Reformulation of parameters of the logistic function applied to power curves of wind turbines

• New method to obtain the parameters of the logistic function applied to wind turbine power curves.
• The parameters of the logistic function are obtained in a deterministic way and they have technical meaning.
• Alternative models, based on the logistic function, to the power curve are proposed considering several aproximations.

The current procedure for obtaining the parameters of the logistic function, used as a model for the power curve of wind turbines, provides meaningless values. These values are different for each wind turbine and obtaining them requires an optimization process. This paper proposes a procedure to obtain the parameters of the 4-parameter logistic function based on the features of the power curve, providing a model that is a function of the power curve parameters supplied by the manufacturer. Furthermore, that model can be used to derive another 4-parameter model and a 3-parameter model is proposed for certain conditions. The three models consist of a continuous function which simplifies the implementation of the curve in a computer program compared to piecewise models. In addition, the probability density function of the output power of a wind turbine is derived by using each model.