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

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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

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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

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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