Offshore Windfarm Hfd 6

7/29/2019 Offshore Windfarm Hfd 6

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Loads, dynamics and structural design

Offshore Wind Farm Design

Michiel Zaaijer

DUWIND


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Overview

Introduction

Modelling offshore wind turbines

Types of analysis and tools

Loads and dynamics in design


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IntroductionLoads, dynamics and structural design


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Harmonic loading

( ) ( ) += tFtF sin

0 1 2 3 4 5 6

1

0

1

Simple Harmonic Loading

Time

Loading

- Gravity loads on blades

- Mass imbalance rotor (1P)

- Aerodynamic imbalance (1P)- Small regular waves

27 RPM = 0.45 Hz


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Non-harmonic periodic loading

0 1 2 3 4 5 6

1

0

1

Complex Cyclic Loading

Time

Loa

ding

- Wind-shear

- Yaw misalignment

- Tower shadow

- Rotational samplingof turbulence

0 1 2 3 4 5 60.5

0

0.51st Signal (0.5 Hz)

Loading

0 1 2 3 4 5 60.5

0

0.52nd Signal (1 Hz)

Loading

0 1 2 3 4 5 60.5

0

0.53rd Signal (1.5 Hz)

Loading

( )

( )0

sink kk

F t

a a F k t

=

+ +

(all 2P or 3P and multiples)

3P


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Non-periodic random loading

0 1 2 3 4 5 6

1

0

1

Random Load

Time

Loading

- Turbulence (small scale)

- Random waves


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Other (non-periodic) loading

Transients

0 1 2 3 4 5 6

1

0

1

Step Load

Time

Loading

Short events

0 1 2 3 4 5 6

1

0

1

Impulsive Load

Time

Loading

- Start/stop

- Turbine failures- Storm front

- Extreme gust

- Extreme waves


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The effect of dynamics

km

k= 1 [N/m]

-2

-1

0

1

2

1

F

Force [N]

-2

-1

0

1

2

1

x

Response [m]

?


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-2

-1

0

1

2

1

-2

-1

0

1

2

1

m = 0.0005 [kg]

-2

-1

0

1

2

1

m = 0.1 [kg]

Force [N]

-2

-1

0

1

2

1

m = 0 [kg]

(Static)


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-2

-1

0

1

2

1

-2

-1

0

1

2

1


km

FSystem

Fintern = k x

Force [N]

m = 0.0005 [kg]

Response [m]Internal forces external forces

due to dynamics

Internal forces drive the design,

not external forces!


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Dynamic amplification factor

0 1 2 3 4 50

1

2

3

4

5

damping ratio = 0.1

damping ratio = 0.2

damping ratio = 0.5

Frequency Ratio

Dyna

micAmplificationFactor(DAF)

Note: the DAF is defined for harmonic excitation

DAF =Dynamic amplitude

Static deformation

fexcitationfnatural

Resonance


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Character of resonance

Excitation frequency natural frequency

Large oscillations

Fatigue damage (due to severe cyclic loading)

Generally not destructive (anticipated in design)

Natural frequencies of wind turbine (-components)

are close to several excitation frequencies


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Classification for wind turbines

1P 3P

soft-soft soft-stiff stiff-stiff

1

DAF

f0

Excitation

Response


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Soft-stiff example

1P = 0.45 Hz

fnatural = 0.55 Hz

3P = 1.35 Hz


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Reduced response to loading

DAF

1

f0

Alleviation of (wind) loading by

shedding loads through motion

soft-soft

structure

Typical rotor loading

frequencies

1P 3PTypical wave loading

frequencies


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Increased response to loading

1-P *-P

Quasi-static or amplified

response to wave loading


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Wind turbine characteristics

Stiffness Material properties / soil properties

Buoyancy of a floating structure Damping

Material properties / soil properties Aerodynamic loading

Control (Viscosity of water / radiation in soil) Inertia

Material properties Hydrodynamic loading (water added mass)

Entrained water mass


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Linear / non-linear systems

x(t) y(t)

ax1(t) + bx2(t) ay1(t) + by2(t)

Linear system:

Non-linear system:

x(t) + x0 y(t) + y0Initial condition x0:

No superposition possible

Possible dependency on initial conditions

Possible variation in output statistics for the sameinput (statistics)


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Non-linearities for wind turbines

Aerodynamic loading

Hydrodynamic loading

extreme waves

waves and currents

Speed and pitch control

some algorithms

settings for various wind speeds

Extreme deformations (2nd order effects)


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IntroductionLoads, dynamics and structural design


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Lifelong response signal

Response

(loading + dynamics)

Time

Extreme events

Lifelong variations


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Effects of loads and dynamics

Ultimate limit state (ULS)

(maximum load carrying resistance) Yield and buckling

Loss of bearing / overturning

Failure of critical components Fatigue limit state (FLS)(effect of cyclic loading)

Repeated wind and wave loading

Repeated gravity loading on blade


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Effects of loads and dynamics

Accidental limit state (ALS)

(accidental event or operational failure, local damageor large displacements allowed)

Ship impact

Serviceability limit state (SLS)(deformations/motion, tolerance for normal use)

Blade tip tower clearance

Vibrations that may damage equipment

Tilt of turbine due to differential settlement


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Design drivers of wind turbinesComponent Design drivers

Ultimate Fatigue

Tower top top mass -

Tower - wind/wave

Submerged wind/wave/current wind/wave

tower

Foundation wind/wave/current -


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Importance of dynamics in design

Increase or decrease of maximum load

Affects Ultimate Limit State conditions

Increase or decrease of number of load cycles andtheir amplitudes

Affects Fatigue Limit State / Lifetime


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Effect on structural design

Monopilesoft-soft

Monopilesoft-stiff

Support structure costSoft-stiff monopile 100 %

Soft-soft monopile 80 %

Energy cost

Soft-stiff monopile 100 %

Soft-soft monopile 95 %


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Use of dynamic models

Analyse system

properties

Avoid resonance

and instabilities

Assess lifelong

loading

Reduce internal

loads and match

resistance

Make lightest

and cheapeststructural design

1. 2. 3.

Validate reliability

and technical

lifetime


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Modelling of offshore wind turbines

Structural models of rotor, nacelle and support structure


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Flexibility of wind turbines

Drive train - Torsion

Blades - Flapwise bending- Edgewise bending

- Torsion

Tower - Bending- Torsion

Rotor - Rotation

Foundation - Rotation- Horizontal- Vertical


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Integrated dynamic model

Wind

Wave

Grid

Controllers

Rotor Drive train Generator

Offshore wind turbine

Support structure


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Rotor model

Aerodynamic properties

Distributed mass-stiffness

Beam theoryFEM

, EIx,y,pTables

Cl

Cd


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Drive train model

Ihub+low speed shaft

Igenerator

Stiffness torsion in

transmission and main shaft;

main shaft bending

Damping transmission

suspension and generator

torque control

Transmission ratio


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Generator model

n0

generator

motor

00

Tk,g

n

synchronous generator:

n0 2n0

induction generator:

Tk,g

0

0

generator

motor

n

Slip


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Tower modelDistributed mass-stiffness

Beam theory

FEM

, EIx,y,p

Modal representation

Deflection

1st

mode

+

Deflection

2nd

mode

=

Total

deformationEffective reduction of DOFs


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Foundation model

=

u

kk

kk

M

H

x

xxx


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Modelling of offshore wind turbinesDeriving parameters for foundation models


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Importance of foundation model

40.0m

5.0m

15.0m

21.0m

3500x75

2500

x100

2800x60

2800

x32

2800

x25

2800

x20

37.0m

(25.0m Penetration)

3.0m

6.0m

2800

x60

15.4m

12.0m

12.0m

12.0m

6.0m

Pile

Tower

Flange

Boat Landing

J-Tube

MSL

x30

3.0m

3.5m

5.0m

Scour Protection

4.6m

x100

Rotor/nacelle mass 130,000 kg

First natural frequency (Hz)

without foundation 0.34627

with foundation 0.29055

with scour 0.28219

Second natural frequency (Hz)

without foundation 2.2006

with foundation 1.3328

with scour 1.2508


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Enhanced foundation model

External shaft friction

(t-z curves)

Internal shaft friction

(t-z curves)

Pile plug resistence(Q-z curves)

Pile point resistance(Q-z curves)

Lateral resistance

(p-y curves)

Use:

Standards (API/DNV)

Existing software(In exercise: ANSYS Macros)


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Scour

General scour depth

Local scour depth

Overburden reduction depth

No scour condition

General scour only

Local scour condition

Vertical effective soil pressure0

Pile

Seabed

Typically 6 times pilediameter

Typically 1-1.5 times

pile diameter


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Effective fixity length

Seabed

Effective

fixity

length

3.3 D 3.7 DExperience withoffshore turbines

6 DGeneral calculations

7 D 8 DVery soft silt

3.5 D 4.5 DStiff clay

Effective fixitylength

Configuration


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Stiffness matrix

Stiffness matrix

Seabed

Tower

Run two load cases with FEM

model with py-curves

(See next slide)

=

u

kk

kk

M

H

x

xx x


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FEM-based pile-head stiffness

4. Check assumption with another FEM solution

111 += xxx kukF

111 +=

kukM x

1. Solve FEM for F1,M1(F1,M1 near loading situation of interest)

222 += xxx kukF

222 +=

kukM x

2. Solve FEM for F2,M2(F2,M2 near loading situation of interest)

3. Scratch one equation and solve kxx, kx, k(k

x = kx, assume matrix equal for both loads)


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Selection of pile foundation models

Foundation flexibility significant enough to require

close consideration of modelling Effective fixity length model dissuaded

Stiffness matrix much more favourable than uncoupled

springsFor exercise: Monopile in Bladed modeled with uncoupled springs(unfortunately)


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Vertical

Horizontal

Rocking

InertiaViscousdamping

Springstiffness

( )

13

3DG

( )

87

116

DG

1

2 DG

( )

13265.0

4GD

( )

246.4

2 GD

( )

14

4.3

2GD

( )

13264.0

5D

( )

2876.0

3D

( )

18

08.13

D

GBSLumped springs

and dashpots for:

- Horizontal- Vertical

- Rocking

Documented GBS model parameters


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Types of analysis and toolsNatural frequency and mode analysis


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FEM modal analysisFEM analysis provides:

Natural frequencies

Mode shapes

(Pre-processed)

matrices of structural

properties:

Mass

Stiffness Damping

1

XY

Z

Parametric support structure model generation


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Natural frequencies

0

0.5

1

1.5

2

2.5

3

3.5

Monopile Monopod Tripod Truss

Naturalfrequencies


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Modes of the support structure

Monopile 1st mode 2nd mode


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Rayleigh's method

=

Z Velocity:

Maximum

strain energy2~ Z

( )2max

2

1

:

xkV

SDOF

=

Maximum

kinetic energy22~ Z

( )( )

( )22

2

0max

2

12

1

:

xm

xmT

SDOF

=

= &

( ) ( ) ( )tZxtxv sin, =


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Rayleigh's method

To estimate first natural frequency (lowest)

Based on energy conservation in undamped, freevibration: Exchange of energy between motion andstrain

Mode shape must fit boundary conditions

Best estimate of mode shape results in lowest estimateof natural frequency

(Deflection under static top-load gives educated guessof mode shape)


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Rayleighs method for stepped tower

( )2 322

2 4

44 48

3

top eq

foundeq

m m L LT C

EI

+= +

See document on Blackboard for:

Derivation of this equation

Explanation of EIeq, meq, Cfound


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Free vibration of cylinder in water

( ) ( )cwcwDcMwM xvxvDCxDCaDCf &&&& += ,,2

,

2

2

1

41

4

Inertia force Drag force

Inertia force due to moving cylinder

Still water remaining inertia term is called water added mass

With CM 2 water added mass mass of replaced water

But related to water surrounding the cylinder!

Use water added mass in analysis of natural frequency and modes

T f l i d t l


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Types of analysis and toolsResponse analysis


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Types of response analysis

Static analysis with dynamic response factors

Time domain simulation Frequency domain analysis

Mixtures

All approaches can also be divided in:

Integrated combined loading

Superposition of effect of load components (wind, wave,current, gravity)


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Static + dynamic response factors

Calculate static response for several loading conditions

(separate wind, wave, g) Estimate a dynamic response factor per condition

(comparison of characteristic frequencies) Typical 1.2-1.5

Superimpose results (including partial safety factorsper loading type)

Superposition of forces


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Superposition of forces

SuperpositionWaves +

current

Wind

on tower

ThrustGravity


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Mixing time- and frequency domain


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TD simulation:

- Transfer function tower top

loading (linearisation)

- Aerodynamic damping

FD analysis:

- Transfer function for wind loading

- Aerodynamic damping as extra

structural damping- Linear wave loading

+

Mixing time and frequency domain


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U(1-a)

Aerodynamic dampingTower for-aft motion

Blade motion

Vblade

Angle of attack

decreases/increases

-Vblade

Lift/thrust force

diminishes/increases

L

L opposite Vblade


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Some relevant analysis tools

ANSYSSesam

Adams WT

PhatasBladed

Flex

Turbu

FEM Time Freq Rotor Offshore

XX X X XX X X X

X X X XX X X X

X X X XX X X X



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oads a d dy a cs des gOverview of the process

Suggested steps


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gg p

Choose a limited set of load cases

Make preliminary design based on static loads Check for resonance*

Check extreme loads with time domain simulations*

Check fatigue damage*

*Adjust design when necessary


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Values for safety factors


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Importance of structural component w.r.t.

consequence of failure considered Typically between 0.7 and 1.35

1.0 for favourable loads!

Load factor 1.0 for fatigue (safety in resistance) See e.g. Offshore standard DNV-OS-J101

Design of offshore wind turbine structures



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gChoose load cases


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Load cases: Combine conditions


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Load cases: Combine conditions

extreme

normal

external conditions

stand-by

operational conditions

normal conditions

start-uppower production

normal shut-down

fault conditions

condition after occurrence of a fault

erection

The number ofcombinations that

is required in the

standards is

enormous!

Reducing number of load cases


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Reducing number of load cases(extremes)

Select a few independent extreme conditions that might

be design driving, e.g.: Extreme loading during normal operation

Extreme loading during failure

Extreme wind loading above cut-out

Extreme wave loading

And combine these with reduced conditions for the otheraspects (wind, wave, current)


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Knowledge about load case selection:


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T

VVrated Vcut-out

Ideal pitch

Stall

Response

to gust/failure

Vextreme

~V2

~V-1

~V2

Thrust curves

Extreme and reduced conditions


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Hmax 1.86 Hs

Hreduced 1.32 Hs Vgust,max 1.2 V10 min Vgust,reduced (1.2 / 1.1) V10 min



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Make preliminary design

Preliminary support structure design


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Determine largest loads at several heights

Estimate wind, wave, current and gravity loadse.g. CD,AX = 8/9 (Betz) at Vrated & linear wave & DAF & safety

Superimpose and determine largest at each height

Dimension tower (moments / section modulus)

Rule of thump D/t 200 tower section ~60 driven foundation pile (see e.g. API on BB)

Estimate pile size with Blums method(See document on Blackboard!)



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Check for resonance

Campbell diagram


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p g

forbidden

area

margin

Characteristicfrequen

cy

Rotor speed

1e lead-lag

3-P

1-P

1e flap

1st tower frequency

1st tower frequency 1st tower frequency

Soft-

stiff

Soft-

soft

Stiff-

stiff

Wave-excitation

Soft-stiff

Soft-soft

Design adaptations


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Change diameters and/or wall thicknesses

Shift massese.g. move transformer from nacelle to platform

Adjust rotor speed controle.g. skip resonance in partial load region

Change concepte.g. to braced tower / tripod



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Check lifetime fatigue

Fatigue


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Fstatic

F

time

failure

number of cycles

fatigue test

Fatigue: after a number of cycles of a varying load below static

strength failure occurs.

S-N curves


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log N

log amp

UTS

1:20?Carbon-Epoxy

1:10

Glass-Polyester

Steel (Welded)

1:3

Variable amplitude loading


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amp

log N

n1n2

n3n4

n5

N1N2

N3N

3N4

N5

Miners Damage Rule:5

5

4

4

3

3

2

2

1

1

N

n

N

n

N

n

N

n

N

n

N

n

i

i++++=

Damage < 1.0

Stochastic loading


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Stress history can be converted to blocks of constant

amplitude loadings (using counting method)

amp

log N

stress histogram

Time

Stress history

Information about sequence lost

Rainflow counting


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Two parametric method: Range and mean

Display series of extremes with vertical time axis

Drip rain from each extreme, stop at a larger extreme

Start and stop combine to one stress cycle

Rainflow counting


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Established method

Several equivalent algorithms exist

Reservoir method

Intermediate extremes in groups of 4

Principle based on stress-strain hysteresis loops:

Frequency domain approach


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Rayleigh: Theoretical, narrow band signals:

Dirlik: Empirical, wide band signals:

Used for spectra of random, Gaussian, stationary processes

Lifetime fatigue analysis


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Hs\ \ Tz 0- 1s 1- 2s 2- 3s 3- 4s 4- 5s 5- 6s 6- 7s 7- 8s 8- 9s total

5.5- 6m 0.0

5- 5.5m 0.08 0.1

4.5- 5m Idling, high: Vw>=Vcut_out 0.04 0.3 0.3

4- 4.5m 0.3 0.08 0.4

3.5- 4m lumpedseastate 0.7 0.7

3- 3.5m 0.7 0.7

2.5- 3m 0.6 0.04 0.7

2- 2.5m 0.2 0.2

1.5- 2m idling, low: Vw


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Integrated system dynamics


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0

10

20

30

40

50

Equivalent

bendingmom

ent

wind

wave

windloading

waveloading

super-position

separate analyse

combinedloading

integrated

analysis

combined

Offshore Windfarm Hfd 6

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