Stochastic Dynamic Response Analysis of a 10 MW Tension Leg Platform Floating Horizontal Axis Wind Turbine

energies

Article Stochastic Dynamic Response Analysis of a 10 MW Tension Leg Platform Floating Horizontal Axis Wind Turbine

Tao Luo 1,*, De Tian 1, Ruoyu Wang 1 and Caicai Liao 2 1 State Key Laboratory for Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, China; [email protected] (D.T.); [email protected] (R.W.) 2 CAS Key Laboratory of Wind Energy Utilization, Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing 100190, China; [email protected] * Correspondence: [email protected]; Tel.: +10-6177-2682

Received: 2 October 2018; Accepted: 23 November 2018; Published: 30 November 2018

Abstract: The dynamic response of floating horizontal axis wind turbines (FHWATs) are affected by the viscous and inertia effects. In free decay motion, viscous drag reduces the amplitude of pitch and roll fluctuation, the quasi-static mooring system overestimates the resonant amplitude values of pitch and roll. In this paper, the quasi-static mooring system is modified by introducing linear damping and quadratic damping. The dynamic response characteristics of the FHAWT modified model of the DTU 10 MW tension leg platform (TLP) were studied. Dynamic response of the blade was mainly caused by wind load, while the wave increased the blade short-term damage equivalent load. The tower base bending moment was affected by inclination of the tower and the misaligned angle βwave between wind and wave. Except the yaw motion, other degrees of freedom motions of the TLP were substantially affected by βwave. Ultimate tension of the mooring system was related to the displacement caused by pitch and roll motions, and standard deviation of the tension was significantly affected by the wave frequency response. Under the action of wave load, the viscous drag would stimulate the mooring system and increase the resonance of the platform motion.

Keywords: ﬂoating horizontal axis wind turbines; dynamic response analysis; tension leg platform; mooring system; viscous drag

1. Introduction In order to cope with the increasingly serious problems of fossil energy shortages and environmental pollution, renewable energy technologies have developed rapidly in recent years. Among the various types of renewable energy, wind energy has the most promising prospects and has received wide public attention [1,2]. So far, most wind farms have been deployed onshore due to the relatively lower cost of construction, operation, and maintenance [3]. However, offshore wind farms have higher wind speeds and smaller turbulence, and they are also less sensitive to space utilization, noise constraints, visual pollution and regulation issues. What is more, they can provide more and better green energy than onshore wind farms [4,5]. Although the cost of construction, operation and maintenance of offshore wind farms is relatively higher compared to onshore wind farms, as more and more research is being invested in offshore projects, as the advantages of offshore wind farms are gradually emerging. The substantial increment of offshore wind power capacity in the future may meet the need of the demand for green energy [4]. In shallow water areas (<50 m), offshore wind turbines, such as monopiles, gravity-based structures, jackets and buckets, are usually supported by bottom-ﬁxed foundations [6,7]; when the offshore wind turbines are constructed in deep water areas (>50 m), the ﬂoating support platform has

Energies 2018, 11, 3341; doi:10.3390/en11123341 www.mdpi.com/journal/energies Energies 2018, 11, 3341 2 of 24 more advantages from an economic point of view [8,9]. According to the static stability method, there are mainly three types of FHAWTs: spar type, semi-submersibles, and TLP type [9–12]. The spar-type platform is usually a stable ballast in a small horizontal plane area; the semi-submersible floater neceds a large water line restoring moment to achieve sufficient stability; the TLP type is stabilized by tendons or tightened mooring lines to resists the wave-induced motions, thus reducing generator power variations and reducing the impact to the grid [6]. In the case of wind-wave alignment, both the spar platform and the semi-submersible platform showed large fatigue damage. In contrast, the limited platform motion of the TLP FHAWT could reduce the structural loads on the tower and the blades, resulting in less fatigue damage [13]. FHAWT operates in a complex environment which withstands loads from a variety of sources, including wind, wave, and ocean currents. Considering the mobility of floating platforms, FHAWT is a much more complex system than an onshore wind turbine or a stationary offshore wind turbine. Bachynski et al. conducted a series of studies in order to understand the dynamic response of the FHAWT more accurately [11,13]. According to the design considerations of a TLP FHAWT in deep sea water, they studied the design parameters of the TLP wind turbine which used full coupling simulation to evaluate the motion of the platform and the structural loads of the wind turbine components and mooring line. Significant works on TLP wind turbines had been done by the National Renewable Energy Laboratory and Massachusetts Institute of Technology [14]. Li et al. studied effects of the vertical heave motion, the aerodynamic forces and the quadratic wave forces on a TLP-type wind turbine [15]. Glosten Associates Company has designed PelaStar TLP for water depths ranging from 50 m to 200 m. This platform has the advantages of small displacement, economical to transport and install, low energy cost and capable of supporting 5–10 MW wind turbines [16]. Sant et al. conducted an experiment on TLP wind turbines, compared the power coefficient measured by the experiment with the power coefficient predicted by three independent models, and studied influences of the platform surge motion on the time average power coefficient [17]. Nihei et al. conducted a number of model tests to determine stochastic dynamic performances of three floating wind turbines on the Spar platform, TLP and semi-submersible platforms, respectively, and concluded that the TLP model showed the best performance [18]. However, due to the scale effect, the viscosity phenomenon cannot be accurately simulated in the model test. The dynamic response of the TLP FHAWT depends on several factors such as the aerodynamic loads on the wind rotor, the hydrodynamic loads on the floating platform, the recovery effects of the mooring system, and the structural characteristics of the wind turbine and floating platform [19]. Viscous drag and inertia effects are two important factors affecting the dynamic response of FHAWT, approximate mooring systems simulated by quasi-static mooring lines (i.e., ignoring inertial effects and viscous drag) overestimates the pitch resonant amplitude values to some extent [20]. Farrugia’s research showed a linear relationship between the amplitude of the surge velocity and the amplitude of the aerodynamic load response [21], which indicated that the aerodynamic load was affected by the surge motion [22]. The experimental results of Stewart et al. showed that the quadratic damping caused by viscous drag played an important role in the low-frequency zones where the radiation damping disappears [23]. Most studies assumed that the mooring system is a quasi-static system, in order to better predict the dynamic response of FHAWT, this paper considered the inertial effect and viscous drag in the mooring system and corrected the quasi-static mooring system. The stochastic dynamic response analysis of the modified 10 MW TLP FHAWT is carried out to understand the operating law and load characteristics of the TLP FHAWT more accurately. Most of the studies on FHAWT dynamic analysis are limited to the environmental conditions in which wind waves are assumed to have the same direction of propagation. However, according to observational data, although there is less than 5% of the incident that the angle between wind and wave is greater than 60 degrees, the angle can usually reach 30 degrees [24]. Wind and waves may be significantly misaligned, especially under stable atmospheric conditions [25]. Barj et al. [26] observed that the spar-type FHAWT wind-wave misalignment could increase the extreme side-tower loads Energies 2018, 11, 3341 3 of 24 in numerical simulations. In the monopile installed at Bockstigen by Trumars, it was observed that the lateral load was increased under a 90◦ misalignment conditions, but it was difficult to interpret the results due to the lack of information on environmental conditions (ECs) [27]. Aerodynamic and viscous damping are keys to determine the pitch resonance amplitude [20]. When the wave comes from a different direction with the wind direction, the aerodynamic damping is less effective in relieving the wave load [13]. Especially in the extreme case where the wind and wave direction are different from 90◦, because there is no aerodynamic damping, the inertial force generated by the sway motion is likely to cause roll resonance response. It is estimated that the viscous drag and inertia effect of the mooring system would be more obvious at this time. In addition, due to the high stiffness of the mooring system, TLP is susceptible to high frequency excitation, which generates heave resonance and pitch motion, and causes fatigue damage to the mooring system. When the wind and waves misalignment, the hydrodynamic load exceeds the aerodynamic load, which dominates the system response. Therefore, the modified model including viscous drag and inertia effects is used to study the wind and wave misalignment. The structure of this paper is as follows: Section2 introduces the numerical method of fully coupled dynamic analysis and the environmental conditions of wind turbine operation used in TLP FHAWT modeling simulation. Aiming at the problem that the quasi-static mooring system overestimates the surge and pitch motion, a method for modifying the model is proposed. Section3 introduces the structure of the FHAWT and the data parameters used in the modeling and simulation, also corrects the simulation model. Section4 discusses the dynamic response characteristics of TLP FHAWT based on statistical methods and frequency domain analysis methods: (1) Compared the differences in dynamic characteristics of TLP FHAWT and equivalent onshore HAWT; (2) Analyzed the response characteristics of wind turbines with and without waves. Based on the above analysis, the impact of wind-waves misalignment on the turbine is analyzed. The effects of inertial and viscous effects on the TLP wind turbine response are also demonstrated by typical wind and wave misalignment. The conclusions are summarized in Section5.

2. Theories and Methods

2.1. Aerodynamic Modeling Aerodynamic load on the blade is calculated based on the blade element momentum (BEM) theory and the wake influence was calculated by the induction factor [28]. Since BEM theory is originally developed for wind-stabilized wind turbines, the transient wind field should be corrected. Assuming that the pressure/momentum loss in the plane of the wind rotor is caused by the air flowing through the rotor blade planar element, the induced velocity resulting from loss of axial and tangential momentum in the flow field can be computed, and the aerodynamic and induced velocity near the rotor can be iteratively determined. The correction factor F is:

2 F = cos−1 e− f (1) π Tip-Loss Model: B(R − r) f = (2) 2r sin ϕ Hub-Loss Model: B(r − R ) f = hub (3) 2r sin ϕ The dynamic stall model [29] is commonly used to solve the transient aerodynamic problems caused by turbulent wind, yawing, rotational speed regulation and pitch regulation. The dynamic stall phenomena of airfoils have been extensively experimentally analyzed and studied [30,31]. In the literature, the B-L mode is widely used in helicopter and wind turbine analysis [3]. When using the Energies 2018, 11, 3341 4 of 24 semi-empirical Gonzalez and Minnema/Pierce models to calculate aerodynamic loads, a reasonable hysteresis can be generated in the normal force, tangential force, and pitching moment coefficient if the model parameters are set appropriately [32]. The potential-flow model uses the analytical potential-flow solution for the surrounding flow of a cylinder to model the tower dam effect on upwind rotors. Aerodynamic loads on the tower are calculated based on tower diameter, drag coefficient, and local relative velocity between free incoming flow and analytical node structure of each tower [32].

2.2. Hydrodynamic Modeling In the simulation calculation, it is assumed that the TLP is a rigid structure and the mooring line is represented by a finite beam element. The loads acting on the TLP include first-order wave forces, quadratic sum-frequency forces and viscous forces. The first-order wave force is processed by the linear potential flow model. The quadratic sum-frequency forces is solved according to the complete quadratic potential flow. The viscous force is provided by the semi-empirical Morison equation [33]. The potential flow model in Sesam/Wadam deduces a first-order wave transfer function, additional mass, and radiation damping [34]. The general form of the complete time-domain equation of motion for coupled wind turbines and supporting platform systems is [35]: .. . Mij(q, u, t)qj = fi q, q, u, t (4) where Mij is the (i, j) component of the volumetric mass (inertia) matrix, which depends nonlinearly .. on the set of system degree of freedom q, control inputs u and time t; qj is the second time derivative of degree of freedom qj; fi is the force function component associated with the degree of freedom qi; The force function fi depends nonlinearly on the system degree of freedom and the first time derivatives . (q and q respectively), as well as the control inputs u and time t. The total external load on TLP are:

Plat f orm .. Hydro Lines Fi = −Aijqj + Fi + Fi (5)

Hydro where Aij is the (i, j) component of the hydrodynamic-added-mass matrix; Fi is the ith component Lines of the applied hydrodynamic load on the TLP associated with everything but Aij; Fi is the ith component of the applied load on the TLP from the contribution of all mooring lines; For each TLP degree of freedom qi, where q1 is surge, q2 is sway, q3 is heave, q4 is roll, q5 is pitch and q6 is yaw. Hydro In hydrodynamics problems, the form of Fi is as follows:

Z t Hydro Wave Hydrostratic Fi = Fi + ρgV0δi3 − Cij qj − Kij(t − τ)qj(τ)dτ (6) 0

Waves The expression of the ﬁrst term Fi on the right-hand side of Equation (6) is:

Z ∞ Wave 1 q 2−Sided jωt Fi = W(ω) 2πSζ (ω)Xi(ω, β)e dω (7) 2π −∞ where W(ω) represents a Fourier transform of a realization of the white Gaussian noise time-series 2−Sided process with zero mean and unit variance; Sζ represents the expected two-sided power spectral density of the wave elevation per unit time; Xi(ω, β) represents the wave-excitation force normalized per unit wave amplitude on the TLP. The combination of the second and third terms on the right-hand side of Equation (6) Hydrostatic ρgV0δi3 − Cij qj represents the load contribution from hydrostatics. ρ is the density of seawater; g is the gravitational acceleration; V0 is the displaced volume of ﬂuid when the TLP is in the undisplaced position; δi3 is the (i,3) component (water depth) of the Kronecker-Delta function (unit matrix), and Energies 2018, 11, 3341 5 of 24

Hydrostatic Cij is the (i, j) component of the linear hydrostatic-restoring matrix. The last term on the R t right-hand side of Equation (6), − 0 Kij(t − τ)qj(τ)dτ is a convolution integral representing the load contribution from wave-radiation damping. For mooring systems approximated by quasi-static mooring lines, the total loads on the TLP from Lines the contribution of all mooring lines Fi would be:

Lines Lines,0 Lines Fi = Fi − Cij qj (8)

Lines Lines,0 where Cij is the (i, j) component of the linearized restoring matrix from all mooring lines; Fi is the ith component of the mooring system load acting on the TLP in the undisplaced position. It can be seen from the above equations that the mooring system ﬁtted with a quasi-static mooring line ignores the inertia effect and the viscous drag, which overestimates the pitch and the surge resonance amplitude to some extent. Because the coupling between axial and transversal motions contributes a lot to the pitch damping [20]. In order to correct the inertia effect neglected in the mooring system, two-thirds of the total dry weight of the mooring mass is added to the quality of the supporting platform. The quadratic damping is calculated using the method proposed by Hoff [36] to correct the viscous drag that is neglected in the mooring system. The pitch motion can be considered as a single degree of freedom system, and is assumed governed by the following form of an equation:

.. . φ + βF(φ) + G(φ) = 0 (9)

. where φ is the pitch angle; F(φ) is the nonlinear pitch damping characteristics; G(φ) is the restoring moment characteristic; β is the assumed small scaling parameter. For linear damping and quadratic damping terms:

. . . .

F(φ) = b1φ + b2 φ φ (10)

For small to moderate pitch angles, a positive cubic term restoring moment characteristic is usually appropriate: 2 2 2 G(φ) = ω0φ 1 + ε φ (11) where ω0 is the undamped natural pitch frequency. The average energy loss rate per cycle, namely the energy loss function L(V) is:

β Z T(V) L(V) = F(φ)φdt (12) T(V) 0 where T(V) is the periodic time of an undamped oscillation. In the calculation of L(V), V is held constant, and the variation of φ(t) thus corresponds to the case of undamped free oscillations. In this case, we can write: q √ U(φ) = V cos θ0 (13)

. √ φ = − 2V sin θ0 (14) R φ where U(φ) = 0 G(ξ)dξ; θ0(t) is a time-dependent phase angle. The ﬁnal energy loss function L(V) is:

h 3/2 i L(V) = β b1VA(V) + b2V B(V) (15) Energies 2018, 11, 3341 6 of 24

where 2 I A(V) = sin2 θ (t)dt (16) T(V) 0 √ 2 2 I B(V) = sin3 θ (t) dt (17) T(V) 0 Perform dimensionless processing on the loss function L(V) to get the function Q(V)

L(V) Q(V) = (18) 2ω0V

In view of the linear and quadratic damping term format, we may convert the loss function to a non-dimensional Q(V) function as:

∗ ∗ Q(V) = b1 A(V) + b2 D(V) (19) where: ∗ βb1 b1 = (20) 2ω0 βb b∗ = 2 (21) 2 2 √ VB(V) D(V) = (22) ω0 ∗ ∗ To ﬁnd the appropriate value for b1 and b2 , assuming that there are N estimates _ _ _ Q(V1), Q(V2), ··· , Q(VN), according to the least squares method:

N _ 2 e = ∑ Q(Vi) − Q(Vi) (23) i=1

∗ ∗ ∗ In order to get the best b1 and b2 , the e is derived and to obtain the simultaneous equation of b1 ∗ and b2 : ∂e ∂e ∗ = ∗ = 0 (24) ∂b1 ∂b2 ∗ ∗ The ﬁnal solutions b1 and b2 : S S − S S ∗ = 3 4 2 5 b1 2 (25) S1S3 − S2 S S − S S ∗ = 1 5 2 4 b2 2 (26) S1S3 − S2 where: N 2 S1 = ∑ A (Vi) (27) i=1 N S2 = ∑ A(Vi)D(Vi) (28) i=1 N 2 S3 = ∑ D (Vi) (29) i=1

N _ S4 = ∑ A(Vi)Q(Vi) (30) i=1 Energies 2018, 11, 3341 7 of 24

N _ S5 = ∑ D(Vi)Q(Vi) (31) i=1

2.3. Environmental Conditions Normal wind profile model are used in the operational conditions. In the normal wind profile conditions, the wind profile U(z) is the average wind speed as a function of the height z above the free water level: !α z U(z) = Ure f (32) zre f where Uref is the reference wind speed at hub height; zref is hub height; α is the power law index, typically between 0.07 and 0.15, and the α value of the TLP FHAWT is set to 0.14 according to IEC 61400-3 [37]. Turbulent winds and irregular waves are considered related. For normal turbulence model, based on the Kaimal turbulence model for IEC Class C, turbulent wind fields are generated using the TurbSim program of NREL. For the irregular wave, the significant wave height (Hs) and Peak-spectral period (Tp) were set based on their correlation with the wind speed at the Statfjord site in the North Sea [38], and the irregular wave time history was generated by using the JONSWAP wave model.

3. Modeling and Calibration

3.1. Modeling The 10 MW TLP FHAWT model included a 10 MW DTU wind turbine, a TLP, and a mooring system. As shown in Table1, the wind turbine adopts the DTU 10 MW reference wind turbine developed by DTU Wind Energy and Vestas in the Light Rotor project [39]; Table2 lists the TLP and mooring system characteristics.

Table 1. Speciﬁcations of the DTU 10 MW turbine.

Description Value Turbine power 10 MW Rotor orientation conﬁguration Upwind, 3 blades Control Variable speed, collective pitch Drivetrain Medium speed, multiple stage gearbox Rotor, Hub diameter 178.3 m, 5.6 m Hub height 119 m Cut-in, Rated, Cut-out wind speed 4 m/s, 11.4 m/s, 25 m/s Cut-in, Rated rotor speed 6 rpm, 9.6 rpm Rotor mass 229,000 kg Nacelle mass 446,000 kg Tower mass 605,000 kg

Table 2. Speciﬁcation of the TLP and mooring lines.

Description Value Platform Diameter 19.8 m Platform Draft 47.89 m Water Depth 200 m Mooring System Angle 90◦ Total Displacement 14,745.69 m3 Platform mass 8,013,000 kg Center of mass −40.612 m Center of buoyancy –23.945 m Number of mooring lines 8 Mooring lines length 152.11 m Viscous-drag coefﬁcients 0.6 Energies 2018, 11, x FOR PEER REVIEW 8 of 24

Water Depth 200 m Mooring System Angle 90° Total Displacement 14,745.69 m3 Platform mass 8,013,000 kg Center of mass −40.612 m Center of buoyancy –23.945 m Number of mooring lines 8 Mooring lines length 152.11 m Energies 2018, 11, 3341 8 of 24 Viscous-drag coefficients 0.6

In order to study the impact of wind-wave misalignment, the rotor was aligned with the wind and Inthe order direction to study of the the wave impact was of defined wind-wave relative misalignment, to the wind the direction rotor was under aligned the conditions with the wind of EC1– and theEC7. direction During ofthe the process wave wasof research, deﬁned relativeone wind to thedirect windion direction(0°) and four-wave under the conditionsdirections of(0°, EC1–EC7. 30°, 60°, During the process of research, one wind direction (0◦) and four-wave directions (0◦, 30◦, 60◦, and 90◦) and 90°) were considered. The wind-wave misalignment angle was denoted by βwave, as shown in wereFigure considered. 1. The wind-wave misalignment angle was denoted by βwave, as shown in Figure1.

Mooring line 2,6

Mooring line 3,7 Wave 0° Wind 0° Mooring line 1,5

Mooring line 4,8

Wave90°

FigureFigure 1.1. TheThe toptop viewview ofof wind-wavewind-wave misalignmentmisalignmentconditions. conditions.

3.2.3.2. ValidationValidation TheThe fullyfully coupledcoupled aero-hydro-servo-elasticaero-hydro-servo-elastic timetime domaindomain simulationssimulations performedperformed onon thethe DTUDTU 1010 MWMW referencereference windwind turbineturbine cancan bebe carriedcarried outout byby usingusing thethe codecode FASTFAST [[40]40] whichwhich isis aa windwind turbineturbine designdesign codecode developeddeveloped byby thethe NationalNational RenewableRenewable EnergyEnergy LaboratoryLaboratory (NREL).(NREL). TheThe FASTFAST simulationsimulation modelmodel waswas comparedcompared withwith thethe parametersparameters ofof thethe DTUDTU referencereference windwind turbine to assess the accuracy. UnderUnder thethe samesame operating operating conditions, conditions, the the rotor rotor speed speedw wand and the the blade blade pitch pitch angle angleθ calculatedθ calculated by the by calculationthe calculation model model must must be consistent be consistent with thewith corresponding the corresponding parameters parameters in the in DTU the model DTU model for a given for a windgiven speed windV speedm/s. V Thrust m/s. Thrust is the mostis the important most important aerodynamic aerodynamic factor in factor the overall in the dynamicsoverall dynamics of a wind of turbine,a wind turbine, so the calculation so the calculation model needs model to needs match to the match thrust the of thrust the DTU of the 10 DTU MW reference10 MW reference wind turbine wind atturbine eachwind at each speed wind section. speed By section. matching By thematchi aboveng keythe systemabove features,key system the testfeatures, and calibrationthe test and of thecalibration calculation of the model calculation were completed. model were As completed. can be seen As from can Figurebe seen2 ,from except Figure for the 2, except low wind for the speed low regionwind speed of 4–7 region m/s, theof 4–7 remaining m/s, the positionsremaining are position well matched.s are well The matched. larger The error larger at low error wind at speedslow wind is duespeeds to the is due fact thatto the the fact simulation that the simulation model uses model simple uses PI control simple and PI control does not and pitch does to 5not◦ as pitch in the to DTU5° as referencein the DTU wind reference turbine. wind Therefore, turbine. a wind Therefore, speed a of wind 7 m/s speed and aboveof 7 m/s were and selected above forwere simulation. selected for simulation.Surge and pitch motions are the most important in the six motions of rigid-body floating platforms becauseSurge they and dominate pitch themotions dynamic are responsethe most of important the system. in The the experimental six motions dataof rigid-body of the DTU floating 10 MW referenceplatforms wind because turbine they scaling dominate model the wasdynamic used respon to testse and of verifythe system. the simulation The experimental results of data the surgeof the freeDTU decay 10MW motion reference [41]. wind All the turbine experimental scaling resultsmodel was were used extrapolated to test and to verify the full the size. simulation results of theThe surge relationships free decay betweenmotion [41]. the All length, the experime the time,ntal and results the mass were of extrapolated the full-size to model the full and size. the experimental model were shown in Equation (33). In the surge free decay motion test, the full-scale displacement of the platform in the surge direction was 6.72 m. The comparison among experimental data, FAST simulation results, and modified model simulation results including inertial effects and viscous drag were shown in Figure3. It can be seen from the figure that the free decay motion obtained by the modified model is closer to the experimental data than the FAST simulation. And the quasi-static Energies 2018, 11, 3341 9 of 24

mooring system of FAST simulation overestimates the amplitude of the turbulence to some extent due to the neglected of viscous drag:  √ T = t λ  L = lλ (33)  3  M = mλ ρsw/ρ f w

where λ = 60 is the geometric scaling factor; ρsw and ρ f w are the densities of seawater and fresh water, respectively; L, T and M are the length, time and mass for the full-size model, respectively; l, t and m Energiesare the 2018 length,, 11, x FOR time PEER and REVIEW mass of the scaled experimental model, respectively. 9 of 24

DTU 25 10.0 FAST DTU 9.5 20 FAST 9.0 ）

） 15

8.5 deg rpm （

（ 8.0 10 7.5

7.0 pitch blade 5 rotor speed rotor 6.5

6.0 0 5.5 5 10152025 0 5 10 15 20 25 wind（m/s） wind（m/s） (a) (b) x103 1.6 DTU FAST 1.4 ）

kN 1.2 （ 1.0

0.8

0.6

Mean-thrust T force 0.4

0.2

5 10152025 Wind（m/s） (c)

FigureFigure 2. 2.ModelModel calibration: calibration: (a) ( arotor) rotor speed; speed; (b ()b pitch) pitch angle angle θθ;(; (c) wind rotor thrust.

TheAs shownrelationships in Figure between4, the pitch the resonancelength, the frequency time, and response the mass predicted of the byfull-size the modified model modeland the is experimentalsmaller than model it predicted were byshown FAST. in TheEquation peak value(33). In of the the surge modified free modeldecay motion pitch response test, the amplitudefull-scale displacementoperator (RAO) of the is approximatelyplatform in the 2/3surge of direction the peak was value 6.72 predicted m. The comparison by FAST, which among is causedexperimental by the data,damping FAST effects simulation of the results, viscous and drag modified on the mooring model simulation system; The results natural including frequency inertial of the effects modified and viscousmodel changesdrag were from shown 0.1918 in Hz Figure to 0.1896 3. It Hz can because be seen of thefrom neglecting the figure of viscousthat the dampingfree decay and motion inertia obtainedeffects of by the the mooring modified system. model The is closer difference to the could experimental be explained data than by both the theFAST viscous simulation. damping And effect the quasi-staticand the inertial mooring effect system reducing of theFAST natural simulation frequency. overestimates the amplitude of the turbulence to some extent due to the neglected of viscous drag:

Tt= λ  Ll= λ (33)  = λ 3 ρρ Mm swfw ρ ρ where λ = 60 is the geometric scaling factor; sw and fw are the densities of seawater and fresh water, respectively; L, T and M are the length, time and mass for the full-size model, respectively; l, t and m are the length, time and mass of the scaled experimental model, respectively.

Energies 2018, 11, x FOR PEER REVIEW 10 of 24

8 Original model Correction model 6 Experiment

Energies 2018, 11, 33412 10 of 24 Energies 2018, 11, x FOR PEER REVIEW 10 of 24 0 Surge(m) 8 Original model -2 Correction model 6 Experiment -4 4 -6 20 100 200 300 400 500 Time(s)

0 Surge(m) Figure 3. Surge free decay motion. -2 As shown in Figure 4, the pitch resonance frequency response predicted by the modified model is smaller than it predicted-4 by FAST. The peak value of the modified model pitch response amplitude operator (RAO) is approximately 2/3 of the peak value predicted by FAST, which is caused by the -6 damping effects of the0 viscous 100drag on the 200mooring system; 300 The natural 400 frequency 500 of the modified Time(s) model changes from 0.1918 Hz to 0.1896 Hz because of the neglecting of viscous damping and inertia effects of the mooring system. The difference could be explained by both the viscous damping effect FigureFigure 3.3. Surge free decay motion. motion. and the inertial effect reducing the natural frequency. As shown in Figure 4, the pitch resonance frequency response predicted by the modified model is smaller than it predicted by FAST. The peak value of the modified Original modelmodel pitch response amplitude 0.8 Correction model operator (RAO) is approximately 2/3 of the peak value predicted by FAST, which is caused by the damping effects of the viscous drag on the mooring system; The natural frequency of the modified 0.6 model changes from 0.1918 Hz to 0.1896 Hz because of the neglecting of viscous damping and inertia effects of the mooring system. The difference could be explained by both the viscous damping effect and the inertial effect redu0.4cing the natural frequency.

Pitch RAO (deg/m) RAO Pitch 0.2 Original model 0.8 Correction model

0.0 0.60.0 0.1 0.2 0.3 0.4 Frequency (Hz)

0.4 Figure 4. Pitch amplitude response operator.

Pitch RAO (deg/m) RAO Pitch 0.2 ThroughThrough the the surge surge free decay motion verification verification and pitch response amplitude operator test, test, the results showed that the modifiedmodified model could provide more accurate results for the stochastic dynamic response of the 10 MW0.0 FHAWT. dynamic response of the 10 MW0.0 FHAWT. 0.1 0.2 0.3 0.4 Frequency (Hz) 4. Simulation Research 4. Simulation Research Figure 4. Pitch amplitude response operator. For the modified model that considered the inertial effects and viscous drag in the mooring system, For the modified model that considered the inertial effects and viscous drag in the mooring a series of representative working conditions EC1–EC7 as shown in Table3 were selected to perform system,Through a series theof representative surge free decay working motion conditio verificationns EC1–EC7 and pitch as response shown inamplitude Table 3 were operator selected test, to a 600 s fully coupled time domain simulation. The stochastic dynamic response of FHAWT under performthe results a 600 showed s fully coupledthat the modifiedtime domain model simula couldtion. provide The stochasticmore accurate dynamic results response for the stochastic of FHAWT various wind and wave conditions was studied by the statistical analysis (mean, standard deviation, underdynamic various response wind of and the wave10 MW conditions FHAWT. was studied by the statistical analysis (mean, standard maximum/minimum value) and frequency domain analysis. Firstly, the differences between TLP deviation, maximum/minimum value) and frequency domain analysis. Firstly, the differences FHAWT and equivalent onshore HAWT responses were compared and analyzed; then the effect of between4. Simulation TLP FHAWT Research and equivalent onshore HAWT responses were compared and analyzed; then waves on TLP FHAWT was studied. the effectFor of the waves modified on TLP model FHAWT that consideredwas studied. the inertial effects and viscous drag in the mooring system, a series of representative working conditions EC1–EC7 as shown in Table 3 were selected to perform a 600 s fully coupled time domain simulation. The stochastic dynamic response of FHAWT under various wind and wave conditions was studied by the statistical analysis (mean, standard deviation, maximum/minimum value) and frequency domain analysis. Firstly, the differences between TLP FHAWT and equivalent onshore HAWT responses were compared and analyzed; then the effect of waves on TLP FHAWT was studied.

Energies 2018, 11, 3341 11 of 24 Energies 2018, 11, x FOR PEER REVIEW 11 of 24

TableTable 3. 3. TurbulentTurbulent winds winds and and irregular irregular wave wave conditions. conditions.

ConditionConditionUS (m/s) US(m/s) TpTp(s) (s) Hs (m)Hs (m) Wind Turbine Wind Status Turbine Status EC1EC1 77 9.569.56 2.34 2.34 EC2EC2 8.58.5 9.719.71 3.3 3.3 EC3EC3 11.411.4 10.0410.04 4.14 4.14 EC4EC4 14.714.7 10.2910.29 5.16 5.16 OperatingOperating EC5EC5 17.817.8 10.5110.51 6.18 6.18 EC6EC6 21.321.3 11.1211.12 6.99 6.99 EC7 25 11.68 7.8 EC7 25 11.68 7.8

4.1.4.1. Comparison Comparison of of TLP TLP FHAWT FHAWT and and Onshore Onshore HAWT HAWT InIn this this section, section, the the equivalent equivalent onshore onshore HAWT HAWT used used the the same same wind wind turbine turbine blade blade as as the the TLP TLP FHAWTFHAWT with with the the difference difference that that the the former former was was mo mountedunted on on a a fixed fixed base base on on the the ground. ground. Therefore, Therefore, comparingcomparing and and analyzing analyzing the the stochastic stochastic dynamic dynamic re responsessponses of of the the two two could could provide provide a a solution solution of of designingdesigning the the TLP TLP FHAWT. FHAWT. In Inthe the comparative comparative analys analysisis process, process, the same the same turbulent turbulent wind windloads were loads appliedwere applied to the toTLP the FHAWT TLP FHAWT and onshore and onshore HAWT HAWT while whilethe wave the waveload was load only was applied only applied to the to TLP the FHAWT.TLP FHAWT. TheThe blade blade root root is is the the connecting connecting part part between between the the blade blade and and the the turbine turbine hub, hub, and and the the load load on on it it cancan reflect reflect the the load load characteristics characteristics of of the the blade blade un underder the the coupled coupled action action of of wind wind and and wave. wave. Figure Figure 5 showsshows the the statistical statistical analysis analysis of of the the blade blade root root bending bending moment moment and and the the corresponding corresponding short-term short-term damagedamage equivalent equivalent load load of of the the TLP TLP FHAWT FHAWT and and those those of of the the equivalent equivalent onshore onshore HAWT. HAWT. It It can can be be seenseen from from Figure Figure 55a,ba,b that the two mean values of the blade root bending moments are almost the same,same, which which indicates indicates that that the the dynamic dynamic response response of the ofthe blade blade is mainly is mainly caused caused by the by wind the wind load; load;The differenceThe difference between between the two the standard two standard deviations deviations of blade of root blade bending root bending moment moment is quite islarge, quite which large, iswhich related is relatedto the effects to the effectsof wave of load. wave The load. maxi Themum maximum difference difference is up to is 3400 up to kNm 3400 when kNm the when wind the speedwind speedis 14.7 ism/s. 14.7 It m/s.can be It seen can befrom seen Figure from 5c Figure that 5short-termc that short-term damage damage equivalent equivalent load of loadthe out-ofof the planeout-of-plane moment moment My at theMy bladeat the root blade of root the ofTLP the FHWAT TLP FHWAT is larger is larger than thanthat thatof the of onshore the onshore HAWT HAWT in thein themid-high mid-high wind wind speed. speed. The The difference difference reaches reaches a maximum a maximum value value of of 10,480 10,480 kNm kNm when when the the wind wind speedspeed is is 14.7 14.7 m/s, which which indicates indicates that the wavewave loadload willwill increaseincrease the the blade blade fatigue fatigue damage; damage; It It can can be beseen seen from from Figure Figure5d that5d that short-term short-term damage damage equivalent equivalent load load of the of in-plane the in-plane moment momentMx at Mx the at blade the bladeroot ofroot the of TLP the FHAWTTLP FHAWT is basically is basically consistent consistent with with that that of the of onshorethe onshore HAWT, HAWT, which which indicates indicates that thatthe pitchthe pitch control control can can reduce reduce the influencethe influence of the of wavethe wave load load on the on torquethe torque fluctuation. fluctuation.

TLP-FHAWT-mean 4 TLP-FHAWT-mean Onshore HAWT-mean X104 Onshore HAWT-mean X10 2.5 TLP-FHAWT-max Onshore HAWT-max TLP-FHAWT-max TLP-FHAWT-STD Onshore HAWT-STD 5 Onshore HAWT-max TLP-FHAWT-STD 2.0 Onshore HAWT-STD 4 1.5 3

2 1.0 Blade root My(kNm) Blade root Mx(kNm) root Blade 1 0.5

0 0.0 8 1012141618202224 8 1012141618202224 Wind speed(m/s) Wind speed(m/s) (a) (b)

Figure 5. Cont.

Energies 2018, 11, x FOR PEER REVIEW 12 of 24 Energies 2018, 11, 3341 12 of 24

Figure 5. Cont.

4 4 X10 X104 TLP-FHAWT 3.0 TLP-FHAWT 2.2 TLP-FHAWT Onshore-HAWT Onshore-HAWT 2.5 2.0

2.0 1.8

1.5 1.6 Blade root Mx DEL(m/s) Mx root Blade

Blade rootBlade DEL(kNm) My 1.4

1.0 DEL(m/s) Mx root Blade

Blade rootBlade DEL(kNm) My 1.0 1.4

0.5 1.2 8 1012141618202224 8 1012141618202224 Wind speed(m/s) Wind speed(m/s) (c) (d)

FigureFigure 5. 5. TheThe statistical statistical analysis analysis of of the the bending bending mome momentnt and and short-term short-term damage-equivalent damage-equivalent load: load: (a (a) ) TheThe statistical statistical analysis analysis of of blade blade root root out-of-plane out-of-plane bending bending moment moment MyMy; ;((bb)) The The statistical statistical analysis analysis of of bladeblade root root in-plane in-plane bending bending moment moment MxMx; ;((cc)) short-term short-term damage damage equivalent equivalent load load of of the the out-of-plane out-of-plane momentmoment MyMy; ;((dd)) short-term short-term damage damage equivalent equivalent load load of of the the in-plane in-plane moment moment MxMx..

TheThe stability stability of of the the nacelle nacelle is is very very important important for for th thee safe safe operation operation of of the the wind wind turbine. turbine. Therefore, Therefore, thethe fore-aft fore-aft displacement displacement and and corresponding corresponding acce accelerationslerations at at the the tower-top tower-top of of the the TLP TLP FHAWT FHAWT and and thethe onshore onshore HAWT HAWT were were compared compared and and analyzed. As As shown shown in in Figure Figure 66a,a, thethe averageaverage fore-aftfore-aft displacementdisplacement at thethe tower-toptower-top of of the the TLP TLP FHAWT FHAWT is slightly is slightly larger larger than thatthan of that the equivalentof the equivalent onshore onshoreHAWT, HAWT, and the differenceand the difference is 0.02 m is at 0.02 the m rated at the wind rated speeds. wind speeds. This was This caused was caused by the surgeby the motion surge motionof the TLP. of the The TLP. standard The standard deviation deviation of the fore-aft of the displacementfore-aft displacement at the tower-top at the tower-top of the TLP of the FHAWT TLP FHAWTis greater is than greater that than of the that equivalent of the equivalent onshore HAWT,onshore andHAWT, the differenceand the difference between thebetween two increases the two increasessigniﬁcantly significantly as the wave as the increases. wave increases. It can be explainedIt can be explained by the wave by the load wave effects load from effects Figure from6b, Figure which 6b,indicates which thatindicates the wave that loadthe wave will affectload will the stabilityaffect the of stability the nacelle. of the There nacelle. was There a similar was conclusion a similar conclusionabout the maximum about the valuemaximum of the value fore-aft of displacement the fore-aft displacement at the tower-top. at the The tower-top. spectrum analysisThe spectrum (under analysisthe rated (under conditions) the rated of Figureconditions)6d shows of Figure that the 6d linearshowsacceleration that the linear at theacceleration tower-top atof the the tower-top onshore ofHAWT the onshore is more HAWT sensitive is tomore the 3Psensitive frequency, to the which 3P frequency, indicates that which the towerindicates of the that TLP the FHAWT tower of is the less TLPsensitive FHAWT to the is less passing sensitive frequency to the of passing the blades. frequency of the blades.

-3 TLP-FHAWT-mean Onshore-HAWT-mean x10-3 1.8 TLP-FHAWT-STD Onshore-HAWT-STD 1.8 TLP FHAWT TLP-FHAWT-max Onshore-HAWT-max

TLP-FHAWT-max Onshore-HAWT-max /Hz) wind frequency response Onshore HAWT /Hz) 2 1.6 wind frequency response Onshore HAWT 2 1.6 1.2 1.4 1.0 1.2 wave frequency response 0.8 wave frequency response 0.8 1.0 ft deflection(m) ft deflection(m) 0.6 0.8 0.6 0.4 0.4 0.2 Tower top fore-a Tower top fore-a 0.2 3P Tower topfore-aft PSD(m Tower deflection 0.0 topfore-aft PSD(m Tower deflection 0.0 8 1012141618202224 0.0 8 1012141618202224 0.0 0.2 0.4 0.6 0.8 1.0 Wind speed(m/s) Wind speed(m/s) Frequency(Hz) (a) (b)

Figure 6. Cont.

EnergiesEnergies 20182018,, 1111,, xx FORFOR PEERPEER REVIEWREVIEW 1313 ofof 2424 Energies 2018, 11, 3341 13 of 24 FigureFigure 6.6. Cont.Cont.

） -3

） -3 ）

） x10 2 1.5 x10 2 1.5 TLP FHAWT TLP FHAWT TLP FHAWT /Hz 5 TLP FHAWT /Hz

2 5

2 wave frequency response )

m/s wave frequency response ) 2

m/s Onshore HAWT OnshoreOnshore HAWTHAWT 2 Onshore HAWT （（ 1.0

1.0 (m/s (m/s 4 （ 4 （ 0.50.5 33 surgesurge resonant resonant response response

nal acceleration 0.0 nal acceleration 0.0 22 3P3P -0.5-0.5

1 -1.0-1.0 1 Tower top transitio Tower top transitio -1.5-1.5 00 100 200 300 400 500 600 0.00.0 0.2 0.2 0.4 0.4 0.6 0.6 0.8 0.8 1.0 1.0 100 200 300 400 500 600 PSD acceleration transitional top Tower Tower top transitional acceleration PSD acceleration transitional top Tower （） timetime（（ss）） FrequencyFrequency（HzHz） ((cc)) ((dd))

FigureFigureFigure 6.6. 6. TowerTowerTower toptop top displacementdisplacement displacement statistics,statistics, statistics, accelerationacceleration acceleration timetime time historyhistory history andand and correspondingcorresponding corresponding powerpower power spectrum;spectrum;spectrum; ((aa ()a) )TowerTower Tower toptop top fore-aftfore-aft fore-aft displacementdisplacement displacement statistics;statistics; statistics; ((bb ()b) )TowerTower Tower toptop top fore-aftfore-aft fore-aft displacementdisplacement displacement powerpower power spectrum;spectrum;spectrum; ((cc ())c )towertower tower toptop top fore-aftfore-aft fore-aft displacementdisplacement displacement accelerationacceleration acceleration timetime time history;history; history; ((dd ()d) )towertower tower toptop top fore-aftfore-aft fore-aft displacementdisplacementdisplacement accelerationacceleration acceleration powerpower power spectrum.spectrum. spectrum.

Moreover,Moreover,Moreover, thethe the bendingbending bending momentmoment moment atat at towertower tower basebase base isis is anan an importantimportant important factorfactor factor toto to considerconsider consider whenwhen when designingdesigning designing thethethe tower,tower, tower, soso so thethe the bendingbending bending momentsmoments moments atat at towertower tower basebase base ofof of TLPTLP TLP FHAWTFHAWT FHAWT andand and equivalentequivalent equivalent onshoreonshore onshore HAWTHAWT HAWT werewerewere investigated.investigated. investigated. ItIt It isis is observedobserved observed inin in FigureFigure Figure 7a7a7a thatthat thethe meanmean towertower basebase fore-aftfore-aft momentmoment MyMyMy ofofof thethe the TLPTLPTLP FHAWTFHAWT FHAWT isis is slightlyslightly slightly greatergreater greater thanthan than thatthat that ofof of thethe the equivalentequivalent equivalent onshoreonshore onshore HAWTHAWT HAWT atat at lowlow low windwind wind speeds,speeds, speeds, thethe the differencedifferencedifference reachesreaches reaches aa a maximummaximum maximum valuevalue value ofof of 4702.374702.37 4702.37 kNmkNm kNm atat at thethe the ratedrated rated windwind wind speed.speed. speed.

TLP-FHAWT-mean Onshore-HAWT-mean x1088 5 TLP-FHAWT-mean Onshore-HAWT-mean x10 x10x105 1.41.4 TLPTLP FHAWTFHAWT TLP-FHAWT-STD TLP-FHAWT-STD Onshore-HAWT-STD Onshore-HAWT-STD wind frequency response 3.5 ） wind frequency response Onshore HAWT 3.5 TLP-FHAWT-max TLP-FHAWT-max Onshore-HAWT-max Onshore-HAWT-max ） Onshore HAWT

/Hz 1.2 /Hz

2 1.2 2 3.03.0 wavewave frequency frequency response response

） 1.0

） 1.0 (kNm) 2.52.5 (kNm) （（ kNm kNm 0.80.8 （（ 2.02.0 0.60.6 1.51.5 0.40.4 1.01.0 Towerbase My Towerbase Towerbase My Towerbase 0.2 Towerbase My PSD 0.2 0.50.5 Towerbase My PSD 0.0 0.0 0.0 0.0 0.00.0 0.1 0.1 0.2 0.2 0.3 0.3 0.4 0.4 0.5 0.5 88 1012141618202224 1012141618202224 FrequencyFrequency（（HzHz）） WindWind（（m/sm/s）） ((aa)) ((bb))

FigureFigureFigure 7.7. 7. TowerTowerTower basebase base bendingbending bending momentmoment moment statisticalstatistical statistical analysisanalysis analysis andand and correspondingcorresponding corresponding powerpower power spectrum:spectrum: spectrum: ((aa)) TowerTower(a) Tower basebase base fore-aftfore-aft fore-aft bendingbending bending momentmoment moment MyMyMy statisticalstatisticalstatistical analysis;analysis; analysis; ((bb)) ( bTowerTower) Tower basebase base fore-aftfore-aft fore-aft bendingbending bending momentmomentmoment MyMyMy powerpowerpower spectrum.spectrum. spectrum.

ThisThisThis couldcould could bebe be explainedexplained explained byby by thethe the non-zeronon-zero non-zero tilttilt tilt angleangle angle ofof of thethe the TLPTLP TLP FHAWTFHAWT FHAWT towertower tower causescauses causes gravitygravity gravity toto to generategenerategenerate bendingbending bending moments.moments. moments. TheThe The standardstandard standard deviationdeviation deviation ofof fore-aftfore-aft of fore-aft bendingbending bending momentmoment moment atat towertower at tower basebase base ofof thethe of TLPTLPthe FHAWT TLPFHAWT FHAWT isis greatergreater is greater thanthan thanthatthat of thatof thethe of equivaleequivale the equivalentntnt onshoreonshore onshore HAWT,HAWT, HAWT, andand the andthe differencedifference the difference betweenbetween between thethe twotwothe increases twoincreases increases significantlysignificantly signiﬁcantly asas thethe as thewavewave wave increaseincrease increases.s.s. TheThe The differencedifference difference reachesreaches reaches aa amaximummaximum maximum valuevalue value ofof of 46,525.4846,525.4846,525.48 kNmkNm kNm whenwhen when thethe the windwind wind speedspeed speed isis is 24.824.8 24.8 m/s.m/s. ThereThere There waswas was alsoalso also aa a similarsimilar similar conclusionconclusion conclusion aboutabout about thethe the maximummaximummaximum valuevalue value ofof of fore-aftfore-aft fore-aft bendingbending bending momentmoment moment atat at towetowe towerrr base.base. base. TheThe The standardstandard standard deviationdeviation deviation couldcould could reflectreflect reﬂect thethe the fatiguefatiguefatigue loadload load ofof of thethe the structurestructure to to aa certaincertain extent extentextent and andand the thethe maximum maximummaximum value valuevalue indicated indicatedindicated the thethe limit limitlimit load loadload that thatthat the thethestructure structurestructure faced. faced.faced. Therefore, Therefore,Therefore, compared comparedcompared with withwith the onshorethethe onshoreonshore HAWT, HAWT,HAWT, the tower thethe towertower of the ofof TLP thethe FHAWT TLPTLP FHAWTFHAWT needed neededneededan enhanced anan enhancedenhanced design. design.design. It is observed ItIt isis observedobserved in Figure inin 7 FiguFigub thatrere the7b7b thatthat tower thethe base towertower fore-aft basebase fore-aft momentfore-aft momentmoment My of the MyMy TLP ofof

Energies 2018 11 Energies 2018, ,11, ,x 3341 FOR PEER REVIEW 1414 of of 24 24 the TLP FHAWT has a amplitude near the wave frequency of 0.12 Hz, again indicating that the wave FHAWT has a amplitude near the wave frequency of 0.12 Hz, again indicating that the wave load has load has a significant effect on the tower. There was a similar result observed for the tower base side- a signiﬁcant effect on the tower. There was a similar result observed for the tower base side-to-side to-side moment Mx of TLP FHAWT. moment Mx of TLP FHAWT.

4.2.4.2. Influence Inﬂuence of of Wave Wave on on TLP TLP FHAWT FHAWT ManyMany studies onon the the TLP TLP FHAWT FHAWT dynamic dynamic analysis anal wereysis limitedwere limited to the environmental to the environmental conditions conditionsof wind load of wind and waveload and load wave in the load same in propagationthe same propagation direction. direction. However, However, the wind the and wind wave and can wavebe signiﬁcantly can be significantly misaligned, misaligned, and it is expected and it is that expected such misalignments that such misalignments would affect would the motions affect the and motionsstructural and responses structural of responses the wind turbine.of the wind turbine.

4.2.1.4.2.1. The The Influence Inﬂuence of ofthe the Wave Wave TheThe mean mean value value of of out-of-plane out-of-plane moment moment MyMy atat the the blade blade root root under under the the waving waving conditions conditions was was equalequal to to that that under under the the non-waving non-waving conditions. conditions. It It means means that that the the wave wave loads loads had had very very limited limited effects effects onon out-of-plane out-of-plane moment moment MyMy atat the the blade blade root. root. There There was was a a simila similarr result result observed observed from from the the in-plane in-plane momentmoment Mx atat thethe blade blade root. root. Those Those were were consistent consistent with with the conclusion the conclusion from thefrom comparative the comparative analysis analysisof TLP FHAWTof TLP FHAWT and equivalent and equivalent onshore HAWT onshore in SectionHAWT 4.1in Sectionthat the 4.1 loads that on the the loads wind on turbine the wind blade turbinewere mainly blade causedwere mainly by turbulent caused wind.by turbulent The blade wind. structure The blade design structure mainly design considered mainly the considered wind load, thebut wind it should load, be but noted it should thatthe be noted wave wouldthat the increase wave would the blade increase fatigue the load. blade fatigue load. TowerTower base base bending bending moments moments were were significantly signiﬁcantly affected affected by by wave wave loads loads and and it it was was up up to to the the nacellenacelle movement movement relative relative to to the the TLP, TLP, the the thrust, thrust, the the inertia inertia transmitted transmitted to to the the platform platform and and the the mooringmooring line line tension. tension. According According to tothe the Figure Figure 8a8, a,the the mean mean value value of tower of tower base base fore-aft fore-aft moment moment My underMy under the waves the waves conditions conditions is consistent is consistent with withthat under that under the non-waves the non-waves conditions, conditions, indicating indicating that thethat mean the mean value value is mainly is mainly affected affected by the by wind; the wind; The Thelarge large difference difference in standard in standard deviations deviations can canbe explainedbe explained based based on the on power the power spectrum spectrum (under (under the rated the rated conditions) conditions) of Figure of Figure 8b that8b the that wave the wave load causesload causes the tower the tower to generate to generate wave wavefrequency frequency response. response. When When the wind the wind speed speed was was24.8 24.8m/s, m/s,the standardthe standard deviation deviation of tower of tower base fore-aft base fore-aft moment moment My reachedMy reached the maximum the maximum value of value 46,130.38 of 46,130.38 kNm. TherekNm. was There a wassimilar a similar conclusion conclusion abou aboutt tower tower base base side-to-side side-to-side moment moment MxMx. Therefore,. Therefore, the the tower tower fatiguefatigue load load caused caused by by waves waves must must be be taken taken into into consideration consideration during during the the design design phase. phase.

5 mean with wave mean without wave 8 x10 x10 3.5 STD with wave STD without wave 1.4 wind frequency response with wave max with wave max without wave ） wave frequency response without wave

3.0 /Hz 1.2 2

） 2.5 1.0 (kNm) kNm （

（ 2.0 0.8 surge resonant response

1.5 0.6

1.0 0.4 Towerbase My 0.5 0.2 Towerbase My PSD

0.0 0.0 8 1012141618202224 0.00.10.20.30.40.5 Wind（m/s） Frequency（Hz）

(a) (b)

FigureFigure 8. 8. TowerTower base base bending bending moment moment statistical statistical analysis analysis and and corresponding corresponding power power spectrum: spectrum: (a) Tower(a) Tower base base fore-aft fore-aft bending bending moment moment MyMy statisticalstatistical analysis; analysis; (b) ( bTower) Tower base base fore-aft fore-aft bending bending momentmoment MyMy powerpower spectrum. spectrum.

FigureFigure 99 showsshows the the statistical analysis analysis and and spectral analysis (under the rated conditions) of the surge,surge, heave heave and pitch motionsmotions ofof thethe TLP TLP FHAWT FHAWT with with and and without without waves. waves. Motions Motions of sway,of sway, roll roll and andyaw yaw were were not discussednot discussed because because they werethey verywere smallvery duesmall to due the symmetryto the symme of structurestry of structures and external and externalloads [42 loads]. It can [42]. be seenIt can from be seen Figure from9a that Figure the two 9a meanthat the values two (onemean with values wave (one and anotherwith wave without and another without wave) of surge motion of the TLP are substantially identical. And similar results was

Energies 2018, 11, 3341 15 of 24 wave) of surge motion of the TLP are substantially identical. And similar results was observed from the Figure9c,e for the heave and pitch motions. As can be seen from Figure9b,d, the standard deviations of the surge motion and heave motion are mainly composed of the wave frequency response component and the surgeEnergies resonance 2018, 11, x FOR response PEER REVIEW component, and the former is much smaller than15 of 24 latter induced by low-frequencyobserved wind.from the Since Figure the9c,e for heave the heave resonance and pitch frequencymotions. As can was be high,seen from there Figure was 9b and no necessary to consider theFigure heave 9d, resonance the standard response. deviations of The the surge pitch motion natural and frequencyheave motion is are reduced mainly composed to 1.85 Hzof as shown in the wave frequency response component and the surge resonance response component, and the Figure9f dueformer to the is shiftmuch ofsmaller the pitchthan latter natural induced frequency by low-frequency caused wind. by the Since TLP-tower the heave resonance coupling effect [ 43]. The standardfrequency deviation was high, of pitch there was motion no necessary was the to co combinednsider the heave actions resonance of wind response. and The wave pitch loads, i.e., the inertia of thenatural surge frequency motion is reduced and the to 1.85 hydrodynamic Hz as shown in Figure coupling. 9f due Theto the pitchshift of motionthe pitch natural consisted of surge frequency caused by the TLP-tower coupling effect [43]. The standard deviation of pitch motion was resonance responsethe combined component, actions of wavewind and response wave loads, component, i.e., the inertia and of pitch the resonancesurge motionresponse and the component. Based on thehydrodynamic above analysis, coupling. it The could pitch motion be inferred consisted that of surge the resonance surge resonance response component, and the wave pitch resonance affected theresponse motions component, of the TLPand pitch platform resonance deeply, response andcomponent. they Based should on the be above considered analysis, it incould the TLP design be inferred that the surge resonance and the pitch resonance affected the motions of the TLP platform phase as keydeeply, issues. and they should be considered in the TLP design phase as key issues.

mean with wave 18 7 STD with wave with wave 16 max with wave 6 surge resonant response without wave mean without wave 14

STD without wave ） 5 12 max without wave /Hz 2 ） m

m 10 4 （（ 8 3 Surge 6

Surge PSD 2 4 2 1 wave frequency response 0 8 1012141618202224 0 Wind（m/s） 0.0 0.1 0.2 0.3 0.4 0.5 Frequency（Hz）

(a) (b) 0.6 mean with wave mean without wave 3.5 STD with wave STD without wave surge resonant response with wave 0.4 without wave min with wave min without wave 3.0 0.2 ） 2.5 /Hz

0.0 2 ） m m 2.0 （（ -0.2 1.5

Heave -0.4

-0.6 PSD Heave 1.0

-0.8 0.5 wave frequency response

-1.0 Energies 2018, 11, x FOR PEER REVIEW 0.0 16 of 24 8 1012141618202224 0.0 0.1 0.2 0.3 0.4 0.5 Wind（m/s） Frequency（Hz） (c) Figure 9. Cont. (d)

mean with wave mean without wave 5.0 with wave 0.7 STD with wave STD without wave surge resonant response without wave max with wave max without wave 4.5 0.6 4.0 wave frequency response ） 0.5 3.5 /Hz 2

） 3.0

0.4 deg pitch resonant response deg （ 2.5 （ 0.3 2.0 Pitch 0.2 1.5 Pitch PSD Pitch 1.0 0.1 0.5 0.0 0.0 8 1012141618202224 0.0 0.1 0.2 0.3 0.4 0.5 Wind（m/s） Frequency（Hz）

(e) (f)

Figure 9. StatisticalFigure 9. Statistical analysis analysis and correspondingand corresponding power power spectrum spectrum of Surge, of Heave Surge, and Heave Pitch motions. and Pitch motions. (a) Surge motion statistical analysis; (b) Surge motion power spectrum; (c) Heave motion Statistical (a) Surge motionanalysis; statistical (d) Heave motion analysis; power (b spectrum;) Surge ( motione) Pitch motion power Statistical spectrum; analysis; (c )(d Heave) Pitch motion motion Statistical analysis; (d)power Heave spectrum. motion power spectrum; (e) Pitch motion Statistical analysis; (f) Pitch motion power spectrum. Since the mooring system was related to the safety of the wind turbine, the mooring line tension was also investigated. While the mooring line 3 was in the upwind position, with greater tension than the downwind mooring lines, the mooring line 3 was selected to be analyzed. It can be seen from the Figure 10a that the wave load has almost no effect on the mean value of mooring line tension, but it has a great influence on the standard deviation. According to the Figure 10b, the standard deviation response of the tension is affected by the wave-frequency excitation and the pitch resonance response, which is similar to the pitch motion in Figure 9. Therefore, reducing the surge resonance response and pitch resonance response were effective ways to ensure the safety of the TLP FHAWT.

mean with wave mean without wave x104 3 x10 STD with wave STD without wave 1.8 with wave 7 max with wave max without wave surge resonant response 1.6 without wave 6 ） 1.4 /Hz 5 2 1.2

） wave frequency response (kN) 1.0 kN 4 （（ 0.8 pitch resonant response 3 0.6 Tension 2 Tension PSD Tension 0.4

1 0.2

0 0.0 8 1012141618202224 0.0 0.1 0.2 0.3 0.4 0.5 Wind（m/s） Frequency（Hz） (a) (b)

Figure 10. Mooring line tension statistical analysis and corresponding power spectrum: (a) Mooring line 3 tension statistical analysis; (b) Mooring line 3 tension power spectrum.

4.2.2. The Influence of the Wind-Wave Misalignment From the results of the study with and without wave loading in Section 4, it was expected that wind-wave misalignment would affect the dynamic response of the TLP FHAWT, including the structural loads of the blade and tower, platform motion and mooring line tension. The mean of the dynamic response of TLP FHAWT was mainly induced by wind, so the dynamic standard deviation (STD) of TLP FHAWT was mainly analyzed [44].

Energies 2018, 11, x FOR PEER REVIEW 16 of 24

Figure 9. Cont.

） 3.0

0.4 deg pitch resonant response deg （ 2.5 （ 0.3 2.0 Pitch 0.2 1.5 Pitch PSD Pitch 1.0 0.1 0.5 0.0 0.0 8 1012141618202224 0.0 0.1 0.2 0.3 0.4 0.5 Wind（m/s） Frequency（Hz）

(e) (f)

Figure 9. Statistical analysis and corresponding power spectrum of Surge, Heave and Pitch motions. (a) Surge motion statistical analysis; (b) Surge motion power spectrum; (c) Heave motion Statistical Energiesanalysis;2018, 11, 3341(d) Heave motion power spectrum; (e) Pitch motion Statistical analysis; (d) Pitch motion16 of 24 power spectrum.

SinceSince the the mooring mooring system system was was related related to to the the safety safety of of the the wind wind turbine, turbine, the the mooring mooring line line tension tension waswas also also investigated. investigated. While While the the mooring mooring line line 3 3 was was in in the the upwind upwind position, position, with with greater greater tension tension than than thethe downwind downwind mooring mooring lines, lines, the the mooring mooring line line 3 3 was was selected selected to to be be analyzed. analyzed. It It can can be be seen seen from from the the FigureFigure 10 10aa that that the the wave wave load load has has almost almost no no effect effect on on the the mean mean value value of of mooring mooring line line tension, tension, but but it it hashas a a great great inﬂuence influence on on the the standard standard deviation. deviation. According According to to the the Figure Figure 10 10b,b, the the standard standard deviation deviation responseresponse of of the the tension tension is is affected affected by by the the wave-frequencywave-frequency excitation excitation and and the the pitchpitch resonanceresonance response,response, whichwhich is is similar similar to to the the pitch pitch motion motion in Figurein Figure9. Therefore, 9. Therefore, reducing reducing the surge the surge resonance resonance response response and pitchand pitch resonance resonance response response were effectivewere effective ways towa ensureys to ensure the safety the safety of the of TLP the FHAWT. TLP FHAWT.

mean with wave mean without wave x104 3 x10 STD with wave STD without wave 1.8 with wave 7 max with wave max without wave surge resonant response 1.6 without wave 6 ） 1.4 /Hz 5 2 1.2

） wave frequency response (kN) 1.0 kN 4 （（ 0.8 pitch resonant response 3 0.6 Tension 2 Tension PSD Tension 0.4

1 0.2

0 0.0 8 1012141618202224 0.00.10.20.30.40.5 Frequency（Hz） Wind（m/s） (a) (b)

FigureFigure 10. 10.Mooring Mooring line line tension tension statistical statistical analysis analysis and and corresponding corresponding power power spectrum: spectrum: ( a(a)) Mooring Mooring lineline 3 3 tension tension statistical statistical analysis; analysis; ( b(b)) Mooring Mooring line line 3 3 tension tension power power spectrum. spectrum.

4.2.2.4.2.2. The The InfluenceInfluence of the Wind-Wave Wind-Wave Misalignment Misalignment FromFrom thethe resultsresults ofof the study study with with and and without without wave wave loading loading in inSection Section 4, 4it, was it was expected expected that thatwind-wave wind-wave misalignment misalignment would would affect affect the the dynami dynamicc response response of of the the TLP TLP FHAWT, includingincluding thethe structuralstructural loads loads of of the the blade blade and and tower, tower, platform platform motion motion and and mooring mooring line line tension. tension. The The mean mean of of the the dynamicdynamic response response of of TLP TLP FHAWT FHAWT was was mainly mainly induced induced by by wind, wind, so so the the dynamic dynamic standard standard deviation deviation (STD)(STD) of of TLP TLP FHAWT FHAWT was was mainly mainly analyzed analyzed [44 [44].]. The standard deviations of the blade root bending moments, the tower base bending moments and the tension of the mooring lines were shown as functions of the wind-wave misalignment angle βwave in Figure 11. As shown in Figure 11a,b, the standard deviations of the blade in-plane moment Mx at the blade root and out-of-plane moment My at the blade root are basically not affected by βwave at the low wind speed. While under the high wind speed conditions, the standard deviation of the in-plane moment Mx at the blade root increases slightly as βwave increases and the standard deviation of the out-of-plane moment My at the blade root decreases as βwave increases. According to Figure 11c,d, it can be seen that the tower base moment changes significantly as βwave increases. This was because the tilting of the platform shifts the center of gravity of the wind turbine nacelle thus changed the tower base bending moment. When βwave changed, the weight of the rotor and nacelle components changed the contribution to the tower base side-to-side moment Mx and tower base fore-aft moment My. The standard deviation of the tower base side-to-side moment Mx reaches a maximum value of ◦ 58,219.14 kNm when the FHAWT operates in EC7, βwave is 90 , and the standard deviation of tower base fore-aft moment My reaches a maximum value of 73,157.88 kNm when the FHAWT operates in ◦ EC7, βwave is 0 . Under the low wind speed conditions EC1-EC2, the fore-aft tilt angles of the tower are very small, the wind and wave misalignment has little influence on the fore-aft bending moments. While at mid-high wind speeds, the tilt angle of the tower increases, resulting in a significant influence. The mooring line 2 and the mooring line 3 were respectively located on the rotating tension side and Energies 2018, 11, x FOR PEER REVIEW 17 of 24

The standard deviations of the blade root bending moments, the tower base bending moments and the tension of the mooring lines were shown as functions of the wind-wave misalignment angle βwave in Figure 11. As shown in Figure 11a,b, the standard deviations of the blade in-plane moment Mx at the blade root and out-of-plane moment My at the blade root are basically not affected by βwave at the low wind speed. While under the high wind speed conditions, the standard deviation of the in-plane moment Mx at the blade root increases slightly as βwave increases and the standard deviation of the out-of-plane moment My at the blade root decreases as βwave increases. According to Figure 11c,d, it can be seen that the tower base moment changes significantly as βwave increases. This was because the tilting of the platform shifts the center of gravity of the wind turbine nacelle thus changed the tower base bending moment. When βwave changed, the weight of the rotor and nacelle components changed the contribution to the tower base side-to-side moment Mx and tower base fore-aft moment My. The standard deviation of the tower base side-to-side moment Mx reaches a maximum value of Energies 2018,58,219.1411, 3341 kNm when the FHAWT operates in EC7, βwave is 90°, and the standard deviation of tower 17 of 24 base fore-aft moment My reaches a maximum value of 73,157.88 kNm when the FHAWT operates in EC7, βwave is 0°. Under the low wind speed conditions EC1-EC2, the fore-aft tilt angles of the tower the downwindare very side small, of the wind rotor, and which wave misalignment meant they ha woulds little influence bear larger on the fore-aft loads thanbending other moments. mooring lines. It can be seenWhile from at Figure mid-high 11 e,fwind that speeds, the standard the tilt angle deviation of the tower of tension increases, of resulting the mooring in a significant line 2 increases with influence. The mooring line 2 and the mooring line 3 were respectively located on the rotating tension the incrementside and of β thewave downwind, while the side standard of the rotor, deviation which meant of they the tensionwould bear of larger the mooring loads than lineother 3 is opposite. This performancemooring lines. is more It can pronounced be seen from Figure at high 11e,f windthat the speed standard conditions. deviation of tension The standard of the mooring deviation of the β tension of mooringline 2 increases line with 2reaches the increment a maximum of wave, while value the standard of 329.55 deviation kN of when the tension the windof the mooring speed is 24.8 m/s, ◦line 3 is opposite. This performance is more pronounced at high wind speed conditions. The standard βwave is 90 deviation, and the of standardthe tension deviationof mooring line of the2 reaches tension a maximum of mooring value of line 329.55 3 reaches kN when a the maximum wind value of ◦ 552.12kN whenspeed is the 24.8 wind m/s, βwave speed is 90°, is and 24.8 the m/s,standardβwave deviationis 0 .of The the tension mooring of mooring line 3 line had 3 reaches the same a tendency β as the pitchmaximum motion, value which of 552.12kN meant when that the the wind pitch speed motion is 24.8 m/s, had wave a is great 0°. The inﬂuence mooring line on 3 had the the tension of the mooring linesame 3. tendency as the pitch motion, which meant that the pitch motion had a great influence on the tension of the mooring line 3.

3 x10 EC1 x103 EC1 6.5 EC2 EC2 8.60 EC3 EC3 6.0 ）） EC4 EC4 8.55 EC5 EC5 kNm kNm EC6 5.5 EC6 （（ 8.50 EC7 EC7 5.0

8.45 4.5

8.40 4.0 STD of blade root My root blade STD of

STD of blade rootof blade STD Mx 8.35 3.5

8.30 3.0 0 20 40 60 80 100 0 306090 Misalignment angle（deg） Misalignment angle（deg） Energies 2018, 11, x FOR PEER REVIEW 18 of 24 (a) (b)

4 4 x10 EC1 x10 EC1 EC2 8 EC2 6 EC3 EC3

） EC4 ） 7 EC4 5 EC5 EC5 kNm EC6 kNm 6 EC6 （ 4 EC7 （ EC7 5 3 4 2 3

STD of towerbase Mx STD of towerbase 1 STD of Towerbase My Towerbase STD of 2 0 0306090 0 306090 Misalignment angle（deg） Misalignment angle（deg） (c) (d) 2 x102 x10 EC1 EC1 3.5 EC2

） EC2

） 5.5 EC3 EC3 kN

3.0 EC4 kNm EC4 （ 5.0 EC5 （ EC5 EC6 2.5 4.5 EC6 EC7 EC7 2.0 4.0

1.5 3.5

1.0 3.0 2.5 0.5 STD of tension of mooring line2 mooring of tension of STD STD of tension of mooring line3 mooring of tension STD of 2.0 0 306090 0306090 Misalignment angle（deg） Misaglinment angle（deg） (e) (f)

Figure 11. The standard deviations of the blade root bending moment, the tower base bending Figure 11. The standard deviations of the blade root bending moment, the tower base bending moment moment and the tension of the mooring lines are shown as a function of the wind-wave misalignment and the tensionangle β ofwave the: (a) mooringThe standard lines deviations are shown of the blade as a functionroot in-plane of moment the wind-wave Mx; (b) The misalignmentstandard angle βwave:(a) Thedeviations standard of the deviations blade root out-of-plane of the blade moment root My in-plane; (c) The standard moment deviationsMx;(b of) Thethe tower standard base deviations of the bladeside-to-side root out-of-plane bending moment moment My; (dMy) The;( cstandard) The standard deviations deviationsof the tower ofbase the fore-aft tower bending base side-to-side moment My; (e) the standard deviation of tension of the mooring line 2; (f) the standard deviation of bending moment My;(d) The standard deviations of the tower base fore-aft bending moment My; tension of the mooring line 3. (e) the standard deviation of tension of the mooring line 2; (f) the standard deviation of tension of the mooring lineThe3. standard deviation of the platform motion was shown as a function of the wind-wave misalignment angle βwave in Figure 12. Figure 12a shows that the standard deviation of the surge motion increases as βwave increases at low to medium wind conditions EC1-EC5. This was because the aerodynamic damping decreases as βwave increases, resulting in an increment in low frequency surge motion. It can also be observed that the standard deviation of surge motion under high wind speed condition EC6-7 decreases as βwave increases. This was because the viscous hydrodynamic load in the TLP surge direction was greatly reduced as the wind speed increases, so that the wave-frequency surge motion decreased significantly as βwave increased. As shown in Figure 12b, the standard deviation of the sway motion at a low wind speed is the minimum when βwave is 30°, and in the case of mid-high wind speed, the sway motion increases as βwave increases due to the larger effective wave height and the longer wave period. As shown in Figure 12c, the standard deviation of the heave motion at low and medium wind speeds increases slightly with the increment of βwave, because the viscous fluid dynamic load decreases slightly as the increment of βwave. While at high wind speeds, the dynamic load of viscous fluid decreases significantly as βwave increases, and the standard deviation of the heave motion decreases with the increase of βwave. According to Figure 12d, it can be seen that the standard deviation of the roll motion increases as βwave increases.

Energies 2018, 11, 3341 18 of 24

The standard deviation of the platform motion was shown as a function of the wind-wave misalignment angle βwave in Figure 12. Figure 12a shows that the standard deviation of the surge motion increases as βwave increases at low to medium wind conditions EC1-EC5. This was because the aerodynamic damping decreases as βwave increases, resulting in an increment in low frequency surge motion. It can also be observed that the standard deviation of surge motion under high wind speed condition EC6-7 decreases as βwave increases. This was because the viscous hydrodynamic load in the TLP surge direction was greatly reduced as the wind speed increases, so that the wave-frequency surge motion decreased significantly as βwave increased. As shown in Figure 12b, the standard deviation of ◦ the sway motion at a low wind speed is the minimum when βwave is 30 , and in the case of mid-high wind speed, the sway motion increases as βwave increases due to the larger effective wave height and the longer wave period. As shown in Figure 12c, the standard deviation of the heave motion at low and medium wind speeds increases slightly with the increment of βwave, because the viscous fluid dynamic load decreases slightly as the increment of βwave. While at high wind speeds, the dynamic load of viscous fluid decreases significantly as βwave increases, and the standard deviation of the heave motion decreases with the increase of βwave. According to Figure 12d, it can be seen that the standard deviation of the roll motion increases as βwave increases. From Figure 12e, it can be seen that the standard deviation of the pitch motion decreases as βwave increases. This was because as βwave increases, the contribution of the wave load to the Y direction increased and the contribution to the X direction decreased. As shown in Figure 12f, the standard deviation of yaw motion is not sensitive to the wave directions of all ECs, indicating that it is mainly affected by changes in wind speed. From the above analysis, we could conclude that, with the exception of yaw motion, the other degrees of freedom motions of TLP were significantly affected by the misalignment of wind and waves. The influence of wind and wave misalignment on the platform could be reduced by increasing the aerodynamic damping of the wind turbine. From the above analysis, it could be concluded that the wind-wave misalignment had obvious influence on the surge, pitch, sway and roll motion of the TLP. In order to demonstrate the influence of the viscous drag and inertial effect of quasi-static mooring system on the stochastic dynamic response of wind turbines, the power spectrum comparison analysis was carried out for the standard deviation of TLP motions of the original model and the correction model under wind-wave misalignment. Figure 13 shows the spectral analysis of the standard deviation of surge and pitch motion at the wind speed of 24.8 m/s (the maximum standard deviation of the pitch motion is occurred at this time). ◦ Among them, Figure 13a,b show the situation when βwave is 0 , and Figure 13c,d show the situation ◦ when βwave is 90 . It can be seen from Figure 13a,c that, for the surge motion, the surge component in the correction model is larger, indicating that the viscous drag has an effect on the fluctuation of the TLP motion; according to the power spectrum analysis of pitch motion in Figure 13b,d, for the modified model, the inertial force generated by the surge motion causes larger pitch resonance response, which indicates that the viscous resistance and inertia effect of the mooring system should be considered. It can be seen by comparing Figure 13a,c that the fluctuations of the surge motion are different for ◦ different βwave angles. It has bigger effect on the surge motion when βwave is 0 , while the effect is ◦ smaller when βwave is 90 . There are similar conclusions about the pitch motion. Energies 2018, 11, 3341 19 of 24 Energies 2018, 11, x FOR PEER REVIEW 19 of 24

4.0 EC1 1.4 EC1 EC2 EC2 EC3 3.5 EC3 EC4 1.2 ）

） EC4 m EC5 m EC5 （ 3.0 EC6 （ EC6 EC7 1.0 2.5 EC7

0.8 2.0

1.5 0.6 STD of surge motions of surge STD STD of sway motions of sway STD 1.0 0.4 0 306090 Misalignment angle（deg） 0 306090 Misalignment angle（deg） (a) (b) 0.09 0.18 EC1 EC1 EC2 EC2 0.08 0.16 EC3 EC3 ）

） EC4 EC4 m 0.14 EC5 0.07 EC5 （ EC6 degree EC6 0.12 EC7 （ 0.06 EC7

0.10 0.05

0.08 0.04 0.06

STD of heave motion 0.03 STD of roll motions roll STD of 0.04 0.02 0.02 0 306090 0 306090 Misalignment angle（deg） Misalignment angle（deg） (c) (d) 0.11 EC1 2.2 EC1 0.10 EC2 EC2 ） EC3 ） 2.0 EC3 0.09 EC4 EC4 EC5 degree degree 1.8 EC5 （ EC6 （ 0.08 EC6 EC7 1.6 EC7 0.07 1.4 0.06 1.2 0.05 STD ofSTD yaw motions STD of pitch motions 1.0 0.04 0.8 0306090 0306090 Misaglignment angle（deg） Misalignment angle（deg） (e) (f)

FigureFigure 12. 12. TheThe standard standard deviation deviation of of the the platform platform moti motionon is is shown shown as as a afunction function of of the the wind-wave wind-wave β misalignmentmisalignment angle angle waveβwave: (a:() aThe) The standard standard deviation deviation of of the the platform platform surge surge motion; motion; (b (b) )The The standard standard deviationdeviation of of the the platform platform sway sway motion; motion; (c) (Thec) The standard standard deviation deviation of the of platform the platform heave heave motion; motion; (d) The(d) Thestandard standard deviation deviation of the of theplatform platform roll roll motion; motion; (e) (Thee) The standard standard deviation deviation of of the the platform platform pitch pitch motion;motion; (f ()f )The The standard standard deviation deviation of of the the platform platform yaw yaw motion. motion.

From Figure 12e, it can be seen that the standard deviation of the pitch motion decreases as βwave increases. This was because as βwave increases, the contribution of the wave load to the Y direction increased and the contribution to the X direction decreased. As shown in Figure 12f, the standard deviation of yaw motion is not sensitive to the wave directions of all ECs, indicating that it is mainly affected by changes in wind speed. From the above analysis, we could conclude that, with the exception of yaw motion, the other degrees of freedom

Energies 2018, 11, x FOR PEER REVIEW 20 of 24

motions of TLP were significantly affected by the misalignment of wind and waves. The influence of wind and wave misalignment on the platform could be reduced by increasing the aerodynamic damping of the wind turbine. From the above analysis, it could be concluded that the wind-wave misalignment had obvious influence on the surge, pitch, sway and roll motion of the TLP. In order to demonstrate the influence of the viscous drag and inertial effect of quasi-static mooring system on the stochastic dynamic response of wind turbines, the power spectrum comparison analysis was carried out for the standard Energiesdeviation2018 ,of11 ,TLP 3341 motions of the original model and the correction model under wind-wave20 of 24 misalignment.

x10-1 x10-4 5 Correction model 7 Correction model Original model Original model surge resonant response 6 wave frequency response 4 ））

/Hz 5 2 /Hz 2 pitch resonant response m 3 deg 4 （（ 3 2 wave frequency response 2 Pitch PSD Pitch Surge PSD 1 1

0 0 0.0 0.1 0.2 0.3 0.4 0.5 0.00.10.20.30.40.5 Frequency（Hz） Frequency（Hz）

(a) (b) x10-1 Correction model x10-4 4.5 2.5 Correction model Original model Original model 4.0 pitch resonant response

） 2.0 ） 3.5 surge resonant response /Hz /Hz 2

2 3.0 wave frequency response

m 1.5 deg

（ 2.5 （ 2.0 1.0 1.5 Pitch PSD Surge PSD 1.0 0.5 0.5 0.0 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 Frequency（Hz） Frequency（Hz）

Figure 13. 13. PowerPower spectrum spectrum ofof standard standard deviation deviation of pl ofatform platform surge surge and andpitch pitch motion motion under under different different wind-waves misalignment: misalignment: (a ()a Power) Power spectrum spectrum of standard of standard deviat deviationion of platform of platform surge surge motion motion when when β ◦ β ◦ βwave == 0°; 0 (;(b)b Power) Power spectrum spectrum of standard of standard deviation deviation of platform of platform pitch motion pitch motion when whenwave = 0°βwave; (c) = 0 ; β ◦ Power(c) Power spectrum spectrum of standard of standard deviatio deviationn of platform of platform surge motion surge when motion wave = when 90°; (dβwave) Power= 90 spectrum;(d) Power βwave ◦ ofspectrum standard of deviation standard of deviation platform ofpitch platform motion pitch when motion = when90°. βwave = 90 .

Figure 1314 shows shows the the spectral sway and analysis roll spectrumof the standard analysis deviation of the standardof surge and deviation pitch motion of the at sway the and rollwind motion speed of at 24.8 the windm/s (the speed maximum of 24.8 standard m/s (the deviat maximumion of standardthe pitch motion deviation is occurred of the roll at this motion time). occurs Among them, Figure 13a,b show the situation when βwave is 0°, and Figure 13c,d◦ show the situation at this time). Among them, Figure 14a,b show the situation when βwave is 0 , and Figure 14c,d show when βwave is 90°. It can be seen◦ from Figure 13a,c that, for the surge motion, the surge component in the situation when βwave is 90 . It can be seen from Figure 14a,c that, when wind and wave in the same the correction model is larger, indicating that the viscous drag has an effect on the fluctuation◦ of the direction, the fluctuation of the sway motion is not much different. While for βwave is 90 , due to the TLP motion; according to the power spectrum analysis of pitch motion in Figure 13b,d, for the inclusion of viscous drag, a larger deviation of the sway motion is produced under the wave loads modified model, the inertial force generated by the surge motion causes larger pitch resonance in the corrected model. According to the power spectrum analysis of the roll motion in Figure 14b,d, response, which indicates that the viscous resistance and inertia effect of the mooring system should when β is 90◦, for the modified model, the inertial force generated by the sway motion causes a be considered.wave It can be seen by comparing Figure 13a,c that the fluctuations of the surge motion are larger roll resonance response, which indicates that the viscous drag and inertia effects of the mooring system should be considered. Comparing Figure 14a,c, the fluctuations of the sway motion are different for different βwave angles. Which is exactly the opposite of the surge motion, it has smaller effects ◦ ◦ on the sway motion when βwave is 0 , while the effect is bigger when βwave is 90 . There are similar conclusions about the roll motion. Energies 2018, 11, x FOR PEER REVIEW 21 of 24 differentEnergies 2018 for, 11 different, 3341 βwave angles. It has bigger effect on the surge motion when βwave is 0°, while21 the of 24 effect is smaller when βwave is 90°. There are similar conclusions about the pitch motion.

-1 x10 x10-4 1.2 Correction model 7 Correction model Original model original model 1.0 6 ）） sway resonant response 5 /Hz sway resonant response /Hz

2 0.8 2 m deg

（ 4

0.6 （ 3 0.4

Sway PSD 2 wave frequency response Roll Roll PSD 0.2 1 roll resonant response 0.0 0 0.0 0.1 0.2 0.3 0.4 0.5 0.00.10.20.30.40.5 Frequency（Hz） Frequency（Hz） (a) (b) -1 -4 x10 x10 Correction model 2.5 Correction model 8 Original model resonant model 7 sway resonant response 2.0 sway resonant response ）） 6 wave frequency response /Hz /Hz 2 2

m 1.5 5 deg

（ wave frequency response

（ 4 1.0 3 roll resonant response Sway PSD Roll PSD 2 0.5 1 0.0 0 0.0 0.1 0.2 0.3 0.4 0.5 0.00.10.20.30.40.5 Frequency（Hz） Frequency（Hz）

FigureFigure 14. 14. PowerPower spectrum spectrum of of standard standard deviation deviation of of pl platformatform sway sway and and roll roll motion motion under under different different wind-waveswind-waves misalignment: misalignment: (a (a) )Power Power spectrum spectrum of of standard standard deviat deviationion of of platform platform sway sway motion motion when when β ◦ β ◦ βwavewave = =0°; 0 (;(b)b Power) Power spectrum spectrum of of standard standard deviat deviationion of of platform platform roll roll motion motion when when βwavewave == 0° 0; (;(c)c Power) Power β ◦ spectrumspectrum of of standard standard deviation deviation of of platform platform sway sway motion motion when when βwavewave = =90° 90; ;((dd) )Power Power spectrum spectrum of of ◦ standardstandard deviation deviation of of platform platform roll roll motion motion when when ββwavewave = =90° 90. .

5. ConclusionsFigure 14 shows the sway and roll spectrum analysis of the standard deviation of the sway and roll motionIn this at paper, the wind the speed quasi-mooring of 24.8 m/s system (the ma wasximum modified standard by calculatingdeviation of the the quadratic roll motion damping, occurs atand this an time). improved Among model them, simulating Figure 14a,b the 10show MW the TLP situation FHAWT when was constructedβwave is 0°, and based Figure on the14c,d modified show themooring situation system. when Then βwave is the 90°. response It can be characteristics seen from Figure of the 14 TLPa,c that, FHAWT when were wind analyzed and wave and in comparedthe same direction,with the equivalentthe fluctuation onshore of the HAWT sway to mo determinetion is not effects much of different. the wave While on dynamic for βwave responses is 90°, due of the to the TLP inclusionFHAWT. of Moreover, viscous drag, the influence a larger deviation of turbulent of the wind sway loads motion and waveis produced loads misalignment under the wave on loads FHAWT in theunder corrected typical model. operating According conditions to the was power studied. spectrum Finally, analysis the differencesof the roll motion between in theFigure correction 14b,d, whenmodel βwave and is the90°, original for the modified model TLP model, response the inertial are analyzed. force generated On thebasis by the of sway those motion works, causes it can bea largerconcluded roll resonance that: response, which indicates that the viscous drag and inertia effects of the mooring system should be considered. Comparing Figure 14a,c, the fluctuations of the sway motion are (1) Both mean values of blade root bending moments of the TLP FHAWT and of the equivalent different for different βwave angles. Which is exactly the opposite of the surge motion, it has smaller onshore HAWT were almost the same. Loads on the blade root were mainly caused by turbulent effects on the sway motion when βwave is 0°, while the effect is bigger when βwave is 90°. There are similarwind, conclusions but short-term about the damage roll motion. equivalent loads on the blade were dramatically affected by the wave. Due to inclination of the tower, mean value of tower bending moment of the TLP FHAWT 5. Conclusionswas greater than it of the equivalent onshore HAWT. At the rated wind speed, My value of the TLP FHAWT exceeded it of the equivalent Onshore HAWT My value by 4702.37 kNm. In this paper, the quasi-mooring system was modified by calculating the quadratic damping, (2) Vibration of the TLP FHAWT tower was substantially affected by the wind-wave misalignment. and an improved model simulating the 10 MW TLP FHAWT was constructed based on the modified The aerodynamic damping generated by rotation of the rotor could significantly reduce vibration

Energies 2018, 11, 3341 22 of 24

of the tower caused by wave loads. As βwave increased, inclination of the platform caused the center of gravity of the nacelle to shift which further increased bending moments of the tower base. Therefore, reinforcement design for the TLP FHAWT tower should supposed to be enhanced. (3) Ultimate tension of the mooring system was mainly related to the displacement caused by pitch motion. Standard deviation of the tension was signiﬁcantly affected by the wave frequency response. Therefore, ultimate tension of the mooring line should be decreased by reducing the pitch motion. (4) Amplitudes of the pitch and roll motion were overestimated in the free decay motion due to the neglected of viscous drag of the mooring system. Viscous drag would increase the resonance of the platform under the wave loads, while the quasi-static mooring system correction model could capture those resonances better. Wave loads mainly affected the pitch and surge motion ◦ when βwave is 0 . The inertial force caused by the surge motion would generate high-frequency moments which would cause pitch resonance. When the wind-wave misalignment, the inertial force caused by the sway motion would generate high-frequency moments without the inhibition of aerodynamic damping, which would cause roll resonance.

Author Contributions: The analysis and interpretation of modeling and simulation were carried out by T.L., who was also responsible for writing the manuscript of this paper. D.T. conducts analysis and guidance, who also revised the manuscript critically. R.W. is in charge of data statistics and analysis. C.L. provides technical guidance. Funding: This research was funded by the CAS Key Laboratory of Wind Energy Utilization of China, Grant number KLWEU-2016-0101 and the Fundamental Research Funds for the Central Universities, Grant number 2018QN060. Conﬂicts of Interest: The authors declare no conﬂict of interest.

References

1. Danao, L.A.; Edwards, J.; Eboibi, O.; Howell, R. A numerical investigation into the influence of unsteady wind on the performance and aerodynamics of a vertical axis wind turbine. Appl. Energy 2014, 116, 111–124. [CrossRef] 2. Sun, H.; Luo, X.; Wang, J. Feasibility study of a hybrid wind turbine system—Integration with compressed air energy storage. Appl. Energy 2015, 137, 617–628. [CrossRef] 3. Liu, X.; Lu, C.; Li, G.; Godbole, A.; Chen, Y. Effects of aerodynamic damping on the tower load of offshore horizontal axis wind turbines. Appl. Energy 2017, 204, 1101–1114. [CrossRef] 4. Esteban, M.; Leary, D. Current developments and future prospects of offshore wind and ocean energy. Appl. Energy 2012, 90, 128–136. [CrossRef] 5. Shu, Z.R.; Li, Q.S.; Chan, P.W. Investigation of offshore wind energy potential in Hong Kong based on Weibull distribution function. Appl. Energy 2015, 156, 362–373. [CrossRef] 6. Han, Y.; Le, C.; Ding, H.; Cheng, Z.; Zhang, P. Stability and dynamic response analysis of a submerged tension leg platform for offshore wind turbines. Ocean Eng. 2017, 129, 68–82. [CrossRef] 7. Ding, H.; Liu, Y.; Zhang, P.; Le, C. Model tests on the bearing capacity of wide-shallow composite bucket foundations for offshore wind turbines in clay. Ocean Eng. 2015, 103, 114–122. [CrossRef] 8. Wayman, E.N.; Sclavounos, P.D.; Butterfield, S.; Jonkman, J.; Musial, W. Coupled dynamic modeling of floating wind turbine systems. In Proceedings of the Offshore Technology Conference, Houston, TX, USA, 1–4 May 2006. [CrossRef] 9. Karimirad, M.; Moan, T. Wave-and wind-induced dynamic response of a spar-type offshore wind turbine. J. Waterw. Port Coast. Ocean Eng. 2011, 138, 9–20. [CrossRef] 10. Jonkman, J.M.; Matha, D. Dynamics of offshore floating wind turbines—Analysis of three concepts. Wind Energy 2011, 14, 557–569. [CrossRef] 11. Bachynski, E.E.; Moan, T. Design considerations for tension leg platform wind turbines. Mar. Struct. 2012, 29, 89–114. [CrossRef] 12. Luan, C.; Gao, Z.; Moan, T. Modelling and analysis of a semi-submersible wind turbine with a central tower with emphasis on the brace system. In Proceedings of the ASME 2013 32nd International Conference on Ocean, Offshore and Arctic, Nantes, France, 9–14 June 2013. [CrossRef] Energies 2018, 11, 3341 23 of 24

13. Bachynski, E.E.; Kvittem, M.I.; Luan, C.; Moan, T. Wind-wave misalignment effects on floating wind turbines: Motions and tower load effects. J. Offshore Mech. Arctic Eng. 2014, 136, 041902. [CrossRef] 14. Matha, D. Model development and loads analysis of an offshore wind turbine on a tension leg platform with a comparison to other floating turbine concepts. In Proceedings of the European Offshore Wind 2009, Stockholm, Sweden, 14–16 September 2009. [CrossRef] 15. Li, Y.; Tang, Y.; Zhu, Q.; Qu, X.; Wang, B.; Zhang, R. Effects of second-order wave forces and aerodynamic forces on dynamic responses of a TLP-type floating offshore wind turbine considering the set-down motion. J. Renew. Sustain. Energy 2017, 9, 063302. [CrossRef] 16. Vita, L.; Ramachandran, G.K.V.; Krieger, A.; Kvittem, M.I.; Merino, D.; Cross-Whiter, J.; Ackers, B.B. Comparison of numerical models and verification against experimental data, using Pelastar TLP concept. In Proceedings of the ASME 2015 34th International Conference on Ocean, Offshore and Arctic Engineering, St. John’s, NL, Canada, 31 May–5 June 2015. [CrossRef] 17. Sant, T.; Bonnici, D.; Farrugia, R.; Micallef, D. Measurements and modelling of the power performance of a model floating wind turbine under controlled conditions. Wind Energy 2015, 18, 811–834. [CrossRef] 18. Nihei, Y.; Iijima, K.; Murai, M.; Ikoma, T. A comparative study of motion performance of four different FOWT designs in combined wind and wave loads. In Proceedings of the ASME 2014 33rd International Conference on Ocean, Offshore and Arctic Engineering, San Francisco, CA, USA, 8–13 June 2014. [CrossRef] 19. Liu, X.; Lu, C.; Liang, S.; Godbole, A.; Chen, Y. Vibration-induced aerodynamic loads on large horizontal axis wind turbine blades. Appl. Energy 2017, 185, 1109–1119. [CrossRef] 20. Shen, M.; Hu, Z.; Liu, G. Dynamic response and viscous effect analysis of a TLP-type floating wind turbine using a coupled aero-hydro-mooring dynamic code. Renew. Energy 2016, 99, 800–812. [CrossRef] 21. Farrugia, R.; Sant, T.; Micallef, D. A study on the aerodynamics of a floating wind turbine rotor. Renew. Energy 2016, 86, 770–784. [CrossRef] 22. Salehyar, S.; Zhu, Q. Aerodynamic dissipation effects on the rotating blades of floating wind turbines. Renew. Energy 2015, 78, 119–127. [CrossRef] 23. Stewart, G.M.; Lackner, M.A.; Robertson, A.; Jonkman, J.; Goupee, A.J. Calibration and validation of a FAST floating wind turbine model of the Deep C wind scaled tension-leg platform. In Proceedings of the 22nd International Offshore and Polar Engineering Conference, Rhodes, Greece, 17–22 June 2015; pp. 1–8. 24. Stewart, G.M.; Robertson, A.; Jonkman, J.; Lackner, M.A. The creation of a comprehensive metocean data set for offshore wind turbine simulations. Wind Energy 2016, 19, 1151–1159. [CrossRef] 25. Barth, S.; Eecen, P.J. Description of The Relation of Wind, Wave and Current Characteristics at The Offshore Wind Farm Egmond Aan Zee (Owez) Location in 2006; ECN: Amsterdam, The Netherlands, 2007. 26. Barj, L.; Jonkman, J.M.; Robertson, A.; Stewart, G.M.; Lackner, M.A.; Haid, L.; Stewart, S.W. Wind/wave misalignment in the loads analysis of a floating offshore wind turbine. In Proceedings of the 32nd ASME Wind Energy Symposium, National Harbor, MD, USA, 13–17 January 2014. [CrossRef] 27. Trumars, J.M.; Jonsson, J.O.; Bergdahl, L. The effect of wind and wave misalignment on the response of a wind turbine at Bockstigen. In Proceedings of the 25th International Conference on Offshore Mechanics and Arctic Engineering, Hamburg, Germany, 4–9 June 2006; pp. 635–641. 28. Moriarty, P.J.; Hansen, A.C. AeroDyn Theory Manual; National Renewable Energy Laboratory: Golden, CO, USA, 2005. 29. Leishman, J.G.; Beddoes, T.S. A Semi-Empirical model for dynamic stall. J. Am. Helicopter Soc. 1989, 34, 3–17. [CrossRef] 30. Gharali, K.; Johnson, D.A. Numerical modeling of an S809 airfoil under dynamic stall, erosion and high reduced frequencies. Appl. Energy 2012, 93, 45–52. [CrossRef] 31. Gharali, K.; Johnson, D.A. Dynamic stall simulation of a pitching airfoil under unsteady freestream velocity. J. Fluid. Struct. 2013, 42, 228–244. [CrossRef] 32. Jonkman, J.M.; Hayman, G.J.; Jonkman, B.J.; Damiani, R.R.; Murray, R.E. AeroDyn V15 User’s Guide and Theory Manual; NREL: Golden, CO, USA, 2015. 33. Wang, K.; Moan, T.; Hansen, M.O. Stochastic dynamic response analysis of a floating vertical-axis wind turbine with a semi-submersible floater. Wind Energy 2016, 19, 1853–1870. [CrossRef] 34. Veritas, D.N. Sesam User Manual: Wadam; SEP: Boulder, CO, USA, 2010. 35. Jonkman, J.M. Dynamics of offshore floating wind turbines—Model development and verification. Wind Energy 2009, 12, 459–492. [CrossRef] Energies 2018, 11, 3341 24 of 24

36. Hoff, J.R. Estimation of linear and quadratic roll damping from free-decay tests. Available online: http: //www.ivt.ntnu.no/imt/courses/tmr7/resources/decay.pdf (accessed on 6 July 2001). 37. International Electrotechnical Commission (IEC). Wind Turbines-Part 3: Design Requirements for Offshore Wind Turbines; International Electrotechnical Commission (IEC): London, UK, 2009. 38. Johannessen, K.; Meling, T.S.; Hayer, S. Joint distribution for wind and waves in the northern north sea. In Proceedings of the Eleventh International Offshore and Polar Engineering Conference, Stavanger, Norway, 17–22 June 2001. 39. Bak, C.; Zahle, F.; Bitsche, R.; Kim, T.; Yde, A.; Henriksen, L.C.; Natarajan, A. The DTU 10-MW Reference Wind Turbine; DTU: Lyngby, Denmark, 2013. 40. Jonkman, J.M.; Buhl, M.L., Jr. FAST User’s Guide-Updated 05; National Renewable Energy Laboratory (NREL): Golden, CO, USA, 2005. 41. Bredmose, H.; Mikkelsen, R.; Hansen, A.M.; Laugesen, R.; Heilskov, N.; Jensen, B.; Kirkegaard, J. Experimental study of the DTU 10 MW wind turbine on a TLP floater in waves and wind. In Proceedings of the EWEA Offshore Conference, Copenhagen, Denmark, 10–12 March 2015. [CrossRef] 42. Bae, Y.H.; Kim, M.H. Rotor-floater-tether coupled dynamics including second-order sum–frequency wave loads for a mono-column-TLP-type FOWT (floating offshore wind turbine). Ocean Eng. 2013, 61, 109–122. [CrossRef] 43. Matha, D.; Fischer, T.; Kuhn, M.; Jonkman, J. Model Development and Loads Analysis of a Wind Turbine on a Floating Offshore Tension Leg Platform; National Renewable Energy Lab. (NREL): Golden, CO, USA, 2010. 44. Bachynski, E.E.; Moan, T. Second order wave force effects on tension leg platform wind turbines in misaligned wind and waves. In Proceedings of the ASME 2014 33rd International Conference on Ocean, Offshore and Arctic Engineering, San Francisco, CA, USA, 8–13 June 2014; V09AT09A006.

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