Identification of aerodynamic damping in wind turbines using time-frequency analysis

Abstract

The paper presents a wavelet-based linearization method for evaluating aerodynamic damping of a wind turbine during operation. The method is used to estimate the aerodynamic damping solely from actual measurements of the dynamic response of the operating wind turbine due to ambient excitation from air turbulence and control forces. Based on the response measurements the generalised displacement, velocity and acceleration vectors related to a given aeroelastic model and an available aeroelastic code are estimated by a state observer. Then, the external generalised load vector, depending on the generalised velocity vector, is obtained from the aeroelastic code. Next, the external generalised load vector is linearized into two parts: a quasi-static load vector independent on the generalised velocity vector and a first order term linearly proportional to the velocity vector indicating the aerodynamic damping matrix. Filtering technique is applied to evaluate the quasi-static load vector from the actual measurements of the structural stiffness force, made up as a product of the time-dependent stiffness matrix and the estimated generalised displacement vector. Finally, the time-dependent aerodynamic damping matrix has been evaluated by wavelet analysis at each time step. Unlike other inverse-based approaches, this wavelet-based method can avoid calculating the inverse of the velocity vector covariance matrix, which is singular. The proposed method has been illustrated by a reduced 13-DOF aeroelastic model, which is used to mimic the in situ response measured on the wind turbine.