Finite element analysis of the structural behaviour and fatigue life of a dynamic power cable

20th EAWE PhD Seminar on Wind Energy 24 - 26 September 2024 Visby, Sweden Finite element analysis of the structural behaviour and fatigue life of a dynamic power cable Esteban Cadavid Gila, Kris Hectorsa, Wim De Waelea a Ghent University / OWI-Lab, Faculty of Engineering and Architecture, Department of Electromechanical, Systems, and Metal Engineering, Technologiepark-Zwijnaarde 46, Belgium E-mail: esteban.cadavidg[email protected] Keywords: Offshore Wind, Fatigue, Power Cable, Nonlinear Behavior, Finite Element Abstract This extended abstract introduces an approach based on a 3D finite element model aimed at analyzing the local stress state of a three-core dynamic power cable subjected to cyclic loading conditions. The study emphasizes detailed modelling of the cable and its components such as the conductors, metal screens, and armouring. Key aspects include the helical shape of components, inelastic material behaviour, friction and normal separation between cable components, and large deformations. The selection of the element types, the formulation of the friction effect, and the constitutive properties of inelastic material behaviour will be determined by balancing the computational cost with results accuracy. This approach is intended to contribute to a deeper understanding of the mechanical performance of dynamic power cables, vital for ensuring their reliable operation in the offshore floating wind industry. 1. Introduction Floating offshore wind installations represent a clean and sustainable technology for renewable electric energy generation by exploiting the wind power. The electric energy generated by wind turbines is transported through dynamic power cables, which are subjected to rough environmental and operational conditions, such as windand wave-induced motions. These harsh loading conditions represent a risk of fatigue damage in dynamic power cables, potentially reducing their operational lifespan. Therefore, the dynamic, mechanical behaviour of power cables must be carefully predicted to ensure a reliable mechanical design that can fulfill the economic and technical challenges that arise [1]. For this purpose, both global and local analyses of dynamic power cables will be performed. The global analysis estimates the global loads on the power cables in response to the actions of the currents, waves, wind and the movements of the floating platform itself. These global loads (bending, tension and torsion) can then be transferred to the local analysis, which uses sub-models of the power cable to calculate the time series of stresses acting in individual components and their fatigue life [2]. Consequently, these sub-models must incorporate accurate representations of all cable components, such as electrical conductors, metal screens, insulations, fillers, inner and outer sheaths, and armouring (as illustrated in Figure 1). Due to the complex and heterogeneous geometry of the cable components, together with the variety of types of materials resulting in different mechanical properties, detailed 3D FE models are necessary for the local analysis. This study is part of the BEL-Float project funded by FPS Economy through the Energy Transition Fund of the Federal Government of Belgium. The main goal is to assess the dynamic power cable deformation, stress and integrity using numerical modelling. The next section summarizes a review of the state of the art in finite element modeling of the structural behaviour of dynamic power cables. Next, a strategy is proposed to perform a local Session 224: Reliability, monitoring and sensing technology 152 20th EAWE PhD Seminar on Wind Energy 24 - 26 September 2024 Visby, Sweden analysis of stresses acting on cable components with greater modelling detail compared to the state of the art. Finally, some preliminary results are presented, followed by a discussion of the forthcoming work. 2. State-of-the-art From the global analysis point of view, a case study of a point-absorber wave energy converter system is reported in [3]. In this work, the fatigue damage analysis was carried out by modelling the cables using beam elements with constant cross sections. Although the developed model was shown to be useful for analysing the dynamics and fatigue characteristics of the power cables, a detailed local model was required to simulate the interaction between the cable components. In [4], the global analysis of a floating offshore wind turbine (FOWT) was performed using the software SIMO/RIFLEX. In this analysis, the mooring lines were modelled as bar elements with only axial stiffness included, whereas the power cables were modelled as beam elements with specified axial, bending, and torsional stiffness. The achieved results showed that the mechanical response of the mooring lines and dynamic cables was dominated by the floater motions and sea current. A local analysis, on the other hand, requires a more detailed modelling approach since dynamic power cables comprise an assembly of several components with different geometries and material properties. Moreover, some components such as the conductor and the armouring are formed by individual wires creating a complex helical shape. In [1], stresses in the armouring were estimated using a 3D finite element model along with periodic boundary conditions to reduce the computational time. In addition, this FE model accounted for the contact and friction effects between cable components. In [5], two finite element models with different cable lengths were implemented. One model considered a portion of 250 mm in length, while the other, represented by a RUC (Repeated Unit Cell), had a length of 20 mm. The former was dedicated to evaluating the cable’s overall response in terms of the curvature-bending curve. The latter, validated using the longer model, was developed to compute the stresses in individual components with particular focus on the armouring. In [1] and [5], individual wires forming the armouring were represented as 3D solid elements. Furthermore, the helical shape of other components such as the conductor was not considered. In [6], and based on the results of their previous work [7], the authors reduced the computational expense of the numerical model by using 3D beam element modelling of armouring components. This modelling strategy provided an effective balance between accuracy and numerical efficiency and, compared with 3D solid elements, it resulted in lower computational time. This 3D FE model focused on the local analysis, also using periodic boundary conditions and including the contact between different components, was validated by experimental data and analytical results. The experimental data served to evaluate the overall behavior of the dynamic power cable under a cyclic bending load, whereas analytical models available in literature were used to validate the local analysis results. In [8], both experimental tests and finite element simulations were carried out to study the non-linear reciprocating bending response of a copper conductor. 3. Methodology for local stress analysis This work focuses on the local analysis of stresses in individual components of a dynamic power cable, which will be used to assess the cable integrity and fatigue life. Contrary to 3D FE models found in literature that tend to focus only on the armouring, and as a consequence only the helical shape and individual wires of this cable component are included, this research also intends to account for the helical geometry and composition of the conductor and metal screen. The conductor serves the purpose of transmitting the produced electrical power through the dynamic power cable. The metal screen provides electromagnetic shielding that protects the cable from electromagnetic interference. Both components are made up of a large number of wires. The metal screen is formed by winding thin copper wires around the metal conductor (made of aluminium or copper) at a particular laying angle. In the conductor, from the mechanical point of view, interaction between each individual wire in the same layer and among different layers leads to contact and friction effects. As a result, and together with the non-linear constitutive behaviour of some cable components, the whole structure undergoes a non-linear response under bending loading. Since reciprocating bending behaviour is the key factor leading to fatigue damage of dynamic power cable components, research on the reciprocating bending response of power cables tends to focus solely on the mechanical properties of the steel wires in the armouring, which are designed to give the cable the required bending flexibility and axial and torsional resistance to withstand the severe operational conditions. As a result, other components such as the conductor, are often ignored. For this reason, this work also aims to analyze the non-linear bending response of the conductor and metal screen needed to accurately predict the fatigue life of the power cable. Session 224: Reliability, monitoring and sensing technology 153 20th EAWE PhD Seminar on Wind Energy 24 - 26 September 2024 Visby, Sweden In addition, the 3D FE model aims to consider each cable component separately. Contact mechanisms such as stick-slip behaviour and allowed normal separation between components will be taken into account. As shown in image (b) of Figure 1, the cross section of a preliminary 3D FE model of the dynamic power cable under analysis is depicted. The three metal components of interest - conductor, metal screen and armouring - are highlighted. Furthermore, a flowchart illustrating the general procedure of this research is presented in image (c). (a) (b) (c) Figure 1: (a) Power cable components [9]. (b) Cross section of the studied power cable. (c) Flowchart of local stress analysis of a power cable segment Preliminary benchmark results were obtained by performing finite element simulations of a 3D model in the commercial software Abaqus (version 2023). A 500 mm long segment of a dynamic power cable was modelled and subjected to a concentrated bending moment at one end, while the other end was fixed. The purpose of this preliminary study was to compute the axial stress in the metal screen as a function of the bending curvature. It is important to highlight that linear material behaviour was considered for this study. All components were modelled using first-order 3D elements with reduced integration scheme (C3D8R). In this preliminary study, the individual wires of the armouring, conductor and metal screen and tangential friction were not included to reduce computational time. Thus, these components were represented as cylinders and their helical shape was neglected. To compensate for the effect of these geometrical simplifications on the mechanical response of the power cable, the Young’s modulus of these components was adjusted to (i) account for the angled orientation with respect to the main loading direction (using analytical equations available in literature [10]), and (ii) realize similar axial and bending stiffness of the real and simplified geometries. . Normal separation between all cable components was allowed. The following image illustrates the obtained results: (a) (b) (c) Figure 2: Axial stress distribution over the cross section. (b) and (c) Deformed cable segment. 4. Future work Session 224: Reliability, monitoring and sensing technology 154 20th EAWE PhD Seminar on Wind Energy 24 - 26 September 2024 Visby, Sweden To accurately compute the stresses in the individual components of the dynamic power cable, the preliminary 3D FE model will be enhanced to account for factors that significantly affect the non-linear bending response of the power cable. The primary modifications are the following: - The helical geometry of the armouring, conductor and metal screen will be included, as well as individual wires that constitute these components. - Two types of finite elements will be considered to model the individual wires of the aforementioned components: (i) 3D solid elements and (ii) 3D beam elements. The selection of one of both element types will be based on balancing computational cost and results accuracy. - Friction between all cable components will be included, and a sensitivity analysis will be performed to determine whether it has significant effect on the results. - Inelastic material behaviour of the cable components will eventually be considered. However, its inclusion in the FE model will depend on the computational cost. - The calculated stress states in individual components will serve as input to fatigue damage models to assess the lifetime of the dynamic power cable. 5. Acknowledgements This work is financially supported by the FPS Economy under the call 2022 of the Energy Transition Fund of the Belgian Federal Government through the BEL-Float project. References [1] J.-M. Leroy, Y. Poirette, N. Brusselle Dupend, and F. Caleyron, ‘Assessing Mechanical Stresses in Dynamic Power Cables for Floating Offshore Wind Farms’, in Volume 10: Ocean Renewable Energy, Trondheim, Norway: American Society of Mechanical Engineers, Jun. 2017, p. V010T09A050. doi: 10.1115/OMAE2017-61630. [2] D. G. Young, C. Ng, S. Oterkus, Q. Li, and L. Johanning, ‘Assessing the mechanical stresses of dynamic cables for floating offshore wind applications’, J. Phys. Conf. Ser., vol. 1102, p. 012016, Oct. 2018, doi: 10.1088/1742-6596/1102/1/012016. [3] S.-H. Yang, J. W. Ringsberg, and E. Johnson, ‘Parametric study of the dynamic motions and mechanical characteristics of power cables for wave energy converters’, J. Mar. Sci. Technol., vol. 23, no. 1, pp. 10–29, Mar. 2018, doi: 10.1007/s00773-017-0451-0. [4] S. Zhao, Y. Cheng, P. Chen, Y. Nie, and K. Fan, ‘A comparison of two dynamic power cable configurations for a floating offshore wind turbine in shallow water’, AIP Adv., vol. 11, no. 3, p. 035302, Mar. 2021, doi: 10.1063/5.0039221. [5] P. Fang, X. Li, X. Jiang, H. Hopman, and Y. Bai, ‘Bending study of submarine power cables based on a repeated unit cell model’, Eng. Struct., vol. 293, p. 116606, Oct. 2023, doi: 10.1016/j.engstruct.2023.116606. [6] F. Ménard and P. Cartraud, ‘A computationally efficient finite element model for the analysis of the nonlinear bending behaviour of a dynamic submarine power cable’, Mar. Struct., vol. 91, p. 103465, Sep. 2023, doi: 10.1016/j.marstruc.2023.103465. [7] F. Ménard and P. Cartraud, ‘Solid and 3D beam finite element models for the nonlinear elastic analysis of helical strands within a computational homogenization framework’, Comput. Struct., vol. 257, p. 106675, Dec. 2021, doi: 10.1016/j.compstruc.2021.106675. [8] H. Hu, J. Yan, S. Sævik, N. Ye, Q. Lu, and Y. Bu, ‘Nonlinear bending behavior of a multilayer copper conductor in a dynamic power cable’, Ocean Eng., vol. 250, p. 110831, Apr. 2022, doi: 10.1016/j.oceaneng.2022.110831. [9] B. Taormina et al., ‘A review of potential impacts of submarine power cables on the marine environment: Knowledge gaps, recommendations and future directions’, Renew. Sustain. Energy Rev., vol. 96, pp. 380– 391, Nov. 2018, doi: 10.1016/j.rser.2018.07.026. [10] E. A. W. De Menezes and R. J. Marczak, ‘Comparative analysis of different approaches for computing axial, torsional and bending stiffnesses of cables and wire ropes’, Eng. Struct., vol. 241, p. 112487, Aug. 2021, doi: 10.1016/j.engstruct.2021.112487. Session 224: Reliability, monitoring and sensing technology 155