the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Frequency-domain modeling of floating wind arrays with shared mooring lines
Abstract. A frequency-domain model for floating wind turbine dynamics has been extended to model floating wind farms with couplings from shared mooring systems The model, called RAFT, could previously calculate the mean offsets and wave-induced response spectra for single floating wind turbines. Now, the model supports multiple floating wind turbines, each with their own properties and responses, along with mooring lines that run directly between floating wind turbines in the array, meaning that shared mooring lines or fully suspended dynamic power cables can be included. This capability is achieved by setting up an array-level solution of the system mean offsets and assembling the full system matrices for solving the dynamic response. The quasi-static mooring model MoorPy is used to linearize the mooring system properties. To compute the floating wind turbine relative motions, phase offsets are applied to each turbine's response as a function of wave frequency based on the wavelength and relative positions in the array. These differential motions are then applied to mooring system tension Jacobians to compute the tension loads in the shared mooring lines. Overall, the capability provides a frequency-domain analogue to the floating support structure modeling capabilities in FAST.Farm. Mean offsets and power spectral density plots of responses are compared between RAFT and FAST.Farm to verify the implementation. The results indicate good agreement within the expectations of a frequency-domain modeling approach and suggest correct implementation of the shared mooring aspects. Additionally, a unique comb-like frequency response in the shared mooring line tensions has been observed. This phenomenon has a clear physical basis and may be an important design consideration for future shared mooring systems.
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Status: open (until 14 Jul 2025)
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RC1: 'Comment on wes-2025-58', Anonymous Referee #1, 01 Jul 2025
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This work describes the new capability of the open-source frequency domain tool RAFT in modeling shared mooring lines between multiple floating offshore wind turbines (FOWTs). The study focuses on first-order wave frequency response of the system in aligned steady wind and long-crested irregular waves. The mooring system is modeled quasi-statically. A case study of two semisubmerisble FOWTs with a single shared mooring line between them was used to verify the model against time-domain simulations in FAST.Farm. A single sea state applied in 3 directions was used for the verification. Reasonable agreement was found between the two models, except for shared mooring line tension response due to unmodeled line dynamics. Additionally, the effect of the phase difference in the wave loading between the two FOWTs resulted in what the authors refer to as a “comb-like” frequency response. A phenomenon in which the spectrum of the shared line tension has multiple sharp peaks as a result of the two FOWTs moving in and out of phase at different frequencies.
The paper is generally clear, and the results are well presented. Some comments and suggestions to improve the manuscript are given in the attached PDF.
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RC2: 'Comment on wes-2025-58', Anonymous Referee #2, 02 Jul 2025
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In this study, the authors present a frequency-domain model for multiple floating offshore wind turbines (FOWTs), incorporating the coupling effects introduced by shared mooring line systems. The implementation is benchmarked against the widely recognized time-domain tool FAST.Farm, providing a solid foundation for verification. A clear and concise theoretical description of the model formulation is provided, and its performance is demonstrated through a case study involving two inter-connected FOWTs sharing a single mooring line.
Overall, the proposed frequency-domain model shows good agreement with FAST.Farm results, within the expected limitations of frequency-domain methods. The characteristic comb-like frequency response of the shared mooring line is effectively captured and it is aligned with the results shown in previous studies that used similar shared mooring line configurations. This study offers a more explicit treatment and deeper investigation of this phenomenon compared to prior works.
Minor comments and questions:
- (Section 3.1, Table 3) – Is there a specific reason for the difference in sign for the mean yaw offset calculated using RAFT vs. FAST.Farm?
- (Section 3.2) – In the sentence, “The shared mooring line tensions in the 0° and 90° cases have a distinct comb-like frequency response, which we explore more in Sect. 4,” should the angles be 0° and 45° instead?
- (Section 3.2) – What is the total duration of the simulated time series in FAST.Farm?
- (Section 4) – Please revise the sentence: “Because Turbine 1’s reference position is at the origin, the wave elevations it experiences have nearly zero phase (appearing as real-valued complex amplitudes).”
Citation: https://doi.org/10.5194/wes-2025-58-RC2
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