Influence of Azimuth Averaging on the Linearised Modal Analysis of Floating Offshore Wind Turbines

The natural frequencies and damping ratios of floating offshore wind turbines are commonly obtained by linearising a coupled OpenFAST model at several rotor azimuths and averaging the transformed matrices over one revolution. The accuracy of this averaged model depends on the azimuth count, the averaging rule and the discarded periodicity, not yet examined together on full-order models. This study measures them for the IEA 15 MW semi-submersible and the NREL 5 MW OC3 spar, using Floquet analysis and new linearisations. The largest error arises from the rotor azimuth state. A coarse average aliases tower-passage harmonics of the azimuth column into a spurious stiffness, and the resulting rotor pendulum can couple with surge and nearly triple its damping ratio. A two-mode model gives the coupling condition, met only by floating platforms among eight reference configurations. Azimuth counts that are not multiples of the blade number reduced the error to a few percent or less. Pinning the azimuth direction to the neutral mode of a dense average removes almost all of the error, identifying its source, while deleting the azimuth state shifts the surge damping by up to 7%. The discarded periodicity is small and can be estimated without a periodic solution.