Effect of hydrostatic nonlinearity on the large amplitude response of a spar type floating wind turbine

The hydrostatic forces of a floating platform play an important role in the stability and dynamic behavior of floating wind turbines. Hydrostatic forces are most commonly obtained from a linear hydrostatic stiffness matrix. Linear hydrostatic stiffness is based on the initial position of the floating platform and thus neglects the rotational motion of the floating wind turbine. In this article, the nonlinear hydrostatic stiffness of a floating spar platform was analytically derived with the aim of studying the effect of hydrostatic nonlinearity on the dynamic response. The floating wind turbine was modeled as a multibody system for which the equation of motion was obtained by using the Newton-Euler approach. The mooring lines connected to the floating wind turbine were modeled quasi-statically using catenary equations. A sensitivity analysis based on the comparison of linear and nonlinear hydrostatic forces was conducted to quantitatively evaluate the importance of hydrostatic non linearity. The effect of hydrostatic nonlinearity on the response of the floating wind turbine was investigated through analysis of the OC3-Hywind wind turbine in extreme environmental conditions. Results showed that in the case of large amplitude rotations, the use of nonlinear hydrostatic stiffness predicted the response with improved accuracy by accounting for rotational motion.