An analytical model for estimating aerodynamic damping of wind turbines in the shutdown state

As wind farms are constantly being constructed, the risk of tower failure for wind turbines increases significantly under strong winds. Compared with the extensively concerned wind-induced behaviors during the operating state, those ones during the shutdown state attract little attention but may lead to serious problems of damages or even collapse. To clearly grasp the aero-structure interaction in the shutdown state, this paper develops an analytical model for estimating aerodynamic damping of wind turbines. In this method, an analytical expression of aerodynamic damping coupling matrix is derived via the combination of multibody dynamics and first-order Taylor expansion. This matrix is further quantified as the ratio of modal aerodynamic damping with the aid of state-space equation and complex eigenvalue analysis. This treatment can facilitate the straightforward application of efficient calculation methods, such as frequency domain analysis and uncoupled analysis. More importantly, the developed model is able to simultaneously consider multiple realistic factors, such as blade flexibility, tower top rotation, yaw error, wind shear, and pitch angle. This model may have the high calculation efficiency and accuracy, as well as strong applicability for estimating the aerodynamic damping. Numerical examples based on a typical 5 MW wind turbine are employed to validate the effectiveness of the developed model. Experimental analyses demonstrate that this model outperforms the existing formula and presents a high consistency with OpenFAST in the estimation of aerodynamic damping. Meanwhile, the influence of multiple realistic factors is quantitatively analyzed, which even makes the estimation error exceed 70%.