Analysis Catenary Moored Spar

European Offshore Wind Conference 2009, Sweden

Corresponding Author, Madjid Karimirad PhD candidate, Centre for Ships and Ocean Structures (CeSOS), Norwegian University of Science and Technology (NTNU), Norway Email: [email protected] Phone: +47 94484785

Dynamic Motion Analysis of Catenary Moored Spar Wind Turbine in Extreme Environmental Condition

Madjid Karimirad Zhen Gao Torgeir Moan CeSOS, NTNU, Norway CeSOS, NTNU, Norway CeSOS, NTNU, Norway

[email protected] [email protected] [email protected] Abstract Survivability is an important design aspect of all types of structures, also floating wind turbines which are subjected to dynamic response due to stochastic wave and wind loads. Wind turbines should be designed for different conditions such as Operational and Survival conditions. In high sea states the response can be quite different from operational condition. The present paper deals with coupled wave and wind induced motions in harsh condition up to 15 (m) significant wave height and 50 (m/sec) average wind speed. The deep draft of spar platforms makes it necessary to consider the instantaneous position for calculating wave forces. This instantaneous position adds some nonlinearity to the equation of motions. It is found that nonlinear dynamic effects have more effects around natural frequencies and less effect in wave frequency part. In harsh conditions the coupled dynamic response is dominated by wind induced response. The dynamic response of the rigid and elastic floating wind turbine (FWT) in harsh condition is found to be almost the same. A comparison between constant and turbulent wind showed that the constant wind excites the pitch natural frequency and the turbulent wind excites both low frequency (surge natural frequency) and pitch natural frequency (the pitch resonance response due to steady wind load is dominant). No instability problem was found in the current analysis. As the aerodynamic damping in a parked turbine is less than for an operating turbine, introduction of more hydrodynamic damping can decrease the pitch resonance response. Keywords: Floating Wind Turbine, Survivability, Stochastic Dynamic Response, Spar Platform

Nomenclature Cd= Quadratic Drag Coefficient CG= Center of Gravity FEM= Finite Element Method FWT= Floating Wind Turbine Hs= Significant wave height Tp= Peak spectral period

50V = Reference 10-min average wind speed with a return period of 50 year 1 Introduction First accepted establishment of the use of Wind Turbine was in the tenth century in Persia. In the region in Sistan, east of Iran where the wind drives mills and raises water from the streams [1]. European Union has a target to make 22.1% of its electricity by 2020 from renewable energy. Regarding Kyoto protocol wind energy has become a mainstream source of energy in the EU [2]. The vast deepwater wind resource represents a potential to use floating offshore wind turbines to power much of the world with renewable energy [3, 4]. Large sea areas with stronger and steadier winds are available for wind farm development and 5MW wind turbine towers located 30 Km from the coastline are invisible. A Floating Wind Turbine (FWT) is designed to take off power from offshore wind resources. Proper performance of the structure requires among other things that its failure probability is sufficiently small. This would imply design for survival in extreme condition. In harsh environmental conditions the wind turbine is parked. The behaviour of a spar type floating wind turbine in parked and parked plus fault load cases are discussed in present paper. The floating wind turbine is a new challenging Ocean-wind technology. Limited works have been done regarding coupled aero-hydro-elastic time domain dynamic


Madjid Karimirad 2

response analysis of these ocean structures. There are different environmental conditions in which the structure should survive. The response of the floating wind turbine in harsh conditions is important as well as in operational condition. In IEC standard the load cases are defined for eight situations: Power production, Power production plus fault, Start up, Normal shut down, emergency shut down, Parked, Parked plus fault and Transport, assembly, maintenance and repair [5]. In North Sea the height of the wave with one hundred year return period can be up to 15 metre. This survival cases can cause damage to mooring lines, tower and blades or in worse case loosing the total structure. There are several ways for dealing with the dynamic response of floating wind turbines [6]. In order to get accurate results, coupled aero-hydro-elastic time domain dynamic response analysis has been performed in present study. In the present paper DeepC [7], well known software for calculating coupled dynamic response of moored floating structures and HAWC2 [8] well known software for analysing dynamic response of wind turbines, have been used. Hydrodynamic analysis of HAWC2 was validated by use of DeepC [9]. A nonlinear FEM model of the mooring lines including clump weight and delta lines is modeled in Simo/Riflex [10] for large deflections and applied as nonlinear spring stiffness in HAWC2 through a Dynamic Link Library (DLL) Interface. Hydrodynamic part of the problem in HAWC2 is compared [9] by the DeepC results in operational condition with (Hs=5 m, Tp=12 sec and No Wind). Also a comparison between experimental results of testing the similar structure has been done [11]. Hydrodynamic forces in HAWC2 are calculated based on Morison equation considering instantaneous position of the structure, so the nonlinear hydrodynamic loading is applied. Nonlinear Coupling of surge/pitch which is very important for harsh sea environment has been considered. Results of Morison and Panel method of DeepC (Simo/Riflex) have been compared. Excitation forces for both Morison and Panel method have been carried out in HydroD [12] based on WADAM [13]. Modeling of the structures has been done by SESAM-Patran Pre [14] and MultiSurf [15].

The harsh sea environment with 15 (m) significant wave height, 19 (sec) spectrum peak period and 50 (m/sec) mean wind speed has been chosen to study extreme environmental condition. Motion response of the system for elastic and rigid structures has been discussed. The motion of the system due to turbulent and constant wind has been obtained. 2 Floating Wind Turbine, Catenary Moored Deep Spar Concept Spar platform in offshore industry has showed reliable concept for producing oil in deep sea zones. In this paper we focus on Floating Wind Turbine, Based on a Catenary Moored Spar Platform. The NREL 5 MW Wind Turbine has been chosen and mounted on a 120 meters draft spar platform. In the Figure 1, the schematic of the system has been plotted. The main characteristics of the system are mentioned in the tables 1-3. In table 4 the natural periods of the rigid body motion has been summarized.

Figure 1: Catenary Moored Deep Spar

Floating Wind Turbine


Madjid Karimirad 3

Turbine Part Mass (kg) Tower 347,460 Nacelle 240,000 Blades (3 blades) 53,220 Hub 95,711

Table 1: Wind Turbine Main Characteristics

Table 2: Spar (Platform) Characteristics

Table 3: System Mass Properties

Motion Natural Period (s) Surge 115 Sway 125 Heave 31.4 Roll 32.7 Pitch 32.7 Yaw 7.5

Table 4: System natural periods 2.1 Mooring system The mooring lines forces have been modeled as an external force in surge, sway, heave and yaw which has been found to be the main mooring line stiffness (The contribution in roll and pitch has been neglected, also the heave contribution of mooring lines are small). Using DeepC the displacement-force of mooring lines has been calculated (Figure 2-5) and applied in HAWC2 as external forces at fairleads. As the mooring system consists of 3 lines, the stiffness for surge motion is different in negative and positive direction. The FEM model of mooring lines including clump mass and delta lines for nonlinear large deflection has been modeled in DeepC. The delta lines provide enough yaw stiffness. In conventional spar without wind turbine

mounted at the top the yaw stiffness is less and the natural period of rigid yaw motion is more that 100 seconds. But for floating wind turbine it is reduced to less than 8 seconds.

Surge Mooring line Stiffness (positive direction)

y = -0.0037x4 + 31.949x3 - 852.54x2 + 42718x

0.E+001.E+062.E+063.E+064.E+065.E+066.E+06

0 20 40 60Surge (m)

Forc

e (N

)

Figure 2: Surge mooring line stiffness

(Positive direction)

Surge Mooring line Stiffness (negetive direction)

y = -2.4088x4 + 339.87x3 - 3877.5x2 + 56910x

0.E+00

1.E+06

2.E+06

3.E+06

4.E+06

5.E+06

6.E+06

0 10 20 30Surge (m)

Forc

e (N

)

Figure 3: Surge mooring line stiffness

(Negative direction)

Sway Mooring Line Stiffness

y = 42089x

0.0E+00

1.0E+05

2.0E+05

3.0E+05

4.0E+05

5.0E+05

6.0E+05

0 4 8 12Sway (m)

Forc

e (N

)

Figure 4: Sway mooring line stiffness

Yaw Mooring Line Stiffness

0.0E+00

5.0E+06

1.0E+07

1.5E+07

2.0E+07

2.5E+07

0 10 20 30 40Yaw (deg)

Mom

ent (

N.m

)

Figure 5: Yaw mooring line stiffness

Total Draft 120 m Diameter Above Taper 6.5 m Diameter Below Taper 9.4 m Mass, Including Ballast 7593,000 kg Centre of Gravity, CG -92.58 m Roll Inertia about CG 4.489E+09 kgm2 Pitch Inertia about CG 4.489E+09 kgm2 Yaw Inertia about Centerline 1.672E+08 kgm2

TOTAL MASS 8329,230 kg

Centre of Gravity, CG -78.61 m

Pitch Inertia about Origin 7.34E+10 kgm2

Yaw Inertia about Centerline 1.68E+08 kgm2


Madjid Karimirad 4

3 Comparison of Panel Method and Morisons Formula in DeepC The coupled Hydrodynamic response of moored spar due to wave forces has been considered to show the possibility of using Morison method for this type of structure. Morison formula has been developed originally for slender structures and is proper for our structure. The JONSWAP Spectrum, Hs=5 (m) and Tp=12 (sec) has been defined. In following (Figures 6-9) the spectrum of mooring line force, surge, pitch and heave responses have been compared. Good agreements between results of two methods have been found except for heave motion. As we avoided the Mathieu instability the heave motion is not very important for our case and we can use Morison approach (No instability was seen). Mathieu instability for a spar platform arises when there is a harmonic variation in the pitch restoring coefficients caused by large heave motion and the period of the heave motion is half of the pitch natural period. The pitch restoring coefficient can be represented by a function of the displaced volume and the metacentric height of spar hull. Due to heave motion, the displaced volume and the metacentric height of the spar platform change in time and this heave/pitch coupling can be represented by Mathieus equation [16]. Also it is possible to have this instability for other ratio of heave/pitch natural frequency. Haslum et al., 1999 showed these ratios for a system with no damping, no excitation and no coupling between pitch and surge to be 0.5, 1, 1.5 and 2 [17]. The Mathieu instability has been avoided in present study by considering criteria mentioned by Haslum et al., 1994 and Koo et al., 2004.

Mooring Line Tension Spectrum

0.0E+005.0E+081.0E+09

1.5E+092.0E+092.5E+093.0E+09

3.5E+094.0E+09

0 0.5 1 1.5 2Frequency (rad/sec)

Spec

trum

(N^2

*S)

Panel MethodMorison

Figure 6: Mooring line tension spectrum

comparison

Surge Motion Spectrum

0.0

1.0

2.0

3.0

4.0

5.0

6.0


Spec

trum

(m^2

*s)

Panel MethodMorison

Figure 7: Surge motion spectrum

comparison

Pitch Motion Spectrum

0.0E+005.0E-051.0E-041.5E-042.0E-042.5E-043.0E-043.5E-044.0E-044.5E-04


Spec

trum

(rad

^2*s

)

Panel MethodMorison

Figure 8: Pitch motion spectrum comparison

Heave Motion Spectrum

0.000.020.040.060.080.100.120.140.160.180.20


Spec

trum

(m^2

*s)

Panel MethodMorison

Figure 9: Heave spectrum comparison

4. Comparative study of wave induced response Hydrodynamic analysis of DeepC (Linear and Nonlinear) and HAWC2 will be discussed in this part. The deep draft of spar platforms makes it necessary to consider the instantaneous position for calculating wave forces. This instantaneous position adds some nonlinearity to the equation of motions. By considering instantaneous position of spar for calculating forces due to wave in DeepC nonlinear effects can be added to the model.


Madjid Karimirad 5

4.1 Comparison of Hydrodynamic models in HAWC2 and DeepC Dynamic response of the structure due to wave excitation forces have been compared for DeepC and HAWC2 for a moderate sea state with Hs=5 m and Tp=12 sec. Hydrodynamic part in DeepC is based on Panel method. The quadratic viscous forces have been added to the model in DeepC through Morison elements. The coupled time domain analysis of the moored spar has been calculated by using retardation functions. HAWC2 is based on Morison formula and accounts for the instantaneous position of the structure when calculating the forces (Figure 10 and 11). All the methods show good agreement for wave frequency response. There is a difference in low frequency (surge resonant response) which can be investigated more (Linear response cannot capture the low frequency resonant response).

Figure 10: Surge motion spectrum (at mean

water level)

Figure 11: Pitch motion spectrum

4.2 Comparison of wave induced motion obtained by HAWC2 and Experiments

The Nacelle surge of the floating wind turbine obtained by HAWC2 (Figure 12) has been compared with similar experimental result which has been carried out for StatoilHydro by MARINTEK. Nielsen et al. has published this experimental result in OMAE2006 [11]. The floating wind turbine tested by MARINTEK and our model are not exactly same but qualitatively the results are similar.

HAWC2 Surge Nacelle

012345678

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4Frequency (Hz)

Sqrt

(S(f)

)

Figure 12: HAWC2 analysis (Hs=5 m, Tp=12

sec) 5 Dynamic motion analysis of floating wind turbine The dynamic motion of the catenary moored spar floating wind turbine will be discussed in this section. 5.1 Dynamic wave induced motion in Harsh Sea (Without wind) Dynamic motion of the system due to wave in harsh condition has been considered in HAWC2. A harsh sea state with one hundred year return period has been defined. The JONSWAP wave spectrum (Hs=15 m and Tp=19 sec) is plotted in Figure 13. For nacelle surge the wave frequency part is dominant (Figure 14 and 16) and for pitch motion the pitch natural frequency has been excited and dominant (Figure 15 and 17).

0 0.5 1 1.50

20

40

60

80

100Wave Spectral density

Frequency [rad/s]

S(

) [m

2 s

/ rad

]

p = 0.33 [rad/s]

Hs=15 (m)Tp=19 (sec)

Figure 13: Jonswap wave spectrum


Madjid Karimirad 6

0 0.5 10

50

100

Nacelle Surge Spectral density

Frequency [rad/s]

S(

) [m

2 s

/ rad

]

p1 = 0.32 [rad/s]p2 = 0.18 [rad/s]

Figure 14: Nacelle Surge motion spectrum

0 0.2 0.4 0.6 0.8 10

10

20

30

40Pitch Spectral density

Frequency [rad/s]

S(

) [de

g2 s

/ ra

d]

p1 = 0.18 [rad/s]p2 = 0.32 [rad/s]


1000 1500 2000 2500 3000 3500

-10

-5

0

5

10Nacelle Surge

Surg

e (m

)

time (sec) Figure 16: Nacelle Surge motion time history

1000 1500 2000 2500 3000 3500-5

0

5

time (sec)

Pitch

Pitc

h (d

eg)

Figure 17: Pitch motion time history

5.2 Motions in Moderate Sea and High Wind The dynamic response of the floating wind turbine in moderate sea and extreme wind is considered to show the role of wind in harsh condition. The wind and wave spectrums are plotted in Figure 18 and 19 respectively. In harsh conditions the coupled dynamic response is dominated by wind induced

response. The wind can excite the pitch natural frequency. In both nacelle surge and pitch motion the pitch induced wind is dominant (Figure 20-23).

0 1 2 30

0.5

1

1.5

2

Wave Spectral density

Frequency [rad/s]

S(

) [m

2 s

/ rad

]

p = 0.78 [rad/s]

Hs=3 (m)Tp=8 (sec)

Figure 18: Wave spectrum

0 0.5 1 1.5 20

50

100

Wind Spectral density

Frequency [rad/s]

S(

) [(m

/s)2

s /

rad]

p1 = 0.077 [rad/s]p2 = 0.17 [rad/s]p3 = 0.26 [rad/s]p4 = 0.47 [rad/s]

Mean velocity: 50 (m/sec)Turbulence intensity: 0.15

Figure 19: Wind spectrum

0 0.2 0.4 0.6 0.8 10

500

1000


Frequency [rad/s]

S(

) [m

2 s

/ rad

]

p1 = 0.21 [rad/s]p2 = 0.077 [rad/s]


0 0.2 0.4 0.6 0.8 10

100

200

300

400

Pitch Spectral density

Frequency [rad/s]

S(

) [de

g2 s

/ ra

d]

p = 0.21 [rad/s]



Madjid Karimirad 7

1000 1500 2000 2500 3000 3500

80

100

120

time (sec)

Surg

e (m

)

Nacelle Surge

Figure 22: Nacelle Surge motion time history

1000 1500 2000 2500 3000 35000

5

10

15

20

Pitch

time (sec)

Pitc

h (d

eg)

Figure 23: Pitch motion time history 5.3 Motions in Harsh Environment 5.3.1 Environmental Condition Wave and wind climate are correlated, because waves usually are wind-generated. The correlation between wave data and wind data shall be accounted for design. Survival condition for floating wind turbine is chosen to be 100 year return period sea with Hs=15 m and Tp=19 sec. Extreme winds are usually given in terms of 10-minute mean wind speeds, which occur with some prescribed recurrence period, e.g. the 50-year wind speed [18]. For a 10-min averaging period, the reference hub-height wind speed with a recurrence period of 50 years, 50V has been considered to be 50 m/s [3, 4]. The wind spectrum (Figure 19)

and wave spectrum (Figure 13), both have energy around pitch natural frequency. The wind spectrum also has great amount close to low surge natural frequency. 5.3.2 Load Cases for parked turbine (General case, wave and wind) In harsh environmental condition (wave and wind) the wind turbine is parked. Parked condition is a non-operational machine state in which the machine is not generating power. Care is required in selecting the turbine configurations to be considered in the investigation of this case [19]. In case of the sideways wind loading, the maximum load occurs when one of the blades is vertical. The wind is acting perpendicular to the nacelle (load case 1), i.e. with a full drag on the nacelle, and the blades are pitched to give a full drag also on the blades [18]. For the pitch regulated wind turbines the critical non-operational (parked) condition occurs when wind is from the front, one of the blades is vertical and load results from the blade lift (load case 2) [19]. In the table 5 the non-operational (survival) load cases which have been considered in this paper are summarised. In load case 2, loads result from blade lift rather than drag, it is right angles to the loading on the tower (mainly in sway direction), so the total moment at the tower-spar interface is less [19]. We can see later that this force can make large resonance around sway natural frequency.

Table 5: Survival (Non-Operational) Load Cases 5.3.3 Comparison of dynamic response for Elastic and Rigid Structure (Load Case 1) The dynamic response of structure due to survival wave and wind condition has been calculated for both rigid and elastic structure. The response due to wave and

steady wind in survival condition has been found the same (Figure 24-25).

Case No.

Wave direction

Wave Height and

Peak Period

Wind Speed and Direction

Yaw Blade Description

1 0 15 m- 19 sec 50 (m/sec)- 0 90 Flat to wind Drag loading of Blades

2

0 15 m- 19 sec 50 (m/sec)- 0 0 Parallel to wind Lift loading of Blades


Madjid Karimirad 8

0 0.2 0.4 0.6 0.8 10

500

1000


Frequency [rad/s]

S(

) [m

2 s

/ rad

]

p1 = 0.21 [rad/s]p2 = 0.32 [rad/s]

Black Dot: ElasticSolid Red: Rigid


0 0.2 0.4 0.6 0.8 10

100

200

300

400


Frequency [rad/s]

S(

) [de

g2 s

/ ra

d]

p = 0.21 [rad/s]

Black Dot: ElasticSolid Red: Rigid


5.3.4 Comparison of response for Constant and Turbulent Wind (Load Case 1) The motion of the structure due to survival wave and wind condition has been calculated for both constant and turbulent Wind. The mean (steady) wind force can excite the pitch natural frequency (Figure 26-29). As we are doing the coupled analysis the wind force has a component with pitch natural frequency through relative motion.

0 0.2 0.4 0.6 0.8 10

500

1000


Frequency [rad/s]

S(

) [m

2 s

/ rad

]

p1 = 0.21 [rad/s]p2 = 0.077 [rad/s]

Solid:Turbulent windDash: Constant wind


0 0.2 0.4 0.6 0.8 10

100

200

300

400


Frequency [rad/s]

S(

) [de

g2 s

/ ra

d]

p = 0.21 [rad/s]

Solid: Turbulent windDash: Constant wind


1000 1500 2000 2500 3000 3500

80

100

120

140

time (sec)Su

rge

(m)

Nacelle Surge


1000 1500 2000 2500 3000 35000

5

10

15

20

time (sec)

Pitc

h (d

eg)

Pitch


5.3.5 Dynamic response of system in non-operational situation (Load Case 2) The load case 1 is a very conservative load case. In case of fault or lose of grid connection load case 1 can occur. The sideways wind loading on a wind turbine can arise (Load case 1) if yaw drive is disabled by the grid loss. If the grid security is enough high and the yaw drive is programmed to remain operational in high winds then it is not necessary to consider sideways loading (3 blades flat to wind, Drag loading of blades) [18]. Jonkman has considered the parked plus fault condition with zero yaw and one of the blades flat to wind [3, 4]. Also he has investigated load case 2 as non-operational (parked) condition. The nacelle surge motion is reduced due to decrease of force in surge direction (Figure 30). The peak value related to pitch natural frequency (Figure 31) in nacelle surge motion is damped. The wind force excites sway


Madjid Karimirad 9

natural frequency in load case 2 as well as surge natural frequency (Figure 34). The motion obtained from load case 2 is significantly less than similar motions in load case 2. The only challenge here is enough break power for keeping the blades not to rotate. The maximum torque in this case is 20000 (KNm). The mechanical break should resist this moment and keep the blades from rotating. In Figure 30-37 the motions of the floating wind turbine due to wave and wind in harsh condition has been plotted for load case2.

0 0.2 0.4 0.6 0.8 10

100

200

300

400


Frequency [rad/s]

S(

) [m

2 s

/ rad

]

p1 = 0.069 [rad/s]p2 = 0.18 [rad/s]p3 = 0.33 [rad/s]


0 0.5 10

100

200

300


Frequency [rad/s]

S(

) [de

g2 s

/ ra

d]

p = 0.18 [rad/s]


1000 1500 2000 2500 3000 350020

40

60

80

time (sec)

Surg

e (m

)

Nacelle Surge


In the above load cases we have seen resonance around natural frequencies (mainly for pitch and surge natural frequencies). Resonance should not be confused with instability. Resonant motion requires external excitation and grows

linearly (not exponentially as in the case of instability). Also, in a resonance, the frequency of the external excitation coincides with one of the systems natural frequencies [20].

1000 1500 2000 2500 3000 3500

-5

0

5

10

time (sec)

Pitc

h (d

eg)

Pitch


0 0.1 0.2 0.3 0.40

1000

2000

3000

Nacelle Sway Spectral density

Frequency [rad/s]

S(

) [m

2 s

/ rad

]

p = 0.042 [rad/s]

Figure 34: Nacelle Sway motion spectrum

0 0.2 0.4 0.6 0.8 10

10

20

30

Roll Spectral density

Frequency [rad/s]

S(

) [de

g2 s

/ ra

d]

p = 0.18 [rad/s]

Figure 35: Roll motion spectrum

1000 1500 2000 2500 3000 3500-20

0

20

time (sec)

sway

(m)

Nacelle Sway

Figure 36: Nacelle Sway motion time history


Madjid Karimirad 10

1000 1500 2000 2500 3000 3500-5

0

5

time (sec)

Rol

l (de

g)

Roll

Figure 37: Roll motion time history

6. Conclusion This paper deals with the motion analysis of floating offshore wind turbines in harsh environmental condition. Floating wind turbine is a new ocean technology and limited works have been down regarding response in extreme situation (Harsh environmental conditions). In harsh conditions the coupled dynamic response is dominated by wind induced response. The motion response of the rigid and elastic floating wind turbine (FWT) in harsh condition is found to be almost the same. A comparison between constant and turbulent wind showed that the constant wind excites the pitch natural frequency and the turbulent wind excites both low frequency (surge natural frequency) and pitch natural frequency but the pitch resonance response due to steady wind load is dominant. No instability was found in the responses. As the large motion due to excitation of natural frequencies (resonance) is mainly due to wind force and the wind spectrum covers a wide range of frequencies, changing the pitch natural frequency can not help too much, while introduction of more hydrodynamic damping can reduce the pitch resonance response. 7. Acknowledgement The authors would like to acknowledge the financial support from the Norwegian Research Council which has been granted through CeSOS. References 1. Spera D A. Wind Turbine Technology Fundamental Concepts of Wind Turbine Engineering; ASME PRESS: USA, 1998 2. Van Der Tempel J. Design of Support Structures for Offshore Wind Turbines; Delft University of Technology: Netherland, 2006 3. Jonkman J M, Buhl J. Loads Analysis of a Floating Offshore Wind Turbine Using Fully

Coupled Simulation; National Renewable Energy Laboratory (NREL), Golden, Colorado, 80401-3393: USA, 2007 4. Jonkman J M. Dynamics Modeling and Loads Analysis of an Offshore Floating Wind Turbine; National Renewable Energy Laboratory (NREL), Technical Report, NREL/TP-500-41958: USA, 2007 5. Manwell J F, McGowan J G, Rogers A L. Wind Energy Explained, Theory, Design and Application; John Wiley and Sons Ltd: England, 2002 6. Karimirad M. Dynamic Response of floating wind turbine (FWT) due to wave and wind loads; Internal Report, CeSOS, NTNU: Norway, 2008 7. DNV. DeepC User Manual; Norway, 2008 8. Ris National Laboratory Technical University of Denmark. HAWC2 User Manual: Denmark, 2008 9. Karimirad M, Gao Z, Moan T. Validation of HAWC2; Internal Report, CeSOS, NTNU: Norway, 2009 10. MARINTEK. Simo/Riflex User Manual; Norway, 2008 11. Nielsen F G, Hanson T D, Skaara B. Integrated Dynamic Analysis of Floating Offshore wind Turbine; OMAE2006-92291: Germany, 2006 12. DNV. HydroD User Manual; Norway, 2008 13. DNV. WADAM User Manual; Norway, 2005 14. DNV. SESAM-Patran Pre User Manual; Norway, 2004 15. AeroHydro. MultiSurf User Manual; USA, 2008 16. Koo B J, Kim M H, Randall R E. Mathieu instability of a spar platform with mooring and risers; Ocean Engineering Journal, Vol. 31, Page 21752208, 2004 17. Haslum H A, Faltinsen O M. Alternative shape of Spar Platform for Use in Hostile Areas; Offshore Technology conference, OTC 10953: USA, 1999 18. DNV/Ris. Guidelines for Design of Wind Turbines; 2nd Edition, Jydsk Centraltrykkeri: Denmark, 2002 19. Burton T, Sharpe D, Jenkins N, Bossanyi E. Wind Energy Handbook; John Wiley and Sons Ltd: England, 2008 20. Bir G, Jonkman J. Aeroelastic Instabilities of Large Offshore and Onshore Wind Turbines; EAWE Torque from Wind Conference: Denmark, 2007

Documents

Analysis Catenary Moored Spar