# Methods to Apply a 3-Parameter Logistic Model to Wind Turbine Data
## 5 Case Study
* Comparing Clustering and Cluster simulation methods, they provide very similar results in this case. * In the case of the Max error cluster method, the values of errors are a bit higher in all cases. \begin{table}
\begin{tabular}{c||c c c c c} \hline  & **2013** & **2014** & **2015** & **2016** & **2017** \\ \hline CD MAPE spline (\%) & 1.50 & 1.42 & 1.76 & 1.64 & 1.75 \\ MV MAPE spline (\%) & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 \\ CD MAPE clustering (\%) & 2.42 & 2.42 & 2.80 & 2.82 & 2.78 \\ MV MAPE clustering (\%) & 1.11 & 1.26 & 1.27 & 1.18 & 1.18 \\ CD MAPE cloud data (\%) & 2.03 & 1.89 & 2.35 & 2.22 & 2.35 \\ MV MAPE cloud data (\%) & 6.57 & 5.99 & 5.09 & 6.33 & 6.11 \\ CD MAPE cluster simulation (\%) & 2.31 & 2.30 & 2.69 & 2.64 & 2.70 \\ MV MAPE cluster simulation (\%) & 1.14 & 1.32 & 1.29 & 1.24 & 1.19 \\ CD MAPE max error cluster (\%) & 2.54 & 2.68 & 3.51 & 2.89 & 3.04 \\ MV MAPE max error cluster (\%) & 1.41 & 1.28 & 1.46 & 1.64 & 2.19 \\ \hline \end{tabular}
\end{table} 
Table 4: Performance of wind turbine R80736 for different methods. Analyzing the second wind turbine, a similar discussion can be made and the following comments can be added:  
* The CD MAPE for the Spline is a bit lower than in the case of the first wind turbine. The reason may be that the variability of the output power of that wind turbine is lower than in the first one which can be due to performance reasons. * The MV MAPE Cloud data is higher than in the first wind turbine while the CD Cloud data is lower. The reason may be the same as in the first comment, the pairs of points are not very dispersed, therefore, they provide a very good model, when assessing all data. For the third wind turbine, the following comments can be made:
* It is the wind turbine with the lower errors from a general point of view. The MV MAPE Clustering and the MV MAPE Cluster simulation errors are close to 1%. * Its behavior and levels of errors are very similar to the ones of the first one. In the fourth wind turbine some differences can be pointed out with respect to former wind turbines:  
* The CD MAPE for the spline is over 2% (very high compared with the others). * The CD MAPE Clustering is also very high (more than 3%). * The MV MAPE for Clustering and Cluster simulation are very similar to the rest of wind turbines. * The rest of errors are out of the ranges of the other three wind turbines. In Table 6, the mean values of the error measurements are provided organized by method and by type of measurement in order to assess the performance of each method on its own. The Cloud data is the one that provides a lower percentage of error when it is measured using the CD MAPE. However, when considering the MV MAPE, the error obtained is far from the expected (7.06%). The reason may be that the data are dispersed. Besides, the method based on the maximum error of the clusters is not a good option due to the results provided in both cases, the worst in the CD MAPE (3.19%) and the next to the worst in the MV MAPE (2.16%). Also, influence of aging can be assessed and compared for the proposed methods. In general, it can be said that there is no specific influence but the slight increment of the error values with the aging for all the methods. Finally, both methods based on clustering provide good results and, after discarding the others, the results obtained are the best when assessing the CD MAPE (Clustering simulation) and the MV MAPE (Clustering).