1. Introduction
Offshore wind power technology is emerging as a key renewable energy source in response to climate change and increasing energy demand. Offshore wind turbines (OWTs) are categorized into bottom-fixed types and floating types, enabling energy production in diverse marine environments. Bottom-fixed offshore wind turbines (BOWTs) are typically installed in shallow waters, while floating offshore wind turbines (FOWTs) are gaining prominence in deep-sea regions where BOWTs are difficult to deploy (Gueydon and Weller, 2013; Lieng, 2024; Musial, 2005; Nah et al., 2011; Rim et al., 2011). Research on 5 MW-class FOWT platforms began in the 2000s (Jonkman et al., 2009; Lefebvre and Collu, 2012; Lienard et al., 2020). Additionally, studies on commercial FOWT farms have been reported (Choi et al., 2021; Kim and Maeng, 2023; Neira et al., 2021).
FOWTs must ensure excellent motion performance during the design phase to operate reliably in their installed marine environments for a minimum design life of 20 years. This is because FOWTs are constantly exposed to strong waves and winds, and superior motion performance not only enhances power generation efficiency but also reduces the loads acting on the FOWT. Consequently, experimental studies to validate the motion performance of FOWTs are actively being conducted. These studies are essential for evaluating the performance of offshore wind turbines, as they play a critical role in assessing equipment durability and long-term performance.
Ha et al. (2022), Li et al. (2023), Yang et al. (2019) evaluated motion performance by simulating real ocean conditions through basin model experiments. Ahn et al. (2022) conducted model tests for a 10 MW-class semi-submersible platform, considering the offshore environmental conditions of Ulsan, while Sim (2024) proposed wind load coefficients applicable at the design stage by predicting wind loads on a 10 MW-class FOWT using simplified formulas and comparing them with wind tunnel test results. Fowler et al. (2023) compared basin test results of a 1:70 scaled model of a 15 MW FOWT with OpenFAST simulation results, confirming that the reference open source controller (ROSCO) effectively reduced platform pitch responses and tower base loads. Bae et al.(2022) introduced a hybrid substructure concept (MSPAR), combining the advantages of spar-type and semi-submersible designs, and assessed stability at each installation stage through tank model experiments. Chen et al. (2022) analyzed the pros and cons of physical model experiments and real-time hybrid experiments for tank testing of FOWTs. These experimental studies provide foundational data to verify and improve the accuracy of numerical analyses, further advancing the design and operational capabilities of FOWTs.
However, experimental research requires significant time and cost, leading to an increasing reliance on numerical simulations. Sohn et al. (2015) calculated the equivalent design wave that induces the maximum response from environmental loads acting on a floating wave-wind hybrid power generation system and applied it in structural analysis. Yang and Lee (2024) analyzed changes in the drag coefficient during surge motion of Floating Offshore Wind Turbines (FOWTs) using computational fluid dynamics (CFD) simulations. Liu et al. (2020) proposed a fault diagnosis method that detects mooring system failures using wave loads based on a linear model and resolves major issues in advance. Zhang et al. (2024) optimized the design and performance of FOWT controllers using CFD, simultaneously improving stability and power generation efficiency
The substructure types of FOWTs are classified into spar type, semi-submersible type, and barge type, while the mooring systems for station-keeping are categorized into taut type and catenary type. Each substructure type is selected to avoid resonance with the natural frequency of the installation site, depending on wave characteristics. Hu et al. (2024) and Nihei et al. (2014) conducted comparative studies on the motion performances of various substructures.
The spar substructure, due to its small water plane area, exhibits limited heave motion and is considered suitable for relatively deep waters (Musial, 2005; Nah et al., 2011; Rim et al., 2011; Wang et al., 2024). Tension leg platforms are designed for high durability in deep waters and maintain stability under extreme conditions such as strong waves (Barooni et al., 2023; Boo et al., 2024; Udoh et al., 2023). On the other hand, barge-type substructures have poor seakeeping performance due to their large water plane area but can secure stability by reducing the water plane area using moon pools (Kharade & Kapadiya, 2014; Zhai et al., 2022a, 2022b). Research on optimizing FOWT performance through sensitivity analysis of semi-submersible substructure designs has been ongoing (Lee et al., 2018; Zhong et al., 2023; Zhou et al., 2023). Lemmer et al. (2020) and Park and Shin (2015) analyzed various design variables of semi-submersible substructures and proposed improvements for performance enhancement.
Semi-submersible substructures are classified as center column type when the tower is positioned at the center of a triangle, and as side column type when the main columns support the tower. According to Saunders and Nagamune (2023), the turbine position significantly impacts the platform’s long-term fatigue performance and dynamic stability. Ivanov et al. (2023) proposed design solutions focusing on manufacturing costs and strength through structural analysis of various column and pontoon shapes, particularly suggesting the superiority of an asymmetric hexagonal column reinforced with bracing. However, this study did not analyze the relationship between substructure dimensions and dynamic responses.
Harger et al. (2023) conducted resonance analysis by examining the dynamic behavior of a 15 MW semi-submersible FOWT through modal analysis. Nevertheless, the sensitivity of motion responses to design variables was not addressed.
Previous studies have focused on analyzing dynamic responses according to FOWT substructure design variables. However, this study aims to propose an improved design by analyzing motion responses in frequency domain based on the dominant design variables of the reference FOWT substructure.
2. Reference FOWT
In this study, the basic specifications of a floating offshore wind turbine (FOWT) were determined by referencing a 15 MW-class open FOWT (Allen et al., 2020; Gaertner et al., 2020), as shown in Fig. 1. The fundamental specifications and properties of the turbine, substructure, and mooring system are presented in Table 1, Table 2, Table 3 respectively.
3. Sensitivity Analyses
3.1 Design Criteria
In this study, the pitch angle, RNA acceleration, and heave natural period were determined as indicators for evaluating the performance of a FOWT. The pitch angle refers to the maximum tilt that can occur during the operation of the FOWT. A larger pitch angle results in a greater tilt of the FOWT’s superstructure, which significantly affects power generation efficiency. An increase in RNA acceleration imposes substantial loads on the electrical and mechanical components inside the rotor and nacelle, leading to potential failures and fatigue damage. Heave refers to the vertical motion of the FOWT. To ensure that the heave natural period does not fall within the high-energy region of the wave spectrum—thereby avoiding resonance—it is necessary to design the heave natural period to be sufficiently large.
Table 4 presents the design criteria for the three indicators mentioned above, as specified in DNV (2018, 2019). According to DNV-RP-0286 (DNV, 2019), the allowable pitch angle is specified as 15 degrees under the design load case 6.1 (DLC 6.1). In this study, the allowable tilt angle was also determined to be 15 degrees. Additionally, for operational conditions, a valid acceleration range of 2.94 m/s² is suggested. In this study, referencing this standard, it was set to 3.0 m/s2. DNV-ST-0119 (DNV, 2018) states that the natural period of floating structures generally falls outside the wave period range, except in extreme conditions. In this study, the heave natural period was set to 20 seconds (0.314 rad/s) to avoid resonance with the wave spectrum in extreme sea state (ESS) conditions (refer to Table 9).
3.2 Study Flowchart
The overall flowchart for the research is presented in Fig. 2. To determine the optimal substructure shape that satisfies the three design criteria for FOWTs, design variables and their ranges and levels are established. The geometric shape of the FOWT substructure below the draft is modeled corresponding to the determined design variables. For this purpose, a Python script that can run in Abaqus/CAE was developed to automate the modeling process.
Hydrodynamic analyses of the FOWT substructure are conducted to derive hydrodynamic coefficients and 1st & 2nd wave excitation forces. In this study, the Ansys/Aqwa LINE module was used for this purpose. The equilibrium position of the FOWT is determined when environmental loads (wind speed and wind direction) are applied to the FOWT combined with mooring information such as unstretched length, mooring chain link size, and anchor position. For this purpose, the Ansys/Aqwa LIBRIUM module was used. Ansys/Aqwa LIBRIUM calculates wind speed as drag force, and the resulting offset of the FOWT is considered the equilibrium position.
Mooring information and environmental load information are also applied to hydrodynamic analyses to obtain frequency response spectra. In this study, the Ansys/Aqwa FER module was used for this purpose. The heave natural period of the moored FOWT is derived at this stage.
The long-term values corresponding to a 20-year return period are derived by numerically processing the spectra of pitch angles and RNA acceleration for each wave direction obtained through Ansys/Aqwa FER module analysis. For this purpose, an in-house code called INHA-LT was used. INHA-LT assumes that the response follows a 2-parameter Weibull probability density function.
The optimal FOWT substructure shape can be determined by comparing the derived heave natural period, long-term pitch angle, and long-term RNA acceleration with the design criteria.
The Ansys/Aqwa FER module solves the frequency domain equation of motion as shown in Equation (1). This equation includes the displacement matrix M, the added mass matrix A(ω), the coefficient matrix B(ω), and the stiffness matrix C on the left-hand side, while the wave excitation force vector ⃗(ω) is on the right-hand side. The matrix B(ω) can include both radiation damping and viscous damping, but in this study, only the radiation damping coefficient is considered. For FOWTs, C requires both hydrostatic stiffness and mooring stiffness.
The solution to Eq. (1) is given by Equation (2). η(ω) is the motion response vector of the structure at a specific frequency ω, which is the displacement seen by the structure for a given external force. Z(ω) is the complex impedance matrix, which is equal to Eq. (3). The relationship between the motion response of FOWTs and wave excitation is referred to as the response amplitude operator (RAO), expressed in Eq. (4). This method is effective across the frequency spectrum, allowing for linear assumptions to analyze the overall system behavior by summing responses at various frequencies.
Ultimately, Eq. (1)–(2) demonstrate how frequency domain analysis simplifies the solution process for specific dynamic systems, particularly under harmonic excitations. In this study, hydrodynamic coefficients such as added mass and radiation damping coefficients were obtained using the Ansys/Aqwa LINE module, while the Ansys/Aqwa FER module was employed to derive solutions for Eq. (1).
3.3 Dominant Design Variables
The draft, circumradius, main column diameter, and pontoon breadth were determined as design variables expected to have the greatest impact on the motion response performance of FOWTs. Since the draft determines the displacement of the FOWT, this study first determined the displacement corresponding to the draft and then calculated the ballast mass to satisfy it. The circumradius greatly affects roll and pitch stiffnesses. As the circumradius widens, roll and pitch motions become more stable, but the increased circumradius requires significant structural reinforcement of the deck and pontoons. The diameter of the column determines heave stiffness but also affects roll and pitch stiffnesses. For the same draft, a larger main column diameter increases heave stiffness, reducing the FOWT’s heave motion. The pontoon breadth determines the damping coefficient. A wider pontoon breadth increases the influence of radiation damping and viscous damping, effectively suppressing motion.
To determine the dimensions of the members for parametric study, this research prepared four cases (T10, T15, T18, and T25) with the same displacement as the reference (Allen et al., 2020) but with different drafts, as shown in Table 5. In the case of T10, with a 10 m draft, the column diameter was 19.74 m, showing a significant difference from the reference (Allen et al., 2020), so this study adopted a 15 m draft (T15 in Table 5). Additionally, for the 25m draft case, the column diameter was calculated to be about 12.48 m, which was excessively slender. Therefore, this study adopted an 18 m draft (T18 in Table 5). Fig. 3 shows the visualization of the four cases.
Table 6 presents the levels and ranges of the four parameters determined in this study for the parametric study. By detailing the main column diameter, pontoon breadth, and circumradius into five levels each, the changes in responses resulting from variations in these three parameters were meticulously observed.
From Table 6, 250 analysis cases were generated. However, since it was assumed that the pontoon breadth cannot be greater than the diameter of the column, those cases were excluded, and analyses were conducted on 220 cases. The case numbers were assigned in ascending order based on draft, circumradius, pontoon breadth, and main column diameter. As presented in Table 7, for example, the [draft, circumradius, pontoon breadth, main column diameter] values for Case 1 and Case 6 are [15 m, 40 m, 6 m, 15 m] and [15 m, 40 m, 9 m, 15 m], respectively.
3.4 Geometry and Mass Modeling
The automation of input file generation for Ansys/Aqwa LINE analysis was implemented due to the extreme difficulty of manually creating 220 models. To achieve this, a Python code was developed in the commercial finite element analysis code’s pre/post processor Abaqus/CAE, which could generate input files in Abaqus format. This allowed for the automatic creation of 220 analysis models based on design variables. The size of diffraction elements below the waterline was set to be smaller than 1/7 of the wavelength corresponding to the minimum wave frequency considered in this study. Consequently, the number of elements used was approximately 15,000 to 20,000. Since the automatically generated files were in Abaqus input file format, they were converted to Ansys/Aqwa input file format using an in-house code developed specifically for this purpose.
Mass information for each case was categorized into superstructure, substructure, and ballast water. The superstructure mass presented in the reference (Barter et al., 2022) was used without modification. Assuming a substructure shell thickness of 20mm, the substructure’s mass, center of mass, and mass moment of inertia were obtained from the Abaqus input file. The ballast water mass was calculated by subtracting the superstructure mass and substructure mass from the displacement. In all 220 cases, the ballast water fully filled the pontoons, with the remaining ballast water partially loaded into the main columns. The center of mass and mass moment of inertia of the ballast water were determined from the geometric shapes of the fully loaded pontoon and partially loaded side columns. The FOWT’s center of mass was derived using the first moment of mass from the masses and centers of mass of the superstructure, substructure, and ballast water. The FOWT’s 2nd moment of mass was calculated by applying the parallel axis theorem to the 2nd moment of mass of the superstructure, substructure, and ballast water with respect to the center of mass.
3.5 Environmental Condition
To solve Eq. (4), hydrodynamic coefficients such as added mass, radiation damping coefficient, and hydrostatic stiffness, as well as the wave excitation force, are required. The wave direction and wave frequency applied to obtain these hydrodynamic coefficients using the Ansys/Aqwa LINE module are presented in Table 8. While the wave direction for solving Eq. (4) was set to 0 degrees, a multi-directional wave effect was considered by applying wave directions at intervals of 22.5 degrees to estimate the long-term values of the 20-year recurrence period from the RAOs response.
For future validation of the proposed design in the time domain, added mass and radiation damping coefficients converged at infinite wave frequency are necessary. Therefore, the maximum frequency was determined to be 3.0 rad/s. The wave frequency was divided into 50 segments from 0.1 rad/s to 3.0 rad/s, resulting in 49 equal divisions. The viscous damping coefficient was not considered in Eq. (4).
In this study, it was assumed that the maximum pitch angle occurs under extreme sea state (ESS) conditions. To observe this, Case-MPA was prepared. The wind speed and wave height applied in this case correspond to a 50-year return period based on the marine conditions surveyed in the Ulsan offshore region of South Korea. The maximum RNA acceleration was predicted to occur when the turbine is operating at the rated wind speed, so Case-RNA was prepared to observe this scenario. The wave conditions in this case correspond to a severe sea state (SSS).
For both cases, the wind speed, significant wave height, peak period, Joint North Sea Wave Project (JONSWAP) spectrum’s peakness factor, and current speed are presented in Table 9. Additionally, wind direction, wave direction, and current direction, which are not listed in Table 9, are illustrated in Fig. 4.
4. Sensitivity Analysis Results
4.1 Heave Natural Period
As shown in Fig. 5, the heave natural period increased as the draft became deeper. This is because, even if the waterplane area remains constant, the increase in displacement due to the deeper draft results in an increase in the heave natural period.
Fig. 6 presents the changes in the heave natural period according to variations in main column diameter, circumradius, and pontoon breadth. It can be observed that the heave natural period is more sensitive to the main column diameter than to the circumradius. It was also confirmed that pontoon breadth can significantly affect the heave natural period. Since the pontoon breadth is located underwater, it has a considerable impact on viscous damping; however, viscous damping was not considered in this study. Therefore, changes in response due to variations in pontoon breadth can be attributed to changes in mass properties (center of gravity, displacement, and mass moment of inertia).
For a detailed sensitivity analysis, two-dimensional curves were analyzed based on changes in main column radius and pontoon breadth at a specific circumradius. Specifically, Fig. 7 illustrates how the heave natural period varies with changes in main column diameter. When the pontoon breadth increases, the heave natural period becomes more sensitive to increases in main column diameter. This sensitivity intensifies as the draft becomes deeper because an increase in pontoon breadth leads to an increase in displacement, thereby lengthening the period of heave motion.
When the main column diameter increases, the change in heave natural period becomes less sensitive as pontoon breadth increases. This is because the proportion of increased displacement due to a larger pontoon breadth becomes relatively smaller compared to the overall displacement.
4.2 Pitch Angle
Looking at Fig. 8, a large pitch angle was observed when the draft was small. When the draft increases while keeping the column diameter constant, both displacement and the second moment of mass increase simultaneously, which likely reduces the pitch motion. Fig. 9 presents the long-term pitch angle changes due to variations in main column diameter, circumradius, and pontoon breadth. The long-term pitch angle is sensitive to all three parameters: circumradius, main column diameter, and pontoon breadth. To conduct a detailed sensitivity analysis, a two-dimensional curve analysis was performed to observe changes in main column radius and pontoon breadth at specific circumradius values.
Fig. 10 shows how the long-term pitch angle changes with variations in the main column diameter. As pontoon breadth increases, the long-term pitch angle tends to decrease, and this trend intensifies as the main column diameter increases. Although it was expected that an increase in circumradius would enhance pitch stiffness and reduce the pitch angle, the results instead showed an increasing trend in the long-term pitch angle. As displayed in Fig. 11(a), an analysis of the pitch motion RAO revealed that an increase in circumradius results in a higher pitch natural frequency. Fig. 11(b) further illustrates that due to resonance effects, the pitch angle spectrum increased, leading to a corresponding rise in the long-term pitch angle.
4.3 RNA Acceleration
As shown in Fig. 12, RNA acceleration increased as the draft decreased. When the draft increased while maintaining the same column diameter, both the displacement and the second moment of mass increased simultaneously, which is presumed to have reduced pitch motion.
Fig. 13 presents the long-term RNA acceleration as affected by changes in main column diameter, circumradius, and pontoon breadth. It can be observed that long-term RNA acceleration is sensitive to all three variables: circumradius, main column diameter, and pontoon breadth. To conduct a detailed sensitivity analysis, a two-dimensional curve was presented in Fig. 14, showing changes in main column radius and pontoon breadth at a specific circumradius. However, no consistent or distinct trends could be identified.
As shown in Fig. 15(a), an analysis of the pitch acceleration RAO at the center of mass revealed that increasing the pontoon breadth reduced the natural frequency of pitch acceleration. However, in certain cases (e.g., Case 125), due to second-order resonance, the pitch acceleration spectrum did not consistently increase or decrease with a clear trend. Therefore, for RNA acceleration, it is more important to determine resonance based on wave excitation forces rather than relying on trends related to substructure geometry.
4.4 Selected Substructures
In this study, models satisfying three indicators were collected. For the collected models, weights were assigned to three performance metrics (heave natural frequency, long-term pitch angle, and long-term RNA acceleration) at 50%, 25%, and 25%, respectively. A large weight of 50% was applied to the long-term RNA acceleration because lower values are advantageous for stable electricity production in FOWTs. The pitch angle can be considered partially dependent on RNA acceleration. In other words, as the pitch angle increases, it can potentially induce greater acceleration in the RNA, so a weight of 25% was assigned. Heave natural frequency was given a weight of 25% because it can narrow the air gap and potentially cause blade damage, rather than directly affecting electricity production.
After normalizing each model’s performance based on the average performance of 220 models, the weights were applied. The models with the minimum values for the three normalized performances are presented in Table 10, ranked by their performance. The draft for all four models was consistently 18m, while a circumradius of 60 m, pontoon breadth of 15 m, and main column radius of 15 m were found to be advantageous for performance.
5. Verification of the Selected Model
In this study, performance evaluations were conducted for both the reference model (VolturnUS-S) and the model predicted to perform best through parameter studies (Case 241). To achieve this, time-domain load analyses for DLC 1.3 were performed using OpenFAST, a tool developed by NREL. DLC 1.3 corresponds to wind conditions of the normal turbulence model (NTM) and wave conditions of ESS, with detailed conditions presented in Table 11. The environmental conditions in Table 11 are considered suitable for evaluating the performance of the proposed optimal floating platform, as they do not sufficiently induce resonance, as shown in Fig. 16.
The roll natural frequency of the optimal Case 241 model is similar to that of the VolturnUS-S reference model, resulting in no significant differences in roll motion, as illustrated in Fig. 17(a). On the other hand, the pitch stiffness of the Case 241 optimal model increased significantly compared to the VolturnUS-S reference model due to increases in circumradius and column diameter. Consequently, notable differences were observed in pitch motion between the two models. The significant difference in the average pitch angle between the two models is attributed to a reduction in initial pitch trim caused by the increased pitch stiffness. As shown in Table 12, while the heave natural periods of the two models are similar, the maximum pitch angle of Case 241 was significantly improved. However, an increase in maximum nacelle acceleration was observed due to the rise in pitch stiffness.
6. Conclusions
In this study, the draft, main column diameter, circumradius, and pontoon breadth of a center column type semi-submersible substructure were determined as the main design variables. Using the Aqwa LINE module, hydrodynamic coefficients were derived for 220 models based on variations in these design variables. Frequency domain load analyses were then conducted for the same 220 models under a single environmental load combination using the Aqwa FER module. The results of the load analysis for the 220 models were compared against design criteria to evaluate the heave natural period. Additionally, pitch angle RAO and RNA acceleration RAO obtained from the load analysis results were statistically processed to derive long-term values, which were also compared with the design criteria.
The findings revealed that the main column diameter had the most significant impact on the heave natural period. It was also necessary to design the substructure’s heave stiffness sufficiently high to avoid resonance with wave excitation forces. While the main column diameter was the most dominant variable in determining pitch angle RAO, for substructures with specific dimensions, long-term pitch angles exhibited greater sensitivity to pontoon breadth due to resonance effects. For RNA acceleration, it was difficult to identify consistent trends based on design variables due to resonance. Therefore, it is essential in the early design stages to assess resonance by observing RNA acceleration RAO or spectra. By assigning greater weight to stable electricity production among three performance indicators, rankings for each model were evaluated and presented. The superiority of the selected optimal model over a reference model was verified through time-domain analysis.
Furthermore, this study focused on center column type FOWT substructures, highlighting the need for future comparative studies on side column type substructures.
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