Actuator control of edgewise vibrations in wind turbine blades

Abstract

Edgewise vibrations with low aerodynamic damping are of particular concern in modern multi-megawatt wind turbines, as large amplitude cyclic oscillations may significantly shorten the life-time of wind turbine components, and even lead to structural damages or failures. In this paper, a new blade design with active controllers is proposed for controlling edgewise vibrations. The control is based on a pair of actuators/active tendons mounted inside each blade, allowing a variable control force to be applied in the edgewise direction. The control forces are appropriately manipulated according to a prescribed control law. A mathematical model of the wind turbine equipped with active controllers has been formulated using an Euler–Lagrangian approach. The model describes the dynamics of edgewise vibrations considering the aerodynamic properties of the blade, variable mass and stiffness per unit length and taking into account the effect of centrifugal stiffening, gravity and the interaction between the blades and the tower. Aerodynamic loads corresponding to a combination of steady wind including the wind shear and the effect of turbulence are computed by applying the modified Blade Element Momentum (BEM) theory. Multi-Blade Coordinate (MBC) transformation is applied to an edgewise reduced order model, leading to a linear time-invariant (LTI) representation of the dynamic model. The LTI description obtained is used for the design of the active control algorithm. Linear Quadratic (LQ) regulator designed for the MBC transformed system is compared with the control synthesis performed directly on an assumed nominal representation of the time-varying system. The LQ regulator is also compared against vibration control performance using Direct Velocity Feedback (DVF). Numerical simulations have been carried out using data from a 5-MW three-bladed Horizontal-Axis Wind Turbine (HAWT) model in order to study the effectiveness of the proposed active controlled blade design in reducing edgewise vibrations. Results show that the use of the proposed control scheme significantly improves the response of the blade and promising performances can be achieved. Furthermore, under the conditions considered in this study quantitative comparisons of the LQ-based control strategies reveal that there is a marginal improvement in the performances obtained by applying the MBC transformation on the time-varying edgewise vibration model of the wind turbine.