## 4 Power Curve Uncertainty
### Uncertainty in Free-Stream Wind Speed from Nacelle LIDAR
To evaluate \(\mathrm{u_{FS,NL4}}\), the calibration of the tilt inclinometers was carried out in accordance with the procedure in DTU Wind Energy E-0020 [32; 33]. The opening angle, \(\alpha\), was first calibrated by an iterative process of blocking and unblocking using a jig designed for beam detection at a distance of  
Figure 5: Nacelle LIDAR measurement height relative to hub height. Figure 6: Relative uncertainty in wind speed due to variation in nacelle LIDAR measurement height. 29.85 m. The measured opening angle was confirmed to be 30.06\({}^{\circ}\), and the maximum error of beam detection pointing, \(\Delta\)H, was 21 mm. Next, the tilt value was measured using a theodolite Leica TM50. The uncertainty for tilt, \(\upmu_{\beta}\), was estimated using the following equation:  
\[\upmu_{\beta}=\sqrt{\left(2\left(\frac{\Delta\mathrm{H}}{2\mathrm{L}\mathrm{ cos}\left(\frac{\upmu}{2}\right)^{2}+\Delta\upmu_{\mathrm{T}}^{2}}\right) \right.} \tag{6}\]  
where \(\Delta\upmu_{\mathrm{T}}^{2}\) is the standard uncertainty of the theodolite associated with the tilt measurement, which was 0.03\({}^{\circ}\) according to the instrument calibration report. \(\upmu_{\beta}\) can be used to obtain the vertical length at a measurement distance of 2.5 times the rotor diameter, \(\Delta z_{1}\), using Equation (7) [27]:  
\[\Delta z_{1}=2.5\mathrm{D}\mathrm{T}\mathrm{a}\mathrm{n}\mathrm{(}\upmu_{\beta}) \tag{7}\]  
Finally, \(\upmu_{\mathrm{FS,NL4}}\) can be determined by the following equation assuming that wind shear follows a power-law profile with a shear exponent of 0.2:  
\[\upmu_{\mathrm{NL,FS4}}=\left(\left(\frac{\upmu_{\mathrm{h}\mathrm{b}}+\Delta z _{1}}{\mathrm{z}_{\mathrm{h}\mathrm{b}\mathrm{b}\mathrm{b}\mathrm{b}}}\right)^ {0.2}-1\right)\mathrm{V}_{\mathrm{i,m}} \tag{8}\]  
Additionally, the two sensitivity factors for category B uncertainty in wind speed for estimating power curve uncertainty, \(\mathrm{c}_{\mathrm{V,PC,i}}\), and AEP uncertainty, \(\mathrm{c}_{\mathrm{V,AEP,i}}\), were calculated using the following equations [22]:  
\[\mathrm{c}_{\mathrm{V,PC,i}}\approx\ \frac{1}{2}\cdot\left(\frac{\left( \mathrm{P}_{\mathrm{i}+1}-\mathrm{P}_{\mathrm{i}}\right)}{\left(\mathrm{V}_{ \mathrm{i}+1}-\mathrm{V}_{\mathrm{i}}\right)}+\frac{\left(\mathrm{P}_{ \mathrm{i}}-\mathrm{P}_{\mathrm{i}-1}\right)}{\left(\mathrm{V}_{\mathrm{i}- 1}\right)}\right) \tag{9}\]  
\[\mathrm{c}_{\mathrm{V,AEP,i}}\approx\ \frac{\mathrm{P}_{\mathrm{i}}-\mathrm{P}_{ \mathrm{i}-1}}{\mathrm{V}_{\mathrm{i}}-\mathrm{V}_{\mathrm{i}-1}} \tag{10}\]  
where \(\mathrm{P}_{\mathrm{i}+1}\), \(\mathrm{P}_{\mathrm{i}}\) and \(\mathrm{P}_{\mathrm{i}-1}\) are bin-averaged power output in bins \(\mathrm{i+1}\), \(\mathrm{i}\) and \(\mathrm{i-1}\), respectively. \(\mathrm{V}_{\mathrm{i}+1}\), \(\mathrm{V}_{\mathrm{i}}\) and \(\mathrm{V}_{\mathrm{i}-1}\) are bin-averaged wind speed in bins \(\mathrm{i+1}\), \(\mathrm{i}\) and \(\mathrm{i-1}\), respectively. The sensitivity factors for category B uncertainties in the air density and method were also evaluated using other related equations presented in IEC 61400-12-2.