Floating wind turbine stability and time response analysis with rotating modes

Abstract

The periodic azimuthal time dependence of a linearized simple floating wind turbine model with four degrees of freedom is dealt with by developing a particular procedure that enables a stability analysis calculation and reduces computational efforts to calculate time responses. We apply Hill’s method for the aeroelastic stability analysis by generating a constant state-space hyper-matrix that takes into account the periodic azimuthal dependence of the system. It is used to compute precisely the time domain response and to solve an overall eigenvalue problem where natural frequency and modal damping are determined through the eigenvalues. For a varying rotational speed with a fixed air density, eigenfrequencies from Hill’s method are displayed on a Campbell diagram that is based on a waterfall plot of the frequencies obtained by decay tests peaks using the time domain model. Through the modal analysis as well, an investigation of the impact of aerodynamic damping is done following the same procedures by rather fixing the rotational speed and varying air density. In the end, a forcing moment of the platform pitch motion is added to analyze the accuracy of fast time response calculations compared to the time domain model benchmark results.