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JOURNAL OF RENEWABLE AND SUSTAINABLE ENERGY 2, 033104 �2010�

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indFloat: A floating foundation for offshore wind turbinesDominique Roddier,1,a� Christian Cermelli,2 Alexia Aubault,2 andAlla Weinstein1

1Principle Power, Inc., Seattle, Washington, USA2Marine Innovation and Technology, 2610 Marin Ave., Berkeley, California 94708, USA

�Received 8 January 2010; accepted 2 May 2010; published online 15 June 2010�

This manuscript summarizes the feasibility study conducted for the WindFloat tech-nology. The WindFloat is a three-legged floating foundation for multimegawattoffshore wind turbines. It is designed to accommodate a wind turbine, 5 MW orlarger, on one of the columns of the hull with minimal modifications to the nacelleand rotor. Potential redesign of the tower and of the turbine control software can beexpected. Technologies for floating foundations for offshore wind turbines areevolving. It is agreed by most experts that the offshore wind industry will see asignificant increase in activity in the near future. Fixed offshore turbines are limitedin water depth to �30–50 m. Market transition to deeper waters is inevitable,provided that suitable technologies can be developed. Despite the increase in com-plexity, a floating foundation offers the following distinct advantages: Flexibility insite location; access to superior wind resources further offshore; ability to locate incoastal regions with limited shallow continental shelf; ability to locate further off-shore to eliminate visual impacts; an integrated hull, without a need to redesign thetransition piece between the tower and the submerged structure for every project;simplified offshore installation procedures. Anchors are significantly cheaper toinstall than fixed foundations and large diameter towers. This paper focuses first onthe design basis for wind turbine floating foundations and explores the require-ments that must be addressed by design teams in this new field. It shows that thedesign of the hull for a large wind turbine must draw on the synergies with oil andgas offshore platform technology, while accounting for the different design require-ments and functionality of the wind turbine. This paper describes next the hydro-dynamic analysis of the hull, as well as ongoing work consisting of coupling hullhydrodynamics with wind turbine aerodynamic forces. Three main approaches arepresented: The numerical hydrodynamic model of the platform and its mooringsystem; wave tank testing of a scale model of the platform with simplified aerody-namic simulation of the wind turbine; FAST, an aeroservoelastic software packagefor wind turbine analysis with the ability to be coupled to the hydrodynamic model.Finally, this paper focuses on the structural engineering that was performed as partof the feasibility study conducted for qualification of the technology. Specifically,the preliminary scantling is described and the strength and fatigue analysis meth-odologies are explained, focusing on the following aspects: The coupling betweenthe wind turbine and the hull and the interface between the hydrodynamic loadingand the structural response. © 2010 American Institute of Physics.�doi:10.1063/1.3435339�

. INTRODUCTION

Currently, there are a number of offshore wind turbine floating foundation concepts in varioustages of development. They fall into three main categories: Spars, tension leg platforms �TLPs�,

�Author to whom correspondence should be addressed. Electronic mail: [email protected]. Tel.: 510-
200-0530 ext 101.
2, 033104-1941-7012/2010/2�3�/033104/34/$30.00 © 2010 American Institute of Physics

http://dx.doi.org/10.1063/1.3435339

http://dx.doi.org/10.1063/1.3435339

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033104-2 Roddier et al. J. Renewable Sustainable Energy 2, 033104 �2010�

nd semisubmersible/hybrid systems. A barge-type support structure has been studied1 but is notncluded in this discussion due to its significant angular motions that hinder its commercial de-elopment. In general terms, spar type has better heave performance than semisubmersibles due tots deep draft and reduced vertical wave-exciting forces, but it has more pitch and roll motionsince the water plane area contribution to stability is reduced. TLPs have very good heave andngular motions, but the complexity and cost of the mooring installation, the change in tendonension due to tidal variations, and the structural frequency coupling between the mast and the

ooring system are three major hurdles for such systems. When comparing floater types, wavend wind-induced motions are not the only elements of performance to consider. Economics playsignificant role. It is, therefore, important to carefully study the fabrication, installation, com-issioning, and ease of access for maintenance methodologies.2,3

Even though there have been a few visionary papers on the topic of floating wind turbines,ignificant research and development efforts only started at the turn of this century.4 In the U.S.,esearchers from NREL and MIT started a significant R&D effort5 with the development ofoupled hydroaerotools,6–8 while model test campaigns were performed at Marintek in Norway onspar hull,9 the first version of the HyWind spar concept. The use of a semisubmersible hull as aoating foundation was proposed independently by Fulton et al.10 and Zambrano et al.11 The latteraper’s proposed design was a MiniFloat hull, the predecessor of the presented WindFloatesign.12

Over the past few years, academic interest in floating foundations for offshore wind turbinesas reached industry, and a significant amount of funding has been allocated to prototype devel-pment. Leading the effort, shown in Fig. 1 from top left to bottom right, are the Statoil Norsk-ydro Hywind spar, �top left�, the Blue H TLP recent prototype �top right�, the SWAY spar/TLPybrid �bottom left�, and the Force Technology WindSea semi submersible �bottom right�.

The WindFloat hull is semisubmersible fitted with heave plates. Extensive technical qualifi-ation of the hull has been performed over the past 5 years by Marine Innovation & Technology.ultiple studies have been performed on the MiniFloat—the trademark of the original hull

ame—and are published in permanent literature.13–15. These include model tests, hydrodynamicnd structural studies, along with specific tasks based on oil and gas and other industry require-ents. The work described herein is based on the learning from those previous studies.

The WindFloat system described in this paper aims at enabling floating offshore wind tech-ology by providing both technical and economical solutions. Its intent is to provide acceptabletatic and dynamic motions for the operation of large wind turbines while limiting expensiveffshore installation and maintenance procedures.16–18

The challenges associated with design and operations of floating wind turbines are significant.floater supporting a large payload �wind turbine and nacelle� with large aerodynamic loads high

bove the water surface challenges basic naval architecture principles due to the raised center ofravity and large overturning moment. The static and dynamic stability criteria are difficult tochieve especially in the context of offshore wind energy production where economics requires theull weight to be minimal.19,20

The following fundamental aspects must be addressed to design such system: �1� The influ-nce of the turbine on the floater and �2� the influence of the floater motions on the turbineerformance. A large body of work has been published on the hydrodynamics of floating plat-orms; see Refs. 21 and 22 for comprehensive overviews. Hydrodynamics of a minimal floatinglatform with similar substructure was discussed by Cermelli and Roddier.23 Wind loads on float-ng structures discussed in the above references are normally computed using a simple relationetween the apparent wind speed and loading based on empirical drag coefficients or results fromind-tunnel tests. In the case of a floating offshore wind turbine, wind load components generatedy the turbine and their effects on platform motion are significant and may lead to couplingffects, which cannot be accounted for using conventional methods.

The following methodology is applied in this paper, with increasing level of refinement of theoupling effects between the wind turbine and platform motion. In the first step, consisting of
lobal sizing of the floater, coupling between the turbine and floater is accounted for using the

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033104-3 WindFloat: Offshore floating wind J. Renewable Sustainable Energy 2, 033104 �2010�

ollowing approximation: The wind thrust is determined by assuming that the base of the turbines fixed and it is applied as force and overturning moment at the base of the mast. This approachs further described in Ref. 11.

The second step involves time-domain simulations of the hydrodynamic response of thelatform using TIMEFLOAT software. The software was modified to compute wind turbine loadsased on an equivalent drag model, which provides suitable wind thrust at the hub, and alsoenerates aerodynamic damping. Gyroscopic effects due to the gyration of the rotor coupled withlatform rotations are also included. This model is relatively simple to implement numerically, andould also be adapted to an experimental setup in order to verify the platform motion predictionsuring wave tank testing of a small-scale model. Results obtained at the UC Berkeley ship-modelesting facility are presented. This model does not account for turbine flexibilities and the variousontrol systems installed on large wind turbines, which have the ability to pitch the rotor bladesesulting in variable thrust and torque, in order to keep the rotor speed constant and the towertable, despite variable wind velocities.

In the third and most advanced step, the aeroservoelastic calculation software FAST developedt the National Renewable Energy Laboratory �NREL�5,8,18 was coupled with the hull hydrody-amic software TIMEFLOAT to compute the platform motion and wind turbine loads including theffects of turbine dynamics and the effect of platform motion on the resulting aerodynamic forces.

FIG. 1. HyWind �spar�, blue H �tension leg�, SWAY �tension leg/spar�, and WindSea �semisubmersible�.

his offers the ability to compute simultaneously the effects of the mooring system, water-

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ntrapment plates, as well as all wind-induced loads on the turbine. The methodology is similar tohat of Jonkman1 but coupling with TIMEFLOAT allows accurate modeling of the nonlinear viscousorces generated by the water-entrapment plates.

To address the influence of the floater motion on turbine performance, a study was performedn which floater motions determined using the approach presented in this paper were applied at thease of the mast and turbine performance was evaluated. The MSC.ADAMS with the ADAMS-TO-

ERODYN interface software allows for motion time series input, similar to earthquake loading.he resulting forces in the various components of the turbine were compared to the case of a fixedase. Results of this study will be published shortly.

As part of the design qualification process, a global structural analysis must be performed andtructural sizing and reinforcement of the components of the WindFloat were achieved. Thetructural assessment of the design necessitates the use of a methodology and design criteria thatccount for the specificities of the structure. Large wind forces and hydrodynamic loading need toe accounted for accurately. In the absence of full-scale experience, the foundation is designedccording to a combination of recommendations for offshore oil and gas platforms, and for fixedffshore wind turbines. To ensure that the design is sufficiently conservative, an extensive numeri-al analysis is carried out on all novel parts of the structure, such as the truss connecting theolumns together, and the turbine tower and its interface with the hull. In a later phase of theroject, structural optimizations of the platform will be carried out to reduce overall steel weight.

A review of the available design standards for the WindFloat is presented briefly, along withsummary of the main characteristics of the platform and preliminary scantling of the columns.ections XVI and XVII of the present paper focuses on the design of the truss and tower withnite-element analysis using the full description of environmental loads on the platform fromydrodynamic analysis. Strength and fatigue analyses are performed. The design of the tower is ofarticular interest since it is at the interface between the floater and the wind turbine.

Space does not permit a complete description of the system, in particular, wall thicknesses inarious parts of the structure. The intent of this paper is to not provide specific results for a giveneometry, but rather to expose practical methodologies that can be used for design, while includ-ng all significant hydrodynamic and aerodynamic loading contributions.

I. STANDARDS

There are presently no standards specific to floating offshore wind turbines. There are, how-ver, rules and guidelines for offshore floaters and for offshore fixed wind turbines. Saiga et al.24

ad a very useful discussion on the various design guidelines. In the scope of this preliminaryork, the following documents provided sufficient information for the framework of the project.e note that the IEC standards are very similar to those of DNV and Germanischer Lloyd. The

atter were used for this work.

. Hull and mooring

• American Bureau of Shipping �ABS�• Guide for Building and Classing Floating Production Installations, 2004• Rules for Building and Classing Mobile Offshore Drilling Units, 2006• American Petroleum Institute �API�• API RP 2SK, Recommended Practice for Design and Analysis of Stationkeeping Systems for

Floating Structures, 2005• API RP 2SM, Recommended Practice for Design, Manufacture, Installation, and Mainte-

nance of Synthetic Fiber Ropes for Offshore Mooring, 2001• API RP 2A-WSD Recommended Practice for Planning, Designing and Constructing Fixed

Offshore Platforms—Working Stress Design, 22nd edition

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• International Maritime Organization �IMO�• IMO International Convention for the Safety of Life at Sea �SOLAS�, 1974

. Offshore turbine

• Germanischer Lloyd �GL�• Guideline for the Certification of Offshore Wind Turbines, 2005

An alternative set of design codes published by Det Norske Veritas �DNV� will be consideredin the next phase of work. These include:

• DNV-OS-C101 Design of Offshore Steel Structures, General �LRFD method�, April 2004�October 2007�

• DNV-OS-C103 Structural Design of Column Stabilized Units �LRFD method�, April 2004�October 2007�

• DNV-OS-C201 Structural Design of Offshore Units �WSD method�, April 2005 �April 2008�• DNV-OS-C301 Stability and Watertight Integrity, January 2001 �April 2007�• DNV-OS-C401 Fabrication and Testing of Offshore Structures, April 2004 �October 2007�• DNV-RP-A203, Qualification Procedures for New Technology. Sept. 2001• DNV-OS-J101 Design of Offshore Wind Turbine Structures, October 2007• DNV-OS-J102 Design and Manufacture of Wind Turbine Blades, Offshore and Onshore

Wind Turbines, October 2006

II. WINDFLOAT DESCRIPTION

The WindFloat technology consists of a column-stabilized offshore platform with water-ntrapment plates and an asymmetric mooring system. A wind turbine mast is positioned directlybove one of the stabilizing columns �see Fig. 2�.

It is comprised of the following elements:

• Three columns, which provide buoyancy to support the turbine and stability from the waterplane inertia. These columns are commonly used elements in floating offshore platforms andone may rely on standard industry criteria, such as the ABS rules for column-stabilized unitsfor their design. The external cylindrical shell is stiffened with regularly spaced ring girdersand vertical L-shape stringers to provide sufficient local and global buckling stiffness to thecolumn. Scantling of the structural elements of the hull aims to determine the thickness ofshells, girders, and webs, as well as the size of their stiffeners and flanges. Since deeper shellsare subject to larger pressure loads, the hull is divided horizontally into four sections that aresized according to their largest head overflow. This helps reduce the amount of steel requiredto build the columns. It is important to note that such rules have been designed to extremelylow failure rates for structures undergoing heavy operational burden, such as the MobileDrilling Units. Constraints include the ability to withstand collisions with supply vessels, theability to support heavy equipment including rotating machinery, and frequent moves overlarge distances. These will undoubtedly result in overly conservative scantlings for offshorerenewable energy systems. Further studies will be aimed at minimizing structural weightwhile ensuring sufficient robustness, and will require extensive use of reliability analysis.

• Horizontal plates at the bottom of the columns, which �1� increase the added mass, henceshift the natural period away from the wave energy, and �2�, increase the viscous damping inroll, pitch, and heave. Stiffeners cantilevered from the bottom of the columns with bracingtying these stiffeners back to the columns support the plates. The water-entrapment platesprovide additional hydrodynamic inertia to the structure due to the large amount of waterdisplaced as the platform moves. In addition, vortices generated at the edge of the platesgenerate large damping forces that further impede platform motion. Structural design of thewater-entrapment plates at the keel had to be carried out numerically since design codes donot provide specific guidelines for such components. The authors have performed finite-
element analysis of the heave plates for a variety of projects, including a minimal water-


injection platform for deep water marginal oil and gas fields, which is similar in payload anddisplacement, and whose water-entrapment plates have the same edge length and surfacearea. The results described by Aubault et al. �2006� are used to determine the size of stiff-eners and stringers on the water-entrapment plate, as illustrated in Fig. 3.

• Permanent water ballast, inside the bottom of the columns, to lower the platform to its targetoperational draft, once installed. An active ballast system moves water from column tocolumn to compensate for the mean wind loading on the turbine. This movable ballastcompensates for significant changes in wind speed and directions. It aims at keeping the mastvertical to improve the turbine performance. Up to 200 ton of ballast water can be transferredin approximately 30 min using two independent flow paths with redundant pumping capa-

FIG. 2. Detail of structural reinforcement of water-entrapment plate on WindFloat.

bility. The active ballast compartment is located in the upper half of each column. The

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damage design case includes the possibility of all the active ballast water being in the worsecompartment.

• Six mooring lines, made of conventional components �drag-embedment anchors, chains,shackles, fairleads, and chain jacks�.

• An offshore wind turbine, with as little requalification that is possible from existing fixedoffshore turbines. The tower is made of a number of sections with tapered diameter andconstant wall thickness that are welded together. At its lower end, the turbine tower extendsinto the column in order to maximize continuity of the structure, leading to minimized stressconcentration in critical areas of the structure where bending moments are highest �due towind-induced overturning moment� and where large tubulars connect to the other stabilizingcolumns. The connection is located above the wave zone, with a clearance above the largestwave crests. The tower diameter is smaller than the column. A heavily stiffened top ofcolumn section is designed to carry the tower loads into the column shell. The yaw bearingis installed at the top of the tower and keeps the turbine headed into the wind.

The WindFloat, in its described configuration in this paper, has dimensions listed in Table I.e note that this is not a final design and that each specific wind farm, being subjected to differentind and wave environments, will have variations from this configuration. It is also noted that theresent design has significant safety margins. Subsequent design work was performed by the

FIG. 3. WindFloat hull and turbine.

ABLE I. WindFloat main dimensions.

ser-input hull dimensions

olumn diameter 35 ft 10.7 m

ength of heave plate edge 45 ft 13.7 m

olumn center to center 185 ft 56.4 m

ontoon diameter 6 ft 1.8 m

perating draft 75 ft 22.9 m

irgap 35 ft 10.7 m

racing diameter 4 ft 1.2 m

isplacement 7833 st 7105 ton

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uthors since these initial studies indicate that the hull presented in this paper has the capability toupport the loading forces of what can be expected of typical wind turbines with rated power upo 10 MW.

The stabilizing columns are spread out forming an equilateral triangle between the threeolumn centers. A boat landing is installed on one or two of these columns to access the structure.he columns are interconnected with a truss structure composed of main beams connecting col-mns and bracings connecting main beams to columns or other main beams.

Minimal deck space is required between the tops of the columns. Figure 2 shows a gangwayonnecting one column to the next and is the main deck element. Additional areas may be used toupport secondary structures, such as auxiliary solar cells, and to provide access around the windurbine mast. The height of the deck is positioned such that the highest expected wave crests willot damage deck equipment or the turbine blades. The structure is anchored to the seabed usingonventional mooring lines arranged in an asymmetrical fashion. The turbine supporting tower isarrying more mooring lines than the other two.

V. WIND TURBINE

The philosophy of the WindFloat is to accommodate turbines from different manufacturers. Its therefore important to work with the turbine manufacturers and use their data to optimize theesign. Figure 4 shows a typical turbine thrust loading on the tower as a function of wind speed.his is a very useful information, which is used to understand the mean force and the moment the

urbine will apply on the top of the column, and is a key driver to the sizing of the hull.Figure 5 shows a typical turbine rated power as a function of wind speed. This information is

ecessary to predict the total amount of electricity that the turbine will produce when it is linkedirectly with the wind data for a specific site.

In the initial phase of this feasibility study, conservative assumptions were made to develophe platform global sizing. It was assumed that the wind-induced thrust at the top of the mast coulde estimated based on a drag coefficient applied to the overall area covered by the rotor, i.e., a 413t �126 m� diameter disk. The selected drag coefficient was 1.2 for wind speeds up to 12 m/s and.4 thereafter up to 25 m/s wind. The turbine was assumed parked for higher wind speeds. Thisodel is conservative and has been being significantly improved since these studies. NREL

urbine code FAST has been integrated with MI&T’s floating body motion prediction code TIME-

LOAT. Fully coupled simulations can be performed to better understand the influence of hull

FIG. 4. Turbine thrust vs wind speed.

otions on the turbine and vice versa.

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The turbine and mast main specifics for a 5 MW turbine are listed in Table II. These numbersre specific to a manufacturer but most large turbines of the same size are very similar with respecto principal weights and dimensions.

. ENVIRONMENTAL DATA

Currently, two concurrent sites are being evaluated for the WindFloat: First, the West coast ofhe U.S., from Northern California to Washington; second, the Atlantic coast of Portugal. In bothases, the wind resources are acceptable for a wind farm development and the wave conditions areuite severe. This paper focuses on the WindFloat design performed for the Western U.S. site. Aetailed metocean analysis was performed for the site shown in Figure 6. 25 years of wind andave data from the National Oceanic and Atmospheric Administration �NOAA� buoy 46022 weresed for the analysis.

. Geographical location of the wind farm

The WindFloat is envisioned to be located 15–20 km �10–12 miles� offshore so as to minimizeisks/nuisance to the general public, and to mitigate the view impact from the coastline. The waterepth is assumed to be 500 ft ��150 m�. The WindFloat is intended to be suitable for open oceanocations with relatively harsh metocean conditions over a wide range of water depths, and mostikely will be cost efficient at or beyond 50 m water depths. In this design phase, the conditionsssumed are those of Northern California, as shown in Fig. 6. This location was chosen in an earlyssessment based on the good wind resources and the geographical proximity of Humboldt Bay.he metocean conditions north of the Eureka site �Oregon, Washington� will be typical of the

FIG. 5. Turbine rated power vs wind speed.

ABLE II. 5 MW turbine characteristics.

otor mass 121 st 135 mt

acelle mass 264 st 294 mt

ast mass 383 st 425 mt

ast diameter 26.25 ft 8 m

otor diameter 413.4 ft 126 m

learance between TOC and bottom of blade 16.4 ft 5 m

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ureka site, but will most likely have slightly larger significant wave height �Hs� value. There arenumber of NOAA buoys that can be used to derive the exact extreme conditions and will be used

n the detail design of a specific project.

. Operational and survival „extreme… conditions

From the wave data, three design sea states were defined. An operational case is shown inable III, an extreme sea state with a wind gust, as defined in GL design guidelines and shown inable IV and the 100 year storm shown in Table V. The extreme wave event assumes a 100 yeareturn period in keeping with common practice from the offshore industry. It is noted that offshoreind turbine codes, such as Germanischer Lloyd “Guideline for the Certification of Offshore Windurbines,” only require 50 year return period events to be considered for design. Although like-

ihood of failure of an offshore wind turbine foundation may be comparable to that of an offshorelatform, the consequences are far less severe because they are unmanned structures and do notave the potential for large pollutions. In the context of this feasibility study, 100 year returneriod events were considered for preliminary design. This offers an element of robustness, whichs useful since the design typically evolves significantly at this early stage. Once the projecteasibility has been demonstrated, a reliability study will be conducted to set the final criteria forhe design of an offshore wind farm, with the objective of minimizing the overall project cost.

The data were also processed to find out if there are any directional effects between the windnd waves. It was remarked that the wind and waves are collinear when they are both coming fromhe north; however, when the wind came from the south, the waves had a tendency to come fromhe west. Hence directional criteria are shown in Table VI.

FIG. 6. WindFloat location and metocean data buoy.

TABLE III. Operational metocean case.

Sea state Operational

Significant wave height 7.8 ft �2.4 m�Peak period 10 sWind speed at 10 m elevation 40 ft/s �12.2 m/s�Current speed 0.98 ft/s �0.3 m/s�

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I. OPERATIONAL REQUIREMENTS

The operational requirements provided in this section are typical of an offshore floater. Theyorm the basis of the initial design to be carried out as development work progresses further.

. WindFloat normal operation „anchored…

As a base case, the WindFloat is assumed to be permanently moored using a conventionalnchoring system made of a chain jack, chain and wire sections, and an anchor. That means theindFloat will not be disconnected in case of extreme weather conditions.

The main purpose of the WindFloat is to generate electricity from the wind turbine. Therefore,he WindFloat should be designed to maximize the amount of time the turbine is operational. Sincexisting turbines stop operating at 25 m/s wind speed, it is desirable for the wave-induced motionsn waves typical of those wind speeds not to interfere with this operational limit. It is anticipatedhat the turbine may need to be strengthened to survive extreme storms in their parked positionsue to the additional inertial accelerations caused by the wave-induced motions.

A closed-loop active ballast system is designed to compensate for the mean wind force andirection. Water needs to be moved between columns such that the mast remains vertical, henceptimizing electricity production. It is not envisioned that this active ballast system compensatesor the dynamic motions of the floater, as it should have a response time of between 30 and 60in. In rapidly changing wind conditions, including wind turbulence, pitching of the blades

reduction in thrust� is performed to help minimize the wind-induced trim if necessary. Theesponse time for this mode is of the order of minutes or less.

. Storm conditions

The WindFloat is designed to withstand very significant storms without failure. Borrowingrom the requirements for oil and gas platforms, the WindFloat hull was designed for the 100 yeareturn storm at the site.

There are three separate regimes for the turbine that are wind speed dependent.

1� The blades are optimally pitched to maximize electricity production.2� The blades are pitched as to minimize the loading on the blades, but the turbine keeps

spinning.3� The rotor is not spinning and the turbine is either idling or locked down, in survival mode,

depending on the severity of the environment.

TABLE IV. ECG.

Sea state ECG

Significant wave height 7.8 ft �2.4 m�Peak period 10 sWind speed at 10 m elevation 0 to 85 ft/s �25.9 m/s� in 10 sCurrent speed 0.98 ft/s �0.3 m/s�

TABLE V. 100 year storm.

Sea state 100 year storm

Significant wave height 44.25 ft �13.5 m�Peak period 17 sWind speed at 10 m elevation 85 ft/s �25.9 m/s�Current speed 2.6 ft/s �0.8 m/s�

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This is typical of large wind turbines. However, as the platform moves in large waves, oneust recognize that regime 3 may occur sooner than expected due to the WindFloat wave re-

ponse. As part of the turbine qualification work, a specific turbine operational envelope must beefined.

. Emergency operations

The philosophy behind the emergency shut down system is to preserve the structure andinimize the loss of equipment. Since the platform is normally unmanned, both automated and

emote shut down procedures must be in place.The following points are a nonexhaustive list of key actions that should trigger a series of

hecks and possible shutdown of the turbine.

• Failure of the active ballast system, noted by either a large mean pitch that does not diminish,coupled with an abnormal power requirement of the pumps.

• Water leaks in a column, noted by a heel of the platform into that column, which cannot becompensated by the functioning active ballast system.

• Large accelerations measured in the turbine, which would induce stresses above the designthreshold.

• Inability for the turbine to rotate into the wind, noted by a discrepancy between the measuredwind direction and the turbine heading.

• Power failure.• Loss of communication between the WindFloat and the remote operator.

here should be enough backup power available on the WindFloat to complete an emergencyhutdown procedure and keep emergency and safety systems, such as navigation lights, opera-ional until maintenance can be performed.

II. FABRICATION, INSTALLATION, AND COMMISSIONING REQUIREMENTS

There are very strong synergies between the WindFloat hull and the MiniFloat oil and gaslatform in terms of fabrication, installation, and commissioning. The MiniFloat design philoso-hy is to optimize the economics by reducing cost in all phases of the project. The same philoso-hy is applied here and design decisions are made after clearly understanding their impact to alltages of the process.

. Fabrication: Quayside

The mast and turbine are fully integrated with the platform at quayside during fabrication. Thelatform is then towed to its installation site using a tugboat. Due to its exceptional stability

TABLE VI. Directional extreme events.

Wind dominated Wave dominated

Collinear case 1 Bi case 2 Collinear case 3 Bi case 4

Hs m 11.2 11.2 13.5 13.5

Tp s 16.67 16.67 19 19

Wave direction deg 0 270 0 270

Wind speed m/s 19.6 25.5 18.4 23.2

Wind direction deg 0 180 0 180

Current speed m/s 0.59 0.76 0.55 0.70

Current direction deg 0 180 0 180

erformance, this operation can be conducted with minimal restrictions on weather conditions.

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nlike fixed offshore wind foundations, there is no requirement in lifting the turbine at theffshore installation site, which was proven to be difficult and costly. Such heavy lift operationsor 5 MW turbines have been performed from floating heavy lift vessels in summer in the Northea but have been limited to 2 ft seas and hence, almost impossible off the Northern Californiaoast. With the proposed WindFloat floating platform, integration of the mast, turbine, and plat-orm is performed at quayside, and on-site operations consist only of deploying mooring lines andonnecting to the platform. In the case of an unexpected failure of the wind turbine, the installationequence can be reversed and the platform towed back to a port for repairs.

The fabrication site should meet the following requirements.

• The structure should be designed to minimize welding at the assembly yard, by providinglarge preassembled cylindrical sections of the columns, which can be efficiently fabricated ina workshop using automatic welding machines.

• It should be in the vicinity of a waterway, deep enough to allow for the WindFloat to betowed, at transit draft to the open ocean. The WindFloat is designed to be stable at its transitdraft. Temporary buoyancy may be attached to the column carrying the turbine to accommo-date the depth of the channel.

• The mast, nacelle, and turbine should be installed at quayside. This implies the use of a largecrane.

• The means of loading out the hull from the integration site into the water should be consid-ered early on when considering specific yards. Possible solutions are single lift from a heavylift crane, dry dock/graving dock, or submersible barges.

. Installation: Transit

The transit phase studies should address the following points.

• The platform is towed after precommissioning to avoid the large cost and risk of placing thetower and turbine onto a floater in open water.

• If a buoyancy module is needed to get out of the fabrication yard, then it should be removedas soon as practical and the platform can be ballasted down to be even keel, with approxi-mately 50 ft �15 m� draft.

• The transit route should be as short as possible, which means that the location of the fabri-cation yard is project specific. This is important especially since an offshore wind farm willbe comprised of multiple WindFloat units and each hull has to be towed.

• Proper selection of the installation vessel is fundamental to project economics. The benefitsof using the same vessel with the ability to perform: �1� The mooring installation, �2� thetowing of the WindFloat platforms, and �3� the power cable installation could be significant.

. Installation: Commissioning

It is important to minimize the offshore commissioning phase since offshore operations,ncluding mobilization of people and vessels offshore, are very expensive. The following pointsre important to keep the cost down.

• The mooring system needs to be prelaid and ready to be connected.• The anchor-handling vessel recovers the messenger lines from the platform and pulls in the

chain section of the mooring line. The connection to the wire section is done above the water.• Tensioning of the mooring lines should be done from the platform with chain jacks. Space

limitations on the column supporting the tower and turbine should be considered carefully.• Since the turbine will be already installed, the procedure involved to start up the turbine

should be simplified as much as possible.• Installation and connection of the power cable are complex. The need to protect the subsea

cable for stability and to prevent damage should be assessed early on. Cable burying or
protective shells may be considered.

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III. TECHNICAL QUALIFICATION

Details on the methodology used to design the WindFloat, i.e., to predict its motion, size, andtructure, are discussed next. The work that has been performed to date includes the following:

• global sizing, including rules check and hydrostatics;• stability;• hydrodynamics, including model tests and hydroaerocoupling of the turbine and the hull;• structural design, scantling, strength, fatigue of the trusses, and the mast.

X. STABILITY

To assess the stability characteristics of the platform, the restoring moment is computed inntact and damaged conditions at different wind headings. The downflooding angle—heeling angleor which the vents above the top of columns are underwater—is also calculated and is shown inable VII.

The restoring moment curves obtained are compared to the curves of wind overturning mo-ent to determine the heeling angle at equilibrium. Combined with a factor of safety, the com-

arison provides an estimation of the stability of the platform. A rough assessment of the windverturning moment under steady wind was carried out in this analysis, based on a range of thrustoefficients for a 10 MW wind turbine. A worst case scenario �failure mode� is considered with aombination of wind overturning moment and a faulty active ballast system. Wind headings every0° are considered for this analysis.

Damage cases are also taken into account by assuming that a section of one column is flooded.he damage remains limited due to compartmentation of the columns. In all considered configu-

ations, the angle of static equilibrium is smaller than the downflooding angle with a comfortableafety margin and the platform remains stable in damaged conditions.

. HYDRODYNAMIC MODEL

The time-domain software TIMEFLOAT was developed by the authors for coupled analysis ofoating structures. It uses WAMIT as a preprocessor to compute wave interaction effects andomputes the time-domain response of one or more floaters subjected to waves, wind, current, andonnected with moorings, tendons, hawsers, fenders, or any other mechanical connections. It takesnto account the viscous forces due to shedding around the hull and wave drift forces. The solutions fully coupled, as the influence of vessel motion on tether forces is taken into account at eachime step, and conversely, the influence of tethers on vessel motion is also included at each timetep. A summary of the algorithm is presented next.

In the frequency domain, the equation of motion of a floater is

�m + a��x + b��x + cx = F�� , �1�

here a�� and b�� are frequency-dependent added mass and radiation damping coefficients, and�� is the sum of forces applied to the floater including the wave-exciting force.

ABLE VII. Summary of stability characteristics.

Heeling angle in calm sea�deg�

Down flooding angle�deg�

Metacentric height�ft�

ntact case at 0° wind heading 0 20.5 53

ntact case at 30° wind heading 0 22.5 53

amaged case at 0° wind heading 4.5 18 38

In the time domain, one can show that the equation of motion has the following general form:

w

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�m + a��x�t� + �−�

t

K�t − ��x��d� + cx�t� = F�t� , �2�

here a� is frequency independent and K is the retardation function,

�a� = a�� +1

��

0

�

K��sin��d�

K�� =2

��

0

�

b��cos��d� . � �3�

hese integrals are calculated numerically.TIMEFLOAT uses an explicit scheme to solve up to 12 degree of freedom �DOF� equations of

otion for a two-body system. The WindFloat is the only vessel considered in this analysis andhe software only solves 6-DOF equations. The general equation of motion is discretized in timend the following linear vectorial equation is solved at each time step,

��M� + �A��ak + �B��vk + �C�xk = Fmem + Fdiff + Fvisc + Fdrift + Fmoor + Fwind. �4�

he left-hand side of Newton’s equation of motion �4� contains terms proportional to the 6-DOFcceleration �ak�, velocity �vk�, and motion of the floater �xk�, with the following notations: �M� ishe mass matrix, �A�� is the 6�6 infinite-frequency added-mass matrix, and �B�� is the 6�6atrix of retardation coefficients for t=0, which are integrals of the frequency-dependent radiation

amping coefficients due to outgoing waves generated by the moving floater. The damping coef-cients are computed by WAMIT and integrated at the beginning of the time-domain simulation toenerate the retardation function matrix. �C� is the 6�6 hydrostatic stiffness matrix computed byAMIT. Only the terms C�3,3�, C�4,4�, C�5,5�, C�3,4�, C�3,5�, and C�4,5� are nonzero. Refer toAMIT manual for details.25 Figure 7 shows the hull geometry used in the WAMIT computations.

The right-hand side includes the various external forces. A brief description of the terms inhis equation is given below. Fmem represents the memory effect, i.e., the effects of wave compo-ents generated by past motion of the floater, described by the convolution of the retardationunction with body velocity, as shown in Eq. �3� above.

FIG. 7. Wetted hull of the WindFloat for the WAMIT model.

Fdiff is the 6-DOF wave-exciting force determined by a Fourier series using the WAMIT

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requency-dependent wave-exciting force components and wave amplitude components represent-ng the specified wave spectrum. A random phase and random frequency algorithms are used toenerate irregular wave trains efficiently and accurately.

Fvisc is the 6-DOF viscous force resulting from drag effects on the vessel columns and water-ntrapment plates. These are computed using a modified Morison equation model based on theelative velocity of the wave/current kinematics and of special line members. Results of multipleodel test campaigns have been used to calibrate the empirical viscous force model. The effect of

cean currents is captured with this viscous force model.Fdrift is the 6-DOF drift force on the vessel computed based on the WAMIT mean drift

requency-dependent coefficients obtained with the pressure integration or momentum approachnd the wave amplitude components. Newman’s approximation is used. Alternatively, a fullecond-order diffraction model can be used if the WAMIT second order module is run. Previousork has shown that the second-order potential solution was not required for the WindFloat.

Fmoor is the 6-DOF force on the vessel resulting from all mooring lines. Mooring lines areodeled either with cable elements or nonlinear springs. For cable elements, a finite-difference

cheme is used to yield the dynamic mooring line configuration and mooring tensions at each timetep. The mooring dynamics and hydrodynamic loads are included using a Morison type formu-ation. The nonlinear finite-difference equations are solved using a Newton–Raphson algorithm, asescribed by Chatjigeorgiou and Mavrakos.26

Fwind is the 6-DOF wind turbine force on the vessel superstructure. The wind force model wasodified to capture some of the aerodynamic coupling between the turbine and the WindFloat

latform. It was assumed that the wind force applied on the rotor was proportional to the squaref the relative velocity between the wind and the hub. It was determined that an equivalent disk inhe rotor plane with 72.7 m diameter would provide the maximum rated thrust of a 10 MWurbine, assuming a 1.2 drag coefficient on the disk. The wind force is perpendicular to the disknd its direction varies in time with the platform rotations. The gyroscopic moment was estimatedrom

Mgyro = I� � p , �5�

here I is the moment of inertia of the spinning rotor, p is the rotational velocity vector of theotor around its axis, and � is the rotational velocity vector of the platform around the pitch andaw axes. The gyroscopic moment Mgyro is added to the moment contribution of Fwind.

Newton’s equation is applied in an inertial frame of reference which coincides with the vesselrame of reference at t=0. The origin of the vessel frame of reference is located at the mean waterevel directly under the center of gravity. The X-axis points toward the bow, i.e., the columnupporting the wind turbine tower, the Y-axis toward port side, and the Z-axis upward.

TIMEFLOAT is written in FORTRAN. Information is provided to the software through an inputle in text format, with all vessel, mooring, and numerical parameters. Additional input consist of

he WAMIT files and the wind and current coefficients files. After reading the input, TIMEFLOAT

olves an initial static phase, in which mean wind and current loads are applied as well as theooring line pretension. This phase serves to reduce the transient phases and quickly provides

tatic information if needed. Then, the solution is advanced in time using a Runge–Kutta algorithmor the 6-DOF rigid-body motion and velocities. At each of the four fractional steps used in thisrocess, external forces are updated.

WAMIT6.3 software was used to compute added-mass and damping coefficients as well asave-exciting forces and mean drift coefficients. Only the underwater part of the hull is modeled.he model includes the columns, water-entrapment plates, and main tubulars connecting columns.he bracings are only modeled as line members using the Morison equation. Dipole elements are
sed to discretize the water-entrapment plate since they are thin structural elements.

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I. DESIGN CASES

In the preliminary design phase, a selected number of design cases were defined based on aombination of offshore mooring design codes and offshore wind turbine design codes, i.e.,PI-RP2SK �Ref. 27� and Germanischer Lloyd.28 The design cases that were thought to be the mostnerous for the platform motions were checked. These included the extreme coherent gust �ECG�nd the 100 year storm �13.5 m Hs� shown in Tables IV and V. In addition, a number of operatingases were run corresponding to the turbine maximum thrust wind speed ��12 m /s� with asso-iated waves ��2 m Hs�, and the maximum wind speed with turbine spinning ��25 m /s� withssociated waves ��4 m Hs�.

For detail design and certification, a much larger number of design cases will have to beonsidered; however, the return period of the maximum events will likely be 50 years in accor-ance with wind turbine design codes, rather than the 100 year return period selected for thisreliminary study. Space does not allow for an extensive presentation of the hydrodynamic simu-ations; however, some results of numerical predictions are provided later and compared to modelest results for key parameters.

II. MODEL TESTS SETUP

A model test campaign was conducted at the UC Berkeley 200 ft long �61 m� ship-modelesting facility to test the validity of the numerical analysis tools. A 1/105 scale model of thelatform was fabricated out of the acrylic. Lead weights were placed inside the columns and on

FIG. 8. Picture of the WindFloat model.

he water-entrapment plates to adjust the center of gravity to its target position; item �1� in Fig. 8.

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he platform motion was measured using a digital video camera tracking the motion of lightmitting diodes placed on model �2�. The system provides 3-DOF measurements of the motion inhe plane of the camera.

Tower �3� was made of a thin �not-to-scale� 1 in. outside diameter acrylic pipe because theevice used to model the wind turbine was relatively heavy and it was not possible to obtain theorrect center of gravity with the lead weights if the tower was modeled with a 3 in. diametercrylic pipe, as originally planned. Stays made of thin string were connected to the tower toncrease its stiffness.

The turbine model device was connected to the top of the tower onto a load cell �4�, whicheasured the axial force perpendicular to the tower. A large disk �5� made of foam board was

laced on the model to attract wind loads corresponding to the design wind force. No attemptsere made to match the atmospheric turbulence. The wind maker naturally produces turbulence

nd the turbulent wind fluctuations are somewhat averaged by the large disk. In the end, the windorce was measured and the turbulence level will be compared to variations in the aerodynamicorces generated by a prototype wind turbine. The disk diameter is a third of the total area coveredy the rotor. The drag coefficient on the disk is estimated to be 1.2.

An electrical motor �6� was placed at the top of the tower to model the gyroscopic effect. Thisell-known mechanical force arises when a rotor spinning around a certain axis undergoes a

otation around a different axis. For instance, platform pitch and yaw would lead to gyroscopicorces applied on the tower. These forces are a significant design issue for the blades and thehaft/bearings, but they may also have a contribution to the global response of the floater. Theotor was adjusted to spin at the Froude-scaled turbine speed of 2 Hz �approximately 12 rpm in

rototype scale�, and the inertia of the blades was approximately modeled with two weights �7�ositioned on an aluminum rod �8�.

The model was kept in position in the tank using four soft springs—two of them connected toolumn 1 which holds the turbine and one on each of the other columns. The mooring lines wereonnected at the edges of a 7�7 ft2 square frame placed on the tank floor. This provided a topngle for the mooring lines of approximately 45°. This equivalent mooring model provided hori-ontal stiffness similar to that of the prototype six line catenary mooring system, yielding a 65 sesonant period in surge. However, the prototype mooring design has not been finalized and theocus of these tests was placed on platform motion. No attempts were made to measure mooringension or validate mooring dynamics.

A plunger type wave maker is located at one end of the tank and a parabolic wave absorptioneach at the other end. A set of five large wind fans was assembled to generate the required windoading on the turbine model, as shown in Fig. 9. The effect of the active ballast system was

odeled by shifting lead ballast on the model to compensate for the mean wind overturningoment.

A 3 h long realization of the 100 year waves was generated. The associated wind is 25 m/s,hich is the maximum wind speed at which the wind turbine is allowed to rotate. Such wave

vents may occur at the site with wind speed under the cutoff speed due to swells. Most likely, theotor would be parked if such wave conditions arise; however, this conservative design case wasenerated to establish upper bounds of platform motion. The 100 year wave run was repeatedithout wind. Additionally, regular waves were run with and without wind to determine response

mplitude operators �RAOs�.

III. RESULTS

Results of the 100 year storm simulation are summarized in Table VIII. Time series oflatform surge, heave, and pitch were processed to yield rms, maximum, and minimum values.hese show a satisfactory agreement between the model test results and numerical simulationserformed with TIMEFLOAT. The pitch rms is slightly underpredicted by the software �1.15° versus.27° measured�, and the minimum and maximum pitch angles are off by 1° due to some differ-nces in the predicted versus measured wind overturning moment; the platform response is,
owever, deemed extremely well behaved, with maximum pitch angle of 5° in a 13.5 m Hs sea

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tate. The maximum crest to trough pitch is 7° with a 21.3 m maximum wave height �crest torough�. Similar responses and trends were observed for all tested platform headings �0° and 90°�nd for runs with and without wind. The maximum yaw angle measured in the 90° runs was under0°.

RAOs were computed for wave periods between 6 and 18 s. Figure 10 shows the RAOs inurge, heave, and pitch for 0° wave heading. The presence of wind does not affect surge or swayignificantly, but its effects are slightly more pronounced on the pitch RAOs. Although wind speeds constant in all the regular wave runs, it does impact the regular wave response because theave-induced motions generate a sinusoidal variation in the relative speed between the wind and

he disk, which results in an additional periodic force component on the disk leading to a corre-ponding periodic pitch moment.

Regular wave tests were repeated with 90° wave heading to investigate the platform yawesponse; i.e., the model orientation was changed by rotating the anchoring frame to 90°. There iso wave-induced yaw for 0° heading since the platform is port/starboard symmetric; the yaw RAOt 90° is shown in Fig. 11. Additional tests were carried out by adding two large triangular verticallates on each column �named yaw plates� with the bottom edge extending outward to the edge ofhe heave plate and the side extending from the heave plate to 20 ft below the mean water level inrototype scale. The effects of “yaw plates” in reducing first-order yaw were minimal. The irregu-

FIG. 9. WindFloat model in the 100 year storm.

ABLE VIII. Numerical and model test results in the 100 year storm with 0° wave heading and 25 m/s steady wind.

eading 0Wind surge

�ft�85 ft/s heave

�ft�Steady pitch

�ft�

ms Model tests 10.56 6.88 1.27

Time float 9.18 6.40 1.15

aximum Model tests 48.46 18.97 4.87

Time float 43.51 16.18 5.77

inimum Model tests �22.16 �22.05 �3.87

Time float �17.28 �22.61 �2.67

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ar wave test showed that the second-order yaw was also not significantly reduced. Overall, thexperiment did not point to serious limitations of the numerical modeling ability.

IV. COUPLED AEROHYDRODYNAMIC MODEL

The forces generated by the wind turbine are reasonably well computed by the modifiedIMEFLOAT software and are correspondingly well modeled experimentally for a steady windpeed. However in reality, the wind speed is constantly changing due to naturally occurringurbulence in the atmosphere. Large wind turbines are equipped with sophisticated control systemsenerally designed to keep the rotor speed constant at all times using a variable torque generatornd a blade pitching mechanism �changing the angle of attack of the blades by rotating themround their local axis�. This technique, known as “blade pitching,” can have significant effects onoating platforms, as observed by Nielsen et al.9 and by Jonkman.29 The control system may

FIG. 10. RAO in surge, heave, and pitch at 0° with and without wind.

FIG. 11. RAO in yaw at 90° without wind.

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nduce negative damping, which results in resonant oscillations of the platform at its pitch naturaleriod.

In order to assess the effects of blade pitching on the floater, as well as to provide accurateomputation of all loads induced by the wind turbine on a moving foundation, a software dedi-ated to wind turbine design, FAST, was interfaced with TIMEFLOAT to provide a fully couplederoservoelastic/hydrodynamic time-domain numerical model of the WindFloat platform with a 5W wind turbine.

FAST, which stands for “fatigue, aerodynamics, structures, and turbulence” is an aeroser-oelastic modal code for horizontal axis wind turbines developed by the National Renewablenergy Laboratory �NREL�. FAST models the wind turbine as a combination of rigid and flexibleodies. The rigid bodies are the earth, nacelle, hub, and optional tip brakes. The flexible bodiesnclude blades, tower, and drive shaft. The model connects these bodies with several DOFs,ncluding tower bending, blade bending, nacelle yaw, rotor teeter, rotor speed, and drive shaftorsional flexibility. FAST uses Kane’s method to set up equations of motion, which are solved byumerical integration. The AERODYN subroutine package developed by Windward Engineering issed to generate aerodynamic forces along the blades.

The FAST and TIMEFLOAT FORTRAN source codes were modified to change TIMEFLOAT into aubroutine called by FAST. Hydrodynamic forces, including wave-exciting forces, viscous forces,nd mooring forces are computed by TIMEFLOAT and passed to FAST, which solves the coupledurbine tower problem and passes platform motion back to TIMEFLOAT.

The FAST model of a utility-scale multimegawatt turbine known as the “NREL offshore 5 MWaseline wind turbine” was developed by Jonkman et al.21 using publicly available informationrom turbine manufacturers. This wind turbine is a conventional three-bladed upwind variable-peed variable blade-pitch-to-feather-controlled turbine. A conventional control system was usedith a generator-torque controller whose goal is to maximize power capture below the ratedperation point and a blade-pitch controller designed to regulate rotor speed above the ratedperation point.

The coupled FAST-TIMEFLOAT model was run using the validated WindFloat hydrodynamicodel described in Sec. X. Sample results are provided for a 4 m significant sea state with 12 s

eak period and a 12 m/s steady wind. Waves and wind are at 0° heading, along the symmetry axisf the WindFloat. A Jonswap wave spectrum is assumed with peakness factor �=2.4. No atmo-pheric turbulence is assumed in this simulation.

Figure 12 shows sample time series of the platform roll, pitch, and yaw over a 5 min durationfter the initial transients generated at the beginning of the numerical simulation have disappeared.

slight asymmetry is present due to the rotation of the rotor in one direction, generating a smallean roll ��1°� and yaw ��2°� component. A background platform pitch oscillation of approxi-ately �2° is caused by the blade-pitch controller, which excites the platform at its pitch resonant

eriod around 30 s. This was later tuned out by modifying the controller coefficients and addingn additional filter. Superposed to the resonant pitch cycles are wave-induced pitch oscillations,hich result in slight changes between resonant cycles, but are overall a small contribution to thelatform pitch in this sea state.

In Fig. 13, time series of the base of the tower are shown. Wave-induced surge is clearlyisible in this 4 m irregular wave sea state. Mean surge is primarily driven by mean aerodynamicoads on the turbine. The platform pitch oscillation results in vertical movement of the tower baset the same period as the pitch cycles.

Figure 14 presents the blade-pitch angle time series �at the bottom� and power out-take �at theop�. The blade-pitch controller locks into the platform pitch resonance with 30 s cycling of thelades. A drop in produced power occurs for approximately 2 s at each cycle when the relativepeed between the nacelle and incoming wind drops below the threshold for maximum power
utput. This does not have a large impact on mean produced power, which is 4.95 MW on average,

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ut would require filtering. Further investigations of the control system have been performedollowing the recommendations of Jonkman29 and Nielsen9 to eliminate this resonant response inrder to maximize power production and minimize fatigue loading of all components and systems.esults will be published shortly.

FIG. 12. WindFloat rotations in 4 m seas with 12 m/s wind.

FIG. 13. Tower base motion in 4 m seas with 12 m/s wind.

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V. DESIGN STANDARDS AND ENVIRONMENTAL CONDITIONS

The WindFloat is a novel offshore structure, which combines a wind turbine and a floater. Noormal design code has been developed yet for the design of structural reinforcement and scant-ing. Existing standards for offshore wind turbines were developed in the past decade from knowl-dge of onshore wind turbines and growing experience in near-shore operations of wind energyevices. However, their scope remains limited to wind turbines in shallow waters with fixedoundations.

The WindFloat is a moored platform with a complex dynamic behavior, which cannot beverlooked in the structural design of critical elements, such as the tower. Although offshore windnergy codes, such as the Germanischer Lloyd Guidelines for the Certification of Offshore Windurbines,28 provide critical information about the extent of wind loading on the structure, theesign criteria may not be sufficiently conservative for a floater.

To ensure a high reliability of the design, the structural analysis of the WindFloat is largelyased on standards from the oil and gas industry, including the ABS rules for Mobile Offshorerilling Units30 and the API Recommended Practice for Fixed Offshore Platforms.27 The DNVecommended Practice C202 �Ref. 31� is used to assess shell buckling of the tower. These designriteria need to be combined with a realistic model of the wind loading effects and conservativestimation of environmental loadings on the hull.

The environmental loadings in both cases are obtained for sea states in the wave scatteriagram encountered at the intended location of the WindFloat, off the coast of Northern Califor-ia. For each peak period �Tp� in the wave scatter diagram, the sea state with highest significantave height �Hs� is identified. The 12 resulting sea states with characteristics listed in Table IX

epresent the steepest wave conditions for each peak period. The strength analysis may be basedn these sea states. All peak periods are included in the strength analysis since wave loadingepends on wavelength. The largest wave height does not necessarily result in largest loading onhe platform. The fatigue analysis requires the generation of extensive numerical data. The fatigueamage must be calculated for all sea states in the wave scatter diagram, based on a time series ofominal stress. To avoid the production of large amounts of data and to save CPU time, the stress

FIG. 14. Power outtake and blade pitch in 4 m seas with 12 m/s wind.

ange is computed only for those 12 identified sea states. For a given peak period, the level of

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tress is assumed to be linear with significant wave height. Thus, the level of stress is scaled withignificant wave height to complete the wave scatter diagram and determine the fatigue life of alltructural elements.

For the truss and the tower of WindFloat, strength and fatigue analyses are carried out. Theomputation of local forces and moments is achieved with finite-element software SAP by Com-uter & Structures, Inc., Berkeley, CA, using beam theory. The structural calculations are linear. Atatic analysis is sufficient on the truss since the natural period of its elements are too low to bexcited by environmental loading. However, a dynamic analysis is necessary to account for thexcitation of the natural period of the tower. The applied loads are obtained from TIMEFLOAT timeeries for each sea state. External forces and moments are applied at the extremities of the tubularlements in the finite-element model or as distributed loads. For the dynamic analysis of the tower,he acceleration load calculated in TIMEFLOAT is directly applied at the base of the tower.

The purpose of this study is to identify the weakest points on the elements and to run areliminary structural analysis to ensure the reliability of the elements. For the strength analysis,he most extreme stresses are used to compute recommended strength ratios. When necessary, thehickness of the tubular elements was adjusted to meet the appropriate safety factors in strength.n tubular elements, fatigue assessment is especially critical at the joints. A hot-spot stress ap-roach as recommended in API is used to estimate the fatigue at the joints between bracinglements. This method entails the calculation of stress concentration factors �SCFs� at the joints.he fatigue life is computed based on the nominal stress as provided by a beam-column finite-lement model multiplied by the SCF. The damage and fatigue life are computed with a formu-ation from DNV Recommended Practice RP-C203 for a short term Rayleigh distribution of stressevels.

The annual damage for all sea states and in three directions is combined with Miner’s rule,

D =Td

A� 1 +

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2 �

seastatespii�2�2��m, �6�

here � is the range of the nominal stress, pi the probability of occurrence of a sea state in anyiven year, and i is the frequency of cycles, which may be taken to the zero-up crossing fre-uency. Recall that Td is the design life and A and m are parameters of the API X S-N curve.

VI. STRENGTH AND FATIGUE DESIGN OF THE TRUSS

The primary function of the truss is to provide the WindFloat hull with sufficient globaltructural stiffness to withstand environmental loads. A three-dimensional �3D� model of the

TABLE IX. Sea states for structural strength analysis.

Case No.Tp

�s�Hs

�m�Hs

�ft�

01 20 12.5 41.002 16.7 11.5 37.703 14.3 9.5 31.204 12.5 8.5 27.905 11.1 7.5 24.606 10 7.5 24.607 9.1 7.5 24.608 8.3 6.5 21.309 7.1 5.5 18.010 6.3 4.5 14.811 5.3 3.5 11.512 4.2 1.5 4.9

indFloat is created �Fig. 15�. The columns and bracing are modeled with tubular grade 50 steel

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eam-column elements. Main horizontal bracing members are 150 ft �45.7 m� long cylinders thatupport the horizontal loads between columns. Light bracing members provide reinforcement at/3 of their length. These bracing members are diagonal between the main bracings and columnsor vertical stiffness and horizontal between main bracing elements to provide horizontal stiffness.he joints between the column and the bracing are modeled with an element of stiffness, ten times

hat of the bracing element, and consistent with API recommendations. The water-entrapmentlates are not included in this model but the applied forces on the plates are calculated externallynd transferred to the base of the columns.

External and inertia forces applied to each structural member are computed using dedicatedoftware, based on the TIMEFLOAT program, which computes hydrodynamic loads by integration ofhe diffraction and radiation pressures on each part of the structure. The software also matches theydrodynamic panels with corresponding structural elements. The time-domain force componentsassed to the finite-element model include weight of all elements, radiation, and diffraction pres-ures, as well as mass inertia and hydrostatic stiffness effects. Wave exciting forces, including

FIG. 15. Truss finite-element model.

roude–Krylov effects, are passed via the diffraction pressure. The viscous forces, reflecting

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iscous loads on heave plates, columns, and truss members, are applied to the corresponding partsf the structure. The mooring forces are applied vertically to the chain stoppers at the top ofolumn since they set the column in compression. The horizontal component of the mooring ispplied to the fairlead at the keel, with a 45° top angle. The wind-induced forces �thrust andorque� are applied horizontally at the top of the tower. Drift forces are neglected since they areelatively small on individual elements. It is verified that the sum of external forces and inertiaorces on all parts of the structure is approximately null.

The truss consists of unstiffened tubular elements. For the analysis of tubular members, APIP2A-WSD defines allowable axial, bending shear, and hoop stresses. Maximum predicted

tresses on the elements in design environmental conditions are computed with finite-elementnalysis. The overall structural reliability of a member is estimated by combination of the maxi-um to allowable stress ratios with appropriate safety factors. All computed ratios must be less

han 1 to comply with API.The stress on the truss is determined using a static finite-element algorithm on the model

ubject to all environmental loads including rigid-body dynamics contributions. To capture theighest stress level, the forces are calculated for a 1 min snapshot of the most extreme wave of ah simulation on all relevant sea states for three headings.

The maximum API stress ratios increase with larger sea states. Thus, sea state 1, with theargest significant wave height, is associated with the maximum stress ratio at 90°, heading for

ost frame elements. Figure 16 represents the maximum API ratios calculated in the worst case,t 90° heading for sea state 1, plotted directly on the structure. The shell thickness and diameter ofhe truss elements were adjusted to ensure compliance with API criteria.

It was determined through further analysis that the wind loads were driving the design of theruss in strength analysis. Figure 17 illustrates the effect of wave and wind loading on the shape ofhe truss: The main horizontal bracing elements undergo significant bending.

Next, the fatigue analysis is performed on the truss. The target design life of the WindFloat is0 years. In this design cycle, a safety factor of 10 is applied and a calculated fatigue life of 200ears is required. This is very conservative and can be reduced as the engineering is refined.

The fatigue analysis is critical at the joints between bracing elements and the fatigue life of theonnection is determined based on the stress ranges calculated by beam theory. To apply theot-spot stress curve, the SCF needs to be determined. For a nominal stress away from the weldingoe on a beam model of the tubular element, it is reasonable to expect the SCF to be between fournd six for a well-designed connection. The Von Mises stress at the connection obtained fromeam-column finite-element modeling is used as nominal stress in this case. A sensitivity analysiss carried out on the value of the SCF. The exact stress ratio between the maximum stress at theeld toe and Von Mises stress in beam theory will be determined precisely by finite-element

nalysis with a 3D model of the connection in follow on studies. It should also be noted that weldrofile control is assumed at the joints of truss elements so that the API X-curve may be used toefine the relationship between hot-spot stress range and number of cycles to failure.

The maximum levels of Von Mises stress in the truss are observed for peak periods betweenand 10 s depending on the heading. This is consistent with wave loads on the columns when theavelength is half the distance between columns.

The stress ranges are determined for all sea states in the scatter diagram and combined tobtain the fatigue life. Results are summarized in Table X. Assuming that the stress at the weld isccurately computed by the beam model and that no increase in wall thickness is implemented athe connection, the minimum fatigue life of the nodes is 670 years. This optimistic assumptionill be verified with a detailed finite element of the connection. It is likely that increase in wall

hickness over a short section near the node will be required to achieve fatigue life targets.stimates of fatigue life based on a can with wall thickness equal to twice the nominal wall

hickness of the tubular members are provided in Table XI.

X

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VII. STRUCTURAL ANALYSIS OF THE TOWER

The design of the tower must take into account wind and wave-induced motions. A dynamicnalysis of the tower is required since the first lateral mode of resonance is near 3 s. At sucheriods, some wave energy may be transmitted to the tower through the platform rigid-bodyotions.

The tower is a tapered unstiffened 220 ft �67 m� high tube, with increasing wall thicknessrom top to bottom. It supports a 300 ton nacelle and rotor at the top. It is connected to the columnt the bottom with a bolted or welded flange joint. The buckling strength of the tubular element isetermined for extreme environmental conditions and the fatigue life of the joint at the base of theolumn is calculated.

The numerical model is composed of a number of beam elements with decreasing diameternd thickness from bottom to top. Beam elements are sufficient for this study since there is noxternal pressure distribution on the tower. A convergence analysis is carried out to determine theinimum number of elements necessary to correctly represent the dynamic characteristics of the

ower. With eight elements, the mass and stiffness of the structure have converged.1 h time series of accelerations at the base of the tower are generated for all twelve relevant

FIG. 16. Maximum API design ratios on WindFloat platform in 90° heading sea state 1.

ea states in the wave scatter diagram. Additionally, the largest wind force �the maximum of the

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hrust versus wind speed curve� is applied horizontally at the top and the tower supports its owneight as well as the weight of the turbine. The deflections of the tower are computed using lineaream theory with a time-domain finite-element algorithm.

In Fig. 18, the bending moment �top� and the sway motion at the base of the tower �bottom�re plotted during the largest wave event of the 1 h time series for sea state 1, which correspondso the 100 year storm. The maximum horizontal excursion at the base of the turbine tower is 60 ft18 m� crest to trough during a single wave cycle, corresponding to a 70 ft �21 m� wave crest to

FIG. 17. Deformed �50�� shape of WindFloat structure in worst loading conditions �sea state 1 at 90° heading�.

TABLE X. Fatigue life on connection between bracings based on nominal wall thickness.

SCFDamage

�per year�Fatigue life

�year�

1 1.7�10−03 670

1.5 8.2�10−03 121

2 2.8�10−02 36

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rough. The bending moment time series clearly shows the dynamic response of the tower, whichncludes oscillations with a period below 3 s superimposed to the wave-induced component withperiod around 20 s.

A 2% ratio of critical damping is applied to the numerical model. This is the level of dampingxpected on the tower when the turbine is parked. In most scenarios, when the turbine rotates, theamping ratio increases on the tower due to aerodynamic drag. A sensitivity analysis is performedo evaluate the effect of damping on tower fatigue.

In Fig. 19, the bending stress at the base of the tower is plotted for 2% and 5% criticalamping ratios, highlighting the variations in the dynamic response of the tower. Yet, the energyt the natural period of the tower is small compared to wave-induced variations in bending stress.he structural damping does not affect the fatigue results significantly: The rms of bendingoment varies by only 1% when damping is increased from 2% to 5% of critical damping in this

igh sea state.The natural period of the tower is low enough to not interfere with wave-induced motion of

he platform. The unsupported section of the WindFloat tower is much shorter than onshore towersecause the hub is slightly lower than onshore, and the platform truss provides lateral stiffness tohe tower up to 33 ft �10 m� elevation above the mean water line.

Bending moment at the base of the tower is also plotted in Fig. 20 for sea state 12 �Tp

4.2 s�. The bottom of the figure shows a time series of the sway motion, which is a combinationf linear wave dynamics with period of 4.2 s and slow-drift cycles with period of approximately

TABLE XI. Fatigue life with double wall thickness at the connection.

SCFDamage

�per year�Fatiguelife�year�

1 6.7�10−05 14 9341.5 3.8�10−04 26232 1.5�10−03 670

FIG. 18. Bending stress �kips/ft� and sway �ft� at the base of the tower at the largest wave of sea state 1.

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0 s. Only the energy from first-order wave dynamics at low periods is transmitted to the tower.xcitation of the tower natural periods is not apparent due to the small magnitude of tower baseotion.

For the strength analysis, the design recommendations from DNV-RP C202 are used. Thehell buckling assessment is based on formulas for unstiffened tubular elements. The column

FIG. 19. Sensitivity of bending stress with damping ratio in sea state 1 at 90° heading.

FIG. 20. Bending stress �kips/ft� and sway �ft� at the base of the tower at the largest wave of sea state 12.

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uckling does not need to be computed since �kL / i�2�2.5 E / fY, where kL is the effective length,is the radius of gyration of the cross section, E is Young’s modulus, and fY is the yield strengthf steel.

The largest events are identified over a 1 h time series. The shell buckling ratio is calculatedt the lower end of each of the eight elements using the local wall thickness and diameter for thislement. Stress is largest at these lowest ends since the axial force and bending moment increaseoward the base of the tower, as illustrated in one time step in Fig. 21.

It may be noted that even for extreme events of the largest sea states, wind force on the turbineontributes up to 70% of the axial stress on the tower. The wind force is critical to the design ofhe tower in strength.

Shell buckling ratios are computed for these extreme events according to DNV recommenda-ions. At the base of the tower, the largest design equivalent to the Von Mises stress to design shelluckling strength ratio is 0.4, which is 40% of the maximum allowed. Thus, the tower will not beffected by buckling from dynamic wave loads and wind thrust.

The fatigue analysis is assessed at the joint between floater and turbine at the base of theower. The column and the tower meet in a flange connection, which is bolted or welded. Thetandard deviation of the Von Mises stress is determined over a 1 h simulation of the structuralesponse to the 12 relevant sea states. The bending moment is computed at a point at the base ofhe tower for a number of wave directions between 0° and 180°, to account for the directionalityf waves at the Northern California location. Each heading is given identical probability ofccurrence for this analysis.

The hot-spot stress S-N curve with a Rayleigh approximation is used to determine the damageer year on the connection. The SCF should be computed from a 3D finite-element analysis of theonnection. However, this work will be performed in a later phase of the project once structuraletails of the connection are established. In a preliminary analysis, a sensitivity study is carried outn the SCF at the base of the tower.

Results are summarized in Table XII. The calculated fatigue life is 37 280 years based onominal wave-induced stress. Damping level is conservatively assumed to be 2% of critical for allea states, although it will likely be higher when the turbine is spinning. The design of theonnection between the tower base and top of column will have to be carefully designed to reduceCFs to acceptable levels based on fatigue life targets. Fatigue due to cycling of the wind loadsnd tower vibrations due to the spinning rotor have not been included in this model. Detailed

FIG. 21. �Left� Axial force in compression. �right� Bending moment at largest event of sea state 1 at 90° heading.

erodynamic calculations will be performed to account for these additional fatigue sources.

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VIII. CONCLUSION

The work presented herein was aimed at providing sufficient technical information about theystem to highlight challenging areas for any offshore floating wind turbine foundations. The mostrominent areas are as follows.

• The turbines in their “as-is” configurations may not be able to withstand some of the floaterinduced motions. It is therefore critical to involve the turbine manufacturers, to verify that thenew motion envelopes are within their design criteria. It is further important to minimize thefloater motions, most critically the pitch motion, to eliminate any potential for the bladeinterference with the mast due to the gyroscopic force, which maintains the blades in theirturning plane.

• Fabrication and installation: The foundation should be fabricated and integrated near theinstallation site. However, the infrastructure required for the construction of such a largesystem may not exist near some of the potential wind farm areas and might have significantcost implication on the project.

• Steel cost has been rising significantly recently, but so has the welding and fabrication costs.Optimizing the structure for steel weight may not yield the most inexpensive hull. Under-standing the fabricator constraints during the design phase is very important to reduce fab-rication complexities and associated cost run-ups.

This paper also discusses the hydrodynamic analysis of the WindFloat. Numerical analysisas first carried out with simplified models of the wind turbine forces. This work was done withfully coupled time-domain algorithm, which accounts for diffraction-radiation effects, as well asiscous forces and the influence of the mooring. Model tests were performed to validate theredictive ability of the numerical hydrodynamic algorithm. This experimental work consisted ofenerating wave loads in a wave tank facility, as well as wind loads using fans and a drag disklaced on the model, and a rotor to model gyroscopic effects.

A coupled aeroelastic-hydrodynamic model was then implemented to provide better resolutionf wind turbine loads and take into account the effects of the turbine control system. For this work,he validated hydrodynamic model discussed above was interfaced with FAST software developedy NREL for design of wind turbines. It was shown that interactions between the wind turbineontrol system and the platform generate small rotational oscillations with long periods �30 s�, which, in some cases, could result in slightly reduced power output. Further work will be

arried out to improve the turbine control system, and assess the effects of coupled aeroelastic-ydrodynamic loads on the WindFloat components.

Lastly, this paper discusses the preliminary structural assessment of the WindFloat. It focusesn the methodology designed to estimate the strength and fatigue of WindFloat’s novel structuralomponents. It is assumed that structural loading on the underwater elements of the platform, suchs the columns and the water-entrapment plates, is mostly dependent on wave loading. Theirreliminary design can be conservatively established using design guidelines developed for theffshore industry. Novel elements, such as the truss or the interface between the wind turbine and

TABLE XII. Summary of sensitivity of fatigue damage on SCF.

Damping�%� SCF

Damage�per year�

Fatigue life�year�

2 1 2.68�10−05 37 2802 2 5.59�10−04 17902 4 1.16�10−02 862 6 6.87�10−02 15

he columns, i.e., the tower, must be analyzed thoroughly due to the importance of aerodynamic

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oading on their design. A strength and fatigue analysis is performed using a simplified beamodel to assess the structural reliability of the structure under conservative environmental loading

nd identifies the areas that will require further detailed analysis.The work presented herein was focused on providing sufficient technical information about

he system to highlight follow on design challenges. A few critical topics have been identified onhe truss and tower design. The wind force is essential to the strength behavior of the WindFloatince its contribution to the bending stress of the structural members is significant. It is essentialo include the effect of aerodynamics in the detailed structural analysis, but in the preliminarynalysis, a large factor of safety sufficed to conclude the global structural reliability of the Wind-loat. A detailed analysis of the truss node fatigue is required involving 3D finite-element models.

The analysis presented herein was sufficient to verify that the general arrangement and di-ensions of the main structural components of the structure are compatible with expected envi-

onmental loading. Local reinforcement of the structure will be required but are not expected toignificantly alter initial weight and cost estimates.

CKNOWLEDGMENTS

Financial support of this work by the Principal Power Inc. is gratefully acknowledged.

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2 American Petroleum Institute, Recommended Practice for Planning and Constructing Fixed Offshore Platforms—Working Stress Design, 2000.

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4 A. R. Henderson and M. H. Patel, Wind Energy 6, 53 �2003�.5 S. Butterfield, W. Musial, J. Jonkman, P. Sclavounos, and L. Wayman, in “Engineering Challenges for Floating OffshoreWind Turbines,” Copenhagen Offshore Wind 2005 Conference and Expedition Proceedings, Copenhagen, Denmark,26–28 October 2005.

6 J. M. Jonkman and P. D. Sclavounos, “Development of Fully Coupled Aeroelastic and Hydrodynamic Models forOffshore Wind Turbines,” 44th AIAA Aerospace Sciences Meeting and Exhibit, 9–12 January 2006, Reno, NV.

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8 J. Jonkman, S. Butterfield, W. Musial, and G. Scott, “Definition of a 5-MW Reference Wind Turbine for Offshore SystemDevelopment,” NREL Report No. TP-500-38060, February 2007.

9 F. G. Nielsen, T. D. Hanson, and B. Skaare, in “Integrated Dynamic Analysis of Floating Offshore Wind Turbines,”Pro-ceedings of the OMAE2006, 25th International Conference on Offshore Mechanics and Arctic Engineering”, Hamburg,Germany, 4–9 June 2006.

0 G. R. Fulton, D. J. Malcolm, and E. Moroz, in “Design of a Semi-Submersible Platform for a 5MW Wind Turbine,” 44thAIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, 9–12 January 2006.

1 T. Zambrano, T. MacCready, T. Kiceniuk, D. G. Roddier, and C. A. Cermelli, Dynamic Modeling of Deepwater OffshoreWind Turbine Structures in Gulf of Mexico Storm Conditions �OMAE, Hamburg, 2006�.

2 D. Roddier, C. Cermelli, and A. Weinstein, in “WindFloat: A Floating Foundation for Offshore Wind Turbines Part I:Design Basis and Qualification Process,” Proceedings of the OMAE’09, 28th International Conference on OffshoreMechanics and Arctic Engineering, Honolulu, HI, 31 May–5 June 2009.

3 C. Cermelli, D. Roddier, and A. Aubault, Remote Power Generation for Deployment of Subsea Technologies in DeepWater Marginal Fields, Offshore Magazine, January 2008.

4 C. Cermelli, D. Roddier, and C. Busso, in “MINIFLOAT: A Novel Concept of Minimal Floating Platform for MarginalField Development,”Proceedings of the 14th International Offshore and Polar Engineering Conference, Toulon, France,May 2004.

5 A. Aubault, C. Cermelli, and D. Roddier, in “Structural Design of a Semi-Submersible Platform with Water-EntrapmentPlates Based on a Time-Domain Hydrodynamic Algorithm Coupled with Finite-Elements,” Proceedings of the 16thInternational Offshore and Polar Engineering Conference, San Francisco, California, 28 May–2 June 2006.

6 J. J. Jensen and A. E. Mansour, in “Extreme Motion Prediction for Deepwater TLP Floaters for Offshore Wind Turbines,”Proceedings of the Fourth International Hydroelasticity Conference, 2006.

7 S. Joensen, J. Jensen, and A. Mansour, in “Extreme Value Predictions for Wave- and Wind- Induced Loads on FloatingOffshore Wind Turbines Using FORM,” Proceedings of the PRADS, Houston, TX, 2007.

8 J. M. Jonkman and P. D. Sclavounos, in “Development of Fully Coupled Aero-Elastic and Hydrodynamic Models forOffshore Wind Turbines,” 44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, 9–12 January 2006.

9 C. Cermelli, D. Roddier, and A. Aubault, in “WindFloat: A Floating Foundation for Offshore Wind Turbines Part II:Hydrodynamics,” Proceedings of the OMAE 2009, 28th International Conference on Offshore Mechanics and ArcticEngineering, Honolulu, HI, May 2009.

0 D. Roddier, T. Zambrano, T. McCready, and C. Cermelli, in “Design and Installation of a Tension Moored Wind
Turbine,” Proceedings of the OMAE’07, 26th International Conference on Offshore Mechanics and Arctic Engineering,
http://dx.doi.org/10.1002/we.83

2

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San Diego, 11–16 June 2007.1 S. K. Chakrabarti, Hydrodynamics of Offshore Structures �Springer-Verlag, Berlin, 1987�.2 O. Faltinsen, Sea Loads on Ships and Offshore Structures �Cambridge University Press, Cambridge, 1993�.3 C. Cermelli and D. Roddier, in “Experimental and Numerical Investigation of the Stabilizing Effects of a Water-Entrapment Plate on a Deepwater Minimal Floating Platform,” Proceedings of the 24th International Conference onOffshore Mechanics and Arctic Engineering, Halkidiki, Greece, June 2005.

4 R. K. Saiga, D. Dolan, A. D. Kiureghian, T. Camp, and C. E. Smith, in “Comparison of Design Guidelines forOffshore Wind Energy Systems,” Offshore Technology Conference, Houston, TX, 30 April–3 May 2007, Paper No. OTC18984-PP.

5 See: http://www.wamit.com/manual.htm for WAMIT user manual.6 I. K. Chatjigeorgiou and S. A. Mavrakos, in “Assessment of Bottom-Cable Interaction Effects on Mooring Line Dynam-ics,” 17th International Conference on Offshore Mechanics Arctic Engineering, 1998, Paper No. OMAE98-0355.

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8 Germanischer Lloyd, Guideline for the Certification of Offshore Wind Turbines, Rules and Guidelines ed., 2005.9 J. Jonkman, in “Influence of Control on the Pitch Damping of a Floating Wind Turbine,” Presented at the 2008 ASMEWind Energy Symposium, Reno, NV, 7–10 January 2008.

0 American Bureau of Shipping, Rules for Building and Classing Mobile Offshore Drilling Units �Hull Construction andEquipment, Houston, TX, 2001�, Pt. 3.

1 DNV, Buckling Strength of Shell, Recommended Practice DNV-RP-C202, 2002.

http://www.wamit.com/manual.htm

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