## 4 Experimental Results and Discussion
### Impact of Sudden Variations on the Performance of the WT System
#### 4.2.2 Wind Speed Variation  
The sudden change of wind speed represents the most critical situation for the wind system stability. Despite the variation of wind speed, the \(p_{WT}\) must reach the \(P_{\text{lim}}\) recommended by the user. A wind speed profile varying from 6.5, 5.5 to 4.5 m/s and a limited power of 50 W are selected (Figure 18). Based on different tests performed to characterize the WT for the selected wind speeds, a presentation of \(p_{WT}\)-\(v_{WT}\) and \(p_{WT}\)- \(t\) curves are illustrated in Figure 19. As can be clearly observed,  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & \multicolumn{2}{c}{\(p_{WT}\) (W)} \\ \hline
**Control Strategy Method** & **LPP1 (Mean \(\pm\) SD)** & **LPP2 (Mean \(\pm\) SD)** \\ \hline Fix step size & 48.6 \(\pm\) 15.4 & 49.8 \(\pm\) 19.3 \\ [PERSON]’s method & 49.5 \(\pm\) 10.0 & 48.3 \(\pm\) 12.7 \\ Fuzzy logic & 49.6 \(\pm\) 2.4 & 49.3 \(\pm\) 5.6 \\ \hline \hline \end{tabular}
\end{table}
Table 2: \(p_{WT}\) reached using different control method strategies. SD: standard deviation.  
Figure 16: Statistical analysis of experimental results: (**a**) evolution of \(p_{WT}\) at LPP1; (**b**) evolution of \(p_{WT}\) at LPP2.  
all proposed power control strategies have an identical behavior during wind speed variation. At the start, the wind speed is 6.5 m/s and the system is following the \(P_{\text{lim}}\) of 50 W which is situated at point 1 with a voltage of 63 V. With the weather's variation, the wind speed drops to 5.5 m/s, but the \(P_{\text{lim}}\) is maintained at 50 W. Indeed, prior to reach point 2, the power decreases to 12 W and is then raised to reach the \(P_{\text{lim}}\). In this case, the WT is still able to deliver that power since \(P_{\text{lim}}\)\(\in\)\(p_{\text{WT}}\)-\(v_{\text{WT}}\) curve. Later on, the wind speed drops to 4.5 m/s and, thus, the power drops to 20 W. Since the \(P_{\text{lim}}\) has become higher than the maximum power that can be generated for this wind speed, the system is unable to deliver it. In such case, the algorithms of the proposed power control strategies are adapted to avoid the drop in power to 0 W if the \(P_{\text{lim}}\) cannot be reached. Therefore, as can be seen in Figure 19a, when the \(P_{\text{lim}}\) is not found, the system searches for the MPP (point 3) delivered under this wind speed. In addition, it is also important to notice that the time required to make the transition to the new operating point is almost similar for all proposed power control strategies. However, what changes is the oscillations' state around \(P_{\text{lim}}\). Overall, there are very large oscillations around \(P_{\text{lim}}\) when the wind speed is high, which could be related to the increase in machine vibrations. Furthermore, it is evident that the FL technique allows for getting better performances around \(P_{\text{lim}}\) even with a sudden change of wind speed compared to the fixed step size and [PERSON]'s methods.  
Figure 17: Drop in power: (**a**) sudden increase of \(P_{\text{lim}}\); (**b**) sudden decrease in \(P_{\text{lim}}\).