Fast response methods for aero-elastic floating wind turbine design

Fast response calculations are valuable for early-stage floating wind turbine design. To explore novel fast response methods, we develop a simplified and azimuthally periodic floating wind turbine model and fully linearize it. However, directly incorporating aero-elastic rotor loads remains challenging due to time-dependent system matrices.To overcome this, we introduce a perturbation approach that reformulates the system response into independent equations, each with a constant system matrix and input forcing. Inspired by Hill’s method, we use the Fourier decomposition to extract these matrices, improving the response accuracy with higher-order corrections while leveraging the Fast Fourier Transform for efficiency.We also develop a Laplace-based perturbation method as a comparison. Simulations cover various inflow conditions (constant, sheared or turbulent) and floater pitch motion excitations (harmonic or stochastic). Response accuracy is evaluated through exceedance probability plots and a standard deviation relative error, showing peak values and standard deviation errors of 2% and 3.5%, respectively.Among fast response methods, the double perturbation balances speed and accuracy, making it ideal for design and optimization purposes. In a 4096 seconds simulation, the double perturbation method runs in 2.5 seconds, outperforming the linear (45 seconds) and time-domain models (90 seconds) while maintaining a 3.5% accuracy level.