Dynamics and control of vibrations in wind turbines with variable rotor speed

Abstract

This paper proposes the modeling and control of vibrations in wind turbines due to change in the rotational speed of the blades. Structural and/or electrical faults occurring in a wind turbine may lead to fluctuations of the angular velocity of the rotor blades. The impact of these fluctuations on the mechanical vibrations has not been extensively explored yet. A multi-modal mathematical model describing the dynamics of flexible rotor blades and their interaction with the turbine tower is formulated using a Lagrangian approach. The blade model considers variable mass and stiffness per unit length. It also includes the effects of gravity and centrifugal stiffening due to the rotation of the blades. Further, the equations of motion of the wind turbine are derived by taking the variable rotor speed into account. This leads to a time varying model with time dependent mass, stiffness and damping matrices. Using the proposed model, the focus of the present paper is to investigate the impact of realistic changes in the rotational speed on the edgewise vibration of the blades due to some grid faults. A numerical investigation is carried out to examine the influence of rotor speed variations on the mechanical vibrations affecting the wind turbine structure. An active controller based on active tendons is proposed to mitigate wind induced edgewise vibrations. A reduced order model is designed for the synthesis of an appropriate control law. Simulations results show that the proposed control scheme is successful in improving the blade response. Further, under the conditions considered in this study, the numerical investigation reveals that the controller is robust with respect to rotor speed variations under circumstances when grid fault occurs.