1. Introduction
Global climate change has prompted many countries to achieve carbon neutrality by 2050 (IEA, 2021). Two approaches are essential to reach carbon neutrality: reducing carbon emissions from major sources, such as coal-fired power plants and factories, and absorbing the emitted carbon. In particular, reducing carbon emissions from electricity generation requires the development of renewable energy sources such as solar, wind, wave, and tidal power. As of 2024, the global renewable energy capacity is approximately 4,450 GW, with wind power accounting for around 1,130 GW, approximately 25% of the total (IRENA, 2025). On the other hand, offshore wind power, which is considered the most commercially viable with high potential for capacity expansion, remains underdeveloped, with a current capacity of around 80 GW. Onshore wind power faces challenges such as turbine noise, electromagnetic interference, and limited land availability for large-scale installations. In contrast, offshore wind power avoids these issues and offers a broader range of installation areas (Kyong et al., 2003). Moreover, deeper waters often provide stronger and more consistent wind resources than those found in onshore or nearshore locations. In water depths exceeding 40 meters, floating wind farms are more economical than bottom-fixed platforms, highlighting the need for continued technological development in this area (Bae and Kim, 2013).
Enhancing the dynamic stability of floating offshore wind turbines (FOWTs) is essential for improving power generation efficiency and facilitating platform maintenance. In offshore environments, areas with strong winds are typically accompanied by high waves. Therefore, hybrid power generation systems that extract wind and wave energy simultaneously can improve the stability of FOWTs and be more economical in terms of construction and installation compared to building the two systems separately, while also reducing the variability in energy extraction from wind power through wave energy conversion (Kim et al., 2015).
Several studies have been conducted to enhance the stability of FOWTs. One such approach involves attaching additional power generators to the wind power platform to achieve increased energy production and improved stability simultaneously, forming a hybrid energy platform. Muliawan et al. (2013) proposed the Spar-Torus combination (STC) model, which integrates a wave-bob type wave energy converter (WEC) with a spar-type FOWT. They compared the motion performance and wind power efficiency of the hybrid model with those of a single model without a WEC. Their results showed that while the heave response of the hybrid model increased slightly because of the power take-off (PTO) system, the surge and pitch responses decreased. Ghafari et al. (2021a) presented a model combining wave-star type WECs with a spar-type FOWT and investigated the effect of the number of WECs on platform motion responses. Their fast Fourier transform (FFT) analysis of the heave and pitch responses of the platform showed two distinct peaks. Low-frequency peak motion, unaffected by incident waves, decreased as the number of WECs increased, while the wave-dependent peak motion increased. They also reported that the distance between them decreased as the number of WECs increased, enhancing power generation through structural interactions among the WECs.
Ghafari et al. (2021b) proposed a model combining wave-star type WECs with the OC4 semi-submersible FOWT developed by the National Renewable Energy Laboratory (NREL). They arranged three, six, nine, and 12 WECs concentrically between the pontoons of the OC4 model and compared the results. When three WECs were attached, the power output varied by approximately 36% depending on the incident wave direction, but this variation decreased as the number of WECs increased. Kim and Koo (2024) attached two wave-star type WECs in alignment with the incident wave direction on a spar-type FOWT and conducted experiments and numerical simulations. Under conditions with no wind, they analyzed the motion performance of the hybrid energy platform with WEC motion constraints and the effect of the PTO system. Their results suggested that the pitch response of the hybrid platform decreased significantly because of the attached WECs, and the resulting reduction in heave and pitch motions led to a decrease in mooring line tension.
In the aforementioned studies on the motion response of hybrid energy platforms, the total volume of the wave-star type WECs was only approximately 0.01%–0.02% of the FOWT volume, resulting in minimal influence of WEC motion on the FOWT (Ghafari et al., 2021a; 2021b). In contrast, Kim and Koo (2024) used WECs with a total volume of approximately 13.4% of the FOWT, which had a significant impact on the dynamic response of the platform. Owing to limitations of the experimental setup in a two-dimensional wave tank, they installed two WECs aligned with the incident wave direction at the front and rear of the FOWT to analyze the impact on heave and pitch responses. Nevertheless, such a WEC configuration has limitations when studying the motion response of hybrid energy platforms under open sea conditions with various incident wave directions.
Therefore, this study extends the work of Kim and Koo (2024) by attaching four WECs at 90° intervals around the FOWT platform. The motion responses of the hybrid energy platform were analyzed through experiments and numerical simulations. Although the experiment was conducted for a single incident wave direction, various wave directions were considered in the numerical analysis. The four WECs were arranged in two configurations (“+” and “×” types) around the FOWT, considering the size limitations of the two-dimensional wave tank. Based on previous studies in which the WEC volume was relatively small compared to that of the platform, the total volume of the WECs in this study was set to approximately 22% of the platform volume. This configuration is larger than that of the WECs used in the commercial Wave Star C5–1000 kW system. The power generation, roughly estimated based on the volume ratio, is expected to be approximately four times that of an individual WEC (50 kW) in the C5–1000 kW system. A numerical model that included the side walls was used to evaluate the influence of wall-induced wave scattering (wall effect) on platform motion because the WECs were placed close to the side walls of the wave tank. Few studies have compared the results of numerical simulations with and without wave tank walls to validate floating body motion response experiments conducted in two-dimensional wave tanks. Therefore, this study investigated these effects through numerical analysis.
This study analyzed the motion responses of a hybrid wind-wave energy platform composed of a FOWT integrated with four WECs. The FOWT platform was based on the MIT-NREL 5MW tension leg platform (TLP) model, modified into a spar-type platform with inclined taut mooring lines and scaled to fit the size of the wave tank. The WECs were cylindrical wave-star types. Four of them were installed at 90° intervals around the FOWT platform using hinge connections. In the two-dimensional wave tank experiments, the incident wave direction was fixed, and the WECs were arranged in two configurations relative to the platform center: “+” type (Fig. 2(a)) and “×” type (Fig. 2(b)). The numerical analysis evaluated the motion performance and maximum mooring line tension of the hybrid platform under various incident wave directions at 15° intervals. The influence of the WECs was assessed by comparing the motion performance of the hybrid platform with that of a single platform without WECs. The wind conditions were not considered in this study to isolate the effects of WEC attachment, incident wave direction, and wall effect. The tower and turbine were assumed to be rigid bodies. A PTO damping coefficient was applied in the numerical model to examine the influence of energy conversion by the WECs. In addition, a numerical analysis was conducted to simulate an abnormal WEC response, assuming the WECs were rigidly fixed to the platform (one rigid body condition), and the resulting motion responses were compared.
2. Experimental and Numerical Models
2.1 Experimental Model
This study analyzed the motion responses of a Spar-type FOWT Experimental and Numerical Study on the Motion Response of a Hybrid Wind-Wave Energy Platform with Different WEC 447 platform, based on the MIT-NREL 5MW TLP and equipped with a taut mooring system. Fig. 1 shows the overall configuration of the experimental model of a hybrid wind-wave energy platform. Four cylindrical wave-star type WECs were attached to the platform at 90° intervals. The moment of inertia in the experimental model was implemented by placing counterweights appropriately at the bottom of the platform. The wind turbine tower was designed based on the specifications of the NREL 5MW reference turbine (Jonkman et al., 2009), and the rotor-nacelle assembly (RNA) was simplified as a point mass mounted at the top of the tower. Each WEC was connected to the platform using a hinge constraint, allowing only one degree of freedom in pitch motion relative to the platform. A taut mooring system was implemented using four tension springs.
The experiment was conducted in a two-dimensional wave tank, 6 m in length, 0.3 m in width, and 0.5 m in depth. Considering the size of the tank, the experimental model was constructed at a 1/256 scale of the full-scale platform using Froude scaling. Table 1 lists the dimensions and specifications of the hybrid wind-wave energy platform. Fig. 2 presents an overview of the experimental setup for the platform. The WECs connected to the platform were arranged in two configurations relative to the incident wave direction: “+” type (Fig. 2(a)) and “×” type (Fig. 2(b)). Incident waves were generated using a piston-type wave maker, and the wave height was measured with a TSPC-30S2 ultrasonic wave gauge from Senix. A porous plate-type wave absorber was installed to control wave reflection from the end of the tank; its wave-damping performance has been validated in a previous study (Jung and Koo, 2021). The motion responses of the platform were measured using a Prime 13 motion capture camera from OptiTrack. In this study, aerodynamic effects were not considered to allow focus on the motion response characteristics of the hybrid wind-wave energy platform according to the WEC configuration.
2.2 Mathematical Formulation and Numerical Model
The motion responses of the hybrid energy platform were calculated using AQWA, a commercial hydrodynamic software developed by ANSYS, based on the boundary element method (BEM) and linear potential flow theory (ANSYS, 2021). Fig. 3 shows the overall numerical analysis procedure. First, frequency-domain analysis was performed using the AQWA-LINE module to calculate the hydrodynamic coefficients that account for the interactions between the FOWT and the WECs under incident wave frequencies. These coefficients were used as input data for the time-domain analysis module AQWA-NAUT, which calculates the external forces acting on the hybrid platform. In AQWA-NAUT, hinge constraints were applied to connect the FOWT and four WECs. Time-domain simulations were conducted considering the nonlinear Froude–Krylov forces and nonlinear restoring forces resulting from changes in the wetted surface of the floating bodies.
2.2.1 Mathematical formulation
The three-dimensional frequency-domain commercial software AQWA-LINE was used to obtain the hydrodynamic coefficients of the hybrid energy platform. This software is a numerical hydrodynamic analysis program based on the BEM and linear potential flow theory. The flow can be described by a velocity potential assuming that the fluid field in the computational domain is inviscid, irrotational, and incompressible, and the time-domain velocity potential is expressed as Eq. (1). Under these assumptions, the governing equation in the computational domain becomes the Laplace equation, as shown in Eq. (2):
where X → ( X , Y , Z )
where φ1 and φd are the first-order incident and diffraction velocity potentials, respectively. φrj denotes the radiation velocity potential caused by unit amplitude motion in the jth direction. φ1 can be obtained using the theoretical expression shown in Eq. (4).
where g represents gravitational acceleration; k is the wavenumber; h is the water depth; and α is the incident wave angle. To calculate φd and φr Green’s theorem and Green’s function were applied to Eq. (2), resulting in the following boundary integral equation:
where S represents the wetted surface of the body, and n →
(6)
where ξ(ξ, η, ζ) represents the source position in the source distribution method, and J0 is the Bessel function of the first kind:
φd and φr can be obtained by solving the diffraction and radiation problems, respectively, by substituting the following boundary conditions into Eq. (5).
where v →
The Froude–Krylov force and diffraction force acting on the body due to the incident wave are calculated using φ1 and φd. In addition, φr is used to calculate the radiation force caused by the motion of the body, which is represented by the added mass and radiation damping coefficients. Using these, the equation of motion of the body is formulated as follows:
where M is the mass matrix of the hybrid platform. Ma and C are the added mass matrix and radiation damping matrix, respectively, which consider multi-body interactions. Khys represents the stiffness matrix of the platform, and Km denotes the stiffness matrix of the mooring lines. F is the external force vector acting on the platform, consisting of the sum of the Froude–Krylov force, diffraction force, and PTO system force.
The time-domain numerical analysis of the hybrid energy platform was performed using AQWA-NAUT. The equations of motion of the platform are expressed in the time domain using Cummins’ equation, as shown in Eq. (10).
where R denotes the velocity impulse function matrix; F(t) represents the external force. When Eq. (10) is defined as the equations of motion for the FOWT and the WEC, respectively, they can be expressed as Eqs. (11) and (12).
where Fm and Km represent the force and stiffness exerted by the mooring lines, respectively, and FEX is the wave excitation force, which is the sum of the Froude–Krylov force and diffraction force acting on the floating body. cPTO is the PTO damping coefficient acting on the WEC, and FFOWT,con and FWEC,con denote the constraint forces acting on the FOWT and WEC because of the hinge constraints. Detailed mathematical formulations can be found in the AQWA theory manual (ANSYS, 2021).
2.2.2 Numerical model
The motion responses of the hybrid wind-wave energy platform were calculated by modeling the numerical model connecting four cylindrical Wave-star type WECs to a spar-type FOWT identically to the experimental setup, as shown in Fig. 4(a). The tethers with the same characteristics as the tension springs used in the experiment were implemented in the numerical model. In the experiment, the WECs were connected to the FOWT with hinge constraints allowing only one degree of rotational freedom (pitch). The PTO system was modeled by applying a rotational damping coefficient at the hinge points (Ghafari et al., 2021a). The wall effect may influence the motion response of the FOWT because the distance between the installed WECs and the tank walls in the two-dimensional wave tank experiments is small. Numerical simulations were conducted by modeling two side walls (Fig. 4(b)) to include the wall effect, and the results were analyzed. Convergence tests for the numerical model are described in Section 3.1.
3. Numerical Simulation and Experimental Results
3.1 Convergence Test
Before conducting numerical simulations for the hybrid wind-wave energy platform, a convergence test was performed on the panel size and time step of the numerical model to obtain more accurate results. For this purpose, a single FOWT model was derived from the WEC-attached model shown in Fig. 4(a) by removing the WECs, and the numerical results were compared and analyzed. For convenience, the numerical model used in the convergence test was scaled to 100 times the size of the experimental model using Froude scaling. Fig. 5 compares the surge added mass (M11) for various panel sizes. The value of M11 tended to decrease as the panel size decreased. On the other hand, the reduction in M11 became less significant when the panel size was reduced below a certain level. Based on this, the panel size was set so that one side length was approximately 0.35 m. Under this condition, the feasible range of incident wave frequencies for numerical simulation was sufficiently wide, from 0.05 to 4.996 rad/s (corresponding to a panel size of 1/160 to 1/470 of the incident wavelength λ), balancing accuracy and computational efficiency. The FOWT model consisted of 3,648 panels below the water surface and 1,472 panels above it (total of 5,120 panels), and each WEC consisted of 776 panels below the water surface and 592 panels above it (total of 1,368 panels).
Experimental and Numerical Study on the Motion Response of a Hybrid Wind-Wave Energy Platform with Different WEC 451 The appropriate time step for the time-domain analysis was determined by comparing the heave responses of the single FOWT model under various time steps, as shown in Fig. 6. When the time step increased, the motion responses tended to diverge during long-duration simulations. Therefore, a time step of 0.04 s was selected to ensure stable results even for time histories exceeding 300 wave periods.
3.2 Comparison of Time Series Results Between Experiment and Numerical Results
Table 2 lists the incident wave conditions used in the two-dimensional wave tank experiment. The input value for the wave maker to generate the desired wave height was approximately 15 mm, but the actual wave height produced by the wave maker was approximately 80% of the input value, depending on the wave period. This discrepancy occurs because the bottom of the piston-type wave paddle is open, resulting in a reduced generated wave height compared to the input wave height.
Fig. 7 compares the time series responses of surge, heave, and pitch motions of the single FOWT platform between the experimental and numerical results. The wave period (T) and wave height (H) were 0.65 s and 13.3 mm, respectively, corresponding to 10.4 s and 1.33 m in full scale. The FOWT motions were compared over 20 wave periods after the initial transient phase had passed and steady-state conditions were reached. Overall, the experimental and numerical results showed good agreement.
3.3 Comparison of Numerical Results with and without Tank Walls
In the two-dimensional wave tank, the close proximity between the WEC connected to the FOWT and the tank walls can affect the motion response of the FOWT because of the wall effect. This was investigated by directly modeling a 300-m-long vertical wall using panels according to the method reported by Wang et al. (2024). The wall modeling was performed by placing a cylindrical floating body, 2 m in diameter with a 2 m draft, 2 m in front of the wall (distance from the center of the body to the wall). The vertical motion of the floating body due to incident waves approaching perpendicular to the wall was then calculated. Fig. 8(a) shows the panels representing the wall and the cylindrical floating body, while Fig. 8(b) presents the heave RAO of the body. When the incident wave approaches the wall perpendicularly, the heave RAO of the floating body under long-wave conditions converges to 2 because of the wall-reflected wave. Fig. 8(b) presents this trend, indicating that the wall modeling was successfully implemented. Nevertheless, slight variations in the motion response occur at low frequencies (long periods) because the modeled wall in this study does not have infinite length.
The effects of the tank walls on the motions of the FOWT and the hybrid platform were investigated by modeling two vertical walls, each 300 m in length, as shown in Fig. 4(b) to represent the side walls of the two-dimensional wave tank. The platform was modeled at a 1:100 scale based on the experiment, with the convergence test results as a reference. The panel size for the walls was determined using a convergence test, setting each panel side length to 2 m (λ/28–λ/93). Six thousand three hundred panels were used to model both walls, with 2,700 panels below the water surface and 450 panels above on each side. All subsequent numerical computations were performed on the 1:100 experimental scale, and the results were scaled to the full scale (1:256). Fig. 9 compares the heave RAOs of the single FOWT model and the hybrid wind-wave energy platform with and without the tank walls. The results revealed negligible differences in the motions of the floating bodies because of the presence of the walls. In particular, the wall effects on the motion responses of the combined platform with WECs were minimal. Hence, the motions of the hybrid platform can be measured accurately under the conditions of the present study, even in a two-dimensional wave tank experiment.
3.4 Comparison of the Motion Responses and Maximum Mooring Line Tensions
The numerical results obtained without wall modeling were compared with the experimental results because the differences in the motion responses of the platforms with and without the tank walls were small, as shown in Fig. 9. The results for the full-scale model were modeled by scaling the experimental results by a factor of 256 using Froude scaling. First, the experimental and numerical results of the motion responses of the single FOWT were compared (Fig. 10). All motion responses generally showed good agreement, but the numerical results exhibited significantly higher values near the heave resonance frequency (0.55 rad/s) because of the resonance effects caused by the linear numerical analysis.
Figs. 11 and 12 compare the wave-induced motions of the hybrid platform for two types of WEC configurations. For both types, the surge and heave responses showed good agreement between the experimental and numerical results. The pitch response generally matched at low frequencies but exhibited significant discrepancies at higher frequencies. This was attributed to the pitch natural frequency of the WEC, which was identified as approximately 0.65 rad/s through pitch-free decay tests on the hybrid platform. Near this frequency, linear numerical analysis tended to overestimate the WEC motion, resulting in an amplified pitch motion of the hybrid platform. This appears to be because damping was not considered in the numerical analysis, and it is expected that applying damping would make the results more consistent with the experimental data. In addition, while the experimental model included physical constraints on the motion of the WEC, the numerical analysis does not impose such constraints, which is believed to have influenced the motion of the platform. If the hinge constraint between the FOWT and WEC is changed to a fixed constraint, limiting the pitch motion of the WEC, the hybrid platform would move as a single rigid body, and the pitch response of the platform at high frequencies is expected to decrease. A detailed analysis of this will be discussed later.
Fig. 13 compares the numerical results of motion responses of the single FOWT from Fig. 10 with those of the hybrid platform having a (+)-type WEC arrangement from Fig. 11. The surge response showed little difference regardless of the interaction between the FOWT and WECs. The heave response, however, exhibited a significant difference in resonance frequency between the single FOWT and the hybrid platform. This shift occurred because the heave resonance frequency of the hybrid platform shifted to a lower frequency range because of the addition of the WECs. Consequently, the attachment of the WECs lowers the heave resonance frequency, causing resonance to occur in the long-period wave region (approximately 15.7 s), where wave occurrences are relatively infrequent in offshore environments, suggesting an improvement in wave-induced motion performance. On the other hand, the pitch response of the hybrid platform was significantly higher than that of the single FOWT at high frequencies. This was attributed to the pitch resonance frequency of the WEC being around 0.65 rad/s, and relatively large, excessive pitch motion of the WECs was induced because the total volume of the four WECs was approximately 22% of the FOWT platform volume.
Fig. 14 compares the maximum tensions in the L1 and L2 mooring lines connected to the single FOWT and the hybrid platform with two different WEC configurations. The maximum mooring line tension occurred at the heave resonance frequency of each platform, indicating a strong correlation between the heave response and the peak mooring line tension. Specifically, the maximum mooring line tensions of the hybrid platform were lower than those of the single FOWT, showing that the hybrid platform with installed WECs contributes to the motion stability of the FOWT and the stability of the mooring lines.
3.5 Motion Responses of the Hybrid Platform according to the Direction of Incident Waves
Fig. 15 compares the motion responses of the hybrid platform combined with (+)-type WEC arrangement under various incident wave directions. Four incident wave directions were considered: 0°, 15°, 30°, and 45°. The heave response showed little variation regardless of the incident wave direction, whereas the surge and pitch responses were largest at the head sea (0°) and decreased gradually as the incident wave angle increased. In particular, the pitch response showed a more significant decrease at the wave frequency of 0.65 rad/s (period of 9.6 s) when the wave direction increased compared to other frequencies. This is because this frequency is close to the WEC’s resonance frequency, causing substantial changes in the WEC motion depending on the incident wave direction.
3.6 Comparison of Platform Motion Responses according to Changes in WEC Motion
A PTO system must be implemented in the WEC to harness ocean wave energy under real sea conditions. Ghafari et al. (2021a) conducted simulations in which the hydraulic PTO piston was replaced with a hinge joint incorporating a selected rotational damping coefficient. Falnes (2002) suggested that PTO damping should be set equal to frequency-dependent hydrodynamic damping, a method investigated by Burgaç and Yavuz (2020).
In this study, the pitch PTO damping coefficient of the WTC was selected as a frequency-dependent pitch damping coefficient (CPTO = C55 (ω)) and applied at the hinge point connecting the FOWT and WEC to analyze how the WEC motion affects the overall response of the hybrid platform. The hinge points were positioned at 90° intervals along a circle with a diameter of 20.48 m, located 10.24 m above the still water level (SWL). The responses of the platform showed little variation regardless of the application of the PTO coefficients, as shown in Fig. 16. When PTO damping was applied, however, the surge and pitch responses showed a slight reduction near 0.65 rad/s, which can be attributed to the decrease in WEC motion caused by the PTO system. The surge and pitch motions with PTO damping were approximately 8.5% lower than those without PTO damping.
Fig. 17 compares the angular velocities of the WECs with and without the PTO system applied. WEC 1, WEC 2, and WEC 3 were positioned at the front in the + configuration, at the rear of the platform, and on the side, respectively (see Fig. 2(a)). All angular velocities were calculated as the relative angular velocities, accounting for the rotational motions of the spar platform and the WEC. The angular velocity of the WECs increased around 0.4 rad/s, which was attributed to the heave resonance frequency of the platform, as shown in Figs. 11,–13. In addition, the angular velocity of the WECs increased with frequency, likely influenced by the increasing pitch response of the platform. The WEC 1 and 2 angular velocities had a slight reduction near 0.65 rad/s when the PTO damping coefficient was applied, similar to the decrease in platform pitch motion.
If the WECs are assumed to be rigidly fixed to the FOWT platform under abnormal conditions, the WECs and FOWT platform behave as a single rigid body, resulting in significantly different motion responses compared to the original hybrid platform (Fig. 18). The surge response shows little change regardless of the WEC attachment, but the heave and pitch responses differ markedly, especially at high frequencies where they exhibit opposite trends. Therefore, the large total volume of the WECs relative to the FOWT platform (the total volume of four WECs was approximately 22%) substantially influences the motions of the platform. Therefore, by leveraging these motion characteristics, appropriate sizing and motion control of the WECs could stabilize the motions of the FOWT under specific sea conditions and improve power generation efficiency.
4. Conclusions and Future Works
This study conducted a comparative analysis of the motion responses of a hybrid wind-wave energy platform, consisting of a FOWT with four WECs attached via hinge constraints, through experiments and numerical simulations. The WECs were arranged around the platform in two different configurations, and the differences in motion responses were investigated according to the incident wave direction. Experiments were conducted in a two-dimensional wave tank, where wall modeling was conducted to examine the effects of tank walls on the platform motions. Under the conditions of this study, the numerical results indicated that the presence of the tank walls had little influence on the responses of the platform.
The surge response was similar in the single FOWT and the hybrid platforms, while the heave natural frequency of the hybrid platform shifted to a lower frequency range compared to the single FOWT. In addition, the pitch response was significantly larger in the hybrid platforms because of the amplified motion response of the WECs. The maximum mooring line tension occurred at the heave resonance frequency, indicating a strong correlation between the heave response and mooring line tension. In particular, the maximum mooring line tension of the hybrid platform was smaller than that of the single FOWT.
Regarding the effect of the incident wave direction on platform motions, the heave response showed almost no change, whereas the surge and pitch responses were largest at head sea (0°) and gradually decreased as the incident wave angle increased. Even with the application of PTO damping coefficients to the WECs, the motions of the hybrid platform showed no significant change. The angular velocity of the WECs increased near the heave resonance frequency (0.4 rad/s) of the platform and gradually rose as the wave frequency increased, influencing the pitch response of the platform. However, the heave and pitch responses of the platform exhibited significant changes under abnormal conditions where the WECs were rigidly fixed to the platform.
This study had some limitations because of the constraints of the experimental wave tank, which prevented an exploration of a broader range of WEC configurations and mooring conditions, limiting a more comprehensive comparative analysis. In future work, incorporating wind conditions and irregular waves into numerical simulations will enable a more realistic assessment of the motion characteristics of the combined wind–wave platform and the associated mooring line tensions. These insights can help in developing strategies to stabilize the motion of FOWTs under specific sea states by appropriately sizing and controlling the WECs, improving overall power generation efficiency. Furthermore, determining the optimal PTO damping coefficient will be essential for accurately estimating the power output of the WEC.
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