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Along-the-path exponential integration for Floquet stability analysis of wind turbines

Traditionally, stability assessment of wind turbines has been performed by eigenanalysis of the azimuthally-averaged linearized system after applying the Multi-Blade Coordinate (MBC) transformation. However, due to internal or external anisotropy, the MBC transform does not produce an exact Linear Time-Invariant (LTI) system, and a Floquet analysis is required to capture the influence of all periodic terms, leading to a more accurate stability analysis. In this paper exponential integration methods that use system linearizations at different blade azimuth positions are used to integrate the perturbed system state and compute the Floquet monodromy matrix. The proposed procedure is assessed for a simple 6 DOF wind turbine model and a more complex aeroelastic model of a 5MW onshore wind turbine. The defined along-the-path or moving-point exponential integrator is found to be the suitable in order to perform a Floquet stability analysis even using a coarse linearization grid.