We propose a computationally efficient stochastic framework and an associated mathematical formulation to assess the improvement in the vibration response of wind turbines with active structural controllers. Uncertainties in the turbulent wind speed as well as in the structural parameters are considered in the formulation for analyzing the 2 important (rated and cut-out) wind speed conditions. A multimodal wind turbine model based on a NREL 5-MW wind turbine model is adopted for analysis, and an active tendon controller is used to develop the stochastic framework. Dynamic interaction between the rotor blades and the supporting tower, as well as the coupling induced by the pretwist of the blades, and a collective pitch controller are considered. A time-evolving phase spectrum method together with a phase delay spectrum model is used to simulate the stochastic wind field, which is computationally less expensive. The probability density contours and the extreme value distributions of the blade tip displacements with and without the active controller are obtained by the wavelet-based probability density evolution method, followed by the computation of the corresponding failure probabilities. It is observed that the improvement in reliability and performance of the rotor blades with the controller becomes statistically more effective as the wind speed increases (e.g., significant beneficial effects are noticed from the probability distributions in terms of the spread at the cut-out wind speed).

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stochastic wind field collective pitch controller vibration response mathematical formulation coupling reliability multimodal wind turbine model the blade tip displacements important rated and cutout wind speed extreme value distributions timeevolving phase spectrum method failure probabilities performance rotor blades structural parameters waveletbased probability density evolution method uncertainties active tendon controller stochastic framework dynamic interaction between the rotor blades and the supporting tower

Weifeng Tao, Biswajit Basu, Jie Li,.Reliability analysis of active tendon-controlled wind turbines by a computationally efficient wavelet-based probability density evolution method. 25 (2),.

Weifeng Tao, Biswajit Basu, Jie Li,"Reliability analysis of active tendon-controlled wind turbines by a computationally efficient wavelet-based probability density evolution method" 25

Weifeng Tao, Biswajit Basu, Jie Li,"Reliability analysis of active tendon-controlled wind turbines by a computationally efficient wavelet-based probability density evolution method"