Master of Science Thesis

KTH School of Industrial Engineering and Management

Energy Technology TRITA-ITM-EX 2020:558

Division of Heat & Power

SE-100 44 STOCKHOLM

Floating Offshore Wind Turbines:

Mooring System Optimization for

LCOE Reduction

Florian Thierry Stephan CASTILLO

Master of Science Thesis

TRITA-ITM-EX 2020:558

Floating Offshore Wind Turbines:

Mooring System Optimization

for LCOE Reduction

Florian Thierry Stephan Castillo

Approved

2020-10-23

Examiner

Miroslav Petrov - KTH/ITM/EGI

Supervisor at KTH

Miroslav Petrov

Commissioner

INNOSEA - COREWIND

Supervisor at INNOSEA

Valentin Arramounet

Abstract

Offshore wind has a large potential in terms of electricity production and is becoming an important focus

of interest for massive expansion of wind power.

While encountering harsh environmental conditions and facing challenges in deployment and maintenance,

offshore wind turbines benefit a lot from higher and more regular wind speeds if compared to conventional

onshore wind turbine sites. Floating offshore wind turbines (FOWT) in deep waters offer the possibility to

increase the accessibility and unleash an enormous resource base by cost-competitive solutions further away

from the shore. However, associated costs are still relatively high compared to other sources of energy.

These costs could be reduced by developing technological breakthroughs and improving design processes.

The work presented in this report is part of the H2020 EU project COREWIND, aiming to reduce FOWT

costs by optimizing the mooring system technology and by introducing dynamic moor cable solutions. The

main objective of this study in particular is to develop an optimization tool for the design of a cost-effective

and reliable mooring system for floating offshore wind turbines.

The scope of the study implies the development of an optimization strategy, involving Isight - a Dassault

System software used for the analysis. The work also involves OrcaFlex, a finite-element software developed

by Orcina, applied in dynamic analysis methods. A Python-based code was created to realize the coupling

between the two software tools. OrcaFlex simulation models were built for two test cases provided by the

project partners, validation of these models was performed based on results obtained using FAST.

Finally, results obtained for a case study using one floater and one location of the COREWIND project are

also presented and analyzed. The case study involves the development of a mooring system using the hereby

validated optimization tool; and is testing its integrity on critical design load cases. The work has shown how

an optimization tool could be constructed and applied to improve design process and reduce costs.

SAMMANFATTNING

Havsbaserad vindkraft har en stor potential när det gäller elproduktion och intresset för dess utveckling

växer enormt för att kunna möjliggöra en enorm expansion av ren förnyelsebar energiproduktion.

Samtidigt som havsbaserade vindturbiner stöter på tuffa miljöförhållanden och möter utmaningar vid

utbyggnad och underhåll, de jämna och pålitliga vindresurserna till havs är en stor fördel som kan tas tillvara.

Ju längre fjärran från kusten desto högre och mer regelbundna vindhastigheterna blir jämfört med

vindkraftverk på land, samtidigt som havsgrunden blir djupare och svårare för turbinbyggnad. Flytande

havsbaserade vindkraftverk (Floating Offshore Wind Turbines, FOWT) i djupa vatten ger möjlighet att öka

tillgängligheten och frigöra en enorm resursbas genom kostnadseffektiva lösningar längre ut till havs. De

tillhörande kostnaderna är dock fortfarande relativt höga jämfört med andra energikällor. Dessa kostnader

kan minskas genom vidareutvecklingen av tekniska genombrott och förbättrade designprocesser.

Examensarbetet härmed är en del av H2020 EU-projektet COREWIND, som syftar till att minska FOWT-

kostnaderna genom optimering av förtöjningssystemstekniken och genom införandet av dynamiska

förtöjningslösningar. I synnerhet, det huvudsakliga målet för denna studie är att utveckla ett

optimeringsverktyg för design av kostnadseffektiva och pålitliga ankarsystem för flytande havsbaserade

vindkraftverk.

Studiens omfattning inkluderar utvecklingen av en optimeringsstrategi som involverar Isight – en mjukvara

från Dassault Systems som använts för analysen. Arbetet involverar också OrcaFlex, en programvara för

finite element analys som utvecklats av Orcina, tillämpad i dynamiska analysmetoder. En Python-baserad

kod skapades för att förverkliga kopplingen mellan de två programvaruverktygen. OrcaFlex-

simuleringsmodeller byggdes för två testfall, validering av dessa modeller utfördes baserat på resultat

erhållna med hjälp av FAST.

Slutligen presenteras och analyseras resultat som erhållits för en fallstudie med en flottör och en särskild

position för COREWIND-projektet. Fallstudien involverar utvecklingen av ett förtöjningssystem med det

härmed validerade optimeringsverktyget; och testar dess integritet i kritiska belastningsförhållanden. Arbetet

har visat hur ett optimeringsverktyg kan konstrueras och tillämpas för att förbättra designprocessen och

minska kostnaderna.

2

Contents List of Figures ........................................................................................................................................... 4

List of Tables ............................................................................................................................................ 5

Acknowledgments ................................................................................................................................... 7

1. Introduction ..................................................................................................................................... 7

2. State of the art ................................................................................................................................ 9

2.1. Floating foundations................................................................................................................ 9

2.2. Station keeping ...................................................................................................................... 11

2.2.1. Configuration ................................................................................................................. 11

2.2.2. Components .................................................................................................................. 13

2.3. Costs analysis ......................................................................................................................... 17

2.3.1. Generalities ................................................................................................................... 17

2.3.2. Mooring systems costs estimation ............................................................................... 18

3. Theoretical aspect ........................................................................................................................ 21

3.1. General aspect ....................................................................................................................... 21

3.2. Hydrodynamic theory ............................................................................................................ 21

3.3. Motion resolution .................................................................................................................. 22

3.4. Mooring lines theory ............................................................................................................. 23

3.5. Aerodynamic theory ............................................................................................................. 24

3.6. Optimization .......................................................................................................................... 24

3.7. Project philosophy ................................................................................................................. 25

4. Design considerations ................................................................................................................... 26

4.1. Design criteria ........................................................................................................................ 27

4.2. Corrosion ............................................................................................................................... 29

4.3. Marine growth ....................................................................................................................... 29

5. Software ........................................................................................................................................ 31

5.1. Isight ...................................................................................................................................... 31

5.2. Orcaflex ................................................................................................................................. 31

5.3. FAST ....................................................................................................................................... 31

5.4. Python Interface .................................................................................................................... 31

6. Input data ...................................................................................................................................... 32

6.1. Referecence frame ................................................................................................................ 32

6.2. Environmental condition ....................................................................................................... 32

6.2.1. Wind data ...................................................................................................................... 32

6.2.2. Waves ............................................................................................................................ 34

6.2.3. Current ........................................................................................................................... 36

3

6.3. Floating platforms ................................................................................................................ 37

6.3.1. WindCrete Spar ................................................................................................................. 37

6.3.1.1. Floater description .................................................................................................... 37

6.3.1.2. Modelisation strategy................................................................................................ 39

6.3.1.3. Hydrodynamic model ............................................................................................... 39

6.3.1.4. Mooring system ......................................................................................................... 40

6.3.2. ActiveFloat semisubmersible............................................................................................. 41

6.3.2.1. Floater description .................................................................................................... 41

6.3.2.2. Modelization strategy................................................................................................ 42

6.3.2.3. Hydrodynamic model ................................................................................................ 42

6.3.2.4. Mooring system ......................................................................................................... 43

7. Mooring Optimization ................................................................................................................... 45

7.1. Optimization process ............................................................................................................. 45

7.1.1. Generalities ................................................................................................................... 45

7.1.2. Design variables ............................................................................................................. 47

7.1.3. Design Constraints ......................................................................................................... 49

7.1.4. Objective function ......................................................................................................... 49

7.1.5. Material ......................................................................................................................... 50

7.1.6. DLCs ............................................................................................................................... 50

8. Methodology ................................................................................................................................. 52

8.1. Models ................................................................................................................................... 52

8.2. Environmental conditions ..................................................................................................... 52

8.3. Results analysis ...................................................................................................................... 52

9. Results ........................................................................................................................................... 53

9.1. WindCrete model comparison .............................................................................................. 53

9.1.1. Static Equilibrium .......................................................................................................... 53

9.1.2. Decay tests .................................................................................................................... 53

9.2. ActiveFloat models comparison ........................................................................................... 55

9.2.1. Static Equilibrium .......................................................................................................... 55

9.2.2. Decay tests .................................................................................................................... 56

9.3. FAST model verification ......................................................................................................... 57

9.4. Aerodynamic loads selection................................................................................................. 58

9.5. Cases considered ................................................................................................................... 59

9.6. Optimization results .............................................................................................................. 59

10. Conclusion and perspective ...................................................................................................... 67

References ............................................................................................................................................. 68

4

List of Figures Figure 1-1 Project structure [1] ............................................................................................................... 8

Figure 2-1 Floating platform stability triangle [18] ................................................................................. 9

Figure 2-2 Floating platform concepts [19] ........................................................................................... 10

Figure 2-3 Floatgen: a barge-type floater by Ideol [17] ........................................................................ 10

Figure 2-4 Mooring systems [22] ........................................................................................................... 12

Figure 2-5 Stud-Link and Studless chain [29] ........................................................................................ 13

Figure 2-6 Connectors commonly used in offshore industry [34] ......................................................... 15

Figure 2-7 Clump weight [35] ................................................................................................................ 15

Figure 2-8 Application of buoyancy modules [36] ................................................................................ 16

Figure 2-9 Anchors types depending on type of soil and water depth (Vryhof) ................................... 16

Figure 2-10 Cost function using equation from COREWIND and DTOCEAN+ ....................................... 18

Figure 2-11 Cost function comparison for different synthetic ropes .................................................... 19

Figure 3-1 Degrees of freedom definition ............................................................................................. 22

Figure 3-2 OrcaFlex line modelization [31] ........................................................................................... 24

Figure 3-3 Relation between software and their tasks ......................................................................... 25

Figure 4-1 Corrosion allowance [46] ..................................................................................................... 29

Figure 4-2 Marine growth data depending on location [46] ................................................................. 30

Figure 6-1 Fixed inertia frame definition (INNOSEA) ............................................................................ 32

Figure 6-2 Wind rose for 1-hour mean speed at Gran Canaria [43]...................................................... 34

Figure 6-3 Wave Rose at Gran Canaria [43] .......................................................................................... 36

Figure 6-4 WindCrete sketch [58] ......................................................................................................... 38

Figure 6-5 OrcaFlex view of the mooring system .................................................................................. 40

Figure 6-6 ActiveFloat floater sketch [58] ............................................................................................. 41

Figure 6-7 Main dimensions of ActiveFloat [58] ................................................................................... 41

Figure 6-8 Sketch of the real platform (left) and of the FAST model (right) ......................................... 43

Figure 7-1 Optimization screening tool: iterative process .................................................................... 45

Figure 7-2 Optimization screening tool: loop processes ...................................................................... 46

Figure 7-3 Sketch of mooring system to illustrate line length and anchor radius dependency ........... 49

Figure 9-1 Decay tests of WindCrete floater ......................................................................................... 54

Figure 9-2 Decay tests of WindCrete floater: few periods .................................................................... 54

Figure 9-3 Spectral density of platform in surge and yaw. ................................................................... 55

Figure 9-4 Decay tests of ActiveFloat floater ........................................................................................ 57

Figure 9-5 Decay tests of ActiveFloat floater: few periods ................................................................... 57

Figure 9-6 Yaw bearing force Fxp for Vref = 10.56 m/s ...................................................................... 58

Figure 9-7 WindCrete mooring system group definition: Group1-red line, Group2: blue lines, Group3:

green lines ............................................................................................................................................. 60

Figure 9-8 Maximum dynamic offset obtained for DLC 6.2 (Start of life) ............................................. 62

Figure 9-9 Yaw motion (up) and pitch motion (down) obtained for DLC 1.6 using FAST without enough

stiffness ................................................................................................................................................. 62

Figure 9-10 Yaw motion (up) and pitch motion (down) obtained for DLC 1.6 using coupling FAST-

OrcaFlex without enough stiffness ........................................................................................................ 63

Figure 9-11 Yaw motion (up) and pitch motion (down) obtained for DLC 1.6 using coupling FAST-

OrcaFlex with enough stiffness ............................................................................................................. 64

5

Figure 9-12 WindCrete optimized mooring system: yaw motion (up) and pitch motion (down)

obtained for DLC 1.6 using coupling FAST-OrcaFlex design 2 ............................................................... 65

List of Tables Table 2-1 Typical natural periods for each floater ................................................................................ 11

Table 2-2 Value for coefficient c using into MBL calculation ................................................................ 13

Table 4-1 Load factor requirements for design of mooring lines.......................................................... 27

Table 4-2 Design criteria for Gran Canaria ............................................................................................ 28

Table 4-3 Design fatigue factor for mooring chain................................................................................ 28

Table 6-1 10-minute mean wind speed profile ..................................................................................... 33

Table 6-2 Extreme wind profile for a return period of 50 years ........................................................... 33

Table 6-3 Extreme waves data for Gran Canaria (from [43]) ................................................................ 34

Table 6-4 Scatter diagram for Gran Canaria .......................................................................................... 35

Table 6-5 Current speed profile for a return period of 50 years ........................................................... 37

Table 6-6 Main properties of WindCrete Spar [58] ............................................................................... 39

Table 6-7 WindCrete masses [58] ......................................................................................................... 39

Table 6-8 Keulegan-Carpenter numbers for WindCrete platform ........................................................ 40

Table 6-9 WindCrete mooring system main properties [58] ................................................................ 40

Table 6-10 WindCrete : mass and inertia [58] ....................................................................................... 42

Table 6-11 WindCrete : elements’ masses [58] ..................................................................................... 42

Table 6-12 ActiveFloat : Drag properties for real platform and model [58] ......................................... 43

Table 6-13 ActiveFloat mooring system main properties [58] .............................................................. 44

Table 7-1 Example of parameters used for one group of lines made in chain ..................................... 47

Table 7-2 Example of parameters used for one group of lines made in chain and wire ...................... 48

Table 9-1 WindCrete static equilibrium analysis: comparison between OrcaFlex and FAST models ... 53

Table 9-2 Mooring stiffness matrix for WindCrete platform ................................................................ 53

Table 9-3 WindCrete: Comparison between natural frequencies obtained using FAST and OrcaFlex. 54

Table 9-4 ActiveFloat static equilibrium analysis: comparison between OrcaFlex and FAST models .. 56

Table 9-5 Mooring stiffness matrix for ActiveFloat platform ................................................................ 56

Table 9-6 ActiveFloat : Comparison between natural frequencies obtained using FAST and OrcaFlex.

............................................................................................................................................................... 56

Table 9-7 Yaw bearing forces Fxp and Fyp obtained for different yaw misalignement at Gran Canaria

............................................................................................................................................................... 58

Table 9-8 Design variables: allowed values ........................................................................................... 59

Table 9-9 WindCrete initial mooring system description ...................................................................... 59

Table 9-10 WindCrete chain configuration: optimized mooring system description ........................... 59

Table 9-11 WindCrete optimized mooring system with chain: static equilibrium ................................ 60

Table 9-12 WindCrete optimized mooring system with chain: natural periods ................................... 60

Table 9-13 Results obtained from DLCs for Windcrete chain optimized system .................................. 61

Table 9-14 WindCrete chain configuration: optimized mooring system design 2 ................................ 64

Table 9-15 WindCrete optimized mooring system design 2: static state ............................................. 64

Table 9-16 WindCrete optimized mooring system with chain design 2: natural periods ..................... 65

Table 9-17 Results obtained from DLCs for Windcrete chain optimized system design 2.................... 66

6

7

Acknowledgments Working as an intern at INNOSEA was a real pleasure. I would like to thank all my colleagues for the

last six months spent in the company. The great atmosphere made this thesis a perfect ending for my

student life. I would like particularly to thank the “ocean team” for their advices and their kindness

that helped me to realize this work. Many thanks to Valentin my supervisor at Innosea, who trusted

me for this project. Your advices allow me to learn a lot.

I would like to thank KTH, the school of Industrial Engineering and Management, the MSc Sustainable

Energy Engineering staff for the last 2 years spent in Sweden and their learnings. Many thanks to

Miroslav Petrov, my supervisor at KTH, who helped to choose this thesis and allowed me to have a

subject making a link between my studies at Ecole Centrale de Nantes and KTH.

Finally, I would like to thank COREWIND project partners for the different exchanges during this

project. Their opinions were very informative, and I learnt a lot working in an international

environment on a European project.

1. Introduction This master thesis takes place within a project supported by the European Commission, COREWIND [1]

& [2] (COst REduction and increase performance of floating WIND technology), that aims to achieve

significant cost reductions and improve the performances of floating wind technology. It is undertaken

at INNOSEA [3], an independent engineering firm specialized in Marine Renewable Energies (MRE).

The company is leading a work package dedicated to the design and the optimization of station keeping

systems (i.e. mooring and anchoring systems for a floating structure).

Offshore wind is an ongoing development energy. The annual offshore wind capacity globally increased

from 2.5 GW of cumulative installed capacity in 2009 to about 23 GW in 2020 [4]. Longtime dominated

by United Kingdom and Germany [4] in Europe, offshore wind projects have started to become more

integrated into national energy plans ( [5], [6]) to meet EU renewable energy target (32 % by 2030 [7]).

Offshore wind turbines benefit from advantages such as higher capacity factors than other variable

renewable energies [8], less turbulences compared to onshore turbines [9] and a greater population

acceptance [10]. However, to the contrary turbines encounter harder environmental conditions

(combination of wind, current and waves, saltwater, humid air, storms etc.).

Deep offshore areas represent about 60-80 % of the offshore wind potential [11]. LCOE increases with

water depth [4] which tends to make floating foundations competitive compared to traditional

bottom-fixed offshore wind turbines (BFOWT) [12]. However, FOWT are still very expensive, with an

average LCOE about 130€/MWh [13]. Expectations for LCOE reduction aim to achieve a cost about

80€/MWh in 2050. COREWIND aims to achieve those costs 10 years ahead of this target. To do so, the

project focuses on mooring systems and dynamic cables (export cables) at each step of a project (from

engineering to installation). Figure 1-1 summarized covered topics by the consortium.

8

Figure 1-1 Project structure [1]

Costs associated to anchors and moorings represent approximatively 8 % of the overall CAPEX [14]

without installation, which is about 13 % of the CAPEX. The Carbon Trust estimates that anchors and

moorings optimization could lead to about 4 % of total costs reduction, while installation procedures

improvement could lead to about 5 % of reduction [14]. The Carbon Thrust also underlines the

variability of these figures depending on the type of floater considered.

Today, the common approach when designing a mooring system follows an iterative method. Based

on engineering judgements, a first loop is realized to check that the mooring system follows standards

requirements. With this approach only a few numbers of iterations are done without real costs and

performances optimization. The aim of the work package two is to develop a tool that allows a large

screening of mooring configurations resulting to costs and performances optimization as well as time

saving. To achieve this goal, two software, Isight and Orcaflex, are coupled using a Python code. The

aim is to develop an optimization tool that run a complete dynamic analysis to find the best

configuration.

This report presents the main results of this work. The report is divided into two parts. The first is

dedicated to generalities with a brief review of the state of art of offshore wind turbines, followed by

theoretical aspects. Design considerations and standard criteria usually used in offshore wind energy

are also presented. The second part focuses on Corewind project presenting floaters, sites, softwares

used in the project and the process considered to realize the optimization. Results are presented in

the last part of the report followed by a conclusion and reflection on further possible works.

9

2. State of the art

2.1. Floating foundations A lot of FOWT concepts have been deployed since the first full scale floating turbine, Blue H, that was

launched in 2008 [15]. Floating offshore wind designers benefit from practices of oil and gas industry.

FOWT concepts can be categorized into three categories depending on the principle of stability as

shown on Figure 2-1: semisubmersible, spar-buoy and tension leg platform (TLP) (Figure 2-2). Some

concepts can also be categorized as hybrid system among which the barge-type [16]. The prototype

Floatgen (Damping Pool, Ideol [17]) is an example of such a concept (Figure 2-3).

Figure 2-1 Floating platform stability triangle [18]

10

Figure 2-2 Floating platform concepts [19]

Figure 2-3 Floatgen: a barge-type floater by Ideol [17]

The spar buoy is composed of a large steel or concrete cylinder filled with ballast (water or concrete)

that ensures to maintain the center of gravity below the center of buoyancy [16]. This configuration

creates a restoring moment when the foundation is not in vertical position. Hywind, developed by

Equinor, is the first commercial FOWT based on spar concept [20]. Due to their large draft, spar buoys

are well adapted to deep water. Assembled spar FOWT cannot be towed in most cases. It requires to

11

use special vessels that make installation costly [21]. Spars are usually kept stationary by catenary

mooring lines [22].

Semisubmersibles are composed of several columns (usually three or four) connected by pontoons

and braces. The stability is then ensured by columns [16]. Wind turbine can be positioned either on

one of the external columns (WindFloat, Principle Power Inc. [23]) or on the main column in the center

of the floater (DeepCwind, NREL [24]). One advantage of that concept is its ability to be towed fully

assembled, reducing the need to use jack-up or crane vessels at sea and therefore reducing the costs

of installation. Catenary mooring lines are also mainly used for that concept.

Eventually, TLPs’ stability is ensured by tendons. The platform has an excess of buoyancy that is countered by moorings. Natural frequencies in heave, roll and pitch of TLP are usually high above those for SPAR and semisubmersible [25].

Table 2-1 gives typical natural periods for each type of floaters [26].

These periods are important for designers. Indeed, having these periods far from wave periods are

important to avoid peak loads due to extreme responses.

Table 2-1 Typical natural periods for each floater

Type of floaters

Degree of freedom Semisubmersible TLP Spar

Surge >100 >100 >100

Sway >100 >100 >100

Heave 20-50 <5 20-35

Roll 30-60 <5 50-90

Pitch 30-60 <5 50-90

Yaw >100 >100 >100

2.2. Station keeping Station keeping brings together systems that ensure floating platforms stay around an original target

position while limiting excursions and motions, accelerations and induced loads on the floater [27]. In

the oil and gas industry, stations keeping can be ensured either by moorings, tethers (tendons),

dynamic positioning thrusters or a mixed concept [28]. In marine renewable energies, moorings and

tethers are mainly used.

2.2.1. Configuration Two main types of mooring systems are used in marine renewable energies: catenary and taut

mooring. Figure 2-4 gives sketch of these two systems.

For catenary mooring systems, restoring force is due to mooring weight. A part of the line is laying on

the seabed resulting to a higher footprint. Loads encountered by anchors are horizontal. Costs

associated with the use of anchors are therefore lower compared to taut-mooring configurations, but

more material is needed for mooring lines.

In the case of a taut mooring system the restoring force is provided by the line stiffness [16]. Anchors

used for these mooring configurations must support both vertical and horizontal loadings. Taut

12

moorings are usually preferred in deep waters. Indeed, though higher costs due to anchors, the low

footprint leads to reduced need of materials that tilt the balance in favour of taut moorings.

Figure 2-4 Mooring systems [22]

Different configurations exist concerning mooring layout. Moorings can be classified as spread

mooring (distributed around the platform) or single point (attached to one point). The number of lines,

their parameters (materials, diameters, and lengths) or spread angles are mainly determined by

environmental conditions.

13

2.2.2. Components Several components compose a mooring system. Different materials can be used for lines like chains,

wire ropes and synthetic ropes. These materials are detailed in 2.2.2.1. Connectors are used to

assemble lines and connect them to the platform or to anchors such as hackles, kenter or fairleads. In

addition, some modules can be added to change lines properties (buoys, clump weights). Following

sections provide a list of these components.

2.2.2.1. Lines Materials

2.2.2.1.1. Chain

Chain is the most commonly used material for mooring systems. It exists several parameters that allow

to classify chain. Stud-link and studless chain are two types available on the market (Figure 2-5 [29]).

Stud-link chain are mainly used for temporary moorings whereas studless chain are used for

permanent moorings. Studless chains are slightly lighter than stud-link at equivalent minimum

breaking load (MBL).

Figure 2-5 Stud-Link and Studless chain [29]

Another parameter that is important regarding chain is the steel grade [30]. Common grades used in

offshore industry are R3, R3S, R4, R4S and R5. Mechanical properties are modified while increasing the

grade. The main advantage of a higher grade, though higher costs, is the increase of MBL without

changing diameter (hydrodynamics loads) and mass per unit length. The minimum breaking load can

be calculated using:

𝑀𝐵𝐿 = 𝑐𝑑2(44 − 80𝑑)𝑘𝑁

with d the bar diameter in mm and 𝑐 a coefficient depending on the grade [30] and presented in Table

2-2.

Table 2-2 Value for coefficient c using into MBL calculation

𝐺𝑟𝑎𝑑𝑒 𝑐 𝑅3 2.23 × 104

𝑅3𝑆 249 × 104 𝑅4 2.74 × 104

𝑅4𝑆 3.04 × 104 𝑅5 3.2 × 104

On the contrary, mass per unit length and axial stiffness per unit length are not grade dependent.

Values can be found on literature [31], [32]. Chain bar diameters available on the market are typically

in the range of 20 to 185 mm. Above a certain depth, costs and weight of mooring chain becomes

limiting. Therefore, other materials can be used.

2.2.2.1.2. Wire ropes

Wire rope is another common material used for moorings. At equivalent MBL wire ropes are lighter

and have a higher elasticity than chain. Costs per unit length are also lower. Wire ropes commonly

14

used in offshore industries are 6-strands, 8-strands and spiral-strands. Wire rope is less sensitive to

corrosion thanks to galvanization or synthetic protection (sheathed wire rope, utilization of high-

density polyethylene or polyurethane). The choice of strands type generally depends on the lifetime

of the mooring systems. When using wire ropes (or synthetic ropes) in a catenary configuration it is

common to combine them with chain. Usually, the line is composed of chain laying on the seabed (due

to higher resistance of chain to abrasion), following by wire rope on the catenary part. Chain is used

on the last part, close to the fairlead, to adjust the pretension during installation [22].

2.2.2.1.3. Synthetic ropes

Synthetic ropes are mainly used in deep and ultradeep waters, thanks to their lightweight and high

elasticity. Amongst synthetic ropes, polyester is most common. Polyester ropes are used in semi-taut

and taut mooring systems, allowing for efficient mooring systems at lower costs. However, other

synthetic ropes are also used such as nylon, HMPE (high modulus polyethylene) or aramid.

2.2.2.2. Connectors

This section is drawn from the review by R.R Arias&all [33] and the data provided in Vryhof catalogue

[34].

Main connectors used in offshore industry are presented in this section. The list is not exhaustive.

Connectors are used to connect two sections of a mooring line, composed of the same material or two

different ones, as well as to connect the line to the fairlead, to the anchor or to an intermediary

component (buoy, clump weight). These connectors are usually classified between those utilized for

permanent mooring systems and temporary ones. The main design parameter is the fatigue life with

connectors having stress concentration points that commonly lead to failures.

The most used connector in offshore industry is the shackle. This connector can be used to connect a

chain line end to a buoy. Shackles can be used both for permanent and temporary moorings systems.

Kenters are connectors used to connect two chain sections with the same diameter. These connectors

are not used for permanent moorings due to their restricted fatigue life. Similarly, pear-shaped

connectors are used in temporary moorings systems to connect two chains with different diameters

and as with kenters, they are not used for permanent moorings. Type C connectors are other

connectors used to link two chains with the same diameter. They differ from Kenters by their opening

systems. The type H connectors are very robust and flexible connectors. One advantage is their

capacity to be used for adjusting lengths during installation. Eventually, the swivel connector is used

to enable some degrees of freedom. It is also used to connect chain and rope.

15

Figure 2-6 Connectors commonly used in offshore industry [34]

(1st line left to right: shackle, kenter, pear shaped. 2nd line left to right: H-connector, swivel)

2.2.2.3. Clump weights

In the case of a catenary mooring system, designers may add clump weights. Clump weights are

components made of cast iron or concrete. They are used as local weight to increase pretension and

stiffness [22], creating a higher restoring force. This leads to a reduction of excursions. Figure 2-7 shows

the use of a clump weight [35]

Figure 2-7 Clump weight [35]

2.2.2.4. Buoyancy modules

For catenary mooring systems, buoyancy modules can be used. Buoyancy module are used to reduce

line dynamic, weight applied on the platform or to decouple motions between lines and floater. These

components are particularly useful for dynamic cables to reduce fatigue. Different configurations,

known as lazy-wave or lazy-S and commonly used on offshore industry, use these components. Figure

2-8 shows application of buoyancy modules for marine renewable energy systems [36]

16

Figure 2-8 Application of buoyancy modules [36]

2.2.2.5. Anchors

There are a lot of anchors types used for offshore application. The choice of anchor type is mainly

driven by mooring system configuration, soil characteristic, requirements regarding anchor loading

and water depths. Main anchor types are presented in this section. Figure 2-9 shows principal types of

anchors [22].

Figure 2-9 Anchors types depending on type of soil and water depth (Vryhof)

The gravity anchor is a dead weight made in steel or concrete. The main advantage of this type of

mooring system is its capacity to handle both vertical loads (compensated by the anchor weight) and

horizontal loads (compensated by friction between the seabed and the anchor). Moreover, it is a low-

cost technology that can be used with a variety of seabed type.

17

Drag embedment anchors (also called fluke anchors) are anchors made of steel having a triangular

geometry at their based. This lower part creates, once buried, the holding capacity of the anchor. These

anchors can handle only horizontal loads. They are, therefore, used only in catenary mooring

configurations. One advantage is their high holding capacity-weight ratio. Drag-anchors require the

use of anchor-handling vessels that progressively load the line to allow ground penetration [37]. The

soil type is decisive when using that kind of anchors. They are well adapted to sandy soils. Anchors can

be removed after utilization.

Piles are cylindrical anchors that can handle both horizontal and vertical loads. The holding capacity is

provided by the friction with the soil and lateral soil resistance. Piles are buried using hammer or

vibrators. Once again, the soil is an important parameter while choosing these anchors. Like gravity

anchors, the removal is complicated.

Suction piles are another type of pile-anchor. The pile has an opening at the base in which the soil

goes. A pump creates a vacuum during installation to help the pile penetrate the ground by pressure

difference. Both vertical and horizontal loads are supported by the suction pile. Suction piles can be

easily removed after utilization. They are used for clay soils.

Plate anchors are kind of a variant of the classical drag-embedded anchors except that they can handle

both vertical and horizontal loads. They are also composed of a geometrical form (usually triangular or

rectangular) to help the penetration into the ground. They have a high holding capacity in vertical

direction making them interesting for taut mooring.

Finally, gravity installed anchors, which can handle both horizontal and vertical loads. The main

advantage of these anchors is their installation, penetrating the ground using their own weight. They

are profiled like a torpedo. Therefore, their utilization is preferred for ultra-deep water.

2.3. Costs analysis

2.3.1. Generalities The levelized cost of energy is a usual indicator used to compare sources of energy. It corresponds to

the minimum unit price of energy and it is calculated using [12]:

𝐿𝐶𝑂𝐸 =(∑

𝐼𝑡 + 𝑀𝑡

(𝐼0 + 𝑟)𝑡 𝑛𝑡=0 )

(∑𝐸𝑡

(𝐼0 + 𝑟)𝑡 𝑛𝑡=0 )

Equation 2-1

With

𝐼𝑡 Investments at time t € 𝑀𝑡 Operation and maintenance costs

at time t €

𝐸𝑡 Energy generation at time t kWh 𝑟 Evaluation of the discount rate 𝑛 Lifetime of the system years

A complete costs analysis written by the Carbon Trust is available [21]. This study gives costs magnitude

for different components of floating offshore wind farm (substructure, mooring systems) as well as

information regarding installation costs

18

2.3.2. Mooring systems costs estimation Costs of mooring system are hard to estimate due to the lack of data. However, formulas depending

on variables used during optimization are required.

2.3.2.1. Chain

Cost estimation depending on steel grade can be found for mooring chain [22]. The dependence of

the cost function to the minimum breaking load is a key point for the mooring optimization. Indeed,

it allows to use the grade as a design variable.

𝐶𝑜𝑠𝑡𝑠𝑐ℎ𝑎𝑖𝑛 = (0.0591 × 𝑀𝐵𝐿 − 89.69) × 𝐿𝑠𝑒𝑐𝑡𝑖𝑜𝑛 Equation 2-2 With

𝐶𝑜𝑠𝑡𝑠𝑐ℎ𝑎𝑖𝑛 Chain section costs $ 𝑀𝐵𝐿 Minimum breaking load 𝑘𝑁

𝐿𝑠𝑒𝑐𝑡𝑖𝑜𝑛 Section length 𝑚

This cost function was compared to data provided in a report from DTOCEAN+ [38]. The aim was to

confirm the order of magnitude. For the cost function used in Corewind, grade 4 steel was used to

follow DTOCEAN+ hypothesis.

Figure 2-10 Cost function using equation from COREWIND and DTOCEAN+

Cost functions are relatively close even though Corewind cost function gives lower costs. In addition,

costs estimation from another study was added (red cross) [12]. This cost corresponds to an estimation

of the mooring system used for Hywind and WindFloat project.

19

2.3.2.2. Wire

Regarding wire rope, cost function is given as a function of the diameter [38].

𝐶𝑜𝑠𝑡𝑠𝑤𝑖𝑟𝑒 = 0.03415 × 𝑑2 × 𝐿𝑠𝑒𝑐𝑡𝑖𝑜𝑛 Equation 2-3 With

𝐶𝑜𝑠𝑡𝑤𝑖𝑟𝑒 Wire section costs € 𝑑 Wire diameter m

𝐿𝑠𝑒𝑐𝑡𝑖𝑜𝑛 Section length m

This cost function was compared to internal data and though some differences, orders of magnitude

were consistent.

2.3.2.3. Synthetic ropes

Cost function for polyester and nylon were missing. Deliverable 4.6 of DTOcean+ [38] provides graph

giving cost per unit length depending on minimum breaking load for different synthetic ropes. Data

were then exacted from this graph for polyester and nylon. A linear regression was used, to obtain cost

function. Pearson correlation coefficient for polyester is 0.9967, validating the use of a linear

regression.

Figure 2-11 Cost function comparison for different synthetic ropes

On Figure 2-11, green functions correspond to polyester, red functions to nylon and blue functions to

HMPE. Dark colors are always higher than light colors because it includes additional costs (protection,

etc.). To compare materials, it was decided to use only material costs (i.e light colors). Purple curve

corresponds to polyester data fitted to obtain cost function.

20

𝐶𝑜𝑠𝑡𝑠𝑝𝑜𝑙𝑦𝑒𝑠𝑡𝑒𝑟 = (0.0138 × 𝑀𝐵𝐿 + 11.281) × 𝐿𝑠𝑒𝑐𝑡𝑖𝑜𝑛 Equation 2-4

With

𝐿𝑠𝑒𝑐𝑡𝑖𝑜𝑛 Section length m 𝑀𝐵𝐿 Polyester minimum breaking

load kN

𝐶𝑜𝑠𝑡𝑃𝑜𝑙𝑦𝑒𝑠𝑡𝑒𝑟 Polyester section costs €

Data were validated by comparison with costs for other projects.

The same method was used for nylon. The Pearson correlation coefficient is 0.9931. The obtained

function is:

𝐶𝑜𝑠𝑡𝑠𝑛𝑦𝑙𝑜𝑛 = (0.0122 × 𝑀𝐵𝐿 + 12.116) × 𝐿𝑠𝑒𝑐𝑡𝑖𝑜𝑛 Equation 2-5

With

𝐶𝑜𝑠𝑡𝑠𝑁𝑦𝑙𝑜𝑛 Nylon section costs $

𝑀𝐵𝐿 Nylon minimum breaking load 𝑘𝑁 𝐿𝑠𝑒𝑐𝑡𝑖𝑜𝑛 Section length 𝑚

2.3.2.4. Anchors

In addition, the costs of anchors are estimated. In a first approximation, only costs associated to drag-

embedded anchors are considered. Costs are given by [39]:

𝐶𝑜𝑠𝑡𝑎𝑛𝑐ℎ𝑜𝑟 = 10.198 × 𝑀𝐵𝐿 Equation 2-6

With

𝐶𝑜𝑠𝑡𝑎𝑛𝑐ℎ𝑜𝑟 Anchor costs $

𝑀𝐵𝐿 Minimum breaking load of the

line 𝑘𝑁

21

3. Theoretical aspect

3.1. General aspect Modelization of floating offshore wind turbines is a complex task because of the interaction of the

structure with its environment (waves, wind and current). Modelization requires understanding of

different areas of engineering such as structural analysis, hydrostatic, hydrodynamic, and

aerodynamic.

Floating offshore wind turbines are usually divided into the substructure (the platform) that interacts

with waves, current and wind, the turbine (tower and RNA) sensitive to wind and the mooring systems.

Platform motions and loads applied on it, are usually obtained by solving the diffraction-radiation

problem that comes from the potential flow theory. The mooring lines are usually modeled using a

finite element method and loads are computing using the so-called Morison equation. Eventually,

wind loads applied on the turbine are obtained using the blade element momentum theory. In

addition, controller theory is needed to correctly model the behavior of the turbine. Sections below

introduced the different theories needed to model a FOWT.

3.2. Hydrodynamic theory Two theories are generally usually used when dealing with loads induced by waves on a structure for

engineering application: the potential flow theory and the Morison theory. To determine which theory

is best adapted to a case it is usual to separate large and small elements of the platform.

Large elements tend to interact with waves: radiation and diffraction phenomena occur. In that cases,

loads are inertia dominated. Drag loads are not created because the flow does not have the time to

create vortex in a wave period. At the contrary, for small elements, viscous effects are dominant. To

determinate which theory suits for an element it is usual to calculate the Keulegan-Carpenter number,

𝐾𝑐. This number is given by:

𝐾𝑐 = 2𝜋𝐴

𝐷 Equation 3-1

Where

𝐴 Wave amplitude 𝑚 𝐷 Characteristic length 𝑚

When 𝐾𝑐 is below 2, the potential flow theory can be used. This theory required the determination of

a hydrodynamic database obtained by solving the potential flow problem. On the contrary for small

elements, characterized by 𝐾𝑐 > 10, the Morison approach is usually used. This approach is a simple

model where drag and inertia forces are calculated using the Morison equation. In between (2 < 𝐾𝑐 <

10) a mixed approach can be used (potential flow and drags loads).

The Morison equation is given by:

𝑑𝐹 = {(1 + 𝐶𝑀)𝜌𝜋

4𝐷2 (

�̇�

�̇�) − 𝜌

𝜋

4𝐷2𝐶𝑀 (

�̈�

�̈�)} 𝑑𝑧

+1

2𝐶𝐷𝐷 (

𝑢 − �̇�

𝑣 − �̇�) √(𝑢 − �̇�)2 + (𝑣 − �̇�)2𝑑𝑧

Equation 3-2

22

With

𝐶𝑀 Added mass coefficient - 𝐷 Diameter 𝑚 𝑑𝑧 Cylinder length 𝑚 𝑢 Normal fluid velocity 𝑚. 𝑠−1

𝐶𝐷 Drag coefficient -

The drag and added mass coefficients are usually calibrated using tank tests, or approximated

following standards [40]. These coefficients depend on the Keulegan-Carpenter number 𝐾𝐶, the

Reynolds number 𝑅𝑒, and the surface roughness 𝑘𝑟.

3.3. Motion resolution There are six degrees of freedom for a floating platform. The surge corresponds to a translation along

the x-axis, the sway to a translation along the y-axis and the heave, a translation along the z-axis. The

roll is the rotation around the x-axis, the pitch the rotation around the y-axis and the yaw the rotation

about the z-axis. Figure 3-1 shows the six degrees of freedom.

Figure 3-1 Degrees of freedom definition

The equation of movement for the degree of freedom 𝑋𝑖 of a platform is given by: [16], [41]

(𝑀 + 𝑀𝑎)𝑑2𝑋𝑖

𝑑𝑡2+ 𝐵

𝑑𝑋𝑖

𝑑𝑡+ (𝐾𝐻 + 𝐾𝑀)𝑋𝑖 = 𝐹(𝑋, 𝑡) Equation 3-3

With

𝑀 Mass matrix of the structure 𝑘𝑔 𝑀𝑎 Added mass matrix 𝑘𝑔 𝐵 Damping matrix 𝑁𝑠/𝑚

𝐾𝐻 Hydrostatic stiffness 𝑁/𝑚

𝐾𝑀 Mooring stiffness

𝑋𝑖 Degree of freedom considered m / rad 𝐹 Excitation forces 𝑁

23

Added mass and damping coefficients depend on the wave frequency. The damping matrix 𝐵 can

obtained after linearization of the left hand side of Equation 3-4 composed of a linear damping term

and a quadratic damping term.

(𝐵𝐿 + 𝐵𝑄

𝑑𝑋𝑖

𝑑𝑡)

𝑑𝑋𝑖

𝑑𝑡= 𝐵

𝑑𝑋𝑖

𝑑𝑡 Equation 3-4

With,

𝐵𝐿 Linear damping matrix 𝑁𝑠/𝑚

𝐵𝑄 Quadratric matric 𝑁𝑠²/𝑚²

𝐵 Damping matrix 𝑁𝑠/𝑚

Displacements of anchored floating structures are decomposed onto three categories depending the

loads: the mean drift forces resulting from combination of wind and current, the wave-frequency 1st

order forces, and the low-frequency 2nd order forces [42].

From Equation 3-3 one can obtain natural frequencies. These parameters are important parameters

during design. Indeed, natural periods exited by waves could lead to extreme responses. Usually, for

SPAR buoys and TLPs, periods are far from wave periods. For semisubmersibles, as shown in

Table 2-1, natural periods are within the range of wave periods. To avoid extreme responses, this type

of floaters has usually damping sources [43]. . These frequencies are obtained by so-called decay tests.

More details are given in 1.1.1.

𝑓𝑖 =1

2𝜋√

𝐾𝐻,𝑖 + 𝐾𝑀 , 𝑖

𝑀𝑖 + 𝑀𝑎,𝑖 Equation 3-5

With

𝑓 Natural frequency for the degree of freedom considering

𝐻𝑧

𝐾𝐻 Hydrodynamic stiffness 𝑁. 𝑚. 𝑟𝑎𝑑−1 𝐾𝑀 Mooring stiffnes 𝑁. 𝑚. 𝑟𝑎𝑑−1 𝑀𝑖 Mass matrix 𝑘𝑔

𝑀𝑎,𝑖 Added mass matrix kg

3.4. Mooring lines theory Mooring lines in OrcaFlex, the software used to perform the dynamic analysis in this project (see

section 5.2) are modelized using a finite element model. Finite element method is a numerical method

used to solve partial differential equations. To solve the problem the system is discretized into small

element, called finite elements. The solution is found by using boundary conditions. [44]

24

Figure 3-2 OrcaFlex line modelization [31]

Figure 3-2 shows mooring line discretization within OrcaFlex [31]. The line is divided into a series of

line segments which are modelled by straight massless model segments with a node at each end.

Properties of the line (mass, weight, buoyancy, drag, etc.) are lumped and assigned to the node.

Segments model the axial and torsional properties of the line.

In details, axial and torsional properties are represented by using spring-dampers. Details can be found

on the OrcaFlex website [31].

3.5. Aerodynamic theory Wind plays a key role for offshore wind turbine. The wind turbine extracts a part of the kinetic energy

to generate power. Wind also creates drag and lift forces on the different part of the turbine, that have

a large impact on the overall structure behavior. Sources of the loads are mainly pressure difference

and skin friction. Details regarding aerodynamic of a wind turbine is given by Hansen O.L Martin [45].

The blade element momentum theory (BEM) is a classical way to determine loads on wind turbines.

FAST, an aero-elastic codes developed by the NREL (see section 5.3), allows to compute these loads.

3.6. Optimization The aim of the project is to develop an optimization tool to optimize costs of floating offshore wind

turbines mooring systems. Therefore, this section gives generality about optimization, to define the

objective function, constraints and design variables.

Optimization is a process that aims to find the best or the most favorable solution to a problem. To

define this problem, an objective function must be determined. This objective function is a function

that depends on variables, so-called design variables. These variables are usually subject to constraints.

The generic form of an optimization can be written as [48]:

min𝑥1,𝑥2,…,𝑥𝑛

𝑓(𝑥1, … , 𝑥𝑛)

𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜 (𝑔𝑖(𝑥1), … , 𝑔𝑖(𝑥𝑛)) ∈ Ω Equation 3-6

Where

25

𝑥1, … 𝑥𝑛 design variables

Ω feasible region

𝑓 the function that must be optimized

𝑔𝑖 constraint functions defined as equalities or inequalities

To solve this kind of problems, optimization algorithms are used. These algorithms are efficient for a

certain type of optimization problems that depend on the type of design space, the number of design

variables, etc.

Sequential quadratic programming is a class of algorithms used for constrained nonlinear

optimizations under some assumptions [49]: the problem is not too large, functions and gradients can

be evaluated with sufficiently high precision and the problem is smooth and well-scaled. In such

algorithms, the optimization problem is replaced by a sequence of simpler problems. These problems

are obtained by linearizing constraints and by approximating the Lagrangian function of the problem.

Based on works realized by Kristine Ekeli Klingan [50] and Christine Krugerud [51], this class of

algorithms is considered in this study. Three algorithms are available in Isight, software presented in

section 5.1:

- NLPQL(P) as used in works aforementioned, which is a Fortran subroutine developed by

Schittkowski [49]

- Multifunction Optimization System Tool (MOST), which solve the problem considering it is

purely continuous to find a peak. If the solution is real, the solution corresponds to variables of

the design space and the algorithm stops here. Otherwise, nearest points are found.

- The Mixed-Integer Sequential Quadratic Programming (MISQP) Technique. More details can be

found in [52].

3.7. Project philosophy In the project, different software are used to solve the different problem presented above. Isight is

used to perform the optimization of mooring lines. OrcaFlex is used to solve the dynamic analysis.

Details are given in section 5 regarding software involved. Communication between Isight and OrcaFlex

is done by an executable coded in Python. Figure 3-3 shows link between software and their role within

the project. Variables written refer to those presented in section 3.6.

Figure 3-3 Relation between software and their tasks

26

4. Design considerations Floating wind turbines, like other offshore structures are designed following criteria established in

codes and standards. These criteria change depending on the purpose of the platform and the

associated risks. The following section lists the main design considerations for mooring systems. These

criteria are based on DNVGL reports. However, requirements are consistent with other standards

though some differences.

The safety philosophy can use either safety class approach or consequence class methodology ( [25]

[53]). Designs of floating structures that follow DNVGL-ST-0119 standard (consequence class

methodology) lead to meet normal safety class approach (DNVGL-ST-0126).

The two safety classes used while dealing with wind turbine structures are the normal safety class

“which applies when a failure results in risk of personal injury and / or economic, environmental, or

social consequences” and the special safety class “which applies when the safety requirements are

determined by local regulations and / or the safety requirements are agreed between the designer and

the customer”.

The consequence class is defined depending on the failure consequence. The two consequences class are defined as followed: Class 1: “where mooring system failure is unlikely to lead to unacceptable consequences such as loss of

life, collision with an adjacent platform, uncontrolled outflow of oil or gas, capsize or sinking”;

Class 2: “where mooring system failure may well lead to unacceptable consequences of these types”.

As recommended in the DNVGL-ST-0119 [25] and DNVGL-ST-0126 [53], excepted if it is specified,

floating structure and its station keeping system are designed using normal safety class and

consequence class 1 meaning that the floating structure is unmanned during severe environmental

loading conditions. The target safety level associated is an annual probability of failure of 10−4.

The design principle uses a so-called design by partial safety factor method. Basically, load and

resistance factors are applied to characteristic values of the governing variables before being

compared to a specified design criterion. Governing variables are classified by the DNVGL into two

subcategories: loads applied on the structure and resistance of the structure or strength of the

materials used.

The design criteria must be design regarding three different limit states. A limit state is defined by

DNVGL as a condition “beyond which a structure or a structural component will no longer satisfy the

design requirements”. Definitions are given in standards [46] and reported below.

An ultimate limit state (ULS): to ensure that the individual mooring lines have adequate strength to

withstand the load effects imposed by extreme environmental actions.

An accidental limit state (ALS): to ensure that the mooring system has adequate capacity to withstand

the failure of one mooring line, failure of one thruster or one failure in the thrusters’ control or power

systems for unknown reasons. A single failure in the control or power systems may cause that several

thrusters are not working.

A fatigue limit state (FLS): to ensure that the individual mooring lines have adequate capacity to

withstand cyclic loading.

Works realized during this study focus on ULS and ALS. FLS will be investigate within another task of

COREWIND project.

In addition, to validate the design of a floater and its mooring system, design load cases (DLCs) are

defined within standards. DLCs list a certain amount of cases, corresponding to potential cases that

27

could occur during the life of the wind turbine. To validate the design, the model should pass all the

cases. DLCs are listed in DNVGL-ST-0437 Loads and sites conditions for wind turbines [47]. More details

on DLCs used within this project is given in section 8.1.6.

4.1. Design criteria Different criteria are listed when designing mooring system. This section provides information

regarding design criteria used within the project.

The design criterion for mooring lines follows the usual partial safety factor method defined above.

The design tension is introduced as the sum of two factored tension as reported in .

𝑇𝑑 = 𝛾𝑚𝑒𝑎𝑛𝑇𝑐,𝑚𝑒𝑎𝑛 + 𝛾𝑑𝑦𝑛𝑇𝑐,𝑑𝑦𝑛 Equation 4-1

Where

𝑇𝑐,𝑚𝑒𝑎𝑛 Characteristic mean tension 𝑁 𝑇𝑐,𝑑𝑦𝑛 Characteristic dynamic tension 𝑁

𝛾𝑚𝑒𝑎𝑛 Load mean factor - 𝛾𝑑𝑦𝑛 Load dynamic factor -

Values for load factors depend on limit state and consequence class considered. Table 4-1 summarized

that values [25].

Table 4-1 Load factor requirements for design of mooring lines

Limit state Load factor Consequence class

1 2

ULS 𝛾𝑚𝑒𝑎𝑛 1.3 1.5

ULS 𝛾𝑑𝑦𝑛 1.75 2.2

ALS 𝛾𝑚𝑒𝑎𝑛 1.00 1.00

ALS 𝛾𝑑𝑦𝑛 1.10 1.25

It is common that statistics for minimum breaking strength are missing. In that case, the characteristic

capacity of the body of the mooring line is linked to the minimum breaking load using the following

relation:

𝑆𝑐 = 0.95. 𝑆𝑚𝑏𝑠 Equation 4-2 With,

𝑆𝑐 Characteristic strength of the mooring line

𝑁

𝑆𝑚𝑏𝑠 Minimum breaking strength of the material

𝑁

The design criteria for both ULS and ALS is given by:

𝛾𝑚𝑒𝑎𝑛𝑇𝑐,𝑚𝑒𝑎𝑛 + 𝛾𝑑𝑦𝑛𝑇𝑐,𝑑𝑦𝑛 = 𝑇𝑑 < 𝑆𝑐 = 0.95. 𝑆𝑚𝑏𝑠 Equation 4-3

The design equation can also be represented using this ratio:

(𝛾𝑚𝑒𝑎𝑛𝑇𝑐,𝑚𝑒𝑎𝑛 + 𝛾𝑑𝑦𝑛𝑇𝑐,𝑑𝑦𝑛)

0.95. 𝑆𝑚𝑏𝑠< 1 Equation 4-4

28

The design basis of a project also contains criteria that must be fulfilled by the system. These criteria

are checked for each design load cases. These criteria could be chosen to respect turbine integrity

(acceleration at RNA) and can also concern motions restrictions. 2 gives design criteria for the

location Gran Canaria, one of the locations studied during the project [43].

Table 4-2 Design criteria for Gran Canaria

Design Criterion Mathematical expression

Tension 𝑇𝑑

0.95𝑆𝑚𝑏𝑠< 1

X offset |𝑋𝑑𝑦𝑛𝑎𝑚𝑖𝑐| < 60 𝑚

Y offset |𝑌𝑑𝑦𝑛𝑎𝑚𝑖𝑐| < 60 𝑚

Acceleration (𝑎𝑐𝑐𝑥 , 𝑎𝑐𝑐𝑦, 𝑎𝑐𝑐𝑧) < 1.85 𝑚/𝑠²

Pitch |𝑅𝑌| < 7 𝑑𝑒𝑔

In addition, mooring lines must be analysis according to the fatigue limit state. Though not study during

this project, a description is given here. To evaluate mooring lines against fatigue failure, the design

cumulative fatigue damage is introduced.

𝐷𝐷 = 𝐷𝐹𝐹. 𝐷𝐶 Equation 4-5 With

𝐷𝑑 Design cumulative fatigue damage

N

𝐷𝑐 Characteristic cumulative fatigue damage

𝑁

𝐷𝐹𝐹 Design fatigue factor Values for design fatigue factor depend on consequence class as shown in

Table 4-3 Design fatigue factor for mooring chain

Consequence class 𝐷𝐹𝐹 1 5

2 10

The design characteristic cumulative fatigue damage is calculated using the Miner’s sum defined as:

𝐷𝑐 = ∑𝑛𝐶,𝑖

𝑁𝐶,𝑖

𝐼

𝑖=1

Equation 4-6

With

𝐼 Number of stress ranges 𝑛𝐶,𝑖 Number of cycles over a time

period

𝑁𝐶,𝑖 Number of stress cycles until failure at the given stress range

The associated design criterion is given by:

𝐷𝐷 ≤ 1.0 Equation 4-7

29

4.2. Corrosion Most projects have a design lifetime of 25 years. Therefore, mooring system must be designed to resist

during that time in harsh marine environment to avoid mooring lines replacement that would

significantly increase costs. Particularly, standards give requirements regarding corrosion allowance

and marine growth [46]. Analysis taking into account these effects must be realized. These analyses

are known as end of life analyses.

Figure 4-1 Corrosion allowance summarized corrosion allowance recommended.

The corrosion is accounted by adding an annual deterioration.

Figure 4-1 Corrosion allowance [46]

The corroded diameter is then calculated by:

𝐷𝑐𝑜𝑟𝑟 = 𝐷𝑛𝑒𝑤 − 𝑐 × 𝐿𝑇 Equation 4-8 With

𝐷𝑐𝑜𝑟𝑟 Corroded chain diameter 𝑚

𝐷𝑛𝑒𝑤 New (un-corroded) chain diameter

𝑚

𝑐 Corrosion allowance 𝑚. 𝑦𝑒𝑎𝑟𝑠−1

𝐿𝑇 Lifetime 𝑦𝑒𝑎𝑟𝑠

The resulting MBL is given by:

𝑆𝑚𝑏𝑠−𝑐𝑜𝑟𝑟 = 𝑆𝑚𝑏𝑠 (𝐷𝑐𝑜𝑟𝑟

𝐷𝑛𝑒𝑤)

2

Equation 4-9

It is common to realize calculations using MBL corresponding to corroded diameter and to keep the

uncorroded diameter to calculate drag forces as well as the mass per unit length and the elastic

modulus [16].

4.3. Marine growth Marine growth occurs naturally onto submerged structure. The development of fauna and flora will

change hydrodynamic diameter and properties of materials. Marine growth increases the weight of

the components, changes the geometry (diameter) conducting to changes on loads and dynamic

responses (change of drag forces) and modifies the roughness [47]. DNVGL recommends taking into

account marine growth by increasing the weight of the line and the drag coefficients [46]. Figure 4-2

gives main data regarding marine growth.

30

Figure 4-2 Marine growth data depending on location [46]

The new line mass with marine growth is given by:

𝑀𝑙𝑖𝑛𝑒 = 𝑀𝑖𝑛𝑖𝑡𝑖𝑎𝑙 +𝜋

4[(𝐷𝑛𝑜𝑚 + 2Δ𝑇)2 − 𝐷𝑛𝑜𝑚

2 ]. 𝜌𝑔𝑟𝑜𝑤𝑡ℎ. 𝜇 Equation 4-10

Where,

𝑀𝑙𝑖𝑛𝑒 Mass of the line per unit length 𝑘𝑔/𝑚

𝑀𝑖𝑛𝑖𝑡𝑖𝑎𝑙 Mass per unit length without

marine growth 𝑘𝑔/𝑚

𝜌𝑔𝑟𝑜𝑤𝑡ℎ marine growth density 𝑘𝑔. 𝑚−3

𝜇 Coefficient equals to 1.0 for

wire rope and to 2.0 for chain /

𝐷𝑛𝑜𝑚 Nominal diameter (i.e bar

diameter) m

∆𝑇 Marine growth thickness m

The drag coefficient with marine growth is given by:

𝐶𝐷𝑔𝑟𝑜𝑤𝑡ℎ = 𝐶𝐷[𝐷𝑛𝑜𝑚 + 2Δ𝑇𝑔𝑟𝑜𝑤𝑡ℎ

𝐷𝑛𝑜𝑚] Equation 4-11

𝐶𝐷𝑔𝑟𝑜𝑤𝑡ℎ Drag coefficient with marine

growth

𝐶𝐷 Drag coefficient without

marine growth

𝐷𝑛𝑜𝑚 Nominal diameter (i.e bar

diameter) 𝑚𝑚

Δ𝑇𝑔𝑟𝑜𝑤𝑡ℎ Marine growth thickness 𝑚𝑚

Marine growth has a relatively low density (closed to salt water) so it is usual to exclude marine growth

for buoyancy calculation.

31

5. Software The project involved different softwares and programming languages as briefly introduced in section

3.7. This section gives a description of the softwares and their utilization within the project.

5.1. Isight Isight is a software developed by Dassault Systèmes. It is a multi-tasks tool for “effectively and

efficiently managing simulation-based design processes”. It proposes different implemented tools like

optimization process, design of experiments or Monte Carlo analysis. In addition, the software allows

to combine these components with existing commercial software such as Abaqus, Excel, Ansys and

others. Design is simplified by a visual and flexible workbench. Isight is used within the project for its

optimization component. Isight allows to communicate with external softwares. Particularly, a module

allows to run an executable. Communication between Isight and this executable is done using text files.

5.2. Orcaflex OrcaFlex is a software developed by Orcina. OrcaFlex allows to perform dynamic analysis for offshore

marine systems. It proposes different features to model offshore floating wind turbines and their

mooring systems. OrcaFlex is preferred to FAST for its ability to model different kind of mooring

systems. In addition, OrcaFlex has a Python interface developed by Orcina, that facilitates

development of the coupling with Isight.

OrcaFlex proposes different options to model mooring lines. Mooring lines can be composed of

different line sections. Each line section can be modelled using a line type. A line type is an OrcaFlex

object in which line properties, such as mass, axial stiffness, diameters, are listed. Line type can be

created using an interface integrated to OrcaFlex, called Wizard, or directly by the user. The Wizard

has its own database that allows to set up the line type (mass, drag coefficients) based on a selected

material and selected diameter.

5.3. FAST FAST code is an opensource code developed by the National Renewable Energy Laboratory (NREL) that

allows to model land-based, fixed-bottom offshore and floating offshore wind turbine. FAST offers the

possibility to perform a coupled analysis with aero-servo-hydro and elasto modules. Information can

be found on NREL website and OpenFast Github [54] [55].In this project, FAST is used to generate time

series representing aerodynamic loads applied in OrcaFlex. Results from FAST models defined by

partners are also used to be compared with those obtained with OrcaFlex.

5.4. Python Interface Python is an interpreted, high-level, general-purpose programming language [56]. This programming

language is used to realize the coupling between Isight and OrcaFlex, using OrcaFlex API.

32

6. Input data

6.1. Referecence frame The origin of the fixed inertial frame is defined at the intersection of the tower centerline and the

mean sea level (MSL). The X-axis is directed in the wind, wave and current direction. Z-axis, is

directed vertically upwards. The Y-axis is defined to ensure that the reference frame is a Cartesian

direct coordinate system.

Figure 6-1 Fixed inertia frame definition (INNOSEA)

6.2. Environmental condition The project focuses on three different sites: West of Bara Island, Gran Canaria Island, and Morro Bay.

This section provides a brief review of environmental conditions for Gran Canaria. This summary

presents environmental data that are used in the project for the optimization. Complete information

can be found on the public design basis established within the project [43].

Gran Canaria Island is one of the Spanish islands of the Canarias, situated in Atlantic Ocean. The water

depth of the studied location is set to 200 m. Information regarding water level can be found in [43].

6.2.1. Wind data Wind data are obtained from data provided by the Spanish Ports Authority using the SIMAR point

4038006. Results are based on simulations that give the 1-hour wind speed at 10 m.

The 1-hour mean wind speed is equal to 9 𝑚. 𝑠−1. This data is obtained using wind speed series of the

last 10 years. Extrapolation, given in section 2.3.2.11 in [40], allows to obtain the 10-minute wind speed

[43], which is calculated to be 9.83 𝑚. 𝑠−1. A logarithmic law, found to be the best fit for the wind

profile [43], is then used to interpolate values at different heights above the sea level. Results are

presented in .

33

Table 6-1 10-minute mean wind speed profile

Normal wind profile

Height [m] Speed [m/s]

10 9.83

20 10.48

50 11.33

100 11.98

119 12.14

150 12.36

The maximum 1-hour average wind speed is 19.0 𝑚. 𝑠−1 at 10 m. Again, this value is used to calculate

the maximum 10-minute average wind speed, equal to 20.75 𝑚. 𝑠−1. In order to obtain the extreme

wind speed profile, for a return period of 50 years and 10 minutes mean at different heights, a power

low formula provided in the standard IEC-61400-1 is applied [57].

𝑉(𝑧) = 𝑉𝑟𝑒𝑓 . (𝑧

𝑧𝑟𝑒𝑓)

𝛼

With

𝑉 Maximum 10-minute average wind at z 𝑚. 𝑠−1 𝑉𝑟𝑒𝑓 Maximum 10-minute average wind at 𝑧𝑟𝑒𝑓 𝑚. 𝑠−1 𝑧𝑟𝑒𝑓 Reference height, here 10 m 𝑚

𝛼 Power law exponent, here 0.12 Results are presented below:

Table 6-2 Extreme wind profile for a return period of 50 years

Normal wind profile

Height [m] Maximum wind Speed

[𝑚. 𝑠−1]

10 20.75

20 22.55

50 25.17

100 27.35

119 27.93

150 28.72

More information can be found on the design basis of the project COREWIND regarding wind

histogram, wind spectrum and wind gust characteristics [43]. However, these data are not used in the

next section and are, therefore, not presented here.

The wind rose for the 1-hour mean speed is shown in Figure 6-2. These data are obtained using data

from 1959 to 2019.

34

Figure 6-2 Wind rose for 1-hour mean speed at Gran Canaria [43]

6.2.2. Waves Data used for waves are obtained using tool developed by the Spanish Ports Authority using the SIMAR

point 4038006. Extreme waves are given below for different return periods.

Table 6-3 Extreme waves data for Gran Canaria (from [43])

Return period (years) Hs (m) Tp (s)

50 5.11 9.0-11.0

20 4.69 9.0-11.0

10 4.40 9.0-11.0

1 3.35 8.0-10.0

Another common information that is required to analyze sea states is the wave scatter diagram that

gives the probability of occurrence for a couple significant height 𝐻𝑠 and a peak period 𝑇𝑝.

35

Table 6-4 Scatter diagram for Gran Canaria

% Significant Wave Height (m)

0 - 1 1--2 2--3 3--4 4--5 Total

Pea

k P

erio

d (

s)

1--2 0,037 0,001 0 0 0 0,038

2--3 0,771 0,300 0 0 0 1,071

3--4 2,603 1,845 0 0 0 4,448

4--5 4,524 5,132 0,003 0 0 9,659

5--6 5,392 10,973 0,049 0 0 16,414

6--7 4,907 14,608 0,465 0 0 19,980

7--8 4,211 9,569 2,593 0,012 0 16,385

8--9 3,504 5,006 2,552 0,110 0 11,172

9--10 2,836 3,119 1,087 0,147 0,001 7,190

10--11

2,252 1,865 0,522 0,073 0,003 4,715

11--12

1,766 1,250 0,275 0,028 0 3,319

12--13

1,244 0,823 0,161 0,005 0 2,233

13--14

0,827 0,542 0,120 0,001 0 1,490

14--15

0,512 0,326 0,085 0,002 0 0,925

15--16

0,270 0,210 0,052 0,003 0 0,535

16--17

0,129 0,119 0,034 0,001 0 0,283

17--18

0,040 0,058 0,005 0 0 0,103

18--19

0,010 0,018 0 0 0 0,028

19--20

0,001 0,006 0,001 0 0 0,008

20--21

0 0,002 0 0 0 0,002

21--22

0 0,001 0 0 0 0,001

Total 35,836 55,773 8,004 0,382 0,004 100,000

Eventually, the wave rose is given here.

36

Figure 6-3 Wave Rose at Gran Canaria [43]

More information can be found on the Design basis of the project regarding wind and waves combined

conditions.

6.2.3. Current Current data are presented here. They are based on available data from SIMAR point 4038006 and

extrapolations. The current is usually distinguished into current induced by wind and tidal current. The

current speed for a 50-years return period induced by wind is 0.57 𝑚. 𝑠−1 at the sea surface. This value

is obtained using [43]:

𝑉𝑐 = 𝑘 𝑈1−ℎ𝑜𝑢𝑟

With

𝑘 0.03

𝑈1−ℎ𝑜𝑢𝑟 19 1-hour maximum annual wind speed at 10m

Direction associated to this wind current is taken as the most probable wind direction, which is a north-

northeast (NNE) to south-southwest (SSW) direction.

Based on data available for the northeast cost of the island, a deep-water current, also known as tidal

current, for a return period of 50 years is taken equal to 0.49 𝑚. 𝑠−1. This current follows the coast

and is, therefore, also set to a NNE-SSW direction.

Current profiles for both wind current and tidal follow recommendation given in the report DNVGL-

RP-C205 [40]. Current speeds are presented below.

37

Table 6-5 Current speed profile for a return period of 50 years

Depth (m) Wind

Component (m/s)

Tidal Component

(m/s)

Total current speed (m/s)

0 0,57 0,49 1,06

-10 0,52 0,49 1,01

-20 0,48 0,48 0,96

-30 0,43 0,48 0,91

-40 0,39 0,48 0,87

-50 0,34 0,47 0,81

-60 0,3 0,47 0,77

-70 0,25 0,47 0,72

-80 0,21 0,46 0,67

-90 0,16 0,46 0,62

-100 0,11 0,46 0,57

-110 0,07 0,45 0,52

-120 0,02 0,45 0,47

-130 0 0,44 0,44

-140 0 0,44 0,44

-150 0 0,43 0,43

-160 0 0,42 0,42

-170 0 0,42 0,42

-180 0 0,41 0,41

-190 0 0,4 0,4

-200 0 0,39 0,39

The total current speed is directly equal to the sum of the wind component and tidal component

because currents have the same direction.

6.3. Floating platforms The project focuses on two floating platforms, the WindCrete spar concept developed by the University

of Catalonia (UPC) and the ActiveFloat concept, a semi-submersible, developed by Cobra. In this part,

public information about floaters are listed. This list mainly refers to the deliverable D1.3 “Public design

and FAST models of the two 15MW floater-turbine concepts” [58] of COREWIND. Platforms are design

for Gran Canaria location, one of the three locations chosen for the project.

Additionally, FAST models are implemented in OrcaFlex to be used for the optimization. Therefore,

static state and natural periods are investigated to ensure consistence between models.

6.3.1. WindCrete Spar

6.3.1.1. Floater description WindCrete is a spar developed by the Universitat politècnica de Catalunya.

The platform is composed of a concrete cylinder with ballast and the turbine tower on top..

The tower height is 129.495 m, designed to ensure a hub height of 135 m above the sea mean level

(MSL). This height is adjusted to ensure the respect of three design criteria based on IEC 61400-3-2

standard:

38

- 1)Access platform to be out of the reach of the 50-years wave crest;

- 2) Minimum air gap of 20% of Hs or 1.50 meters;

- 3) Hub height to be 6 meters plus the semi-rotor diameter [58].

Wind turbine has been redesigned compared to the initial IEA 15 MW used as a reference.

The tower base, located at the MSL, has a diameter of 13.2 m. The top tower has a diameter of 6.5 m

to ensure the connection with the wind turbine.

The transition piece between the tower and the substructure is composed of a truncated cone of 15

m height. The top diameter is 13.2 m and the base diameter of 18.6m.

The substructure is composed of two parts. A column with a diameter of 18.6 m and 135.7 m height

and an hemisphere of 9.3 m height.

The total draft, including transition piece is 155 m. The corresponding displacement is 40540 𝑚3.

Figure 6-4 WindCrete sketch [58]

from [58] gives a sketch of the WindCrete spar structure.

The platform contains a solid aggregate ballast of 44.15 height, with a bulk density of 2500 kg.m3. This

ballast is added to achieve the required stiffness in pitch and roll. This ballast is represented in brown

in Figure 6-4 .

39

The main properties of the WindCrete spar are summarized in the following table.

Table 6-6 Main properties of WindCrete Spar [58]

Total Mass [t] 3.9805e+4

Center of Mass (CM) Height [m] from MSL -98.41

Ixx [t.m²] from CM 155.36e+6

Iyy [t.m²] from CM 155.36e+6

Izz [t.m²] from CM 1.9025e+6

Masses used are summarized below.

Table 6-7 WindCrete masses [58]

Platform mass [t] 36550.0

Tower mass [t] 3258.9

Total Substructure mass [t] 39809.0

Nacelle Mass [t] 630.9

Hub mass [t] 384.9

Total RNA [t] 1015.9

Total mass [t] 40824.7

6.3.1.2. Modelisation strategy In FAST, the first 10 m of the tower are accounted in HydroDyn (i.e as part of the substructure).

Therefore, this part is also modelized in OrcaFlex. The top diameter of that part is 12.42 m. More details

about FAST models are given in section 5.2 of the public report [58].

In FAST and OrcaFlex, the bottom hemisphere is modelized as a cylinder with a diameter of 15.19 m.

This equivalent diameter is calculated to respect the buoyancy. Each part of the model is discretized in

1 m height element.

Inertias given in Table 6-6 are those used in OrcaFlex. Indeed, the FAST model makes a difference

between the substructure and the tower to compute aerodynamic loads. These loads are not

calculated in OrcaFlex. Instead a point force is used.

It was decided to use three points mass to model the masses. The platform and the tower (total

substructure mass) located at their center of mass (0; 0; -98.41). The hub and the nacelle are separated

to respect as much as possible the FAST model. Inertia were also added to these points mass.

6.3.1.3. Hydrodynamic model The section “Hydrodynamic model” of the public report [58] lists the hydrodynamic properties of the

platform. As explained, the hydrodynamic of the WindCrete spar model is inertia dominated. To

achieve that conclusion, the calculation of the Keulegan-Carpenter number is done.

As explained in section 3.2, a Keulegan-Carpenter number lower than 2 leads to inertia domination

[42]. For each part of the floating platform, the Keulegan-Carpenter number associated to the lowest

diameter is calculated for a wave amplitude corresponding to 𝐻𝑠,50𝑦𝑒𝑎𝑟𝑠 given in the design basis of

the project [43].

40

Table 6-8 Keulegan-Carpenter numbers for WindCrete platform

2𝜋𝐴 (m) 16.05

Diameter (m) Kc

18.60 0.86

13.20 1.22

12.42 1.29

15.19 1.06

The potential flow theory is therefore applicable. The ANSYS-AQWA potential-flow solutions outputs

are imported into OrcaFlex to be used. Details can be found in [58] regarding first order

hydrodynamics, radiation solution and second order forces. In addition, drag forces are applied using

Morison equation. This is done by adding drag coefficients in OrcaFlex.

The transverse drag coefficient is taken equal to 0.7 for the submerged substructure [58]. An axial drag

coefficient was set to 0.2 for the bottom hemisphere in accordance with the same report. Two

different models.

6.3.1.4. Mooring system The mooring system presented here is the initial design proposed by partners.

The mooring system is composed of three catenary lines. Each line is composed of one section from

the anchor to a delta plate followed by two delta lines (known as crowfoot system). Fairleads are

located 90 m below the MSL. The first section of lines is 565 m and the two delta lines are 50 m long.

The main properties are presented in the table below. The diameter listed here is the equivalent

diameter given in FAST. This is the diameter that gives the same buoyancy of the chain used. The drag

diameter of the lines is set to 0.160m.

Table 6-9 WindCrete mooring system main properties [58]

Number of lines 3

Diameter [mm] 160

Dry Weight [kg/m] 561.2521

Stiffness EA [kN] 2.3040e6

Main line length [m] 565

Delta line length [m] 50

Mooring stiffness YAW [𝑁. 𝑚. 𝑟𝑎𝑑−1] 5.1545e+08

Mooring stiffness SURGE [𝑁. 𝑚−1] 5.0523e+05

Figure 6-5 OrcaFlex view of the mooring system

Friction is not accounted for the simulation to follow MoorDyn set up.

41

6.3.2. ActiveFloat semisubmersible 6.3.2.

6.3.2.1. Floater description ActiveFloat is a semi-submersible designed by COBRA (currently developed by COBRA and ESTEYCO).

The platform is a concrete semisubmersible with 3 external columns and one center column on which

the tower is connected. External columns are connected to the central one using pontoons. As

reported in [58], the floater is transported fully assembled but unballasted to reduce the draft (11-13

m instead of 26.50 m in operation). This characteristic is one advantage of semisubmersible platforms

to avoid offshore lifting. The displacement of the platform in operating conditions is 36431.22 𝑚3.

Each external column has a heave plate at its base. This provides heave added mass and damping.

Figure 6-6 ActiveFloat floater sketch [58]

The main dimensions of the platform are summarized below. The tower height is adjusted to a

respective hub height of 135 m from MSL following standard as explained in 6.3.1.

Figure 6-7 Main dimensions of ActiveFloat [58]

Hub height (m) 135.00

Columns Diameter (m) 17.00

Columns separation (center to tower center) (m) 34.00

Columns height (m) 35.50

Central cone base diameter (m) 19.60

Central cone top diameter (m) 11.00

Tower base diameter (m) 10.00

Tower top diameter (m) 6.50

Tower length (m) 120.50

Pontoons height (m) 11.50

Heave plate cantilever (m) 4.00

Overall beam (m) 83.90

The platform includes a permanent ballast as well as an active ballast system. Pontoons are fully

ballasted while external columns are partially ballasted. The active ballast system allows to transfer

water between columns to compensate mean pitch.

42

Platform information are listed below.

Table 6-10 WindCrete : mass and inertia [58]

Mass [t] 3.524e+4

Center of Mass (CM) Height [m] -17.37

Ixx [t.m²] from CM 1.570e+7

Iyy [t.m²] from CM 1.570e+7

Izz [t.m²] from CM 2.580e+7

Table 6-11 WindCrete : elements’ masses [58]

Platform mass [t] 3.524e+4

Tower mass [t] 1141.41

Nacelle Mass [t] 630.888

Hub mass [t] 384.998

Total RNA [t] 1015.885

Total mass [t] 38413.181

6.3.2.2. Modelization strategy The tower and the substructure masses are modeled as two different lumped buoys in OrcaFlex,

contrary to WindCrete. The tower is also lighter compared to the one modeled with WindCrete

because it is made of steel.

Each element of the OrcaFlex model is discretized into a 1 m height element.

Seven elements were used to model the floater, three representing each external column, one for the

central one and three for the pontoons.

6.3.2.3. Hydrodynamic model The hydrodynamic model is described in [58]. Viscous forces are modeled using Morison equation. This

section provides information regarding this modelization.

Drag coefficients for the central column are calculated following the methodology provided in standard

[40]. In this approach, drag coefficients are calculated using the diameter and the surface roughness,

as followed:

𝐶𝐷𝑆(Δ) = {

0.65 ∶ Δ < 10−4

29 + 4 log(Δ)

20∶ 10−4 < Δ < 10−2

1.05 ∶ Δ > 10−2

Δ =𝑘

𝐷

Where,

𝐶𝐷𝑆 Drag coefficient Δ Ratio surface roughness/diameter 𝑘 Surface roughness 𝑚 𝐷 Diameter 𝑚

The surface roughness is set to 3 mm [58]. The corresponding transverse drag coefficients are between

0.737 and 0.687. The same process is used to calculate the drag coefficient for external columns

resulting to a coefficient equal to 0.699.

43

The methodology to obtained drag coefficients for the pontoons of the platform is fully described in

[58]. In FAST only cylindrical shaped members can be used. Therefore, drag coefficients must be

corrected to ensure that loads applied are equal to the real ones. To do that, drag coefficients of the

real platform are calculated using literature, as well as cross-section areas.

Figure 6-8 Sketch of the real platform (left) and of the FAST model (right)

Figure 6-8 represents the difference between the real platform and the FAST model. The inner heave

plate, originally triangular, is modeled by a circle. The pontoon, in red, is modeled by a cylinder with a

lower cross-section. The outer heave plate is modeled using the external column cross-section area. ,

from [58], summarizes dimensions and drag coefficients for both real platform and model. To be

consistent with FAST, values are kept in OrcaFlex.

Table 6-12 ActiveFloat : Drag properties for real platform and model [58]

Property Real Platform FAST/OrcaFlex model

Pontoon leg height 11.5m 11.5m

Pontoon leg width 17m 11.5m

Transverse drag coefficient of for pontoon

𝐶𝑑 = 2.05 𝐶𝑑 = 2.05

Outer heave plate area 𝐴 = 451.94𝑚2 𝐴 = 302.33𝑚2 Outer heave plate drag

coefficient 𝐶𝑑 = 10 𝐶𝑑 = 40.9

Central heave plate area 𝐴 = 125.14𝑚2 𝐴 = 226.98𝑚2 Central have plate coefficient 𝐶𝑑 = 2.05 𝐶𝑑 = 5.7

6.3.2.4. Mooring system The mooring system implemented with Activefloat is very similar to the one used for WindCrete. The

main difference is the length of the line. Three catenary lines of 614 m unstretched were used. Lines

are directly connected to the platform without delta lines system. Main parameters are listed below.

This mooring system was designed to limit surge offset when experiencing the maximum rotor thrust

and to avoid vertical loads on the anchor. The friction was not accounted to follow MoorDyn

characteristic.

44

Table 6-13 ActiveFloat mooring system main properties [58]

Number of lines 3

Diameter [mm] 160

Dry Weight [kg/m] 561.2521

Stiffness EA [kN] 2.3040e6

Main line length [m] 614

45

7. Mooring Optimization

7.1. Optimization process

7.1.1. Generalities Many parameters are involved when dealing with mooring system optimization. As presented in

section 0, mooring systems imply a lot of elements, materials and configurations. To simplify the

optimization process, it was decided to act iteratively. In other word, a configuration is chosen, e.g. a

spread mooring system composed of 3 chain-made mooring lines, and optimized. Therefore, the user

defines different mooring system configurations based on engineering judgment and optimizes each

one. Eventually, an analysis is performed to choose the best system among those obtained. This

approach easily creates an optimization process and screen many configurations.

Once the design chosen, Figure 7-1 shows the process used to find the best configuration. The research

is carried out in two steps. The first step scans the design space and tries configurations. At the end,

the minimum found is used as the starting point for the second loop. This loop tries to refine results

around the minimum to potentially identify a better point.

Figure 7-1 Optimization screening tool: iterative process

Figure 7-2 shows processes involved during one iteration. The dashed and purple rectangle represents

functions included in the executable, i.e. coded in Python. At each iteration parameters are defined

and written in text files by Isight before being read by the executable. In parallel, the OrcaFlex model

is loaded and read.

Each line of the mooring system belongs to a group of lines. Each group of lines is treated equally, the

same properties are applied. Functions set up the model for each line of each group before running

the simulation depending on the choice of the user (either using a FAST-OrcaFlex approach or only

OrcaFlex). A group of functions can then calculate results for each line. At this stage, criteria imposed

by the design basis are checked. If they are respected an end of life analysis (marine growth and

corrosion accounted) is realized. If not, the program stops and returns only start of life results. This

46

reduces computational time. Results are written in text files to be sent back to Isight. There, criteria

are evaluated, and a new sample of configurations is tested.

Isight allows parallelization. Therefore, 8 simulations are tested simultaneously.

Figure 7-2 Optimization screening tool: loop processes

47

Line changes functions include creation of new line types (see section 5.2 for details) (diameter, mass

per unit length, axial stiffness, drag coefficients), change of anchors positions, change of lines lengths

and lines types and calculation of minimum breaking loads. As explain bellow, it includes also

positioning of clump weights and buoyancy modules if used. Spread angles (angles between anchors)

are kept constant.

Results functions include calculation of design tension for each line section and calculation of the

tension criterion (using MBL of the section), tension at anchors, distance between anchors and

touchdown points, maximum dynamic displacements of the platform for the six degrees of freedom,

and maximum nacelle accelerations in translation. Materials costs for lines and anchors are estimated

using formula provided in section 2.3.2.

Before running dynamic analysis, a static analysis without wind, current and waves is performed to

obtained static equilibrium.

Some design considerations have been chosen to simplify the optimization process. One parameter

that is always changed is the line length. To avoid introducing several lengths for each line section it

was decided to introduce a coefficient ci somewhere between 0 and 1. If the line is composed of N

sections, the length of the top part of the line is not changed. Indeed, this section is usually composed

of chain that is used to adapt the length during the installation. The length of the section starting at

the anchor is changed to Li × ci. The last section (or the last sections) is set to Li × (1 − ci) (or Li(1−ci)

N−2

with N the number of section). This assumption is particularly important when the line is a mixed line,

e.g. chain and wire. If needed, the parameter 𝑐𝑖 could be included as a design parameter.

If clump weights are included in the model, their mass and their number could be optimized. Five types

are clump weights are defined. Clump weights are positioned from both side of the touchdown point

in static state. The same approach is used for buoyancy modules, but they are positioned before the

touchdown point. Distance between two clump weights or two buoyancy modules is kept constant but

could be optimized if needed.

7.1.2. Design variables Design variables considered in this study are line diameters, chain grades, line lengths and anchor

radius. If the line is composed of several sections, each composed of one material, there are as many

diameters as materials used. Following tables illustrate this by giving examples for two systems:

- Three mooring lines composed of chain, each one composed of one section;

- Three mooring lines composed of two chain-made sections and one section of wire. In this

example, the two chain sections have the same diameters.

Table 7-1 Example of parameters used for one group of lines made in chain

Design Variable

𝐷𝑐ℎ𝑎𝑖𝑛

𝐿𝑡𝑜𝑡𝑎𝑙 𝐺𝑟𝑎𝑑𝑒

𝑅

48

Table 7-2 Example of parameters used for one group of lines made in chain and wire

Design Variable

𝐷𝑐ℎ𝑎𝑖𝑛

𝐷𝑤𝑖𝑟𝑒

𝐿𝑡𝑜𝑡𝑎𝑙 𝐺𝑟𝑎𝑑𝑒

𝑅 The anchor radius and the total line length are highly dependent and geometrically the line length is

bounded. Figure 7-3 represents a sketch of a basic anchored floating platform on which characteristic

lengths are represented. It is easy to establish relations below for an unstretched line.

√𝑟2 + ℎ2 ≤ 𝐿 ≤ 𝑟 + ℎ

With,

𝐿 Line length 𝑚 𝑟 Anchor radius 𝑚 ℎ Water depth 𝑚

For a catenary mooring line, the line length must be even higher than the lower bound (to ensure that

there is line laying on the seabed). To deal with this rule during the optimization, instead of directly

optimize the anchor radius, a coefficient is introduced. Therefore, the coefficient is used as a design

variable and the anchor radius is calculated following a linear regression.

Let us define 𝑥𝑚𝑎𝑥 and 𝑥𝑚𝑖𝑛 coefficients for which the anchor radius is respectively

𝑅𝑚𝑎𝑥 = √𝐿2 − ℎ2 and 𝑅𝑚𝑖𝑛 = 𝐿 − ℎ.

Therefore, the anchor radius is given by 𝑅𝑚𝑎𝑥−𝑅𝑚𝑖𝑛

𝑥𝑚𝑎𝑥−𝑥𝑚𝑖𝑛(𝑥 − 𝑥𝑚𝑎𝑥) + 𝑅𝑚𝑎𝑥

With 𝑥 ∈ [𝑥𝑚𝑖𝑛 , 𝑥𝑚𝑎𝑥].

49

Figure 7-3 Sketch of mooring system to illustrate line length and anchor radius dependency

On the contrary, for a semi-taut mooring system, the radius is calculated based on the unstretched line

length and the depth (precisely the distance between the fairlead and the seabed):

𝑅 = √𝐿2 − ℎ2

The anchor radius does not change the costs of the mooring system. It will only change the pretension

of the mooring system that could conduct to reject or validate a mooring design.

In addition, several cases are considered: each system is composed of several lines with fixed sections

(in term of materials). This way, materials are kind of a design parameter of the optimization.

7.1.3. Design Constraints Constraints considered in this study are the following:

- Tension criterion: Criterion defined within section 4.1

- Touchdown point criterion: this criterion is selected when considering catenary mooring

system. It results of the evaluation of the minimum length defined by the anchor position and

the position of the touchdown point. This criterion ensures that loads on the anchor are

horizontal.

- Wire/Rope criterion: it is selected when considered other material than chain in the line. The

aim is to ensure that this material does not touch the seabed.

- Other criteria: Criteria defined within section 4.1

7.1.4. Objective function The objective function is to minimize the cost of the mooring system. This cost includes line costs and

anchor costs.

50

𝐶𝑜𝑠𝑡𝑠 = ∑ (∑ 𝑐𝑗 × 𝐿𝑗

𝑠𝑖

𝑗=1

)

𝑖

+ 𝑐𝑎𝑛𝑐ℎ𝑜𝑟,𝑖

𝑁

𝑖=1

With

𝑁 Number of lines 𝑠𝑖 Number of sections per line 𝑐𝑗 Cost per unit length of the material of the

section 𝐿𝑗 Length of section

𝑐𝑎𝑛𝑐ℎ𝑜𝑟,𝑖 Costs of the anchor

Costs are obtained based on formula provided in section 2.3.2. It was decided to not include

installation costs. During the optimization, a coefficient of 0.93 €/$ was used to give costs in euros [59].

7.1.5. Material Different materials are used within the project as presented above. This section provides information

regarding how materials are modelized in OrcaFlex.

For chains, the OrcaFlex’s wizard is used. The wizard uses its own formulas to set up the model based

on the bar diameter (mass, outer diameter, axial stiffness, etc.). Readers can find information about

these data in the help section of OrcaFlex [31].

For the wire, depending on the lifetime of the system, the user can choose to use easier 6-strands or

spiral wire. The 6-strands being set up using the wizard just like chain. 6x19 wire with wire core is

automatically used. For the spiral strand wire rope, data were taken from Vryhof catalogue [34]. It was

decided to use sheathed data, to reduce corrosion on mooring lines. The outer diameter is calculated

based on the difference between the nominal weight and the submerged nominal weight using

Equation 7-1. The bending stiffness is set to 0, as well as the torsional stiffness. Transverse drag

coefficients are set to 1.2 according to standards, while longitudinal one is equal to 0 [46].

𝐷 = 2√(𝑚𝑑𝑟𝑦 − 𝑚𝑤𝑒𝑡)

𝜋𝜌𝑠𝑎𝑙𝑡 𝑤𝑎𝑡𝑒𝑟 Equation 7-1

Nylon was based on the superline nylon developed by Bridon [60]. Once again, the outer diameter is

calculated thanks to the difference between in air and submerged nominal mass. Transverse drag

coefficients are set to 1.6 [46]. One characteristic of the nylon is the dependence of the axial stiffness

to the applied load. To take it into account, a variable axial stiffness is used following “Load vs

Extension” curve, provided by the manufacturer.

The polyester used is the DeepRope polyester Acordis Polyester 855TN, developed by Bexco [61].

7.1.6. DLCs Costs optimization on all the DLCs recommended by standards (see section 4) would require a

considerable time resource. It was decided to reduce the study on design load cases considered as

most critical for the mooring system. DLC 6.1 and 6.2 were therefore considered. Particularly, one case

from these DLCs is used for the optimization.

51

These loads cases imply that the turbine is parked (standing still or idling), which implies in the studied

case a blade pitch angle of 90°. Wind conditions considered are the extreme wind model, the waves

model the extreme sea state, and the current model the extreme current model.

Extreme sea state is obtained using a Jonswap spectra with a significant height equal to the significant

height for a 50-years return period and the maximal most probable period associated. The extreme

current is obtained using current with a 50-years return period. The extreme wind model is also

obtained using a wind speed with a 50-years return period. Values for Gran Canaria can be found in

section 6.2.

According to standard, 396 cases are defined for DLCs 6.2 and 72 for DLC 6.1. These cases correspond

to different wave periods, turbine yaw misalignments, still water levels, waves directions. 6 seeds are

used (to generate waves spectra and aerodynamic loads). Three yaw misalignments, corresponding

to -8°, 0°, 8° are used for the DLC 6.1. Readers can find values ±15° in standards [47], which are

recommended while dealing with steady wind [57]. For the DLC 6.2, 10 yaw misalignments are used

covering range ±180°.

In addition, one case corresponding to DLC 1.6 is used. DLC 1.6 corresponds to the turbine in

production, with normal wind conditions, a severe sea state and normal current model. Without

information on severe sea state conditions, standards recommend to use extreme sea state conditions.

52

8. Methodology

8.1. Models FAST models presented below are implemented into OrcaFlex to be use during the optimization.

Comparisons between FAST models and OrcaFlex models are realized. These comparisons correspond

to static state analysis and decay tests. Results are presented in section 9.1 and 9.2. In addition, the

FAST model used to generate aerodynamic loads is checked by comparing the thrust force obtained at

the rated wind speed with the one given in [58]. To do so, all FAST features are activated (i.e ElastoDyn,

ServoDyn, Inflow, Aero) and a 500 s simulation is run. Section 9.3 corresponds to this analysis.

8.2. Environmental conditions Environmental conditions chosen corresponds to thus recommended by standards for DLC 6.1 and 6.2

and presented in section 7.1.6. For aerodynamic loads, time histories are extracted from FAST for each

DLC, using an onshore model and using rigid body conditions. The yaw misalignment that leads to

highest loads is used for the optimization. FAST simulations were performed during 5200s. Therefore,

the first 1600s are neglected, to avoid error induced by transitory state.

8.3. Results analysis Once the optimization is realized, cases corresponding to DLC 6.1 and 6.2 are run and criteria are

checked. Section 9.6 presents these results.

53

9. Results

9.1. WindCrete model comparison FAST WindCrete spar model was implemented into OrcaFlex. The report D1.3 gives a list of simulation

results that can be used for comparison.

9.1.1. Static Equilibrium The static equilibrium was calculated in OrcaFlex. Offsets, for each degree of freedom, are reported

below and compared to the reference. The difference is also reported as a percentage of the draft,

which is 155m.

Table 9-1 WindCrete static equilibrium analysis: comparison between OrcaFlex and FAST models

Position (m) Orientation (deg)

Surge Sway Heave Roll Pitch Yaw

Reference [58] -1.01 0,00 -0.16 0.00 -0.64 0.00

OrcaFlex model -0,99 0.00 -0,16 0.00 -0.64 0.00

Δ 0.02 0.00 0,00 0.00 0.00 0.00

% Draft 0,01% 0.00% 0,00% 0.00% 0,00% 0.00%

Results are similar between OrcaFlex and FAST. The offsets in surge and pitch are due to the position

of the center of mass of the RNA. The mooring discretization could slightly change results but within a

small interval.

The mooring stiffness matrix is also reported below. Values were calculated from OrcaFlex.

Table 9-2 Mooring stiffness matrix for WindCrete platform

Mooring stiffness [𝑘𝑁. 𝑚−1] Mooring stiffness [𝑘𝑁. 𝑚. 𝑟𝑎𝑑−1]

Surge Sway Heave Roll Pitch Yaw

Surge 544,72 6,86e-9 -0,20 438,12e-9 -48,61e3 -8,90e-6

Sway 7,11e-9 545,70 -3,13e-9 48,67e3 -475,63e-9 638,26

Heave -0,20 -2,95e-9 107,77 1,49e-6 -107,71 10,59e-9

Roll 465,36e-9 48,67e3 1,47e-6 42,19e6 4,39e-6 403,46e3

Pitch -48,61e3 -440,05e-9 -107,71 7,57e-6 42,19e6 0,00

Yaw -8,89e-6 638,26 2,33e-9 53,80e3 751,18e-6 559,95e3

The matrix shows existence of coupling between some DOFs. Mooring stiffnesses have an impact on

natural periods. These values are affected by the discretization of the mooring lines. A sensitive

analysis was performed to analyze the effect of the discretization. Results were negligible and are not

reported here. For the optimization, the discretization will be chosen to make a balance between CPU

time and precision.

9.1.2. Decay tests Decay tests are performed. It consists of moving the platform from its static equilibrium position

before leaving it oscillating freely without environmental conditions. The aim of these tests is to

identify natural periods of the platform. Free decays were performed in heave, surge, pitch and yaw

and compared to results provided in the report.

54

Results presented in Table 9-3 are similar between OrcaFlex and FAST models for the four degrees of

freedom tested. Figure 9-1 shows floater response for each DOF on 1500 seconds. Figure 9-2 shows 10

natural periods for each DOF to allow a better overview of behaviors.

Figure 9-1 Decay tests of WindCrete floater

Figure 9-2 Decay tests of WindCrete floater: few periods

Decay tests

Natural Frequency [Hz] Natural Period [s]

OrcaFlex Reference [58]

Relative Difference

OrcaFlex Reference [58]

Relative Difference

Surge 0,01267 0,01221 3,77% 76.81 81,90 3,63%

Heave 0,02935 0,03052 3,83% 34,07 32,77 3,99%

Pitch 0,02401 0,02441 1,64% 41,65 40,97 1,67%

Yaw 0,09072 0,09155 0,91% 13,63 10,92 0,91%

Table 9-3 WindCrete: Comparison between natural frequencies obtained using FAST and OrcaFlex.

55

The behavior in surge, sway and heave is a consequence of a coupling between the studied degree of

freedom and another one. The mooring stiffness matrix shows this coupling. The spectral density of

the result is plotted to underline that. Figure 9-3 represents spectral density in heave and surge. The

two curves show one peak at the natural frequency and another one. In both cases, this peak is around

0.024 Hz. After analyzing the mooring stiffness matrix, one can conclude that there is a coupling

between surge and pitch and between yaw and roll.

Figure 9-3 Spectral density of platform in surge and yaw.

Based on these results, it can be concluded that the two models are similar and thus, the OrcaFlex

model can be used to realize the optimization.

9.2. ActiveFloat models comparison

9.2.1. Static Equilibrium The static equilibrium analysis was performed to compare results with those given in the report. Offsets, for each degree of

freedom, are reported below and compared to the reference. The difference is also reported as a percentage of the draft, which is 26.5 m. Results are very consistent. In addition, the matrix stiffness is given in

Table 9-5.

56

Table 9-4 ActiveFloat static equilibrium analysis: comparison between OrcaFlex and FAST models

DOF Posititon (m) Orientation (deg)

X Y Z Rot1 Rot2 Rot3

DL1.3 0,05 0,00 0,03 0,00 -1,80 0,00

OrcaFlex 0,07 0,00 -0,08 0,00 -1,68 0,00

Delta 0,01 0,00 0,86 0,00 0,10 0,00

% draft 0.08% 0.00% 0.42% 0.00% 0.45% 0.00%

Table 9-5 Mooring stiffness matrix for ActiveFloat platform

Mooring stiffness [𝑘𝑁. 𝑚−1] Mooring stiffness [𝑘𝑁. 𝑚. 𝑟𝑎𝑑−1]

Surge Sway Heave Roll Pitch Yaw

Surge 122,72 737,14e-9 -0,75 -121,22e-6 320,28 -91,56e-6

Sway 737,28e-9 123,66 -1,14e-6 -484,85 121,20e-6 58,95

Heave -0,75 -1,14e-6 69,10 169,29e-6 -112,37 19,84e-9

Roll -121,22e-6 -484,85 169,29e-6 4,28e6 -0,002 52,05e3

Pitch 320,28 121,2e-6 -112,37 -0,002 4,27e6 0,18

Yaw -91,56e-6 58,95 15,32e-9 -4236,28 -0,006 270,16e3

9.2.2. Decay tests Decay tests are also performed to estimate natural periods of the ActiveFloat platform. These periods

are then compared with those given in the public design report [58].

Table 9-6 ActiveFloat : Comparison between natural frequencies obtained using FAST and OrcaFlex.

The difference between natural periods in heave and pitch is small. The difference in surge and yaw is

higher. However, the difference in term of seconds is relatively small in pitch, and the period is high in

surge. The difference was therefore considered acceptable.

Decay tests are shown in Figure 9-4 and Figure 9-5. The surge curve shows the coupling between surge

and pitch.

Decay tests

Frequency [Hz] Period [s]

OrcaFlex Reference [58]

Relative difference

OrcaFlex Reference [58]

Relative difference

Surge 0,00667 0,00610 9,27 % 149,93 163,83 8,49 %

Heave 0,05403 0,05493 1,64 % 18,51 18,20 1,67 %

Pitch 0,03335 0,03052 9,27 % 29,99 32,77 8,49 %

Yaw 0,01201 0,01221 1,64 % 83,26 81,90 1,67 %

57

Figure 9-4 Decay tests of ActiveFloat floater

Figure 9-5 Decay tests of ActiveFloat floater: few periods

9.3. FAST model verification Figure 9-6 shows the evolution of the yaw bearing force Fxp for a wind speed equal to the rated wind

speed. The yaw bearing force obtained is 2375kN. This value is close to the rated roter thrust given in

58

[58], 2400kN. Therefore, the FAST model is considering correctly implemented and can be used to

generate time series for the optimization.

Figure 9-6 Yaw bearing force Fxp for 𝑉𝑟𝑒𝑓 = 10.56 𝑚/𝑠

9.4. Aerodynamic loads selection Results for yaw bearing forces from FAST simulations corresponding to DLC 6.1 and 6.2, presented in

section 7.1.6, are presented in Table 9-7.

Table 9-7 Yaw bearing forces Fxp and Fyp obtained for different yaw misalignement at Gran Canaria

Yaw misalignment [°] 𝑉𝑟𝑒𝑓[𝑚. 𝑠−1] 𝐹𝑥𝑝 [𝑘𝑁] 𝐹𝑦𝑝 [𝑘𝑁]

DLC 6.1

0 28.35 361 -88.3

+8 28.35 367 -266

-8 28.35 363 67.4

DLC 6.2

+180 28.35 399 -92.7

+150 28.35 435 20.6

+120 28.35 634 25.7

+90 28.35 630 -112

+60 28.35 646 -313

+30 39.58 440 -347

-30 39.58 458 232

-60 39.58 643 126

-90 39.58 625 -68

-120 39.58 645 -220

-150 39.58 437 -206

Maximum loads are obtained with a yaw misalignment equal to 60°: 𝐹𝑥𝑝 = 646 𝑘𝑁 and 𝐹𝑦𝑝 =

−313 𝑘𝑁. Time series corresponding to this yaw misalignment is therefore used in OrcaFlex.

59

9.5. Cases considered In this thesis, one configuration is tested based on WindCrete design.It is a simple chain configuration.

It was decided to separate the upwind line, the delta lines and the two downwind lines into three

groups. Therefore, each group could be optimized. gives allowed values for parameters involved in

the optimization. It must be noted that this table summarizes the last optimization realized on this

configuration. This configuration was the first one optimized. Therefore, it has required several tries

to correct some errors. Allowed values presented here are reduced, based on results obtained on

different tries.

Table 9-8 Design variables: allowed values

WindCrete Chain

Group 1 Group 2 Group 3

Chain Chain Chain

D (mm) L (m) Grade D (mm) L (m) Grade D (mm) L (m) Grade

From 68 to

78

From 600 to

750

From R3 to R4S

From 62 to 76

50 From R3 to R4S

From 62 to 76

From 500 to

650

From R3 to R4S

9.6. Optimization results This section provides results for optimized mooring systems obtained for the case study. Only results

for WindCrete composed of chain are presented. Analysis is indeed very similar for each floater and

different materials.

Table 9-10 WindCrete chain configuration: optimized mooring system description and give mooring system characteristics for the initial mooring system (used within work package 1) and for the chain configuration optimized system. The initial mooring system costs is estimated to be between 2293 k€ and 3363 k€ depending the type of steel grade used (

Table 9-10 WindCrete chain configuration: optimized mooring system description). Costs for the

optimized mooring configuration is estimated at 389k€ (). Thus, optimization conducts to a reduction

of 83%. Once again, these costs include only materials costs used for mooring lines and anchors.

The initial mooring system is composed of three lines. Each line is composed of a bottom part, and two

delta lines. In the following table, the three bottom parts correspond to Group 1 (i.e they have the

same properties). Delta lines, six lines, are listed as Group 2.

Table 9-9 WindCrete initial mooring system description

Original WindCrete

Group 1 Group 2 Costs

Chain Chain From 2293 k€ (Grade R3) to

3363 k€ (Grade R5) D (mm) L (m) Grade D (mm) L (m) Grade

160 565 Unknown 160 50 Unknown

Table 9-10 WindCrete chain configuration: optimized mooring system description

WindCrete Chain

Group 1 Group 2 Group 3 Costs

Chain Chain Chain

389k€ D (mm) L (m) Grade D (mm) L (m) Grade D (mm) L (m) Grade

70 700 R4 62 50 R3S 62 500 R3

60

Figure 9-7 shows a sketch of WindCrete, highlighting groups defined in . Lines of one group have the

same properties and each group is optimized independently. The red line corresponds to the line the

most loaded.

Figure 9-7 WindCrete mooring system group definition: Group1-red line, Group2: blue lines, Group3: green lines

summarizes static equilibrium of the platform. The offset in surge is due the highest mass of the

upwind line. The offset in pitch could be explain by the position of the center of gravity of the nacelle

and the dissymmetry of the mooring system, while the offset in heave (+4.6) is due to a lighter mooring

system compare to the original. Heave offset could be cancelled by increasing ballast mass. gives

platform natural periods for each DOF. The initial mooring system was design to provide sufficient

stiffness in surge and yaw, to have natural periods respectively around 80 seconds and 10 seconds.

These periods are no longer in that range. Moreover, a high coupling between yaw and roll is observed.

Table 9-11 WindCrete optimized mooring system with chain: static equilibrium

Position (m) Orientation (deg)

Surge Sway Heave Roll Pitch Yaw

OrcaFlex model -3.62 0.00 4.60 0.00 -0.64 0.00

Table 9-12 WindCrete optimized mooring system with chain: natural periods

61

Decay tests Frequency [Hz] Period [s]

Surge 0.003 333

Sway 0.003 333

Heave 0,029 34.5

Roll 0.025 40.0

Pitch 0,024 41.7

Yaw 0,021 47.6

Criteria listed in section 4.1 were checked for every case. Moreover, an end of life analysis was

performed, and criteria evaluated. gives maximum result obtained for different parameters for the

two DLCs and the two analysis. X and Y offsets corresponds to maximum dynamic offsets obtained

taking absolute value.

Table 9-13 Results obtained from DLCs for Windcrete chain optimized system

DLC – Analysis

Design Tension [kN]

Tension criterion

X offset

[m]

Y offset

[m]

Horizontal acceleration

[m/s²]

Vertical acceleration

[m/s²]

|Pitch| [deg]

6.1-Start of life

2109 0.45 19.71 -16.99 1.55 0.15 1.68

6.1-End of life

2193 0.88 19.15 -16.1 1.55 0.15 1.68

6.2-Start of life

1895 0.39 22.91 -21.87 1.56 0.11 2.72

6.2-End of life

1929 0.77 22.39 -20.93 1.56 0.15 2.71

DLCs also establish a map with dynamic maximum offsets (both positives and negatives). It is used as

an input by export cable designers to optimize their system. Figure 9-8 gives such a map for the DLC

6.2. Each point corresponds to one case of the DLC.

62

Figure 9-8 Maximum dynamic offset obtained for DLC 6.2 (Start of life)

A case corresponding to DLC 1.6 is tested to verify the floater behavior in operation. This case is tested

using FAST.

After few iterations, the simulation stopped due to wide motions range. It appears that the yaw motion

becomes instable. Figure 9-9 shows yaw (up) and pitch (down) motions of the platform from FAST

simulation. After 1650s, yaw starts to achieve high value before becoming unstable after 1900s. Skaree

& all [62] explains that yaw is mainly excited by aerodynamic loads and gyroscopic effect. This explains

why instability are not observed within DLC 6.1 and 6.2 (turbine parked). Mooring system is the only

source of stiffness in yaw. Therefore, the optimized mooring system appears to be too soft in yaw.

Figure 9-9 Yaw motion (up) and pitch motion (down) obtained for DLC 1.6 using FAST without enough stiffness

63

To erase doubt on potential numerical error from FAST, the same case is reproduced using a coupling

FAST-OrcaFlex. Mooring system and hydrodynamic is solved by OrcaFlex and use by FAST for the

coupling analysis. The same instability is observed as shown on Figure 9-10.

Figure 9-10 Yaw motion (up) and pitch motion (down) obtained for DLC 1.6 using coupling FAST-OrcaFlex without enough stiffness

The same case was performed using a new mooring system with a higher yaw mooring stiffness. Figure

9-11 shows yaw and pitch motions with this new mooring system. This time, the instability is not

observed, which means that a higher yaw mooring stiffness is sufficient to provide restoring force in

yaw. Decay test shows that yaw natural period for this system is below 12s.

It was decided to add a component for SPAR floaters that checks the mooring stiffness matrix before

running the dynamic analysis. If the mooring system is sufficiently stiff, then the dynamic analysis is

performed. Also, simulation is stopped there and send back to Isight. It was observed that a yaw natural

period between 10 and 14s corresponds to a certain range of yaw mooring stiffness in OrcaFlex. This

criterion was then added to run a new optimization.

64

Figure 9-11 Yaw motion (up) and pitch motion (down) obtained for DLC 1.6 using coupling FAST-OrcaFlex with enough stiffness

Table 9-14 WindCrete chain configuration: optimized mooring system design 2

WindCrete Chain

Group 1 Group 2 Group 3 Costs

Chain Chain Chain

1426 k€ D (mm) L (m) Grade D (mm) L (m) Grade D (mm) L (m) Grade

111 700 R4 111 50 R3 100 750 R3S

The new optimization taking into account yaw mooring stiffness leads to higher costs for the mooring

system. However, the optimized system is still cheaper than the initial mooring system. Decay tests

are realized to check natural periods. The yaw natural period is now below 12s which was wanted.

Table 9-15 WindCrete optimized mooring system design 2: static state

Position (m) Orientation (deg)

Surge Sway Heave Roll Pitch Yaw

OrcaFlex model -2.79 0.00 2.48 0.00 -0.65 0.00

65

Table 9-16 WindCrete optimized mooring system with chain design 2: natural periods

Decay tests Frequency [Hz] Period [s]

Surge 0.0124 80.7

Heave 0,029 34.5

Pitch 0,02401 41.7

Yaw 0,084 11.9

DLC 1.6 has also be checked using the same condition as used for the first case. Yaw and pitch motions

are shown on Figure 9-11. No instability is observed and motions are within values defined in the

design basis.

Figure 9-12 WindCrete optimized mooring system: yaw motion (up) and pitch motion (down) obtained for DLC 1.6 using coupling FAST-OrcaFlex design 2

66

Table 9-17 Results obtained from DLCs for Windcrete chain optimized system design 2

DLC – Analysis

Design Tension [kN]

Tension criterion

X offset

[m]

Y offset

[m]

Horizontal acceleration

[m/s²]

Vertical acceleration

[m/s²]

|Pitch| [deg]

6.1-Start of life

6360 0.56 5.33 -3.24 1.58 0.15 1.71

6.1-End of life

8836.7 0.9 5.02 -2.87 1.59 1.08 1.69

6.2-Start of life

4969.92

0.44

7.39

-4.03

1.57

0.15 2.74

6.2-End of life

6857.77 0.70 6.97 -3.91 1.57 0.15 2.74

shows that the new mooring stiffness induce lower offset on the platform, because restoring forces

are higher. Therefore, dynamic cable could be more optimized compared to the first design, which

should imply costs savings.

The optimized mooring system allows to reduce costs for WindCrete Spar (costs of procurement

decrease of at least 38% up to 58% depending the grade used), while keeping performance within

range defined by the design basis.

67

10. Conclusion and perspective Work realized within this master thesis aims to optimized mooring systems costs for both SPARs and

semisubmersibles. To do so, it was decided to work iteratively by first screening the design space and

then refining results. Different materials have been implemented such as chain, nylon, wire and

polyester. Costs functions have been established based on literature and constraints defined using

design basis and standards.

A python code was developed to allow coupling between OrcaFlex used for the dynamic analysis and

Isight used for the optimization. The optimization algorithm used within this project was chosen based

on literature.

Application, performed on a SPAR at Gran Canaria, as part of COREWIND project, has shown how

optimization could reduce mooring system costs. Design space screening allowed the testing of several

configurations before selecting the cheapest one that satisfied criteria defined within the design basis.

The method developed has shown satisfying results, particularly, assumptions realized on

environmental conditions used seem satisfying to perform the optimization. Indeed, optimized system

respect criteria when going through the entire DLCs list even though only one case is considered for

the optimization.

Considering only DLC 6.1 and 6.2 has shown its limits when dealing with a SPAR buoy, even though

these DLCs are critical for lines tensions. DLC 1.6 appears to be critical for Spars yaw motions excited

by aerodynamic loads and gyroscopic effect. Also, this DLC should be tested after the optimization, to

check yaw motion.

Some assumptions have been realized to reduce time required for the optimization, such as limiting

line length to multiple of 50. Further work could improve refining stage to reduce costs. Modules

concerning buoys and clump weight could also be developed to diversify mooring system considering.

Further work could be realized on the selection of the optimization algorithm which was not the focus

of this thesis. A module could be developed to include TLPs optimization. Costs used in this thesis were

only procurement estimations. To improve the optimization, one can include installation costs

estimations as well as improving anchors costs estimations by allowing definition of different type of

anchors. The end of life analysis could be investigated more precisely. Indeed, marine growth density

and corrosion allowance were considered constant in this work which likely led to errors or oversized

systems.

Costs presented in this work are only estimation. Precise costs calculation will be performed by

partners to estimation LCOE.

68

References

[1] C. consortium. [Online]. Available: http://corewind.eu/. [Accessed 26 02 2020].

[2] C. E. Commission, "Cordis project," [Online]. Available:

https://cordis.europa.eu/project/id/815083. [Accessed 26 01 2020].

[3] INNOSEA, "INNOSEA," [Online]. Available: http://www.innosea.fr/. [Accessed 02 26 2020].

[4] WindEurope, "Offshore Wind in Europe, Key trends and statistics 2019," 2020.

[5] M. d. l. t. é. e. solidaire, "Stratégie française pour l'energie et le climat, programmation

pluriannuelle de l'énergie 2019-2023/2024-2028, Projet pour consultation," 2020.

[6] E. Reporters, "Ireland promises offshore wind 'revolution'," 2019. [Online]. Available:

https://www.energy-reporters.com/policy/ireland-promises-offshore-wind-revolution/.

[Accessed 27 01 2020].

[7] E. Commission, "A clean Planet for all, A European strategic long-term vision for a prosperous,

modern, competitive and climate neutral economy," 2018.

[8] I. E. Agency, "Offshore Wind Outlook 2019".

[9] T. Ackermann, Offshore Wind Energy as part of EG2340 Wind Power Systems, KTH, Stockholm ,

2019.

[10] B. M. Jacob Ladenburg, "Attitude and acceptance of offshore wind farms - The influence of

travel time and wind farm attributes," Elsevier-Renewable and Sustainable Energy Reviews, pp.

4223-4235, 2011.

[11] WindEurope, "Floating Offshore Wind Vision Statement," 2017.

[12] C. N. A. Å. T. A. Anders Myhr, "Levelised cost of energy for offshore floating wind turbines in a

life cycle perspective," Renewable Energy , vol. 66, pp. 714-728, 2014.

[13] C. consortium, "Proposal-SEP," 2019.

[14] C. Trust, "Floating offshore wind market technology review," 2015.

[15] N.Bastick, "Blue H-the worlrd's first floating wind turbine," in The First Dutch Offshore Wind

Energy Conference, Den Helder, 2009.

[16] L. Y. T. K. C.-T. W. Y. Ma Kai-Tung, Mooring System Engineering for Offshore Structures, Elsevier

Science, 2019.

69

[17] Ideol, "Technology," [Online]. Available: https://www.ideol-offshore.com/en/technology.

[Accessed 02 03 2020].

[18] W. M. J. J. a. P. S. S Butterfiel, "Engineering Challenges for Floating offshore wind turbines," in

NREL/CP-500-38776, Copenhagen, 2005.

[19] M. Guzzetti. [Online]. Available: https://green-giraffe.eu/blog/floating-offshore-wind-coming-

age. [Accessed 10 09 2020].

[20] Equinor. [Online]. Available: https://www.equinor.com/en/what-we-do/floating-wind.html.

[Accessed 2020 03 04].

[21] C. Trust, "Floating Offshore Wind: Market and Technology Review," 2015.

[22] C. consortium, "Review of the state of the art of mooring sustem design," 2020.

[23] P. P. Inc., "windfloat," [Online]. Available: http://www.principlepowerinc.com/en/windfloat.

[Accessed 11 05 2020].

[24] J. a. a. A.Robertson, "Definition of the Semisubmersible Floating System for Phase II of OC4,"

2014.

[25] DNV-GL, "DNV-GL-0119 Floating wind turbine structures," 2018.

[26] DNV, "DNV-RP-F205 Global performance analysis of deepwater floating structures," 2010.

[27] J. G. f. E. C. d. Nantes, Wave structure interactions and moorings: Introduction to mooring

systems, 2019.

[28] Floating Structures: a guide for design and analysis, N.D.P Barltrop, 1998.

[29] P. Re, "Mooring systems analysis for floting wind turbines in the Italian seas," 2016/2017.

[30] DNVGL, "DNVGL-OS-E302 Offshore mooring chain," 2015.

[31] O. L. Orcaflex, "OrcaFlex Help," [Online]. Available:

https://www.orcina.com/webhelp/OrcaFlex/Default.htm. [Accessed 30 03 2020].

[32] B. N.D.P, Floating Structures, A guide for Design and Anlysis Volumes 1-2, N.D.P Barltrop, 1998.

[33] V. D.-C. Laura Castro-Santos, Floating Offshore Wind Farms, Springer, 2016.

[34] V. anchors, Anchor Manual 2010, 2010.

[35] A. Larson, "Clump weights in offshore mooring systems," [Online]. Available:

https://www.powermag.com/clump-weights-in-offshore-mooring-systems/. [Accessed 22 08

2020].

[36] K. S. J. a. L. M. Karimirad, "Application of offshore mooring and foundation technologies for

marine renewable energy (MRE) device arrays," 2014.

70

[37] K. S. L. L. Z. G. L.Z Wang, "Integrated analysis of drag embedment anchor installation," Ocean

Engineering, Elsevier, vol. 88, pp. 149-163, 2014.

[38] T. U. o. E. W. E. C. F. E. M. University college Cork, "Deliverable 4.6: Framework for the

prediction of the reliability, economic and environmental criteria and addessment

methodologies for Moorings and Foundations," 2015.

[39] P. C. F. S. T. S. C. B. H-D Pharm, "Dynamic modeling of nylon mooring lines for a floating wind

turbine," 2019.

[40] DNVGL, "DNVGL-RP-C205 Environmental conditions and environmental loads," 2017.

[41] P. P. Ferrant, Wave-Structure interactions, Ecole Centrale de Nantes, Nantes, 2017.

[42] B. Molin, Hydrodynamique des structures offshore, Édition Technip, 2002.

[43] C. consortium, "D1.2 Design Basis," 2019.

[44] P. P. Repar, MJ2424 Computational Methods in Energy Technology, Stockholm, 2019.

[45] H. O. Martin, Aerodynamics of wind turbines.

[46] DNVGL, "DNVGL-OS-E301 Position mooring," 2018.

[47] DNVGL, "DNVGL-ST-0437 Loads and Site Conditions for Wind Turbines," 2016.

[48] R. C. A. J. Sioshansi, Optimization in Engineering: Models and Algorithms, 2017.

[49] K.Schittkowski, "NLPQLP: A Fortran Implementation of a Sequential Quadratic Programming

Algorithm with Distributed and Non-Monotone Line Search," 2015.

[50] K. E. Klingan, "Automated Optimization and Design of Mooring Systems for Deep Water," 2016.

[51] C. Krugerud, "Design and Automated Optimizationf of Mooring Systems for Shallow Water and

Harsh Environments," 2016.

[52] D. Systèmes, "Isight 2019 Component Guide".

[53] DNVGL, "DNVGL-ST-0126 Support structures for wind turbines," 2018.

[54] NREL, "NREL," [Online]. Available: https://www.nrel.gov/wind/data-tools.html. [Accessed 07 08

2020].

[55] NREL, "GitHub OpenFAST," [Online]. Available: https://github.com/openfast. [Accessed 07 08

2020].

[56] Wikipedia, "Python (programming language)," [Online]. Available:

https://en.wikipedia.org/wiki/Python_(programming_language). [Accessed 7 8 2020].

[57] IEC, "IEC-61400-1 Wind energy generation systems," 2019.

71

[58] C. consortium, "Public design and FAST models of the two 15MW floater-turbine concepts,"

2020.

[59] B. d. France, "Taux de change," 23 Mars 2020. [Online]. Available: https://www.banque-

france.fr/statistiques/taux-de-change-parites-quotidiennes-23-mars-2020. [Accessed 23 Mars

2020].

[60] Fibre, "Bridon Fibre Rope Catalogue".

[61] Bexco, "DeepRope Manual 2004 : Polyester & Dyneema mooring ropes manual 2004," 2004.

[62] F. G. N. T. D. H. R. Y. O. H. a. A. R. Bjørn Skaare, "Analysis of measurements and simulations

from the Hywind Demo floating wind turbine," 2014.

[63] G. Cobra. [Online]. Available: http://www.grupocobra.com/en/proyecto-innovacion/corewind/.

[Accessed 02 03 2020].

[64] K.Schittkowski, "NLPQLP: A Fortran Implementation of a Sequential Quadratic Programming

Algorithm with Distributed and Non-Monotone Line Search".