# Effects of Blade Extension on Power Production and Ultimate Loads of Wind Turbines
## 4 Dynamic Load Evaluations  
### Ultimate Loads in Turbulence Wind Condition  
Turbulence wind condition includes the normal turbulence model (NTM) and extreme turbulence model (ETM). For the normal turbulence model (NTM) [23], the longitudinal turbulence standard deviation \(\sigma_{1}\) at the hub height can be calculated by:  
\[\sigma_{1}=I_{ref}(0.75V_{hub}+b) \tag{8}\]  
where \(I_{ref}\) is the reference turbulence intensity at 15 m/s, \(V_{hub}\) is the average wind speed at the hub height and \(b\) is a constant value, equal to 5.6 m/s. The lateral standard deviation \(\sigma_{2}\) and vertical standard deviation \(\sigma_{3}\) should satisfy Equations (9) and (10). \[\sigma_{2}\geq 0.7\sigma_{1} \tag{9}\]  
\[\sigma_{3}\geq 0.5\sigma_{1} \tag{10}\]  
For the extreme turbulence model (ETM) [23], the average wind speed is a function of height \(z\), and it can be given by:  
\[V(z)=V_{hub}(z/z_{hub})^{\alpha},\ \alpha=0.2 \tag{11}\]  
The longitudinal turbulence standard deviation is computed as:  
\[\sigma_{1}=cI_{ref}\bigg{(}0.072\bigg{(}\frac{V_{ave}}{c}+3\bigg{)}\bigg{(} \frac{V_{hub}}{c}-4\bigg{)}+10\bigg{)} \tag{12}\]  
where \(c\) is a constant value, equal to 2 m/s; \(V_{ave}\) is annual average wind speed, which can be determined as:  
\[V_{ave}=0.2V_{ref} \tag{13}\]  
Figure 9: Diagram of loads of the wind wheel. where \(V_{\it{ref}}\) is reference wind speed. In this paper, we use the II class wind turbine and the corresponding reference value is 42.5 m/s. The simulation duration is 600 s. For each wind speed, twelve turbulent wind files are selected for each simulation. The operating conditions including the power production (DLC 1.3 in the IEC 61400-1 standard), power production plus occurrence of fault (DLC 2.1 and DLC 2.2 in IEC 61400-1 standard) and emergency shutdown (DLC 5.1 in IEC 61400-1 standard) are evaluated. The fault and emergency shutdown occur at 10 s after the simulation startup. The ultimate loads of the blade root with blade extension and the original design in turbulence wind condition are shown in Table 7. As shown in the table, the ultimate loads at blade root all increase after the blade extension, and \(M_{y}\) shows an obvious increasing trend with the blade extension. We can select five load cases which have the highest \(M_{y}\) at blade root with blade extension and the original design for further analysis, and the corresponding histogram is shown in Figure 10. Similar as the above analysis, an obvious increase in \(M_{y}\) can be observed due to the blade extension. The ultimate loads of \(M_{y}\) at blade root and the corresponding load cases are shown in Table 8. The table shows that the ultimate loads of \(M_{y}\) all occur at DLC 2.2, which \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **37.5 m** & **38.5 m/** & **39 m/** & **39.5 m/** \\  & **37.5 m** & **37.5 m** & **37.5 m** & **37.5 m** \\ \hline \(M_{x}\) & 2251.6 & 104.26\% & 105.11\% & 103.58\% \\ \(M_{y}\) & 3462 & 105.35\% & 107.92\% & 112.49\% \\ \(M_{yy}\) & 4027.4 & 106.57\% & 107.77\% & 110.59\% \\ \(M_{z}\) & 51.1 & 129.16\% & 150.29\% & 161.25\% \\ \(F_{x}\) & 175.9 & 104.78\% & 104.72\% & 107.39\% \\ \(F_{y}\) & 142 & 102.46\% & 105.56\% & 99.08\% \\ \(F_{yy}\) & 222.2 & 104.55\% & 103.60\% & 105.54\% \\ \(F_{z}\) & 326.4 & 101.84\% & 101.90\% & 102.14\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Ultimate loads at blade root. Figure 10: Histogram of \(M_{y}\) at blade root. (The label of the load case: the first letter refers to wind speed, “d” for 20 m/s and ”e” for 25 m/s; the second letter refers to the type of fault and “b” for pitch runaway (blade 1 pitcher towards fine at \(-8\) deg/s); the last number refers to the random seed number). corresponds to the wind speed of 20 m/s and 25 m/s with the pitching system failure. The corresponding load time series are shown in Figure 11. The load under turbulence shows random fluctuations, but its variation trend is basically the same under the operating conditions.