Passive control of wind turbine vibrations including blade/tower interaction and rotationally sampled turbulence

Abstract

This paper investigates the use of a passive control device, namely, a tuned mass damper (TMD), for the mitigation of vibrations due to the along-wind forced vibration response of a simplified wind turbine.The wind turbine assembly consists of three rotating uniform rotor blades connected to the top of a flexible uniform annular tower, constituting a multi-body dynamic system.First,the free vibration properties of the tower and rotating blades are each obtained separately using a discrete parameter approach, with those of the tower including the presence of a rigid mass at the top, representing the nacelle, and those of the blade including the effects of centrifugal stiffening due to blade rotation and self-weight. Dragbased loading is assumed to act on the rotating blades, in which the phenomenon of rotationally sampled wind turbulence is included. Blade response time histories are obtained using the mode acceleration method, allowing base shear forces due to flapping motion for the three blades to be calculated. The resultant base shear is imparted into the top of the tower. Wind drag loading on the tower is also considered, and includes Davenport-type spatial coherence information. The tower/nacelle is then coupled with the rotating blades by combining their equations of motion. A TMD is placed at the top of the tower, and when added to the formulation, a Fourier transform approach allows for the solution of the displacement at the top of the tower under compatibility of response conditions. An inverse Fourier transform of this frequency domain response yields the response time history of the coupled blades/tower/damper system. A numerical example is included to qualitatively investigate the influence of the damper. Figure 4. Transfer function for the coupled tower/nacelle and rotating blades model (Ω = 15 rev min -1 ) including and excluding the TMD 314 P. J. Murtagh et al.Figure 7. Simulated displacement response at the top of the tower coupled tower/nacelle and rotating blades model (Ω = 30 rev min -1 ) including and excluding the TMD 316 P. J. Murtagh et al.

Active Control of Edgewise Vibrations in Wind Turbine Blades Using Stochastic Disturbance Accommodating Control

“…The blade is assumed as a Bernoulli Euler cantilever beams,the mathematical model can be carried out based on energy formulation using Euler-Lagrange formulation.The blades are attached at the root to the tower/nacelle which rotate at a constant rotational speed Ωrad/s about the rotor hub's horizontal axis.The blade have distribute mass µ(x) and distribute bending stiffness EI(x) per unit length along the length L. The tower is modeled as Bernoulli cantilever beam.The dynamic coupling between the blade and the tower has been included through the motion of the nacelle.In practice, it is often suppress the tower vibration using passive TMD [15] or TLCD [19],in order to consider its effect,there is one DOF about TMD in the model at the top of the tower in side-side direction which the mass,stiffness and damper are m tmd ,k tmd and c tmd .…”

Emerging trends in vibration control of wind turbines: a focus on a dual control strategy

“…The inclusion of the degrees of freedom (d.f.) associated with the tower into the Lagrangian formulation allows one to capture the dynamic coupling between the blades and the tower [11]. The blade-tower interaction has been found to have a significant impact on the dynamic response of the turbine [8] Each mode of vibration is associated with the corresponding mode shape, for which an appropriate function approximation can be computed from the eigen-analysis of the blade structural data.…”

Dynamic analysis of wind turbines including nacelle–tower–foundation interaction for condition of incomplete structural parameters

“…The blade characteristics in the low-order vibration conditions were investigated by Ye et al 9 Murtagh et al 12,13 investigated the dynamic interaction between the rotor blades and the tower and developed an analytical model for passive control of wind turbine vibrations. A hybrid multibody system method was proposed for wind turbine structure analysis, which could capture all the rigid and elastic mechanical components, couplings, and important motions based on nonlinear kinetics.…”