Fast response methods for aero-elastic floating wind turbine design

Abstract

Fast response calculations in the frequency domain are valuable during the initial design of floating wind turbines, where many design variants must be evaluated. A direct frequency-domain treatment of aero-elastic rotor loads is typically infeasible due to the azimuthal time dependence of the system matrices. To overcome this limitation, we introduce a perturbation-based formulation inspired by Hill's method, which reformulates the response equations into separate orders involving constant system matrices derived via Fourier decomposition. This enables accurate and efficient response computation using the fast Fourier transform (FFT). For comparison, a Laplace-based perturbation method is also developed using the Laplace transform instead of the Fourier transform. To evaluate the novel fast response methods, we develop an azimuthally periodic and fully linearized model of a floating wind turbine. The response to various load cases is computed under different inflow and floater motion conditions. The proposed Fourier-based fast response method achieves high accuracy, with peak and standard deviation errors of 2 % and 3.5 %, respectively, while reducing computation time to 2.5 s for a 4096 s simulation-significantly faster than linear (45 s) and time-domain (90 s) models. Through detailed comparison, we find that one of our approaches, the so-called single perturbation method, offers an effective trade-off between accuracy and speed, making it suitable for design and optimization studies.