hazim namik and karl stol department of mechanical engineering the university of auckland
DESCRIPTION
Disturbance Accommodating Control of Floating Wind Turbines. Hazim Namik and Karl Stol Department of Mechanical Engineering The University of Auckland. Outline. Introduction Individual vs. Collective Blade Pitching Implemented controllers Gain Scheduled PI Periodic LQR Periodic DAC - PowerPoint PPT PresentationTRANSCRIPT
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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
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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
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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
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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
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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.
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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.
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Wind and Wave
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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
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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