## 2 Materials and Methods  
### Initial Dataset and Exploratory Analysis  
The materials for this research are the data about the power generation output of a real wind power plant (nominal capacity of 3.6 MW) and the data about wind speed. These data were recorded by the SCADA system of the real wind turbine in Turkey [33]. It is an open dataset (Kaggle). The data discretization step equals 10 min, and there are 50,530 samples contained in the data, from 1 January 2018 00:00 to 31 December 2018 23:50 (the number of missing values is 3.86%). Next, parameters are presented from the collected data:  
* Date and time;
* Generated active power, kW;
* Wind speed at turbine height, m/s;
* Theoretical electrical power values that the turbine generates with that wind speed as given by the turbine manufacturer, kW;
* Wind direction at turbine height (while the turbine is turned so that the wind wheel is perpendicular to the wind flow). Figure 1: Theoretical (traditional) power curve of a wind turbine (red) and areas of the outliers (blue); “\(1\)”—power output values close to zero despite significant wind speeds; “2”—real values are substantially exceeding calculated values; “3”—real values are significantly lower than calculated. Visual analysis of the data readily reveals outliers in the first group (Figure 2). It is evident that these can be attributed only to errors in the measurement and data collection system. Therefore, such values (where power is zero and wind speed exceeds 3 m/s) are excluded. As a result, the number of samples (rows) has been reduced from 50,530 to 46,976 (7%). For all other outliers, it is impossible to confidently assert that they are solely due to incorrect power readings, so they are kept. Figure 3 shows that the dataset does not contain outliers in the second group. It is impossible to definitively determine whether data points in group 3 are incorrect values or not; therefore, they were not excluded from the dataset. For instance, these could be values where the actual power is lower than theoretical at high wind speeds due to the turbines' inertial properties or sudden changes in wind direction, as the rotation of the wind turbine nacelle does not occur instantaneously. Figure 4 shows the theoretical power curve and observations from the SCADA system. The theoretical (calculated) dependence of power generation on wind speed has a significant error, and determination of the actual generation based on data from the calculated model only will have a greater deviation than that based on a model that takes into account wind speed and additional parameters. Statistical evaluation of the initial data and preprocessing were performed before implementation of any ML models. To look at the current state of the data, common statistical metrics were used, such as average value, standard deviation value, percentile values, and minimum and maximum values. The results of the statistical evaluation are presented in Table 2. Figure 5 presents the distribution of the features; Figure 6 shows the scatter plot of wind direction. When the wind speed exceeds a certain threshold, the output power stops increasing. It explains the second extremum on the density plot of wind turbine power. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Date and Time** & **Real** & **Wind Speed, m/s** & **Theoretical** & **Wind Direction**\({}^{\circ}\) \\  & **Power, kW** & **Power, kW** & **Wind Direction**\({}^{\circ}\) \\ \hline
1 January 2018 00:00 & 380.047791 & 5.311336 & 416.328908 & 259.994904 \\
1 January 2018 00:10 & 453.769196 & 5.672167 & 519.917511 & 268.641113 \\
1 January 2018 00:20 & 306.376587 & 5.216037 & 390.900016 & 272.5964789 \\
1 January 2018 00:30 & 419.645905 & 5.659674 & 516.127569 & 271.258087 \\
1 January 2018 00:40 & 380.650696 & 5.577941 & 491.702972 & 265.674286 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Initial data fragment. Figure 2: Visual highlight of outliers of the first group; the red lines highlight areas containing outliers.