Constant Wind Analyses on Eight Floating Wind Turbines

1. Introduction

Wind energy is essential socially and economically to increase the sustainability and development in many countries around the world [1]. From this perspective, wind energy sources including floating wind turbines have become an essential electricity generation source [2].

To achieve zero carbon emissions, implementing offshore including floating wind energy in deep water areas has become a requirement [3,4,5,6,7,8].

Floating wind energy represents 80% of offshore wind energy resources due to its feasibility in high water depths [9,10].

The main two advantages of floating wind energy are the generation of electricity in deep waters, as well as the elimination of the global warming (climate change) threats that are due to excessive carbon emissions according to the Paris Agreement [11,12,13,14,15,16,17,18,19]. This applies especially in Europe, the US, and Japan which have limited shallow water depth offshore areas. This will necessitate cost reduction of floating wind levelized cost of energy compared to that of onshore and offshore bottom-fixed wind to facilitate implementation of such turbines [20,21,22,23,24,25].

Floating wind turbines are implemented in harsh environments such as high wave and high wind speed areas which makes their design and maintenance challenging [26,27]. Moreover, floating wind fatigue numerical analyses are challenging due to the complexity of wind and ocean environmental conditions [28]. A solution for this could be real-time monitoring in terms of mooring line fatigue computation for example [29].

The increasing floating wind sizes and their corresponding harsh environmental load conditions in deep water made it essential to carry out dynamic analyses for such systems [30].

A main challenge for implementing floating wind turbines is the instability resulting from the floating support structure and the controller [31]. A further difficulty in implementing TLP floating wind turbines for example is the necessity of pre-tensioned vertical mooring lines and a reliable anchor design which makes it difficult to implement such turbines [32].

Bottom-fixed offshore wind turbines currently have competitive costs as compared to onshore wind turbines in terms of electricity production [33]. A suggestion for reducing floating wind implementation costs is to implement floating wind farms with shared mooring lines [34]. This suggestion has the potential to be one of the most effective solutions for reducing such costs [35].

As of 2019, the European offshore wind capacity has been reported to be 22 GW, and it is expected to reach 300 GW in 2030 which will necessitate implementing floating wind turbines in deep water areas [36,37].

Knowledge of offshore wind environmental loading conditions is essential in designing such turbines [38]. A challenge of floating wind turbines is resonant motions which will influence their costs, performance, and lifespan and it needs to be studied and prevented [39].

Integrated analysis using aero-hydro-servo-elastic tools is essential for accurate numerical results of floating wind turbines [40]. Software for determining the global responses of such turbines implements numerically generated wind using aero-hydro-servo-elastic analyses [41,42].

Floating wind turbines have recently become the topic of interest in the fields of naval architecture and renewable energy. Therefore, conducting an analysis illustrating their response offsets is very important. From this perspective, this paper will cover the six-degree-of-freedom motion amplitudes for each of the eight floating wind turbines considered in the study throughout this paper.

Figure 1 shows the four floating wind turbine types from which three of them are analyzed throughout the eight concepts covered in the floating wind turbine analyses carried out in this paper.

The eight floating wind turbines considered in the study were also included in a previously published paper by the authors covering a complete and up-to-date literature review and aspects of relevance to modern floating wind turbines [43].

Table 1, Table 2, Table 3, Table 4, Table 5, Table 6, Table 7 and Table 8 show the characteristics of the different floating wind turbine models studied throughout this paper and implemented in the Sima 4.6.4 software. Figure 2, Figure 3, Figure 4, Figure 5, Figure 6, Figure 7, Figure 8 and Figure 9 and Table 1, Table 2, Table 3, Table 4, Table 5, Table 6, Table 7 and Table 8 show the eight floating wind turbines covered throughout these analyses, as well as their characteristics that are implemented in SIMA software.

Figure 2 and Table 1 illustrate the layout and the characteristics of the OO-Star floating wind turbine implemented in SIMA software.

Figure 3 and Table 2 illustrate the layout and the characteristics of the CSC floating wind turbine implemented in SIMA software.

Figure 4 and Table 3 illustrate the layout and the characteristics of the WindFloat floating wind turbine implemented in SIMA software.

Figure 5 and Table 4 illustrate the layout and the characteristics of the DTU Spar 1 floating wind turbine implemented in SIMA software.

Figure 6 and Table 5 illustrate the layout and the characteristics of the DTU Spar 2 floating wind turbine implemented in SIMA software.

Figure 7 and Table 6 illustrate the layout and the characteristics of the TLPWT floating wind turbine implemented in SIMA software.

Figure 8 and Table 7 illustrate the layout and the characteristics of the INO-WINDMOOR floating wind turbine implemented in SIMA software.

Figure 9 and Table 8 illustrate the layout and the characteristics of the VolturnUS-S floating wind turbine implemented in SIMA software.

Figure 2, Figure 3, Figure 4, Figure 8 and Figure 9 presented above show five semi-submersible floating wind turbine concepts (OO-Star, CSC, WindFloat, INO-WINDMOOR, and U-Maine Volturn-US). The first three floating wind turbines have a power capacity of 10 MW each. While the latter two have 12 and 15 MW power capacity respectively. It is to be noted that floating wind turbines with a power capacity of 10 MW throughout this paper have a rated wind speed of 11.4 m/s each. While the other floating wind turbines with 12 and 15 MW respectively have a rated wind speed of 10.6 m/s. It is also to be noted that all the presented floating wind turbines throughout this study implement upwind turbines except the INO-WINDMOOR semi-submersible which implements a downwind turbine. This means that the latter floating wind turbine generates energy by allowing the wind to hit the backside of its blades (See Figure 8 which illustrates the directions of wind and wave by arrows).

Figure 5 and Figure 6 show floating wind turbines with a spar type. Both turbines have the same power capacity of 10 MW and share most characteristics including water depth with a slight modification in the height of their support structures (See Figure 5 and Figure 6 and Table 4 and Table 5 for further details).

Figure 7 shows a floating wind turbine with a TLP type. This turbine has a conventional power capacity of 10 MW.

The models of the analyzed eight floating wind turbines in this paper were taken from Reference [46]. These Sima 4.6.4 models were used to carry out the constant wind analyses and their output data are presented in Section 3 of this paper.

Further state-of-the-art tools and external references related to floating wind turbines are as follows.

References [47,48,49] present innovative aspects of relevance to floating wind turbines’ building and classing standards and dynamic responses.

References [50,51,52,53,54,55,56] show innovative aspects related to floating wind inter-array dynamic power cables’ analyses, design, software, and information relevant to floating wind mooring systems.

References [57,58,59] present innovative aspects relevant to floating wind turbines' operations, and structural design tools.

References [60,61,62,63,64,65,66,67] present floating wind turbine analysis software such as SESAM (including GeniE, HydroD, Sima, etc.), Bladed, OrcaFlex, Riflex, and DeepC.

Reference [68] presents bottom-fixed and floating wind turbine failure analyses concerning their components.

References [69,70] present floating wind turbines’ design aspects, response, and reliability analyses.

Reference [71] presents bottom-fixed and floating wind turbines' response analyses, software, and numerical tools.

Reference [72] presents floating wind farms and array-level floating wind turbines' innovative designs and challenges.

References [73,74] present innovative aspects of relevance to floating wind turbine verification and design tools. As well as the design of installation vessels that are specialized in installing floating wind turbines.

References [75,76] present floating wind turbines' redundant components. The main considered components are the blades and drivetrain components including the nacelle, generator, and gearbox. As well as floating wind turbines' hydrodynamic challenges relevant to their implementation in shallow water depths.

Reference [77] presents information relevant to floating wind turbines' station-keeping mooring system design, and anchoring.

References [78,79,80] present dynamic and fatigue analyses related to the power cables of connected floating wind turbines using OrcaFlex software. As well as dynamic power cables' fatigue analyses of relevance to floating wind turbines. As well as floating wind turbines' probabilistic fatigue design using Monte Carlo simulation.

References [81,82] present the Norwegian perspective on the European and global wind energy situation. As well as the positive stability effects controllers have on floating wind turbines implemented in high water depths.

References [83,84] present the positive effects of relevance to the repositioning of some floating wind turbines to enhance their electricity power output. These references also present bottom-fixed and floating wind turbines' power performance as well as extreme load analyses. As well as predictions and challenges relevant to huge floating wind turbines.

References [85,86] show offshore wind certification requirements and standards in different countries worldwide. They also present vortex-induced vibration (VIV) fatigue analyses of floating wind dynamic power cables.

The next section will present the materials and methods of relevance to the different floating wind analyses carried out in this paper.

2. Materials and Methods

This section will present some aspects of the mathematical background behind the Sima 4.6.4 software that is used to carry out the constant wind analyses of the eight floating wind turbines studied in this paper.

Sima software is used to carry out these analyses. This software is dedicated to floating wind turbines due to their computational capabilities that allow fully coupled dynamic analyses that are based on aero-hydro-servo-elastic theory. Sima software has the capability of calculating aerodynamic and hydrodynamic loads. It has the capability of controlling dynamic loads using control theory. It has the capability of calculating structural dynamics loads using elastic theory of relevance to the mooring system.

According to Reference [87], Sima software implements SIMO and Riflex models. The SIMO model is used to design the rigid floating support structure. The Riflex model on the other hand is used to design the wind turbine that is coupled to the floating wind support structures using a flexible tower. The RIFLEX model is also used to design the mooring lines that are coupled to the floating wind support structure.

The wind turbine is implemented in RIFLEX based on Blade Element Momentum (BEM) theory. The tower is modeled using tens of beam elements. The mooring lines are designed using bar elements with master super nodes at the support structure’s origin and slave super modes at the fairleads. A further reference related to mooring line design is the following [88]. Controller-related aspects can be found in Reference [89]. This reference especially focuses on the VolturnUS-S floating wind turbine.

The support structure modeled in SIMO is subjected to wave loads and subjected to loads that come from the finite element structures designed in RIFLEX.

According to [87], the implemented time-domain equation of motion in SIMA software is the following.

$$\left(m+A_{\infty }\right)\ddot{x}+D_1\dot{x}+Kx+\underset{0}{\overset{t}{\int }}h\left(t-\tau \right)\dot{x}\left(\tau \right)d\tau =q\left(t,x,\dot{x}\right)$$

(1)

Where:

m: Inertia matrix obtained from platforms steel and ballast masses

$A_{\infty }$: Added mass of infinite frequency

$D_1$: External linear damping matrix

$K$: Restoring hydrostatic matrix

$h$: Retardation matrix

$q$: Vector with external loads which includes first and second-order loads, viscous loads (Morison terms), tower loads, and mooring-induced forces

As was mentioned above, Sima is a software that is dedicated to marine operations and floating wind turbines. It is an aero-hydro-servo-elastic software that uses potential flow theory for generating the sea surface.

According to Reference [90], SIMA software implements potential flow theory that is based on the velocity potential concept which has the assumptions of incompressible and inviscid fluid and irrotational flow. The velocity potential in potential flow theory will satisfy the Laplace equation based on the above assumptions mathematically as follows:

$${\nabla }^2\varphi =0$$

(2)

The constant wind analyses of the eight floating wind turbines analyzed in this paper using Sima software are divided into three types. Only wind analyses, Wind and wave analyses, and Wind, wave, and current analyses. This is to compare the response offsets of the different analysis types.

When carrying out the analyses, 10 thousand seconds was allocated to each analysis to ensure convergence. A time step of 0.005 seconds was selected to ensure accurate results. The time increment of wave/body response was set to 0.1 seconds. The mean values of the time series excluding the transients were used to generate the table values presented in Section 3.

In terms of the analyses concerning no contribution from wave forces (Only wind analyses), the significant wave height was set to 0.001 meters (Hs=0.001 m) and the peak period was set to 20 seconds (Tp=20 s) to ensure no contribution of waves to these analyses.

Furthermore, the three-parameter spectra was implemented in the analyses for generating the waves. The stationary uniform (constant) wind type was implemented in the software for generating the wind.

The next section will present the results of the analyses of the eight floating wind turbines studied in this paper.

3. Results

This section will present the results outputted from the Sima 4.6.4 software regarding the six degrees of freedom of the eight floating wind turbines studied in this paper.

Subsection 3.1 will consider only wind analyses. Meanwhile, Subsection 3.2 will consider wind, wave, and current analyses.

Subsection 3.1 will only study three degrees of freedom (Surge, Roll, and Pitch) in terms of 12 different wind speeds (2-24 m/s). Subsection 3.2 will study the six degrees of freedom in terms of the rated wind speed (11.4 m/s for 10 MW and 10.6 m/s for 12 and 15 MW floating wind turbines respectively).

3.1. Only Wind Analyses

Table 9, Table 10, Table 11, Table 12, Table 13, Table 14, Table 15, Table 16 and Table 17 and Figure 10, Figure 11, Figure 12, Figure 13, Figure 14, Figure 15, Figure 16, Figure 17 and Figure 18 show the only wind constant wind analysis results of the eight floating wind turbines studied in this paper.

Table 9 and Figure 10 show that the OO-Star only-wind Surge offset is 4.7-29.18-12.8 m for the wind speeds 4-11.4-24 m/s. Note that the maximum response offset is reached at the rated wind speed (11.6 m/s for 10 MW and 10.6 m/s for 12 and 15 MW floating wind turbines) which is between the maximum and minimum wind speeds. This is the reason for listing three wind speeds and three corresponding response offsets in presenting the tables of this subsection.

CSC Surge offset is 1.5-11.74-4.4 m for wind speeds 4-11.4-24 m/s respectively.

WindFloat Surge response offset is 1.8-13.36-5.06 m for wind speeds 4-11.4-24 m/s respectively.

TLPWT Surge response offset is 0.4-2.2-1.18 m for wind speeds 4-11.4-24 m/s respectively.

Table 10 and Figure 11 show only wind Roll response offset for OO-Star, CSC, WindFloat, and TLPWT floating wind turbines.

OO-Star Roll response offset is 0.02-0.36-0.29° for wind speeds 4-11.4-24 m/s respectively.

CSC Roll response offset is 0.01-0.34-0.38° for wind speeds 4-11.4-24 m/s respectively.

WindFloat Roll response offset is 0.009-0.3003-0.33° for wind speeds 4-11.4-24 m/s respectively.

TLPWT Roll response offset is 0.000014-0.00164-0.002° for wind speeds 4-11.4-24 m/s respectively.

Table 11 and Figure 12 show the only wind Pitch response offset for OO-Star, CSC, WindFloat, and TLPWT floating wind turbines.

OO-Star only wind Pitch response offset is 0.6-5.9-2.2° for wind speeds 4-11.4-24 m/s respectively.

CSC only wind Pitch response offset is 0.7-6.7-2.5° for wind speeds 4-11.4-24 m/s respectively.

WindFloat Pitch response offset is 6.09-12.4-7.9° for wind speeds 4-11.4-24 m/s respectively.

TLPWT Pitch response offset is 0.0007-0.005-0.002° for wind speeds 4-11.4-24 m/s respectively.

Table 12 and Figure 13 show only the Surge response offset of VolturnUS-S and INO-WINDMOOR floating wind turbines.

VolturnUS-S Surge response offset is 4.2-15.9-9.9 m for wind speeds 4-10.6-24 m/s respectively.

INO-WINDMOOR Surge response offset is 3.3-10.3-7.5 m for wind speeds 4-10.6-24 m/s respectively.

Table 13 and Figure 14 show only wind Roll response offset of VolturnUS-S and INO-WINDMOOR floating wind turbines.

VolturnUS-S has only wind Roll response offset is 0.02-0.334-0.337° for wind speeds 4-10.6-24 m/s respectively.

INO-WINDMOOR only wind Roll response offset is 0.07-0.5-0.37° for wind speeds 4-10.6-24 m/s respectively.

Table 14 and Figure 15 show only wind Pitch response offset of VolturnUS-S and INO-WINDMOOR floating wind turbines.

VolturnUS-S Pitch response offset is 0.6-2.6-0.8° for wind speeds 4-10.6-24 m/s respectively.

INO-WINDMOOR Pitch response offset is 0.7-4.4-1.5° for wind speeds 4-10.6-24 m/s respectively.

Table 15 and Figure 16 show only wind Surge response offset of DTU Spar 1 and DTU Spar 2 floating wind turbines.

DTU Spar 1 only wind Surge response offset is 6.1-37.9-16.8 m for wind speeds 4-11.4-24 m/s respectively.

DTU Spar 2 only wind Surge response offset is 4.64-26.3-13.5 m for wind speeds 4-11.4-24 m/s respectively.

Table 16 and Figure 17 show only wind Roll response offset of DTU Spar 1 and DTU Spar 2 floating wind turbines.

DTU Spar 1 only wind Roll response offset is 0.0102-0.24-0.19° for wind speeds 4-11.4-24 m/s respectively.

DTU Spar 2 only wind Roll response offset is 0.017-0.35-0.28° for wind speeds 4-11.4-24 m/s respectively.

Table 17 and Figure 18 show only wind Pitch response offset for DTU Spar 1 and DTU Spar 2 floating wind turbines.

DTU Spar 1 only wind Pitch response offset is 1.08-7.57-3.2° for wind speeds 4-11.4-24 m/s respectively.

DTU Spar 2 only wind Pitch response offset is 1.46-10.27-4.42° for wind speeds 4-11.4-24 m/s respectively.

3.2. Wind, Wave, and Current Analyses

This subsection will show wind, wave, and current constant wind analyses of the eight floating wind turbines studied in this paper. External references with corresponding analysis results will also be cited and compared.

Table 18, Table 19, Table 20, Table 21, Table 22, Table 23, Table 24 and Table 25 show wind, wave, and current six-degrees-of-freedom response offset for OO-Star, CSC, WindFloat, TLPWT, VolturnUS-S, INO-WINDMOOR, DTU Spar 1, and DTU Spar 2 floating wind turbines. As mentioned above, unlike Subsection 3.1 which covered 12 different wind speeds 92-24 m/s) for each response offset simulation, this subsection will only consider the rated wind speed (11.4 m/s for the 10 MW and 10.6 m/s for the 12 and 15 MW floating wind turbines respectively). This is due to the complexity of the analyzed data.

Table 18, Table 19, Table 20, Table 21, Table 22, Table 23, Table 24 and Table 25 only present analysis results with two different sea states (Hs = 2.5 m, Tp = 10 s and Hs = 4 m, Tp=12 s). These two sea states are analyzed with and without current effects as illustrated in the tables. The implemented current speed in these analyses is 2 m/s and it is only applied at the sea surface (z=0).

Table 18 shows that the OO-Star Surge response offset is 29.18-58.3 m.

Paper [91] has analyzed the OO-Star Surge motion and concluded that it is 20 m. Note that the input data of both analyses is different.

OO-Star Sway response offset ranges between 0.1514-0.222 m.

OO-Star Heave response offset ranges between 0.47-0.59 m.

Paper [91] has analyzed the OO-Star Heave motion and concluded that it is 0.4 m. Note that the input data of both analyses is different.

OO-Star Roll response offset ranges between 0.3684-0.3853°.

OO-Star Pitch response offset ranges between 3.6-5.9°.

Paper [91] has analyzed the OO-Star Surge offset and concluded that it is 5.9°. Note that the input data of both analyses is different.

OO-Star Yaw response offset ranges between 0.1213-0.1253°.

Reference [92] present aspects regarding OO-Star Semi-submersible floating wind turbines, as well as further predictions on the future of 20 MW floating wind turbines.

Table 19 shows that the CSC Surge response offset is 11.7-39.08 m.

Paper [35] has analyzed CSC Surge motion and concluded that it is 8.5-10 m. Note that the input data of both analyses is different.

CSC Sway response offset ranges between 0.019 and 0.1 m.

Paper [35] has analyzed CSC Sway motion and concluded that it is 4.5-9 m. Note that the input data of both analyses is different.

CSC Heave response offset ranges between 0.17 and 0.619 m.

Paper [35] has analyzed CSC Heave motion and concluded that it is 3.5-5.5 m. Note that the input data of both analyses is different.

CSC Roll response offset ranges between 0.301 and 0.347°.

Paper [35] has analyzed CSC Roll offset and concluded that it is 3°. Note that the input data of both analyses is different.

CSC Pitch response offset ranges between 4.51 and 6.76°.

Paper [35] has analyzed CSC Pitch offset and concluded that it is 4.2-6.8°. Note that the input data of both analyses is different.

CSC Yaw response offset ranges between 0.082 and 0.105°.

Paper [35] has conducted an analysis for CSC Yaw offset and concluded that it is 1.8-1.9°. Note that the input data of both analyses is different.

Reference [93] reports natural period values for the CSC floating wind turbine as 25.57 s for heave, 35.47 s for roll, and 35.47 s for pitch. Note that the input data of both analyses is different.

Reference [94] presents a 5 MW CSC Semi-submersible floating wind turbine's design and response reduction analyses using SESAM software.

Table 20 shows that the WindFloat Surge response offset is 13.2-34.9 m.

Paper [95] has analyzed WindFloat Surge motion and concluded that it is 15 m. Note that the input data of both analyses is different.

WindFloat Sway response offset ranges between 0.016 and 0.14 m.

WindFloat Heave response offset ranges between 1.37 and 1.44 m.

Paper [95] has analyzed WindFloat Heave motion and concluded that it is 1.7 m. Note that the input data of both analyses is different.

WindFloat Roll response offset ranges between 0.255 and 0.3009°.

WindFloat Pitch response offset ranges between 11.2 and 12.4°.

Paper [95] has analyzed WindFloat Pitch offset and concluded that it is 2°. Note that the input data of both analyses is different.

WindFloat Yaw response offset ranges between 0.02 and 0.05°.

Table 21 shows that the TLPWT Surge response offset is 2.2-4.83 m.

TLPWT Sway response offset ranges between 0.002 and 0.0075 m.

TLPWT Heave response offset ranges between 0.068 and 0.17 m.

TLPWT Roll response offset ranges between 0.0015 and 0.002°.

TLPWT Pitch response offset ranges between 0.0053 and 0.00576°.

TLPWT Yaw response offset ranges between 0.0832 and 0.0949°.

References [96,97] present a review of multidisciplinary design optimization of relevance to Spar, Semi-submersible, and TLP floating wind turbines. As well as guidelines relevant to the design of floating wind turbines.

Reference [98] presents 5 MW Tension-Leg-Buoy (TLB) validation using tank tests and coupled aero-hydro-servo-elastic numerical tools.

Table 22 shows that the VolturnUS-S Surge response offset is 15.9-24.29 m.

Paper [99] has reported VolturnUS-S Surge motion as 8.8 m. Note that the input data of both analyses is different.

VolturnUS-S Sway response offset ranges between 0.0803 and 0.1004 m.

VolturnUS-S Heave response offset ranges between 0.12 and 0.201 m.

VolturnUS-S Roll response offset ranges between 0.334 and 0.397°.

VolturnUS-S Pitch response offset ranges between 2.607 and 4.03°.

Paper [99] has reported VolturnUS-S Pitch offset as 2.7-5.2°. Note that the input data of both analyses is different.

VolturnUS-S Yaw response offset ranges between 0.241 and 0.31°.

Papers [100,101] report frequency-domain analyses for the VolturnUS floating wind turbine in contrast to our work considering time-domain analyses. These papers also present structural analyses of relevance to the 15 MW VolturnUS-S Semi-submersible floating wind turbine using Bladed and SESAM software.

Table 23 shows that the INO-WINDMOOR Surge response offset is 10.3-41.07 m.

INO-WINDMOOR Sway response offset ranges between 0.031 and 0.0604 m.

INO-WINDMOOR Heave response offset ranges between 0.077 and 0.453 m.

INO-WINDMOOR Roll response offset ranges between 0.5053 and 0.5266°.

INO-WINDMOOR Pitch response offset ranges between 2.362 and 4.464°.

INO-WINDMOOR Yaw response offset ranges between 0.051 and 0.589°.

Papers [39,102] report the six degrees of freedom of INO-WINDMOOR and other floating wind turbines, but as a function of natural period, and not as a function of response offset as is the case in our work in this paper.

References [39,103] present WINDMOOR 12 MW floating wind turbine hydrostatic stability and hydrodynamics analyses using SIMA, SIMO, RFLEX, and WAMIT software.

Reference [104] present 15 MW Semi-submersible floating wind turbine time-domain stress analyses.

Table 24 shows that the DTU Spar 1 Surge response offset is 37.6-62.18 m.

DTU Spar 1 Sway response offset ranges between 0.309 and 0.324 m.

DTU Spar 1 Heave response offset ranges between 1.34 and 3.38 m.

DTU Spar 1 Roll response offset ranges between 0.217 and 0.224°.

DTU Spar 1 Pitch response offset ranges between 7.57 and 8.24°.

Paper [30] reported a Spar pitch offset as 7-14°. Note that the input data of both analyses is different.

DTU Spar 1 Yaw response offset ranges between 0.31 and 0.35°.

References [105,106,107] present state-of-the-art aspects relevant to the OC3-Hywind Spar floating wind turbine aero-hydro-servo-elastic analyses, and multidisciplinary design optimization analyses. They also present relevant numerical simulations and experiments.

References [108,109,110,111,112,113] present the 10 MW DTU wind turbine mounted on bottom-fixed turbines. They also present the designs and dynamic responses of Spar, Semi-submersible, and TLP floating wind support structures.

References [114,115] present a study of selecting suitable floating wind support structures from the point of view of their hydrodynamic and aerodynamic performances. They also present wind models' sensitivity analyses of relevance to the dynamic response of floating wind turbines.

Table 25 shows that the DTU Spar 2 Surge response offset is 26.3-50.7 m.

Paper [115] reports Spar Surge motion as 24 m. Note that the input data of both analyses is different.

DTU Spar 2 Sway response offset ranges between 0.28 and 0.302 m.

Paper [115] reports Spar Sway motion as 0.5-4 m. Note that the input data of both analyses is different.

DTU Spar 2 Heave response offset ranges between 1.302 and 3.34 m.

Paper [115] reports Spar Heave motion as 1.8-6 m. Note that the input data of both analyses is different.

DTU Spar 2 Roll response offset ranges between 0.313 and 0.35°.

Paper [115] reports Spar Roll offset as 0.3-3.5°. Note that the input data of both analyses is different.

DTU Spar 2 Pitch response offset ranges between 10.2 and 10.9°.

Paper [115] reports Spar Pitch offset as 2.5-8.5°. Note that the input data of both analyses is different.

DTU Spar 2 Yaw response offset ranges between 0.26 and 0.31°.

Paper [115] reports Spar Yaw offset as 0.5-5°. Note that the input data of both analyses is different.

Paper [6] reports two-bladed spar floating wind turbine degrees of freedom as 8-18 m for surge, 0.5-0.75 m for heave, and 3-5° for pitch. Note that the input data and the floating wind concepts of both analyses are different.

5. Conclusions

This paper has considered only wind constant wind analyses. As well as wind, wave, and current constant wind analyses of eight floating wind turbines.

Due to the complexity of the presented results, this section will only present the minimum and maximum response offset of each of the presented degrees of freedom along with their corresponding floating wind turbine concepts (See Table 26 below).

Section 3.1 has considered only wind response offset analyses in terms of 12 different wind speeds (2-24 m/s) for three degrees of freedom (Surge, Roll, and Pitch). These analyses have shown the maximum response offsets correspond to the rated wind speeds (11.4 m/s for 10 MW and 10.6 m/s for 12 and 15 MW).

Section 3.2 has considered wind, wave, and current constant wind analyses for all the degrees of freedom in terms of the corresponding rated wind speeds. According to Table 26 below, the minimum Surge response offset is 4.834 m and corresponds to the TLPWT floating wind turbine. The maximum Surge response offset is 62.18 m and corresponds to DTU Spar 1 floating wind turbine.

The minimum Sway response offset is 0.007561 m and corresponds to the TLPWT floating wind turbine. The maximum Sway response offset is 0.3243 m and corresponds to DTU Spar 1 floating wind turbine.

The minimum Heave response offset is 0.1718 m and corresponds to the TLPWT floating wind turbine. The maximum Heave response offset is 3.384 m and corresponds to DTU Spar 1 floating wind turbine.

The minimum Roll response offset is 0.002142° and corresponds to the TLPWT floating wind turbine. The maximum Roll response offset is 0.5266° and corresponds to the INO-WINDMOOR floating wind turbine.

The minimum Pitch response offset is 0.005766° and corresponds to the TLPWT floating wind turbine. The maximum Pitch response offset is 10.93° and corresponds to DTU Spar 2 floating wind turbine.

The minimum Yaw response offset is 0.05138° and corresponds to WindFloat floating wind turbine. The maximum Yaw response offset is 0.58993° and corresponds to the INO-WINDMOOR floating wind turbine.