ME75-2014-myan076-report

IMPROVING REGION TRANSITION FORFLOATING WIND TURBINES

M. Yang

Project Report ME75-2014

PROJECT IN MECHANICAL ENGINEERING

Co-worker: N. Farquhar

Supervisor: Dr. Hazim Namik

Department of Mechanical EngineeringThe University of Auckland

24 September 2014

ME75-2014

IMPROVING REGION TRANSITION FOR FLOATING WIND TURBINES

M. Yang

ABSTRACT

At certain wind speeds a wind turbine will transition from operating at belowdesign specifications to above design specifications. This transition causes dipsin power capture and increased loads which reduces overall performance andlife-span. The goal of this project is to improve the region transition specificallyfor a offshore floating wind turbine.

The project will be purely simulation based with the aid of an aero-servo-elastic simulator called FAST which is coupled with MATLABr’s Simulinkr

to provide the control system interface. A 5 MW wind turbine placed on abarge platform will be used as the baseline.

Two different directions were taken to improve region transition; the first waschanges to try reduce platform motion, and the second was a change to thetorque behaviour of the wind turbine generator.

The largest reduction in transition time occurred using a different torque com-mand compared to the baseline. Transitions now ranged from 3 % to 10 % oftotal time compared to 17 % for the baseline. Power captured in region 2 alsoincreased by around 11-34 %.

The use of individual blade pitch control to regulate motion showed the greatestimprovement to energy capture in region 3 with reduction in lost power captureof 15 %.

Load reductions were most effective using motion reduction objectives withreductions of up to 14 %. However, there were cases where a load increased byas much as 32 %.

A combination controller was tested and results showed that there were furtherimprovements when operating within the transition region.

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Table of Contents

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi

Glossary of Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Wind Energy Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Offshore Wind Energy . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Wind Turbines Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2.1 Floating Offshore Wind Turbines . . . . . . . . . . . . . . . . . . . . 31.3 Wind Turbine Control Overview . . . . . . . . . . . . . . . . . . . . . . . . . 41.4 Project Goals and Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Floating Wind Turbine Control Overview . . . . . . . . . . . . . . . . . . . . . 62.1 Power Curve Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2 Platform Motion Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.3 Wind Preview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.4 Model Predictive Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3 Simulation and Analysis Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.1 The Baseline Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.2 IEC Standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.3 Performance Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4 Controller Implementation and Testing . . . . . . . . . . . . . . . . . . . . . . . 144.1 Collective Pitch Proportional Control . . . . . . . . . . . . . . . . . . . . . 15

4.1.1 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 164.2 Individual Blade Pitch Control . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4.2.1 Linearisation and Weighting . . . . . . . . . . . . . . . . . . . . . . . 184.2.2 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4.3 Alternative Torque Trajectories . . . . . . . . . . . . . . . . . . . . . . . . . 194.3.1 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4.4 Linearised Torque Trajectory . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.4.1 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.5 Combined Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

6 Future Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Appendix A Simulink Model and FAST diagram . . . . . . . . . . . . . . . . . . 29

Appendix B Design Load Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Appendix C Weibull Weighted Average . . . . . . . . . . . . . . . . . . . . . . . . 33

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Appendix D Results Graphs and Plots . . . . . . . . . . . . . . . . . . . . . . . . 35

Appendix E Cp Plot and Verification Calculations . . . . . . . . . . . . . . . . . 44

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List of Figures

Figure 1 Combined global wind energy capacity from 1996-2012 . . . . . . . . 1Figure 2 Platform DOF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Figure 3 The four main platform designs . . . . . . . . . . . . . . . . . . . . . 4Figure 4 Ideal power capture curve . . . . . . . . . . . . . . . . . . . . . . . . 5Figure 5 Simple representation of the power curve . . . . . . . . . . . . . . . . 7Figure 6 Trajectory comparison of TTC and baseline . . . . . . . . . . . . . . 8Figure 7 Diagram of the 5-mass model . . . . . . . . . . . . . . . . . . . . . . 9Figure 8 Baseline controller Simulink model . . . . . . . . . . . . . . . . . . . 11Figure 9 Baseline torque controller trajectory . . . . . . . . . . . . . . . . . . . 12Figure 10 Baseline simulation with waves and without waves . . . . . . . . . . 15Figure 11 Simplified P control implemented in Simulink . . . . . . . . . . . . . 15Figure 12 Platform pitch response at a turbulent mean wind speed of 14 m/s . . 16Figure 13 Individual blade pitch control diagram . . . . . . . . . . . . . . . . . 17Figure 14 Trajectory 1 curve against baseline . . . . . . . . . . . . . . . . . . . 20Figure 15 Time series plot of Trajectory 2 . . . . . . . . . . . . . . . . . . . . . 21Figure 16 Trajectory 2 transition plot against baseline . . . . . . . . . . . . . . . 22Figure 17 Linearised torque trajectory against baseline . . . . . . . . . . . . . . 23Figure 18 Baseline and linearised torque region transition plot . . . . . . . . . . 23Figure 19 Region transition plot of combined implementation against baseline . 24Figure 20 Combined control comparison graph . . . . . . . . . . . . . . . . . . . 25Figure A1 FAST relationships with different modules . . . . . . . . . . . . . . . 29Figure A2 Detailed schematic of baseline controller . . . . . . . . . . . . . . . . 30Figure C1 Weibull Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33Figure D1 P controller metrics graph . . . . . . . . . . . . . . . . . . . . . . . . 36Figure D2 Individual blade pitch metrics graph . . . . . . . . . . . . . . . . . . . 37Figure D3 Time spent in transition for the trajectories against baseline . . . . . . 38Figure D4 Region 2 performance metrics for the trajectories against baseline . . 38Figure D5 Region 3 performance metrics for the trajectories against baseline . . 39Figure D6 Trajectories’ loads and motions against baseline . . . . . . . . . . . . 39Figure D7 Comparison of different trajectories on roll . . . . . . . . . . . . . . . 40Figure D8 Linearised torque metrics graph . . . . . . . . . . . . . . . . . . . . . 41Figure D9 Combined control metrics graph . . . . . . . . . . . . . . . . . . . . . 42Figure D10 Time series for the combined controller . . . . . . . . . . . . . . . . . 43Figure E1 Cp envelop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

List of Tables

Table 1 Wind speed range within each region . . . . . . . . . . . . . . . . . . 5Table 2 Properties of the NREL 5MW wind turbine . . . . . . . . . . . . . . . 13Table 3 Trajectories characteristics . . . . . . . . . . . . . . . . . . . . . . . . . 20Table B1 Wind speed bins and the parameters for each DLC . . . . . . . . . . . 31Table C1 Weibull scaling values . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

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Acknowledgements

I would like to thank my partner Nick Farquhar for putting up with me and helping methroughout this project. He has been an integral part of the team and progress would havebeen hard without him. I would also like to extend my thanks to Dr Hazim Namik for hisguidance, advice and patience in helping us along with this project.

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Glossary of Terms

Damage equivalentload

The same amount of damage that would be imparted if theloading had constant amplitude at some frequency compared tothe more stochastic loadings.

Integral wind-up The situation where a proportional integral derivative controllercan accumulate a large error term due to a large change inregulation set point causing overshoot past regulation point.

Linear state-spacematrix

A set of first-order differential equations that describes thestates and the outputs of the model.

States Variables that describe the characteristics of the system whichcan completely define what the system is doing at any point intime.

Abbreviations

BP Blade pitch

DEL Damage equivalent load

DLC Design load case

DOF Degree of freedom

EEA European Environment Agency

FAST Fatigue, aerodynamic, structural, turbulence

FSFB Full-state feedback

GSPI Gain schedule proportional integral

HAWT Horizontal axis wind turbine

HSS High speed shaft

IEC International Electrotechnical Commission

LIDAR Light detection and ranging

LQR Linear quadratic regulator

LSS Low speed shaft

LTI Linear time invariant

MBC Multi-blade coordinate transformation

MIMO Multiple-input multiple-output

MPC Model predictive control or controller

NREL National Renewable Energy Laboratory

P Proportional

PI Proportional integral

SISO Single-input single-output

SS Side-side

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VAWT Vertical axis wind turbine

VPPC Variable power pitch controller

VSVP Variable speed, variable pitch

VSWT Variable speed wind turbine

Nomenclature

Symbols

A Turbine state matrix –

B Turbine actuators gain matrix –

C Turbine model output matrix –

D Controlled inputs in relation to measurments matrix –

e Error at some time value –

ID Inertia of the drivetrain kg•m2

c Scaling parameter for Weibull distribution –

k Shape factor for Weibull distribution –

NGear Gear ratio from high-speed to low-speed –

NR Non-rotating frame –

∂P∂θ

Sensitivity of the aerodynamic power to blade pitch angle W/rad

Prated Rated generator power W

Q Weighting matrix –

Q′ Augmented weighting matrix –

si Weibull scaling factor –

t Time s

Tgen Generator torque Nm

uNR Input vector in the non-rotating frame –

U Mean wind speed over 10 minutes m/s

xNR States vector in the non-rotating frame –

yNR

Meaurements vector in the non-rotating frame –

Greek Symbols

ηgen Generator efficiency –

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Ω0 Rated generator speed rad/s

Ωgen Generator rotational speed rad/s

ωn Natural frequency of the response rad/s

ωpitch Platform pitching velocity deg/s

ωr Set point generator speed rpm

ψ Azimuth angle degree

θ Collective blade pitch angle degree

θ1 Blade one angle degree

θ2 Blade two angle degree

θ3 Blade three angle degree

θcc Cosine-cyclic rotating input degree

θc Collective rotating input degree

θpitch Platform pitch angle degree

θsc Sine-cyclic rotating input degree

ζ Damping ratio –

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1. Introduction

Renewable energy has become increasingly sought after as fossil fuel energy is harmful tothe environment with a limited supply. This has led to the proliferation of wind energycapture in recent years with offshore wind turbines being an area of research. This sectionwill give a brief overview of wind energy, wind turbines and control of wind turbines. Theproblem area will be introduced and the project objective and scope will be defined.

1.1 Wind Energy Overview

Wind energy is a vast and inexhaustible source of energy. Renewable energy production,in general, has grown with sources such as wind, geothermal, solar, and other sources(excluding hydro) up 1% in February 2014 compared to the previous year [1]. This wasreconciled with a fall of 1% from energy generation from fossil fuels. There has beenannual growth of renewable energy sources, and wind energy has been one of the majorcontributors for this [1, 2]. This has led to the wind energy industry becoming morecompetitive as companies and governments seek to expand this technology in a bid todiversify their mix of energy production. This diversification leads to environmental andeconomical benefits which is something that traditional fossil fuel energy generation cannotmeet [2].

By the end of 2012, the global wind power capacity was 282.5 GW [2] which was agrowth of 19% from the previous year. Figure 1 shows the rapid growth of the totalinstalled wind capacity of the world [2]. The Asian market was the largest of wind energyfor the fifth consecutive year with China as the main contributor followed by India. Chinahad seen tremendous growth since 2009 when it had a capacity of 25.8 GW to its levelnow of 75.3 GW. India had also seen growth, where wind energy was 8% of their totalelectricity generation in 2012. However, the country with the largest proportion of windenergy consumption was Denmark with more than 30% of electricity requirements coveredby wind energy at the end of 2012 [2].

0

50000

100000

150000

200000

250000

300000

1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012

To

tal

inst

alle

d (

MW

)

Year

Figure 1 Combined global wind energy capacity from 1996-2012 (adapted from [2])

Looking forward, many countries have placed targets on wind energy capture. For example,Mexico had placed a target that wind energy is to produce 15% of total power requirementsby 2020. Forecasts have shown that the average growth rate was expected to be 13.7%from 2012 to 2017 which was well below the previous year’s growth rates of 22%. Policiesand infrastructure are the major hurdles to overcome to drive the industry towards a highgrowth rate [2].

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1.1.1 Offshore Wind Energy

The first offshore wind farm was built in Vindeby, Denmark, in 1991 and has a 4.95 MWcapacity [2, 3]. By the end of 2012, global installed offshore wind energy capacity was5.415 GW making it 2% of the combined installed wind energy capacity. Over 90% ofthe current offshore wind energy capacity is installed within the northern Europe coastalarea (Baltic, North, and Irish Seas, and the English Channel). The other 10% is mainlymade up within the east coast of China, where it is used as demonstration sites. BothEurope and China have placed targets from offshore sites to produce a percentage of totalenergy requirements by 2020 [4]. Japan and South Korea also have plans to expand ontheir offshore farms to meet targets set by their governments towards sustainable energygeneration levels. The United States have just recently deployed a prototype of a floatingwind turbine in the waters of the Penobscot River in Maine where it will be towed out tosea for testing [5].

There is significant potential for energy to be captured offshore and the European Envir-onment Agency (EEA) has estimated that the potential energy is capable of meeting theenergy demand of Europe seven times over [6].

1.2 Wind Turbines Overview

Wind turbines can either be a vertical axis wind turbine (VAWT) or a horizontal axis windturbine (HAWT). We will be focusing on the HAWT variants which are the traditionalland-based wind turbines and offshore wind turbines. Land based wind turbines occupylarge sections of area which could otherwise have been used for agriculture, housing, ortownship developments. For example, the Roscoe wind turbine farm in Texas, United Stateshas 627 wind turbines spread over an area of 100,000 acres. These wind farms are typicallysituated far from large cities which places greater demand on efficient and effective powertransmission lines. This is a major barrier to the development of wind energy capture [7].Furthermore, land based wind turbines may be considered unsightly and produce noise thatis significant enough to be a nuisance for some. Professor William E. Heronemus saw theneed to alleviate these concerns and proposed that large offshore floating wind farms beused in 1972. It was only until the 1990s that the offshore wind turbine industry was setup [8]. This establishment has led to much research in the area.

Offshore wind turbines can be either fixed bottom, if placed in shallow waters (less than50 m) or floating. There are several advantages of placing wind turbines offshore and theseare listed below [4, 7, 9, 10]:

• Wind energy found offshore is generally much greater, more stable with less turbu-lence and shear, allowing for greater energy capture from fewer turbines.

• The distance to major cities, usually situated along coastal areas, is not as great thusreducing the need for long transmission lines.

• Visual impact is avoided if placed sufficiently far away (L =√

2HR, where L is thedistance from shore to turbine to be invisible, H is the hub height plus the radius ofa blade, and R is the radius of the earth). Auditory impact is also avoided.

• The size of an offshore wind turbine farm is not restricted (for example, no nearbyinfrastructure to limit size).

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• Land that would have been used for wind turbine farms can now be used for otherinfrastructure.

• The offshore wind turbine can be expected to recover its energy cost used for theinitial installation, manufacture, transportation, maintenance and operation, and de-commissioning in three months.

X

Y

Z

Wind

Figure 2 Platform DOFs (modi-fied from [9])

There will be, however, disadvantages associated with off-shore wind turbines and these include [7, 9]:

• Greater initial capital investment due to the addedobstacles faced with placing a wind turbine offshore.

• Increased downtime and cost of maintenance of windturbines due to it being less accessible.

• Increased complexity of design as there are extra con-siderations to be made, such as loading from wavesand platform movements for floating turbines.

1.2.1 Floating Offshore Wind Turbines

The first successful full-scale test of a floating wind turbinewas the Hywind project which was installed in 200 m deepwater on the south-western coast of Norway in 2009 [5].This was a 2.3 MW turbine, produced by Siemens, placedon a spar buoy platform. The configuration of the platformwill be discussed below. The successful test of this turbinehas led to further full scale testing to better understand and advance the technology.

Because of the fact that a floating wind turbine is no longer rigidly fixed upon a foundation,there are an additional six degrees of freedom (DOFs) to consider; three linear, and threerotational. The linear DOFs are surge, sway, and heave along the X, Y, Z axis respectively.Roll, pitch, and yaw applied along the X, Y, Z axis respectively, make up the final three.Figure 2 illustrates the additional DOFs. The motion of the waves on the platform causesadditional challenges to the design of a wind turbine and must be accounted for whendetermining a solution.

There are many possible configurations for offshore wind turbines, one of which hasalready been stated: the spar buoy platform. This configuration is one of four main typesderived from the oil and gas industry [8]. Figure 3 highlights the different designs. Eachplatform’s name relates to how the platform is moored and stabilised. The spar-buoy typeis characterized by a large ballast which is usually constructed from steel or concrete andfilled with water. The ballast lowers the centre of mass (CoM) well below its centre ofbuoyancy (CoB). This design inherently makes the turbine difficult to capsize. It is usuallymoored using taut or catenary lines made from chains, steel cables or synthetic fibres. Thistype must be assembled offshore. The tension leg platform (TLP) consists of a submergedplatform which uses tensioned tethers, achieved from the buoyancy of the platform, toprovide stability. This means that the TLP has less dynamic response to incident wavescompared to the other types. The barge type platform employs a large floating structureand is moored by taut or catenary lines. Stability is achieved through the distributed

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buoyancy where the water-plane area provides a righting moment. This design is moresusceptible to the waves’ motions [7, 8]. The semi-submersible type is constructed fromthree columns which are held together with tubular structures. The columns have ballastsin them and stability is achieved through the water-plane area. Mooring is provided usingtaut or catenary lines [8].

Barge TLP Spar-Buoy

Moo

ring

lin

es n

ot to

sca

le

(a)

(b) (c)

Figure 3 Sub-Figure a) shows the three main types [9] and sub-figures b) and c) show the semi-submersibletype [8]

1.3 Wind Turbine Control Overview

A HAWT can be classified as either a fixed-speed or variable-speed wind turbine (VSWT).This project will focus on the control systems of the latter because VSWT can be usedin a range of wind conditions whereas the fixed-speed is only efficient at a single windspeed [11]. The control can be split into two categories. The first is supervisory controlwhich is primarily concerned with the start-up and shut-down of a wind turbine. Thesecond is closed-loop control which is concerned with operational parameters when thewind turbine is generating power [9]. A typical VSWT has a torque controller and bladepitch (BP) controller to regulate power capture. To better determine the control strategiesfor closed-loop control, wind turbines have three distinct regions of operation [7, 9, 12]shown in Figure 4:

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Figure 4 Ideal power capture curve show-ing the regions

Region 1 In this region, the wind speed is below awind speed called the cut-in wind speed. Nopower is extracted from the wind. This re-gion accelerates the rotor to start up the windturbine.

Region 2 This region is concerned with optimisingpower capture where it operates between thecut-in and the rated wind speed. The BP isheld constant and the torque controller is usedto maximise power capture.

Region 3 Here, the wind speed is above the designor rated wind speed. Power capture is restricted to protect components from damage.The BP can vary to maintain constant rotor speed, while the generator torque canvary inversely to the generator speed to maintain constant power. Above a certainwind speed, the cut-off wind speed, the turbine will go into shut-down.

There exists a region called region 2.5 which is a transition from region 2 to region 3.This region is needed due to limitations on tip speed to meet structural vibration and noiseconstraints, resulting in regions 2 and 3 not intersecting at the rated speed. Both the BPangle and torque varies here [7, 12, 13]. This region presents some problems in obtainingsmooth switching between the two main regions while maintaining effective power captureas the two controllers clash with each other. Change in control authority causes problemswhen one controller is saturated while the other is operating [14]. Rapid actuations by thecontrollers causes additional loads on the turbine which can reduce the useful life of theturbine [13, 15]. Platform motion further exacerbates the problem as this causes the rotorspeed to vary leading to poorer power regulation [16]. The wind speeds in each region isshown in Table 1 and these are obtained from [7].

Table 1 Wind speed range within each region

Region Wind Speed Range (m/s)

1 0 ≤ V < 32 3 ≤ V < 10.2

2.5 10.2 ≤ V < 11.43 11.4 ≤ V < 25

Shutdown V ≥ 25

The controller can vary in complexitybased on its design. The controller caneither be single-input single-output (SISO)or multiple-input multiple-output (MIMO)[7, 9, 17]. The SISO controller takes ina single input, such as generator speed,and calculates a single signal that is passedthrough to an actuator, or the same signalto multiple actuators. A MIMO controllertakes in multiple inputs, such as generator speed and a structural load measurement, andsends different signals to their respective actuators to regulate these. The advantage ofusing MIMO is that it can exhibit an improvement in speed regulation and load reductionover a SISO controller. However, it does not work well in region 2.5 where it can accu-mulate a large error signal thus causing excess overshoot which is undesirable as it leadsto poor controllability [17]. This is referred to as integral wind-up and a SISO controllerhas greater controllability over this [17]. The blades can either be controlled collectively(SISO) or individually (MIMO), with individual BP control being more complex. Further

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complications arise with coupling between controller inputs and outputs where the outputsof each controller can affect structural loads, weather adversely or favourably, even if it isnot the design goal for that controller [17].

1.4 Project Goals and Scope

The project goal is to design and test, or implement existing transition control strategies toinvestigate its effects on power capture and structural loads. The objectives will then be toimprove region transition while reducing loads and improving power capture. Some areasthat are outside the scope of the project are defined below:

• Wind speeds well above and below rated will not be considered. We are onlyinterested in wind speeds around rated, and therefore the transition region.

• Analysis will be limited to the barge platform.

• Region transition is defined as the time spent in switching between regions, whereswitching occurs when the controller spends less than 15 secs within a region.

• No extreme or ultimate loads investigation will be conducted. This project will focuson fatigue loads during normal operation where the controllers are in effect.

• No changes to platform or turbine such as optimisation of design or adding additionalcomponents.

• We will not consider yaw control as this has little to no impact on power capture [9].

• The project will be purely simulation based as having access to a model to test isnot feasible.

2. Floating Wind Turbine Control Overview

Few research has been done into transition controllers and its effect on power capture andstructural loads. Much of the past research has been centred around the above-rated windregion. This section will give an overview of controllers that are designed, or could beadapted, for transition.

2.1 Power Curve Tracking

Tracking the power curve more efficiently is one way to improve power capture and lead tosmooth transitions [11]. This curve is the locus of operating points that maximises powercapture. The coefficient of power (Cp), which is a function of BP angle and tip speedratio (TSR), is used to derive this curve. Once the curve is found, the regulation policiesfor rotor speed, BP and rotor torque can be found [18]. Normally, the optimum Cp curveis not tracked because in turbulent wind the rotor reaches a speed which causes the rotorblades to stall leading to lower power conversion. This point where the turbine stalls iscalled the stall front. Thus to avoid reaching the stall front, a lower, less optimal, Cp curveis tracked. [11]. This is especially true of large wind turbines which have larger rotationalinertia. Therefore it is usually better to track a Cp curve slightly below (around 5 %) theCp max curve [11, 19].

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C C

B

B A

Rated power curveCp max locus

Rated

RatedGenerator speed (rad/s)

Gen

erat

or to

rqu

e (N

m)

Figure 5 Simple representation of the power curve (adapted from [11])

When the controllers are switching between regions, it is found that often there are largedips in torque and thus power generation. Around rated wind speeds, there are many regiontransitions occurring which also leads to poorer power capture as the controller is oftenswitching between logic. Bianchi et al. [11] offers a solution to this by altering the powercurve which leads to smoother transition at the cost of power capture as shown in Figure 5by the AB’C’C trajectory. In region 2, the control tracks on the optimal Cp curve untilpoint B’ where the torque ramps up to rated torque. This strategy tries to clearly definethe regions where each controller acts. From A to C’, the torque controller acts withoutinterference from the BP controller, which is dominant around point C [11].

Bossanyi [19] proposes that the path ABC be followed. This allows for better trackingof the Cp curve and therefore better power extraction. To do this, he implements aproportional integral (PI) torque controller and tested it on a 5 MW fixed offshore windturbine. It is hard to say if there are improvements as there are no comparisons to areference turbine. [20].

Bianchi et al. [11] and Bossanyi [19] both present a similar method to improve powercapture and load reduction. At the rated wind speed, the BP begins to pitch slowly as windspeed increases, while torque continues to increase. This means that the rated power willbe attained at a higher wind speed, effectively stretching out the transition region. Bossanyisuggests that the torque controller and the BP controller be coupled with inclusion of atorque error term into the BP control logic. At wind speeds far above and below rated, thecontrollers act independently, but close to rated, the two controllers will work in tandem.Bossanyi also states that it would be necessary to “ratchet” the torque to prevent dips atabove rated wind speeds as the BP are not at their optimal angle. The path that thisstrategy follows is given by ABC in Figure 5.

2.2 Platform Motion Control

Work on reducing platform motion in a bid to improve power capture and reduce loadshave been conducted in region 3. In this region when the platform is pitching towardsthe wind, the apparent wind seen by the turbine increase and will induce the rotor bladesto spin faster. Therefore, to maintain a constant rotor speed, the pitch controller willactuate the blades to reduce the lift generation. This has the effect of reducing rotor thrust,which acts to provide a restoring moment on the wind turbine, and thus exacerbates themotion towards the wind. The same ideas can be used when pitching backwards where

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the apparent wind decreases. This removes some of the restoring moment and worsens thepitching. Lackner [16] proposes a simple solution to this by altering the set point of theBP controller. This approach is referred to as the variable power collective pitch control(VPPC) and is given below:

ωr = 1173.7(1 + kωpitch) (1)

where ωr is the set point generator speed (rpm), k is a constant, and ωpitch is the pitchingvelocity of the platform. When the platform is pitching forwards, the set point increases sothat the rotor will continue to extract power and provide thrust and so provide a restoringmoment to counter the pitching. Results from simulation with the National RenewableEnergy Laboratory (NREL) 5 MW floating wind turbine show that there are improvements.For a k of -0.025 there were, on average, a 3-8% increase in speed and power error,and a 15% reduction in the root mean square (RMS) platform pitch angle and RMS pitchrate [16].

2.3 Wind Preview

Most of the literature pertaining to the preview of wind uses light detection and ranging(LIDAR) as the method. LIDAR looks ahead and measures the wind to allow the con-trol system to generate a smooth and optimised trajectory to track. However, there aremeasurement inaccuracies when LIDAR is used in turbulent wind. This requires the useof a low-pass filter to filter the measurements. Aho et al. [13] used simulated LIDARmeasurements to design a trajectory tracking controller (TTC) and ran simulations usingthe NREL 5 MW turbine with five different turbulent wind profiles for 600 seconds each.The LIDAR was centred at the hub and used three beams to sample the wind. It wasfocused at 75% of the blade length at 107 m upwind of the turbine. It was found thatthe TTC reduced loads and led to smoother transitions between regions compared to thebaseline, except for the low speed shaft DEL [13]. Figure 6 shows the difference in thetrajectory between the baseline and the TTC.

Rated

Rated

Rated power

Cp max locus

Rotor speed (rpm)

Gen

erat

or to

rqu

e (N

m)

Baseline

TTC

Figure 6 Trajectory comparison of TTC and baseline (adapted from [13])

8

2.4 Model Predictive Control

A model predictive controller (MPC) was originally designed for systems with slow dy-namics, such as the process industry, because of on-the-fly calculations [14]. This naturallyrequires heavy use of computations. Research into MPC has become more common inthe last five years as technology has allowed for much faster calculations making it morewidely accepted [14, 21, 22].

The core of a MPC is an objective function defining the control objectives and a setof equations which describes the dynamics of the system. This, therefore, becomes anoptimisation problem. Some of the strengths of MPC is its ability to incorporate systemconstraints and disturbance predictions into the problem. MPC uses past system states,such as the wind speed, to predict the future state at a discrete time step and thus setsthe objective function. Weights are used to determine relative importance of each controlgoal and varies depending on the operation region. For example in region 3 wind speeds,the power output is to be kept constant and so the weighting associated with maintainingconstant power is high [14].

Figure 7 Diagram of the 5-massmodel (3 lump masses for the blades,and 2 for the drive train) [14]

Lindeberg et al. [14] formulated a linear MPC model,by using a series of linear controllers to model the non-linear behaviour of a wind turbine, and used a 5-masswind turbine model, seen in Figure 7, on a floating plat-form. This proof-of-concept model was called “bumplesstransfer” where the switching of controllers is not suddenbut rather a gradual change. Using weightings obtainedfrom a trial and error basis, the power output was foundto be smoother than the case where the weightings led tosudden control change. Spencer [22] investigated currentwind versus predicted wind, using wind preview, and itseffect, and implemented MPC on the NREL 5 MW tur-bine. He isolated simulations within region 2 and 3. Inregion 3, there was significant load reduction, when windpreview was used, in extreme winds while less reductionwas seen with more normal turbulent winds. In region2, Spencer implemented two controllers, one to maximisepower capture and the other to minimise fatigue loads. He found that there was only im-provement in power capture with the former controller in more extreme winds. Laks [21]used MPC in conjunction with LIDAR and found that it was effective in alleviating loads inturbulent wind conditions using a three-bladed Controls Advance Research Turbine (CART)at the NREL centre.

3. Simulation and Analysis Tools

To aid in the analysis and modelling of a floating offshore wind turbine, there are twotools that will be used together for the simulations. Fatigue, Aerodynamics, Structures, andTurbulence (FAST) which is a code that can be used to to simulate the aerodynamics andstructural dynamics of a HAWT given a wind profile. It was developed by the NREL andcertified by Germanischer Lloyd WindEnergie GmbH. This is available free of charge onthe NREL website [23]. This is coupled with MATLABr’s Simulinkr (here on referred to

9

as Simulink) which provides the interface for designing the control systems. FAST modelsthe wind turbine as both a rigid and flexible model with full control over the DOF. Fora three-bladed HAWT, FAST models this with 24 DOFs. These are six DOFs related totranslational motion (surge, sway, and heave), and rotational motion (roll, pitch, and yaw).Four DOFs relating to the motion of the tower; two for the fore-aft modes and two forthe side-to-side modes. One DOF for the yawing motion of the nacelle (the housing of theturbine components). A DOF for the azimuth angle of the generator, and a DOF for theinteraction of the rotor and generator in the drivetrain. The azimuth angle is the angle ofthe blade relative to 0 , which is the position of the blade at its vertical position with thetip pointing straight up. There are two flap-wise bending modes DOF and one DOF forthe edge-wise bending mode, for each blade. The flap-wise load is the load on the bladeas it moves perpendicularly out of plane, the plane being the vertical plane of the rotorface against the oncoming wind., and the edge-wise is in plane loading. The last two relateto the rotation of the hub and nacelle [24]. In this project, the nacelle and hub will beheld as rigid bodies and yawing motion ignored giving a total of 21 DOF. The FAST codeutilises the AeroDyn module which is an aerodynamics analysis routine for HAWT, andHydroDyn, a module required to model the dynamics of a floating platform [9, 23]. Thismakes FAST a robust simulator. Figure A1 in Appendix A shows the relationship betweenthe modules.

Limitations of the FAST model

Although FAST has been certified, the HydroDyn code has yet to be certified. However,the Offshore Code Comparison Collaboration (OC3) project has given indications that thecode developed is acceptable [9]. Therefore, the limitations of this tool should be noted.Listed below are some assumptions used in the code [9]:

• Small angles of platform motion (less than 20º).

• Tower is perpendicular to the platform and is modelled as a cantilever.

• Mooring lines have no bending stiffness

The wind turbine model (conceptual model) that will be used is based on componentsthat are publicly available. This wind turbine is referred to as the “NREL offshore 5-MWbaseline wind turbine” and will be coupled with a 40 x 40 x 10 m barge platform [25].From here on, this reference turbine will be known as the baseline. Table 2 lists someproperties of this turbine with full details found in [25]. Figure 8 shows a simplified versionof the controller model implemented within the baseline coupled with the FAST interface(called wind turbine in the figure) [9]. This model uses a gain scheduled proportionalintegral (GSPI) controller for the BP control and is an example of SISO where the soleobjective is to regulate the rotor speed. Note that the region selection input is not aparameter that is trying to be controlled. Because the BP controller acts throughout thewhole operation, the region selection input is required to inform the BP controller that itis in region 3 so that the signal will be passed into the wind turbine block to actuate theblades. A complete schematic of the model can be found in appendix A. The project willbased off of this baseline control model. As alternations to the control logic are made,simulation results will be compared to the baseline to ascertain if improvements have beengained.

Once a satisfactory control strategy has been implemented, that appears to work for simplewinds, with waves and without waves, it will need to be verified that the logic does

10

smooth out transition while maintaining effective power capture with more realistic winds.TurbSim, which is also a free package from NREL, is a stochastic, full-field, turbulent-windsimulator, will be used to generate different wind profiles within the transition region forverification of the logic.

Torque

Controller

Blade Pitch

Controller

Region

Selection

Filtered generator speed

Generator

torque

Blade

pitch

Wind Turbine

Figure 8 Baseline controller Simulink model (adapted from [9])

3.1 The Baseline Controller

The baseline is a variable-speed, variable-pitch (VSVP) wind turbine with two basic controlsystems: a generator torque controller and a collective BP controller. It was designed byJonkman to alleviate platform motion [26]. The generator torque controller works mostlyindependently of the BP controller and its goal is to optimise power capture in the belowrated wind speed (region 2). The BP controller operates in the above rated wind speed(region 3) where it pitches to feather (pitching the leading edge to face the wind to reducelift generation) to regulate rotor speed and hence power capture. The filtered generator speedmeasurement is used as the sole feedback input for both the torque and BP controllers.The torque commanded varies depending on which region the wind turbine is operating in.Figure 9 shows the trajectory that the torque follows. Region 1 to 2 (region 1.5) follows alinear transition used to place a lower limit on the turbine’s operating speed range. Region2 follows a squared relationship of the generator speed, using a constant of proportionalityof 0.025576386 Nm/rpm2. There is another linear transition from region 2 to 3, and region3 follows an inversely proportional relationship to generator speed as given by equation 2where Tgen is the generator torque, Prated is the rated power, ηgen is the efficiency of thegenerator, and Ωgen is the generator speed. This is so that power generated is kept constant.

Tgen =PratedηgenΩgen

(2)

The GSPI for the BP control is given by [25, 26]:

θ(t) = Kpe(t) +Ki

tˆ

0

e(τ)dτ

where

e(t) = Ωgen − Ω0

11

Kp =2IDΩ0ζωn

NGear

(−∂P

∂θ

)Ki =

IDΩ0ω2n

NGear

(−∂P

∂θ

)and Ω0 is the rated rotor speed, Ngear is the gearbox ratio, ∂P

∂θis the sensitivity of the

aerodynamic power to the BP angle, ID is the inertia of the drivetrain, ζ is the dampingratio and ωn is the natural frequency of the response. Full derivations can be found in [25].

Figure 9 Baseline torque controller trajectory [7]

The generator speed is passed through a low-pass filter with a corner frequency of 0.25 Hz.This is one-quarter of the blade’s first edgewise natural frequency chosen to prevent destabil-ising of flexible modes [7, 27].

For this project the gain values used were proposed by Jonkman [25] and are Kp =0.01255121s, and Ki = 0.0003586059. These are referred to as the detuned gains andwere a result of improving the platform pitch response in region 3 [7]. Integral wind-upmeasures are also taken to prevent signal overshoot for the BP controller.

3.2 IEC Standards

The wind files generated will be based on Design Load Case (DLC) 1.2 in the IEC 61400-3standard which are used to analyse the fatigue load performance of an offshore wind turbineunder normal operating conditions [28]. This standard was developed by the InternationalElectrotechnical Commission (IEC) and is for a fixed offshore wind turbine. Currently,there are no standards for floating wind turbines therefore this standard is used.

Wind profiles generated will be between 8 m/s and 14 m/s in 1 m/s increments because thisis the region of interest in this project. The IEC standard requires that six different 600-second simulations, of the same mean wind speed, be run. This is achieved using turbulent

12

Table 2 Properties of the NREL 5MW wind turbine

Power Rating 5MWNumber of Blades 3Rotor, Hub Diameter 126m, 3mHub Height 90mCut-in, Rated, Cut-Out Wind Speed 3m/s, 11.4m/s, 25m/sCut-in, Rated Rotor Speed 6.9rpm, 12.1rpmRated Generator Torque 43,093NmGearbox Ratio 97:1Blade Operation Pitch to featherControls Variable speed, collective variable pitch

wind and irregular waves generated using different random seeds. These six simulations,or DLC, constitute a wind speed bin [29].

The standard for DLC 1.2 requires that there is full knowledge of probability distributionsfor wind speed, wave period and significant wave height. These are not fully known,however, and so DLC 1.1 conditions for expected significant wave heights is used for agiven wind speed range. DLC 1.2 also specifies that wind and wave conditions be co-directional and multi-directional. But because the barge platform is axisymmetric, the waveand wind considered will be from one direction only.

Wave conditions used are the same used by Jonkman [7] and Namik [9]. This referencesite is situated in the north-east of Scotland.

Appendix B shows the properties used to generate the stochastic wind conditions used foreach wind speed bin kindly provided by Dr. Hazim Namik.

3.3 Performance Metrics

Comparison of each DLC against the baseline will be made using performance metricsdesigned by Namik [9]. These metrics can be divided up into four basic categories:

• Region 3 performance metrics

– Region 3 time ratio

– Power (kW), torque (kNm), and speed (rpm) error

– Blade usage (pitch rate and max pitch rate (deg/s))

• Region 2 performance metrics

– Region 2 time ratio

– Power captured (kW) and efficiency

• Fatigue loads (kNm):

– Blade loads (flap-wise and edge-wise)

– Tower loads (fore-aft and side-side (SS))

– Low speed shaft (LSS)

13

• Platform motions (deg and deg/s):

– Roll and roll rate

– Pitch and pitch rate

– Yaw and yaw rate

Transition time is found from subtracting the region ratios from 1. Minimising this value isa goal of this project. Region 3 metrics and motions are calculated as a root mean square(RMS) value. The error is the deviation from the rated value. Reducing motions is desirableas they lead to lower loads on the tower. Fatigue loads are calculated as damage equivalentloads (DEL). This is used to calculate an equivalent load as the stochastic loading, using aperiodic loading of a calculated amplitude at a given frequency of 1 Hz [9].

The performance metrics are calculated for each simulation and then averaged within awind speed bin. The full set of bins are then averaged again using a weighting based onthe amount of time in a year that that wind speed will occur at a particular site. Thiswill give an overall average and a clearer view of performance comparisons against thebaseline as it is unrealistic to say that a location will experience equal amounts of timeat each wind speed. This weighted average will be done using a Weibull distributiondiscussed in Appendix C. Comparisons made between the proposed control implementationand the baseline will be based off of these weighted average values and are referred toas the overall or total. For the region 3, fatigue loads, and platform motions metrics,these weighted averages will be expressed as a normalised value against the baseline tofind a percentage change as results are bound by the assumptions and limitations of thesimulation tools. Comparing results on a relative sense will give a clearer meaning to thecontroller’s effect regardless of weather or not the simulation results are truly representativeof a physical wind turbine. However, in saying so, region 2 metrics will be comparedusing the absolute values because the region transition is already a percentage value andwill give a clearer understanding of any change.

4. Controller Implementation and Testing

An initial simulation of the baseline, with waves and without waves, using a ramp windfrom 9.5 m/s to 13 m/s is shown in Figure 10. It shows that the effect of waves on the regiondetection was pronounced with the waves causing a significant amount of switching betweenthe regions. This in turn affects the generator power capture by increasing the number ofpower dips. These dips are caused by the waves resulting in the wind turbine pitchingforwards or backwards thus changing the apparent wind seen by the wind turbine. A furtherexplanation can be found in subsection 2.2. It can also be seen that the controller does notoperate in region 2.5 for any significant amount of time compared to the baseline withoutwaves. This means that the torque controller is causing a large change in torque commandeach time there is a transition which causes large torque spikes or dips and thus affectingthe power capture. The difference in operating point can be seen in Figure 9. Simulationsusing turbulent wind profiles shows the same characteristics with region transition occurring17 % of overall time compared to 6.3 % without waves. This further emphasises the effectwaves have on region transition.

Thus, research into regulating the motions of the wind turbine, given wave disturbances,and changing the transition logic has been performed to analyse their effect on regiontransitions and power capture.

14

0 20 40 60 80 100 120 140 160 180 200

0

10

20

Win

d sp

eed

(m/s

)

&

Wav

e (m

)

0 20 40 60 80 100 120 140 160 180 2000

5000

Gen

erat

or p

ower

(kW

)

0 20 40 60 80 100 120 140 160 180 2001

2

3

Time (sec)

Reg

ion

Baseline with waves Baseline without waves

Figure 10 Baseline simulation with waves and without waves

Stol et al. [30] showed that individual blade pitching is effective in reducing tower side-sidefatigue loads by around 70 % compared to a reference turbine in above rated wind speeds.For comparison, collective pitch only reduced loads by 25 %. In region 2, collectivepitch reduced tower for-aft loads by 70 %. These results arise from field tests using aonshore CART rated at 600 kW. Therefore, these two control methods will be tested on anoffshore wind turbine to ascertain their effect on region transition, power capture, and loadmitigation. Blade pitch actuation will also be allowed in region 2 as well as 3 to allowmotion reduction regulation for a wider wind speed range.

4.1 Collective Pitch Proportional Control

A method to reduce the motions of the platform is the use of a positive feedback pro-portional (P) controller. This is a SISO controller which takes in the platform pitchingvelocity and applies a gain value to it. For example, if the platform is pitching forwards(negative velocity), the gain applied will give a signal into the summing junction to reducethe BP to provide a restoring thrust force. The output will then change the BP commandfrom the baseline resulting in an overall higher amount of blade usage. Figure 11 showsa simplified model which was based off of research performed by Lazaro et al. [17]. TheBP signal required within the region selection control is taken before the subtraction of thegain value to maintain the same region selection as the baseline so that only the effects ofthe gain value are tested.

Wind

Turbine

Torque

Controller

Blade Pitch

Controller

Region Selection

Filtered generator speed

Generator

torque

Blade

pitch

+

gainPitching velocity

++

Figure 11 Simplified P control implemented in Simulink

15

A series of gains were selected based on 5 % of the maximum Cp value found on theCp envelop. Derivation of the Cp curve is explained in Appendix E. The first gain valueis selected based on the intersection of this Cp value and the Cp envelop and two othervalues are selected relatively to this. This will give a broad view of how different gainsaffect the motions. These are 0.0175, 0.0349 and 0.0524 rads which translates to 1, 2, and3 degree of blade pitch actuation per deg/s of platform fore-aft motion.

4.1.1 Results and Discussion

In region 3, it was found from an initial analysis that the P controller is not effective inreducing motion. While the BP controller is trying to regulate rotor speed, the signal fromthe P controller cancels this and changes the rotor speed thus causing a different thrust onthe turbine. This, at times, results in no motion reduction occurring. This is evident inFigure 12 where only some of the peaks are reduced while a majority is at the same levelas the baseline. Reduction in motion occurs only when there are a high pitching velocity(seen as the peaks in the figure).

0 20 40 60 80 100 120 140 160 180 200−4

−2

0

2

4

6

Time (sec)

Pla

tform

pitc

hing

velo

city

(de

g/s)

Baseline P Controller

Figure 12 Platform pitch response at a turbulent mean wind speed of 14 m/s

The gain that produced the highest reductions was 0.0524 rads. As expected RMS pitchand RMS pitch rate reduced by 6-14 % and 12-27 % respectively. RMS roll and RMS rollrate decreased by 7-17 % and 9-20 % respectively. There was no significant change to yawas expected as no unsymmetrical loads are produced with collective pitching. As a resultof the reduced motion, the fore-aft DEL and SS DEL both reduced by 9-14 % and 5-11 %respectively. There was higher blade usage (as high as 97 % more). Consequently, theblade flap DEL increased, by around 2-8 %, as expected, as a higher amount of thrust isproduced to reduce the pitching motion of the wind turbine. The LSS DEL reduced by6 % for all gain values.

There was improvement using all the gains in region transition, again with the gain of0.0524 rads being the best performer. There were small improvements in all wind speedbins with overall time spent in transition varying from 16-14 %, for each respective gain,compared to 17 % using the baseline. A bar graph showing the performance metrics canbe found in Figure D1 in appendix D.

4.2 Individual Blade Pitch Control

Individual blade pitching causes an unsymmetrical loading on the blades in the rotor plane.This will induce a moment about the nacelle which causes a motion of the wind turbine. Toimplement this a negative feedback MIMO control that actuates each blade independentlyis used. Figure 13 shows a simplified model of the implementation in Simulink. It can be

16

Wind

Turbine

Torque

Controller

Blade Pitch

Controller

Region Selection

Filtered generator speed

Generator

torque

Blade

pitch

MIMO Motion

Reduction Controller

x

uΔθ ΔTgen

+_

+_

Figure 13 Individual blade pitch control diagram

seen that this controller is decoupled from the baseline which allows the MIMO to onlyregulate motion and thus region selection will be maintained by the baseline alone.

This controller requires the azimuth angle (ψ) to be known. However, because the systemis highly periodic, a coordinate transformation is required to transform the dynamics in therotating frame into a fixed frame of reference [9, 17, 31]. This is known as a multi-bladecoordinate transformation (MBC). The transformed system is not time-invariant. However,Stol et al. found that averaging the resultant state matrices does not result in loss ofinformation [30]. The result of the transformation and averaging is the linear time invariant(LTI) system given in equation 3 where the subscript refers to non-rotating frame, ∆ is aterm for perturbations, x are the states, u are the inputs, and y are the outputs. A,B,C,and D are averaged linear state-space matrices.

∆xNR = A∆xNR+ B∆uNR

∆yNR

= C∆xNR+ D∆uNR(3)

Individual blade pitching is then achieved when the new coordinates are transformed backinto a rotating frame of reference. The new coordinates are called collective (θc), cosine-cyclic (θcc), and sine-cyclic (θsc) which are then transformed to give the three commandedBP angles θ1, θ2, and θ3 as given in equation 4.

θ1θ2θ3

=

1 cos(ψ) sin(ψ)1 cos(ψ + 2π/3) sin(ψ + 2π/3)1 cos(ψ + 4π/3) sin(ψ + 4π/3)

θcθccθsc

(4)

The MIMO control is designed as a full-state feedback (FSFB) controller that utiliseslinear quadratic regulation (LQR). A characteristic quadratic cost function (J) is requiredto describe the relationship between state regulation objectives and control actuations. Thesolution which fulfils the FSFB control law is the LQR controller. FSFB works by takingin a vector of system states and passing it through a gain matrix. These are then passedas inputs into the systems.

The states used were produced using FAST’s linearisation function. Different states requiredcan be selected based on which DOF are active. FAST linearised the system until asteady state was achieved. The periodic equation was then calculated and the linearisationand operating points were found [24]. This work used eight states which are the threedisplacements and velocities of the roll, pitch, and yaw as shown in equation 5. Theazimuth angle and generator speed was required in order to complete linearisation.

17

x =[θroll θpitch θyaw ψ ωroll ωpitch ωyaw Ωgen

]T (5)

Because we are only interested in regulating the motions of the platform, the output vector(equation 6) is used in cost function given in equation 7. Q and R are weighting matricesand depends on the control objectives. The augmented matrix Q′NR used in the cost functionis related to QNR shown in equation 8. This shows the interaction between the C matrix,the output signals, and the states. LQR tools in MATLABr was used to calculate the gainsmatrix required to minimise the cost function and ensure system stability. Gains for ψ andΩgen are set to zero so that there will not be conflicting regulation against the baseline.

y =[θroll θpitch θyaw ωroll ωpitch ωyaw

]T (6)

J =

∞

0

(yT

NRQ′NRyNR

+ uTNRRNRuNR

)dt (7)

QNR = CTNRQ

′NRCNR (8)

4.2.1 Linearisation and Weighting

From an initial analysis of individual blade pitching using a single linearisation point at14 m/s, it became apparent that operations in region 2 was not effective because of thedifferent control goals in each region. Therefore two linearisation points are used, onepoint at 8 m/s and the other at 14 m/s. This is based off of work done by Stol et al. [32],who linearised at 8 and 18 m/s. 14 m/s was chosen as the linearisation point for this workas it was closer to region transition and it was reasoned that the closer operating pointwould improve performance. Stol et al. used the rotor speed to determine which operatingpoint to use while this work will use the region selection, which is a function of rotorspeed.

The tuning of the controller was performed individually for each operating point. Thegoal of the process was to reduce fluctuations in the rotor speed thus improving the signalrequired for region selection. Tower fore-aft pitching velocity had a higher weight than theroll and yaw velocities to make the reduction of the pitching velocity the objective. Theweights on the displacements of the wind turbine were required to be significantly lowerthan the velocity values because displacement regulation requires a significant amount ofactuation. Thus, using higher weights would destabilise the system. For the region 2operating point, the input regulation matrix placed a higher weight on the torque value andcollective pitch to reduce torque utilisation and thus reduce disturbances to the baselinetorque controller. Region 3 had equal weights allowing torque to be used more readily.

4.2.2 Results and Discussion

Simulation results showed that there was motion reduction but this resulted in higher loadson the tower and blades. There was a significant reduction in RMS yaw and RMS yawrate at 42 % and 53 % respectively. This is an improvement over using just a P controllerin subsection 4.1 because the MIMO is active in regulating yaw while the P controller’ssole purpose was to try reduce pitch. RMS roll decreased by 17 % and RMS roll ratedecreased by 10 %. The RMS pitch saw the smallest decrease at 9 % while the RMS pitch

18

rate decreased by 17 %. This was unexpected as the weighting placed on platform pitchingrate prioritised its regulation, and currently, the reason for this is unknown. Comparedto the P controller, the reductions in roll and pitch were not as significant. This may beattributed to the fact that the MIMO also has to regulate yaw which affects how the windturbine moves in the pitch and roll direction.

There were both increases and decreases in loads with the tower SS DEL seeing a significantincrease of 32 %. There was a higher max pitch rate (blade actuation) weighted averagemeaning that there are a higher number of actuations at lower wind speeds. The increase inmax pitch rate coincides with a much higher RMS pitch rate which means that there was asignificantly higher amount of blade movements. This is expected because individual bladepitching requires higher blade actuation. Because of this, the blade flap DEL increased by17 % as there was a greater amount of rotor thrust produced to mitigate motion. Towerfore-aft DEL and LSS DEL both saw a reduction of 9 % and 3 % respectively.

Individual blade pitching shows improvement in power capture with a reduction of 15 % inRMS power error as a result of less power dips. Although the controller spent an overallhigher amount of time in region 2 (63 % of total time compared to 61 %), power captureddecreased from 257.55 kWh to 246.55 kWh. This is believed to be because the MIMOis causing a small reduction in torque command and thus a reduction in power capture.The efficiency was similar at around 79 %. Transition time reduced marginally for eachwind speed bin with an overall transition time reducing from 17 % of total time to 15 %.This small change in region transition may be due to the fact that there was only a smallamount of platform reduction. A bar graph of the metrics can be found in Figure D2 inAppendix D.

Compared against the P controller, individual blade pitching allows greater regulation ofpower. However it experiences lower load reductions in fore-aft and LSS, and an increasein SS loading. Motions in roll and pitch are not attenuated as well. However, theremay be improvements in these areas if greater tuning was done or a gain schedule wasimplemented [33]. Transition time was similar between the two suggesting that loads andpower regulation sees the greater affect depending on the type of controller.

4.3 Alternative Torque Trajectories

Changing the trajectory that the torque follows as the generator speed varies is an idea thatwas suggested by Bianchi [11] as explained in subsection 2.1. The generalised shape ofthis new trajectory is given in Figure 5 by AB’C’C. Five different trajectories were made,based off of the generalised shape, to analyse its effect on region transition. Each hadvarying slopes and range where the torque is held at the rated value. Figure 14 shows anexample of the curve overlaid on top of the baseline for comparison and Table 3 showsthe characteristics of each of the five curves. The start of region 2 torque command is thesame as that commanded from the baseline. When it reaches a specified generator speed,the torque is then commanded linearly up to rated torque which is the beginning of region2.5. As shown in Figure 14, region 2.5 is now over a larger range. By extending region2.5 and holding it at constant torque, transition between region 2.5 and 3 will not actuatethe torque as quickly compared to the baseline (the baseline changes torque dramaticallyaround rated generator speed) and so there will be less torque dips and smoother transitionleading to improved power generation. This is evident in Figure D7 in Appendix D.

19

y = 175.17x - 149596

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

50000

600 700 800 900 1000 1100 1200 1300

Gen

erat

or t

orqu

e (N

m)

Generator speed (rpm)

Baseline curve Baseline Region 2 and 2.5Rated Gen speed and torque New Trajectory

New region 2 New 2.5

Baseline 2.5

Figure 14 Trajectory 1 curve against baseline

Table 3 Trajectories characteristics

Trajectory Intersect with BaselineCurve (rpm)

Intersect with Region 2(rpm)

Slope Equation

1 1000 1100 Tgen = 175.17Ωgen − 149596

2 950 1100 Tgen = 133.41Ωgen − 103653

3 1050 1100 Tgen = 297.91Ωgen − 284611

4 1071.7 1150 Tgen = 175.20Ωgen − 158389

5 930.399 1050 Tgen = 175.20Ωgen − 140862

4.3.1 Results and Discussion

Using the different torque trajectories showed that there was vastly improved region trans-ition. There is a noticeable reduction in large region transition compared to the baseline asshown in Figure 16 which leads to fewer torque dips and thus improved power regulation.All five trajectories showed that region transition time was, at most, 11 % of total time orless compared to the baseline of 17 %. Figure 16 shows average percentage of time spentwithin region 2, 3, or in transition for trajectory 2. It can be seen that there was markedimprovement in region transition up to 13 m/s, with smaller improvement thereafter. Asshown, the transition is a lot smoother around rated wind speed of 11.4 m/s, resulting inan overall time spent in transition of 9 %. Overall reduction is shown by the reduction ofthe grey area in Figure 16. Trajectory 5 showed the most improvement in overall regiontransition, spending only 7 % of total time switching. Trajectory 4 was the worst performerat 11 %. The reduced transition time translates to an increase in time spent in region 2and thus power captured. Trajectory 4 had the lowest reduction in region transition andso had the least increase in power captured, whereas trajectory 5 saw the largest increase(321.22 kWh compared to baseline of 239.12 kWh).

For all trajectories there was improvement in the region 3 metrics as time spent in thisregion increased also. On average, there was around 5 % improvement in RMS power

20

error, 3 % improvement in RMS speed error and 4 % improvement in RMS torque error.Trajectory 4 was again the worst performer of the trajectories with less reductions. For theRMS power error there was only a 1 % reduction while RMS speed and RMS torque errorsaw no change from the baseline. In general, there were less actuations of the blades withup to 21 % reduction shown by trajectory 5. Trajectory 4 showed the least reduction with4 %.

For the loads only the blade flap DEL, tower fore-aft, and tower SS saw some improve-ments. There was an increase in loads of 3 % for the LSS using trajectory 3, and 1 %using trajectory 5. Trajectory 2 saw a 3 % decrease and the other two saw a 1 % decrease.There was an increase in RMS pitch of 1 % for all trajectories while there was a decreaseof 1-2 % in yaw for trajectories 2, 3 and 5. RMS roll saw the largest increase with thehighest at 12 % for trajectory 5. Trajectory 4 was the lowest with a 3 % increase. Thisincrease is due to a higher generator torque usage, where the torque causes a moment aboutthe nacelle. Bar graphs of metric comparisons can be found in Figures D3, D4, D5, D6 inAppendix D as well as a figure showing how the increase in generator torque affects roll(Figure D7).

Trajectory 2 is deemed to be the best solution of the five. This is because it had thehighest performance improvements without sacrificing any increase in loads. However, ifa slight increase in a load (1 % increase in LSS DEL) was permissible then trajectory 5would be the best. It had the least time spent in transition (7 % time spent instead of9 % of trajectory 2) with similar load reductions relative to trajectory 2 with variations of1 % between the two. Trajectory 5 saw a small increase in captured energy in region 2(321.22 kWh compared to 313.64 kWh) as a result of the decreased time spent in transition.

From these results, a longer region 2.5 aids in lowering region transition, blade usage andimproving power captured. However using a larger region 2.5 causes less reductions inloads and motions. The effect of the slope, however, is not as easy to determine.

0 20 40 60 80 100 120 140 160 180 2000

5000

Gen

erat

or p

ower

(kW

)

Baseline Trajectory 2

0 20 40 60 80 100 120 140 160 180 2000

50

Gen

erat

or to

rque

(kN

m)

0 20 40 60 80 100 120 140 160 180 2002

2.5

3

Time (sec)

Reg

ion

Figure 15 Trajectory 2 time series plot in turbulent wind with mean speed of 11 m/s

4.4 Linearised Torque Trajectory

FAST has the capability to linearise about a predetermined number of operating pointsto find steady state operating values. Therefore a series of linearisation were performed

21

0%

20%

40%

60%

80%

100%

8 9 10 11 12 13 14

Aver

age

% o

f ti

me

Wind Speed (m/s)

Region Transition

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Region

Transition

Region 3

Region 2

(b) Trajectory 2

Figure 16 Trajectory 2 transition plot against baseline

using constant wind profiles from 5-11 m/s to find the generator torque value that the windturbine ideally operates at during steady state. This was done to see if using the steady statevalues to generator a torque curve would improve performance in turbulent winds. ThreeDOF were used; the generator DOF, surge, and fore-aft pitching. The last two platformDOF were used to simulate the floating platform and to find the steady state position.This has an effect on the wind speed seen by the wind turbine and thus the steady stategenerator torque value. Yaw DOF was ignored because its effect is minimal and the rollDOF was ignored because roll has very little damping and thus will not reach a steadystate solution. Figure 17 shows the linearised points overlaid on top of the baseline. Thelinearised points used to plot this graph were obtained from the linearisation at 8-11 m/s(the second to fourth crosses in Figure 17). Points below these linearisation values (thoseobtained at 5-7 m/s) fell into region 1.5 and were ignored. The intersection into region 1.5(the triangle mark in the figure) was found using a second order quadratic fit (not shown inthe figure) of all the linearised points. As shown, using the linearised points to determinehow the torque command behaves results in an earlier entrance into region 2 comparedto the baseline. Region 2.5 is now narrower as well. At the lower generator speeds,synonymous with lower wind speeds (8-9 m/s), the linearised torque command follows ashallower path while at higher wind speeds (10-11 m/s) it is a step higher compared to thebaseline. From 9-10 m/s there is a large increase in torque command suggesting that theturbine would prefer operating at a higher generator torque from this point onwards. Thelinearised value at 11 m/s lies on the baseline region 2.5 slope suggesting that the baselineallowed the turbine to operate at its optimal state for this wind speed.

To implement this within Simulink® a 1-dimensional look-up table was produced which tookin the generator rotor speed and finds the linearised generator torque value. Interpolationbetween linearised points were performed using MATLAB®’s inbuilt linear interpolationmethod.

4.4.1 Results and Discussion

Following turbulent testing, the improvements found from a preliminary test, using constantwinds with no waves, were not matched up in turbulent winds. It was found that therewere largely no significant changes in loads and power capture. However, there was a3% improvement in region transition as shown in Figure 18. The reduction was mostevident around the transition region (10.2-11.4 m/s) leading to a higher amount of time

22

Baseline curve Rated Gen speed and torqueLinearised points Baseline Region 2 and 2.5

New Region 2

Baseline Region 2

New 2.5

Baseline 2.5

Figure 17 Linearised torque trajectory against baseline

spent in region 2. Because of this, region 2 captured energy increased from 239.12 kWh to264.29 kWh. Combined with a 2 % reduction in RMS power error, overall power capturewould have increased slightly. There were no significant improvements to loads and a 3%increase in RMS roll motion. From these results it can be surmised that using the steadystate operating points found from linearisation does not offer significant improvements topower capture and load reduction. Figure D8 in Appendix D shows a graph of the metrics.These results show that using linearisation points to determine a torque trajectory is notas effective in reducing region transition, improving power capture and loads, as using atrajectory from subsection 4.3. Results also reinforces that a short region 2.5 is ineffective.

0%

20%

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80%

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(a) Baseline

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80%

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Region 2

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100%

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Region 2

0%

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60%

80%

100%

8 9 10 11 12 13 14

Aver

age

% o

f ti

me

Wind Speed (m/s)

Region

Transition

Region 3

Region 2

(b) Linearised torque

Figure 18 Baseline and linearised torque region transition plot

4.5 Combined Implementation

A model was made using a combination of trajectory 2 and the individual blade pitchcontrol to analyse how the two would interact with each other to see if there would be

23

0%

20%

40%

60%

80%

100%

8 9 10 11 12 13 14

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age

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f ti

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Wind Speed (m/s)

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Region 3

Region 2

0%

20%

40%

60%

80%

100%

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Wind Speed (m/s)

Region

Transition

Region 3

Region 2

(a) Baseline

0%

20%

40%

60%

80%

100%

8 9 10 11 12 13 14

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f ti

me

Wind Speed (m/s)

Region Transition

Region 3

Region 2

0%

20%

40%

60%

80%

100%

8 9 10 11 12 13 14

Aver

age

% o

f ti

me

Wind Speed (m/s)

Region

Transition

Region 3

Region 2

(b) Combined implementation

Figure 19 Region transition plot of combined implementation against baseline

further improvements. These two were selected as they showed good improvement inregion transition and power capture. Results showed that there was a further reduction intime spent in transition using a combined approach. Figure 19 shows the improvement inregion transition, across all wind speeds, now only spending 7 % of total time transitioningcompared to 8 % for trajectory 2 alone and 10 % for individual blade pitching alone. Itis interesting to note that the controller spends the most time transitioning at 13 m/s windspeeds, showing that the controller influence is greatest around rated wind speeds. Thisimprovement to region transition is very similar to trajectory 2’s shown in Figure 16.Figure 20 shows the two control methods work together constructively to improve powercapture in region 3 as seen in the RMS power error with a drop of 19 %. Where the loadsor motions for a control was higher than the other, the combined control would often bein between the two. For example, the tower SS, RMS roll, RMS pitch and their respectiveRMS rates were not the highest or the lowest. Tower fore-aft DEL and LSS DEL fellby 9 % and 7 % respectively which was not as high as using individual blade pitchingalone. There was an increase in tower SS DEL which was 22 % higher than the baseline.However it can been seen that the combined control reduced the effect compared to usingindividual alone. In region 2, there was a higher amount of energy captured at 314.51 kWhcompared to 257.55 kWh of the baseline, at a higher efficiency of 83.33 % compared to79.64 %. This was also higher than using individual blade pitching or the trajectory as astand alone. A bar graph of the metrics against the baseline can be found in Figure D9,and an example time series result in Figure D10 in Appendix D.

These results show that improvements to region transition and power capture can be madeusing a combination of changes to the torque controller and blade pitch controller.

5. Conclusions

The objectives of this project was to improve region transition, power capture, and reduceloads. From the simulations it was found that:

• The use of an alternative torque trajectory was found to reduce region transition themost while improving power capture. Region transition fell by as much as 7 %, withthe most effective trajectory resulting in only 7 % of time spent transitioning.

• Power captured in region 2 increased as a result with an increase as high as 82.1 kWh

24

1.0

0

1.0

0

1.0

0

1.0

0

1.0

0

1.0

0

1.0

0

1.0

0

1.0

0

0.9

3

0.9

3

1.0

0

0.9

7

0.9

3

1.1

0

1.0

2 1.1

0

1.0

3

0.8

5 0.9

6

0.9

1

1.3

2

0.9

7

0.8

3 0.9

1

0.9

0

0.8

3

0.8

1 0.9

2

0.9

1

1.2

2

0.9

3

0.9

2

0.9

2

0.9

7

0.8

5

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

RMS Power

Error

RMS Speed

Error

Tower FA

DEL

Tower SS

DEL

LSS DEL RMS Roll RMS Pitch RMS Roll

Rate

RMS Pitch

Rate

Power and Speed Platform Motions

Baseline Trajectory 2 Individual BP Combined Control

Figure 20 Comparison graph of the combined control against baseline and its respective individual controls

over the baseline (239.12 kWh). Using motion reduction, power captured in region 2reduced relative to the baseline as a result of changes to the blade pitch in region 2.

• Power captured improved most using individual blade pitching with a reduction ofRMS power error of 15 %.

• Loads on the tower reduced the most using a P controller with a gain of 0.0525 rads.The fore-aft DEL reduced by 14 %, SS DEL reduced by 11 %, and LSS DEL reducedby 6 %.

• Using a combination of individual blade pitching and trajectory 2 resulted in higherenergy captured in region 2 and 3 compared to using each control alone. Transitiontime reduced as well.

• The two controllers worked together to cancel out their respective load extremesresulting in the combined controller loads being between the two loads of eachcontrollers.

6. Future Works

• Testing of the logic presented in this work on different platform configurations todetermine if similar results can be obtained.

• Perform tuning of the alternative torque trajectory to find an optimal trajectory basedon power optimisation or load minimisation.

• Linearise about a greater number of points to determine a torque trajectory withgreater resolution to ascertain if improvements can be made.

• Research methods to reduce SS loading for the individual BP controller.

• Conduct design and research into a gain scheduled individual BP controller.

• Utilise MPC on individual BP controller and baseline BP controller.

25

References

[1] Monthly Electricity Statistics: February 2014. International Energy Agency. RetrievedJuly 1, 2014 from:http://www.iea.org/stats/surveys/mes.pdf.

[2] Global Wind Report–Annual Market Update 2012. Global Wind Energy Council.

[3] Project Details for Vindeby. 4C Offshore. Retrieved September 2, 2014 from:http://www.4coffshore.com/windfarms/vindeby-denmark-dk06.html.

[4] Global Offshore. Global Wind Energy Council. Retrieved July 1, 2014 :http://www.gwec.net/global-figures/global-offshore/.

[5] Sawyer, S. (2013). Floating Wind Power: The Next Wave? Energy Focus Journal.Retrieved July 1, 2014 from:http://www.gwec.net/wp-content/uploads/2013/09/The-Next-Wave-9-2013.pdf, September.

[6] Offshore wind. Europena Environment Agency. Retrieved July 1, 2014 from:http://www.ewea.org/policy-issues/offshore/.

[7] Jonkman, J. M. (2007). Dynamics modeling and loads analysis of an offshore floatingwind turbine. PhD thesis, University of Colorado.

[8] Wang, C. M., Utsunomiya, T., Wee, S. C., and Choo, Y. S. (2010). Research onfloating wind turbines: a literature survey. The IES Journal Part A: Civil StructuralEngineering, 3(4), pp. 267–277.

[9] Namik, H. (2012). Individual Blade Pitch and Disturbance Accommodating Controlof Floating Offshore Wind Turbines. PhD thesis, The University of Auckland.

[10] Sclavounos, P. D. Floating Wind Turbines. Lecture Powerpoint, Laboratory for Shipand Platform Flows (LSPF), Department of Mechanical Engineering, MassachusettsInstitute of Technology. Retrieved May 28, 2014 from :http://web.mit.edu/windenergy/windweek/Presentations/P6%20-%20Sclavounos.pdf.

[11] Bianchi, F., de Battista, H., and Mantz, R. (2006). Wind Turbine Control Systems:Principles, Modelling and Gain Scheduling Design. Advances in Industrial Control.Springer, London, England. pp. 2, 19–21, 68–78.

[12] Rezaei, V. (2014). Active robust control of wind turbines. PhD thesis, Colorado Schoolof Mines.

[13] Aho, J., Pao, L., and Hauser, J. (2013). Optimal trajectory tracking control for windturbines during operating region transitions. In American Control Conference (ACC),2013, IEEE, pp. 1424–1429.

[14] Lindeberg, E., Svendsen, H. G., and Uhlen, K. (2012). Smooth transition betweencontrollers for floating wind turbines. Energy Procedia, 24, pp. 83–98.

[15] Pao, L. Y., and Johnson, K. E. (2011). Control of wind turbines. Control Systems,IEEE, 31(2), pp. 44–62.

26

[16] Lackner, M. A. (2009). Controlling Platform Motions and Reducing Blade Loads forFloating Wind Turbines. Wind Engineering, 33(6), pp. 541–553.

[17] Lazaro, J. K., Chakiath, M. J., Stol, K. A., and Namik, H. (2010). A study of dynamiccoupling and composite load control for wind turbines. In 48th AIAA AerospaceSciences Meeting, pp. 1–9.

[18] Bottasso, C., Croce, A., Nam, Y., and Riboldi, C. (2012). Power curve tracking inthe presence of a tip speed constraint. Renewable Energy, 40(1), pp. 1–12.

[19] Bossanyi, E. (2000). The design of closed loop controllers for wind turbines. Windenergy, 3(3), pp. 149–163.

[20] Bossanyi, E. (2009). Controller for 5MW reference turbine. Tech. Rep. 11593/BR/04,Garrad Hassan and Partners Limited.

[21] Laks, J. H. (2013). Preview Scheduled Model Predictive Control For Horizontal AxisWind Turbines. PhD thesis, University of Minnesota.

[22] Spencer, M. D., Stol, K. A., Unsworth, C. P., Cater, J. E., and Norris, S. E. (2013).Model predictive control of a wind turbine using short-term wind field predictions.Wind Energy, 16(3), pp. 417–434.

[23] Jonkman, J. NWTC Computer-Aided Engeering Tools: FAST. Retrieved July 2, 2014from:http://wind.nrel.gov/designcodes/simulators/fast/.

[24] Jonkman, J. M., and Buhl Jr, M. L. (2005). FAST user guide. Golden, CO: NationalRenewable Energy Laboratory.

[25] Jonkman, J. M., Butterfield, S., Musial, W., and Scott, G. (2009). Definition of a5-MW reference wind turbine for offshore system development. National RenewableEnergy Laboratory Golden, CO.

[26] Zuo, S., Song, Y., Wang, L., and Song, Q.-W. (2013). Computationally InexpensiveApproach for Pitch Control of Offshore Wind Turbine on Barge Floating Platform.The Scientific World Journal, 2013, pp. 1–9.

[27] Wright, A. D. (2004). Modern Control Design for Flexible Wind Turbines. Tech. Rep.NREL/TP-500-35816, National Renewable Energy Laboratory.

[28] Wind Turbines - Part 3: Design Requirements for Offshore Wind Turbines. Interna-tional Electrotechnical Commission (IEC), 61400-3 Ed. 1 (2009).

[29] Wind Turbines - Part 1: Design Requirements. International Electrotechnical Commis-sion (IEC), 61400-1 Ed. 3 (2005).

[30] Stol, K. A., Zhao, W., and Wright, A. D. (2006). Individual blade pitch control forthe controls advanced research turbine (CART). Journal of solar energy engineering,128(4), pp. 498–505.

[31] Stol, K. A., Moll, H.-G., Bir, G., and Namik, H. (2009). ‘A Comparison of Multi-BladeCoordinate Transformation and Direct Periodic Techniques for Wind Turbine ControlDesign’, paper presented at the 47th AIAA Aerospace Sciences Meeting Including theNew Horizons Forum and Aerospace Exhibition, Orlando, Florida, 5-8 January.

27

[32] Stol, K., and Fingersh, L. (2004). Wind turbine field testing of state-space controldesigns. Tech. Rep. NREL/SR-500-35061.

[33] Kumar, A., and Stol, K. (2009). Scheduled model predictive control of a wind turbine.In Proc. AIAA/ASME Wind Energy Symp, pp. 1–18.

[34] Hau, E. (2006). Wind Turbines : Fundamentals, Technologies, Application, Economics,2nd ed. Springer, New York; New York. pp. 45–59.

28

Appendix A Simulink Model and FAST diagram

Control System

Wind-

Inflow

Aero-

dynamics

Rotor

Dynamics

Drivetrain

Dynamics

Power

Generation

Nacelle Dynamics

Tower Dynamics

Waves &

Currents

Hydro-

dynamics

Platform Dynamics

Mooring Dynamics

Figure A1 FAST relationships with different modules [9].

Figure A1 shows the interactions between FAST and the AeroDyn, and HydroDyn modules.

A detailed view of the Simulink model that controls the 5 MW NREL wind turbine coupledwith the FAST interface is shown in Figure A2 [9]. This is an example of SISO. Thepitch controller takes in only one disturbance input and it tries to regulate this to a setpoint (rated generator rotational speed) by commanding the collective pitch of the blades.Given initial conditions for the rotor speed, blade pitch and platform position, FAST willprocess a specified wind profile and model the behaviour of the wind turbine to this wind.The model will then extract the generator speed which is then passed onto the operatingregion block, and the torque and pitch controller. The controllers will try to maximisepower capture or maintain constant power capture according to which region the controllerthinks it is in. These control inputs are passed into FAST where it will calculate loads andthe associated effects that the inputs will have on other behaviours of the turbine. The yawcontroller is there as a place holder and has no effect on the wind turbine.

29

[w

HS

S _

raw

]

Go t

o 2

Unit D

ela

y

1

z

H

SS

sp

ee

d

Filt

ere

d

w

_

HS

S

( r

pm

)

G

enera

tor

Torq

ue

1 .5

70

8 s

+

1 .5

70

8

spee

d f

ilte

r

W _

HS

S

f(

u )

extr

act

HS

S s

pe

ed

[Pitch ]

Fro

m

Pitch

( d

eg

)

Tg

Sw

itch

[TG

en

]

sw

itch

T

orq

ue c

ontr

oller

sele

cto

r

Torq

ue C

ontr

oller

Pro

duct

−K −

gen e

ff

Gen .

Torq

ue

(N

m

) an

d P

ow

er

( W )

Ou

tDa

ta

Da

ta W

ind an

d W

ave

R

oto

r S

pe

ed

Pla

tform

P

itch

[w

HS

S _

raw

]

Fro

m 2

−K −

To r

ad /

s

yaw

an

d y

aw

ra

te

Yaw

Co

ntr

olle

r

pitch

Yaw

Positio

n

(

rad )

an

d R

ate

(r

ad /

s )

q

[Pitch ]

Fro

m 1

[T

Gen

]

Pitch

In

T_ g

P

ow

er

Bla

de P

itch

T

orq

ue

Filt

ere

d

w

_

HS

S

(r

pm

)

W _

HS

S ( r

pm

)

Pitch

(r

ad )

P

itch C

ontr

olle

r

Bla

de P

itch A

ng

les

(

rad )

F

AS

T N

onlin

ear

Win

d T

urb

ine

qd

ot

Tgen 1

Data

Extr

actio

n

and P

lott

ing

Ge

nera

l

Overv

iew

−K

−

T

o d

eg

[Pitch ]

Go t

o

Figure A2 Detailed schematic of baseline controller [9]

30

Appendix B Design Load Cases

This appendix is a collection of the parameters used to generated the turbulent wind profilesand wave conditions. These are then used for DLC analysis done in accordance to the IEC61400-3 standard [28]. These wind and wave profiles were kindly given by Dr. HazimNamik of the University of Auckland but can be obtained easily using TurbSim and theHydroDyn module of FAST. These are shown below in table B1 . Each wind speed binhas 6 different wind and wave profiles in accordance to IEC 61400-1 standard [29].

Table B1 Wind speed bins and the parameters for each DLC

WindSpeed Bin

(m/s)Wind

RandomSeed 1

WindRandomSeed 2

WaveHeight

(m)

WavePeriods

(s)

WaveRandom Seed

1

WaveRandom Seed

2

8

5411384 1483177

1.9

9.944 1523349375 2555455765296326 1457810 11.929 1620677309 10702286525181267 1432443 13.914 592759340 20610344575066209 1407076 15.900 1459650384 7309727824951151 1381710 17.885 1406812251 12568529254836093 1356343 19.870 349206043 480632481

9

4721035 1330976

2.1

10.272 1613333725 11751364024605977 1305610 12.307 547812589 2976937254490919 1280243 14.343 1086534495 3206064364375861 1254876 16.379 1501255830 5529947654260803 1229509 18.414 1913200166 18054265594145745 1204143 20.450 2060062649 546066822

10

4030687 1178776

2.2

10.613 1748663348 13229458683915629 1153409 12.581 522965888 10163800643800570 1128042 14.548 1995578435 7551830413685512 1102676 16.515 751584415 17841908923570454 1077309 18.483 422185086 12568450653455396 1051942 20.450 539198480 1180522460

11

3340338 1026575

2.3

10.921 1969658395 1628958473225280 1001209 12.827 613834619 1158569983110222 975842 14.733 1626075110 11398790652995164 950475 16.638 1618620905 16732488852880106 925108 18.544 817001235 20057726712765048 899742 20.450 1219387688 278971459

12

2649990 874375

2.6

11.400 1221539510 6683292142534932 849008 13.002 1008008726 11350162662419873 823641 14.604 25559500 3557279382304815 798275 16.206 723965366 12927463752189757 772908 17.808 348283855 5647265342074699 747541 19.410 1705713063 1404624168

Continues to next page...

31

WindSpeed Bin

(m/s)Wind

RandomSeed 1

WindRandomSeed 2

WaveHeight

(m)

WavePeriods

(s)

WaveRandom Seed

1

WaveRandom Seed

2

13

1959641 722174

2.8

11.925 1480076875 3272293041844583 696808 13.300 1606643312 17734284551729525 671441 14.675 967530716 11560815771614467 646074 16.050 180005039 21391830151499409 620707 17.425 491724296 1678806711384351 595341 18.800 1961377049 950644346

14

1269293 569974

3.0

12.324 229035085 1813245981154234 544607 13.523 2065660399 8585267021039176 519240 14.723 19951921 558067441924118 493874 15.922 1664107551 1718133978809060 468507 17.121 1755145301 926454140694002 443140 18.320 1865507675 1955600818

32

Appendix C Weibull Weighted Average

A weighted average of performance is used because the wind speed varies at a givensite. For this project the Weibull distribution and parameters used is based from real data,collected between 1993 to 1997, from the Vindeby offshore wind farm in Denmark. Thisis the same distribution used by Namik [9]. Data from Scotland was not available so thiswas the chosen site. Figure C1 shows the Weibull distribution as well as the distributionof wind throughout a year. This matches closely with the distribution of the scaling factorswhich is expected. The more time a particular wind speed spends within a wind speed fora given year, the higher the weighting will be and so the overall effects of the differentwind speeds on the performance of the turbine will be appropriately averaged. Table C1shows a tabulated form of the scaling values that were of interest for this project. Thesewere kindly provided by Dr. Hazim Namik. Following is a brief explanation of how thefactors were obtained and a more complete explanation can be found in [9].

0 5 10 15 20 250

0.2

0.4

0.6

0.8

1

Wind speeds (m/s)

Sca

ling

fac

tor

0 5 10 15 20 250

2

4

6

8

10

Per

cent

age

tim

e of

yea

r

Scaling FactorPercentage of time

Figure C1 Weibull Distribution

The shape of the Weibull distribution is given by equation C1 where F (U) is the ratio oftime that the mean wind, in an hour, exceeds U , c is the scaling parameter, and k is theshape factor. The percentage time spent in a wind speed bin (in a year) with a range fromU − 0.5 m/s to U + 0.5 m/s can be found using equation C2. The Weibull parameters k andc are 2.3 and 9.1 respectively [9].

F (U) = exp(−(U/c)k) (C1)

33

Table C1 Weibull scaling values

Wind Speed Bin Scaling Value

8 1.00009 0.967010 0.893911 0.791512 0.672413 0.548414 0.4297

Tu = (F (U − 0.5)− F (U + 0.5))× 100 (C2)

The scaling factors, si, used in equation C3 is then found by normalising the all the Tuvalues by the maximum Tu. This gives the highest weighting to the most dominant windspeed bin. The overall performance metric, po, can then be calculated where pi is theaveraged performance within a wind speed bin, i is the current wind speed bin, and n isthe total number of wind speed bins [9].

po =

n∑i=1

sipi

n∑i=1

si

(C3)

34

Appendix D Results Graphs and Plots

This section gives more detailed representations of the results and plots used to analysesimulation data. The bar graphs are all normalised to the baseline unless otherwise stated.

Bar graphs showing normalised results for region 3 metrics, loads and motions for thetrajectories can be found below. Region 2 metrics and transition time graphs are shown inabsolute values.

Figure D1 shows the performance for the P controller. Figure D2 shows the performancefor the individual blade pitch controller.

Figure D3 shows the various reductions in transition time for the different torque trajectories.Figure D4 is a comparison of region 2 performance for the trajectories and Figures D5and D6 shows the region 3 metrics, loads, and motions for the trajectories. The affect ofthe generator torque on roll can be found in Figure D7. The comparison is made betweenusing trajectory 4, which had the shortest region 2.5 region, against trajectory 5 whichhad the largest. This resulted in the RMS roll for trajectory 4 being the closest to thebaseline. Trajectory 4’s torque response is similar to that of the baseline, with smallerpeaks than trajectory 5. This resulted in smaller peaks in roll and thus a lower RMS rollvalue. Another feature of holding region 2.5 wider is that there are no torque overshootsresulting in better regulation.

Figure D8 is the bar graph of the region 3 performance metrics, loads, and motions of thelinearised torque trajectory against the baseline. The region 2 metrics have been omittedfrom the linearised torque metrics graph as they were given in subsection 4.4.

The metrics comparison graph for the combined controller can be found in Figure D10and a time series plot can be found in Figure D10. The time series plot shows howwell the controls track power capture around rated. Compared to the baseline, there aresignificantly less dips in power capture because of less transitions. The individual bladepitch actuations are also evident showing the vast amount of changes in angle for eachindividual blade shown in the blue, black, and dash green coloured lines. Overall trackingwas the same as the baseline in winds above rated, while around rated, the blade pitches donot quickly actuate to 0º as much. This helps in reducing region transition and improvingpower capture. This is evident each time there is a change to 0º BP.

35

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

0.96

0.96

1.25

1.02

0.96

1.02

0.96

0.92

0.95

0.94

0.93

0.94

1.01

0.91

0.88

1.01

0.97

0.97

1.56

1.09

0.98

1.04

0.96

0.88

0.91

0.94

0.87

0.89

1.01

0.85

0.79

1.01

0.96

0.96

1.97

1.16

0.97

1.08

0.96

0.86

0.89

0.94

0.83

0.86

1.01

0.80

0.73

1.00

0.0

0

0.5

0

1.0

0

1.5

0

2.0

0

2.5

0

RM

S P

ow

er

Err

or

RM

S S

pee

d

Err

or

RM

S P

itch

Rat

e

Max

Pit

ch

Rat

e

RM

S T

orq

ue

Err

or

Bla

de

Fla

p

DE

L

Bla

de

Edg

e

DE

L

Tow

er F

A

DE

L

Tow

er S

S

DE

L

LS

S D

EL

RM

S R

oll

RM

S P

itch

RM

S Y

awR

MS

Roll

Rat

e

RM

S P

itch

Rat

e

RM

S Y

aw

Rat

e

Pow

er a

nd S

pee

dA

ctu

ators

Usa

ge

Fat

igue

DE

LP

latf

orm

Mo

tions

Bas

elin

eK

= 0

.01

75

K =

0.0

349

K =

0.0

525

Figure D1 Performance, loads, and motion graph for the P controller against baseline

36

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

0.85

0.96

3.17

1.20

0.97

1.17

0.98

0.91

1.32

0.97

0.83

0.91

0.58

0.90

0.83

0.47

0.0

0

0.5

0

1.0

0

1.5

0

2.0

0

2.5

0

3.0

0

3.5

0

RM

S P

ow

er

Err

or

RM

S S

pee

d

Err

or

RM

S P

itch

Rat

e

Max

Pit

ch

Rat

e

RM

S

Torq

ue

Err

or

Bla

de

Fla

p

DE

L

Bla

de

Edg

e

DE

L

Tow

er F

A

DE

L

Tow

er S

S

DE

L

LS

S D

EL

RM

S R

oll

RM

S P

itch

RM

S Y

awR

MS

Roll

Rat

e

RM

S P

itch

Rat

e

RM

S Y

aw

Rat

e

Pow

er a

nd S

pee

dA

ctu

ators

Usa

ge

Fat

igue

DE

LP

latf

orm

Mo

tions

Bas

elin

eIn

div

idual

Bla

de

Pit

ch

Figure D2 Performance, loads, and motion comparison of the individual blade pitch controller againstbaseline

37

0.17

0.08 0.080.09

0.11

0.07

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

Baseline Trajectory1 Trajectory2 Trajectory3 Trajectory4 Trajectory5

Aver

age

% o

f ti

me

Figure D3 Time spent in transition for the trajectories against baseline

23

9.1

2

80

.43

31

0.5

2

84

.96

31

3.6

4

84

.76

30

7.6

6

83

.18

28

7.3

4

83

.42

32

1.2

2

84

.30

0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

Captured Energy in R2 (kWh) R2 Efficiency

Baseline Trajectory1 Trajectory2 Trajectory3 Trajectory4 Trajectory5

Figure D4 Region 2 performance metrics for the trajectories against baseline

38

1.0

0

1.0

0

1.0

0

1.0

0

1.0

0

0.9

6

0.9

8

0.7

0

0.8

7

0.9

7

0.9

6

0.9

7

0.6

9

0.8

1

0.9

6

0.9

5

0.9

7

0.7

2

0.8

8 0.9

7

0.9

9

1.0

0

0.8

0

0.9

6

1.0

0

0.9

5

0.9

6

0.6

6

0.7

9

0.9

5

0.00

0.20

0.40

0.60

0.80

1.00

1.20

RMS Power Error RMS Speed Error RMS Pitch Rate Max Pitch Rate RMS Torque Error

Baseline Trajectory1 Trajectory2 Trajectory3 Trajectory4 Trajectory5

Figure D5 Region 3 performance metrics for the trajectories against baseline

1.0

0

1.0

0

1.0

0

1.0

0

1.0

0

1.0

0

1.0

0

1.0

0

1.0

0

1.0

0

1.0

0

0.9

7 1.0

0

1.0

0

0.9

7

0.9

9

1.0

8

1.0

1

0.9

9

1.0

8

1.0

1

1.0

0

0.9

6 1.0

0

0.9

9

0.9

7

0.9

7

1.0

7

1.0

1

0.9

9

1.0

6

1.0

1

0.9

9

0.9

7 1.0

0

1.0

0

0.9

8 1.0

3 1.0

8

1.0

1

1.0

0

1.0

8

1.0

1

1.0

0

0.9

9

1.0

0

1.0

0

0.9

9

0.9

9 1.0

3

1.0

1

1.0

0 1.0

3

1.0

0

1.0

0

0.9

5 1.0

0

0.9

9

0.9

8 1.0

1

1.1

2

1.0

1

0.9

8

1.1

2

1.0

2

0.9

8

0.00

0.20

0.40

0.60

0.80

1.00

1.20

Blade Flap DEL Blade Edge DEL Tower FA DEL Tower SS DEL LSS DEL RMS Roll RMS Pitch RMS Yaw RMS Roll Rate RMS Pitch Rate RMS Yaw Rate

Fatigue DEL Platform Motions

Baseline Trajectory1 Trajectory2 Trajectory3 Trajectory4 Trajectory5

Figure D6 Trajectories’ loads and motions against baseline

39

300 350 400 450 500 550 60020

30

40

50

Gen

erat

or to

rque

(kN

m)

Baseline Trajectory 4

300 350 400 450 500 550 600

−1

0

1

Time (sec)

Pla

tfor

m r

oll (

deg)

(a) Trajectory 4

300 350 400 450 500 550 60020

30

40

50

Gen

erat

or to

rque

(k

Nm

)

Baseline Trajectory 5

300 350 400 450 500 550 600

−1

0

1

Time (sec)

Pla

tform

rol

l (de

g)

(b) Trajectory 5

Figure D7 Comparison of the effect of different trajectories on roll at a mean wind speed of 10 m/s

40

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

0.98

1.00

0.89

0.97

1.00

0.99

1.00

1.00

0.99

1.01

1.03

1.00

1.00

1.03

1.00

1.00

0.0

0

0.2

0

0.4

0

0.6

0

0.8

0

1.0

0

1.2

0

RM

S

Pow

er

Err

or

RM

S

Spee

d

Err

or

RM

S P

itch

Rat

e

Max

Pit

ch

Rat

e

RM

S

Torq

ue

Err

or

Bla

de

Fla

p

DE

L

Bla

de

Edg

e

DE

L

Tow

er F

A

DE

L

Tow

er S

S

DE

L

LS

S D

EL

RM

S R

oll

RM

S P

itch

RM

S Y

awR

MS

Ro

ll

Rat

e

RM

S P

itch

Rat

e

RM

S Y

aw

Rat

e

Pow

er a

nd

Sp

eed

Act

uat

ors

Usa

ge

Fat

igu

e D

EL

Pla

tform

Moti

ons

Bas

elin

eL

inea

rise

d T

orq

ue

Figure D8 Performance, loads, and motion comparison of the linearised torque against baseline

41

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

0.81

0.92

3.00

1.20

0.93

1.13

0.98

0.91

1.22

0.93

0.92

0.92

0.58

0.97

0.85

0.47

0.0

0

0.5

0

1.0

0

1.5

0

2.0

0

2.5

0

3.0

0

3.5

0

RM

S

Pow

er

Err

or

RM

S

Spee

d

Err

or

RM

S

Pit

ch R

ate

Max

Pit

ch

Rat

e

RM

S

Torq

ue

Err

or

Bla

de

Fla

p D

EL

Bla

de

Edg

e D

EL

Tow

er F

A

DE

L

Tow

er S

S

DE

L

LS

S D

EL

RM

S R

oll

RM

S

Pit

ch

RM

S Y

awR

MS

Ro

ll

Rat

e

RM

S

Pit

ch R

ate

RM

S Y

aw

Rat

e

Pow

er a

nd

Sp

eed

Act

uat

ors

Usa

ge

Fat

igu

e D

EL

Pla

tform

Moti

ons

Bas

elin

eC

om

bin

ed C

ontr

ol

Figure D9 Performance, loads, and motion comparison of the combined control against baseline

42

020

4060

8010

012

014

016

018

020

001020

Wind speed(m/s)

020

4060

8010

012

014

016

018

020

0

1000

2000

3000

4000

5000

Generator power(kN)

020

4060

8010

012

014

016

018

020

002040

Generator torque(kNm)

020

4060

8010

012

014

016

018

020

0-5051015

Blade pitch angles (deg)

020

4060

8010

012

014

016

018

020

02

2.53

Region

Tim

e (s

ec)

Bas

elin

eC

ombi

ned

Figure D10 Example of the time response of the combined controller in a mean wind speed of 12 m/s

43

Appendix E Cp Plot and Verification Calculations

To find the gain values required for the P controller in subsection 4.1 a Cp envelop wasderived. The envelop was found by running a series of simulations over a range of TSRand BP angles. The TSR was swept by fixing the rotor speed and varying the wind.The simulations were performed with no controls. This was done by removing all DOFsand fixing the BP angle. However, because a floating wind turbine was to be simulated,platform DOFs were maintained to allow motion. Simulations were conducted over 600seconds with time steps of 0.125 seconds, to allow the system to reach steady state, andthe Cp values was calculated using an average of the last 401 steps. Figure E1 shows theCp envelop which has a max Cp of 0.4788 at a TSR of 8. For comparison, Jonkman’s Cpmax was 0.482 at a TSR of 7.55. The differences may be because of which DOF Jonkmanenabled or disabled.

0

5

10

15

20

25

30 0

5

10

15

0

0.1

0.2

0.3

0.4

0.5

TSR

Cp plot against blade pitch and TSR

BladePitch

Cp

Figure E1 Cp envelop

Below are calculations performed to determine if Jonkman’s power curve in region 2differed largely to the power curve obtained from the derived Cp envelop. The constant ofproportionality given by Jonkman in [25] is 0.0255764 Nm/rpm2.

The torque equation, which is a function of the coefficient of torque (Cq), and wind velocity(V (m/s)) is given by [11]:

T (V ) =1

2ρAV 2Cq

where Cq = Cp/λ, V = ΩR/λ, λ is the TSR (8), ρ is air density (1.225 Kg/m3 ), A isthe blade swept area (10099.87 m2), R is the radius of the turbine (63 m), Cp is the powercoefficient (0.4788), and Ω is the rotational speed of the rotor. The blade swept area is theeffective blade area and is 90% of the total radius [34].

44

With the gear ratio as 97:1, generator high speed shaft (HSS) to rotor speed,

Ω =(ωHSS × 2π)

(97× 60)= 1.079× 10−3ωHSS

V = 1.079× 10−3ωHSS ×63

8= 8.5017× 10−3

T (ωHSS) =1

2(1.225)(10099.87)(8.5017× 10−3ωHSS)2(

0.4788

8) = 0.026760ω2

HSS

Because the constant of proportionality calculated is relatively similar to Jonkman’s constant,the difference in torque command would differ by around 4.6 %. Combined with the 0.07 %difference in max Cp, it was reasoned that using this derived curve to find the gains anduse the baseline torque controller to command the torque would be suitable.

45