# Power Curve Modeling of Wind Turbines through Clustering-Based Outlier Elimination +
## 5 Concluding Remarks  
The power curve of wind turbines is the central element for an efficient plant operation and prediction of generation output. It is often the case that the specification power curve provided by the manufacturer may not well account for variations incurred by operational and environmental factors, which may not lead to an efficient operation of wind turbines since the actual power curve hardly coincide with the specification power curve. An accurate estimation of actual power curve may be hindered by manifest and influential outliers and it is necessary that the observed data are preprocessed to detect and eliminate those outliers for the effective estimation of power curves. This study proposes a novel outlier elimination procedure, which can be applied in situations where a sufficient amount of data with proper time resolution is not readily available. More specifically, the popular algorithms of density-based DBSCAN and partition-based K-means are simultaneously adopted. Different parametric models are then employed to fit the refined data and tested for their goodness-of-fit to derive the actual power curve. The applicability of proposed procedure is demonstrated with the hourly measurement data taken from the Hankyung wind farm site in the Republic of Korea over the years 2018-2020. The data from 1.5 MW turbine are well fitted with the Weibull function whereas those from 3.0 MW turbine are best fitted with Gompertz function. It is implied that different parametric models are more suitable for estimating power curves of different turbines. It is asserted that the proposed method is effective in estimating the power curve with data having low temporal resolution. As one of the reviewers pointed out, the measurement data used in this study may exhibit the lack of temporal resolutions. The acquisition of data with high enough resolutions is highly limited for individual wind turbines in many sites. To the best of authors' knowledge, this study is the first attempt for power curve modeling with hourly measurement data available in the Republic of Korea. Nonetheless, a more precise derivation of power curve need to be enabled by securing data with high enough temporal resolutions. In addition, it will be meaningful to examine the nonparametric methods in modeling power curves, which has hardly been investigated in the current literature.  
Conceptualization, C.P. and Y.J.K.; methodology, C.P.; software, Y.C.; validation, Y.J.K. and Y.C.; formal analysis, C.P.; investigation, Y.J.K.; data curation, Y.C.; writing--original draft preparation, C.P.; writing--review and editing, Y.J.K. and Y.C.; visualization, Y.C.; supervision, C.P.; project administration, C.P.; funding acquisition, Y.J.K. All authors have read and agreed to the published version of the manuscript.  
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2021R11H1A3047456).  
The data presented in this study are available upon request from the corresponding author with the permission granted by the provider.  
The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Turbine** & **Models** & **RMSE** & **MAE** & \(\mathbf{R^{2}}\) \\ \hline \multirow{4}{*}{1.5 MW} & Polynomial & **0.0855** & 0.0618 & 0.9525 \\  & Gompertz & 0.0889 & 0.0663 & 0.9487 \\  & Logistics & 0.0871 & 0.0641 & 0.9507 \\  & Weibull & 0.0878 & **0.0611** & **0.9530** \\ \hline \multirow{4}{*}{3.0 MW} & Polynomial & 0.1644 & 0.0981 & 0.9567 \\  & Gompertz & **0.1643** & **0.0976** & **0.9567** \\ \cline{1-1}  & Logistics & 0.1654 & 0.0995 & 0.9567 \\ \cline{1-1}  & Weibull & 0.1660 & 0.0998 & 0.9559 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Goodness-of-Fit Analysis of Different Parametric Models.