Optimization of wind energy capture using BET

The Blade Element Theory (BET) has been used to predict performance of wind turbines, and to optimize energy extraction from the wind. A literature search shows that the number of parameters that can be varied to attempt optimization within BET varies for different authors. However, a repeated assumption is that the BE should be operating at the incidence angle resulting in maximum lift to drag ratio. In the present work, the incidence angle is one of the parameters varied for optimization, along with five others: the two induction factors, the chord, and the flow and setting angles. The optimization satisfies five equality constraints and three inequality constraints. The optimizer uses Levenberg-Marquardt, Conjugate Gradient or Quasi-Newton methods to maximize the power extracted. The equations adopted employ the Prandtl tip loss and require specification of the airfoil for the section, the radius of the turbine, the wind speed and the radial distribution of solidity. Up to twenty five elements can be specified for each turbine. The influence of airfoils on power coefficients is shown, and deviations from the expected maximum lift to drag positions noted. Comparisons to the performance of small wind turbines from the commercial and open literature are attempted. Whereas such comparisons are difficult in that airfoils and solidities are not often specified, they yield a baseline for establishing the validity of the optimization procedure.