# Effects of Blade Extension on Power Production and Ultimate Loads of Wind Turbines
## 3 Steady Power Curve and Operational Loads  
### Wind Turbine Performance  
The \(C_{P}\)-\(\lambda\) curves of turbines with blade extension and the original design are shown in Figure 4. The figure shows that the variation trend of \(C_{P}\)-\(\lambda\) curves is consistent. With the increase in blade length, the optimal tip-speed ratio shifts to the right, and the corresponding power coefficient at \(\lambda_{opt}\) increases slightly. In the high tip-speed ratio region, \(C_{P}\) increases significantly due to the blade extension.  
Figure 5 shows the \(C_{T}\)-\(\lambda\) curves of turbines with different blade extension lengths and the original design. As shown in Figure 4, the thrust coefficient decreases with the blade length.  
Steady power curves of turbines with blade extension and the original design are shown in Figure 6. The rated power of wind turbines is kept unchanged, but a significant increase in the steady power before rated wind speed is observed due to the blade extension. When the blade is extended by 1 m, 1.5 m and 2 m, the power is increased by about 5%, 8% and 10% under the optimal tip-speed ratio, respectively. Meanwhile, the rated wind speed of blade extension wind turbines is reduced from 11.3 m/s to 11 m/s, 10.8 m/s and 10.7 m/s for the extension length of 1 m, 1.5 m and 2 m, respectively.  
The theorical annual energy production (\(AEP\)) is calculated based on the power curve of wind turbines and wind speed distribution.  
\[AEP=Y\int\limits_{V_{in}}^{V_{out}}P(V)f(V)dV \tag{4}\]  
where \(P(V)\) is power curve, \(f(V)\) is the probability density, \(V_{in}\) and \(V_{out}\) correspond to cut-in and cut-out wind speed, and \(Y\) is the hours of a year, taken as 8760 h. Here, the wind speed distribution is assumed as the Weibull distribution.  
Figure 3: Generator torque-speed curves for wind turbines with different blade lengths.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Blade Length (m)** & \(\lambda\) & \(C_{P}\) & \(K_{opt}\) \\ \hline
37.5 & 8.8 & 0.480876 & 0.102538 \\
38.5 & 9.1 & 0.482111 & 0.105666 \\
39 & 9.2 & 0.482825 & 0.109048 \\
39.5 & 9.4 & 0.482835 & 0.10878 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Parameters used to track the optimum tip-speed ratio.  
Figure 4: Variation of \(C_{P}\): (**a**) \(C_{P}\)-\(\lambda\) curve of turbines with different blade lengths; (**b**) Variation of \(C_{Pmax}\) with the blade extension length; (**c**) Variation of \(\lambda_{opt}\) with the blade extension length.  
Assuming that the availability is 99%, the annual energy production of wind turbines with different blade length is calculated and shown in Table 4. As shown in the table, the annual energy production of wind turbines is increased by about 3%, 4% and 6% for the extension length of 1 m, 1.5 m and 2 m, respectively.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(V_{ave}\) (m/s) & \multicolumn{2}{c}{**7.5**} & \multicolumn{2}{c}{**8**} & \multicolumn{2}{c}{**8.5**} \\ \hline
**Blade Length (m)** & **AEP (MWh)** & **\(\Delta\)AEP (\%)** & **AEP (MWh)** & **\(\Delta\)AEP (\%)** & **AEP (MWh)** & **\(\Delta\)AEP (\%)** \\ \hline
37.5 & 5391.84 & — & 5932.44 & — & 6430.44 & — \\
38.5 & 5568.44 & 3.28 & 6109.63 & 2.99 & 6605.93 & 2.73 \\
39 & 5648.53 & 4.76 & 6189.15 & 4.33 & 6683.97 & 3.94 \\
39.5 & 5727.84 & 6.23 & 6267.92 & 5.66 & 6761.3 & 5.15 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Annual energy production of turbines with different blade length.  
Figure 5: \(C_{T}\)-\(\lambda\) curve of turbines with different blade lengths.  
Figure 6: Steady power curves of turbines with different blade lengths.