033104-2 Roddier et al. J. Renewable Sustainable Energy 2, 033104 ͑2010͒and semisubmersible/hybrid systems. A barge-type support structure has been studied1 but is notincluded in this discussion due to its signiﬁcant angular motions that hinder its commercial de-velopment. In general terms, spar type has better heave performance than semisubmersibles due toits deep draft and reduced vertical wave-exciting forces, but it has more pitch and roll motionssince the water plane area contribution to stability is reduced. TLPs have very good heave andangular motions, but the complexity and cost of the mooring installation, the change in tendontension due to tidal variations, and the structural frequency coupling between the mast and themooring system are three major hurdles for such systems. When comparing ﬂoater types, waveand wind-induced motions are not the only elements of performance to consider. Economics playa signiﬁcant role. It is, therefore, important to carefully study the fabrication, installation, com-missioning, 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,signiﬁcant research and development efforts only started at the turn of this century.4 In the U.S.,researchers from NREL and MIT started a signiﬁcant R&D effort5 with the development ofcoupled hydroaerotools,6–8 while model test campaigns were performed at Marintek in Norway ona spar hull,9 the ﬁrst version of the HyWind spar concept. The use of a semisubmersible hull as aﬂoating foundation was proposed independently by Fulton et al.10 and Zambrano et al.11 The latterpaper’s proposed design was a MiniFloat hull, the predecessor of the presented WindFloatdesign.12 Over the past few years, academic interest in ﬂoating foundations for offshore wind turbineshas reached industry, and a signiﬁcant amount of funding has been allocated to prototype devel-opment. Leading the effort, shown in Fig. 1 from top left to bottom right, are the Statoil Norsk-Hydro Hywind spar, ͑top left͒, the Blue H TLP recent prototype ͑top right͒, the SWAY spar/TLPhybrid ͑bottom left͒, and the Force Technology WindSea semi submersible ͑bottom right͒. The WindFloat hull is semisubmersible ﬁtted with heave plates. Extensive technical qualiﬁ-cation of the hull has been performed over the past 5 years by Marine Innovation & Technology.Multiple studies have been performed on the MiniFloat—the trademark of the original hullname—and are published in permanent literature.13–15. These include model tests, hydrodynamicand structural studies, along with speciﬁc tasks based on oil and gas and other industry require-ments. 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-nology by providing both technical and economical solutions. Its intent is to provide acceptablestatic and dynamic motions for the operation of large wind turbines while limiting expensiveoffshore installation and maintenance procedures.16–18 The challenges associated with design and operations of ﬂoating wind turbines are signiﬁcant.A ﬂoater supporting a large payload ͑wind turbine and nacelle͒ with large aerodynamic loads highabove the water surface challenges basic naval architecture principles due to the raised center ofgravity and large overturning moment. The static and dynamic stability criteria are difﬁcult toachieve especially in the context of offshore wind energy production where economics requires thehull weight to be minimal.19,20 The following fundamental aspects must be addressed to design such system: ͑1͒ The inﬂu-ence of the turbine on the ﬂoater and ͑2͒ the inﬂuence of the ﬂoater motions on the turbineperformance. A large body of work has been published on the hydrodynamics of ﬂoating plat-forms; see Refs. 21 and 22 for comprehensive overviews. Hydrodynamics of a minimal ﬂoatingplatform with similar substructure was discussed by Cermelli and Roddier.23 Wind loads on ﬂoat-ing structures discussed in the above references are normally computed using a simple relationbetween the apparent wind speed and loading based on empirical drag coefﬁcients or results fromwind-tunnel tests. In the case of a ﬂoating offshore wind turbine, wind load components generatedby the turbine and their effects on platform motion are signiﬁcant and may lead to couplingeffects, which cannot be accounted for using conventional methods. The following methodology is applied in this paper, with increasing level of reﬁnement of thecoupling effects between the wind turbine and platform motion. In the ﬁrst step, consisting ofglobal sizing of the ﬂoater, coupling between the turbine and ﬂoater is accounted for using the
033104-3 WindFloat: Offshore ﬂoating wind J. Renewable Sustainable Energy 2, 033104 ͑2010͒ FIG. 1. HyWind ͑spar͒, blue H ͑tension leg͒, SWAY ͑tension leg/spar͒, and WindSea ͑semisubmersible͒.following approximation: The wind thrust is determined by assuming that the base of the turbineis ﬁxed and it is applied as force and overturning moment at the base of the mast. This approachis further described in Ref. 11. The second step involves time-domain simulations of the hydrodynamic response of theplatform using TIMEFLOAT software. The software was modiﬁed to compute wind turbine loadsbased on an equivalent drag model, which provides suitable wind thrust at the hub, and alsogenerates aerodynamic damping. Gyroscopic effects due to the gyration of the rotor coupled withplatform rotations are also included. This model is relatively simple to implement numerically, andcould also be adapted to an experimental setup in order to verify the platform motion predictionsduring wave tank testing of a small-scale model. Results obtained at the UC Berkeley ship-modeltesting facility are presented. This model does not account for turbine ﬂexibilities and the variouscontrol systems installed on large wind turbines, which have the ability to pitch the rotor bladesresulting in variable thrust and torque, in order to keep the rotor speed constant and the towerstable, despite variable wind velocities. In the third and most advanced step, the aeroservoelastic calculation software FAST developedat the National Renewable Energy Laboratory ͑NREL͒5,8,18 was coupled with the hull hydrody-namic software TIMEFLOAT to compute the platform motion and wind turbine loads including theeffects of turbine dynamics and the effect of platform motion on the resulting aerodynamic forces.This offers the ability to compute simultaneously the effects of the mooring system, water-
033104-4 Roddier et al. J. Renewable Sustainable Energy 2, 033104 ͑2010͒entrapment plates, as well as all wind-induced loads on the turbine. The methodology is similar tothat of Jonkman1 but coupling with TIMEFLOAT allows accurate modeling of the nonlinear viscousforces generated by the water-entrapment plates. To address the inﬂuence of the ﬂoater motion on turbine performance, a study was performedin which ﬂoater motions determined using the approach presented in this paper were applied at thebase of the mast and turbine performance was evaluated. The MSC.ADAMS with the ADAMS-TO-AERODYN interface software allows for motion time series input, similar to earthquake loading.The resulting forces in the various components of the turbine were compared to the case of a ﬁxedbase. Results of this study will be published shortly. As part of the design qualiﬁcation process, a global structural analysis must be performed andstructural sizing and reinforcement of the components of the WindFloat were achieved. Thestructural assessment of the design necessitates the use of a methodology and design criteria thataccount for the speciﬁcities of the structure. Large wind forces and hydrodynamic loading need tobe accounted for accurately. In the absence of full-scale experience, the foundation is designedaccording to a combination of recommendations for offshore oil and gas platforms, and for ﬁxedoffshore wind turbines. To ensure that the design is sufﬁciently conservative, an extensive numeri-cal analysis is carried out on all novel parts of the structure, such as the truss connecting thecolumns together, and the turbine tower and its interface with the hull. In a later phase of theproject, 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 witha summary of the main characteristics of the platform and preliminary scantling of the columns.Sections XVI and XVII of the present paper focuses on the design of the truss and tower withﬁnite-element analysis using the full description of environmental loads on the platform fromhydrodynamic analysis. Strength and fatigue analyses are performed. The design of the tower is ofparticular 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 invarious parts of the structure. The intent of this paper is to not provide speciﬁc results for a givengeometry, but rather to expose practical methodologies that can be used for design, while includ-ing all signiﬁcant hydrodynamic and aerodynamic loading contributions.II. STANDARDS There are presently no standards speciﬁc to ﬂoating offshore wind turbines. There are, how-ever, rules and guidelines for offshore ﬂoaters and for offshore ﬁxed wind turbines. Saiga et al.24had a very useful discussion on the various design guidelines. In the scope of this preliminarywork, the following documents provided sufﬁcient information for the framework of the project.We note that the IEC standards are very similar to those of DNV and Germanischer Lloyd. Thelatter were used for this work.A. Hull and mooring • American Bureau of Shipping ͑ABS͒ • Guide for Building and Classing Floating Production Installations, 2004 • Rules for Building and Classing Mobile Offshore Drilling Units, 2006 • American Petroleum Institute ͑API͒ • 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
033104-5 WindFloat: Offshore ﬂoating wind J. Renewable Sustainable Energy 2, 033104 ͑2010͒B. Safety • International Maritime Organization ͑IMO͒ • IMO International Convention for the Safety of Life at Sea ͑SOLAS͒, 1974C. Offshore turbine • Germanischer Lloyd ͑GL͒ • Guideline for the Certiﬁcation of Offshore Wind Turbines, 2005 An alternative set of design codes published by Det Norske Veritas ͑DNV͒ will be considered in the next phase of work. These include: • DNV-OS-C101 Design of Offshore Steel Structures, General ͑LRFD method͒, April 2004 ͓October 2007͔ • DNV-OS-C103 Structural Design of Column Stabilized Units ͑LRFD method͒, April 2004 ͓October 2007͔ • DNV-OS-C201 Structural Design of Offshore Units ͑WSD method͒, April 2005 ͓April 2008͔ • DNV-OS-C301 Stability and Watertight Integrity, January 2001 ͓April 2007͔ • DNV-OS-C401 Fabrication and Testing of Offshore Structures, April 2004 ͓October 2007͔ • 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 2006III. WINDFLOAT DESCRIPTION The WindFloat technology consists of a column-stabilized offshore platform with water-entrapment plates and an asymmetric mooring system. A wind turbine mast is positioned directlyabove one of the stabilizing columns ͑see Fig. 2͒. It is comprised of the following elements: • Three columns, which provide buoyancy to support the turbine and stability from the water plane inertia. These columns are commonly used elements in ﬂoating offshore platforms and one may rely on standard industry criteria, such as the ABS rules for column-stabilized units for their design. The external cylindrical shell is stiffened with regularly spaced ring girders and vertical L-shape stringers to provide sufﬁcient local and global buckling stiffness to the column. Scantling of the structural elements of the hull aims to determine the thickness of shells, girders, and webs, as well as the size of their stiffeners and ﬂanges. Since deeper shells are subject to larger pressure loads, the hull is divided horizontally into four sections that are sized according to their largest head overﬂow. This helps reduce the amount of steel required to build the columns. It is important to note that such rules have been designed to extremely low failure rates for structures undergoing heavy operational burden, such as the Mobile Drilling Units. Constraints include the ability to withstand collisions with supply vessels, the ability to support heavy equipment including rotating machinery, and frequent moves over large distances. These will undoubtedly result in overly conservative scantlings for offshore renewable energy systems. Further studies will be aimed at minimizing structural weight while ensuring sufﬁcient robustness, and will require extensive use of reliability analysis. • Horizontal plates at the bottom of the columns, which ͑1͒ increase the added mass, hence shift the natural period away from the wave energy, and ͑2͒, increase the viscous damping in roll, pitch, and heave. Stiffeners cantilevered from the bottom of the columns with bracing tying these stiffeners back to the columns support the plates. The water-entrapment plates provide additional hydrodynamic inertia to the structure due to the large amount of water displaced as the platform moves. In addition, vortices generated at the edge of the plates generate large damping forces that further impede platform motion. Structural design of the water-entrapment plates at the keel had to be carried out numerically since design codes do not 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-
033104-6 Roddier et al. J. Renewable Sustainable Energy 2, 033104 ͑2010͒ FIG. 2. Detail of structural reinforcement of water-entrapment plate on WindFloat. injection platform for deep water marginal oil and gas ﬁelds, which is similar in payload and displacement, and whose water-entrapment plates have the same edge length and surface area. The results described by Aubault et al. ͑2006͒ 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 target operational draft, once installed. An active ballast system moves water from column to column to compensate for the mean wind loading on the turbine. This movable ballast compensates for signiﬁcant changes in wind speed and directions. It aims at keeping the mast vertical to improve the turbine performance. Up to 200 ton of ballast water can be transferred in approximately 30 min using two independent ﬂow paths with redundant pumping capa- bility. The active ballast compartment is located in the upper half of each column. The
033104-7 WindFloat: Offshore ﬂoating wind J. Renewable Sustainable Energy 2, 033104 ͑2010͒ FIG. 3. WindFloat hull and turbine. damage design case includes the possibility of all the active ballast water being in the worse compartment. • Six mooring lines, made of conventional components ͑drag-embedment anchors, chains, shackles, fairleads, and chain jacks͒. • An offshore wind turbine, with as little requaliﬁcation that is possible from existing ﬁxed offshore turbines. The tower is made of a number of sections with tapered diameter and constant wall thickness that are welded together. At its lower end, the turbine tower extends into the column in order to maximize continuity of the structure, leading to minimized stress concentration in critical areas of the structure where bending moments are highest ͑due to wind-induced overturning moment͒ and where large tubulars connect to the other stabilizing columns. The connection is located above the wave zone, with a clearance above the largest wave crests. The tower diameter is smaller than the column. A heavily stiffened top of column section is designed to carry the tower loads into the column shell. The yaw bearing is 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.We note that this is not a ﬁnal design and that each speciﬁc wind farm, being subjected to differentwind and wave environments, will have variations from this conﬁguration. It is also noted that thepresent design has signiﬁcant safety margins. Subsequent design work was performed by theTABLE I. WindFloat main dimensions.User-input hull dimensionsColumn diameter 35 ft 10.7 mLength of heave plate edge 45 ft 13.7 mColumn center to center 185 ft 56.4 mPontoon diameter 6 ft 1.8 mOperating draft 75 ft 22.9 mAirgap 35 ft 10.7 mBracing diameter 4 ft 1.2 mDisplacement 7833 st 7105 ton
033104-8 Roddier et al. J. Renewable Sustainable Energy 2, 033104 ͑2010͒ FIG. 4. Turbine thrust vs wind speed.authors since these initial studies indicate that the hull presented in this paper has the capability tosupport the loading forces of what can be expected of typical wind turbines with rated power upto 10 MW. The stabilizing columns are spread out forming an equilateral triangle between the threecolumn centers. A boat landing is installed on one or two of these columns to access the structure.The columns are interconnected with a truss structure composed of main beams connecting col-umns 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 gangwayconnecting one column to the next and is the main deck element. Additional areas may be used tosupport secondary structures, such as auxiliary solar cells, and to provide access around the windturbine mast. The height of the deck is positioned such that the highest expected wave crests willnot damage deck equipment or the turbine blades. The structure is anchored to the seabed usingconventional mooring lines arranged in an asymmetrical fashion. The turbine supporting tower iscarrying more mooring lines than the other two.IV. WIND TURBINE The philosophy of the WindFloat is to accommodate turbines from different manufacturers. Itis therefore important to work with the turbine manufacturers and use their data to optimize thedesign. Figure 4 shows a typical turbine thrust loading on the tower as a function of wind speed.This is a very useful information, which is used to understand the mean force and the moment theturbine 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 isnecessary to predict the total amount of electricity that the turbine will produce when it is linkeddirectly with the wind data for a speciﬁc site. In the initial phase of this feasibility study, conservative assumptions were made to developthe platform global sizing. It was assumed that the wind-induced thrust at the top of the mast couldbe estimated based on a drag coefﬁcient applied to the overall area covered by the rotor, i.e., a 413ft ͑126 m͒ diameter disk. The selected drag coefﬁcient was 1.2 for wind speeds up to 12 m/s and0.4 thereafter up to 25 m/s wind. The turbine was assumed parked for higher wind speeds. Thismodel is conservative and has been being signiﬁcantly improved since these studies. NRELturbine code FAST has been integrated with MI&T’s ﬂoating body motion prediction code TIME-FLOAT. Fully coupled simulations can be performed to better understand the inﬂuence of hullmotions on the turbine and vice versa.
033104-9 WindFloat: Offshore ﬂoating wind J. Renewable Sustainable Energy 2, 033104 ͑2010͒ FIG. 5. Turbine rated power vs wind speed. The turbine and mast main speciﬁcs for a 5 MW turbine are listed in Table II. These numbersare speciﬁc to a manufacturer but most large turbines of the same size are very similar with respectto principal weights and dimensions.V. ENVIRONMENTAL DATA Currently, two concurrent sites are being evaluated for the WindFloat: First, the West coast ofthe U.S., from Northern California to Washington; second, the Atlantic coast of Portugal. In bothcases, the wind resources are acceptable for a wind farm development and the wave conditions arequite severe. This paper focuses on the WindFloat design performed for the Western U.S. site. Adetailed metocean analysis was performed for the site shown in Figure 6. 25 years of wind andwave data from the National Oceanic and Atmospheric Administration ͑NOAA͒ buoy 46022 wereused for the analysis.A. Geographical location of the wind farm The WindFloat is envisioned to be located 15–20 km ͑10–12 miles͒ offshore so as to minimizerisks/nuisance to the general public, and to mitigate the view impact from the coastline. The waterdepth is assumed to be 500 ft ͑ϳ150 m͒. The WindFloat is intended to be suitable for open oceanlocations with relatively harsh metocean conditions over a wide range of water depths, and mostlikely will be cost efﬁcient at or beyond 50 m water depths. In this design phase, the conditionsassumed are those of Northern California, as shown in Fig. 6. This location was chosen in an earlyassessment based on the good wind resources and the geographical proximity of Humboldt Bay.The metocean conditions north of the Eureka site ͑Oregon, Washington͒ will be typical of theTABLE II. 5 MW turbine characteristics.Rotor mass 121 st 135 mtNacelle mass 264 st 294 mtMast mass 383 st 425 mtMast diameter 26.25 ft 8 mRotor diameter 413.4 ft 126 mClearance between TOC and bottom of blade 16.4 ft 5 m
033104-10 Roddier et al. J. Renewable Sustainable Energy 2, 033104 ͑2010͒ FIG. 6. WindFloat location and metocean data buoy.Eureka site, but will most likely have slightly larger signiﬁcant wave height ͑Hs͒ value. There area number of NOAA buoys that can be used to derive the exact extreme conditions and will be usedin the detail design of a speciﬁc project.B. Operational and survival „extreme… conditions From the wave data, three design sea states were deﬁned. An operational case is shown inTable III, an extreme sea state with a wind gust, as deﬁned in GL design guidelines and shown inTable IV and the 100 year storm shown in Table V. The extreme wave event assumes a 100 yearreturn period in keeping with common practice from the offshore industry. It is noted that offshorewind turbine codes, such as Germanischer Lloyd “Guideline for the Certiﬁcation of Offshore WindTurbines,” only require 50 year return period events to be considered for design. Although like-lihood of failure of an offshore wind turbine foundation may be comparable to that of an offshoreplatform, the consequences are far less severe because they are unmanned structures and do nothave the potential for large pollutions. In the context of this feasibility study, 100 year returnperiod events were considered for preliminary design. This offers an element of robustness, whichis useful since the design typically evolves signiﬁcantly at this early stage. Once the projectfeasibility has been demonstrated, a reliability study will be conducted to set the ﬁnal criteria forthe 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 windand waves. It was remarked that the wind and waves are collinear when they are both coming fromthe north; however, when the wind came from the south, the waves had a tendency to come fromthe west. Hence directional criteria are shown in Table VI. TABLE III. Operational metocean case. Sea state Operational Signiﬁcant wave height 7.8 ft ͑2.4 m͒ Peak period 10 s Wind speed at 10 m elevation 40 ft/s ͑12.2 m/s͒ Current speed 0.98 ft/s ͑0.3 m/s͒
033104-11 WindFloat: Offshore ﬂoating wind J. Renewable Sustainable Energy 2, 033104 ͑2010͒ TABLE IV. ECG. Sea state ECG Signiﬁcant wave height 7.8 ft ͑2.4 m͒ Peak period 10 s Wind speed at 10 m elevation 0 to 85 ft/s ͑25.9 m/s͒ in 10 s Current speed 0.98 ft/s ͑0.3 m/s͒VI. OPERATIONAL REQUIREMENTS The operational requirements provided in this section are typical of an offshore ﬂoater. Theyform the basis of the initial design to be carried out as development work progresses further.A. WindFloat normal operation „anchored… As a base case, the WindFloat is assumed to be permanently moored using a conventionalanchoring system made of a chain jack, chain and wire sections, and an anchor. That means theWindFloat 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,the WindFloat should be designed to maximize the amount of time the turbine is operational. Sinceexisting turbines stop operating at 25 m/s wind speed, it is desirable for the wave-induced motionsin waves typical of those wind speeds not to interfere with this operational limit. It is anticipatedthat the turbine may need to be strengthened to survive extreme storms in their parked positionsdue 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 anddirection. Water needs to be moved between columns such that the mast remains vertical, henceoptimizing electricity production. It is not envisioned that this active ballast system compensatesfor the dynamic motions of the ﬂoater, as it should have a response time of between 30 and 60min. In rapidly changing wind conditions, including wind turbulence, pitching of the blades͑reduction in thrust͒ is performed to help minimize the wind-induced trim if necessary. Theresponse time for this mode is of the order of minutes or less.B. Storm conditions The WindFloat is designed to withstand very signiﬁcant storms without failure. Borrowingfrom the requirements for oil and gas platforms, the WindFloat hull was designed for the 100 yearreturn storm at the site. There are three separate regimes for the turbine that are wind speed dependent.͑1͒ The blades are optimally pitched to maximize electricity production.͑2͒ The blades are pitched as to minimize the loading on the blades, but the turbine keeps spinning.͑3͒ 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 V. 100 year storm. Sea state 100 year storm Signiﬁcant wave height 44.25 ft ͑13.5 m͒ Peak period 17 s Wind speed at 10 m elevation 85 ft/s ͑25.9 m/s͒ Current speed 2.6 ft/s ͑0.8 m/s͒
033104-12 Roddier et al. J. Renewable Sustainable Energy 2, 033104 ͑2010͒ 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 This is typical of large wind turbines. However, as the platform moves in large waves, onemust recognize that regime 3 may occur sooner than expected due to the WindFloat wave re-sponse. As part of the turbine qualiﬁcation work, a speciﬁc turbine operational envelope must bedeﬁned.C. Emergency operations The philosophy behind the emergency shut down system is to preserve the structure andminimize the loss of equipment. Since the platform is normally unmanned, both automated andremote shut down procedures must be in place. The following points are a nonexhaustive list of key actions that should trigger a series ofchecks 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 be compensated by the functioning active ballast system. • Large accelerations measured in the turbine, which would induce stresses above the design threshold. • Inability for the turbine to rotate into the wind, noted by a discrepancy between the measured wind direction and the turbine heading. • Power failure. • Loss of communication between the WindFloat and the remote operator.There should be enough backup power available on the WindFloat to complete an emergencyshutdown procedure and keep emergency and safety systems, such as navigation lights, opera-tional until maintenance can be performed.VII. FABRICATION, INSTALLATION, AND COMMISSIONING REQUIREMENTS There are very strong synergies between the WindFloat hull and the MiniFloat oil and gasplatform in terms of fabrication, installation, and commissioning. The MiniFloat design philoso-phy is to optimize the economics by reducing cost in all phases of the project. The same philoso-phy is applied here and design decisions are made after clearly understanding their impact to allstages of the process.A. Fabrication: Quayside The mast and turbine are fully integrated with the platform at quayside during fabrication. Theplatform is then towed to its installation site using a tugboat. Due to its exceptional stabilityperformance, this operation can be conducted with minimal restrictions on weather conditions.
033104-13 WindFloat: Offshore ﬂoating wind J. Renewable Sustainable Energy 2, 033104 ͑2010͒Unlike ﬁxed offshore wind foundations, there is no requirement in lifting the turbine at theoffshore installation site, which was proven to be difﬁcult and costly. Such heavy lift operationsfor 5 MW turbines have been performed from ﬂoating heavy lift vessels in summer in the NorthSea but have been limited to 2 ft seas and hence, almost impossible off the Northern Californiacoast. With the proposed WindFloat ﬂoating platform, integration of the mast, turbine, and plat-form is performed at quayside, and on-site operations consist only of deploying mooring lines andconnecting to the platform. In the case of an unexpected failure of the wind turbine, the installationsequence 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 providing large preassembled cylindrical sections of the columns, which can be efﬁciently fabricated in a workshop using automatic welding machines. • It should be in the vicinity of a waterway, deep enough to allow for the WindFloat to be towed, at transit draft to the open ocean. The WindFloat is designed to be stable at its transit draft. 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 large crane. • 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 heavy lift crane, dry dock/graving dock, or submersible barges.B. 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 the tower 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 removed as soon as practical and the platform can be ballasted down to be even keel, with approxi- mately 50 ft ͑15 m͒ 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 will be comprised of multiple WindFloat units and each hull has to be towed. • Proper selection of the installation vessel is fundamental to project economics. The beneﬁts of using the same vessel with the ability to perform: ͑1͒ The mooring installation, ͑2͒ the towing of the WindFloat platforms, and ͑3͒ the power cable installation could be signiﬁcant.C. Installation: Commissioning It is important to minimize the offshore commissioning phase since offshore operations,including mobilization of people and vessels offshore, are very expensive. The following pointsare 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.
033104-14 Roddier et al. J. Renewable Sustainable Energy 2, 033104 ͑2010͒TABLE VII. Summary of stability characteristics. Heeling angle in calm sea Down ﬂooding angle Metacentric height ͑deg͒ ͑deg͒ ͑ft͒Intact case at 0° wind heading 0 20.5 53Intact case at 30° wind heading 0 22.5 53Damaged case at 0° wind heading 4.5 18 38VIII. TECHNICAL QUALIFICATION Details on the methodology used to design the WindFloat, i.e., to predict its motion, size, andstructure, 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.IX. STABILITY To assess the stability characteristics of the platform, the restoring moment is computed inintact and damaged conditions at different wind headings. The downﬂooding angle—heeling anglefor which the vents above the top of columns are underwater—is also calculated and is shown inTable VII. The restoring moment curves obtained are compared to the curves of wind overturning mo-ment to determine the heeling angle at equilibrium. Combined with a factor of safety, the com-parison provides an estimation of the stability of the platform. A rough assessment of the windoverturning moment under steady wind was carried out in this analysis, based on a range of thrustcoefﬁcients for a 10 MW wind turbine. A worst case scenario ͑failure mode͒ is considered with acombination of wind overturning moment and a faulty active ballast system. Wind headings every30° are considered for this analysis. Damage cases are also taken into account by assuming that a section of one column is ﬂooded.The damage remains limited due to compartmentation of the columns. In all considered conﬁgu-rations, the angle of static equilibrium is smaller than the downﬂooding angle with a comfortablesafety margin and the platform remains stable in damaged conditions.X. HYDRODYNAMIC MODEL The time-domain software TIMEFLOAT was developed by the authors for coupled analysis ofﬂoating structures. It uses WAMIT as a preprocessor to compute wave interaction effects andcomputes the time-domain response of one or more ﬂoaters subjected to waves, wind, current, andconnected with moorings, tendons, hawsers, fenders, or any other mechanical connections. It takesinto account the viscous forces due to shedding around the hull and wave drift forces. The solutionis fully coupled, as the inﬂuence of vessel motion on tether forces is taken into account at eachtime step, and conversely, the inﬂuence of tethers on vessel motion is also included at each timestep. A summary of the algorithm is presented next. In the frequency domain, the equation of motion of a ﬂoater is ͓m + a͔͑͒x + b͑͒x + cx = F͑͒, ¨ ˙ ͑1͒where a͑͒ and b͑͒ are frequency-dependent added mass and radiation damping coefﬁcients, andF͑͒ is the sum of forces applied to the ﬂoater including the wave-exciting force. In the time domain, one can show that the equation of motion has the following general form:
033104-15 WindFloat: Offshore ﬂoating wind J. Renewable Sustainable Energy 2, 033104 ͑2010͒ FIG. 7. Wetted hull of the WindFloat for the WAMIT model. ͑m + aЈ͒x͑t͒ + ¨ ͵ −ϱ t K͑t − ͒x͑͒d + cx͑t͒ = F͑t͒, ˙ ͑2͒where aЈ is frequency independent and K is the retardation function, ͵ Ά · ϱ 1 aЈ = a͑͒ + K͑͒sin͑͒d 0 ͑3͒ K͑͒ = 2 ͵ 0 ϱ b͑͒cos͑͒d .These integrals are calculated numerically. TIMEFLOAT uses an explicit scheme to solve up to 12 degree of freedom ͑DOF͒ equations ofmotion for a two-body system. The WindFloat is the only vessel considered in this analysis andthe software only solves 6-DOF equations. The general equation of motion is discretized in timeand the following linear vectorial equation is solved at each time step, ͓͑M͔ + ͓AЈ͔͒ak + ͓BЈ͔vk + ͓C͔xk = Fmem + Fdiff + Fvisc + Fdrift + Fmoor + Fwind . ͑4͒The left-hand side of Newton’s equation of motion ͑4͒ contains terms proportional to the 6-DOFacceleration ͑ak͒, velocity ͑vk͒, and motion of the ﬂoater ͑xk͒, with the following notations: ͓M͔ isthe mass matrix, ͓AЈ͔ is the 6 ϫ 6 inﬁnite-frequency added-mass matrix, and ͓BЈ͔ is the 6 ϫ 6matrix of retardation coefﬁcients for t = 0, which are integrals of the frequency-dependent radiationdamping coefﬁcients due to outgoing waves generated by the moving ﬂoater. The damping coef-ﬁcients are computed by WAMIT and integrated at the beginning of the time-domain simulation togenerate the retardation function matrix. ͓C͔ is the 6 ϫ 6 hydrostatic stiffness matrix computed byWAMIT. Only the terms C͑3,3͒, C͑4,4͒, C͑5,5͒, C͑3,4͒, C͑3,5͒, and C͑4,5͒ are nonzero. Refer to 25WAMIT manual for details. 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 inthis equation is given below. Fmem represents the memory effect, i.e., the effects of wave compo-nents generated by past motion of the ﬂoater, described by the convolution of the retardationfunction with body velocity, as shown in Eq. ͑3͒ above. Fdiff is the 6-DOF wave-exciting force determined by a Fourier series using the WAMIT
033104-16 Roddier et al. J. Renewable Sustainable Energy 2, 033104 ͑2010͒frequency-dependent wave-exciting force components and wave amplitude components represent-ing the speciﬁed wave spectrum. A random phase and random frequency algorithms are used togenerate irregular wave trains efﬁciently and accurately. Fvisc is the 6-DOF viscous force resulting from drag effects on the vessel columns and water-entrapment plates. These are computed using a modiﬁed Morison equation model based on therelative velocity of the wave/current kinematics and of special line members. Results of multiplemodel test campaigns have been used to calibrate the empirical viscous force model. The effect ofocean currents is captured with this viscous force model. Fdrift is the 6-DOF drift force on the vessel computed based on the WAMIT mean driftfrequency-dependent coefﬁcients obtained with the pressure integration or momentum approachand the wave amplitude components. Newman’s approximation is used. Alternatively, a fullsecond-order diffraction model can be used if the WAMIT second order module is run. Previouswork 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 aremodeled either with cable elements or nonlinear springs. For cable elements, a ﬁnite-differencescheme is used to yield the dynamic mooring line conﬁguration and mooring tensions at each timestep. The mooring dynamics and hydrodynamic loads are included using a Morison type formu-lation. The nonlinear ﬁnite-difference equations are solved using a Newton–Raphson algorithm, asdescribed by Chatjigeorgiou and Mavrakos.26 Fwind is the 6-DOF wind turbine force on the vessel superstructure. The wind force model wasmodiﬁed to capture some of the aerodynamic coupling between the turbine and the WindFloatplatform. It was assumed that the wind force applied on the rotor was proportional to the squareof the relative velocity between the wind and the hub. It was determined that an equivalent disk inthe rotor plane with 72.7 m diameter would provide the maximum rated thrust of a 10 MWturbine, assuming a 1.2 drag coefﬁcient on the disk. The wind force is perpendicular to the diskand its direction varies in time with the platform rotations. The gyroscopic moment was estimatedfrom Mgyro = I⍀ ϫ p, ͑5͒where I is the moment of inertia of the spinning rotor, p is the rotational velocity vector of therotor around its axis, and ⍀ is the rotational velocity vector of the platform around the pitch andyaw 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 vesselframe of reference at t = 0. The origin of the vessel frame of reference is located at the mean waterlevel directly under the center of gravity. The X-axis points toward the bow, i.e., the columnsupporting 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 inputﬁle in text format, with all vessel, mooring, and numerical parameters. Additional input consist ofthe WAMIT ﬁles and the wind and current coefﬁcients ﬁles. After reading the input, TIMEFLOATsolves an initial static phase, in which mean wind and current loads are applied as well as themooring line pretension. This phase serves to reduce the transient phases and quickly providesstatic information if needed. Then, the solution is advanced in time using a Runge–Kutta algorithmfor the 6-DOF rigid-body motion and velocities. At each of the four fractional steps used in thisprocess, external forces are updated. WAMIT6.3 software was used to compute added-mass and damping coefﬁcients as well aswave-exciting forces and mean drift coefﬁcients. Only the underwater part of the hull is modeled.The model includes the columns, water-entrapment plates, and main tubulars connecting columns.The bracings are only modeled as line members using the Morison equation. Dipole elements areused to discretize the water-entrapment plate since they are thin structural elements.
033104-17 WindFloat: Offshore ﬂoating wind J. Renewable Sustainable Energy 2, 033104 ͑2010͒ FIG. 8. Picture of the WindFloat model.XI. DESIGN CASES In the preliminary design phase, a selected number of design cases were deﬁned based on acombination of offshore mooring design codes and offshore wind turbine design codes, i.e., 28API-RP2SK ͑Ref. 27͒ and Germanischer Lloyd. The design cases that were thought to be the mostonerous for the platform motions were checked. These included the extreme coherent gust ͑ECG͒and the 100 year storm ͑13.5 m Hs͒ shown in Tables IV and V. In addition, a number of operatingcases were run corresponding to the turbine maximum thrust wind speed ͑ϳ12 m / s͒ with asso-ciated waves ͑ϳ2 m Hs͒, and the maximum wind speed with turbine spinning ͑ϳ25 m / s͒ withassociated waves ͑ϳ4 m Hs͒. For detail design and certiﬁcation, a much larger number of design cases will have to beconsidered; however, the return period of the maximum events will likely be 50 years in accor-dance with wind turbine design codes, rather than the 100 year return period selected for thispreliminary study. Space does not allow for an extensive presentation of the hydrodynamic simu-lations; however, some results of numerical predictions are provided later and compared to modeltest results for key parameters.XII. MODEL TESTS SETUP A model test campaign was conducted at the UC Berkeley 200 ft long ͑61 m͒ ship-modeltesting facility to test the validity of the numerical analysis tools. A 1/105 scale model of theplatform was fabricated out of the acrylic. Lead weights were placed inside the columns and onthe water-entrapment plates to adjust the center of gravity to its target position; item ͑1͒ in Fig. 8.
033104-18 Roddier et al. J. Renewable Sustainable Energy 2, 033104 ͑2010͒The platform motion was measured using a digital video camera tracking the motion of lightemitting diodes placed on model ͑2͒. The system provides 3-DOF measurements of the motion inthe plane of the camera. Tower ͑3͒ was made of a thin ͑not-to-scale͒ 1 in. outside diameter acrylic pipe because thedevice used to model the wind turbine was relatively heavy and it was not possible to obtain thecorrect center of gravity with the lead weights if the tower was modeled with a 3 in. diameteracrylic pipe, as originally planned. Stays made of thin string were connected to the tower toincrease its stiffness. The turbine model device was connected to the top of the tower onto a load cell ͑4͒, whichmeasured the axial force perpendicular to the tower. A large disk ͑5͒ made of foam board wasplaced on the model to attract wind loads corresponding to the design wind force. No attemptswere made to match the atmospheric turbulence. The wind maker naturally produces turbulenceand the turbulent wind ﬂuctuations are somewhat averaged by the large disk. In the end, the windforce was measured and the turbulence level will be compared to variations in the aerodynamicforces generated by a prototype wind turbine. The disk diameter is a third of the total area coveredby the rotor. The drag coefﬁcient on the disk is estimated to be 1.2. An electrical motor ͑6͒ was placed at the top of the tower to model the gyroscopic effect. Thiswell-known mechanical force arises when a rotor spinning around a certain axis undergoes arotation around a different axis. For instance, platform pitch and yaw would lead to gyroscopicforces applied on the tower. These forces are a signiﬁcant design issue for the blades and theshaft/bearings, but they may also have a contribution to the global response of the ﬂoater. Themotor was adjusted to spin at the Froude-scaled turbine speed of 2 Hz ͑approximately 12 rpm inprototype scale͒, and the inertia of the blades was approximately modeled with two weights ͑7͒positioned on an aluminum rod ͑8͒. The model was kept in position in the tank using four soft springs—two of them connected tocolumn 1 which holds the turbine and one on each of the other columns. The mooring lines wereconnected at the edges of a 7 ϫ 7 ft2 square frame placed on the tank ﬂoor. This provided a topangle for the mooring lines of approximately 45°. This equivalent mooring model provided hori-zontal stiffness similar to that of the prototype six line catenary mooring system, yielding a 65 sresonant period in surge. However, the prototype mooring design has not been ﬁnalized and thefocus of these tests was placed on platform motion. No attempts were made to measure mooringtension or validate mooring dynamics. A plunger type wave maker is located at one end of the tank and a parabolic wave absorptionbeach at the other end. A set of ﬁve large wind fans was assembled to generate the required windloading on the turbine model, as shown in Fig. 9. The effect of the active ballast system wasmodeled by shifting lead ballast on the model to compensate for the mean wind overturningmoment. A 3 h long realization of the 100 year waves was generated. The associated wind is 25 m/s,which is the maximum wind speed at which the wind turbine is allowed to rotate. Such waveevents may occur at the site with wind speed under the cutoff speed due to swells. Most likely, therotor would be parked if such wave conditions arise; however, this conservative design case wasgenerated to establish upper bounds of platform motion. The 100 year wave run was repeatedwithout wind. Additionally, regular waves were run with and without wind to determine responseamplitude operators ͑RAOs͒.XIII. RESULTS Results of the 100 year storm simulation are summarized in Table VIII. Time series ofplatform surge, heave, and pitch were processed to yield rms, maximum, and minimum values.These show a satisfactory agreement between the model test results and numerical simulationsperformed with TIMEFLOAT. The pitch rms is slightly underpredicted by the software ͑1.15° versus1.27° measured͒, and the minimum and maximum pitch angles are off by 1° due to some differ-ences in the predicted versus measured wind overturning moment; the platform response is,however, deemed extremely well behaved, with maximum pitch angle of 5° in a 13.5 m Hs sea
033104-19 WindFloat: Offshore ﬂoating wind J. Renewable Sustainable Energy 2, 033104 ͑2010͒ FIG. 9. WindFloat model in the 100 year storm.state. The maximum crest to trough pitch is 7° with a 21.3 m maximum wave height ͑crest totrough͒. Similar responses and trends were observed for all tested platform headings ͑0° and 90°͒and for runs with and without wind. The maximum yaw angle measured in the 90° runs was under10°. RAOs were computed for wave periods between 6 and 18 s. Figure 10 shows the RAOs insurge, heave, and pitch for 0° wave heading. The presence of wind does not affect surge or swaysigniﬁcantly, but its effects are slightly more pronounced on the pitch RAOs. Although wind speedis constant in all the regular wave runs, it does impact the regular wave response because thewave-induced motions generate a sinusoidal variation in the relative speed between the wind andthe disk, which results in an additional periodic force component on the disk leading to a corre-sponding periodic pitch moment. Regular wave tests were repeated with 90° wave heading to investigate the platform yawresponse; i.e., the model orientation was changed by rotating the anchoring frame to 90°. There isno wave-induced yaw for 0° heading since the platform is port/starboard symmetric; the yaw RAOat 90° is shown in Fig. 11. Additional tests were carried out by adding two large triangular verticalplates on each column ͑named yaw plates͒ with the bottom edge extending outward to the edge ofthe heave plate and the side extending from the heave plate to 20 ft below the mean water level inprototype scale. The effects of “yaw plates” in reducing ﬁrst-order yaw were minimal. The irregu-TABLE VIII. Numerical and model test results in the 100 year storm with 0° wave heading and 25 m/s steady wind. Wind surge 85 ft/s heave Steady pitchHeading 0 ͑ft͒ ͑ft͒ ͑ft͒rms Model tests 10.56 6.88 1.27 Time ﬂoat 9.18 6.40 1.15Maximum Model tests 48.46 18.97 4.87 Time ﬂoat 43.51 16.18 5.77Minimum Model tests Ϫ22.16 Ϫ22.05 Ϫ3.87 Time ﬂoat Ϫ17.28 Ϫ22.61 Ϫ2.67
033104-20 Roddier et al. J. Renewable Sustainable Energy 2, 033104 ͑2010͒ FIG. 10. RAO in surge, heave, and pitch at 0° with and without wind.lar wave test showed that the second-order yaw was also not signiﬁcantly reduced. Overall, theexperiment did not point to serious limitations of the numerical modeling ability.XIV. COUPLED AEROHYDRODYNAMIC MODEL The forces generated by the wind turbine are reasonably well computed by the modiﬁedTIMEFLOAT software and are correspondingly well modeled experimentally for a steady windspeed. However in reality, the wind speed is constantly changing due to naturally occurringturbulence in the atmosphere. Large wind turbines are equipped with sophisticated control systemsgenerally designed to keep the rotor speed constant at all times using a variable torque generatorand a blade pitching mechanism ͑changing the angle of attack of the blades by rotating themaround their local axis͒. This technique, known as “blade pitching,” can have signiﬁcant effects onﬂoating platforms, as observed by Nielsen et al.9 and by Jonkman.29 The control system may FIG. 11. RAO in yaw at 90° without wind.
033104-21 WindFloat: Offshore ﬂoating wind J. Renewable Sustainable Energy 2, 033104 ͑2010͒induce negative damping, which results in resonant oscillations of the platform at its pitch naturalperiod. In order to assess the effects of blade pitching on the ﬂoater, as well as to provide accuratecomputation of all loads induced by the wind turbine on a moving foundation, a software dedi-cated to wind turbine design, FAST, was interfaced with TIMEFLOAT to provide a fully coupledaeroservoelastic/hydrodynamic time-domain numerical model of the WindFloat platform with a 5MW wind turbine. FAST, which stands for “fatigue, aerodynamics, structures, and turbulence” is an aeroser-voelastic modal code for horizontal axis wind turbines developed by the National RenewableEnergy Laboratory ͑NREL͒. FAST models the wind turbine as a combination of rigid and ﬂexiblebodies. The rigid bodies are the earth, nacelle, hub, and optional tip brakes. The ﬂexible bodiesinclude blades, tower, and drive shaft. The model connects these bodies with several DOFs,including tower bending, blade bending, nacelle yaw, rotor teeter, rotor speed, and drive shafttorsional ﬂexibility. FAST uses Kane’s method to set up equations of motion, which are solved bynumerical integration. The AERODYN subroutine package developed by Windward Engineering isused to generate aerodynamic forces along the blades. The FAST and TIMEFLOAT FORTRAN source codes were modiﬁed to change TIMEFLOAT into asubroutine called by FAST. Hydrodynamic forces, including wave-exciting forces, viscous forces,and mooring forces are computed by TIMEFLOAT and passed to FAST, which solves the coupledturbine tower problem and passes platform motion back to TIMEFLOAT. The FAST model of a utility-scale multimegawatt turbine known as the “NREL offshore 5 MWbaseline wind turbine” was developed by Jonkman et al.21 using publicly available informationfrom turbine manufacturers. This wind turbine is a conventional three-bladed upwind variable-speed variable blade-pitch-to-feather-controlled turbine. A conventional control system was usedwith a generator-torque controller whose goal is to maximize power capture below the ratedoperation point and a blade-pitch controller designed to regulate rotor speed above the ratedoperation point. The coupled FAST-TIMEFLOAT model was run using the validated WindFloat hydrodynamicmodel described in Sec. X. Sample results are provided for a 4 m signiﬁcant sea state with 12 speak period and a 12 m/s steady wind. Waves and wind are at 0° heading, along the symmetry axisof the WindFloat. A Jonswap wave spectrum is assumed with peakness factor ␥ = 2.4. No atmo-spheric turbulence is assumed in this simulation. Figure 12 shows sample time series of the platform roll, pitch, and yaw over a 5 min durationafter the initial transients generated at the beginning of the numerical simulation have disappeared.A slight asymmetry is present due to the rotation of the rotor in one direction, generating a smallmean roll ͑ϳ1°͒ and yaw ͑ϳ2°͒ component. A background platform pitch oscillation of approxi-mately Ϯ2° is caused by the blade-pitch controller, which excites the platform at its pitch resonantperiod around 30 s. This was later tuned out by modifying the controller coefﬁcients and addingan additional ﬁlter. Superposed to the resonant pitch cycles are wave-induced pitch oscillations,which result in slight changes between resonant cycles, but are overall a small contribution to theplatform pitch in this sea state. In Fig. 13, time series of the base of the tower are shown. Wave-induced surge is clearlyvisible in this 4 m irregular wave sea state. Mean surge is primarily driven by mean aerodynamicloads on the turbine. The platform pitch oscillation results in vertical movement of the tower baseat the same period as the pitch cycles. Figure 14 presents the blade-pitch angle time series ͑at the bottom͒ and power out-take ͑at thetop͒. The blade-pitch controller locks into the platform pitch resonance with 30 s cycling of theblades. A drop in produced power occurs for approximately 2 s at each cycle when the relativespeed between the nacelle and incoming wind drops below the threshold for maximum poweroutput. This does not have a large impact on mean produced power, which is 4.95 MW on average,
033104-22 Roddier et al. J. Renewable Sustainable Energy 2, 033104 ͑2010͒ FIG. 12. WindFloat rotations in 4 m seas with 12 m/s wind.but would require ﬁltering. Further investigations of the control system have been performedfollowing the recommendations of Jonkman29 and Nielsen9 to eliminate this resonant response inorder to maximize power production and minimize fatigue loading of all components and systems.Results will be published shortly. FIG. 13. Tower base motion in 4 m seas with 12 m/s wind.
033104-23 WindFloat: Offshore ﬂoating wind J. Renewable Sustainable Energy 2, 033104 ͑2010͒ FIG. 14. Power outtake and blade pitch in 4 m seas with 12 m/s wind.XV. DESIGN STANDARDS AND ENVIRONMENTAL CONDITIONS The WindFloat is a novel offshore structure, which combines a wind turbine and a ﬂoater. Noformal design code has been developed yet for the design of structural reinforcement and scant-ling. Existing standards for offshore wind turbines were developed in the past decade from knowl-edge of onshore wind turbines and growing experience in near-shore operations of wind energydevices. However, their scope remains limited to wind turbines in shallow waters with ﬁxedfoundations. The WindFloat is a moored platform with a complex dynamic behavior, which cannot beoverlooked in the structural design of critical elements, such as the tower. Although offshore windenergy codes, such as the Germanischer Lloyd Guidelines for the Certiﬁcation of Offshore WindTurbines,28 provide critical information about the extent of wind loading on the structure, thedesign criteria may not be sufﬁciently conservative for a ﬂoater. To ensure a high reliability of the design, the structural analysis of the WindFloat is largelybased on standards from the oil and gas industry, including the ABS rules for Mobile OffshoreDrilling Units30 and the API Recommended Practice for Fixed Offshore Platforms.27 The DNVRecommended Practice C202 ͑Ref. 31͒ is used to assess shell buckling of the tower. These designcriteria need to be combined with a realistic model of the wind loading effects and conservativeestimation of environmental loadings on the hull. The environmental loadings in both cases are obtained for sea states in the wave scatterdiagram encountered at the intended location of the WindFloat, off the coast of Northern Califor-nia. For each peak period ͑Tp͒ in the wave scatter diagram, the sea state with highest signiﬁcantwave height ͑Hs͒ is identiﬁed. The 12 resulting sea states with characteristics listed in Table IXrepresent the steepest wave conditions for each peak period. The strength analysis may be basedon these sea states. All peak periods are included in the strength analysis since wave loadingdepends on wavelength. The largest wave height does not necessarily result in largest loading onthe platform. The fatigue analysis requires the generation of extensive numerical data. The fatiguedamage must be calculated for all sea states in the wave scatter diagram, based on a time series ofnominal stress. To avoid the production of large amounts of data and to save CPU time, the stressrange is computed only for those 12 identiﬁed sea states. For a given peak period, the level of
033104-24 Roddier et al. J. Renewable Sustainable Energy 2, 033104 ͑2010͒ TABLE IX. Sea states for structural strength analysis. Tp Hs Hs Case No. ͑s͒ ͑m͒ ͑ft͒ 01 20 12.5 41.0 02 16.7 11.5 37.7 03 14.3 9.5 31.2 04 12.5 8.5 27.9 05 11.1 7.5 24.6 06 10 7.5 24.6 07 9.1 7.5 24.6 08 8.3 6.5 21.3 09 7.1 5.5 18.0 10 6.3 4.5 14.8 11 5.3 3.5 11.5 12 4.2 1.5 4.9stress is assumed to be linear with signiﬁcant wave height. Thus, the level of stress is scaled withsigniﬁcant wave height to complete the wave scatter diagram and determine the fatigue life of allstructural elements. For the truss and the tower of WindFloat, strength and fatigue analyses are carried out. Thecomputation of local forces and moments is achieved with ﬁnite-element software SAP by Com-puter & Structures, Inc., Berkeley, CA, using beam theory. The structural calculations are linear. Astatic analysis is sufﬁcient on the truss since the natural period of its elements are too low to beexcited by environmental loading. However, a dynamic analysis is necessary to account for theexcitation of the natural period of the tower. The applied loads are obtained from TIMEFLOAT timeseries for each sea state. External forces and moments are applied at the extremities of the tubularelements in the ﬁnite-element model or as distributed loads. For the dynamic analysis of the tower,the 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 apreliminary structural analysis to ensure the reliability of the elements. For the strength analysis,the most extreme stresses are used to compute recommended strength ratios. When necessary, thethickness of the tubular elements was adjusted to meet the appropriate safety factors in strength.On tubular elements, fatigue assessment is especially critical at the joints. A hot-spot stress ap-proach as recommended in API is used to estimate the fatigue at the joints between bracingelements. This method entails the calculation of stress concentration factors ͑SCFs͒ at the joints.The fatigue life is computed based on the nominal stress as provided by a beam-column ﬁnite-element model multiplied by the SCF. The damage and fatigue life are computed with a formu-lation from DNV Recommended Practice RP-C203 for a short term Rayleigh distribution of stresslevels. The annual damage for all sea states and in three directions is combined with Miner’s rule, D= Td A ͩ ͚ͪ ϫ⌫ 1+ m 2 seastates pii͑2ͱ2͒m , ͑6͒where is the range of the nominal stress, pi the probability of occurrence of a sea state in anygiven year, and i is the frequency of cycles, which may be taken to the zero-up crossing fre-quency. Recall that Td is the design life and A and m are parameters of the API X S-N curve.XVI. STRENGTH AND FATIGUE DESIGN OF THE TRUSS The primary function of the truss is to provide the WindFloat hull with sufﬁcient globalstructural stiffness to withstand environmental loads. A three-dimensional ͑3D͒ model of theWindFloat is created ͑Fig. 15͒. The columns and bracing are modeled with tubular grade 50 steel
033104-25 WindFloat: Offshore ﬂoating wind J. Renewable Sustainable Energy 2, 033104 ͑2010͒ FIG. 15. Truss ﬁnite-element model.beam-column elements. Main horizontal bracing members are 150 ft ͑45.7 m͒ long cylinders thatsupport the horizontal loads between columns. Light bracing members provide reinforcement at1/3 of their length. These bracing members are diagonal between the main bracings and columnsfor vertical stiffness and horizontal between main bracing elements to provide horizontal stiffness.The joints between the column and the bracing are modeled with an element of stiffness, ten timesthat of the bracing element, and consistent with API recommendations. The water-entrapmentplates are not included in this model but the applied forces on the plates are calculated externallyand transferred to the base of the columns. External and inertia forces applied to each structural member are computed using dedicatedsoftware, based on the TIMEFLOAT program, which computes hydrodynamic loads by integration ofthe diffraction and radiation pressures on each part of the structure. The software also matches thehydrodynamic panels with corresponding structural elements. The time-domain force componentspassed to the ﬁnite-element model include weight of all elements, radiation, and diffraction pres-sures, as well as mass inertia and hydrostatic stiffness effects. Wave exciting forces, includingFroude–Krylov effects, are passed via the diffraction pressure. The viscous forces, reﬂecting
033104-26 Roddier et al. J. Renewable Sustainable Energy 2, 033104 ͑2010͒viscous loads on heave plates, columns, and truss members, are applied to the corresponding partsof the structure. The mooring forces are applied vertically to the chain stoppers at the top ofcolumn since they set the column in compression. The horizontal component of the mooring isapplied to the fairlead at the keel, with a 45° top angle. The wind-induced forces ͑thrust andtorque͒ are applied horizontally at the top of the tower. Drift forces are neglected since they arerelatively small on individual elements. It is veriﬁed that the sum of external forces and inertiaforces on all parts of the structure is approximately null. The truss consists of unstiffened tubular elements. For the analysis of tubular members, APIRP2A-WSD deﬁnes allowable axial, bending shear, and hoop stresses. Maximum predictedstresses on the elements in design environmental conditions are computed with ﬁnite-elementanalysis. The overall structural reliability of a member is estimated by combination of the maxi-mum to allowable stress ratios with appropriate safety factors. All computed ratios must be lessthan 1 to comply with API. The stress on the truss is determined using a static ﬁnite-element algorithm on the modelsubject to all environmental loads including rigid-body dynamics contributions. To capture thehighest stress level, the forces are calculated for a 1 min snapshot of the most extreme wave of a1 h simulation on all relevant sea states for three headings. The maximum API stress ratios increase with larger sea states. Thus, sea state 1, with thelargest signiﬁcant wave height, is associated with the maximum stress ratio at 90°, heading formost frame elements. Figure 16 represents the maximum API ratios calculated in the worst case,at 90° heading for sea state 1, plotted directly on the structure. The shell thickness and diameter ofthe 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 thetruss in strength analysis. Figure 17 illustrates the effect of wave and wind loading on the shape ofthe 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 is20 years. In this design cycle, a safety factor of 10 is applied and a calculated fatigue life of 200years 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 theconnection is determined based on the stress ranges calculated by beam theory. To apply thehot-spot stress curve, the SCF needs to be determined. For a nominal stress away from the weldingtoe on a beam model of the tubular element, it is reasonable to expect the SCF to be between fourand six for a well-designed connection. The Von Mises stress at the connection obtained frombeam-column ﬁnite-element modeling is used as nominal stress in this case. A sensitivity analysisis carried out on the value of the SCF. The exact stress ratio between the maximum stress at theweld toe and Von Mises stress in beam theory will be determined precisely by ﬁnite-elementanalysis with a 3D model of the connection in follow on studies. It should also be noted that weldproﬁle control is assumed at the joints of truss elements so that the API X-curve may be used todeﬁne 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 between6 and 10 s depending on the heading. This is consistent with wave loads on the columns when thewavelength is half the distance between columns. The stress ranges are determined for all sea states in the scatter diagram and combined toobtain the fatigue life. Results are summarized in Table X. Assuming that the stress at the weld isaccurately computed by the beam model and that no increase in wall thickness is implemented atthe connection, the minimum fatigue life of the nodes is 670 years. This optimistic assumptionwill be veriﬁed with a detailed ﬁnite element of the connection. It is likely that increase in wallthickness over a short section near the node will be required to achieve fatigue life targets.Estimates of fatigue life based on a can with wall thickness equal to twice the nominal wallthickness of the tubular members are provided in Table XI.
033104-27 WindFloat: Offshore ﬂoating wind J. Renewable Sustainable Energy 2, 033104 ͑2010͒ FIG. 16. Maximum API design ratios on WindFloat platform in 90° heading sea state 1.XVII. STRUCTURAL ANALYSIS OF THE TOWER The design of the tower must take into account wind and wave-induced motions. A dynamicanalysis of the tower is required since the ﬁrst lateral mode of resonance is near 3 s. At suchperiods, some wave energy may be transmitted to the tower through the platform rigid-bodymotions. The tower is a tapered unstiffened 220 ft ͑67 m͒ high tube, with increasing wall thicknessfrom top to bottom. It supports a 300 ton nacelle and rotor at the top. It is connected to the columnat the bottom with a bolted or welded ﬂange joint. The buckling strength of the tubular element isdetermined for extreme environmental conditions and the fatigue life of the joint at the base of thecolumn is calculated. The numerical model is composed of a number of beam elements with decreasing diameterand thickness from bottom to top. Beam elements are sufﬁcient for this study since there is noexternal pressure distribution on the tower. A convergence analysis is carried out to determine theminimum number of elements necessary to correctly represent the dynamic characteristics of thetower. 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 relevantsea states in the wave scatter diagram. Additionally, the largest wind force ͑the maximum of the
033104-28 Roddier et al. J. Renewable Sustainable Energy 2, 033104 ͑2010͒ FIG. 17. Deformed ͑50ϫ͒ shape of WindFloat structure in worst loading conditions ͑sea state 1 at 90° heading͒.thrust versus wind speed curve͒ is applied horizontally at the top and the tower supports its ownweight as well as the weight of the turbine. The deﬂections of the tower are computed using linearbeam theory with a time-domain ﬁnite-element algorithm. In Fig. 18, the bending moment ͑top͒ and the sway motion at the base of the tower ͑bottom͒are plotted during the largest wave event of the 1 h time series for sea state 1, which correspondsto the 100 year storm. The maximum horizontal excursion at the base of the turbine tower is 60 ft͑18 m͒ crest to trough during a single wave cycle, corresponding to a 70 ft ͑21 m͒ wave crest to TABLE X. Fatigue life on connection between bracings based on nominal wall thickness. Damage Fatigue life SCF ͑per year͒ ͑year͒ 1 1.7ϫ 10−03 670 1.5 8.2ϫ 10−03 121 2 2.8ϫ 10−02 36
033104-29 WindFloat: Offshore ﬂoating wind J. Renewable Sustainable Energy 2, 033104 ͑2010͒ TABLE XI. Fatigue life with double wall thickness at the connection. Damage Fatiguelife SCF ͑per year͒ ͑year͒ 1 6.7ϫ 10−05 14 934 1.5 3.8ϫ 10−04 2623 2 1.5ϫ 10−03 670trough. The bending moment time series clearly shows the dynamic response of the tower, whichincludes oscillations with a period below 3 s superimposed to the wave-induced component witha period around 20 s. A 2% ratio of critical damping is applied to the numerical model. This is the level of dampingexpected on the tower when the turbine is parked. In most scenarios, when the turbine rotates, thedamping ratio increases on the tower due to aerodynamic drag. A sensitivity analysis is performedto 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% criticaldamping ratios, highlighting the variations in the dynamic response of the tower. Yet, the energyat the natural period of the tower is small compared to wave-induced variations in bending stress.The structural damping does not affect the fatigue results signiﬁcantly: The rms of bendingmoment varies by only 1% when damping is increased from 2% to 5% of critical damping in thishigh sea state. The natural period of the tower is low enough to not interfere with wave-induced motion ofthe platform. The unsupported section of the WindFloat tower is much shorter than onshore towersbecause the hub is slightly lower than onshore, and the platform truss provides lateral stiffness tothe tower up to 33 ft ͑10 m͒ 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 s͒. The bottom of the ﬁgure shows a time series of the sway motion, which is a combinationof linear wave dynamics with period of 4.2 s and slow-drift cycles with period of approximately FIG. 18. Bending stress ͑kips/ft͒ and sway ͑ft͒ at the base of the tower at the largest wave of sea state 1.
033104-30 Roddier et al. J. Renewable Sustainable Energy 2, 033104 ͑2010͒ FIG. 19. Sensitivity of bending stress with damping ratio in sea state 1 at 90° heading.50 s. Only the energy from ﬁrst-order wave dynamics at low periods is transmitted to the tower.Excitation of the tower natural periods is not apparent due to the small magnitude of tower basemotion. For the strength analysis, the design recommendations from DNV-RP C202 are used. Theshell buckling assessment is based on formulas for unstiffened tubular elements. The column FIG. 20. Bending stress ͑kips/ft͒ and sway ͑ft͒ at the base of the tower at the largest wave of sea state 12.
033104-31 WindFloat: Offshore ﬂoating wind J. Renewable Sustainable Energy 2, 033104 ͑2010͒ FIG. 21. ͑Left͒ Axial force in compression. ͑right͒ Bending moment at largest event of sea state 1 at 90° heading.buckling does not need to be computed since ͑kL / i͒2 Ͻ 2.5 E / fY, where kL is the effective length,i is the radius of gyration of the cross section, E is Young’s modulus, and fY is the yield strengthof steel. The largest events are identiﬁed over a 1 h time series. The shell buckling ratio is calculatedat the lower end of each of the eight elements using the local wall thickness and diameter for thiselement. Stress is largest at these lowest ends since the axial force and bending moment increasetoward 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 turbinecontributes up to 70% of the axial stress on the tower. The wind force is critical to the design ofthe tower in strength. Shell buckling ratios are computed for these extreme events according to DNV recommenda-tions. At the base of the tower, the largest design equivalent to the Von Mises stress to design shellbuckling strength ratio is 0.4, which is 40% of the maximum allowed. Thus, the tower will not beaffected 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 thetower. The column and the tower meet in a ﬂange connection, which is bolted or welded. Thestandard deviation of the Von Mises stress is determined over a 1 h simulation of the structuralresponse to the 12 relevant sea states. The bending moment is computed at a point at the base ofthe tower for a number of wave directions between 0° and 180°, to account for the directionalityof waves at the Northern California location. Each heading is given identical probability ofoccurrence for this analysis. The hot-spot stress S-N curve with a Rayleigh approximation is used to determine the damageper year on the connection. The SCF should be computed from a 3D ﬁnite-element analysis of theconnection. However, this work will be performed in a later phase of the project once structuraldetails of the connection are established. In a preliminary analysis, a sensitivity study is carried outon the SCF at the base of the tower. Results are summarized in Table XII. The calculated fatigue life is 37 280 years based onnominal wave-induced stress. Damping level is conservatively assumed to be 2% of critical for allsea states, although it will likely be higher when the turbine is spinning. The design of theconnection between the tower base and top of column will have to be carefully designed to reduceSCFs to acceptable levels based on fatigue life targets. Fatigue due to cycling of the wind loadsand tower vibrations due to the spinning rotor have not been included in this model. Detailedaerodynamic calculations will be performed to account for these additional fatigue sources.
033104-32 Roddier et al. J. Renewable Sustainable Energy 2, 033104 ͑2010͒ TABLE XII. Summary of sensitivity of fatigue damage on SCF. Damping Damage Fatigue life ͑%͒ SCF ͑per year͒ ͑year͒ 2 1 2.68ϫ 10−05 37 280 2 2 5.59ϫ 10−04 1790 2 4 1.16ϫ 10−02 86 2 6 6.87ϫ 10−02 15XVIII. CONCLUSION The work presented herein was aimed at providing sufﬁcient technical information about thesystem to highlight challenging areas for any offshore ﬂoating wind turbine foundations. The mostprominent areas are as follows. • The turbines in their “as-is” conﬁgurations may not be able to withstand some of the ﬂoater induced motions. It is therefore critical to involve the turbine manufacturers, to verify that the new motion envelopes are within their design criteria. It is further important to minimize the ﬂoater motions, most critically the pitch motion, to eliminate any potential for the blade interference with the mast due to the gyroscopic force, which maintains the blades in their turning plane. • Fabrication and installation: The foundation should be fabricated and integrated near the installation site. However, the infrastructure required for the construction of such a large system may not exist near some of the potential wind farm areas and might have signiﬁcant cost 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 analysiswas ﬁrst carried out with simpliﬁed models of the wind turbine forces. This work was done witha fully coupled time-domain algorithm, which accounts for diffraction-radiation effects, as well asviscous forces and the inﬂuence of the mooring. Model tests were performed to validate thepredictive ability of the numerical hydrodynamic algorithm. This experimental work consisted ofgenerating wave loads in a wave tank facility, as well as wind loads using fans and a drag diskplaced on the model, and a rotor to model gyroscopic effects. A coupled aeroelastic-hydrodynamic model was then implemented to provide better resolutionof wind turbine loads and take into account the effects of the turbine control system. For this work,the validated hydrodynamic model discussed above was interfaced with FAST software developedby NREL for design of wind turbines. It was shown that interactions between the wind turbinecontrol system and the platform generate small rotational oscillations with long periods ͑ϳ30 s͒, which, in some cases, could result in slightly reduced power output. Further work will becarried out to improve the turbine control system, and assess the effects of coupled aeroelastic-hydrodynamic loads on the WindFloat components. Lastly, this paper discusses the preliminary structural assessment of the WindFloat. It focuseson the methodology designed to estimate the strength and fatigue of WindFloat’s novel structuralcomponents. It is assumed that structural loading on the underwater elements of the platform, suchas the columns and the water-entrapment plates, is mostly dependent on wave loading. Theirpreliminary design can be conservatively established using design guidelines developed for theoffshore industry. Novel elements, such as the truss or the interface between the wind turbine andthe columns, i.e., the tower, must be analyzed thoroughly due to the importance of aerodynamic
033104-33 WindFloat: Offshore ﬂoating wind J. Renewable Sustainable Energy 2, 033104 ͑2010͒loading on their design. A strength and fatigue analysis is performed using a simpliﬁed beammodel to assess the structural reliability of the structure under conservative environmental loadingand identiﬁes the areas that will require further detailed analysis. The work presented herein was focused on providing sufﬁcient technical information aboutthe system to highlight follow on design challenges. A few critical topics have been identiﬁed onthe truss and tower design. The wind force is essential to the strength behavior of the WindFloatsince its contribution to the bending stress of the structural members is signiﬁcant. It is essentialto include the effect of aerodynamics in the detailed structural analysis, but in the preliminaryanalysis, a large factor of safety sufﬁced to conclude the global structural reliability of the Wind-Float. 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-mensions of the main structural components of the structure are compatible with expected envi-ronmental loading. Local reinforcement of the structure will be required but are not expected tosigniﬁcantly alter initial weight and cost estimates.ACKNOWLEDGMENTS Financial support of this work by the Principal Power Inc. is gratefully acknowledged.1 J. M. Jonkman, “Dynamics Modeling and Loads Analysis of an Offshore Floating Wind Turbine,” NREL Technical Report No. TP-500-41958, November 2007. 2 American Petroleum Institute, Recommended Practice for Planning and Constructing Fixed Offshore Platforms— Working Stress Design, 2000. 3 A. Aubault, C. Cermelli, and D. Roddier, in “Parametric Optimization of a Semi-Submersible Platform with Heave Plates,” Proceedings of the OMAE’07, 26th International Conference on Offshore Mechanics and Arctic Engineering, San Diego, 11–16 June 2007. 4 A. R. Henderson and M. H. Patel, Wind Energy 6, 53 ͑2003͒. 5 S. Butterﬁeld, W. Musial, J. Jonkman, P. Sclavounos, and L. Wayman, in “Engineering Challenges for Floating Offshore Wind 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 for Offshore Wind Turbines,” 44th AIAA Aerospace Sciences Meeting and Exhibit, 9–12 January 2006, Reno, NV. 7 E. N. Wayman, P. D. Sclavounos, S. Butterﬁeld, J. Jonkman, and W. Musial, in “Coupled Dynamic Modeling of Floating Wind Turbine Systems,” 2006, Offshore Technology Conference, Houston, TX, 1–4 May 2006. 8 J. Jonkman, S. Butterﬁeld, W. Musial, and G. 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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 Offshore Mechanics and Arctic Engineering, Honolulu, HI, 31 May–5 June 2009.13 C. Cermelli, D. Roddier, and A. Aubault, Remote Power Generation for Deployment of Subsea Technologies in Deep Water Marginal Fields, Offshore Magazine, January 2008.14 C. Cermelli, D. Roddier, and C. Busso, in “MINIFLOAT: A Novel Concept of Minimal Floating Platform for Marginal Field Development,”Proceedings of the 14th International Offshore and Polar Engineering Conference, Toulon, France, May 2004.15 A. Aubault, C. Cermelli, and D. 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033104-34 Roddier et al. J. Renewable Sustainable Energy 2, 033104 ͑2010͒ San Diego, 11–16 June 2007.21 S. K. Chakrabarti, Hydrodynamics of Offshore Structures ͑Springer-Verlag, Berlin, 1987͒.22 O. Faltinsen, Sea Loads on Ships and Offshore Structures ͑Cambridge University Press, Cambridge, 1993͒.23 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 on Offshore Mechanics and Arctic Engineering, Halkidiki, Greece, June 2005.24 R. K. Saiga, D. Dolan, A. D. Kiureghian, T. Camp, and C. E. Smith, in “Comparison of Design Guidelines for Offshore Wind Energy Systems,” Offshore Technology Conference, Houston, TX, 30 April–3 May 2007, Paper No. OTC 18984-PP.25 See: http://www.wamit.com/manual.htm for WAMIT user manual.26 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. OMAE98-0355.27 American Petroleum Institute ͑API͒, API RP 2SK, Recommended Practice for Design and Analysis of Stationkeeping Systems for Floating Structures, 2005.28 Germanischer Lloyd, Guideline for the Certiﬁcation of Offshore Wind Turbines, Rules and Guidelines ed., 2005.29 J. Jonkman, in “Inﬂuence of Control on the Pitch Damping of a Floating Wind Turbine,” Presented at the 2008 ASME Wind Energy Symposium, Reno, NV, 7–10 January 2008.30 American Bureau of Shipping, Rules for Building and Classing Mobile Offshore Drilling Units ͑Hull Construction and Equipment, Houston, TX, 2001͒, Pt. 3.31 DNV, Buckling Strength of Shell, Recommended Practice DNV-RP-C202, 2002.