Optimization of capacity factors based on rated wind speeds of wind turbines

Efficient utilization of wind energy depends on wind turbine selection and wind farm localization. The overall performance of a wind turbine is usually expressed by two important factors: the capacity factor and the annual energy production. These factors have conflicting effects due to rated power of the wind turbine. Higher rated power lowers the capacity factor yet raises the annual energy production. Therefore, a compromise is needed to simultaneously optimize these factors. In this work, a new approach is adopted in which the capacity factor and the annual energy production are formulated based on the rated wind speed. New analytical solutions are presented for the capacity factor using linear, quadratic, cubic, and general empirical wind turbine power models and the Weibull distribution of wind. An optimization technique based on the constrained nonlinear minimization is applied to find optimum values for the objective functions defined by the capacity factor, the normalized annual energy production, and the combination of both. Results of the optimization show that for the obtained optimum rated wind speeds, the capacity factor increases among 0.6-3.7% for the linear model, 7-8% for the quadratic model, 11.5-17% for the cubic model, and 4.2-11.3% for the general power models for practical range of shape factors 1.5 k < 3.5. Details of optimized values are presented in the form of new correlations and discussed.