Floating Offshore Wind Turbines: Mooring System Optimization for LCOE Reduction

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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

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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.

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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.

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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

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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

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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.

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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.

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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]

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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

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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

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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.

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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

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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.

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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]

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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.

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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 =

(∑ 𝐼_𝑡+ 𝑀_𝑡 (𝐼₀+ 𝑟)^𝑡

𝑛𝑡=0 )

(∑ 𝐸_𝑡

(𝐼₀+ 𝑟)^𝑡

𝑛𝑡=0 )

Equation 2-1

With

𝐼_𝑡 Investments at time t €

𝑀_𝑡 Operation and maintenance costs

at time t

€

𝐸_𝑡 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

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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

𝐶𝑜𝑠𝑡𝑠_{𝑐ℎ𝑎𝑖𝑛} Chain section costs $

𝑀𝐵𝐿 Minimum breaking load 𝑘𝑁

𝐿_{𝑠𝑒𝑐𝑡𝑖𝑜𝑛} 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.

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19 2.3.2.2. Wire

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

𝐶𝑜𝑠𝑡𝑠_{𝑤𝑖𝑟𝑒}= 0.03415 × 𝑑²× 𝐿_{𝑠𝑒𝑐𝑡𝑖𝑜𝑛} Equation 2-3 With

𝐶𝑜𝑠𝑡_{𝑤𝑖𝑟𝑒} Wire section costs €

𝑑 Wire diameter m

𝐿_{𝑠𝑒𝑐𝑡𝑖𝑜𝑛} 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.

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𝐶𝑜𝑠𝑡𝑠_{𝑝𝑜𝑙𝑦𝑒𝑠𝑡𝑒𝑟} = (0.0138 × 𝑀𝐵𝐿 + 11.281) × 𝐿_{𝑠𝑒𝑐𝑡𝑖𝑜𝑛} Equation 2-4

With

𝐿_{𝑠𝑒𝑐𝑡𝑖𝑜𝑛} Section length m

𝑀𝐵𝐿 Polyester minimum breaking

load

kN 𝐶𝑜𝑠𝑡_{𝑃𝑜𝑙𝑦𝑒𝑠𝑡𝑒𝑟} 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:

𝐶𝑜𝑠𝑡𝑠_{𝑛𝑦𝑙𝑜𝑛}= (0.0122 × 𝑀𝐵𝐿 + 12.116) × 𝐿_{𝑠𝑒𝑐𝑡𝑖𝑜𝑛} Equation 2-5 With

𝐶𝑜𝑠𝑡𝑠_{𝑁𝑦𝑙𝑜𝑛} Nylon section costs $

𝑀𝐵𝐿 Nylon minimum breaking load 𝑘𝑁

𝐿_{𝑠𝑒𝑐𝑡𝑖𝑜𝑛} 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]:

𝐶𝑜𝑠𝑡_{𝑎𝑛𝑐ℎ𝑜𝑟} = 10.198 × 𝑀𝐵𝐿 Equation 2-6

With

𝐶𝑜𝑠𝑡_{𝑎𝑛𝑐ℎ𝑜𝑟} Anchor costs $

𝑀𝐵𝐿 Minimum breaking load of the

line 𝑘𝑁

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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, 𝐾_𝑐. This number is given by:

𝐾_𝑐= 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 𝐾_𝑐 > 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 + 𝐶_𝑀)𝜌𝜋 4𝐷²(𝑢̇

𝑣̇) − 𝜌𝜋

4𝐷²𝐶_𝑀(𝑢̈

𝑣̈)} 𝑑𝑧 +1

2𝐶_𝐷𝐷 (𝑢 − 𝑥̇

𝑣 − 𝑦̇) √(𝑢 − 𝑥̇)²+ (𝑣 − 𝑦̇)²𝑑𝑧 Equation 3-2

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22 With

𝐶_𝑀 Added mass coefficient -

𝐷 Diameter 𝑚

𝑑𝑧 Cylinder length 𝑚

𝑢 Normal fluid velocity 𝑚. 𝑠⁻¹

𝐶_𝐷 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 𝐾_𝐶, 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 + 𝑀_𝑎)𝑑²𝑋𝑖

𝑑𝑡² + 𝐵𝑑𝑋𝑖

𝑑𝑡 + (𝐾_𝐻+ 𝐾_𝑀)𝑋_𝑖= 𝐹(𝑋, 𝑡) Equation 3-3 With

𝑀 Mass matrix of the structure 𝑘𝑔

𝑀_𝑎 Added mass matrix 𝑘𝑔

𝐵 Damping matrix 𝑁𝑠/𝑚

𝐾_𝐻 Hydrostatic stiffness 𝑁/𝑚

𝐾_𝑀 Mooring stiffness

𝑋𝑖 Degree of freedom considered m / rad

𝐹 Excitation forces 𝑁

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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.

(𝐵_𝐿+ 𝐵_𝑄𝑑𝑋_𝑖 𝑑𝑡)𝑑𝑋_𝑖

𝑑𝑡 = 𝐵 𝑑𝑋_𝑖

𝑑𝑡 Equation 3-4

With,

𝐵𝐿 Linear damping matrix 𝑁𝑠/𝑚

𝐵_𝑄 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 1^st order forces, and the low-frequency 2^nd 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.

𝑓_𝑖 = 1

2𝜋√𝐾_𝐻,𝑖+ 𝐾_𝑀, 𝑖

𝑀_𝑖+ 𝑀_𝑎,𝑖 Equation 3-5

With

𝑓 Natural frequency for the degree of freedom considering

𝐻𝑧 𝐾_𝐻 Hydrodynamic stiffness 𝑁. 𝑚. 𝑟𝑎𝑑⁻¹

𝐾_𝑀 Mooring stiffnes 𝑁. 𝑚. 𝑟𝑎𝑑⁻¹

𝑀_𝑖 Mass matrix 𝑘𝑔

𝑀_𝑎,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]

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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]:

𝑥₁,𝑥min₂,…,𝑥_𝑛𝑓(𝑥₁, … , 𝑥_𝑛)

𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜 (𝑔_𝑖(𝑥₁), … , 𝑔_𝑖(𝑥_𝑛)) ∈ Ω Equation 3-6

Where

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𝑥₁, … 𝑥_𝑛 design variables

Ω feasible region

𝑓 the function that must be

optimized

𝑔_𝑖 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

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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

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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 .

𝑇_𝑑= 𝛾_{𝑚𝑒𝑎𝑛}𝑇_{𝑐,𝑚𝑒𝑎𝑛}+ 𝛾_𝑑𝑦𝑛𝑇_{𝑐,𝑑𝑦𝑛} Equation 4-1 Where

𝑇_{𝑐,𝑚𝑒𝑎𝑛} Characteristic mean tension 𝑁 𝑇_{𝑐,𝑑𝑦𝑛} Characteristic dynamic tension 𝑁

𝛾_{𝑚𝑒𝑎𝑛} Load mean factor -

𝛾_𝑑𝑦𝑛 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 𝛾_{𝑚𝑒𝑎𝑛} 1.3 1.5

ULS 𝛾_𝑑𝑦𝑛 1.75 2.2

ALS 𝛾_{𝑚𝑒𝑎𝑛} 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:

𝑆_𝑐 = 0.95. 𝑆_𝑚𝑏𝑠 Equation 4-2

With,

𝑆_𝑐 Characteristic strength of the mooring line

𝑁 𝑆_𝑚𝑏𝑠 Minimum breaking strength of

the material

𝑁

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

𝛾_{𝑚𝑒𝑎𝑛}𝑇_{𝑐,𝑚𝑒𝑎𝑛}+ 𝛾_𝑑𝑦𝑛𝑇_{𝑐,𝑑𝑦𝑛} = 𝑇_𝑑< 𝑆_𝑐= 0.95. 𝑆_𝑚𝑏𝑠 Equation 4-3

The design equation can also be represented using this ratio:

(𝛾_{𝑚𝑒𝑎𝑛}𝑇_{𝑐,𝑚𝑒𝑎𝑛}+ 𝛾_𝑑𝑦𝑛𝑇_{𝑐,𝑑𝑦𝑛})

0.95. 𝑆_𝑚𝑏𝑠 < 1 Equation 4-4

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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 𝑇_𝑑

0.95𝑆_𝑚𝑏𝑠 < 1 X offset |𝑋𝑑𝑦𝑛𝑎𝑚𝑖𝑐| < 60 𝑚 Y offset |𝑌_{𝑑𝑦𝑛𝑎𝑚𝑖𝑐}| < 60 𝑚 Acceleration (𝑎𝑐𝑐𝑥, 𝑎𝑐𝑐_𝑦, 𝑎𝑐𝑐_𝑧) < 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.

𝐷_𝐷= 𝐷𝐹𝐹. 𝐷_𝐶 Equation 4-5

With

𝐷_𝑑 Design cumulative fatigue damage

N 𝐷_𝑐 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:

𝐷_𝑐= ∑𝑛_𝐶,𝑖 𝑁_𝐶,𝑖

𝐼

𝑖=1

Equation 4-6 With

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

period

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

The associated design criterion is given by:

𝐷_𝐷≤ 1.0 Equation 4-7

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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:

𝐷_{𝑐𝑜𝑟𝑟} = 𝐷_𝑛𝑒𝑤− 𝑐 × 𝐿𝑇 Equation 4-8

With

𝐷_{𝑐𝑜𝑟𝑟} Corroded chain diameter 𝑚

𝐷_𝑛𝑒𝑤 New (un-corroded) chain

diameter ^𝑚

𝑐 Corrosion allowance 𝑚. 𝑦𝑒𝑎𝑟𝑠⁻¹

𝐿𝑇 Lifetime 𝑦𝑒𝑎𝑟𝑠

The resulting MBL is given by:

𝑆_{𝑚𝑏𝑠−𝑐𝑜𝑟𝑟}= 𝑆_𝑚𝑏𝑠(𝐷_{𝑐𝑜𝑟𝑟} 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.

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

The new line mass with marine growth is given by:

𝑀_{𝑙𝑖𝑛𝑒} = 𝑀_{𝑖𝑛𝑖𝑡𝑖𝑎𝑙}+𝜋

4[(𝐷_𝑛𝑜𝑚+ 2Δ𝑇)²− 𝐷_𝑛𝑜𝑚² ]. 𝜌_{𝑔𝑟𝑜𝑤𝑡ℎ}. 𝜇 Equation 4-10 Where,

𝑀_{𝑙𝑖𝑛𝑒} Mass of the line per unit length 𝑘𝑔/𝑚

𝑀_{𝑖𝑛𝑖𝑡𝑖𝑎𝑙} 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 ^/

𝐷_𝑛𝑜𝑚 Nominal diameter (i.e bar

diameter) ^m

∆𝑇 Marine growth thickness ^m

The drag coefficient with marine growth is given by:

𝐶_{𝐷𝑔𝑟𝑜𝑤𝑡ℎ}= 𝐶_𝐷[𝐷_𝑛𝑜𝑚+ 2Δ𝑇_{𝑔𝑟𝑜𝑤𝑡ℎ}

𝐷_𝑛𝑜𝑚 ] Equation 4-11

𝐶_{𝐷𝑔𝑟𝑜𝑤𝑡ℎ} Drag coefficient with marine growth

𝐶_𝐷 Drag coefficient without

marine growth

𝐷_𝑛𝑜𝑚 Nominal diameter (i.e bar

diameter) ^𝑚𝑚

Δ𝑇_{𝑔𝑟𝑜𝑤𝑡ℎ} 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.

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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.

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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 .

Floating Offshore Wind Turbines: Mooring System Optimization for LCOE Reduction

Floating Offshore Wind Turbines:

Mooring System Optimization for LCOE Reduction

Florian Thierry Stephan CASTILLO

Abstract

SAMMANFATTNING

Contents

List of Figures

List of Tables

Acknowledgments

1. Introduction

2. State of the art

2.1. Floating foundations

2.2. Station keeping

2.3. Costs analysis

3. Theoretical aspect

3.1. General aspect

3.2. Hydrodynamic theory

3.3. Motion resolution

3.4. Mooring lines theory

3.5. Aerodynamic theory

3.6. Optimization

3.7. Project philosophy

4. Design considerations

4.1. Design criteria

4.2. Corrosion

4.3. Marine growth

5. Software

5.1. Isight

5.2. Orcaflex

5.3. FAST

5.4. Python Interface

6. Input data

6.1. Referecence frame

6.2. Environmental condition