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Unformatted text preview: Wind Turbine Blade Design Optimization Massachusetts Institute of Technology, Cambridge, MA, 02139, USA We develop a methodology for analyzing wind turbine blade geometries and pitch con- trol schemes over a range of incoming wind speeds. We use this model for an orthogonal array design of experiments, a gradient-based sequential quadratic programming optimiza- tion, and a multi-objective genetic algorithm to maximize the expected power output while minimizing the blade volume and structural stress violations. Design of experiments gen- erates good results with little expense. Sequential quadratic programming with Hessian re-scaling and multiple starting points generates good design vectors with a large compu- tational expense, and heuristic algorithms such as the genetic algorithm are not suited to this problem. The best design point achieves between 60 and 70% of the Betz limit for eﬃciency for a large range of incoming wind speeds. Nomenclature R Blade radius, m Qmax Maximum generator torque, N-m t Blade shell thickness, m k Cut-off velocity in standard deviations above the mean wind speed T Twist distribution vector, radians F Foil shape parameter distribution, non-dimensional C Chord length distribution, m β Pitch control curve, radians x Design vector J ( x, param ) Objective function P E Expected power output, W P Turbine power at a particular wind speed, W Q Turbine torque at a particular wind speed, N-m V blades Blade material volume, m 3 ξ ( x, param ) Penalty function σ r max Maximum blade stress, MPa σ allowable Maximum allowable blade stress, MPa c weibull Scale parameter of the Weibull distribution of incoming wind speeds k weibull Shape parameter of the Weibull distribution of incoming wind speeds ω Angular velocity, rad/s F t / Δ R , F t / Δ R Tangential and axial aerodynamic load distributions on the blade, N/m v Incoming wind speed ahead of the blade, m/s H Hessian matrix, matrix of second derivatives I. Motivation As renewable energies become a growing part of the energy portfolio, focus is being put on increased performance and eﬃciency of proven sources such as horizontal axis wind turbines. Modern commercial power wind turbines are predominantly horizontal-axis, three-bladed behemoths, with a fixed blade design ∗ Graduate Student, Computation for Design and Optimization 1 of 11 American Institute of Aeronautics and Astronautics Anonymous MIT Students that is adapted to varying wind conditions by a blade pitch control mechanism. They are complex systems whose design requires the integration of many engineering disciplines including aerodynamics, structures, controls, and electrical engineering. Previous wind turbine design optimization techniques have focused on specific regions of interest, including optimal control, 1 optimal blade shape, and site-specific performance increases....
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- Fall '03
- Wind turbine, American Institute of Aeronautics and Astronautics, blade radius