# Effects of Blade Extension on Power Production and Ultimate Loads of Wind Turbines
## 4 Dynamic Load Evaluations
### Ultimate Loads in Gust Wind Condition
The ultimate loads of \(M_{y}\) at tower bottom and the corresponding load cases are shown in Table 12 while the load time series are shown in Figure 15. The loads are relatively stable at the beginning, but show a great fluctuation after the gust starts. The ultimate \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** \\ \hline \(M_{x}\) & 6807 & 101.93\% & 102.77\% & 102.71\% \\ \(M_{y}\) & 24,004 & 105.49\% & 111.84\% & 115.43\% \\ \(M_{yy}\) & 24,553 & 104.94\% & 111.17\% & 114.76\% \\ \(M_{z}\) & 1882 & 103.16\% & 104.46\% & 105.50\% \\ \(F_{x}\) & 396.1 & 103.36\% & 109.11\% & 112.47\% \\ \(F_{y}\) & 121.8 & 100.00\% & 100.66\% & 100.82\% \\ \(F_{xy}\) & 403.1 & 103.27\% & 109.45\% & 112.83\% \\ \(F_{z}\) & 1797.9 & 100.13\% & 100.19\% & 100.27\% \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Ultimate loads at tower bottom. Figure 14: Histogram of \(M_{y}\) at tower bottom. (The label of the load case: the first letter refers to wind speed, b for 11.5 m/s and c for 13.5 m/s; the second letter refers to yaw error and “a” for \(-\)8 deg; the middle number refers to wind direction change and 01 for positive direction change; the last number refers to starting azimuth angle, 01 for 0 deg, 02 for 30 deg, 03 for 60 deg and 04 for 90 deg). loads appear at about 17.5 s, and the longer the blade, the greater the amplitude of load fluctuation. Then, after the end of gust, the loads gradually converge. The blade root ultimate loads of turbines with blade extension and the original design in gust wind condition are shown in Table 13. The ultimate loads of \(M_{y}\) show an obviously increasing trend, with the percentage increase of 2.25%, 3.26% and 4.48%. The histogram of five cases with the highest \(M_{y}\) at blade root is shown in Figure 16 and \(M_{y}\) values in each group all significantly increase after the blade extension. The ultimate load of \(M_{y}\) at blade root and the corresponding load cases are shown in Table 14. The ultimate loads all occur at the wind speed of 11.5 m/s, and the number 02 corresponds to negative direction change. The corresponding load time series are shown in Figure 17. As shown in the figure, the amplitude of loads increases during the transient period and the maximum of loads appear at about 14.7 s. \begin{table}
\begin{tabular}{c c c} \hline
**Blade Length (m)** & **Ultimate Load of \(M_{y}\) (kNm)** & **Load Case** \\ \hline
37.5 & 24,004 & 1.4 ca\_01\_04 \\
38.5 & 25,322 & 1.4 ba\_01\_03 \\
39 & 26,846 & 1.4 ba\_01\_04 \\
39.5 & 27,707 & 1.4 ba\_01\_04 \\ \hline \end{tabular}
\end{table} 
Table 12: Ultimate load \(M_{y}\) at tower bottom. (The label of the load case: the first letter refers to wind speed, b for 11.5 m/s and c for 13.5 m/s; the second letter refers to yaw error and “a” for \(-8\) deg; the middle number refers to wind direction change and 01 for positive direction change; the last number refers to starting azimuth angle, 03 for 60 deg and 04 for 90 deg). Figure 15: Load time series of \(M_{y}\) at tower bottom. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Blade Length (m)** & **Ultimate Load of \(M_{y}\) (kNm)** & **Load Case** \\ \hline
37.5 & 3190.3 & 1.4 bc\_02\_03 \\
38.5 & 3262 & 1.4 bc\_02\_03 \\
39 & 3294.4 & 1.4 bc\_02\_03 \\
39.5 & 3333.2 & 1.4 bc\_02\_03 \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Ultimate load \(M_{y}\) at blade root. (The label of the load cases: the first letter refers to wind speed and “b” for 11.5 m/s; the second letter refers to yaw error, “c” for 8 deg; the middle number refers to wind direction change and 02 for negative direction change; the last number refers to starting azimuth angle and 03 for 60 deg). Figure 16: Histogram of \(M_{y}\) at blade root.