## 4 Power Curve Uncertainty
### Uncertainty in Free-Stream Wind Speed from Nacelle LIDAR  
Category B uncertainty in wind speed includes the uncertainty in NTF, which contains the uncertainty in free-stream wind speed. Although the uncertainty component in free-stream wind speed from a met mast, \(\mathrm{u}_{\mathrm{PS,Cup}}\), can be calculated in compliance with IEC 61400-12-2, the uncertainty in free-stream wind speed from nacelle LIDAR, \(\mathrm{u}_{\mathrm{PS,NL}}\), cannot be computed because of no regulation in current IEC standards. Thus, the following components were taken into account according to the following references:  
- The statistical uncertainty of the nacelle LIDAR measurements (\(\mathrm{u}_{\mathrm{FS,NL1}}\)) [8];  
- The uncertainty caused by flow distortion due to terrain (\(\mathrm{u}_{\mathrm{FS,NL2}}\)) [8];  
- The uncertainty related to the measurement height (\(\mathrm{u}_{\mathrm{FS,NL3}}\)) [27];  
- The uncertainty of the tilt inclinometers (\(\mathrm{u}_{\mathrm{FS,NL4}}\)) [27]. \(\mathrm{u}_{\mathrm{PS,NL1}}\) was calculated from the standard deviation of nacelle LIDAR measurements in bin i divided by the square root of the number of data in bin i. \(\mathrm{u}_{\mathrm{FS,NL2}}\) was estimated to be 2% of the wind speed given in IEC 61400-12-2 because the distance between the test wind turbine and the measurement point was less than three times the rotor diameter, and no site calibration was undertaken. Because the nacelle LIDAR tilts due to the motion of the wind turbine nacelle by wind variation, the tilt of the nacelle LIDAR should be set at \(-2.5\%\) of the hub height to measure wind conditions. In addition, nacelle LIDAR measurements should be performed within \(\pm 2.5\%\) of the hub height. Figure 5 illustrates the nacelle LIDAR measurement height relative to the hub height along with the wind speed ratio. The mean values of the bin interval of 0.5 m/s are presented as well. The measurement height increased with an increase in the wind speed until the rated speed and then steadily decreased. This is because of blade pitching, which decreases the thrust force on the rotor after the rated wind speed. It was confirmed that the nacelle LIDAR measurement was carried out within \(\pm 2.5\%\) of the hub height. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**WTs** & **PCs** & **Slope** & **R2** \\ \hline WT no. 1 (Reference: \(\mathrm{PC}_{\mathrm{NTF,\ Cup}}\)) & \(\mathrm{PC}_{\mathrm{NTF,\ NL}}\) & 1.002 & 0.999 \\  & \(\mathrm{PC}_{\mathrm{NL}}\) & 0.992 & 0.997 \\ \hline WT no. 15 (Reference: \(\mathrm{PC}_{\mathrm{Cup}}\)) & \(\mathrm{PC}_{\mathrm{NTF,\ Cup}}\) & 0.997 & 0.997 \\  & \(\mathrm{PC}_{\mathrm{NTF,\ Cup}}\) & 1.010 & 0.998 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results from the two-parametric linear regression analysis between power curves. The uncertainty caused by variation in measurement height due to tilting motion, \(\mathrm{u_{NL,FS3}}\), can be calculated using Equations (4) and (5) [27]:  
\[\mathrm{u_{NL,FS3}}=\frac{1}{\sqrt{3}}(\mathrm{V_{NL,i}}-\mathrm{V_{hub,i}}) \tag{4}\]  
\[\mathrm{V_{hub,i}}=\mathrm{V_{NL,i}}\left(\frac{\mathrm{z_{hub}}}{\mathrm{z_{ NL,i}}}\right)^{0.5} \tag{5}\]  
where \(\mathrm{V_{NL,i}}\) is the average nacelle LIDAR wind speed in bin i, and \(\mathrm{V_{hub,i}}\) is the wind speed extrapolated to the hub height. \(\mathrm{z_{NL,i}}\) is the average nacelle LIDAR measurement height in bin i, and \(\mathrm{z_{hub}}\) is the hub height. In Equation (5), the power law exponent was assumed to be 0.5. Figure 6 shows the relative uncertainty in the nacelle LIDAR wind speed due to the tilt motion, \(\mathrm{u_{NL,FS3}}\), with wind speed ratio. Uncertainties of approximately 0.12% were distributed in low wind speed regions and were very close to zero at 56% rated wind speed. Next, the uncertainty rapidly increased until the rated wind speed, and it gradually decreased after the rated wind speed due to blade pitching.