# Power Curve Modeling of Wind Turbines through Clustering-Based Outlier Elimination +
## 2 Data and Method  
Wind turbines covert the kinetic energy of wind into electric energy by using a wind rotor and the aerodynamic forces are generated when wind passes over the blades of the rotor. When the wind flows over the rotor blades, a lift force is generated due to the difference in air pressure on the two sides of blade which causes the blade to rotate. As the blades rotate, a shaft connected to a generator also rotates to spin the generator and generate electric energy. The amount of energy produced depends upon the wind speed as well as the technical characteristics of WTs. The power curve of wind turbines is a specific type of power curve that describes the relationship between wind speed and the amount of electrical power that can be generated by a wind turbine [11]. The power output of a wind turbine is directly proportional to the wind speed, but the relationship is not linear. Understanding the power curve of a wind turbine is crucial for wind farm operators to maximize the energy output and economic efficiency of their wind turbines. By monitoring and analyzing the power curve over time, operators can identify any issues or inefficiencies with the turbines and take corrective action to improve their performance. Additionally, the power curve can help predict the energy output of a wind farm, which can be used to estimate the economic viability of a project and inform energy planning and policy decisions. A typical power curve for a wind turbine shows that the turbine produces little or no power at wind speeds below a certain threshold, known as the cut-in speed. As wind speed increases beyond the cut-in speed, the power output of the turbine increases, reaching a maximum at the rated wind speed. The rated wind speed is the wind speed at which the turbine is designed to produce its maximum power output. Beyond the rated wind speed, the power output of the turbine begins to level off, and at some point, it reaches its maximum output, known as the rated power output. This point is the maximum amount of power that the turbine can produce, regardless of how strong the wind gets. Beyond the rated wind speed, the power output of the WT may be kept constant via the stall or brake mechanism to avoid the risk of rotor damage from over-speeding. This mechanism explains why the power curve of WTs takes a different form from the usual power curve of cubic function. At some point, the wind speed becomes too high and the turbine needs to shut down to avoid breakdown from further operation. This wind speed is known as the cut-out speed [11]. The shape of the power curve can vary depending on the specific design and characteristics of the wind turbine, as well as the wind conditions at the site where the turbine is installed. For example, some wind turbines may have a steeper increase in power output at lower wind speeds than others, and some may have a lower cut-out wind speed. Figure 1 depicts the traditional specification power curve of WTs, which represents the amount of specified power output with respect to varying wind speed. The turbine begins to generate power at the cut-in speed, and the amount of power generation steadily increases up to the rated output at the rated wind speed. No power can be generated when the wind speed is greater than the cut-out speed. The typical values of cut-in, rated, and cut-out speeds are 3-4 m/s, 11-13 m/s, 23-25 m/s, respectively [12; 13]. As stated earlier, however, the observed data greatly deviate from the specification power curve presumably due to various factors related to the operational characteristics of turbines, environmental conditions, and measurement errors as shown in Figure 2, which plots 1095 data points of power output against wind speed from 1.5 MW and 3.0 MW wind turbines from the Hankyung wind farm site in the Republic of Korea over the period 2018-2020.