Technical Report

NREL/TP-500-47535

May 2010

Definition of the Floating System 

for Phase IV of OC3

J. Jonkman
National Renewable Energy Laboratory

1617 Cole Boulevard, Golden, Colorado 80401-3393

303-275-3000 • www.nrel.gov

NREL is a national laboratory of the U.S. Department of Energy

Office of Energy Efficiency and Renewable Energy

Operated by the Alliance for Sustainable Energy, LLC

Contract No. DE-AC36-08-GO28308

Technical Report

NREL/TP-500-47535

May 2010

Definition of the Floating System 

for Phase IV of OC3

J. Jonkman

Prepared under Task No. WE101211
NOTICE

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i

Table of Contents

1 Introduction................................................................................................................................ 1

2 Tower Properties........................................................................................................................ 2

3 Floating Platform Structural Properties ................................................................................. 4

4 Floating Platform Hydrodynamic Properties ......................................................................... 6

5 Mooring System Properties..................................................................................................... 16

6 Control System Properties...................................................................................................... 22

References.................................................................................................................................... 24
ii

List of Tables

Table 2-1. Distributed Tower Properties ....................................................................................... 2

Table 2-2. Undistributed Tower Properties ................................................................................... 3

Table 3-1. Floating Platform Structural Properties........................................................................ 4

Table 4-1. Periodic Sea State Definitions...................................................................................... 8

Table 4-2. Floating Platform Hydrodynamic Properties.............................................................. 15

Table 5-1. Mooring System Properties........................................................................................ 16

Table 6-1. Baseline Control System Property Modifications...................................................... 23

List of Figures

Figure 3-1. Illustrations of the NREL 5-MW wind turbine on the OC3-Hywind spar.................. 5

Figure 4-1. Dimensionless Parameters for the OC3-Hywind spar ................................................ 9

Figure 4-2. Panel mesh of the OC3-Hywind spar used within WAMIT ..................................... 10

Figure 4-3. Hydrodynamic wave excitation per unit amplitude for the OC3-Hywind spar ........ 10

Figure 4-4. Hydrodynamic added mass and damping for the OC3-Hywind spar ....................... 11

Figure 4-5. Radiation impulse-response functions for the OC3-Hywind spar ............................ 12

Figure 5-1. Load-displacement relationships for the OC3-Hywind mooring system in 1D........ 19

Figure 5-2. Load-displacement relationships for the OC3-Hywind mooring system in 2D........ 20

Figure 5-3. Load-displacement relationships for one OC3-Hywind mooring line...................... 21
1

1 Introduction

Phase IV of the IEA Annex XXIII Offshore Code Comparison Collaboration (OC3) involves the 

modeling of an offshore floating wind turbine. This report documents the specifications of the 

floating system, which are needed by the OC3 participants for building aero-hydro-servo-elastic 

models.

As in previous phases of the OC3 project, Phase IV uses the turbine specifications of the 

National Renewable Energy Laboratory (NREL) offshore 5-MW baseline wind turbine [7], 

which is a representative utility-scale, multi-megawatt turbine that has also been adopted as the 

reference model for the integrated European UpWind research program.1

Numerous floating platform concepts are possible for offshore wind turbines, including sparbuoys, tension leg platforms (TLPs), barges, and hybrid concepts thereof. At the request of the 

OC3 participants, the spar-buoy concept called “Hywind,” developed by Statoil of Norway,

 In Phase IV, the rotornacelle assembly of this 5-MW turbine—including the aerodynamic and structural properties—

remains the same, but the support structure (tower and substructure) and control system 

properties have been changed.

2

11

was 

chosen for the modeling activities of Phase IV. This concept was chosen for its simplicity in 

design, suitability to modeling, and propinquity to commercialization. Finn Gunnar Nielsen and 

Tor David Hanson of Statoil were contacted and graciously supplied detailed platform and 

mooring system data. The data provided was for the conceptual version of the Hywind platform 

developed to support a 5-MW wind turbine, as analyzed by Nielsen, Hanson, and Skaare [ ,12] 

and Larsen and Hanson [9]. At the request of Statoil, the originally supplied data has been 

condensed and sanitized by Jason Jonkman of NREL so that it is suitable for public 

dissemination. Aspects of the original data were also adapted slightly by Jason Jonkman so that 

the platform design is appropriate for supporting the NREL 5-MW baseline turbine, which has 

properties that are slightly different than the turbine properties used by Statoil in their 

development of the system. The new system is referred to as the “OC3-Hywind” system in this 

report, to distinguish it from Statoil’s original Hywind concept.

This report presents the tailored data, as well as data that has been derived apart from that 

supplied by Statoil but which is needed to support the activities of the OC3 project. The material

is presented as follows:

• The tower properties in Section 2

• The floating platform structural properties in Section 3

• The floating platform hydrodynamic properties in Section 4

• The mooring system properties in Section 5

• The control system properties in Section 6

 

1 Web site: http://www.upwind.eu/default.aspx

2 Web site: http://www.statoilhydro.com/en/TechnologyInnovation/NewEnergyAndRenewables/Wind/VindTilHavs/

Pages/Hywind.aspx
2

2 Tower Properties

The base of the tower is coincident with the top of platform and is located at an elevation of 10 m 

above the still water level (SWL). The top of the tower is coincident with the yaw bearing and is 

located at an elevation of 87.6 m above the SWL. This tower-top elevation—and the 

corresponding 90 m elevation of the hub above the SWL—is consistent with the land-based 

version of the NREL 5-MW baseline wind turbine (as given in Ref. [7]). These properties are all 

relative to the undisplaced position of the platform.

The distributed properties of the tower for the NREL 5-MW baseline wind turbine atop the OC3-

Hywind spar-buoy are founded on the base diameter of 6.5 m, which matches the top diameter of 

the platform (see Section 3), and the tower base thickness (0.027 m), top diameter (3.87 m) and 

thickness (0.019 m), and effective mechanical steel properties of the tower used in the DOWEC 

study (as given in Table 9 on page 31 of Ref. [8]). The Young’s modulus was taken to be 210

GPa, the shear modulus was taken to be 80.8 GPa, and the effective density of the steel was 

taken to be 8,500 kg/m3. The density of 8,500 kg/m3 was meant to be an increase above steel’s 

typical value of 7,850 kg/m3 to account for paint, bolts, welds, and flanges that are not included

in the tower thickness data. The radius and thickness of the tower are assumed to be linearly 

tapered from the tower base to tower top. Table 2-1 gives the resulting distributed tower 

properties.

The entries in the first column, “Elevation,” are the vertical locations along the tower centerline 

relative to the SWL. “HtFract” is the fractional height along the tower centerline from the tower 

base (0.0) to the tower top (1.0). The rest of columns are similar to those described for the 

distributed blade properties presented in Ref. [7].

The resulting overall (integrated) tower mass is 249,718 kg and is centered (i.e. the center of 

mass [CM] of the tower, is located) at 43.4 m along the tower centerline above the SWL. This is 

derived from the overall tower length of 77.6 m.

A structural-damping ratio of 1% critical is specified for all modes of the isolated tower 

(cantilevered atop a rigid foundation without the rotor-nacelle assembly mass present), which 

corresponds to the values used in the DOWEC study (from page 21 of Ref. [8]).

Table 2-1. Distributed Tower Properties

Elevation HtFract TMassDen TwFAStif TwSSStif TwGJStif TwEAStif TwFAIner TwSSIner TwFAcgOf TwSScgOf

(m) (-) (kg/m) (N•m2

) (N•m2

) (N•m2) (N) (kg•m) (kg•m) (m) (m)

10.00 0.00000 4667.00 603.903E+9 603.903E+9 464.718E+9 115.302E+9 24443.7 24443.7 0.0 0.0

17.76 0.10000 4345.28 517.644E+9 517.644E+9 398.339E+9 107.354E+9 20952.2 20952.2 0.0 0.0

25.52 0.20000 4034.76 440.925E+9 440.925E+9 339.303E+9 99.682E+9 17847.0 17847.0 0.0 0.0

33.28 0.30000 3735.44 373.022E+9 373.022E+9 287.049E+9 92.287E+9 15098.5 15098.5 0.0 0.0

41.04 0.40000 3447.32 313.236E+9 313.236E+9 241.043E+9 85.169E+9 12678.6 12678.6 0.0 0.0

48.80 0.50000 3170.40 260.897E+9 260.897E+9 200.767E+9 78.328E+9 10560.1 10560.1 0.0 0.0

56.56 0.60000 2904.69 215.365E+9 215.365E+9 165.729E+9 71.763E+9 8717.2 8717.2 0.0 0.0

64.32 0.70000 2650.18 176.028E+9 176.028E+9 135.458E+9 65.475E+9 7124.9 7124.9 0.0 0.0

72.08 0.80000 2406.88 142.301E+9 142.301E+9 109.504E+9 59.464E+9 5759.8 5759.8 0.0 0.0

79.84 0.90000 2174.77 113.630E+9 113.630E+9 87.441E+9 53.730E+9 4599.3 4599.3 0.0 0.0

87.60 1.00000 1953.87 89.488E+9 89.488E+9 68.863E+9 48.272E+9 3622.1 3622.1 0.0 0.0
3

Table 2-2 summarizes the undistributed tower properties discussed in this section.

Table 2-2. Undistributed Tower Properties

Elevation to Tower Base (Platform Top) Above SWL 10 m

Elevation to Tower Top (Yaw Bearing) Above SWL 87.6 m

Overall (Integrated) Tower Mass 249,718 kg

CM Location of Tower Above SWL Along Tower Centerline 43.4 m

Tower Structural-Damping Ratio (All Modes) 1%
4

3 Floating Platform Structural Properties

The tower is cantilevered at an elevation of 10 m above the SWL to the top of the floating 

platform, which—for the purposes of analysis—is considered to be a rigid body. The draft of the 

platform is 120 m. Between the top and bottom of the platform, the OC3-Hywind spar-buoy 

consists of two cylindrical regions connected by a linearly tapered conical region. The cylinder 

diameter of 6.5 m above the taper is more slender than the cylinder diameter of 9.4 m below the 

taper to reduce hydrodynamic loads near the free surface. The linearly tapered conical region 

extends from a depth of 4 m to a depth of 12 m below the SWL. These properties are all relative 

to the undisplaced position of the platform.

The mass, including ballast, of the floating platform is 7,466,330 kg. This mass was calculated 

such that the combined weight of the rotor-nacelle assembly, tower, and platform, plus the 

weight of the mooring system (not including the small portion resting on the seafloor) in water, 

balances with the buoyancy (i.e. weight of the displaced fluid) of the undisplaced platform in still 

water. This mass is centered (i.e. the CM of the floating platform, including ballast, is located) 

89.9155 m along the platform centerline below the SWL, which was derived so as to ensure that 

the CM location of the full system (turbine plus platform) matched that specified in the data 

supplied by Statoil. The roll and pitch inertias of the floating platform about its CM are 

4,229,230,000 kg•m2 and the yaw inertia of the floating platform about its centerline is 

164,230,000 kg•m2. These inertias were calculated using a mass distribution appropriate to the 

floating platform. The inertias of the full OC3-Hywind system are higher than those of Statoil’s 

Hywind system because the NREL offshore 5-MW baseline wind turbine is heavier than the 

turbine in Statoil’s Hywind system.

Table 3-1 summarizes the undistributed tower properties discussed in this section and Figure 3-1

illustrates the concept with an image generated using MSC.ADAMS.

In the sections that remain, several of the platform specifications refer to an inertial reference 

frame and platform degrees of freedom (DOFs). In these sections, X,Y,Z represents the set of 

orthogonal axes of this reference frame, with the XY-plane designating the SWL and the Z-axis 

directed upward opposite gravity along the centerline of the undisplaced platform. The rigidbody platform DOFs include translational surge, sway, and heave motions and rotational roll, 

Table 3-1. Floating Platform Structural Properties

Depth to Platform Base Below SWL (Total Draft) 120 m

Elevation to Platform Top (Tower Base) Above SWL 10 m

Depth to Top of Taper Below SWL 4 m

Depth to Bottom of Taper Below SWL 12 m

Platform Diameter Above Taper 6.5 m

Platform Diameter Below Taper 9.4 m

Platform Mass, Including Ballast 7,466,330 kg

CM Location Below SWL Along Platform Centerline 89.9155 m

Platform Roll Inertia about CM 4,229,230,000 kg•m2

Platform Pitch Inertia about CM 4,229,230,000 kg•m2

Platform Yaw Inertia about Platform Centerline 164,230,000 kg•m2
5

pitch, and yaw motions. Positive surge is defined along the positive X-axis, sway is along the Yaxis, and heave is along the Z-axis. Positive roll is defined about the positive X-axis, pitch is 

about the Y-axis, and yaw is about the Z-axis.

 

Figure 3-1. Illustrations of the NREL 5-MW wind turbine on the OC3-Hywind spar
6

4 Floating Platform Hydrodynamic Properties

Hydrodynamic loads include contributions from linear hydrostatics, linear excitation from 

incident waves, linear radiation from outgoing waves (generated by platform motion), and 

nonlinear effects. The linear hydrostatic properties of the floating platform are presented first; 

presentation of the remaining properties follows.

The total load on the floating platform from linear hydrostatics, Hydrostatic Fi , is

( ) Hydrostatic Hydrostatic F q gV C q i = − ρ δ0 i3 ij j , (4-1)

where ρ is the water density, g is the gravitational acceleration constant, V0 is the displaced 

volume of fluid when the platform is in its undisplaced position, δi3 is the (i,3) component of the 

Kronecker-Delta function (i.e. identity matrix), Hydrostatic Cij is the (i,j) component of the linear 

hydrostatic-restoring matrix from the effects of water-plane area and the center of buoyancy

(COB), and j q is the j

th platform DOF. (Without the subscript, q represents the set of platform 

DOFs. Hydrostatic Fi depends on q as indicated.) In Eq. (4-1), subscripts i and j range from 1 to 6; 

one for each platform DOF (1 = surge, 2 = sway, 3 = heave, 4 = roll, 5 = pitch, 6 = yaw). 

Einstein notation is used here, in which it is implied that when the same subscript appears in 

multiple variables in a single term, there is a sum of all of the possible terms. The loads are

positive in the direction of positive motion of DOF i. Equation (4-1) does not include the 

restoring effects of body weight (i.e. gravitational restoring). Instead, the gravitational restoring 

is assumed to be included within the structural dynamics models.

The first of the terms on the right-hand side of Eq. (4-1) represents the buoyancy force from 

Archimedes’ principle; that is, it is the force directed vertically upward and equal to the weight 

of the displaced fluid when the platform is in its undisplaced position. This term is nonzero only 

for the vertical heave-displacement DOF of the support platform (DOF i = 3) because the COB

lies on the centerline of the undeflected tower. The second of the terms on the right-hand side of 

Eq. (4-1) represents the change in the hydrostatic force and moment as the platform is displaced. 

The formulation for Hydrostatic Cij in terms of a platform’s water-plane shape, displaced volume, and 

COB location is given in Ref. [5].

The water density is chosen to be 1,025 kg/m3. From the external geometry of the floating 

platform, then, ρgV0 and Hydrostatic Cij were calculated to be:

0 ρgV 80,708,100 N = (4-2)

and
7

Hydrostatic

ij

00 0 0 0 0

00 0 0 0 0

0 0 332,941 N m 0 0 0

C

0 0 0 4,999,180,000 Nm rad 0 0

0 0 0 0 4,999,180,000 Nm rad 0

00 0 0 0 0

 

 

= −

−

 

. (4-3)

The roll-roll (4,4) and pitch-pitch (5,5) elements of Hydrostatic Cij are negative-valued because the 

vertical location of the COB is far below the SWL.

The remaining hydrodynamic loads—those associated with excitation from incident waves and 

radiation of outgoing waves from platform motion—depend on whether flow separation occurs. 

For a floating platform interacting with surface waves, different formulations for the 

hydrodynamic loads apply to separated and nonseparated flows. For cylinders, the proper 

formulation—and the hydrodynamic coefficients used within each formulation—depend, among 

other factors, on the Keulegan-Carpenter number, K, and the oscillatory Reynolds number, Re, 

defined as [3]

VT K

D = (4-4)

and

VD Re

ν = , (4-5)

where D is the cylinder diameter, ν is the kinematic viscosity of the fluid, T is the wave period, 

and V is the amplitude of the fluid velocity normal to the cylinder. The diameter to wavelength 

ratio, D/λ, is also an important factor that determines the proper formulation. For linear regular 

(i.e. periodic) waves, the wavelength and (depth-dependent) wave velocity amplitude are related 

to the wave period and the wave height (i.e. twice the wave amplitude), H, by [3]

( )

( )

H cosh k Z h

V

T sinh kh

π   +   = (4-6)

and

2

k

π λ = , (4-7)

where Z is the local depth (negative in value), h is the water depth (positive in value), and k is the 

wave number, which, itself, is related to the wave period through the implicit dispersion 

relationship [3]:
8

( )

2

2

4 k tanh kh

gT

π = . (4-8)

The water depth is taken to be 320 m. From the external geometry of the floating platform and 

the periodic sea states defined in Table 4-1 (from 1 = mild to 8 = extreme sea state), then, the 

Keulegan-Carpenter number, oscillatory Reynolds number, and diameter to wavelength ratio are 

presented in Figure 4-1 as function of depth (Z) along the spar.

The upper and middle charts in Figure 4-1 show that, for the OC3-Hywind spar-buoy, the 

Keulegan-Carpenter and oscillatory Reynolds numbers increase with increasing severity in the 

wave conditions and decrease with depth along the spar. Flow separation occurs when the 

Keulegan-Carpenter number exceeds 2. For values lower than 2, potential-flow theory applies. 

Consequently, potential-flow theory applies all along the spar in all but the most extreme wave 

conditions, where separation will occur along the upper portions of the platform. The bottom 

chart in Figure 4-1 shows that, for the OC3-Hywind spar-buoy, the diameter to wavelength ratio 

decreases with increasing severity of the wave conditions and is lower above the tapered region. 

Diffraction effects are important when this ratio exceeds 0.2 and are unimportant for smaller 

ratios. Consequently, diffraction effects are only important in the spar in mild wave conditions, 

where the hydrodynamic loads are small anyway.

In view of the validity of potential-flow theory across many conditions, the linear potential-flow

problem was solved using the WAMIT computer program [10]. WAMIT uses a threedimensional numerical-panel method in the frequency domain to solve the linearized potentialflow hydrodynamic radiation and diffraction problems for the interaction of surface waves with 

offshore platforms of arbitrary geometry. The solution to the radiation problem, which considers 

the hydrodynamic loads on the platform associated with oscillation of the platform in its various 

modes of motion (of which radiates outgoing waves), is given in terms of oscillation-frequencydependent hydrodynamic-added-mass and -damping matrices, Aij and Bij respectively. The 

solution to the diffraction problem, which considers the hydrodynamic loads on the platform 

associated with excitation from incident waves, is given in terms of the wave-frequency- and -

direction-dependent hydrodynamic-wave-excitation vector, Xi. Whereas Aij and Bij are realvalued, Xi is complex-valued, with the magnitude determining the load normalized per unit wave 

amplitude and the phase determining the lag between the wave elevation and load. The 

subscripts here are consistent with those of Hydrostatic Cij discussed earlier and, as before, the loads 

Table 4-1. Periodic Sea State Definitions

Sea T H

State (s) (m)

1 2.0 0.09

2 4.8 0.67

3 6.5 1.40

4 8.1 2.44

5 9.7 3.66

6 11.3 5.49

7 13.6 9.14

8 17.0 15.24
9

are positive in the direction of positive motion. Reference [5] provides more information on 

potential-flow theory as it relates to floating platforms.

In WAMIT, I modeled the OC3-Hywind spar-buoy with two geometric planes of symmetry with 

3,900 rectangular panels within a quarter of the body. Figure 4-2 shows the panel mesh with 

both symmetries. To improve the accuracy of the WAMIT results, I chose to override three 

default settings, choosing instead to (1) integrate the logarithmic singularity analytically, (2) 

solve the linear system of equations using a direct solver, and (3) remove the effects of irregular 

frequencies by manually paneling the free surface. These settings were necessary because 

-120

-90

-60

-30

0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Keulegan-Carpenter Number (K ), -

Depth along Spar (

Z ), m

Sea State 1

Sea State 2

Sea State 3

Sea State 4

Sea State 5

Sea State 6

Sea State 7

Sea State 8

-120

-90

-60

-30

0

1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 1E+7 1E+8

Oscillatory Reynolds Number (Re ), -

Depth along Spar (

Z ), m

Sea State 1

Sea State 2

Sea State 3

Sea State 4

Sea State 5

Sea State 6

Sea State 7

Sea State 8

-120

-90

-60

-30

0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Diameter to Wavelength Ratio (D/λ ), -

Depth along Spar (

Z ), m

Sea State 1

Sea State 2

Sea State 3

Sea State 4

Sea State 5

Sea State 6

Sea State 7

Sea State 8

Figure 4-1. Dimensionless Parameters for the OC3-Hywind spar
10

subsequent analysis required high-frequency output. The spar was 

analyzed in its undisplaced position (consistent with linear theory) 

and with finite water depth (320 m).

The magnitude and phase of the hydrodynamic-wave-excitation 

vector from the linear diffraction problem are shown as a function of 

wave frequency in Figure 4-3 for incident waves propagating along 

the positive X-axis. For these waves, the loads in the direction of the 

sway, roll, and yaw DOFs are zero due to the symmetries of the spar. 

The magnitudes of the force and moment in the direction of the surge 

and pitch DOFs reach a peak just above and below a wave frequency 

of 0.5 rad/s, respectively. At higher wave frequencies (smaller 

wavelengths), diffraction effects become important and the loads 

drop. The heave force reverses sign at about 0.25 rad/s, reaches a 

peak just above 0.5 rad/s, and then drops in magnitude at higher wave 

frequencies.

The hydrodynamic-added-mass and -damping matrices from the 

linear radiation problem for all six rigid-body modes of motion of the 

platform are shown as a function of oscillation frequency in Figure 

4-4. Only the upper triangular matrix elements are shown because the 

hydrodynamic-added-mass and -damping matrices are symmetric in 

the absence of forward speed. Also, because of the spar’s 

symmetries, the surge-surge elements of the frequency-dependent 

added-mass and damping matrices, A11 and B11, are identical to the 

sway-sway elements, A22 and B22. Likewise, the roll-roll elements, 

A44 and B44, are identical to the pitch-pitch elements, A55 and B55. 

Other matrix elements not shown are zero-valued.

As shown in Figure 4-4, the added mass of the platform varies little 

across oscillation frequency. The zero- and infinite-frequency limits 

of all elements of the damping matrix are zero (not all shown), as 

required by theory, and peak out at some intermediate frequency. But 

the values of the damping in the moment-rotation, force-rotation, and 

Figure 4-2. Panel mesh 

of the OC3-Hywind spar 

used within WAMIT

0.00E+6

0.25E+6

0.50E+6

0.75E+6

1.00E+6

1.25E+6

1.50E+6

0 1 2 3 4 5

Frequency, rad/s

Magnitude of Forces, 

N/m

-180

-120

-60

0

60

120

180

Phase of Forces, o

Magnitude{X1} Magnitude{X2} Magnitude{X3}

Phase{X1} Phase{X2} Phase{X3}

 

0.00E+6

10.00E+6

20.00E+6

30.00E+6

40.00E+6

50.00E+6

60.00E+6

0 1 2 3 4 5

Frequency, rad/s

Magnitude of Moments, 

N·m/m

-180

-120

-60

0

60

120

180

Phase of Moments, o

Magnitude{X4} Magnitude{X5} Magnitude{X6}

Phase{X4} Phase{X5} Phase{X6}

Figure 4-3. Hydrodynamic wave excitation per unit amplitude for the OC3-Hywind spar
11

moment-translation modes are considerably smaller than those of the added-mass, which imply 

that the linear radiation damping, and associated memory effects in the time domain, are also 

small in those modes. Only in the force-translation modes may the linear radiation damping and 

memory effect be important.

The linear memory effect is captured within time-domain hydrodynamics models through the 

time-convolution of the radiation impulse-response functions (i.e. the wave-radiation-retardation 

kernel), Kij, with the platform velocities. The memory effect captures the hydrodynamic load on 

the platform that persists from the outgoing free-surface waves (which induce a pressure field 

within the fluid domain) radiated-away by platform motion. The radiation impulse-response 

functions can be found from the cosine transform of the frequency-dependent hydrodynamic 

damping matrix. The results of this computation, as performed within WAMIT’s frequency-totime (F2T) conversion utility, are shown in Figure 4-5. As before, only the upper triangular 

0.0E+6

2.0E+6

4.0E+6

6.0E+6

8.0E+6

10.0E+6

0 1 2 3 4 5

Frequency, rad/s

Force-Translation Modes, kg

A11

A22

A33

 

0.0E+6

0.1E+6

0.2E+6

0.3E+6

0.4E+6

0.5E+6

0 1 2 3 4 5

Frequency, rad/s

Force-Translation Modes, kg/s

B11

B22

B33

0.0E+6

10,000.0E+6

20,000.0E+6

30,000.0E+6

40,000.0E+6

0 1 2 3 4 5

Frequency, rad/s

Moment-Rotation Modes, kg·m2

A44

A55

A66

 

0.0E+6

20.0E+6

40.0E+6

60.0E+6

80.0E+6

0 1 2 3 4 5

Frequency, rad/s

Moment-Rotation Modes, kg·m2/s

B44

B55

B66

-500.0E+6

-250.0E+6

0.0E+6

250.0E+6

500.0E+6

0 1 2 3 4 5

Frequency, rad/s

Frc-Rot & Mom-Trans Modes, kg·m

A15

A24

 

-4.0E+6

-2.0E+6

0.0E+6

2.0E+6

4.0E+6

0 1 2 3 4 5

Frequency, rad/s

Frc-Rot & Mom-Trans Modes, kg·m/s

B15

B24

Figure 4-4. Hydrodynamic added mass and damping for the OC3-Hywind spar
12

matrix elements of the symmetric Kij matrix are shown, and because of the spar’s symmetries, 

the surge-surge elements, K11, are identical to the sway-sway elements, K22, and the roll-roll 

elements, K44, are identical to the pitch-pitch elements, K55. Most of the response—and linear 

radiation damping—decays to zero after about 20 s even for the force-translation modes that may 

not be negligible. Reference [5] provides more information on radiation theory.

-0.2E+6

-0.1E+6

0.0E+6

0.1E+6

0.2E+6

0.3E+6

0.4E+6

0.5E+6

0 5 10 15 20

Time, s

Force-Translation Modes,

kg/s2

K11

K22

K33

-20.0E+6

-10.0E+6

0.0E+6

10.0E+6

20.0E+6

30.0E+6

40.0E+6

0 5 10 15 20

Time, s

Moment-Rotation Modes,

kg·m2/s2

K44

K55

K66

-3.0E+6

-2.0E+6

-1.0E+6

0.0E+6

1.0E+6

2.0E+6

3.0E+6

0 5 10 15 20

Time, s

Frc-Rot & Mom-Trans Modes,

kg·m/s2

K15

K24

Figure 4-5. Radiation impulse-response functions for the OC3-Hywind spar
13

The second-order potential-flow solution, which includes mean-drift, slow-drift, and sumfrequency excitation, and higher-order solutions, were not solved and are assumed to be 

negligible for the OC3-Hywind spar.

In severe sea conditions, the hydrodynamic loads from linear potential-flow theory must be 

augmented with the loads brought about by flow separation. Moreover, many wind turbine 

dynamics codes cannot model hydrodynamics per linear potential-flow theory. To address these 

situations, a simplified hydrodynamics model using Morison’s formulation is presented next.

The popular hydrodynamic formulation used in the analysis of fixed-bottom support structures 

for offshore wind turbines—Morison’s formulation—is applicable for calculating the 

hydrodynamic loads on cylindrical structures when (1) the effects of diffraction are negligible, 

(2), radiation damping is negligible, and (3) flow separation may occur. The relative form of 

Morison’s equation accounts for the loading from incident-wave-induced excitation, radiationinduced added mass, and flow-separation-induced viscous drag in the directions of the surge, 

sway, roll, and pitch DOFs. Hydrodynamic heave forces are neglected (and hydrodynamic yaw 

moments are zero for cylindrical structures). From the results presented above, then, Morison’s 

equation is valid for the OC3-Hywind spar in most conditions because (1) diffraction effects are 

negligible in moderate to severe sea states, (2) radiation damping in most modes of motion is 

small, and (3) flow separation will occur in severe sea states along the upper regions of the spar.

The added-mass coefficient, CA, to be used in Morison’s equation was selected so as to give 

equivalent added mass in surge regardless of whether one applies linear potential-flow theory or 

Morison’s equation within OC3. If it is assumed that CA is independent of depth and that the 

motion is of low-frequency, this implies that CAρV0 (from Morison’s equation) must equal the 

zero-frequency limit of A11 (from the potential-flow solution of Figure 4-4). By this equivalency, 

then, the added mass coefficient for the OC3-Hywind spar is taken to be 0.969954. Also, Figure 

4-1 shows that the OC3-Hywind spar experiences oscillatory Reynolds numbers exceeding 105 in 

most conditions of importance—that is, in moderate to severe sea conditions. Thus, the viscousdrag coefficient, CD, is taken to be 0.6 (which is the typical coefficient for a cylinder at high 

oscillatory Reynolds numbers as shown in Figure 6.36 on page 254 of Ref. [3]). For the OC3 

project, these coefficients should be applied in all simulations for those analysts who wish to 

apply Morison’s equation. When Morison’s equation is applied, however, the hydrodynamic 

heave forces must be added separately. For a deep-drafted spar, the heave force can be 

approximated as the change in buoyancy brought about by direct integration of the hydrostatic 

pressure dependent on the time-varying wave elevation (as was done by many modelers in OC3

Phase III).

For those OC3 analysts who choose to apply linear potential-flow theory, the hydrodynamic 

calculations in the directions of the surge, sway, roll, and pitch DOFs should be augmented with 

the nonlinear viscous-drag term from the relative form of Morison’s equation. The same 

viscous-drag coefficient discussed above (CD = 0.6) should be used. This augmentation to linear 

potential-flow theory is needed to obtain suitable hydrodynamic damping in severe sea 

conditions, which in the OC3-Hywind spar is dominated by (nonlinear) flow separation.

According to Statoil, the linear radiation damping (from potential-flow theory, which is small) 

and the nonlinear viscous-drag (from the relative form of Morison’s formulation), when 
14

summed, do not capture all of the hydrodynamic damping for the motions of the real Hywind 

platform. As such, Statoil recommended that the hydrodynamics models for the OC3-Hywind 

system, as described above, be augmented with additional linear damping. To determine the 

amount of additional damping required in the OC3-Hywind system, Statoil provided still-water 

free-decay responses for all six rigid-body modes-of-motion of the Hywind system. These 

responses were used as target responses for the OC3-Hywind system. A model of the OC3-

Hywind system was assembled in the FAST code [6], from which still-water free-decay 

responses were simulated with and without additional linear damping. (FAST includes a 

hydrodynamics model that was needed to make these calculations. This hydrodynamics model 

consists of linear potential-flow theory in the time domain augmented with the nonlinear 

viscous-drag term from the relative form of Morison’s equation [5]. The additional linear 

damping was added on top of these hydrodynamic loads.) Additional linear damping of 100,000 

N/(m/s) was needed for surge and sway motions, 130,000 N/(m/s) was needed for heave 

motions, and 13,000,000 Nm/(rad/s) was needed for yaw motions to match the free-decay 

responses supplied by Statoil. (No additional damping was needed for roll and pitch motions.) 

This damping applies to the platform motions directly and not to the relative motion between the 

platform and wave particle velocities. In equation form:

( ) Additional Damping Linear F q Bq i = − ij j   , (4-9)

with:

( )

( )

( )

( )

Linear

ij

100,000 N m s 0 0 0 0 0

0 100,000 N m s 0 0 0 0

0 0 130,000 N m s 0 0 0

B

0 0 000 0

0 0 000 0

0 0 0 0 0 13,000,000 Nm rad s

 

 

=

 

, (4-10)

where Linear Bij is the (i,j) component of the additional linear damping matrix, and j q is the first 

time derivative of the j

th platform DOF. (Without the subscript, q represents the set of first time 

derivatives of the platform DOFs. Additional Damping Fi depends on q as indicated.) In Eq. (4-9), 

subscripts i and j range from 1 to 6; one for each platform DOF (1 = surge, 2 = sway, 3 = heave, 

4 = roll, 5 = pitch, 6 = yaw). Einstein notation is used here, in which it is implied that when the 

same subscript appears in multiple variables in a single term, there is a sum of all of the possible 

terms. The loads are positive in the direction of positive motion of DOF i.

For the OC3 project, all analysts should augment their hydrodynamics models with this 

additional damping in all simulations.
15

Table 4-2 summarizes the hydrodynamic properties (except the linear potential-flow solution)

discussed in this section.

Table 4-2. Floating Platform Hydrodynamic Properties

Water Density (ρ) 1,025 kg/m3

Water Depth (h) 320 m

Buoyancy Force in Undisplaced Position (ρgV0) 80,708,100 N

Hydrostatic Restoring in Heave ( Hydrostatic C33 ) 332,941 N/m

Hydrostatic Restoring in Roll ( Hydrostatic C44 ) -4,999,180,000 Nm/rad

Hydrostatic Restoring in Pitch ( Hydrostatic C55 ) -4,999,180,000 Nm/rad

Added-Mass Coefficient (CA in Morison’s Equation) 0.969954

Viscous-Drag Coefficient (CD in Morison’s Equation) 0.6

Additional Linear Damping in Surge ( Linear B11 ) 100,000 N/(m/s)

Additional Linear Damping in Sway ( Linear B22 ) 100,000 N/(m/s)

Additional Linear Damping in Heave ( Linear B33 ) 130,000 N/(m/s)

Additional Linear Damping in Yaw ( Linear B66 ) 13,000,000 Nm/(rad/s)
16

5 Mooring System Properties

To prevent it from drifting, Statoil’s Hywind platform is moored by a system of three catenary 

lines. The lines attach to the platform via a so-called “crowfoot” (delta connection) to increase 

the moorings’ yaw stiffness. Also, each line consists of multiple segments of varying properties 

and a clump weight.

In order to simplify the analysis of the mooring system within the OC3 project, however, only 

the specifications of an effective system are presented for the OC3-Hywind system. Three

simplifications are made. First, the delta connection is eliminated, which requires that the 

mooring system be augmented with a yaw spring to achieve the proper overall yaw stiffness. 

Second, each of the multisegment lines is replaced with an equivalent homogenous line, with 

properties derived as the weighted-average values of the mass, weight, and stiffness (weighted 

based on the unstretched lengths of each segment). Third, all mooring system damping,

including the hydrodynamic drag and line-to-seabed drag, is neglected. Please note that these 

three simplifications are acceptable for static analysis, but may not be appropriate in all 

dynamical conditions. From these simplifications, the fairleads (body-fixed locations where the 

mooring lines attach to the platform) are located at a depth of 70.0 m below the SWL and at a 

radius of 5.2 m from the platform centerline. The anchors (fixed to the inertia frame) are located 

at a (water) depth of 320 m below the SWL and at a radius of 853.87 m from the platform 

centerline. One of the lines is directed along the positive X-axis (in the XZ-plane). The two 

remaining lines are distributed uniformly around the platform, such that each line, fairlead, and 

anchor is 120o apart when looking from above. These properties are relative to the undisplaced 

position of the platform. Each of the 3 lines has an unstretched length of 902.2 m, a diameter of 

0.09 m, an equivalent mass per unit length of 77.7066 kg/m, an equivalent apparent weight in 

fluid per unit length of 698.094 N/m, and an equivalent extensional stiffness of 384,243,000 N. 

The additional yaw spring has a stiffness of 98,340,000 Nm/rad. Table 5-1 summarizes these 

properties.

Many wind turbine dynamics codes cannot model the individual mooring lines. For these codes, 

three simplified models are presented. The first is a linearized model of the complete mooring 

system. The second is a nonlinear model of the complete mooring system. The third is a 

Table 5-1. Mooring System Properties 

Number of Mooring Lines 3

Angle Between Adjacent Lines 120o

Depth to Anchors Below SWL (Water Depth) 320 m

Depth to Fairleads Below SWL 70.0 m

Radius to Anchors from Platform Centerline 853.87 m

Radius to Fairleads from Platform Centerline 5.2 m

Unstretched Mooring Line Length 902.2 m

Mooring Line Diameter 0.09 m

Equivalent Mooring Line Mass Density 77.7066 kg/m

Equivalent Mooring Line Weight in Water 698.094 N/m

Equivalent Mooring Line Extensional Stiffness 384,243,000 N

Additional Yaw Spring Stiffness 98,340,000 Nm/rad
17

nonlinear model of an individual mooring line. Please note that these simplified models must 

also be augmented with the additional yaw spring specified above (the simplified models

presented below do not include the effects of the additional yaw spring).

If the mooring system compliance were inherently linear and mooring inertia and damping were 

ignored, as assumed in the first simplified model, the total load on the support platform from the 

contribution of all mooring lines, Lines Fi , would be

( ) Lines Lines,0 Lines F q =F C q i i − ij j , (5-1)

where Lines,0 Fi is the i

th component of the total mooring system load acting on the support 

platform in its undisplaced position, Lines Cij is the (i,j) component of the linearized restoring 

matrix from all mooring lines, and j q is the j

th platform DOF. (Without the subscript, q

represents the set of platform DOFs. Lines Fi depends on q as indicated.) For catenary mooring 

lines, Lines,0 Fi represents the pre-tension at the fairleads from the weight of the mooring lines not 

resting on the seafloor in water. Lines Cij is the combined result of the elastic stiffness of the 

mooring lines and the effective geometric stiffness brought about by the weight of the lines in 

water, depending on the layout of the mooring system. In Eq. (5-1), subscripts i and j range from 

1 to 6; one for each platform DOF (1 = surge, 2 = sway, 3 = heave, 4 = roll, 5 = pitch, 6 = yaw). 

Einstein notation is used here, in which it is implied that when the same subscript appears in 

multiple variables in a single term, there is a sum of all of the possible terms. The loads are

positive in the direction of positive motion of DOF i.

For the mooring system considered here, Lines,0 Fi and Lines Cij were calculated by performing a 

linearization analysis in the FAST code [6] about the undisplaced position of the platform (i.e.

about the linearization point where all DOF displacements are zero-valued). (FAST includes a 

mooring system model [5] that was needed to make these calculations.) The linearization 

analysis involves independently perturbing the platform DOFs and measuring the resulting 

variations in mooring loads. Within FAST, the partial derivatives are computed using the 

central-difference-perturbation numerical technique. The results are as follows:

Lines,0

i

0

0

1,607,000 N F

0

0

0

 

 

 

  − =  

 

 

 

 

(5-2)

and
18

Lines

ij

41,180 N m 0 0 0 2,821,000 N rad 0

0 41,180 N m 0 2,821,000 N rad 0 0

0 0 11,940 N m 0 0 0

C

0 2,816,000 Nm m 0 311,100,000 Nm rad 0 0

2,816,000 Nm m 0 0 0 311,100,000 Nm rad 0

0 0 0 0 0 11,560,000 Nm rad

  −

 

=

−

 

.(5-3)

Of course, the linear model is only valid for small displacements about the linearization point. 

For larger displacements, it is important to capture the nonlinear relationships between load and 

displacement, as provided in the second simplified model. In general, all six components of 

Lines F depend nonlinearly on all six displacements of q. (Without the subscript, Lines F represents 

the set of mooring system loads, including three forces and three moments.) For the mooring 

system considered here, these load-displacement relationships were found numerically using the 

FAST code [6] by considering discrete combinations of the displacements. The surge and sway 

displacements (q1 and q2) were varied from −36 to 36 m in steps of 6 m. The heave displacement 

(q3) was varied from −12 to 12 m in steps of 4 m. The roll and pitch displacements ( q4 and q5) 

were varied from −10o to 10o in steps of 2o. The yaw displacement (q6) was varied from −20o to 

20o in steps of 4o. All six components of Lines F were calculated for every combination of these 

displacements, for a total of (13 × 13 × 7 × 11 × 11 × 11 =) 1,574,573 discrete combinations. 

The upper and lower bounds in these variations were determined by estimating the anticipated 

displacement limits through a handful of time-domain simulations of the full system that 

included varying wind and wave conditions and operational status of the wind turbine. The step 

sizes were chosen so as to produce reasonable resolution in the nonlinear response at a minimal 

computational cost. All of the data—that is, all six components of Lines F dependent on all six 

displacements of q—was written to a text file: “MooringSystemFD.txt”.

Figure 5-1 shows the load-displacement relationships for the OC3-Hywind mooring system 

when each platform DOF is varied independently with all other displacements zero-valued (i.e.

Figure 5-1 presents a sample of one-dimensional [1D] load-displacement relationships). The 

relationships include some interesting asymmetries, which result from the nonlinear behavior of 

the three-point mooring system. Whereas the loads are either symmetric or anti-symmetric about 

zero for the sway (q2) and roll (q4) displacements, the loads are asymmetric about zero for the 

surge (q1) and pitch (q5) displacements. For the surge and pitch displacements, the mooring 

system stiffens up—and the surge forces, heave forces, and pitching moments increase 

nonlinearly—when the fairleads translate along the –X-axis. This asymmetry also induces surge 

forces and pitching moments when the fairleads translate along the Y-axis due to sway and roll 

displacements. Also, the heave forces change with all displacements because these 

displacements cause more line to lift off of—or allow more line to settle on—the seabed. The 

slopes of these load-displacement relationships about zero-displacement are consistent with the 

elements of the linearized restoring matrix, Lines Cij , presented above.

Figure 5-2 shows the nonlinear relationships for the surge forces and pitching moments 

associated with surge and pitch displacements and the sway forces and roll moments associated 

with sway and roll displacements with all other displacements zero-valued (i.e. Figure 5-2

presents a sample of two-dimensional [2D] load-displacement relationships). The combinations 

of surge and pitch displacements and sway and roll displacements were plotted because those 

displacements are often correlated. The data in Figure 5-2 shows that, unless large loads are 
19

applied to the platform to react with the rapidly increasing mooring loads, as the platform 

translates positively (or negatively) in surge, it will tend to pitch positively (or negatively) 

accordingly and as the platform translates positively (or negatively) in sway, it will tend to roll 

negatively (or positively) accordingly. The data in Figure 5-2 also shows the asymmetry about 

zero-displacement between translations of the fairlead along the X- and Y-axes (due to surge and 

pitch displacements and sway and roll displacements, respectively) just as the results of Figure 

5-1 showed. The data in Figure 5-2 are also consistent with the results of Figure 5-1, as some of 

the results of Figure 5-1 are slices through the data of Figure 5-2 when one of the displacements 

in Figure 5-2 is zero-valued.

 

 

 Figure 5-1. Load-displacement relationships for the OC3-Hywind mooring system in 1D
20

The two simplified mooring system models presented above only capture the total load acting on 

the support platform from the complete mooring system; no information is given regarding the 

reactions within each individual mooring line. The third simplified mooring system model 

addresses this limitation by giving the load-displacement relationship of an individual mooring 

line. The model is presented in the output format of the MIMOSA mooring analysis software

[2], which gives the qausi-static reactions of an individual mooring line as a function of the 

horizontal distance between the fairlead and anchor. The vertical distance between the fairlead 

and anchor is fixed at ( 320 m – 70 m ) = 250 m in this model; 250 m is equal to the vertical 

distance between the fairlead and anchor when the platform is undisplaced in pitch, roll and 

heave. In the nomenclature of MIMOSA format, “DISTANCE” is the horizontal distance 

between the fairlead and anchor. “TENSION” is the total (vector combination of the horizontal 

and vertical tensions) in the mooring line at the fairlead. “H.TENSION” is the horizontal 

component of this fairlead tension. “SUSPL” is the distance along the line from the fairlead to 

the equivalent point on the unstretched mooring line where the point on the stretched mooring 

line first touches the seabed. “TEN.ANCH” is the total (vector combination of the horizontal 

and vertical tensions) in the mooring line at the anchor.

For the OC3-Hywind mooring lines considered here, this model was derived numerically using 

the FAST code [6] by considering a range of discrete horizontal distances for one of the three 

identical mooring lines. That is, DISTANCE was varied from 653.0 m to 902.5 m in steps of 0.5

m, for a total of 500 discrete steps. The upper and lower bounds were determined by choosing

 

 Figure 5-2. Load-displacement relationships for the OC3-Hywind mooring system in 2D
21

limits far beyond the likely distances that will be covered when the full system model is run in

time-domain simulations. The step size was chosen so as to produce reasonable resolution in the 

nonlinear response at a minimal computational cost. All of the data—that is, TENSION, 

H.TENSION, SUSPL, and TEN.ANCH dependent on DISTANCE—was written to a text file: 

“MooringLineFD.txt”.

Figure 5-3 shows the data. The largest nonlinearities in the mooring line tensions occur for 

horizontal distances, DISTANCE, between 800 – 870 m. Below 858.5 m of DISTANCE, a 

portion of the mooring line rests on the seabed, such that SUSPL is less than the total unstretched 

length of the mooring line, 902.2 m. In this situation, the anchor tension, TEN.ANCH, is purely 

horizontal and—by a balance of external forces on the mooring line that has no drag—is equal to 

the horizontal tension at the fairlead, H.TENSION. The total tension at the fairlead, TENSION, 

is larger than H.TENSION because it includes a vertical component combined from the elastic 

stretching and the weight in water of the mooring line not resting on the seabed. For 

DISTANCE larger than 858.5 m, no portion of the mooring line rests on the seabed, such that 

SUSPL equals 902.2 m and the anchor tension includes a nonzero vertical component, which 

causes TEN.ANCH to exceed the value of H.TENSION. All tensions rise dramatically as the 

mooring line gets more and more taut.

0

200

400

600

800

1,000

1,200

0

2,500

5,000

7,500

10,000

12,500

15,000

650 700 750 800 850 900

Tensions (kN)

SUSPL (m)

DISTANCE (m)

TENSION (kN)

H.TENSION (kN)

TEN.ANCH (kN)

SUSPL (m)

Figure 5-3. Load-displacement relationships for one OC3-Hywind mooring line
22

6 Control System Properties

The NREL 5-MW wind turbine uses a conventional variable-speed, variable blade-pitch-tofeather control system [7]. A consequence of conventional pitch-to-feather control of wind 

turbines, though, is that steady-state rotor thrust is reduced with increasing wind speed above 

rated. As pointed out by Nielsen, Hanson, and Skaare in Ref. [11, p. 673], “this effect may 

introduce negative damping in the system that may lead to large resonant motions of [a] floating 

wind turbine.” As the analyses of Refs. [5,9,11,12] have demonstrated, it is important that the 

damping of the platform-pitch mode be positive and kept as large as possible.

Larsen and Hansen [9] and I [5] have presented modifications to conventional wind turbine 

control systems that aim to eliminate the potential for negative damping of the platform-pitch 

mode and improve a floating turbine system’s response. Two of these modifications were 

applied to the original control system for the NREL 5-MW turbine (as presented in Ref. [7]) to 

arrive at a control system that is suitable for when the turbine is installed on the OC3-Hywind 

spar-buoy.

The first modification was a reduction of gains in the blade-pitch-to-feather control system. In 

an idealized PI-based blade-pitch controller, the rotor azimuth responds as a second-order system 

with a natural frequency and damping ratio [4]. To maintain a reasonable relationship between 

the proportional and integral gains in this control system, the gains were reduced by choosing a 

smaller controller-response natural frequency while preserving the recommended controller 

damping ratio. The value of this frequency as recommended in Ref. [4], and the value selected 

for the baseline control system, of 0.6 rad/s [7] is above the platform-pitch natural frequency of 

about 0.21 rad/s. This relationship between frequencies has the potential to introduce negative 

damping of the platform-pitch mode. Larsen and Hanson [9] found that the smallest controllerresponse natural frequency must be lower than the smallest critical support-structure natural 

frequency to ensure that the support-structure motions of an offshore floating wind turbine with 

active pitch-to-feather control remain positively damped. Reducing the controller-response 

natural frequency to 0.2 rad/s will ensure that it is lower than the platform-pitch natural 

frequency and also lower than wave-excitation frequency of most sea states. Using the 

properties for the NREL 5-MW wind turbine from Ref. [7], this frequency and the damping ratio 

used prior were used to derive the reduced proportional gain at minimum blade-pitch setting of 

0.006275604 s and the reduced integral gain at minimum blade-pitch setting of 0.0008965149. 

The gain-correction factor in the gain-scheduling law of the blade-pitch controller is unaffected 

by this change.

The second modification was a change to the generator-torque control strategy when operating at 

rated power (i.e. control Region 3). That is, the control law in Region 3 was changed from a 

constant generator power to a constant generator-torque control region. The constant generator 

torque is set to the rated torque of 43,093.55 N•m. With this change, the generator-torque 

controller does not introduce negative damping in the rotor-speed response (which must be 

compensated by the blade-pitch controller), and so, reduces the rotor-speed excursions that are 

exaggerated by the reduction in gains in the blade-pitch controller. This improvement, though, 

comes at the expense of some overloading of the generator, as power increases with rotor-speed 
23

excursions above rated. Larson and Hanson [9] have demonstrated the effectiveness of this 

modification.

These modifications were incorporated into an updated version of the baseline control system 

dynamic link library (DLL) suitable for use with the floating system discussed in this report, 

which, as before, is in the style of Garrad Hassan’s BLADED wind turbine software package [1].

Table 6-1 summarizes the updated properties of the baseline control system discussed in this 

section.

Table 6-1. Baseline Control System Property Modifications

Proportional Gain at Minimum Blade-Pitch Setting 0.006275604 s

Integral Gain at Minimum Blade-Pitch Setting 0.0008965149

Constant (Rated) Generator Torque in Region 3 43,093.55 N•m
24

References

[1] Bossanyi, E. A., GH Bladed Version 3.6 User Manual, 282/BR/010, Bristol, UK: Garrad 

Hassan and Partners Limited, December 2003.

[2] Det Norske Veritas. MIMOSA Mooring Analysis Software.

[3] Gudmestad, O. T., et al, Basics of Offshore Petroleum Engineering and Development of 

Marine Facilities — With Emphasis on the Arctic Offshore, Stavanger, Moscow, St. 

Petersburg, Trondheim, December 1998.

[4] Hansen, M. H., Hansen, A., Larsen, T. J., Фye, S., Sørensen, and Fuglsang, P., Control 

Design for a Pitch-Regulated, Variable-Speed Wind Turbine, Risø-R-1500(EN), 

Roskilde, Denmark: Risø National Laboratory, January 2005.

[5] Jonkman, J. M., Dynamics Modeling and Loads Analysis of an Offshore Floating Wind 

Turbine, Ph.D. Thesis, Department of Aerospace Engineering Sciences, University of 

Colorado, Boulder, CO, 2007; NREL/TP-500-41958, Golden, CO: National Renewable 

Energy Laboratory.

[6] Jonkman, J. M. and Buhl Jr., M. L. FAST User’s Guide, NREL/EL-500-38230 

(previously NREL/EL-500-29798), Golden, CO: National Renewable Energy Laboratory, 

August 2005.

[7] Jonkman, J., Butterfield, S., Musial, W., and Scott, G., Definition of a 5-MW Reference 

Wind Turbine for Offshore System Development, NREL/TP-500-38060, Golden, CO: 

National Renewable Energy Laboratory, February 2009.

[8] Kooijman, H. J. T., Lindenburg, C., Winkelaar, D., and van der Hooft, E. L., “DOWEC 6 

MW Pre-Design: Aero-elastic modeling of the DOWEC 6 MW pre-design in PHATAS,” 

DOWEC Dutch Offshore Wind Energy Converter 1997–2003 Public Reports [CD-ROM], 

DOWEC 10046_009, ECN-CX--01-135, Petten, the Netherlands: Energy Research 

Center of the Netherlands, September 2003.

[9] Larsen, T. J. and Hanson, T. D., “A Method to Avoid Negative Damped Low Frequent 

Tower Vibrations for a Floating, Pitch Controlled Wind Turbine,” Journal of Physics: 

Conference Series, The Second Conference on The Science of Making Torque From 

Wind, Copenhagen, Denmark, 28–31 August 2007, [online journal], Vol. 75, 2007, 

012073, URL: http://www.iop.org/EJ/article/1742-6596/75/1/012073/jpconf7_75_

012073.pdf?request-id=SpEuhRBu3BG0xV3r2wi7Kg

[10] Lee, C. H. and Newman, J. N., WAMIT® User Manual, Versions 6.3, 6.3PC, 6.3S, 6.3SPC, Chestnut Hill, MA: WAMIT, Inc., 2006.

, [cited 28 August 2007].

[11] Nielsen, F. G., Hanson, T. D., and Skaare, B., “Integrated Dynamic Analysis of Floating 

Offshore Wind Turbines,” Proceedings of OMAE2006 25th International Conference on 

Offshore Mechanics and Arctic Engineering, 4–9 June 2006, Hamburg, Germany [CD-
25

ROM], Houston, TX: The American Society of Mechanical Engineers (ASME 

International) Ocean, Offshore and Arctic Engineering (OOAE) Division, June 2006, 

OMAE2006-92291.

[12] Skaare, B., Hanson, T. D., and Nielsen, F. G., “Importance of Control Strategies on 

Fatigue Life of Floating Wind Turbines,” Proceedings of OMAE2007 26th International 

Conference on Offshore Mechanics and Arctic Engineering, 10–15 June 2007, San 

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(ASME International) Ocean, Offshore and Arctic Engineering (OOAE) Division, June 

2007, OMAE2007-29277.
F1147-E(10/2008)

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May 2010

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Technical Report

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Definition of the Floating System for Phase IV of OC3

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DE-AC36-08-GO28308

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J. Jonkman

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NREL/TP-500-47535

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WE101211

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Phase IV of the IEA Annex XXIII Offshore Code Comparison Collaboration (OC3) involves the modeling of an 

offshore floating wind turbine. This report documents the specifications of the floating system, which are needed by 

the OC3 participants for building aero-hydro-servo-elastic models.

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offshore floating wind turbine; floating wind turbine; modeling of an offshore floating wind turbine

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