kth.diva-portal.org1519746/...Álvaro Hernando Cabrero Expansion of Existing Gravity-Based Offshore Wind Turbine Foundations i . Abstract English / Engelska / Inglés . Wind energy

Degree Project in Civil Engineering and Urban Management

Expansion of Existing Gravity-Based Offshore Wind Turbine FoundationsÁLVARO HERNANDO CABRERO

Stockholm, Sweden 2020www.kth.se

TRITA-ABE-MBT-20772ISBN: 978-91-7873-750-5

kth royal institute of technology

Álvaro Hernando Cabrero Expansion of Existing G

ravity-Based Off

shore Wind Turbine Foundations

KTH

2020

Expansion of Existing Gravity-Based Offshore

Wind Turbine Foundations

ÁLVARO HERNANDO CABRERO

Master of Science Thesis Stockholm, Sweden 2020

TRITA-ABE-MBT-20772

ISBN: 978-91-7873-750-5

KTH School of ABE

SE-100 44 Stockholm

SWEDEN

© Álvaro Hernando Cabrero, 2020 Royal Institute of Technology (KTH) Department of Civil and Architectural Engineering Division of Concrete Structures

Álvaro Hernando Cabrero Expansion of Existing Gravity-Based Offshore Wind Turbine Foundations

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Abstract

English / Engelska / Inglés

Wind energy is one of the most promising sources of renewable energy worldwide. Its utilization has substantially increased for the last decades, both onshore and offshore. Offshore wind energy will have a lot to offer within the following decades, thus their foundations need to be prepared. Some of the current wind farms and wind turbines are now reaching their lifespan and, the turbines’ market is developing itself so rapidly that current turbines are getting behind the times with tremendous ease. It is here where the scope of this Master Thesis comes: what shall we do? Should we dismantle wind farms when they reach their lifespan, or should we maybe try to give them a further use? Accommodating for a new a larger wind turbine will need to account for new and higher climate actions and loads, namely winds, waves, ocean currents, the water level variation and the always difficult to predict ice actions. What is aimed in this Master Thesis is to set the basis for a procedure to dimension and define feasible solutions for the offshore wind turbines Gravity-Based Foundations to be expanded, avoiding the necessity of replacing them completely, with the environmental and economic benefits this would have. As this could turn to be an unmanageable problem to be solved, a Case Study where details can be set is performed at the Lillgrund Wind Farm site, in the south-west coast of Sweden, in the Öresund that separates Copenhagen and Malmö. A thorough description of the climatic actions and surrounding aspects is performed, while always dealing with uncertainties. With all that information, an analytical stability analysis is performed to account for three failure modes, namely: sliding, tilting and ground failure. Additionally, a numerical FE-model is carried out in ANSYS in the aim of assessing the stresses and deformations that this kind of structure will suffer. Four alternatives are evaluated, and their behaviour is assessed based on the new external design actions. Analytical results show stability difficulties in two of the geometries inspected, while assure it in the other two. The FE-analyses show high concentrations of stresses on the GBS shaft, while model affordable deformations under the load combinations inspected. These results are also compared and contrasted in between them, and sensitivity analyses for the FE-models are performed in order to assure their good behaviour and development, and the trustworthiness of the results found. Based on these results, some conclusions are drawn from the developed processes. The main finding is the width and weight dependence of the solution, as well as the shape and dimensions. Future research needs such as scouring effects are finally accounted for necessary inspection to be made as continuation of the work here presented.

Keywords: Gravity-Based Foundation, climate actions, expansion, failure mode, width, Lillgrund


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Sammanfattning

Swedish / Svenska / Sueco

Vindkraft är en av de mest lovande källorna till förnybar energi världen över. Användningen har ökat de senaste decennierna, och tekniken kan implementeras inte bara på land utan även till havs. Vindkraft till havs kommer ha mycket att erbjuda i framtiden, och därav behöver även fundament för vindkraftverk till havs förberedas. En del av de befintliga vindkraftsparkerna har nått slutet av sin livslängd och framstegen inom vindkraft går så fort att dagens turbiner blir föråldrade inom kort. Detta är omfattningen av följande masterarbete: Hur skall vi gå till väga? Ska vindkraftsparker i slutet av sin livslängd demonteras eller skall dessa bevaras i ett försök för ytterligare användning? För att kunna tillgodose behoven för nya, större vindturbiner behöver hänsyn tas till olika klimataspekter, nämligen vind, vågor, havsströmmar, vattenstånd och den alltid lika svåruppskattade is påverkan. Syftet med detta examensarbete är att fastställa möjliga lösningar för hur, och lägga grunden till dimensionering av, vindkraftsverks gravitationsfundament som skall utvidgas. De ekologiska samt ekonomiska fördelarna kommer vägas mot ifall fundamentet skulle behöva bytas ut fullständigt. Då uppgift kan komma att bli övermäktig och för att göra problemet mer överskådligt, görs en fallstudie med faktiska parametrar för Lillgrunds vindkraftpark, vid södra Sveriges västkust, placerat i Öresund som separerar Malmö och Köpenhamn. En grundlig beskrivning av platsens klimat och de omgivande aspekterna utförs, med hänsyn tagen till eventuella osäkerheter. Utifrån den informationen utförs en analytisk stabilitetsanalys för att ta hänsyn till brott så som glidning, tippning eller skjuvning. Därtill är en numerisk FE-modell skapad i ANSYS, med avseende att bedöma spänningar och deformationer som dessa former av konstruktioner påfrestas av. Fyra alternativ utvärderas, och hur dessa beter sig beräknas baserat på de nya externa designåtgärderna. Analytiska resultat visar stabilitetsproblem i två av de inspekterade geometrier, samtidigt som de försäkrar det om de andra. FE-analyserna visar höga koncentrationer av spänningar på GBS-axeln, medan modellerade prisvärda deformationer under de inspekterade lastkombinationerna. Dessa resultat jämförs och kontrasteras emellan dem, och känslighetsanalyser för FE-modellerna utförs för att säkerställa deras goda beteende och utveckling och pålitligheten för de resultat som hittats. Baserat på dessa resultat dras några slutsatser från de utvecklade processerna. Huvudfyndet är lösningens bredd och viktberoende, liksom form och mått. Framtida forskningsbehov som skureffekter redovisas slutligen för att nödvändig inspektion ska göras som en fortsättning på det arbete som presenteras här.

Nyckelord: Gravitationsfundament, klimatåtgärder, expansion, brottmekanismer, bredd, Lillgrund


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Resumen

Spanish / Spanska / Castellano

La energía eólica es una de las fuentes de energía renovable más prometedoras del mundo. Su uso ha ido en aumento durante las últimas décadas, y su implantación no se realiza únicamente en tierra, sino también en el mar. La energía eólica offshore tiene mucho que decir en las próximas décadas y también por tanto allí donde se sustentan: sus cimentaciones. Algunos de los parques eólicos y turbinas eólicas actuales están alcanzando su vida útil y el mercado de las turbinas se desarrolla tan rápidamente que las turbinas actuales se están quedando obsoletas con tremenda facilidad. Es aquí donde el tema de este Trabajo de Fin de Máster entra en escena: ¿qué deberíamos hacer al respecto? ¿Debemos desmantelar los parques eólicos cuando alcancen su vida útil, o debemos intentar darles una segunda oportunidad? La implantación de un aerogenerador nuevo y más grande deberá tener en cuenta las nuevas acciones climáticas, a saber: vientos, oleaje, corrientes oceánicas, la variación del nivel del mar y las acciones, siempre difíciles de predecir, del hielo. Lo que se pretende en el desarrollo de este Trabajo de Fin de Máster es sentar las bases de un procedimiento para dimensionar y definir soluciones factibles para la ampliación de cimentaciones tipo GBS para aerogeneradores offshore, evitando así la necesidad de reemplazarlas por completo, con los beneficios ambientales y económicos que ello supondría. Como esto podría convertirse en un problema imposible de manejar, dada la amplia variedad de combinaciones climáticas y de cimentaciones existentes en la actualidad, se ha analizado un caso práctico de este problema, en el que es más sencillo concretar ciertos parámetros. El sitio elegido es el parque eólico de Lillgrund en la costa suroeste de Suecia, en el Öresund, que separa a Copenhague y Malmö. Para su análisis se hace una descripción detallada de las acciones climáticas y características del ámbito, así como de las incertidumbres que siempre deben tenerse en cuenta. Con toda esa información, se realiza un estudio analítico de estabilidad en el que considerar los diferentes modos de fallo, como deslizamiento, vuelco o hundimiento. Del mismo modo, se realiza un modelo numérico de elementos finitos en ANSYS con el objetivo de evaluar los esfuerzos y deformaciones a los que se espera que este tipo de estructura esté sometida. Se presentan varias alternativas con el fin de evaluar diferentes posibilidades y su diferente comportamiento ante las acciones de diseño. Los resultados obtenidos se comparan entre sí, y se realiza un análisis de sensibilidad para el modelo de elementos finitos con el fin de evaluar su comportamiento, y la fiabilidad de los resultados obtenidos. Se derivan finalmente algunas conclusiones en base al procedimiento desarrollado, como la dependencia de estas estructuras del ancho de la base de la cimentación, y una serie de futuras líneas de investigación se tienen finalmente en cuenta para una posible continuación del trabajo que aquí se presenta.

Palabras clave: GBS, acciones climáticas, expansión, modo de fallo, anchura, Lillgrund


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Preface

This Master Thesis comes as a result of intensive debates, doubts, sleepless nights and some tough moments, but it is definitely the result of an exhaustive work that has been marvellous to carry out. I have learned so much I would have never expected, not only on wind power but on self-work, especially in this rare and difficult pandemic days of working from home. The performance of this Master Thesis has taught me to make decisions, argue the assumptions that an engineer needs to make on its working life and, all in all, I think it has built me as a world citizen.

I want to express my deep gratitude to my supervisors, both at KTH and UPM, for their tireless support with this Thesis development. To Mr. Erik Nordström, whose gratefulness of giving me the opportunity to work with him in this Thesis I will always appreciate, as well as to Mr. Anders Ansell, who was my very first contact in the development of this text in Stockholm and to whom I am also very grateful for giving me this opportunity. To Mr. Vicente Negro, whose incredible and infinite help through my formative years has helped me on reaching where I am today, and the responsible person of making me love the marine engineering and turning it into what I want to dedicate my professional career to. My most sincere gratitude is for him.

I also would like to dedicate some words to the unconditional people that has gone along with me in the path of becoming a civil engineer: my parents, Yolanda and Javier, whose endless support I will not be able to pay back in a lifetime; my whole family, and specially my uncle Rodolfo, for his undeniable technical influence on my university and desired career life; my friends both in Madrid and Stockholm, that have always encouraged me to give my best at every step on the way; and last but certainly not least to my endless support, Teresa, my fellow in this life-travel and, ultimately, the person without whom this Thesis would not have ever been possible. My deepest thanks to all of them.

Stockholm, December 2020

Álvaro Hernando Cabrero


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To Yolanda and Javier,

to my best friend, Álvaro,

to my soulmate, Teresa.

To Pablo, my beloved grandfather.


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Table of Contents 1 Introduction ........................................................................................................................ 1

1.1 Wind Power State of the Art ....................................................................................... 1

1.2 Aim and scope. Research questions .............................................................................. 4

1.3 Limitations .................................................................................................................. 4

1.4 Rules and Regulations ................................................................................................. 5

1.5 Thesis Outline ............................................................................................................. 6

2 Literature Study & Background Knowledge ........................................................................ 9

2.1 Description of the Case Study: the Lillgrund Wind Farm ............................................ 9

2.2 Wind turbine selection ............................................................................................... 14

3 Methodology ...................................................................................................................... 17

3.1 Actions on the structure ............................................................................................ 17

3.1.1 Wind actions .......................................................................................................... 18

3.1.2 Wind turbine self-weight ........................................................................................ 27

3.1.3 Wave actions ......................................................................................................... 28

3.1.4 Currents actions ..................................................................................................... 36

3.1.5 Water Level ........................................................................................................... 38

3.1.6 Ice actions .............................................................................................................. 38

3.1.7 Design loads ........................................................................................................... 40

3.1.8 Load combinations ................................................................................................. 48

3.1.9 Geotechnical aspects .............................................................................................. 51

3.2 Case Study Considerations ........................................................................................ 52

3.2.1 Wind actions .......................................................................................................... 52

3.2.2 Wind turbine and tower actions ............................................................................. 54

3.2.3 Wave actions ......................................................................................................... 55

3.2.4 Currents actions ..................................................................................................... 56

3.2.5 Water Level ........................................................................................................... 58

3.2.6 Ice Actions ............................................................................................................. 59

3.2.7 Geotechnical Considerations .................................................................................. 61

3.3 Analytical calculations. Dimensioning and stability analysis ..................................... 63

3.3.1 Sliding failure mode ............................................................................................... 63

3.3.2 Tilting failure mode ............................................................................................... 64

3.3.3 Ground failure mode .............................................................................................. 66

3.4 Numerical simulations. Verification ........................................................................... 68


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3.4.1 Analyses performed in ANSYS ............................................................................... 68

3.4.2 Sensitivity analysis and model check ...................................................................... 74

3.5 Guidelines for solutions production ............................................................................ 76

4 Results and comparison ..................................................................................................... 77

4.1 Proposed cross-sections for analysis ........................................................................... 77

4.2 Analytical calculations............................................................................................... 79

4.2.1 Analytical results interpretation ............................................................................ 83

4.3 Numerical simulations ............................................................................................... 83

4.3.1 Sensitivity analysis ................................................................................................. 92

4.3.2 Numerical results interpretation ............................................................................ 96

4.4 Comparison and overview .......................................................................................... 97

5 Discussion ........................................................................................................................ 101

6 Conclusions ..................................................................................................................... 107

7 Further research needs .................................................................................................... 109

References .............................................................................................................................. 111

Literature ........................................................................................................................... 111

Standards ........................................................................................................................... 113

Website links ...................................................................................................................... 114

Appendices ............................................................................................................................. 115

A. Tower weight calculations ........................................................................................... 117

B. Tower base stresses checking ....................................................................................... 119

C. Weibull regression line for HS ...................................................................................... 121

D. Detailed results on analytical calculations ................................................................... 123

E. Additional figures on numerical simulations ................................................................ 139

F. Economic Assessment ................................................................................................. 145


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Abbreviations

ALS Accidental Limit States

CapEx Capital Expenditures

EWM Extreme Wind Speed Model

EOG Extreme Operating Gust

ESS Extreme Sea State

EWH Extreme Wave Height

FEA Finite Element Analysis

FEM Finite Element Method

FLS Fatigue Limit States

GBF Gravity-Based Foundation

GBS Gravity-Based Structure

HAT Highest Astronomical Tide

LAT Lowest Astronomical Tide

LCOE Levelized Cost of Energy

MSL Mean Sea Level

MWL Mean Water Level

NSS Normal Sea State

NTM Normal Turbulence Model

NWH Normal Wave Height

NWP Normal Wind Profile

OpEx Operational Expenditures

O&M Operation and Maintenance

PCF Project Cash Flow

RWH Reduced Wave Height

SLS Serviceability Limit States


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SSS Severe Sea State

SWH Severe Wave Height

SWL Sea Water Level

ULS Ultimate Limit States

Nomenclature

Latin Characters

A Cross-sectional area [m2]

A Scale parameter for tri-parametric Weibull distribution [m]

B Location parameter for tri-parametric Weibull distribution [m]

BM Berm width [m]

C Shape parameter for tri-parametric Weibull distribution [-]

C Wave celerity [m/s]

CT Thrust coefficient [-]

CD Drag coefficient [-]

d Water depth [m]

D Rotor diameter [m]

D Tower mean diameter [m]

E Young’s Modulus [MPa]

fy Yield strength [MPa]

f(z) Tower wind load [kN/m]

F(x) Probability of non-occurrence/non-exceedance [-]

FR Rotor wind load [kN]

Fice Ice load [kN]

g Acceleration of gravity [m/s2]


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h Water depth [m]

hb Offshore water depth at 5 times significant wave height distance [m]

H Wind speed height [m]

H Wave height [m]

H1/n Average wave height for the 1/n highest waves [m]

Hb Breaking wave height [m]

HD Design wave height [m]

HS Significant Wave Height [m]

HS,Tr Significant Wave Height for a given return period [m]

HS,max,Tr Maximum Significant wave height for a given return period [m]

Hmax Maximum Wave Height [m]

Iref Turbulence intensity [-]

K Frost Index [degrees-days]

L Wavelength [m]

L0 Wavelength for offshore depths [m]

LD Design wavelength [m]

M Bending moment [Nm]

N Axial force [N]

N Number of active waves in a sea state [-]

pi Wave pressure intensities [N/m2]

P(x) Probability of occurrence/exceedance [-]

R Resistance [kN]

Re Reynolds number [-]

S Load effect [kN]

t Ice thickness [m]

T Period [s]


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TM Medium wave period [s]

TP Peak wave period [s]

Tr, TR Return period [years]

TS Duration of the sea state [hours]

TZ Mean zero-upcrossing period [s]

v(z) Currents speed at depth z [cm/s]

VEWM Extreme wind speed [m/s]

Vhub,n-yr Extreme wind speed at hub height with a return period of n years [m/s]

V10 10-minute mean wind speed at height H [m/s]

V10,hub,n-yr 10-minute mean wind speed at the hub height with a Tr of n years [m/s]

V(z) Wind speed at height z [m/s]

Vave Annual average wind speed [m/s]

Vin Cut-in wind speed [m/s]

Vcg Wind speed for coherent gust with direction change [m/s]

Vgust Hub height gust magnitude [m/s]

Vhub Wind speed at hub height [m/s]

Vref Reference wind speed [m/s]

Vout Cut-out wind speed [m/s]

wo Specific weight of sea water [N/m3]

W Elastic section modulus [m3]

z Height above sea level [m]

Greek Characters

α Power-law exponent [-]

αi Goda auxiliary coefficients [-]

αI Impulsive pressure coefficient [-]

β Natural terrain steepness [deg]


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γb Break parameter [-]

γf Load factor [-]

γM Resistance factor [-]

γs Specific weight for steel [t/m3]

γice Unit weight for ice [kN/m3]

δ Break indicator [-]

η* Elevation where wave pressure is exerted [m]

θ(t) Extreme direction change transient [deg]

θe Extreme direction change [deg]

θ Wave direction with respect to breakwater [deg]

λi Modification factors dependent on structural type [-]

Λ1 Turbulence scale parameter [-]

μ Friction coefficient [-]

μ Mean value for Peak Period Lognormal Distribution [s]

μ Platform zoning parameter [-]

μx Mean value for Peak Period equivalent Normal Distribution [s]

ν Poisson ratio [-]

ξ Steepness parameter [-]

ρ Air density [kg/m3]

ρo Sea water density [kg/m3]

σ Standard deviation for Peak Period Lognormal Distribution [s]

σadm Bearing capacity of the soil [kN/m2]

σx Standard Deviation for Peak Period equivalent Normal Distribution [s]

σ1 Turbulence standard deviation for NTM [m/s]

σU,c Turbulence standard deviation for EWM [m/s]

φ Soil friction angle [deg]


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Φ(x) Probability of occurrence/exceedance for peak periods [-]

ψ Reduction factor for RWH sea state [-]

Subscripts

c Characteristic value

d, D Design value

i Counter

k Characteristic value

y Yield


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1 Introduction

1.1 Wind Power State of the Art

Over the last 20 years, the usage, design, and implementation of wind power plants has substantially increased all around the world, both at onshore and offshore conditions, [49]. As a result, more time and efforts are being dedicated to the development of this still new way of producing energy for our populations, both in the aim of building more efficient wind turbines and also finding new ways of placing those wind turbines in the most suitable places.

Figure 1.1. Wind energy generation by region. [49].

Onshore wind power is for sure an important factor in the world’s electricity production. As an example, it represents around 90% of the wind power produced in Europe nowadays, [46], [58]. Nevertheless, the total offshore wind power capacity installed has been considerably increasing in the last decade and is thought to continue this tendency in the coming years. Therefore, lots of effort is put in the investigation of new ways of placing offshore wind turbines, where the present winds are significantly higher than onshore, and where a lot of energy is still waiting to be seized.


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Figure 1.2. Total installed wind power capacity in Europe. [58].

In what corresponds to offshore wind power foundations, there is a wide range of design options depending on the boundary conditions that surround the wind power plant site. Among the spectrum, two main groups can be essentially distinguished: direct foundations or floating foundations. A lot could be said about the types of offshore foundations. Being very brief, it could be stated that the first ones base their stability on the contact with the soil, their weight and are usually used in shallow and transitional waters. On the other hand, the floating foundations are thought to perform themselves in deep waters and base their functionality on the mooring and buoyancy characterization.

Within the first group, several types of structures can be presented, like monopiles, gravity-based structures (GBS), tripods, tri-piles, jackets, and others. Among the floating structures, three main types can be defined: spar-buoys, semi-submersibles, and tension-leg platforms (TLP). Figure 1.3 and Figure 1.4 show these kinds of foundations.

Figure 1.3. Types of direct offshore foundations for wind turbines. [42].


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Figure 1.4. Types of floating wind turbines foundations. From left to right: spar-buoys, semi-submersibles

and TLP. [47].

Typically, and as can be seen in Figure 1.5, the direct foundations are used in shallow (0-30 m) and transitional (30-60 m) waters, while the floating structures have their range of action in deep waters (>50-60 m). For the gravity-based foundations (GBS) and according to different authors and regulations, the typical depths’ range is from 0 to 20 or even 25 metres (see Table 1.1). Variations on the limit for direct or floating foundations go from 50 to 60 metres. At this point, it is important for the reader to keep in mind these depth considerations since it will be essential to know them later in the document.

Table 1.1. Foundation recommended water depths according to different authors. Reproduction from [3].

Foundation Water depth (h)

Ashuri et al, 2007

DNV 2013 - 2016

Luengo et al, 2019

GBS 0-10 m 0-25 m 0-20 m

Monopile 0-30 m 0-25 m 20–50 m

Tripod >20 m 20-50 m >30 m

Jacket >20 m 20-50 m >50 m

Floating >50 m >50 m >50 m


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Figure 1.5. Water depths for direct and floating wind turbine foundations. [1].

1.2 Aim and scope. Research questions

The aim of this Master Thesis is to perform a thorough analysis and description of what the necessary processes are to accommodate a larger wind turbine in a pre-existent location. In order to do so, an evaluation of whether the current foundation, or some of its components, can be used or not needs to be done. The inspection will consist in finding if the current foundation, or a modification of it, is able to resist the new actions that it will be subjected to or, in contrast, if it would need to be replaced for a brand new one. In such a case, the proper dimensioning of a new foundation will become necessary. In other words, the aim of this Thesis is to inspect how much larger the foundation needs to be in order to accommodate for the forces that the new wind turbine will subject it to.

Since the formulated problem can be found to be extremely broad, some more data is needed to narrow the scope of the problem and consequently of this Thesis. This narrowing will be based on evaluating the aim of the project on one specific site, and from there, derive conclusions. The selected site for the study corresponds to the Lillgrund Wind Farm, located in the South of Sweden, and owned by Vattenfall. More details on the wind farm are presented in the section dedicated, section 2.1.

1.3 Limitations

During the development of any study, one must always be aware of the limitations that surround the problem, and deal with them in order not to derive inadequate conclusions. For this Master Thesis, a quite strong generalization could be made, which at first sight could be an error, since results and conclusions from a specific case do not necessarily need to be applicable to all other cases. Therefore, a question arises: can one extrapolate the conclusions obtained from this project in order to apply them in any other case? This question will be tried to be answered within this Master Thesis sections.

Additionally, some assumptions must be made during the development of the Thesis, mainly due to the lack of background information in aspects like the wave heights, periods, winds and currents, or geotechnical surveillances. References to standards guidance will be used when data is not available or either not trustworthy.


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Furthermore, this Master Thesis deals with the theoretical definition of actions and loads at a general level, while sets proper values to calculate with mainly in what refers to the case study analysed exclusively, i.e. only for one specific site. Therefore, the generalisation aspect that was previously commented would need to be carefully assessed if procedures here explain were to be applied at other cases under different boundary conditions to the ones Lillgrund Wind Farm sets.

As well as that, reader should also be aware of a big aspect as actions co-directionality is. Due to timespan and simplicity constraints, only loads acting in the same direction are inspected in the development of this Master Thesis. This is considered by the author to be on the safe side and to represent the worst-case scenario, but it is definitely one of the limitations of this Master Thesis since no inspection of this assumption was possible to be made. Secondary effects of, e.g. waves acting in a different direction than wind, are not accounted for in this Thesis, and therefore results and conclusions derived from the performed analyses should only be used within the range of application of the developed calculations.

Moreover, an important issue regarding the level of cross-sectional analyses performed in the numerical simulations must be stated. For simplicity purposes, the material in the model has been assumed to be all formed by concrete, even though it is known that some parts of it are filled with ballast, either sand or gravel. Whether the type and level of stresses where these materials are in reality are found to be problematic, the affection of this definition will need to be assessed. For instance, the stresses in the dividing walls from the foundation’s slab could turn out to be badly captured by the model under this configuration. If troubles were found, specific models for these elements would need to be made or a more detailed model considering different materials could also be necessary.

Last but not least, another very important aspect to consider here is that the calculations are performed only under ultimate limit state (ULS) conditions. This means that no serviceability limit state or fatigue studies have been developed, but only those regarding the stability and structural safety of the foundations.

1.4 Rules and Regulations

For the development of this project, several different rules, regulations, standards, and recommendations are followed. Mainly, standards by DNV-GL (Det Norske Veritas – Germanischer Lloyd) are followed in what relates to dimensioning, loads, and other criteria. Also, some publications of the Eurocodes are used, and some other recommendations are also used. The complete list for standards used in the development of this Master Thesis is:

BS 8004:1986, Code of practice for Foundations, British Standards, September 1986, [30]

DNV-RP-C205, Environmental Conditions and Environmental Loads, October 2010, [31]

DNVGL-ST-0126, Support Structures for Wind Turbines, July 2018, [32]

DNV-OS-C502, Offshore Concrete Structures, October 2010, [33]

DNV-OS-J101, Design of Offshore Wind Turbine Structures, May 2014, [34]

EN 1990:2002, Eurocode – Basis of structural design, December 2005, [35]


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EN 1991-1-4:2005, Eurocode 1: Actions on structures - Part 1-4: General actions - Wind actions, April 2010, [36]

EN 1992-1-1, Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for buildings, [37]

EN 1993-1-1, Eurocode 3: Design of steel structures - Part 1-1: General rules and rules for buildings, [38]

IEC 61400-1, Wind Turbines – Part 1: Design Requirements, [39]

IEC 61400-12-1, Wind Turbines – Part 12-1: Power performance measurements of electricity producing wind turbines, [40]

ISO 19906 - Petroleum and natural gas industries — Arctic offshore structures, [41]

Recommendations for design of offshore foundations exposed to ice loads. Elforsk rapport 09:55, April 2009, [42]

Recomendaciones para Obras Marítimas, Recommendations for Maritime Works, 0.3-91, Waves. Annex I. Maritime Climate in the Spanish Coast, 1992, [43]

Recomendaciones para Obras Marítimas, Recommendations for Maritime Works, 0.5-0.5, Geotechnical recommendations for maritime and harbour works, November 2005, [44]

Shore Protection Manual, Volumes I-III, U.S. Army Coastal Engineering Research Center, 1975-1984, [45]

This list is also included within the references for guidance through the document read.

1.5 Thesis Outline

This first Chapter is been dedicated on introducing wind energy and basic layouts of foundations, while establishing the main goals and topics of the Thesis, while keeping an eye on the limitations that must be considered and the rules and regulations that must be followed.

Chapter 2 presents the literature study that has been done to perform the project, as well as setting the working procedure, in order to lay the groundwork to develop the correct methodology and working process. A brief description of the case study and its type of wind turbine foundation is made, and a comparison of market wind turbine models is made for the selection of the chosen one to perform the case study analysis with.

Chapter 3, consist of a description of the actions that will affect the structure, followed by a group of analytical procedures performed to dimension the foundation and check its stability due to three different failure modes. As well as that, a set of numerical simulations is carried out in ANSYS AQWA and ANSYS Mechanical to verify this dimensioning in terms of internal stresses and deformations of the foundations.

Chapter 4 contains all the results obtained from analyses and compares them in terms of feasibility. What is aimed to show at this point is the results from analytical and numerical


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calculations and a comparison of them. Some interpretations are done both for analytical and numerical results, as well as a brief overview is given for the results as a whole entity.

Chapter 5 is dedicated to the discussion of whether the results shown in Chapter 4 are logical by themselves and within each other, fact that would make the developed analysis robust in the methodology followed. Several statements are done based on the results obtained both from analytical and numerical analysis.

Chapter 6 shows an overview, drawing some conclusions that can be extracted from the developed work and aims to give some guidance for constructability and parameters to work with.

Chapter 7 finally gives some features for further research needs in aspects like the iterative process that could be necessary to perform to find the most suitable geometry in terms of sustainability, economy, and stability requirements.

References regarding literature and previous knowledge, regulations and standards, and useful websites’ links used in the development of the Thesis are given. Finally, some important annexed information is given in separate Appendices.


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2 Literature Study & Background Knowledge

What is aimed to be performed in this Master Thesis is to explain and follow the general procedures that need to be assessed for the general problem and based on them, a specific analysis for a specific case study is fully developed. With these purposes, research needs to be done on the specific case study one is analysing in order to be able to apply the developed methodology to its boundary conditions. As well as that, the selection of a specific wind turbine model that will replace the one on site turns essential so as to be able to derive the proper loads it will generate, e.g. weights and mainly wind loads. With this approach, the repeatability, reproducibility, and replicability of the methodology shown is guaranteed within the main aim of this Thesis, while detailed information and analysis are given by narrowing the scope on one single case.

Most of the information explained in this following section, Section 2.1, has been extracted from the reference “Technical description Lillgrund wind power plant”, [17], and its data is considered very useful for the development of this Master Thesis. It gives a detailed orientation in the magnitude orders that are being treated and in the external actions, that will remain undisturbed for the re-dimensioning that this Master Thesis aims to perform.

2.1 Description of the Case Study: the Lillgrund Wind Farm

The Lillgrund Wind Farm is located in the south of Sweden, close to Malmö and the Öresund Bridge, in the namesake strait. It is about 7 kilometres from the Swedish coast and 9 km from the Danish coast. The wind farm was commissioned in late 2007 and consists of 48 wind turbines of 2,3 MW each of them, made by Siemens Wind Power (SWT-2.3-93), which gives a total power generation capacity of 110 MW in design conditions.


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Figure 2.1. Lillgrund wind farm site layout. [17].

Lillgrund is the largest offshore wind farm in Sweden in terms of power generated, fact that makes possible the electricity supply of around 60.000 households in Sweden. Due to the predominant winds that occur in the Öresund, the site is a perfect place for the disposition of a wind farm. These winds are usually between 8 and 10 m/s in WSW or SW direction.

Figure 2.2. Lillgrund wind farm with the Öresund Bridge in the background. [51].

In what relates to the wind turbines foundations, they are made as gravity-based structures (GBS) or gravity-based foundations (GBF). This means that they remain in place and resist to the forces they are subjected to by their own weight. This also entails that they are usually massive structures that need to be carefully designed so that they are safe enough to withstand the external actions once they are placed on site. According to [5] and [7], three generations can be established for GBS over time, as can be seen in Figure 2.3.


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Figure 2.3. Classification for GBS types. [7].

In the specific case that concerns this project, the GBS was designed as a “large goblet with a great base” to provide the stability needed. Thus, it can be included within the 2nd generation that has just been mentioned. A sketch of the GBS cross-section can be found in Figure 2.4.

Figure 2.4. GBS cross-section sketch. Dimensions in mm. [16].


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As can be seen on the right-hand side of Figure 2.4, there is not only one design for the foundations, since the selected site for the wind farm construction is on varying water depths, varying from 5 to 9 metres, according to [17]. Thus, the design was decided to vary in its shaft height so that the total height of the GBS varied from 10300mm to 14300mm, and consequently ensuring the capacity of the structure to exceed the mean sea level (MSL). Both the base and most of the central hole are filled with gravel and sand ballast in order to increase the weight of the structure as much as possible and to put it down once in place.

Moreover, the foundation is placed on site by the previous development of an appropriate excavation to accommodate for the GBS. The excavation descends about 2,5 metres and once the GBS is placed on site, the surrounding area is re-filled with different materials to avoid scouring and maintain the structure assured on site. A more detailed description can be seen in Figure 2.5.

Figure 2.5. Excavation details for GBS accommodation. Dimensions in mm. [17].

On the other hand, the layout of the GBS is a regular hexagon in the base and has a circular shape in the upper part of the so-called “goblet”, as can be seen in Figure 2.6. The maximum dimension of this base hexagon is of 19 metres and it is internally divided into 6 different cells to allocate for the ballast once put in place. Each cell has a dedicated area of approximately 25 square metres.


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Figure 2.6. Layout for the Lillgrund GBS bottom slab. Dimensions in mm. [17].

In Table 2.1, extracted from [17], the weights for the foundation itself and the ballast needed to fill in the cells can be extracted. This will give an idea of the magnitude order of the weights and volumes that are being treated.

Table 2.1. Weights for the Lillgrund GBS units and ballast fillings. Reproduction from [17].

Type Weight without ballast

(t) Ballast weight

(t) Total Weight

(t) 1 1299 803 2102 2 1318 822 2140 3 1337 841 2178 4 1356 860 2216 5 1375 879 2254


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2.2 Wind turbine selection

Nowadays, the 2,3 MW from the Lillgrund wind turbines are small compared to the products that are being sold in the marketplace. Powers up to 6, 8, 10 or even 12 MW are being made available to buyers by the companies that manufacture the wind turbines. Companies like Siemens Gamesa, General Electric, Vestas or Goldwind are rapidly improving their designs due to the increasing potential that wind power is showing in the last years. Therefore, a comparison between the different available products on the marketplace needs to be done at this point in order to base the selection of a new wind turbine. The following wind turbines are selected from among the ones available:

Table 2.2. Wind turbines comparison. [52], [53], [54], [55].

Model Name Company Installed

power (MW)

Rotor diameter

(m)

Power Density

(m2/kW)

Power Density (W/m2)

SWT 2.3-93 Siemens Wind Power 2,3 93 2,95 338,59 V117-4.2 MW MHI Vestas 4,2 117 2,56 390,65 SWT-6.0-154 Siemens Gamesa 6,0 154 3,10 322,12

Haliade 150-6 MW General Electric 6,0 150 2,95 339,53 GW154-6.7 MW Goldwind 6,7 154 2,78 359,70

SWT-7.0-154 Siemens Gamesa 7,0 154 2,66 375,81 GW175-8.0 MW Goldwind 8,0 175 3,01 332,60 SG 8.0-167 DD Siemens Gamesa 8,0 167 2,74 365,23 V164-10.0 MW MHI Vestas 10,0 164 2,11 473,39

Haliade-X General Electric 12,0 220 3,17 315,68

The first wind turbine shown in the table is the current one for the Lillgrund wind farm.

As can be seen, the wind turbines are ordered based on the installed power they are able to produce. In general terms, the higher the installed power, the larger the rotor diameter and the rotor area is. Nevertheless, there are some variations since, for example, the SG 8.0-167 DD from Siemens Gamesa takes less rotor square meters to produce de same amount of energy (2,74m2/kW) than the one just above it, GW175-8.0 MW from Goldwind, that takes 3,01m2/kW. In these terms, the most efficient wind turbine is the V164-10.0 MW from MHI Vestas, producing 1 kW every 2,11m2 of rotor area.

Moreover, if one compares the power density in terms of power produced per area (W/m2) for each wind turbine design, the conclusions are the same. It can be seen that, again, the most efficient wind turbine is the V164-10.0 MW from MHI Vestas with 473,39 W/m2, more than a 20% more power density than the V117-4.2 MW, also from MHI Vestas, and 50% more than the Haliade-X from General Electric. Also, comparing these values with the ones from the current wind turbine at Lillgrund, the SWT-2.3-93 from Siemens Wind Power, the power density in m2/kW is almost 30% lower and in terms of W/m2 it represents an increase of almost 40%.

Therefore, it seems reasonable that, from among the ones shown for making the decision, the one selected for this degree project should be the V164.10.0 MW from MHI Vestas. Some design parameters for this wind turbine are included in Table 2.3 since they will be used for calculations.


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It is now stated that, apart from the power generated, there is no difference in dimensions, weights, or parameters between the MHI Vestas V164 wind turbines for 8.0, 9.5 or 10.0 MW. According to company’s website, the increase in the power generated comes from modifications in the generator and other aspects out of the scope of this Thesis.

Table 2.3. Wind turbine design parameters. [2].

Basic parameters for wind turbine classes, is given in Table 2.4, as it will be of importance for the following sections. As can be seen in Table 2.4, the wind class for V164-10.0 MW is Class S, as it is almost rule for all offshore wind turbines.

Table 2.4. Basic parameters for wind turbine classes. [39].*

*The parameter Iref stands for the expected value of turbulence intensity at 15 m/s, and it is a non-dimensional parameter.


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3 Methodology For a good investigation to be developed, a strong and meticulous work methodology needs to be set up. Hence, for this study the first step to be taken is a proper study of the literature and standards available, i.e. all information one can find and use for the purposes of the project. In the following subsections of this chapter, the reader will find the definition of the actions present on the structure due to the different surrounding elements that act on it. Once the actions are thoroughly described, the correspondent design loads, and their combinations are performed so as to look for the worst-case scenarios under which the foundation is designed. Based on all this information, the dimensioning of the foundation is analytically performed and afterwards numerically simulated in ANSYS AQWA and ANSYS Mechanical in the aim of verifying how the dimensioned structure behaves under the design loads.

3.1 Actions on the structure

Firstly, and in order to properly describe all the loads that will affect the foundation, a scheme is shown in Figure 3.1 for the actions that mainly act on an offshore wind turbine and on its foundation. Subindex “D” in actions definition stands for Design Conditions. The first and most obvious one is the weight of the wind turbine and the tower that sustains it, followed by the wind and wave loads, either acting on the wind turbine or directly on the GBS.

Typically, having selected the wind turbine, it is necessary to dimension the tower so as to accommodate for the wind loads that it is going to be subjected to, taking into account that generally the designer of the wind turbine does not establish a specific hub height, but gives a range of action with a maximum and a minimum height. In the specific case for MHI Vestas V164-10.0 MW, it is yet specified in [14] that a hub height of 107 metres is given as reference. Thus, it is going to be the design hub height used for this project. Comments on each of the actions on the structure and their shape are done in their respective sub-sections.

It is important to state here that mostly all the procedures given here are based on the DNV-OS-J101 guidelines, [34], unless stated the contrary. It is also important to state that all the calculations are performed as if no shadow effect or other turbulences apply on the wind turbine due to proximity to other wind turbine, being therefore on the safe side in the dimensioning.


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Figure 3.1. External actions on a generic offshore wind turbine. Not to scale.

3.1.1 Wind actions

Wind is essentially the main action on this kind of offshore structures. Hence, it is crucial that wind characterisation is properly done in order to be accurate and precise in the design. [34] and [39] have specific sections dedicated to wind climate and wind conditions and are the guidance for this section. Denominations given in [39] are followed for what refers to wind actions, meaning that the variable V stands for winds.

Wind characterisation

The first step in this characterisation is the definition of the present winds in the site of study. According to [39], it is established that “the mean value of the wind speed over a time period of 10 min shall be assumed to follow a Rayleigh distribution at hub height” given by

( )2

1 exp2

hubR hub

ave

VP V

Vπ

= − −

(3.1)


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Where Vhub stands for the 10-minute mean windspeed at hub height and Vave for the average mean wind speed. This speed shall be chosen as

0,2ave refV V= (3.2)

This means that the wind speed at hub height is assumed to exceed a certain value with a certain probability. This way of expressing environmental variables is very common and will be for guidance in this study.

Figure 3.2. Rayleigh distribution for wind speed ant hub height.

There is a wide range of possibilities of representing the windspeeds profiles in an area. First, the Normal Wind Profile (NWP) is defined, as established in [34], a power law profile can be assumed, as

( ) ( )10z

V z V HH

α =

(3.3)

Where V(z) stands for the wind speed at height z and V10 is the 10-minute mean wind speed at height H, which must both be known values. This way of referring to wind speed as V10 is equivalent to denoting wind speed at hub height, Vhub, as in [37]. Referring at this point to [31], several values depending on the terrain roughness are given for the α exponent, the value of this exponent is defined. The table including those values is shown as Table 3.1.

0

0,2

0,4

0,6

0,8

1

1,2

0 5 10 15 20 25 30 35 40

Pr(

Vhu

b>x)

Vhub (m/s)


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Table 3.1. Terrain roughness parameter z0 and power-law exponent α. [31].

In the case for an offshore wind farm, depending on whether the site is close or far from coast, the value for the α exponent could increase a little from the 0,12 that appears in the table to 0,14, as it is suggested in [34].

On the other hand, data about the existing winds on site is needed at this point. Typically, this entails the performance of field studies or the existence of extensive registers of the wind speeds and directions in the area. Unfortunately, the time for this Thesis performance was limited so no field studies were possible. Thus, it was necessary to search for this information within the available tools. Considerations in this way regarding the Case Study are made in Section 3.2.

Furthermore, the Normal Turbulence Model (NTM) shall also apply. This model establishes a standard deviation for a given hub height wind speed, as

( )1 0,75 ; =5,6 m/sref hubI V b bσ = + (3.4)

Apart from the wind speed at hub height, the turbulence intensity Iref parameter appears in the formula in Eq. (3.4).

Moreover, the return period concept must be stated at this moment. The return period, Tr, expresses the probability of occurrence or exceedance of a certain event in a given time, e.g. the probability that a 10-minute wind speed higher than the mean value occurs over one year. Usually, these kinds of events as winds, waves or others that need to be studied under this probabilistic approach. Therefore, and according to [34], the Extreme Wind Speed Model (EWM) is applicable here, calculating for 50 years return period. It is established that the wind speed at hub for this return period, Uhub,50-yr, should be calculated as


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,50 10, ,501,4hub yr hub yrV V− −= ⋅ (3.5)

Where V10,hub,50-yr stands for the 10-minute mean windspeed for a 50 years return period.

As well as that, the extreme wind speed at the hub height with a return period of one year shall be calculated as

,1 ,500,8hub yr hub yrV V− −= ⋅ (3.6)

The 10-minute mean wind speed at the hub height with a return period of one year shall be calculated as

10, ,1 10, ,500,8hub yr hub yrV V− −= ⋅ (3.7)

Briefly, the standard deviation for the EWM is defined in [34] as

, 10,0,11U c hubVσ = ⋅ (3.8)

The Extreme Operating Gust (EOG) model establishes a wind speed for gusts that may appear, according to the relationship

( ) ,,1 10,1

3,3min 1,35 ;

1 0,1U c

gust hub yr hubV V V D

σ−

= − + Λ

(3.9)

Where Λ1 is the longitudinal turbulence scale parameter, being defined as in Eq. (3.10), and D is the rotor diameter.

1

0,7 6042 60

z z mz m≤

Λ = ≥ (3.10)

Under these circumstances of the EOG model, the wind speed profile can be defined as a function of height and time, as


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( ) ( )

( )

3 20,37 sin 1 cos for 0

,

otherwise

gust

t tV z V t T

T TV z t

V z

π π − ⋅ − ≤ ≤ =

(3.11)

Where V(z) corresponds to the windspeed profile for the NWP. The main purpose of the EOG model is to account for extreme gusts that may occur and that may overcome the wind speeds for the EWM in a given time. It is considered that the period of occurrence for these kinds of events is as T=10,5s. The extreme operating gust graph is shown in Figure 3.3 for the specific case of this study.

Figure 3.3. Extreme Operating Gust wind speed at hub height.

Furthermore, the Extreme Turbulence Model (ETM) combines the NWP with a turbulent wind speed with a standard deviation as

, 0,072 3 4 10 ; 2 m/save hub

U c ref

V Vc I c

c cσ

= ⋅ ⋅ + ⋅ − + =

(3.12)

The Extreme Direction Change (EDC) model establishes the angle of variation of the wind according to the rule

( ),

10, 1

4arctan1 0,1

U ce

hubV D

σθ = ±

+ Λ (3.13)

Given θe, the direction change over time can be expressed as

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12

Win

d sp

eed

(m/s

)

Time (s)


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( )

0º 0

0,5 1 cos 0e

e

t

tt t T

T

t T

πθ θ

θ


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Figure 3.5. Extreme coherent gust amplitude at hub height.

The direction change for this model has the same formulation as EDC, by only changing the parameter θe for θcg in Eq. (3.14), that has a definition as

( )hub

hub ref

180º for V


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Figure 3.6. Extreme horizontal wind shear.

There is also a Reduced Wind Speed Model (RWM) that uses the extreme wind speed from EWM, reduced by a factor ψ usually given a value of 0,79, to be used in combination with the extreme wave height (EWH).

Rotor load

In an offshore wind turbine, the wind is considered to act both on the rotor and on the tower. First, the required procedure to find the rotor load is presented.

The main equation that governs the phenomena is an interpretation of a pressure force and can be written as

( )2 212R T

F R V Cρ π λ= ⋅ ⋅ ⋅ ⋅ (3.18)

Where ρ stands for the air density (1,225 kg/m3 according to [37]), R is the rotor radius, V is the wind speed at hub height and CT is the thrust coefficient. This coefficient is the factor that relates the thrust force that the wind turbine generates against the wind, with the theoretical thrust that acts on the surface the wind turbine generates when turning. If it were a solid surface, the value for CT would obviously be 1 since no air can pass by. Nevertheless, and as the wind passes through the surface generated by the wind turbine blades, some “losses” are to be accounted for with this coefficient. It can be though to calculate this coefficient from the kinetic properties of the wind turbine, and due to the lack of information in these terms, an assumption is going to be made.

The thrust coefficient varies with the wind speed acting on the turbine, between 0 and 1 as it is a relation from the theoretical with the actual thrust force. A typical shape for the coefficient is as shown in Figure 3.7, decreasing while the wind speed increases and the power generated does so. According to [4], it is likely that the thrust coefficient asymptotically decreases until it reaches a threshold value of 0,05, especially for wind speeds equal or higher than the cut-out wind speed, Vout. Therefore, it seems logical to assume that this is going to be accomplished in this case, and

0

2

4

6

8

10

12

14

16

0 2 4 6 8 10 12

Win

d sh

ear

(m/s

)

Time (s)

V(ymax,Hhub,t)+ V(ymax,Hhub,t)-


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hence is reasonable to consider CT as 0,05 for the design conditions if wind speed is sufficiently high.

Figure 3.7. Power curve and Thrust coefficient for V164-8.0MW. [4].

Under these circumstances, the force acting on the rotor is defined once the speed acting on it is. Depending on the load case considered, this value shall vary from among the ones in Table 3.9.

Tower load

Similarly, as for the rotor, the tower of the wind turbine will suffer the action of a wind load in terms of a pressure over a surface. The main equation that governs the phenomena in this case can be written as

( ) ( ) ( )21 Re2 D

f z D V z Cρ= ⋅ ⋅ ⋅ (3.19)

Where the force, f, is a function of the height since the wind speed is so too. In this case it is an actual surface the one the wind acts to, and consequently the value of the coefficient that goes along with the equation must be different. It is known as the drag coefficient and it has been well studied over decades for a lot of people dedicated to aerodynamics. One of the most important studies of this parameter was done by S. F. Hoerner in “Fluid-Dynamic Drag: Practical Information on Aerodynamic Drag and Hydrodynamic Resistance” in 1965, [13]. There, it is specified the drag coefficient for a circular cylinder on an air flow normal to its axis as a function of Reynolds number (see Figure 3.8). This parameter is well-known over the world of engineering, and it is expressed as:

RevDρµ

= (3.20)

Where ρ is the density of the fluid, in this case air, v is the speed in that fluid, D is the diameter of the analysed element and μ is the dynamic viscosity, being of 0,0000174 Pa*s for the air at

0,000,100,200,300,400,500,600,700,800,901,00

0

1

2

3

4

5

6

7

8

9

0 5 10 15 20 25 30

Thr

ust

coef

ficie

nt, C

T

Pow

er (

MW

)

Wind speed (m/s)Power (MW) Thrust coef, CT (-)


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25ºC. Knowing the diameter of the tower and the wind speed acting on the wind turbine, the Reynolds number can be found and with it, from graph in Figure 3.8, the value of the drag coefficient for the force distribution on the tower can then be defined.

Figure 3.8. Drag coefficient for a circular cylinder as a function of the Reynolds number. [13].

3.1.2 Wind turbine self-weight

Once the wind characterisation has been set up, the works in the methodology can go on by the definition of the turbine weights coming to the foundation, both the one from the actual wind turbine, and the one coming from the tower that supports it. Typically values for the first aspect can be extracted from catalogues, so not a lot of description on how to derive their value needs to be done.

On the other hand, the obtainment of the tower weight is not as simple as looking in the wind turbine catalogue, mainly because the hub height is not fixed but a design decision. As said before, once the hub height is fixed, the problem can be solved. Based on this consideration and on the wind considerations, a pre-dimensioning on the tower dimensions needs to be done so as to account for its weight.

Among other important phenomena such as compressive stress, buckling or fatigue, the tower of a wind turbine is fundamentally subjected to bending effects. Thus, it needs to be sufficiently stiff to sustain the bending moments generated by the wind load. Considering the tower as a cantilever, it is subjected to a punctual load on its extreme and a distributed load all along its length, being the rotor load and tower load explained in previous sections. Hence, and simplifying the distributed load as a uniformly distributed load for the wind speed at hub height in all the beam’s length, the bending moment acting on the embedding of the beam can be written as

( )2

2RF f RH

M M M F H f z= + = ⋅ + ⋅ (3.21)

With this said, and considering the tower is completely built of steel as a circular hollow section with a certain yield strength fy, the following expression can be set


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y

M

f M NW Aγ

≥ ± (3.22)

Where M stands for the bending moment, W for the elastic section modulus, N is the axial force, A is the cross-sectional area and γM is the safety factor for the material properties, usually 1,00 for steel. In this equation, all parameters are either known or dependent on the tower cross-sectional properties, i.e. diameter and thickness. Setting this thickness with a certain value, and developing the equation as a function of the diameter, the expression shows as

( )( )( )( )( )( )

222 2 2 2

4 24 2

1 12

2 2 2 4

2 232 4

D T turbine sy

M

HDV C R V C H P D D t Hf

D D t D D tD

πρ ρπ γ

π πγ

⋅ + ⋅ + − − ⋅ ⋅≥ ±

− − − − (3.23)

In Eq. (3.23) all values are known except for the diameter. Therefore, it can be extracted and consequently the tower weight can be calculated. The only assumption that has been done here is that the tower has the same cross-section in its whole length. This is not realistic since typically the shape of these towers is a cone trunk, but as a pre-dimensioning this calculation gives a sufficiently approximated magnitude order from which one can set the dimensions of her tower and then calculate its weight and check its resistance.

3.1.3 Wave actions

For all offshore structures, one of the most crucial things to keep an eye on is the maritime climate, i.e. the effects that waves and their energy shall have on the structures one wants to build. These effects depend on several undulatory parameters such as wavelength, wave period, wave heights, depth, return periods and so on. In this section it is aimed to thoroughly define all these waves’ characteristics in order to evaluate their effects on the structure that is being dimensioned.

To do so, the very first step one needs to take is the acquisition of good data. Therefore, one needs to look for wave properties information in trustworthy sources such as national institutes or government platforms. As an example, all data regarding oceanography in Spain is of free access and can be found in the official site for the Harbours Estate Administration, “Puertos del Estado”. For Sweden seas, the Swedish Meteorological and Hydrological Institute, “Sveriges Meteorologiska och Hydrologiska Institut”, abbreviated SMHI, is the official organism dedicated to these topics. Depending on the country where the study is being developed, one will need to search for this information in one place or another, not always being free-accessible. Fortunately, the SMHI resources are open data, [48], and the development of studies in Sweden is hence easily feasible.


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Available data

For waves’ characterisation data for wave heights and periods need to be available. From SMHI, one can select several sources of data depending on the buoy selected. One should choose a buoy that is as close as possible to the site where she wants to place the structures, in order to have data that is representative enough of the site conditions one is studying. Values for, at least, significant wave heights, peak periods or mean periods, directionality and maximum wave height would be needed for a good derivation of wave actions based on empirical data.

Waves theory

For the waves’ analysis, the guidelines from [32] are going to be followed, as done in wind characterisation, as well as other rules or regulations that will be of guidance in specific cases. The [34] establishes a 10 years period of statistical data for reliable conclusions to be derived from them, but it is a criterion of minimums, and therefore the longer series, the better conclusions.

First, a definition of the main characteristic parameters of a wave needs to be done. Waves are defined based on their period, T, their wavelength, L, the wave height, H and, in case of sea waves, the water depth, d. A scheme of this parameters can be seen in Figure 3.9.

Figure 3.9. Waves parameters definition.

Wavelength and period are measured as the same dimension since time cannot be shown in a graph like Figure 3.9 and also as a result of the relation between those two parameters, that will be explained in the next lines. Another characterisation that has to be made at this point regards the so-called platform zoning. It is based on the platform zoning parameter from Carter’s geometric trio. These 3 parameters are defined as

Break indicator

Steepness parameter

Platform zoning parameter

HdHLdL

δ

ξ

µ

= = =

(3.24)


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Dealing with μ, ranges can be established for the delimitation of the platform, as in Figure 3.10. The ranges are set where μ=d/L is bigger than 1/2, between 1/2 and 1/25, or smaller than 1/25, considering offshore water depths, transition water depths, or shallow water depths, respectively. The value 1/25 is sometimes varied to 1/20. This consideration has conditions on aspects such as the waves shape in their break behaviours (see Figure 3.11).

Figure 3.10. Layout of Platform zoning according to μ parameter.

Figure 3.11. Cross-section of Platform zoning according to μ parameter. Byron Inouye, U. of Hawaii.

What needs to be stated at this point is the definition of the wavelength, that is based on the wave period as

2

0

2

1 for offshore water conditions,

2 22 1 1

tanh for transition water conditions, < < 2 25 2

1 for shallow water conditions,

25

gT dL

LgT d d

LL L

dL CT

L

ππ

π

= >

=

=


P a g e 31 | 157

of shallow water conditions. If at offshore, no perturbation in the wave profile will exist, and therefore will not reach the structure as a perturbated wave. If in transition, the undulatory profile starts to transform from a circle into an ellipse, broader when closer to the coast. Finally, when in shallow waters, the wave brakes depending on the sea bottom steepness (see studies from Iribarren, R., on types of wave breaking for more information).

Waves can be said to follow probability distributions. Generally, it can be assumed that for significant wave heights, a tri-parametric Weibull distribution rules the phenomenon. Its probabilistic distribution is as

( ) expC

R S

x BP H x

A

− ≥ = −

(3.26)

Where A, B and C are the 3 parameters that define the distribution, known as scale, location, and shape parameters, respectively. Defined this function, it is possible to calculate the probability of a certain significant wave height to occur in a certain time, e.g. being A=2, B=0 and C=2, having an HS of 2 meters would give a probability of occurrence of PR=0,368, i.e. a return period of 1/PR=2,7 years. This very simple example serves to state how the working procedure goes on.

Having a wide statistic sample of significant wave heights is a powerful thing to be able to derive the values for A, B and C. The analytical procedure gives a regression line and it is easy to proof and it is included in Appendix C. The conclusions of those process are as

( ) ( )1

ln ln ln ln1 R

C x B C A Y mX nP x

= − − ↔ = − −

(3.27)

( )( )

1ln ln

1

ln

ln

R

nC

YP x

X x Bm C

n C A A e−

= −

= −

= = → =

(3.28)

From these conditions, A and C can be found. The location parameter B needs to be set as 0 in the beginning of the calculations for the regression line and then the formula can be adjusted, depending on the R2 factor, in the aim of maximizing it as much as possible by changing the value of B. This can be done in software for numerical analysis such as Excel or MATLAB with relatively easy procedures. These procedures can be set to recalculate also both A and C to refine them, even though variations will be small. Thus, the 3 parameters of the Weibull distribution will be defined and the significant wave heights for the desired return periods can be found.


P a g e 32 | 157

Figure 3.12. Tri-parametric Weibull cumulative distribution function for significant wave height HS.

With this said, the definition of the other most important parameter in the waves’ theory can be stated: the period. In terms of [34], the peak period of the waves is used, TP, and it is assumed to follow a lognormal distribution, whose accumulated probability can be expressed as

( ) ( )ln1 12 2 2P

xT x erf

µσ

−Φ ≥ = +

(3.29)

Where the erf expression stands for the error function, and μ and σ are the mean value and standard deviation of the lognormal distribution. These two parameters can be extracted from the ones for a normal distribution according to the rules

2

2 2

22

2

ln

ln 1

x

x x

x

x

µµ

µ σ

µσ

σ

=

+

= +

(3.30)

Where μx and σx stand for the mean value and standard deviation of the normal distribution, N(μx,σx), respectively.

As the SMHI, [48], series are in terms of mean periods, TM, a conversion from those into peak periods, TP, needs to be done. According to [43] and in absence of more rules, it is going to be assumed that the rules for the Spanish coast are applicable in terms of the conversion from mean periods to peak periods. In [43] it is stated that, depending on the part of the Spanish coast, the ratio between TP and TM varies from 1,12 to 1,35, being 1,2 the most common value. Hence, this is the value that is going to be considered in this Thesis in the absence of more detailed rules.

0,00

0,20

0,40

0,60

0,80

1,00

1,20

0,0 0,5 1,0 1,5 2,0 2,5 3,0

Pr(

HS>

x)

HS (m)


P a g e 33 | 157

Then, from the series from SMHI, [48], for peak periods to be found the conversion from mean periods needs to be performed. Then, one needs to find the mean value and standard deviation for that series and convert it to the lognormal distribution according to Eq. (3.30). One will then be able to describe the probability cumulative distribution for the peak periods completely.

Figure 3.13. Lognormal Probability Function for Peak Periods.

Last but not least, the maximum wave height can also be characterised based in [34] “as a constant factor times HS”, based on the proposal by Longuet-Higgins. The equation is as

max,

1 0,2886ln

2 2lnmean SH H N

N

= +

(3.31)

Where N is the ratio between the duration TS of the sea state and the mean zero-upcrossing period TZ of the waves. If one knows the duration of the expected sea state, or defines it, and from the HS is able to obtain the mean period, the number of active waves N is defined and the maximum wave height is so. In contrast, and as from SMHI, [48], data for Hmax can be extracted, it is logical to use those series to evaluate the value of the maximum wave height. Or either perform the analysis both ways in order to compare the obtained results as a wat of checking the method and increasing its robustness and internal validity of the procedures monitored.

Waves break

Another important aspect on the wave’s characterisation and wave climate on offshore structures dimensioning is the break of waves, i.e. the evaluation of whether the sinusoidal wave profile in Figure 3.9 is disturbed from that shape and brakes, or not. Generally, the assess of whether the wave breaks itself or not depends at some point of the water depth as

b bH dγ= (3.32)

0,00

0,20

0,40

0,60

0,80

1,00

1,20

2,50 2,75 3,00 3,25 3,50 3,75 4,00

Φ(T

p>x)

Tp (s)


P a g e 34 | 157

Where Hb represents the broken wave height, γb is the breaking factor and d, the water depth. A huge diversity of studies has been done on the definition of this broken wave height and the evaluation of the wave breaking, see [27] for the definition of different criteria. Here, the McCowan criterion is followed as it is the most extended one and the broader one in terms of applicability, being as well the one used in [34]. McCowan states that the value for the breaking factor shall be equal to 0,78, according to [22] & [23]. Therefore, this is the assessment that will be asked for fulfilment in the present Thesis development. Goda definition according to [27] will also be kept in mind in case needed. (see Eq. (3.61)).

Return periods considerations

As established in DNV-OS-J101, [34], in the subsection dedicated to wave modeling, it is stated that the most usual return periods for calculations regarding the significant wave height and consequently the design wave height HD, are either 50 or 100 years. The associated probability to those return periods is defined as (1–1/TR), and therefore the dichotomy turns out to be between a probability of non-occurrence of 0,98 or 0,99, so the difference between the outputs should not be very different (ratio HS,100/HS,50 approximately equal to 1,04-1,05 for certain parts of the Northern Sea). Therefore, and as the difference should not be high, a return period of 50 years is considered sufficient for the definition of the so-called maximum significant wave height associated to a certain wave return period, according to [34]. A 3-hour sea state in one year is considered and hence the number of active waves is set as 2920 according to the DNV regulation. The probability of non-exceedance for a certain significant wave height can be expressed, according to Eq. (3.26) as

( ) ( )1 1 expS

C

H S R S

x BF H x P H x

A

− ≤ = − ≥ = − −

(3.33)

Moreover, the probability of non-exceedance for the maximum significant wave height over one year can be linked to the significant’s one as

( ) ( ),max,1S year S

N

H S H SF H x F H x− ≤ = ≤ (3.34)

Where N is the number of active waves for the calculus sea state, i.e. 2920. From there, the significant wave height for the design return period can be set as

,max,1

1

,

11

R S yearS T HR

H FT−

−

= −

(3.35)

Meaning that the significant wave height with return period TR is the significant wave height whose probability of exceedance in one year is 1/TR, [34]. This can be rewritten as


P a g e 35 | 157

( ), ,1 expR RC

R S T S TR

x BP H x H

T A

− ≥ = = − →

(3.36)

From here, the significant wave height for a design return period (in this case 50 years) can be derived.

Design sea states and wave heights

As a result of previous sections, definition of the sea states conditions and the associated significant wave heights design combinations is developed so as to assess their corresponding load combinations.

The Normal Sea State (NSS) is defined by a significant wave height, a peak period and a wave’s direction, while associated with the mean wind speed, being the 10-minute mean wind speed U10. This state will be used for ULS and FLS. As the HS,NSS and its associated peak period can be known based on their probability distributions, as well as values for U10 defined in the section dedicated, all parameters for this sea state are defined.

The Normal Wave Height (NWH) essentially defines it wave height as the NSS does, HNWH=HS,NSS, coinciding with the U10 too. The main variation from NSS comes when in application in deep waters, but as this will in no case be applied in our study, only one of these sea states is considered as the Normal Sea State.

Moreover, a Severe Sea State (SSS) is established, where its significant wave height HS,SSS and its 10-minute mean wind speed are defined as the 50-years return period ones. This state is to be used for load combinations on ULS and during the wind turbine power production.

Additionally, the Severe Wave Height (SWH) HSWH is characterised as the HS for 50 years and the U10 for 50 years load combination, combined with the different normal wind conditions that can exist during power production for ULS calculations. Again, and as NWH, it is defined for deep waters conditions with a specific periods range and therefore will not be applied in this Thesis. SSS will be considered as the sea state for ULS and power production combination instead.

Also, the Extreme Sea State (ESS) is applicable here and is defined by significant wave heights of both 50- and 1-year return periods, whichever is more conditional for ULS, associated with their correspondent peak periods. No wind actions are defined for this sea state to be combined.

The Extreme Wave Height (EWH) HEWH is defined as the HS,ESS for the relevant return period, i.e. 50 years. As the previous Wave Heights, its application regards to deep waters with peak periods in a certain range and therefore only ESS will be assessed here.

Finally, the Reduced Wave Height (RWH) HRWH will be assessed as a wave height to be used in combination with the extreme wind speed (EWS). It can be reduced with a ψ factor which value has to be less than the unit. This factor is in practice defined as


P a g e 36 | 157

,5

,50

1S yr

S yr

H

Hψ −

−

= < (3.37)

For all Wave Height states, a waves period lower limit is stated as

134,5 tanh0,78

d HT

g d− >

(3.38)

This inferior limitation is established with regard to the breaking wave phenomenon that was explained before, and the McCowan criterion is applied as can be sensed from the 0,78d factor inside the square root.

3.1.4 Currents actions

Sea currents need to be considered as part of the effects on any sea structure. Currents are sea water movements result of wind effects and tidal variations, among others. Therefore, they are defined as a summation of the effects generated by wind, and the ones generated by the tidal changes, and represented by their respective velocities and still water level.

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