A new method to fit logistic functions with wind turbines power curves using manufacturer datasheets

Abstract

The literature contains different methods for estimating logistic functions parameters to fit the power-speed characteristics of a wind turbine (WT). However, their disadvantages are: (1) they require a large amount of supervisory control and data acquisition data; (2) the parameter range needed for constrained optimization is not systematically determined; and/or (3) they do not guarantee monotonically increasing relationship between wind speed and predicted WT output power. This paper proposes a systematic approach to fitting the five- and the six-parameter logistic functions to power-speed data of WTs. The authors introduce new limits on the parameters of these functions, which guarantee their monotonicity. Most of these limits are determined analytically and are obtained from manufacturer datasheets. Afterwards, these limits are passed as optimization constraints for subspace trust region algorithm. The results show that the authors' method generally provides better accuracy with mean absolute percentage error values below 0.02 for the five-parameter logistic function and below 0.005 for the six-parameter logistic function. The authors present accurate fits for a group of WTs of different ratings (from 275 kW to 3000 kW) and 12 unique manufacturers, which proves the versatility of the authors' method.