
-110
010
190
180
270
360
Phas
e (d
eg)
-20
-15
-10
-5
0
5
10
Mag
nitu
de (d
B)
Gain Margin
Phase Margin
Bode plot for open-loop
Stability margins
Phase and gain margins positive
closed loop stable
⇒
16Supergen Student Workshop
Linear Control Basics
24th September 2010
Maximum phase loss possible is 180 degrees
Improvements to all aspects of performance costs phase
Zero sum game
Design trade-off
17Supergen Student Workshop
Linear Control Basics
24th September 2010
Delay of τ seconds has transfer function
Gain = 1 Phase = -τ ω
Does nothing other than lose phase
Performance inevitably lost
Delay
18Supergen Student Workshop
( ) sG s e τ−= ( ) jG j e τωω −=s=jω
Linear Control Basics
24th September 2010
Non-minimum phase zero
19Supergen Student Workshop
0 2 4 6 8 10 12 14 16 18-0.2
0
0.2
0.4
0.6
0.8
1
1.2Step Response
Time (sec)
Ampl
itude
has non-minimum phase zero at 1rad/s2( 1)( )
(2 3 1)sG s
s s− −
=+ +
Non-minimum phase zero is similar to a delay
Again, performance inevitably lost
2 2( 1) ( 1) (1 )
(2 3 1) (2 3 1) (1 )s s s
s s s s s− − + −
=+ + + + +
and 2(1 )(1 )
ss es
−−≈
+
Linear Control Basics
24th September 2010
Performance improves with crossover frequency of open-loop Bode plot
Crossover frequency
20Supergen Student Workshop
-40
-30
-20
-10
0
10
20
Mag
nitu
de (d
B)
10-2
10-1
100
101
-180
-135
-90
-45
0
Phas
e (d
eg)
Bode Diagram
Frequency (rad/sec)
crossover frequency
Linear Control Basics
24th September 2010
Crossover frequency is bounded below by any unstable pole
Crossover frequency is bounded above by any non-minimum phase zero
Unstable poles and non-minimum phase zeros impose absolute bounds on performance
Poles and zeros
21Supergen Student Workshop
Linear Control Basics
24th September 2010
Sensitivity function
22Supergen Student Workshop
Feedback causes the output to track the input
What does it do for the wind speed disturbances?
PlantController+
-
setpointdisturbance
measurement noise
output
Operating strategy Wind speed
Linear Control Basics
24th September 2010
The transfer function between the disturbance and the output is the sensitivity function
Sensitivity function
23Supergen Student Workshop
-40
-30
-20
-10
0
10
20
Mag
nitu
de (d
B)
10-2
10-1
100
101
-180
-135
-90
-45
0
Phas
e (d
eg)
Bode Diagram
Frequency (rad/sec)
-20
-15
-10
-5
0
5
Mag
nitu
de (d
B)
10-2
10-1
100
101
0
30
60
90
Phas
e (d
eg)
Bode Diagram
Frequency (rad/sec)
Bode plot gain for open-loop transfer function
Bode plot gain sensitivity function
The sensitivity function is negative when the open-loop is positive and vice versa
crossover frequency
Linear Control Basics
24th September 2010
Sensitivity function
24Supergen Student Workshop
-20
-15
-10
-5
0
5
Magni
tude (d
B)
10-2
10-1
100
101
0
30
60
90
Phase
(deg)
Bode Diagram
Frequency (rad/sec)
disturbance
Gain << 0dB
Disturbance at frequencies below crossover is attenuated
Disturbance at frequencies above crossover is enhanced
Linear Control Basics
24th September 2010
Wind turbine control
25Supergen Student Workshop
Wind turbine control is a disturbance rejection problem
There are many disturbance above crossover, the spectral peaks at nΩ and dynamic mode frequencies
The dynamics have non-minimum phase zeros
For some strategies have unstable poles
Linear Control Basics
24th September 2010
Smooth Generated Power
Alleviate Loads
Provide Damping
Maximise Energy Capture
Not all apply to all types of turbines
General Control Objectives
26Supergen Student Workshop24th September 2010
General Control Objectives
27Supergen Student Workshop
Drive-train load alleviation
Power quality control
Maximising energy capture
Dynamic mode damping
Avoidance of enhancing structural loads
Actuator activity reduction
Historically, control objectives changed from
simply limiting power fluctuations to:
24th September 2010
The increasing size of machines is driving control development directions. More demands are placed on the control system at the same time as low frequency
dynamic issues have greater importance.
Control systems are now being required to
regulate some fatigue related
dynamic loads
Of strong interest are the tower
loads.
The larger the wind turbine the greater
the requirements
Must be achieved without
compromising turbine
performance
Must be achieved without
increasing pitch activity
General Control Objectives
28Supergen Student Workshop24th September 2010
Stall regulated constant speed WT’s
– No active control
Pitch regulated constant speed WT’s
– Blade pitch
Stall regulated variable speed WT’s
– Generator reaction torque
Pitch regulated variable speed WT’s
– Blade pitch
– Generator reaction torque
General Control Objectives
Control Actions:
Supergen Student Workshop 2924th September 2010
Supergen Student Workshop 30
Pitch Regulated Constant Speed WT’s
24th September 2010
Typical machine rating (1990) 300kW
Pitch Regulated Constant Speed WT’s
Above Rated Operation:
Blade Pitch Control
Objectives
– Maintain Constant Power
– Wind Speed Disturbance Rejection
– Avoid Increasing Tower/Blade Load
Measurement
– Generated power
Below Rated Operation:
No Control
Supergen Student Workshop 3124th September 2010
Above rated control:
• Basically PI augmented by filters at nP and 2nP
Major issues are nonlinear:
• Switching between above and below rated
• WT Dynamics vary strongly with operating point
• Actuator saturation
The nonlinear issues drive the performance
Only look at second in detail
Pitch Regulated Constant Speed WT’s
Supergen Student Workshop 3224th September 2010
Nonlinear dynamics:
• The important nonlinearity is the aerodynamic torque
Pitch
demand
Pitch
angle
Aero
torque
Rotor
Speed
Wind speed
Supergen Student Workshop 33
Pitch Regulated Constant Speed WT’s
actuator drive-trainaerodynamics
24th September 2010
• To operate at rated power, there is a pitch angle, , for each wind speed, .
• Linearising the aerodynamics at ( , ).
• Is gain-scheduling appropriate?• Schedule on wind speed or pitch angle?
0β 0υ
0υ
Supergen Student Workshop 34
Pitch Regulated Constant Speed WT’s
0β
24th September 2010
The aerodynamic gain has a large range
Varies rapidly as the wind speed varies
A priori it’s not appropriate to gain-schedule
Aerodynamic gain
Supergen Student Workshop 35
Pitch Regulated Constant Speed WT’s
24th September 2010
Since the aerodynamic torque is constant along the locus of operating points, its partial derivatives are related by:
It follows that is constant on the locus of operating points provided f and g satisfy
),()(),( 000
00 υβδβδ
υυβυβ
δυδ T
ddT
−=
))()(( υβ gh −
),(),( υβδυδ
υυβ
δβδ
β υυT
ddgT
ddh
==
Pitch Regulated Constant Speed WT’s
Supergen Student Workshop 3624th September 2010
Hence locally to the locus of operating points
for some function τ(ε) such that τ(0)=T0 and 1)0( =ετ
dd
)()()(),( υβεετυβ ghT −=≡
Pitch Regulated Constant Speed WT’s
Supergen Student Workshop 3724th September 2010
Since
Global scheduling is achieved provided the integrator is placed after the scheduled gain
( ) ∫∫ ′=≡= − pdtyhypdthy )(1
Pitch Regulated Constant Speed WT’s
Supergen Student Workshop 3824th September 2010
Typical power time histories for a 300 kW machine at 16 m/s mean wind speed
Time (s)
Power (kW)× 102
gain before integrator gain after integrator
7
20 40 60 80 100
6
0
1
2
3
4
5
Pitch Regulated Constant Speed WT’s
Supergen Student Workshop 3924th September 2010
Structure of controller that deals with all three nonlinear issues.
Supergen Student Workshop 40
Pitch Regulated Constant Speed WT’s
24th September 2010
Supergen Student Workshop 41
Pitch Regulated Constant Speed WT’s
24th September 2010
Nonlinear control:
Sensitivity of the aerodynamic torque to changes in pitch increases faster than to changes in wind speed
Increase bandwidth with wind speed
Supergen Student Workshop 42
Pitch Regulated Constant Speed WT’s
Rate of change wrt wind speed
Rate of change wrt pitch angle
24th September 2010
Nonlinear control:
It is the fatigue loads on the drive-train that need alleviating
Extreme loads do most damage
Alter the distribution of the load transients by pulling in the tails
Supergen Student Workshop 43
Pitch Regulated Constant Speed WT’s
24th September 2010
Nonlinear control: Two-bladed WT
Extreme loads
Supergen Student Workshop 44
Pitch Regulated Constant Speed WT’s
Linear control
Nonlinear control
24th September 2010
Nonlinear control: Three-bladed WT
Extreme loads
Supergen Student Workshop 45
Pitch Regulated Constant Speed WT’s
Linear control
Nonlinear control
24th September 2010
Supergen Student Workshop 46
Stall Regulated Constant Speed WT’s
24th September 2010
Above/Below Rated Operation: Generator reaction torque control Objective
– Increase drive-train damping Measurement
– Generator speed
Stall Regulated Constant Speed WT’s
Above Rated Operation: Objective
– Power/torque regulation by stalling
Below Rated Operation:• Objective
– Maximise energy capture
Supergen Student Workshop 4724th September 2010
Supergen Student Workshop 48
Stall Regulated Constant Speed WT’s
Strategy below rated
24th September 2010
Strategies above rated
Supergen Student Workshop 49
Stall Regulated Constant Speed WT’s
24th September 2010
Control drivers:
• Choose strategy – defining a curve to be tracked
• Dynamics are strongly nonlinear
• Above rated, curve dependent unstable pole and non-minimum phase zero – 0.3r/s and 2.5r/s
• Switching between modes
Supergen Student Workshop 50
Stall Regulated Constant Speed WT’s
24th September 2010
-50
0
50
100
150
200
250
300
350
400
4.25 8.25 12.25 16.25 20.25 24.25 28.25 32.25wind speed (rad/s)
Power (kW)
0
10
20
30
40
50
60
70
80
90
4.25 8.25 12.25 16.25 20.25 24.25 28.25 32.25wind speed (rad/s)
Low-speed shaft torque (kNm)Power Torque
Performance
Supergen Student Workshop 51
Stall Regulated Constant Speed WT’s
24th September 2010
Reproduced with permission of EWEA
Pitch Regulated Variable Speed WT’s
Supergen Student Workshop 5224th September 2010
Typical machine rating (2005) 1-2MW
Pitch Regulated Variable Speed WT’s
Above Rated Operation: Blade Pitch Control
Generator Reaction Torque Control
Objectives– Maintain Constant
Power– Maintain Constant
Speed Measurement
– Generator speed
Below Rated Operation: Same as stall regulated
variable speed WT
Supergen Student Workshop 5324th September 2010
Very Large WTs – 5MW
With the increase in size, wind turbines are more flexible: structural issues important
Bigger blades and tower place structural modes at lower frequencies
Basic control strategies remain, but fatigue reduction must be added onto the control objectives
Control strategies to reduce tower and blade fatigue is currently an active field of research
Fatigue of production cases account for the 89% of the relative damage on the tower
Supergen Student Workshop 54
Pitch Regulated Variable Speed WT’s
24th September 2010
Dynamics: pitch angle to generator speed 3MW WT
Pitch Regulated Variable Speed WT’s
Supergen Student Workshop 55
13 m/s
22 m/s
24th September 2010
The tower fatigue might be reduced by a tower acceleration feedback loop.
Pitch Regulated Variable Speed WT’s
Supergen Student Workshop 56
Feedback loop acts on fore-and-aft tower mode
24th September 2010
Dynamics: pitch angle to tower speed 3MW WT
Pitch Regulated Variable Speed WT’s
Supergen Student Workshop 57
16 m/s
22 m/s
24th September 2010
Proportional control is sometimes not very successful
Pitch Regulated Variable Speed WT’s
Supergen Student Workshop 58
Problem is the interaction with the blade flap mode
With TFL
No TFL
24th September 2010
Instead localise the feedback
Pitch Regulated Variable Speed WT’s
Supergen Student Workshop 5924th September 2010
Much more effective
Pitch Regulated Variable Speed WT’s
Supergen Student Workshop 60
With TFL
No TFL
24th September 2010
Measured as 20 year lifetime equivalent fatigue loads
• Above approach can reduce the tower fatigue by 5% to 8%
• More advanced control can reduce the tower fatique by 12% to 18%
Pitch Regulated Variable Speed WT’s
Supergen Student Workshop 6124th September 2010
62
Hub bending moment (nodding, stationary motion)50 100 150 200 250 300 350 400 450 500 550
-5
0
5
10
15
20
x 106
Time (s)
--- [N
m]
Collective, Stationary hub My [Nm]1P IA, Stationary hub My [Nm]1P+2P IA, Stationary hub My [Nm]
Rotor Load Imbalance Reduction
5MW Supergen exemplar wind turbine
24th September 2010 Supergen Student Workshop
Pitch Regulated Variable Speed WT’s
Concluding Remarks
Reproduced with permission of EWEA
Supergen Student Workshop 6324th September 2010
