# Methods to Apply a 3-Parameter Logistic Model to Wind Turbine Data
## 6 Conclusions  
The power generated by a wind turbine can be different from that predicted by the manufacturer's power curve due to several reasons such as aging, difference between test conditions and real-life ones, or even performance efficiency. A full year of data measurement may be enough to ensure a good  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Optimization Method** & **Cloud Data MAPE (\%)** & **Mean Values MAPE (\%)** \\ \hline Spline & 1.80 & 0.00 \\ Clustering & 3.01 & 1.36 \\ Cloud data & 2.41 & 7.06 \\ Cluster simulation & 2.92 & 1.41 \\ Maximum error of cluster & 3.19 & 2.16 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Comparison of the mean performance of the methods.  
assessment of its current performance, but even in this case good practice recommends data filtering and modeling. The models with low number of parameters, such as the 3 PLE, which is a logistic model, are very useful to obtain instantaneous values and to be combined with other expressions (i.e., wind speed Probability Density Function). In order to obtain the parameters of the model that better fits the data, several methods can be applied. However, some methods have performance errors due to the difference in the number of data available on each interval of the power curve. In this paper, two methods to face this problem are proposed: Clustering and Cluster simulation. In both cases, the optimization is based on intervals and provide better results than those obtained by means of other methods. The second one is specially recommended when there is a low number of available data in some intervals because it can reproduce the behavior of the wind turbine, in order to balance the number of data. Besides, in the case of the IEC 61400-12, the application of the Cluster simulation method can provide better results than just using the data obtained. This means that, for the highest bins, the information may not be enough to properly define some parts of the curve.  
Therefore, the method based on Cluster simulation can be used to obtain the best power curve when there are not so much data available in some of the bins. On the other hand, in the general case the method based on Cluster can be used for the same purpose. Both methods provide acceptable error values when applied to the 3 PLE model, i.e., to a model of just three parameters, which outperforms the spline model, which needs around two hundred. The model obtained can be combined with a wind speed distribution to provide an output power distribution that can be the input for solving the Probabilistic Load Flow problem in an electrical network with wind power.  
Conceptualization, D.V.; methodology, D.V.; software, A.S.; validation, [PERSON] ([PERSON]), A.F. ([PERSON]) and E.M.; formal analysis, D.V.; investigation, A.S.; resources, A.F. ([PERSON]) and E.M.; data curation, A.S.; writing-original draft preparation, D.V.; writing-review and editing, D.V.; visualization, [PERSON] ([PERSON]); supervision, [PERSON] ([PERSON]); project administration, A.F. ([PERSON]) and E.M.; All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Original data downloaded from the French company Enge at https://opendata-renewables. engie.com/, updated on 9 October 2019.  
The authors declare no conflict of interest.