# Enhancing Reliability in Wind Turbine Power Curve Estimation
## 2 Materials and Methods
### Anomaly Filtering  
According to the distribution presented by these points (the anomalies), there are authors such as those of [9] who classify them according to three typologies: (1) power sensor failures, (2) wind speed sensors failure, or (3) due to the starting and stopping effect of the WT. In Figure 5, we see represented the power curves of each WT resulting from directly crossing the wnac_avg_WSpd1 and wgdc_avg_TriGri_PwrAt signals provided by the SCADA. A total of 3/4 of the available signals are used. In some of these curves, anomalies appear, forming horizontal lines, which are attributed to failures of type (1), which are related to the power sensors. The anomalies distributed randomly inside the curves are of type (3), mainly attributed to the phenomenon of starting and stopping the WTs. In any case, the anomalies introduce errors in estimating the wind power curves. Before the estimation of the power curves of each WT, it is necessary to filter them. When estimating the power curve from the data, what is evident from the related literature is the need to filter out anomalies to obtain decent estimates. This filtering determines the rest of the processing chain. The work in [24], which compiles recent state-of-the-art literature on estimating wind-power curves, devotes a section to anomaly classification and determines up to seven different types of anomalies, five of which are systematically treated in the texts. The other two appear less referenced. When discussing anomalies in the context of power curves, the texts systematically explain them graphically, and do so based on the graphical representation of the curve. However, the filtering process is usually based on more or less complicated statistical criteria although, we repeat, they are visually identified clearly in a graph. Our approach may be surprisingly simple, but is very effective. It uses such graphical information. Since we only have the manufacturer's information, we have an idea of the region of the graph where the points must appear. For the first filtering, we use such information. Since we know that the noise in the sensors, the different environmental conditions around the turbine (temperature, turbulence, humidity, etc.) and the averaging \begin{table}
\begin{tabular}{c c c c} \hline \hline \(i\) & \(A_{i}\) & \(a_{i}\) & \(\phi_{i}\) \\ \hline
1 & 4131.2000 & 0.1487 & \(-\)0.2597 \\
2 & 2199.6000 & 0.1909 & 2.8832 \\
3 & 385.6073 & 0.5622 & 1.5075 \\
4 & 86.5623 & 1.1268 & 1.9258 \\
5 & 19.0806 & 2.1933 & \(-\)3.3415 \\
6 & 30.4685 & 1.6828 & \(-\)4.1747 \\
7 & 12.4781 & 2.7778 & \(-\)3.2777 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Coefficients of \(P_{7}(w)\). Figure 4: (**a**) Points in (black squares) of the power curve provided by the manufacturer. (**b**) Continuous function \(P_{7}(w)\) in blue with the square points given by the manufacturer. performed by the SCADA system generate some dispersion in the points around the curve, we select the candidate points in a margin around the nominal curve provided by the manufacturer. Since, as far as we know, the power performances, in practice, are usually slightly lower than those provided by the curve, we establish the criterion of selecting all the points that enter the region in the upper part represented in red in Figure 6. This red curve is made from the points provided by the manufacturer by shifting to the right and down a given distance. So, to filter the data of each WT, we use the continuous manufacturer's curve approximated by \(P_{7}(w)\) given in (1) that we move horizontally to the right \(w_{off}\) and vertically down a distance \(p_{off}\). Considering the signals wnac_avg_WSpd1 and wgdc_avg_TriGri_PwrAt at the point \(k\) to be \(w_{k}\), \(p_{k}\), respectively, then if the following inequality is fulfilled, we establish that \(p_{k}\) is an anomaly:  
\[p_{k}<P_{7}(w_{k}-w_{off})-p_{off} \tag{2}\]  
We initially determine \(w_{off}\) and \(p_{off}\) empirically to 1m/s and 100W, respectively.