# Methods to Apply a 3-Parameter Logistic Model to Wind Turbine Data
## 5 Case Study  
In order to check the performance of the methods, real data measured at the wind farm of Le Haute Borne (Meuse, France) along five years (2013-2017) were used. The data were downloaded from the French company Engie web page, [[https://opendata-renewables.engie.com/](https://opendata-renewables.engie.com/)]([https://opendata-renewables.engie.com/](https://opendata-renewables.engie.com/)), updated on 9 October 2019. In that link data from four wind turbines of the wind farm were available. Each provided measurement that corresponds to the 10-min mean value of each variable. Besides, the data were analyzed by year and by wind turbine in order to reduce possible errors and to improve the models obtained. This means that each wind turbine of the same type may have slight differences on its performance and, from one year to the following, aging may reduce the power supplied. The features of the wind turbines used by Engie in the wind farm of Le Haute Borne are described in Table 1.  
As it was described above, first, raw data were filtered and, then, all the methods were applied for the 3 PLE model. Finally, the methods were assessed by using the two measurements of errors described in the previous section, i.e., Cloud data MAPE (CD MAPE) and Mean values MAPE (MV MAPE). The results of the performance are given in Tables 2-5, where each table corresponds to a different wind turbine. On each one, columns mean a different year and rows a specific combination of method and measurement of error. Notice that including turbulence corrections when applying these methods will be very valuable, however it has been discarded for simplicity. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Manufacturer**} & \multirow{2}{*}{**Model**} & **Rated Power (kW)** & **Hub Height (m)** & **Rotor Diameter (m)** & **Rated Wind Speed (m/s)** & **Cut-in Wind Speed (m/s)** \\ \hline Senvion & MM82 & 2050 & 80 & 82 & 14.5 & 3.5 & 25 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Wind turbine features in Le Haute Borne wind farm. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **2013** & **2014** & **2015** & **2016** & **2017** \\ \hline CD MAPE spline (\%) & 1.71 & 1.64 & 2.14 & 1.94 & 2.08 \\ MV MAPE spline (\%) & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 \\ CD MAPE clustering (\%) & 2.62 & 2.60 & 3.27 & 3.17 & 3.23 \\ MV MAPE clustering (\%) & 1.16 & 1.40 & 1.29 & 1.38 & 1.81 \\ CD MAPE cloud data (\%) & 2.26 & 2.11 & 2.77 & 2.57 & 2.66 \\ MV MAPE cloud data (\%) & 6.86 & 6.34 & 5.87 & 7.07 & 6.94 \\ CD MAPE cluster simulation (\%) & 2.57 & 2.53 & 3.15 & 3.05 & 3.23 \\ MV MAPE cluster simulation (\%) & 1.21 & 1.39 & 1.34 & 1.44 & 2.02 \\ CD MAPE max error cluster (\%) & 2.70 & 2.68 & 3.20 & 3.13 & 4.71 \\ MV MAPE max error cluster (\%) & 1.76 & 1.62 & 2.24 & 2.52 & 4.63 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Performance of wind turbine R80711 for different methods. CD means Cloud Data, MV refers to Mean Value and MAPE is the acronym of Mean Absolut Percentage Error. In the first wind turbine, the analysis of the errors obtained by each combination of method and type of error provides the following items to be pointed out:  
* In the reference case the MV MAPE is always 0 because it is the definition of the reference. However, when obtaining the CD MAPE, the value obtained is close to 2%. The reason is that all the pairs of points do not correspond exactly with the spline models, there is some variability. * In all cases, the MV MAPE is lower than the CD MAPE because the latter measures the errors of all the pairs of points with respect to the model, so the variability is higher. There is an exception to the previous rule and is in the case of the cloud data because, in that case, all the pairs of points participate with the same weight in the model. * The errors provided by the Clustering and the Cluster simulation methods are very low in both cases. In fact, in both cases the difference between the CD MAPE and the MV MAPE is lower than the corresponding one of the spline.