energies
ArticleNumerical Prediction of Tower Loading of Floating Offshore
Wind Turbine Considering Effects of Wind and Wave
Atsushi Yamaguchi, Subanapong Danupon and Takeshi Ishihara *Department of Civil Engineering, The University of Tokyo, Tokyo 113-8656, Japan;
atsushi@bridge.t.u-tokyo.ac.jp (A.Y.); danupon@bridge.t.u-tokyo.ac.jp (S.D.)* Correspondence: ishihara@bridge.t.u-tokyo.ac.jp

Citation: Yamaguchi, A.; Danupon,
S.; Ishihara, T. Numerical Predictionof Tower Loading of Floating
Offshore Wind Turbine Considering
Effects of Wind and Wave. Energies
2022, 15, 2313. https://doi.org/

Abstract: For the design of floating offshore wind turbines (FOWT), all the load cases need to be
calculated by using a coupled model of wind turbine and platform, while the uncoupled approach
will help to reduce the number of simulations for the design and optimization of floating offshore
wind turbines. In this study, the effects of the wind and wave actions on the tower loading of a FOWT
were investigated and an uncoupled approach for the load calculation was proposed and verified bycomparing with the result of coupled simulation. First, the effect of elastic platform was consideredby tuning the Young’s modulus of the tower material when rigid platform model was used in theanalysis. The effect of wind and wave actions on the loading of the tower was then investigated. It
was found that the difference of the wind load between fixed and floating wind turbines is observed
only in the mean component and can be predicted by considering the hydrostatic stiffness of theplatform and mooring stiffness. The standard deviation of the fore-aft tower moment increased as
the significant wave heights increased when the mean wind speeds and peak wave periods were
fixed. This is caused by the increase of the inertia force induced by the pitch and surge motions of theplatform and the increase of the fluctuating pitch angle. On the other hand, the standard deviation of
the fore-aft tower moment decreased as the peak periods increased when the mean wind speeds andsignificant wave heights were fixed. The increase of the peak period caused the decrease of the pitchand surge accelerations of the platform and results in the decrease of the inertia force. Finally, thetower loading in extreme sea states during power production was carried out by using the proposed
uncoupled approach and the results showed good agreement with those by the coupled approach,and the simulation time was reduced to 1/40.

10.3390/en15072313
Academic Editor: Amrit
Shankar Verma

Keywords: numerical prediction of tower loading; floating offshore wind turbine; wind actions;wave actions; coupled approach; uncoupled approach

Received: 18 February 2022
Accepted: 20 March 2022
Published: 22 March 2022

1. Introduction

Publisher’s Note: MDPI stays neutral

Offshore wind is a rapidly maturing renewable energy technology and significant
research has been carried out [1–6]. Among them, substantial offshore wind energy resource
is located in deep water where use of conventional bottom-mounted wind turbines is not
feasible, and floating offshore wind turbines (FOWT) are needed [7,8] and several kinds of
FOWT concepts have been proposed [9,10]. However, the loading on FOWT may increasesignificantly compared to the bottom fixed wind turbines mainly due to the large motionof the platform. Robertson and Jonkman [11] showed that the ultimate tower base bending
moment of a wind turbine on a semi-submersible platform during operation increases
about 30% compared to the bottom fixed turbines. However, there are no clear explanations
on how the wind and wave actions affect the loading of FOWT tower. Therefore, for thedesign verification of FOWT, all the load cases need to be calculated by using coupledmodel of wind turbine and platform, including the aerodynamics of the rotor and tower aswell as the hydrodynamics and mooring systems according to IEC TS 61400-3-2 [12]. If thewind and wave induced loads can be accurately predicted by the uncoupled approach, itwith regard to jurisdictional claims inpublished maps and institutional affiliations.

Copyright: © 2022 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms andconditions of the Creative Commons
Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

Energies 2022, 15, 2313. https://doi.org/10.3390/en15072313

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will help to reduce the number of simulations for the design and optimization of floating
offshore wind turbines.
When modeling FOWT for dynamic simulation, the tower first mode frequency isimportant because it should be carefully chosen so that it does not cause resonance withthe frequency of 1P (rotor rotation frequency) or 3P (blade passing frequency). When thewind turbine is installed on floating platform, the elasticity of the platform and non-fixedboundary condition may cause the increase of the tower first mode frequency and resonancewith the blade passing frequency. Zhang and Ishihara [13] proposed to adjust the lengthof the tower and the predicted frequency showed good agreement with the measurement.
However, this method is difficult to apply for FOWT. Another problem is the validationof the numerical model for FOWT by using the water tank tests. Robertson et al. [14,15]
concluded that any state-of-the-art dynamic simulation model of FOWT underestimates
the low frequency response compared to the water tank test. However, water tank tests
may have several problems, such as the effect of sensor wiring on the platform motion
and the appropriateness of the scaling of the turbulent wind field. The validation of thenumerical model by using full scale measurements is needed.
The characteristic of wave effect on the tower loading is also an important issue.
Kvittem and Moan [16] pointed out that the fatigue load decreases with the increase of thepeak wave period. Long et al. [17] showed that the standard deviation of the tower base
moment increases as the wave height increases. However, the mechanism has not beenclarified yet.
The combination of the wind and wave effects is a key issue when uncoupled simulation approach is used. Xu and Ishihara [18] proposed analytical formulae for the calculationof the standard deviation of fore-aft tower bending moment based on the surge and pitch
motions of platform, in which the tower bending moments caused by surge and pitch
motions were calculated separately, then combined by using the complete quadratic combination (CQC). However, the correlation between surge and pitch motions may be different
from that obtained by the CQC approach which is widely used in the building engineering.
In this study, the numerical models of floating offshore wind turbine by using both
coupled and uncoupled approaches are discussed in Section 2. The characteristics of thewind and wave actions on the FOWT are then investigated by using numerical simulations,and the comparison of coupled and uncoupled approaches is performed for extreme sea
states during power production in Section 3. The conclusions are summarized in Section 4.
2. Numerical Model and Load Calculation
The modeling of the FOWT for the dynamic simulation, including control parametersand hydrodynamic properties are described in Section 2.1. The prediction of tower moment
induced by the platform motion is then explained in Section 2.2. Finally, an uncoupledapproach is proposed in Section 2.3.
2.1. The Load Calculation by Using Coupled Model
The dynamic simulation tool of wind turbine FASTv8 [19] was used for the coupledsimulation. In this simulation, the aerodynamic loading on the rotor blades was consideredby using blade element momentum (BEM) theory. The gravity force and the centrifugal
force were considered in the numerical simulation. Equation (1) expresses the motion of
the system [20].
..
.
Mx + Cx + Kx = fG + fB + fH + fM + fA
(1)
.

..

where M, C, and K are mass, damping, and stiffness matrices, respectively. x, x, and x
stand for displacement, velocity, and acceleration vector of each degree of freedom. fG ,fB , fH , fM , and fA indicate the gravitational, buoyancy, hydrodynamic, mooring line, andaerodynamic force vectors, respectively.
A standard downwind turbine model proposed by the University of Tokyo during the
IEA Task 40 project (UWT80d-2.0) was used to simulate the behavior of the HWT80-2.0.
Table 1 shows the dimension and weight of UWT80d-2.0. For the control, a conventional

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variable-speed, variable blade-pith-to-feather configuration was used [21,22]. The control
parameters used in this study are summarized in Table 2.
Table 1. Description of the dimension and weight of UWT80d-2.0.
Dimension and Weight

Value

Dimension of the nacelle

Length × Width × Height = 11.5 × 3.5 × 4.9 m

Mass of the nacelle

75,168 kg

Length of blade

39 m

Mass of rotor

41,038 kg

Table 2. Summary of control parameters.
Control Parameter

Value

Optimal mode gain for torque control

0.1717 Nm/(rad/s)2

Minimum generator speed

1087.8 rpm

Optimum mode maximum speed

1920.8 rpm

Pitch PI control proportional gain

0.0169 s

Pitch PI control integral gain

0.0090

Rated power

2 MW

Rated torque12,083.6 Nm

Rated generated speed

1715 rpm

The hydrodynamic force is based on the potential flow theory and computational fluid
dynamics (CFD). Ansys AQWA was used for the potential flow analysis and Ansys Fluent
was used for the computational fluid dynamics. The added mass matrix and the radiation
damping matrix, and wave excitation force vectors were based on the potential flow theory.
The viscous damping coefficients were based on the CFD simulation [23]. It was notedthat the viscous damping coefficients were the functions of KC number. In this study, KC
number was assumed to be 4.62 for the surge and sway directions and 0.9 for the heave
direction. The components using the drag coefficients in simulation are shown in Figure 1
and their values are summarized in Table 3.

Figure 1. Components of the semi-submersible platform.

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Table 3. Drag coefficients Cd for each component of platform in Figure 1.
Components of Platform

Cd in the Normal Direction

Cd in the Axial Direction

C and Br

0.65

0

Hp

0.65

17.5

Hp-C

0.65

4.0

Pn-x

2.2

0

Pn-y

7.0

0

The analysis of the mooring lines was performed by using the Mooring Analysis
Program (MAP++) based on the steady-state forces on a multi-segmented, quasi-static(MSQS) mooring line concept [24]. The configuration of the mooring line is shown in
Figure 2 and the properties of the mooring lines are summarized in Table 4.

Figure 2. Mooring line configuration.
Table 4. Description of mooring line properties.
Mooring Line Properties

Value

Number of mooring lines

6

Angle between adjacent lines

60 degrees

Depth to anchors below SWL

120 m

Depth to fairleads below SWL

13.3 mUpstretched mooring line length

680 m

Equivalent mooring line diameter

0.249 mEquivalent mooring line mass density

382.00 kg/m

Equivalent mooring line mass in water

332.08 kg/m

Equivalent mooring line extensional stiffness

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2.2. Prediction of Tower Moment Induced by Platform Motion
The cause of standard deviation of the fore-aft tower bending moment of FOWT wasinvestigated by using the result of the numerical simulation. The fluctuating moment wascontributed to by fluctuating wind and fluctuating platform motion which was mainly
caused by wave. In this section, only the moment induced by the platform motion is
examined to consider the effect of wave height. The platform motion caused the fore-afttower bending moment through three mechanisms below.
The first one is the tower moment Mθy caused by the pitch rotation. When the platform
had a pitch angle, the whole system inclined and the gravity force caused the moment. The
pitch angle fluctuation caused the fluctuation of the tower moment. The tower and therotor nacelle assembly (RNA) were modeled as a lumped mass, as shown in Figure 3. Mθyat the node i can be calculated from the pitch angle θy of platform as follows:NMθy (i ) = ∑ Mk g(hk − hi ) sin θy



(2)

k =i

where Mk is the mass at the node k, hi is the height of node i measured from the center ofgravity of the system.

Figure 3. Lumped mass model of floating wind turbine.

The second one, Mθ.. , caused by the angular acceleration in the pitch direction can bey..

calculated from the pitch angular acceleration θ y as:N..

Mθ.. (i ) = − ∑ Mk (hk − hi )hk θ y
y

(3)

k =i

The last one, Mx.. , is the bending moment caused by the surge acceleration of theplatform and can be calculated by using Equation (4).
N..

Mx.. (i ) = − ∑ Mk (hk − hi ) x

(4)

k =i

The total fore-aft tower bending moment induced by the platform motion MF (i ) canbe defined as the sum of the three moments mentioned above.
MF (i ) = Mθy (i ) + Mθ.. (i ) + Mx.. (i )y(5)Energies 2022, 15, 2313

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The standard deviation of Mθy (i ), Mθ.. (i ), and Mx.. (i ) can be calculated from the stanyh .. i 
dard deviation of platform pitch angle σ θy , pitch angular acceleration σ θ y and surge
 .. 
acceleration σ x as follows by assuming sin(θ ) ≈ θ.
h
i
N
 
σ Mθ y ( i ) = ∑ Mk g ( h k − h i ) σ θ y(6)h .. iNσ Mθ ( i ) = ∑ Mk ( h k − h i ) h k σ θ y(7)N .. 
σ[ Mx.. (i )] = ∑ Mk (hk − hi )σ x

(8)

k =i





..

y

k =i

k =i

2.3. The Load Calculation Based on the Uncoupled Approach
Since the mean fore-aft tower base moment is strongly affected by wind action, themean component can be estimated by using the numerical simulation for the bottom
mounted wind turbine with additional moment caused by the pitch motion of platform.
This additional moment can be calculated by using the mean pitch angle of the system θ y .
The total mean moment M(i ) at the node i can be calculated as follows:N

M (i ) = Mf (i ) + ∑ Mk g(hk − hi ) sin θ y



(9)

k =i

where Mf (i ) is the mean fore-aft moment at the node i for the bottom mounted windturbine, and θ y is the mean pitch angle of the system which can be calculated by solving
Equation (10).

F T L + Mg sin θ y LCG = (K H + K M )θ y
(10)
where F T is the mean thrust force, L is the distance between the center of gravity of theplatform and the nacelle, LCG is the distance between the center of gravity of the systemand the center of gravity of the tower and the RNA, and K H and K M are the hydrostaticand mooring stiffness in the pitch direction, respectively. By assuming sin(θ ) ≈ θ, themean pitch angle θ y can be calculated as follows.
θy =

FT L
(K H + K M ) − MgLCG(11)

The pitch component of the hydrostatic stiffness K H can be calculated by using Equation(12).
K H = ρgx

y2 dA + ρgV0 zGB

(12)

A

where ρ is the water density, A is the cross section of the platform at the water line, y isthe distance from the pitch axis, V0 is the volume of the platform in the water, and zGB is
the distance between the center of gravity and the center of buoyancy. The value of themooring stiffness K M is discussed in Section 3.4.
The maximum fore-aft tower bending moment can be calculated as follows:
Mmax (i ) = M(i ) +q( gwind σwind (i ))2 + ( gwave σwave (i ))2

where M(i) is the mean tower bending moment.

(13)

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The peak factor of the wind load, gwind , is modeled by fitting the simulated peakfactor as:
−0.3 sin π · vin −vh + 3.3(vin < vh ≤ vr )vin −vr
(14)
gwind =v−v
−1.1 sin 0.4π · h r + 4.4 (vr < vh ≤ vout )vout −vr
where vin is the cut-in wind speed, for this case it is 4 m/s. vh is the hub-height wind speed.
vr is the rated wind speed and is 13 m/s, vout is the cut-out wind speed and is 25 m/s. The
standard deviation σwind (i) is the standard deviation of wind loading and can be calculatedby the bottom fixed wind turbine simulation.
The standard deviation σwave (i) is the standard deviation of loading due to the platform
motion by wave and can be calculated by the simulation without wind. The peak factor for
the wave loading, gwave , is estimated by using Gaussian process.
gwave =q

2 ln(v0 T ) + p

0.57722 ln(v0 T )(15)where T is the simulation time length. T is 600 s. v0 is the zero up crossing frequency of
tower base bending moment for Gaussian process:v
uR ∞ 2un S(n)dn
v0 = t 0R ∞0 S ( n ) dn

(16)

where n is the frequency, and S(n) is the power spectral density. σb2 , σr2 , and σt2 are thevariance of the background part, resonant part at the platform pitch motion frequency, andtower resonant part, respectively. In general, there are three peaks corresponding to wave
peak frequency n p , pitch natural frequency nr and tower first natural frequency nt in the
power spectral density of the tower base moment. Since σs2 and σt2 are negligible small
compared to σb2 , the zero up-crossing frequency becomes v0 = n p approximately.
v
u 2 2
u n p σ + n2r σr2 + n2t σt2bv0 ≈ t= np
σb2 + σr2 + σt2(17)

3. Prediction of Tower Bending Moment of FOWT by Coupled andUncoupled Approaches
In this study, the 2 MW offshore wind turbine at Fukushima Floating Offshore Demonstration Project [18] is used to validate the coupled and uncoupled approaches. The windturbine is installed on a semi-submersible platform with six catenary mooring lines. The
detailed information of onsite measurement and metocean conditions are described in
Section 3.1. The effect of flexibility and boundary condition of platform on the tower
first mode frequency is investigated in Section 3.2. The fore-aft tower bending moments
predicted by using the coupled and uncoupled approaches are discussed in Section 3.3. The
effect of wind action is discussed in the low wave height condition and the effect of wave
action is then investigated in the low wind speed condition. Finally, the tower bending
moments in the extreme sea states condition during power production are investigated andthe predicted tower bending moments by both approaches are compared in Section 3.4.
3.1. Onsite Measurement and Metocean Conditions
A 2 MW wind turbine (Hitachi HTW-2.0 80) with semi-submersible platform andcatenary mooring system, Fukushima Mirai, installed at offshore Fukushima, is used in thisstudy. As show in Figure 4a. The tower bending moment is measured by using the strain
gauges installed on the tower of the turbine, and the platform motion is measured by using
accelerometers, gyros and RTK-GPS sensors.

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Figure 4. Overview of 2 MW floating wind turbine and measurement systems. (a) 2 MW windturbine (Fukushima Mirai), (b) floating substation (Fukushima Kizuna).

A floating substation, Fukushima Kizuna, was installed next to the 2 MW wind turbine
and equipped with metocean measurement devices to measure environmental conditions [25] as illustrated in Figure 4b. Wind speed and directions were measured by using
cup anemometers, wind vanes, and sonic anemometers on the met mast, and a doppler
lidar on the main deck. Wave height and period were measured by using the wave meter
installed on the hull of the substation.
The calibration of zero-point of pitch and role angle was performed by using themeasurement data of nacelle rotation test under calm weather condition. Sixteen strain
gauges were installed on the tower, at 25.9 and 63.1 m above mean sea level, to measure thetower bending moment at the tower bottom and the top. At each height, 8 strain gauges
were installed, as shown in Figure 4a.
Figure 5 illustrates the wind and wave conditions at the Fukushima site. The wind speed
frequency distribution is shown Figure 5a and the prevailing wind directions in Figure 5b
are north-north-westerly and southerly. The wave height frequency distribution is plottedin Figure 5c and the prevailing wave direction in Figure 5d is east-south-easterly. Figure 5e
depicts the relationship between significant wave height and peak wave period, which showsa large variance since the Fukushima site faces to the Pacific Ocean. The turbulence intensity
was lower than that measured at onshore sites as shown in Figure 5f. It was found thatthe value of Iref = 7 % was the most appropriate when normal turbulence model (NTM) in
IEC61400-1:2019 [26] was fitted to the bin average value of the turbulence intensity.
3.2. The Effect of Flexibility and Boundary Condition of Platform on the Tower First Mode
Frequency
The FEM models with beam elements were built to investigate the effect of platform
flexibility and boundary condition on wind turbine tower loads. Two boundary conditions
at the bottom of the center platform, fixed and free condition, and two different elasticitiesof the platform, rigid and flexible, were considered. The rigid platform was achieved byassuming that the young modulus of element was relatively high. For the flexible platform,
the actual dimension and properties of platform were used. The rotor and nacelle weremodeled as a concentrated mass with an inertia moment.

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Figure 5. Metocean condition at the Fukushima site: (a) wind speed frequency distribution; (b) windrose; (c) wave height frequency distribution; (d) wave rose; (e) relationship between peak wave
period and significant wave height; (f) turbulence intensity as function of mean wind speed.

Eigenvalue analysis was performed by ABAQUS [27] and the tower natural frequencies were obtained for each model. Table 5 illustrates the natural frequencies of tower firstmode from four FEM models and also the measured frequency. It is clear that the first mode
eigenfrequency predicted by the FEM model with free boundary condition and flexible
platform shows good agreement with the measured frequency.

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Table 5. First mode natural frequency.
Case

Boundary Condition

Platform Flexibility

First Mode
Eigenfrequency

1

Fixed

Rigid

0.773 Hz

2

Fixed

Flexible

0.619 Hz

3

Free

Rigid

0.740 Hz

4

Free

Flexible

0.665 Hz

Measurement

0.664 Hz

Many wind turbine simulation tools, such as FAST, use rigid platform model. Therefore, the tower stiffness of the wind turbine model with rigid platform should be tuned byusing the results of the FEM eigenvalue analysis. The tuning of the tower stiffness can beachieved by tuning the Young’s modulus by using Equation (18) instead of adjusting thelength of the tower [13].
f 2 −Flexible
ET = Free
EO(18)
2
f Free−Rigidwhere EO is the original Young’s modulus and ET is the tuned Young’s modulus, which isused for the dynamic simulation. Two dynamic simulations were performed by using theoriginal Young’s modulus EO and the tuned one ET at 9:40–9:50 a.m. on 16 March 2015 inparked condition. The wind speed was 2.7 m/s, and the significant wave height and thepeak wave period were 1.2 m and 8.0 s. The predicted power spectral density of tower base
moments is shown in Figure 6. The simulation with the tuned Young’s modulus shows
better agreement with the measurement and the overestimation of the tower first mode
frequency was improved.

Figure 6. Power spectral density of fore-aft tower base moment in parked condition.

3.3. The Characteristics of Wind and Wave Actions
The characteristics of wind and wave actions are investigated by using coupled anduncoupled approaches. The mean value and the standard deviation of the fore-aft bending
moment at the tower top and the bottom are obtained from the dynamic simulations andcompared with the measurement.

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11 of 18First, the characteristic of the wind action was investigated. To minimize the effectof the wave, the low wave height case with Hs = 0.5 m was chosen and the wave period
was fixed to 10 s. For the measurement data, the mean value of all the data of which thesignificant wave height was between 0.25 and 0.75 m, and the peak wave periods between
8.0 and 12.0 s were plotted. The Kaimal spectrum for wind and JONSWAP spectrum forwave were used in the simulation. The predicted mean value and standard deviationof the fore-aft tower bending moments in Figure 7 showed good agreement with themeasurements at the tower top and base. The peak values near the rated wind speed wereobserved at the tower base, while these peaks were not obvious at the tower top. These
characteristics were similar to those obtained by Yamaguchi et al. [28] for a bottom fixedoffshore wind turbine at the Choshi site.

Figure 7. Effect of wind speed on (a) mean and (b) standard deviation of the fore-aft bending momentat the tower top and base.

The effect of wave height on the wind turbine tower loadings were then investigated.
In this study, only fore-aft bending moment was investigated, which is usually the dominantfactor in the design of the tower in DLC 1.6, and relevant platform motions such as pitchand surge were discussed. Figure 8 shows the mean and the standard deviation of thefore-aft tower bending moments as function of the significant wave height. The mean windspeed was fixed to 9.0 m/s and the peak wave period is fixed to 10.0 s. For the measurement
data, the mean value of all the data of which the mean wind speed was between 8.0 and 10.0
m/s and the peak wave periods between 8.0 and 12.0 s were plotted. The increase of the
wave height did not cause the increase of the mean tower bending moment. On the other
hand, the standard deviation of the tower bending moment increased as the significant
wave height increased. This conclusion was same as that obtained by Long et al. [17].

Figure 8. Effect of significant wave height on (a) mean and (b) standard deviation of fore-aft tower
bending moments at the tower top and base.

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The contribution of platform motion to the standard deviation of tower bending
moments for different significant wave height was investigated by using the dynamic simulations and Equations (5)–(8). Figure 9 shows the standard deviation of the fore-afth toweribending moment induced by the total platform motion σ[ MF (i )], pitch angle σ Mθy (i ) ,pitch angular acceleration σ Mθ.. (i ) , and surge acceleration σ[ Mx.. (i )] as functions of sigy

nificant wave height. As discussed above, the total standard deviation increased as thewave height increased, which is caused by the fact that all of the platform motions increase
with the significant wave height.

Figure 9. Standard deviation of fore-aft tower bending moments as function of significant wave
height at (a) tower base and (b) tower top.

As shown in Figure 10, the mean tower bending moments were almost unaffected by
the wave period at the tower top and base. However, the standard deviation of the tower
bending moment decreased with the increases of the peak wave period at the tower baseand results in the decrease of fatigue load as mentioned by Kvittem and Moan [16].

Figure 10. Effect of peak wave period on (a) mean and (b) standard deviation of fore-aft tower
bending moments at the tower top and base.

The contribution of platform motion to the standard deviation of fore-aft tower bending moments for different peak wave period are also investigated to clarify the reason ofthis decrease by using the dynamic simulations and Equations(5)–(8) as shown in Figure 11.
It is clear that this decrease was caused by the decrease of σ Mθ.. (i ) and σ[ Mx.. (i )] sinceythe pitch and surge accelerations decrease when the peak period increases, and this causes
the reduction of the total standard deviation of the fore-aft tower bending moment.

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Figure 11. Standard deviation of the fore-aft tower bending moment as function of wave period:(a) tower base; (b) tower top.

3.4. Comparison between Coupled and Uncoupled Approach for the Extreme Sea States
The DLC 1.6 was the one of the most significant design load cases defined by IEC
TS 61400-3-2 [12], which is for the extreme sea state during power production. Notethat the wind turbine was in operation in this load case. For the wind condition, thenormal wind turbulence model was considered. For the wave height, the unconditional
extreme significant wave height, Hs50 , with a recurrence period of 50 years was used as aconservative value instead of the significant wave height, Hs,SSS (V), for each severe sea
state. For the wave period, the designer shall take account of the range of wave period
appropriate to each extreme wave height. In this study, the wind and wave misalignment
was not considered because the wind and wave co-directional case causes the maximum
load in this load case as mentioned IEC TS 61400-3-2 [12].
In this study, the significant wave height of 6.1 m and three wave periods of 7, 10, and13 s were chosen as an example of DLC 1.6. Table 6 shows the environmental conditions
for these extreme sea states. The coupled and uncoupled simulations were performed forthese conditions.
Table 6. The environmental conditions for the extreme sea states.
Wind-Wave MISALIGNMENT(deg.)

Significant Wave
Height (m)Wave Peak Period(s)Mean Wind Speed(m/s)

Iref (%)

0

6.1

7.0, 10.0, 13.0

4–24

7

For the uncoupled simulation, the mooring stiffness K M in Equation (10) needed tobe identified. This value can be estimated by linearizing the relationship of pitch angle ofplatform and restoring moment caused by the mooring line by using analytical solution of thecatenary. Figure 12 shows this relationship between the restoring pitch moment from mooringlines and pitch angle. The mooring stiffness was calculated from the slope as 22.69 MNm/rad.
On the other hand, the hydrostatic stiffness K H in Equation (12) was 496.7 MNm/rad, whichmeans approximately 4% of the pitch stiffness comes from the mooring line and 96% from thehydrostatic stiffness of the platform.
Figure 13 shows the power spectrum density of the tower base fore-aft moment in
extreme sea state during power production, in which three peaks are clearly observed. The
first peak in low frequency region was caused by the background component of wind load,
the second one corresponded to the wave frequency, the third one was due to the rotor
rotation frequency (1P) and tower first mode frequency which are caused by the resonancewith wind. These three peaks were separated each other and implies each component canbe evaluated separately.

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Figure 12. The relationship between the restoring pitch moment from mooring lines and pitch angle.

Figure 13. Power spectrum density of the fore-aft tower base moment in extreme sea stated during
power production.

In the uncoupled simulation, it was assumed that there was no correlation between
the fluctuating wind and wave actions as mentioned in Xu and Ishihara [18]. Figure 14ashows the correlation coefficient ρww between the fore-aft tower base moments caused bywind and wave obtained from the coupled simulations with Tp = 10 s. It indicates that theassumption of no correlation is reasonable. Figure 14b shows the correlation coefficientsρ xθ between the platform pitch motion induced fore-aft tower base moment, Mθy + Mθ.. ,yas shown in Equations (2) and (3), and the platform surge motion induced one, Mx.. , asshown in Equation (4). It was found that these correlation coefficients were negative. Thisis natural as the center of the platform pitch motion is located between the center of gravityof the system and center of buoyancy of the system, which means the surge motion which
is defined at the center of gravity of the system is always negatively correlated with thepitch motion. On the other hand, the CQC method [29] for the calculation of the correlation
between elastic modes of structure shows positive values and results in the overestimationof the fluctuating tower bending moments.

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Figure 14. The correlation coefficient of fluctuating fore-aft tower base moment. (a) Correlation between
wind and wave induced loads, (b) correlation between pitch and surge motion induced loads.

The proposed peak factor as shown in Equations (14) and (15) also needs to be validated. Figure 15a shows the peak factors for wind actions obtained from the simulation ofbottom mounted wind turbine and Equation (14). Figure 15b shows the peak factors forwave action obtained from the platform motion of the coupled simulation and Equation (15).
The proposed peak factors show good agreement with those from the coupled simulations.

Figure 15. Comparison of the peak factors of fore-aft tower base moment: (a) wind load, (b) wave load.

Finally, the extreme load of DLC 1.6 in IEC TS 61400-3-2 [6], in which the wind turbine
is in operation, was calculated by using the coupled and uncoupled approaches. The meanvalue and the maximum value of the fore-aft tower bending moment at the tower base andthe tower top are shown in Figure 16. It was found that the values from the uncoupledapproach showed good agreement with those from the coupled one.
The number of simulations can significantly be reduced by using the proposed uncoupled approach. According to IEC TS 61400-3-2 [6], the coupled simulations need to be
performed under each combination of winds and waves, and at least six realizations ofeach wind and wave combination should be considered by using different random seeds toreduce the uncertainty in the estimation of the maximum value. The total number of thesimulation was then 6 seeds × 12 wind speeds × 3 wave periods, which in total was equal
to 216 cases. For each case, 1 h simulation was required. Therefore, in total the required
simulation time length was 216 h calculated from 216 cases of 1-h simulation. When theuncoupled approach was used, the calculation of wind and wave included loads could
be performed separately. The wind-induced load could be estimated by the simulationof the bottom fixed wind turbine, in which case only a 10-min simulation was required
for each wind speed. The wave induced load can be estimated by using 1 h simulationof only three wave period conditions. Therefore, the total number of the calculation was
equal to 12 wind cases of 10 min simulation plus 3 wave cases of 1 h simulation. In total,

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the required simulation time length was 12 cases × 1/6 h + 3 cases × 1 h, which is equal to
5 h. This means that the uncoupled approach can significantly reduce simulation time to
1/40 compared with the coupled approach.

Figure 16. The fore-aft tower bending moment at the tower base and the top during power production
under severe sea state. (a) Mean tower bending moment, (b) maximum tower bending moment.

4. Conclusions
In this study, the effects of wind and wave actions on FOWT are investigated and an
uncoupled approach for the load calculation is proposed. Following conclusions are obtained.
1.

2.

3.

4.

The elasticity and the bottom boundary condition of the platform had to be consideredto accurately predict the tower first mode frequency. When performing the dynamic
simulation of FOWTs by using rigid platform model such as FAST, the effect of theelasticity of platform could be considered by tuning the Young’s modulus of the tower
material to fit the tower first model frequency obtained by the finite element method.
The predicted power spectrum density of the fore-aft tower base moment by using
the proposed method shows good agreement with the measurement;
The difference of the wind load between the bottom fixed wind turbine and floating
wind turbine was observed only in the mean component and can be corrected byconsidering the hydrostatic stiffness of platform and mooring stiffness, since thefluctuating wind load of wind turbine tower on semi-submersible platforms did notshow difference from that on fixed foundations;
The standard deviation of the fore-aft tower moment increased as the significant
wave heights increased when the mean wind speed and peak wave period were
fixed. On the other hand, the standard deviation of the fore-aft tower bending
moment decreased as the peak wave periods increased when the mean wind speed
and significant wave height were fixed. It was found that the increase of the significant
wave height causes the increase of the pitch and surge motions of the platform
resulting in the increase of the fluctuating fore-aft tower moment, and the increase of
the peak wave period caused the decrease of the pitch and surge accelerations of theplatform resulting in the decrease of the fluctuating fore-aft tower moment;
The predicted tower loading in extreme sea states during power production by the proposed uncoupled approach show good agreement with those by the coupled approach,and the simulation time was reduced to 1/40 for FOWTs on semi-submersible platforms
because the effect of wind action and wave action can be calculated separately.

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Author Contributions: Conceptualization, A.Y. and T.I.; methodology, A.Y. and T.I.; data curation,
S.D.; investigation, A.Y., S.D. and T.I.; formal analysis, S.D.; visualization, S.D; writing—originaldraft, A.Y.; writing—review and editing, T.I.; supervision, T.I.; project administration, T.I.; funding
acquisition, T.I. All authors have read and agreed to the published version of the manuscript.
Funding: This research received no external funding.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: Data sharing not applicable.
Acknowledgments: This research is carried out as a part of the Fukushima floating offshore windfarm demonstration project funded by the Ministry of Economy, Trade, and Industry. The authors
wish to express their deepest gratitude to the concerned parties for their assistance during this study.
Conflicts of Interest: The authors declare no conflict of interest.

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