Reference Power Cable Models for Floating Offshore Wind Applications

The global energy sector is witnessing a significant shift towards renewable energy sources, with wind energy emerging as a leading option. Offshore wind energy, in particular, is undergoing rapid development and upscaling. In the early 1980s, wind turbines had relatively small power ratings, reaching ~50 kW with rotor diameters approaching 15 m. Up to this day, the turbine size has grown significantly, reaching 18 MW with 260 m rotor diameter [1]. The upscaling aims to reduce the Levelized Cost of Energy (LCOE), rendering offshore wind energy more competitive with traditional energy sources. By investing in larger offshore wind farms, there is potential to harness wind power more effectively and sustainably. An estimated 80% of the world’s offshore wind resource potential lies in waters deeper than 60 m, where traditional bottom-fixed wind turbines are not feasible [2]. An outcome is the discernible shift towards the advancement of floating wind turbines for harnessing deep-sea wind resources. Floating offshore wind turbines (FOWTs) and substations necessitate the use of dynamic power cables specifically designed to withstand the complex motions induced by environmental forces such as waves, wind, and currents [3]. The optimization of inter-array cable configurations emerges as one of the key areas for LCOE reduction in offshore wind projects, where cable-related costs constitute approximately 20–30% of the total capital expenditure, as highlighted by Cozzi et al. [4]. In the initial stages of project development, the implementation of accurate and realistic reference power cables is imperative. Advanced numerical models are essential for predicting the fatigue life of the cables and optimizing the layout of the inter-array cable system. As the industry moves towards developing larger turbines with capacities exceeding 20 MW, there is a concurrent need to establish reference designs for suitable dynamic power cables. Such reference designs must accommodate the increased capacity demands and operational challenges associated with large-scale floating wind turbines.

The construction of a dynamic power cable typically consists of multiple material types arranged in several layers combined in a cylindrical or helical configuration [5]. Hence, the power cable can be considered as a multilayer, non-bonded composite flexible structure. Such structures exhibit non-linear mechanical behavior resulting from friction and sliding between components. Due to low bending and torsional stiffness properties, dynamic power cables are flexible in bending and torsional degrees of freedom while having a large axial stiffness. Experimental studies by Maioli [6] indicate that cable construction, e.g., layer arrangement and materials, have a profound influence on the resultant bending stiffness of the cable.

The theoretical foundations of mechanics of helically wound structures were established by Love [7], who derived the theory of thin rods. Love’s theory provided equations describing the equilibrium state of helical rods under external forces and moments. This theory was further expanded by Phillips et al. [8,9], who adapted Love’s framework to model twisted wire ropes analytically. The internal friction effects during bending were investigated by Lutchansky [10], and Vinogradov and Atatekin [11] explored the hysteretic behavior of bending stiffness. A significant advancement was the orthotropic model developed by Hobbs and Raoof [12], where each helical layer is simplified as an orthotropic cylinder. This approach allows for the homogenization of the cable cross-section, significantly reducing the complexity of the problem. The experiments performed by Jolicoeur [13] validated such an approach for predicting axial and torsional stresses in the cable. Nevertheless, the applicability of analytical methods to predict the bending behavior of power cables is limited due to the highly non-linear and variable nature of contact and friction mechanics between internal cable components.

Development of unbonded flexible risers used in the oil and gas industry over the last two decades resulted in significant progress in numerical models capable of accurate prediction of bending behavior of slender composite structures (Sævik et al. [14,15,16,17,18,19,20], ISO [21], DNV [22,23] API [24]). The catalyst was the development of the finite element method (FEM) and the increase in computational power. General-purpose FEM analysis programs allow for a detailed analysis of the bending behavior of simple metallic cables, as shown in Zhang and Ostoja-Starzewski [25] and Jiang [26]. However, even with currently available hardware, the applicability of general-purpose FEM codes to model complete power cable cross-section and accurately capture contact stresses between various layers of the cable requires the use of 3D elements and is computationally expensive. It is often necessary to analyze many design iterations in the initial design stages, and for extensive parametric studies, a fast solution method is needed. Because of that, the focus was shifted towards the development of special-purpose FEM formulations which could exploit the properties of the cable, such as dominant loading in the axial direction, and build upon previous theoretical frameworks, such as the homogenization principle. Sævik [14] developed an eight-degree-of-freedom curved beam element for the purpose of modeling stresses and stick-slip phenomena in the armor wires of flexible pipes. This work was extended in Sævik and Bruaseth [27] into an FEM formulation for predicting the structural response of umbilical cross-sections subjected to tension, torsion, and bending loads, including internal and external pressure and contact mechanics. Lukassen et al. [28] introduced a numerical model designed to predict local stresses in tensile armor wires of flexible pipes, based on the repeated cell unit (RUC) methodology. Their model incorporated nonlinear periodic boundary conditions for both axisymmetric and constant curvature bending loads. Lu et al. [29,30] derived alternative analytical and finite element models of unbonded flexible pipes under various loading conditions, focusing on the thermal loads and expansion coefficients. Fang et al. [31] implemented the RUC-based finite element model in the Abaqus simulation package to efficiently predict the bending behaviors of submarine power cables, demonstrating the model’s robustness and computational efficiency for studying cables under bending conditions. Recently, a computational approach for studying the local stresses in helically wound structures was proposed by Ménard and Cartraud [32]. Their method was based on the homogenization theory of periodic structures which exploited the helical symmetry of the wire. Ménard and Cartraud [33] applied the method to simulate the local stress state in a three-core cable subjected to cyclic bending loading. The development of specialized FEM formulations and hierarchical multilayer models that incorporate concepts of homogenization and advanced friction models enabled the creation of very efficient and highly accurate analysis programs such as Helica (DNV [34]) and UFLEX (SINTEF [35]). The dynamic power cables share many features with the flexible risers and umbilicals. Therefore, it is possible to use the extensive experience and knowledge base from the oil and gas industry and apply it to new application fields such as offshore renewable energy. In the present study, UFLEX is employed to obtain the correct cyclic variations of bending and tension in the modeled dynamic offshore power cables, which are essential for accurate predictions of their global response and fatigue life.

Compared to the number of research studies focusing on the dynamic response of the FOWTs, the number of publications dedicated to the design and analysis of dynamic power cables is relatively limited. Sobhaniasl et al. [36] focused on evaluating the fatigue life of dynamic inter-array power cables for FOWTs. They proposed a comprehensive methodology that accounts for the complex dynamic interactions between the cables and the marine environment. The research highlighted the critical importance of accurate fatigue assessment in ensuring the reliability and longevity of power cables in FOWT applications. The power cable model in Sobhaniasl et al. [36] was taken from Rentschler et al. [37], who presented a novel approach for the design optimization of dynamic inter-array cable systems in floating offshore wind turbines. The study by Rentschler et al. [37] was based on dynamic simulations of an OC4 FOWT with an attached dynamic power cable and employed a genetic algorithm to find the optimal distribution of buoyancy modules and optimal lazy wave geometry. The properties of the power cable modeled by Rentschler et al. [37] are reproduced from Thies et al. [38]. The numerical study by Thies et al. [38] investigated the mechanical loading regimes and fatigue life of marine power cables used in marine energy applications, specifically focusing on those connected to floating wave energy converters. Okpokparoro and Sriramula [39] employed a Kriging model for mapping the input random variables to the short-term fatigue damage along selected points on the dynamic cable. The power cable properties employed in both the study by Thies et al. [38] and Okpokparoro and Sriramula [39] were based on the numerical model of a double-armored dynamic umbilical developed by Martinelli et al. [40]. The cable model developed by Martinelli et al. [40] is an 11kV design with a maximum power rating of 1MW. It is evident that the rapid development of large-scale wind turbines necessitates the development of suitable reference power cable models that are able to keep up with their increasing power outputs.

The present study is organized into four sections: Section 2 presents the physical models of the three considered dynamic power cables. It includes a detailed description of the geometrical and material properties of the cable cross sections. The local analysis numerical model built using UFLEX v2.8.9 special-purpose FEM code is introduced, together with a series of sensitivity studies, ensuring that discretization and modeling errors are minimized. A comprehensive dataset of the mechanical properties of the three investigated cables is provided. Section 3 presents the fully coupled FOWT–power cable model established in the OrcaFlex v11.3a global response analysis software. The input properties of the considered dynamic power cable, the environmental dataset, and the load case matrices for hydrostatic, hydrodynamic, and fatigue simulations are provided. Static and dynamic simulation results and a simple analysis of the expected fatigue life of the cable under different environmental conditions are provided. Section 4 contains the summary of the present work.