# Adaptive Pitch Controller of a Large-Scale Wind Turbine Using Multi-Objective Optimization
## 3 Control Methodology
### Description of the Control Blocks
#### 3.3 Multi-Objective Optimization by Genetic Algorithms
Then, the average of the three methods applied in each solution is calculated, and the solution with ranking equal to 1 is considered the best satisfactory solution. The results of the average ranking method for the ten best possible solutions obtained at the operation point with wind speed of 12 m/s are shown in Table 2. In this case, the best average solution coincides with the best solution obtained by the TOPSIS method. Figure 7 shows the Pareto front obtained for each operation point. In each one, the best solution according to the different MCDM methods and the average ranking solution are also highlighted. As the wind speed increases, the IAE\({}_{\text{avg}}\) index decreases, and the CVR\({}_{\text{xt}}\) index increases. For the operating points associated to wind speed of 12 and 22 m/s, the average ranking solution coincides with the TOPSIS optimal solution. In the case wind speed of 14, 16, and 18 m/s, the TOPSIS solution coincides with the optimal VIKOR solution. \begin{table}
\begin{tabular}{c c c c c} \hline
**Rank** & **Average Rank** & **SAW** & **TOPSIS** & **VIKOR** \\ \hline
**1** & **7.6667** & **10** & **1** & **12** \\
2 & 8.0000 & 12 & 6 & 6 \\
3 & 8.0000 & 13 & 9 & 2 \\
4 & 8.3333 & 3 & 2 & 20 \\
5 & 8.3333 & 11 & 3 & 11 \\
6 & 9.0000 & 14 & 12 & **1** \\
7 & 10.3333 & 2 & 5 & 24 \\
8 & 10.6667 & 9 & 4 & 19 \\
9 & 10.6667 & 15 & 14 & 3 \\
10 & 12.0000 & **1** & 7 & 28 \\ \hline \end{tabular}
\end{table} 
Table 2: The ten best solutions according to the average ranking method in the Pareto front obtained for a wind speed of 12 m/s. Figure 7: Pareto fronts obtained at the six operating points. Table 3 shows the control parameters obtained for the satisfactory solution at each operation point. They are also depicted in Figure 8 together with the obtained parameters for the IAE\({}_{\text{avg}}\) optimal solution and CVR\({}_{\text{at}}\) optimal solution at each operation point. The optimal CVR\({}_{\text{at}}\) solution has only the objective function of reducing the tower f-a displacements as much as possible, while the optimal IAE\({}_{\text{avg}}\) solution only considers minimizing the deviation of the generator speed from its nominal value. From Figure 8, it can be deduced how the different components that collaborate in the proposed control scheme cause an effect on the objective functions IAE\({}_{\text{avg}}\) and CVR\({}_{\text{at}}\) with a certain degree of opposition between them. The following points can be pointed out:  
* To minimize the deviation of the generator speed from its nominal value (optimal IAE\({}_{\text{avg}}\) solution), it is necessary a strong participation of the feedforward control (K\({}_{\text{ff}}\)) and a low intervention of the active tower damping control (K\({}_{\text{f-a}}\)). * To minimize the tower f-a displacements (optimal CVR\({}_{\text{at}}\) solution), it is necessary to combine the PI controller with a low T\({}_{\text{i}}\) together with a lower participation of the feedforward control (K\({}_{\text{ff}}\)) and a higher intervention of active tower damping control (K\({}_{\text{f-a}}\)). * Satisfactory solutions achieve a compromise of both objectives combining an intermediate K\({}_{\text{p}}\) value of the PI controller with a strong participation of the feedforward control (K\({}_{\text{ff}}\)) and a medium intervention of the active tower damping control (K\({}_{\text{f-a}}\)). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(\mathbf{v_{w}}\) (\(\mathbf{m/s}\)) & \(\mathbf{K_{p}}\) & \(\mathbf{T_{i}}\) & \(\mathbf{K_{f-a}}\) & \(\mathbf{K_{ff}}\) \\ \hline
12 & \(-0.0494\) & 6.1350 & 3.9874 & 0.8586 \\
14 & \(-0.0315\) & 4.2592 & 3.7942 & 0.8106 \\
16 & \(-0.0346\) & 6.4161 & 2.2943 & 0.9178 \\
18 & \(-0.0344\) & 6.9279 & 2.0323 & 0.9641 \\
20 & \(-0.0330\) & 6.8686 & 2.0981 & 0.9455 \\
22 & \(-0.0496\) & 6.1413 & 0.7911 & 0.9566 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Control parameters obtained for the satisfactory solution for each operation point.