# Power Curve Modeling of Wind Turbines through Clustering-Based Outlier Elimination +
###### Abstract  
The estimation of power curve is the central task for efficient operation and prediction of wind power generation. It is often the case, however, that the actual data exhibit a great deal of variations in power output with respect to wind speed, and thus the power curve estimation necessitates the detection and proper treatment of outliers. This study proposes a novel procedure for outlier detection and elimination for estimating power curves of wind farms by employing clustering algorithms of vector quantization and density-based spatial clustering of applications with noise. Testing different parametric models of power output curve, the proposed methodology is demonstrated for obtaining power curves of individual wind turbines in a Korean wind farm. It is asserted that the outlier elimination procedure for power curve modeling outlined in this study can be highly efficient at the presence of noises. wind turbine; power curve; wind speed distribution; outlier elimination; clustering algorithm +
Footnote †: This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ([[https://creativecommons.org/licenses/py/4.0/](https://creativecommons.org/licenses/py/4.0/)]([https://creativecommons.org/licenses/py/4.0/](https://creativecommons.org/licenses/py/4.0/))). Footnote †: This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:creativecommons.org/licenses/py/4.0/). Footnote †: This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ([[https://creativecommons.org/licenses/py/4.0/](https://creativecommons.org/licenses/py/4.0/)]([https://creativecommons.org/licenses/py/4.0/](https://creativecommons.org/licenses/py/4.0/))). Footnote †: This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:creativecommons.org/licenses/py/4.0/). Footnote †: This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons. often adopts different machine learning algorithms [7; 8]. Interested readers are also referred to [5; 9] for the development of WT power curve modeling techniques. Since the adequacy of modeling approach is highly dependent upon both the quantity and quality of available data, no one model or method may not be said to be unequivocally or universally superior to others. There exists a general consensus, however, that detecting and removing outliers included in the data prior to modeling is essential for a more proper estimation of power curves no matter which approach is employed [5; 10]. Outliers may be caused by factors directly related to the operation of WTs, such as output curtailment and outage due to failure and maintenance of individual turbines, as well as simple measurement errors [10]. The behavior of outliers is also affected by the time resolution of data, and it is relatively easy to detect outliers with higher time resolution, preferably with less than 10 min of time resolution. It is often the case, however, that a sufficient amount of data with enough time resolutions may not be readily available. For example, the measurement data for wind speed and power output are taken hourly in most wind farms in the Republic of Korea. This study is aimed at outlining the estimation of actual power curves which may better account for operational and environmental variations than the specification power curves. A more efficient and effective planning and operation of WTs may thus be enabled by systematically detecting and eliminating outliers. Proposed is the outlier elimination procedure under variable circumstances by adopting different clustering algorithms frequently used in unsupervised machine learning.