Nomenclature
A: cross-section area
b: normal force vector due to seabed reaction
D: outer diameter of dynamic power cable
E: elastic modulus
F: shear force vector due to bending stiffness
g: gravitational acceleration
i: index for discretized segments and nodes
i: unit vector in local x-direction
I: second moment of area
k: unit vector in local z-direction
kb: bending stiffness in tangential direction of a dynamic power cable
ksb: seabed stiffness
l: length of discretized segment
L: total length of dynamic cable
L1: distance from hang-off point to DBMs section start
L2: DBMs section length
L3: length from end of DBMs section to touchdown point
L4: touchdown length
n: number of discretized segments
T: axial tension vector due to axial stiffness
w: submerged weight vector of dynamic cable segment
w: dry weight of dynamic cable segment
x: horizontal location based on local coordinate system
z: vertical location based on local coordinate system
zsb: water depth from mean seawater level (positive downward)
β: angle between two successive segments
θ: Ez angle, between the initial hang-off angle and the instantaneous hang-off angle
ρw: density of seawater
1. Introduction
The construction of offshore wind farms to utilize abundant wind resources in deep sea areas is gaining attention worldwide (Chen and Kim, 2022; Hong et al., 2024; Oh et al., 2018a). This indicates that technologies to overcome site constraints are advancing. Monopiles and jackets are the main substructures of fixed offshore wind turbines and have been applied in various projects (Doan and Tran, 2022; McCoy et al., 2024; Wang et al., 2018). In addition, floating offshore wind turbines (FOWTs), which can be deployed in deep sea areas with abundant wind resources, are being introduced as a new solution (Barooni et al., 2023; Chitteth Ramachandran et al., 2022; Edwards et al., 2024).
For bottom-fixed substations or bottom-fixed offshore wind turbines, static power cables are used for power transmission, whereas dynamic power cables are required to connect unit FOWTs or floating substations (Prysmian, 2022; TEPCO Renewable Power, Inc. et al., 2022; Moon et al., 2014). In particular, as water depth increases, the subsea length of dynamic power cables also increases, subjecting them to strong ocean currents, waves, and wind-induced external forces (Shim et al., 2021; Young et al., 2018). According to Syed and Muggiasca (2024), dynamic power cables experience an average of four failures over their design lifespan because of external forces, vibrations, and installation errors. Furthermore, failures of dynamic power cables account for 83% of financial losses and insurance claims related to offshore wind power. When a failure occurs, the average time required for repair is 40 days, during which financial losses of 1.2 million to 12 million USD have been reported (Maloney, 2024). A reliable configuration design of dynamic power cables is expected to mitigate responses to external forces, thereby reducing the causes of failure (Cerik and Huang, 2024; WFO, 2024).
Layouts such as catenary, lazy wave, tethered wave, and lazy-s can be applied to dynamic power cables (Doole et al., 2023; Ikhennicheu et al., 2020). Distributed buoyancy modules (DBMs) are used in the lazy wave configuration to reduce the tension acting at the hang-off point where the cable is suspended from the substructure (Ogbeifun et al., 2021; Ruan et al., 2024a). DBMs mitigate the motion response at the substructure hang-off and cable touchdown point induced by waves, thereby reducing fatigue damage (Cheng et al., 2020; Kwon et al., 2019; Oh et al., 2018b). Moreover, since the lazy wave configuration does not require components other than DBMs, it is more cost-effective compared to other configurations (Ruan et al., 2024b).
Numerical studies on the application of lazy wave configurations to dynamic power cables are actively being conducted worldwide (Aninthanen, 2021; Boo and Yang, 2019; Li et al., 2024; Poirette et al., 2017; Schnepf et al., 2023; Okpokparoro and Sriramula, 2023). According to Thies et al. (2012), the lazy wave configuration more effectively reduced maximum tension and fatigue damage compared to the catenary configuration. Rentschler et al. (2019) applied a genetic algorithm to minimize the buoyancy section – the region where DBMs are installed in the lazy wave configuration. Rentschler et al. (2020) conducted parametric analyses of lazy wave configurations to minimize the cable tension and maximize the bend radius for various water depths.
This study aims to design a lazy wave layout for a dynamic power cable applicable to a 15MW-class floating offshore wind turbine (FOWT) to be installed off the coast of Ulsan, South Korea. For this purpose, the DBM properties were set as the design variables: buoyancy, starting position, and the length of the buoyancy section. The initial equilibrium state responses for various combinations of DBM variables were analyzed using MoorDyn (Hall, 2017), the mooring dynamics module within OpenFAST, an open-source analysis code developed by NREL (NREL, 2024). The original MoorDyn had limitations in modeling dynamic cables because it considered only axial stiffness. However, Hall et al. (2021a) validated its accuracy by incorporating a bending stiffness model and comparing it with the commercial analysis code OrcaFlex (Orcina Ltd., 2024). This enhancement enabled MoorDyn to analyze the behavior of dynamic cables, and Lozon et al. (2025) proposed mooring and cable layouts for U.S. deep-sea FOWT systems by linking the quasi-static mooring modeling code MoorPy (Hall, 2021b; 2024) with MoorDyn. Therefore, in this study, MoorDyn is used to evaluate the tension at the hang-off point, Ez angle, and minimum bend radius (MBR) according to different DBM variable combinations, and to propose the optimal DBM configuration for each buoyancy level.
2. Methodology for Dynamic Cable Analysis
2.1 Theoretical Background
MoorDyn is based on the lumped mass method (Low and Langley, 2006). In this model, the cable is discretized into n line segments and n+1 nodes. As shown in Fig. 1, the forces acting at the nodes of the dynamic cable are defined, and the static equilibrium equation shown in Eq. (1) is formulated (Oh et al., 2018). As presented in Eq. (2) and Eq. (3), in Eq. (1), Ti and Fi represent the tensile force and shear force at the ith node, respectively, expressed through the axial stiffness (Low and Langley, 2006) and bending stiffness (Wang et al., 2024) of the cable. In Eq. (1)wi and bi denote the submerged weight and the normal force due to seabed contact acting at the ith node, respectively (Hall and Goupee, 2015). The submerged weight wi is defined as the difference between the dry weight and buoyancy of the cable, as shown in Eq. (6). The normal force bi is expressed in Eq. (7). When the above-defined forces satisfy Eq. (1) at all nodes of the dynamic cable, static equilibrium is achieved.
2.2 Properties of Dynamic Power Cable
Fig. 2 shows a domestically developed 66kV-class dynamic power cable. The dynamic power cable contains three power cores. Each power core consists of a copper conductor, a cross-linked polyethylene (XLPE) insulator for insulating the copper conductor, a metallic screen surrounding the XLPE, and a high density polyethylene (HDPE) sheath protecting the metallic screen. Each power core is further protected by an HDPE sheath. The stiffness of the dynamic power cable is ensured by dozens of steel wire armors. The basic specifications of the dynamic power cable are presented in Table 1.
2.3 Numerical Modeling
In this study, the water depth and draft of the FOWT were assumed to be 148 m and 20 m, respectively. It was assumed that the hang-off point of the dynamic power cable began at the bottom of the FOWT. In other words, the dynamic power cable was assumed to be located 20 m below the mean seawater level.
In actual construction, when the length of the dynamic power cable increases, grid costs increase significantly, so it is necessary to determine an appropriate length. In this study, the length of the dynamic power cable was set sufficiently long at 700 m to prevent the occurrence of unrealistic tensile forces. Additionally, to ensure the accuracy of the analysis, the dynamic power cable was modeled using uniform elements at 1-m intervals, and a total of 700 elements were used.
In the case of the lazy wave configuration, the layout was determined by the DBM design variables. The DBMs consisted of three design variables: total buoyancy, starting position, and buoyancy section length. Therefore, the lazy wave configuration was composed of the distance from the hang-off to the DBMs (L1), the DBMs section length (L2), the distance from the DBMs to the touchdown point (L3), and the touchdown length (L4). Accordingly, L3 and L4 are dependent on L1 and L2. A sketch of the lazy wave configuration is shown in Fig. 3. The DBMs were modeled using the POINT object provided by MoorDyn, and in all cases, the spacing between each DBM was set to 1 m, the same as the cable elements. Additionally, it was assumed that the buoyancy modules have no mass.
The total buoyancy of the DBMs was set to 140% and 230% of the displacement corresponding to a length of 132 m – the suspended length without DBMs. Nine levels of L1 were set from 0.1 L to 0.9 L at intervals of 0.1 L. Furthermore, eleven levels of L2 were set from 0.05 L to 0.25 L at intervals of 0.02 L. Therefore, a total of 198 models were generated from two buoyancy levels, nine L1 levels, and 11 L2 levels (see Table 2). However, since the sum of L1 and L2 cannot exceed the total length of 700 m assumed in this study, static analyses were performed for 176 cases excluding those that exceeded this length.
Due to the presence of DBMs, the lazy wave configuration forms a sag bend and a hog bend. Since sag bends and hog bends that float to the sea surface or sink to the seabed are not desirable, a constraint was imposed such that the sag and hog bends must be located between 20% and 80% of the water depth. In addition, the bend radius that occurs in the dynamic power cable must be larger than the minimum bend radius (MBR). Accordingly, based on the manufacturer’s specification, an MBR of 2.5 m was applied as a constraint in this study. These conditions are summarized in Table 3.
When DBMs were not installed on the cable, the suspended length was 132 m, and the total buoyancy of the DBMs was assumed to be 140% and 230% of the displaced volume corresponding to the suspended length. Nine levels of L1 were set from 0.1 L to 0.9 L at intervals of 0.1 L. Additionally, eleven levels of L2 were set from 0.05 L to 0.25 L at intervals of 0.02 L. As shown in Table 2, accordingly, a total of 198 models were generated from two buoyancy levels, nine levels of L1, and 11 levels of L2. However, since the sum of L1 and L2 cannot exceed the total length of 700 m assumed in this study, static analysis was reduced to 176 cases excluding the cases that exceeded this total length. In the lazy wave configuration, sag bends and hog bends are formed due to the DBMs. Since the dynamic power cable neither floats to the sea surface nor sinks to the seabed, a constraint was set such that the sag bend and hog bend must be located between 20% and 80% of the water depth. Additionally, the bend radius occurring in the dynamic power cable must be greater than the minimum bend radius (MBR). In this study, an MBR of 2.5 m was applied as a constraint based on the manufacturer’s specifications. These conditions are listed in Table 3.
3. Results of Parametric Study
3.1 Response Surface Analyses
The tension response surface at the substructure connection point according to the variations in L1 and L2 is presented in Fig. 4. Regardless of the buoyancy level, it was confirmed that L1 is the dominant variable influencing the tensile force compared to L2. Additionally, it was observed that the tensile force tends to decrease sharply when L1 was below a certain value. When only weight and buoyancy are acting, the angle between the vertical axis and the dynamic power cable at the hang-off point is defined as the initial hang-off angle. To define the instantaneous hang-off angle caused by environmental loads and motion of the FOWT substructure, the Ez angle is used. That is, the Ez angle represents the difference between the initial hang-off angle and the instantaneous hang-off angle. The response surface of the Ez angle according to changes in the lengths of L1 and L2 is shown in Fig. 5. Regardless of the buoyancy level, the Ez angle decreased as the lengths of L1 and L2 increased.
Additionally, a response surface analysis of the minimum bend radius of the dynamic cable generated in the configuration according to changes in L1 and L2 was conducted, and the results are shown in Fig. 6. Regardless of the buoyancy level, the bend radius increased as the lengths of L1 and L2 increased; however, it tended to decrease sharply when the lengths exceeded a certain threshold.
3.2 Optimal configurations
Based on the static load analyses conducted in this study, rankings for hang-off tension, Ez angle, and MBR were derived. It was assumed that all three response variables have equal weighting. One model was selected for each buoyancy level by choosing the configuration that satisfies the constraints in Table 3 and has the smallest arithmetic sum of the rankings. The tension and curvature distributions according to the shape and length of the two selected cases were compared and are shown in Fig. 7. Additionally, the segmental lengths and the DBM properties applied to L2 for the optimal cases are presented in Table 4 and Table 5. The responses for hang-off tension, Ez angle, and MBR for each configuration are summarized in Table 6.
The MBRs of the optimal dynamic power cable layouts determined for the two buoyancy levels significantly exceeded the reference value of 2.5 m; however, the MBR was superior at the 230% buoyancy level. On the other hand, it was observed that the Ez angle developed more prominently at the 230% buoyancy level. In contrast, the hang-off tension showed no significant difference between the two buoyancy levels.
3.3 Verification Under Maximum Horizontal Offset Conditions
FOWTs experience horizontal offset due to external forces, and as a result, the dynamic cable connected to the floating structure also undergoes deformation. Therefore, the configuration of the cable must be designed to reliably accommodate the offset of the floating structure. In this study, the offset limit criteria presented in Table 7 were applied, and the cable deformation, tensile force, and curvature distribution under each condition were analyzed. These results are shown in Fig. 8, Fig. 9, and Fig. 10.
As a result, the designed cable layouts satisfied both the MBR and MAC under all offset conditions. This confirms that the cable layouts proposed in this study ensure structural safety and reliability even under maximum horizontal offset in each scenario. In Part 2 of this paper, time-domain load analyses will be conducted by applying the two optimal layouts to a 15MW reference FOWT, and the dynamic responses of the cables under actual extreme limit states will be analyzed to validate the feasibility of the proposed design.
4. Conclusion
One hundred and ninety-eight cases were generated using the total buoyancy, starting position, and ending position of the DBMs as design variables for the lazy wave configuration of a dynamic power cable, and static load analyses were performed using MoorDyn.
As a result, the hang-off tension was found to be highly sensitive to the starting position of the DBMs, with tension increasing significantly when the starting position was set farther from the hang-off point. The Ez angle was strongly influenced by both the starting and ending positions of the DBMs. The MBR was most pronounced at the touchdown point, and a large MBR was observed when the starting and ending positions of the DBMs were vertically similar.
After applying design constraints such as bend clearance and MBR, valid cases were selected, and a composite ranking was evaluated by assigning equal weight to the three response variables: hang-off tension, Ez angle, and MBR. Based on this, one optimal layout was identified for each buoyancy level.
Furthermore, to examine the cable response to horizontal offset of the floating structure, static analyses were conducted by applying offset limit criteria to the two optimal layouts. The results confirmed that all cases satisfied both the MBR and MAC, securing structural safety and reliability even under maximum offset conditions.
However, this study was based on a static analysis assuming maximum horizontal offset in the absence of external loads. Since the hydrodynamic behavior of the floating structure was not considered, the analysis did not capture the actual responses under extreme environmental conditions. Therefore, a follow-up study will apply ultimate limit state conditions corresponding to a 50-year return period and perform time-domain load analyses considering the hydrodynamic characteristics of the floating structure to validate the structural integrity of the designed layouts.
PDF Links
PubReader
ePub Link
Full text via DOI
Download Citation
Print
