**5. Results**

According to simulations performed to obtain the empirical values of the *Kp* and *Ki* gains, a maximum power factor of 4.47 and the wind speed of 6 m/s were determined under ideal conditions and shaft generator nominal speed of 14.6 rad/s. However, the magnitude of the change in wind speed makes the system unstable, since the thrust force provides different acceleration to the rotor rotation. Therefore, a PI controller with variable gains was proposed to obtain different response times in the controller and soften these changes. The effectiveness of a pitch control using the PI-TLBO algorithm is examined in real operating conditions. The recorded wind speed values are shown in Figure 10.

**Figure 10.** Wind speed recorded in the experiment with the algorithm.

The search time for each value of *Kp* and *Ki* is in a range of 0.4 and 0.75 seconds depending on whether the algorithm makes all interactions or not, so a variable adjustment is made every second. With this result, the convergence speed of the algorithm can be highlighted, where unlike other optimization algorithms, it uses the best iteration solution to update the value of the existing solution, in addition to reducing the processing time since they are only used simple arithmetic operations such as sums and divisions.

Figure 11 shows the development of the algorithm in (a) there is an error of the variable that decreases according to better values of *Kp* and *Ki*, in (b) and (c) we observe how the values *Kp* and *Ki* change respectively.

**Figure 11.** *Cont.*

**Figure 11.** Algorithm development. (**a**) Decrease of the error value, (**b**) adjustment of the *Kp* value, and (**c**) adjustment of the *Ki* value.

The results of the experimentation show that the algorithm of optimization of gains *Kp* and *Ki* generate a better performance of a PI controller. In Figure 12, a comparison is made between the response of a PI controller and a PI-TLBO controller, the speed obtained from the generator shaft behaves more smoothly and close to the nominal speed, which represents a reduction in fatigue in the wind turbine structure and lower saturation in the PMSG.

**Figure 12.** Comparison between the performance of the PI controller and the PI-TLBO controller.

It is also observed that the response of the PI\_TBLO controller has a minor overshoot in the optimization range, the stabilization period is also reduced when a major disturbance occurs. Therefore, it can be suggested that after the TBLO optimization process for calculating the gains of the PI controller, the proposed control model is expected to control the pitch angle under various disturbances.

Figure 13 shows the movement of the *Kp* and *Ki* gains throughout the experimentation.

**Figure 13.** Evolution of gains (**a**) *Kp* and (**b**) *Ki*.

It is important to note the efficiency of the algorithm, a series of simulations were performed to validate the repeatability finding small variations in the response of the controller, this is due to the randomness of the data to generate new responses in the teacher phase. However, any of the responses of the PI-TLBO controller obtained better performance than that of the PI controller, this can be seen in Figure 14.

**Figure 14.** Repeatability of the PI-TLBO controller.

## **6. Discussion**

The use of dynamic models to simulate the aerodynamic behavior of the system allows to know the behavior of a wind system, however, in this type of systems, it is not necessary to know the behavior of the wind speed or the magnitude of its changes that would be the variable input. The multiple variables involved in the output variable make the system nonlinear, which also becomes a problem to calculate the ideal parameters of the controller. That is why a controller that adjusts to various changes in the system variables is proposed, this controller is automatically adjusted by an optimization algorithm based on teaching–learning, which gave the system stability since the controller adjusted its control response according to wind conditions. A better response was obtained by constantly adjusting the controller with a method of close solutions to the optimal one, than by applying a single optimal deterministic method. This is since a suitable adjustment of the controller is required to the sensitivity of the system, since the closer it is to nominal wind speed, the system is more sensitive to wind changes, not so when the system is below the nominal speed.

A PI controller with dynamic gain adjustment and not a PID was used because the differentiation reacts as fast as the input changes with respect to time, the differentiation acts towards the future anticipating the overshoot trying to offer a response according to how quickly it increases or the input signal decreases, however, when applied in a system of dynamic gains, differentiation caused oscillations in the system, this is because it is not necessary to anticipate the future since the calculated gains act in the present. That is why it was decided to use only a PI controller, getting good results.

The presented control system affects the angle of inclination to limit wind energy, however, additional subsystems sugges<sup>t</sup> the implementation of speed control to obtain an optimal electrical frequency and transfer the total electrical energy to the electricity grid.

It is convenient to use new forms of intelligent control, such as fuzzy systems, neural networks, and genetic algorithms. With this type of control, a predictive model for the expected climate would be achieved and with that would anticipate a better control response, which would reduce the frequent stops and starts of the system. In addition, the algorithms of these systems are programmed according to the knowledge and experiences that a human expert would have in the field. This is very useful since you cannot have an exact mathematical model of the meteorological parameters.

It is necessary and essential to prepare more professionals in universities with this new approach, which consists in considering the design of the wind turbine and its integration with the environment.
