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1
Disturbance Accommodating Control of Floating Wind
Turbines
Hazim Namik and Karl Stol
Department of Mechanical Engineering The University of Auckland
22
Outline
• Introduction
• Individual vs. Collective Blade Pitching
• Implemented controllers– Gain Scheduled PI– Periodic LQR– Periodic DAC
• Results
• Summary
33
Introduction
• A recent trend in the wind turbine industry is to go offshore
• The further offshore the better the wind BUT increased foundation costs
• After certain depth, floating wind turbines become feasible
44Source: Jonkman, J.M., Dynamics Modeling and Loads Analysis of an Offshore Floating Wind Turbine, in Department of Aerospace Engineering Sciences. 2007, University of Colorado: Boulder, Colorado.
Floating Wind Turbines
55
NREL 5MW Wind Turbine
• Barge floating platform– 40m×40m×10m
• 5MW power rating
• 126m diameter rotor (3 Blades)
• 90m hub height
• Simulated using FAST and Simulink
x
z
y
rollpitch
yaw
Previous Work
• Implemented a time-invariant state space controller to address multiple objectives– Power and platform pitch regulation
• Performance was improved but...
• Conflicting blade pitch commands were issued due to collective blade pitching– Individual blade pitching was proposed
6
7
Objectives and Scope
• Implement individual blade pitching through periodic control
• Compare performance of DAC on a floating barge system to previously applied controllers
• Disturbance rejection for wind speed changes only
• Above rated wind speed region only
• Barge platform only
88
How to Control a Wind Turbine?
Collective Pitch
Individual Pitch
Control Options
Blade Pitch Generator Torque
Source: US Dept. of Energy
99
Collective Pitch Restoring Mechanism• Works by changing
the symmetric rotor thrust
• As turbine pitches– Forward: Rotor thrust
is increased– Backward: Rotor thrust
is reduced
• Pitching conflicts with speed regulation
1010
Individual Pitch Restoring Mechanism• Works by creating
asymmetric thrust loads
• As turbine pitches– Forward:
• Blades at the top increase thrust
• Blades at the bottom reduce thrust
– Backward: vice versa
1111
Controllers Implemented
• Gain Scheduled PI (GSPI)
• Periodic Linear Quadratic Regulator (PLQR)
• Periodic Disturbance Accommodating Controller (PDAC)
12
Baseline Controller
• Generator torque controller – Regulate power above rated
• Collective pitch controller– Regulate generator speed above rated wind
speed– Gain scheduled PI controller
13
State Space Control
• Requires a linearized state space model
States vector
Actuators vector
Periodic gain matrices
• Control law (requires a state estimator)
utBxtAx )()(
xtGu
Nonlinear Floating Wind Turbine Model
(FAST)
State EstimatorState Regulator
++
+-
Generic Block Diagram
14
x̂
yy
opydu
opu u
u
15
Periodic LQR
• Periodic gains result in individual blade pitching
• Requires 5 degrees of freedom (DOFs) model to ensure stability– Platform Roll and Pitch– Tower 1st side-side bending mode– Generator and Drivetrain twist
• Part of DAC: State regulation
16
Disturbance Accommodating Control• Time variant state space model with disturbances
• Disturbance waveform model
xCy
uBuBxAx dd
zu
zFz
d
17
Disturbance Accommodating Control (Cont.)• Form the DAC law (requires disturbance estimator)
• New state equation becomes
zGxGu d*
zBBGxBGAx dd
• To minimize effect of disturbances
dd BBG
GSPI PLQR PDAC
Gains Calculation
Gain scheduledPeriodic Riccati
EquationPeriodic Riccati Equation + DAC
Blade Pitching
Collective Individual Individual
Pros Simple and robust
MIMO
Multi-objective
Individual Pitching
All PLQR pros +
Disturbance Rejection
ConsSISO
Single-objective
Collective pitching
ComplicatedMost complicated
Requires a dist. estimator
18
GSPI PLQR
Gains Calculation
Gain scheduledPeriodic Riccati
Equation
Blade Pitching
Collective Individual
Pros Simple and robust
MIMO
Multi-objective
Individual Pitching
ConsSISO
Single-objective
Collective pitching
Complicated
Controllers Comparison
GSPI
Gains Calculation
Gain scheduled
Blade Pitching
Collective
Pros Simple and robust
ConsSISO
Single-objective
Collective pitching
SISO: Single-Input Single-Output MIMO: Multi-Input Multi-Output
19
1 DOF DAC Simulation Result
20
Full DOFs Simulation Result
Power and Speed
Fatigue Loads Platform Motions
21
Reasons for Poor Performance
• High Gd gain causing extensive actuator saturation
• System nonlinearities and un-modeled DOFs
• System may not be stable in the nonlinear model
22
Effect of Adding Platform Yaw
Power and Speed
Fatigue Loads Platform Motions
2323
Conclusions
• The periodic LQR significantly improved performance since it utilises individual blade pitching
• Adding DAC gave mixed performance due to actuator saturation
• DAC for the wind fluctuations may not be the ideal controller for a floating barge concept
Future Work
• Variable pitch operating point– Follow optimum
operating point
• DAC for waves– Effect on Bd Matrix– Simple moment
disturbance
24
Wind Speed (m/s)
θlin
Bla
de P
itch
(deg
)
Optimum operating point
DAC collective pitch command
vrated vlin
zGxGu d*
25
Thank You
2626
Offshore Wind Turbines
• Why go offshore?– Better wind conditions
• Stronger and steadier• Less turbulent
– Can be located close to major demand centres– Operate at maximum efficiency (e.g. no noise
regulations)
• Increased foundation costs with increasing water depth
2727
Going Further OffshoreShallow Water
Transitional Depth
Deepwater Floating
Land-Based
0 – 30 m 30 – 50 m 50 – 200 mWater Depth:
Source: Jonkman, J.M., Dynamics Modeling and Loads Analysis of an Offshore Floating Wind Turbine, in Department of Aerospace Engineering Sciences. 2007, University of Colorado: Boulder, Colorado.
2828
FAST Simulation Tool• Fatigue, Aerodynamics, Structures and
Turbulence
Source: Jonkman, J.M., Dynamics Modeling and Loads Analysis of an Offshore Floating Wind Turbine, in Department of Aerospace Engineering Sciences. 2007, University of Colorado: Boulder, Colorado.
2929
Wind and Wave
3030
Power Regions
• Region 1– No power is generated
below the cut in speed
• Region 2– Maximise power
capture
• Region 3– Regulate to the rated
power
3131
Torque Controller
• Region 1
• Region 2
• Region 3
• Regions 1.5 and 2.5 are linear transitions between the regions
2HSSGen KT
0GenT
HSSGen
RatedGen
PT
3232
Applied Generator Torque
0
5
10
15
20
25
30
35
40
45
0 500 1000 1500
Th
ou
san
ds
High Speed Shaft Speed (rpm)
Gen
erat
or
To
rqu
e (N
m) Tg_rated (Nm)
Tg_r1 (Nm)
Tg_r1.5 (Nm)
Tg_r2 (Nm)
Tg_r2.5 (Nm)
Tg_r3 (Nm)
T=Kw 2̂
Torque Controller
Reg
ion
1.0
Reg
ion
1.5
Reg
ion
2.0
Reg
ion
3.0
Region 2.5
3333
Collective Pitch Controller
• PI Controller to regulate generator speed
• Controller gains calculated according to the design parameters– ωn = 0.7 rad/s and ζ = 0.7
• Simple DOF model with PI controller gives
P
N
IKand
PN
IK
Gear
nratedRotorDrivetrainI
Gear
nratedRotorDrivetrainP
2,,2
3434
Gain Scheduled PI GainsGain Scheduled PID Controller
0.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0 5 10 15 20 25
Pitch (deg)
Co
rrec
tio
n F
acto
r
KP(θ)
KI(θ)
3535
Riccati Equations
• Optimal gain and Algebraic Riccati Equation
QPBRPBPAPA
PBRKT
AvgAvgT
TLQR
AvgAvg
Avg
1
1
• Optimal periodic gain and Periodic Riccati Equation
QtPtBRtBtPtAtPtPtAtP
tPtBRtGTT
T
1
1
3636
Simulation Tools
• FAST – Aero-hydro-servo-
elastic simulator– Nonlinear equations of
motion– Can be linked to
Simulink– Find linearized state-
space model for controller design
• MATLAB/Simulink– Design controllers
using linear control theory
– Easy graphical implementation
– Powerful design tools to help design controllers
– Flexible
3737
Periodic Gains
• Changes with rotor azimuth
• Same for each blade but ±120° out of phase
• Gain for state 3 changes sign when blade is at lower half of rotor