# MPPT Control in an Offshore Wind Turbine Optimized with Genetic Algorithms and Unsupervised Neural Networks

Eduardo Muñoz-Palomeque, Jesús Enrique Sierra-García, Matilde Santos

► To cite this version:

Eduardo Muñoz-Palomeque, Jesús Enrique Sierra-García, Matilde Santos. MPPT Control in an Offshore Wind Turbine Optimized with Genetic Algorithms and Unsupervised Neural Networks. 19th IFIP International Conference on Artificial Intelligence Applications and Innovations (AIAI), Jun 2023, León, Spain. pp.465-477, 10.1007/978-3-031-34107-6_37. hal-05498078

HAL Id: hal-05498078

https://inria.hal.science/hal-05498078v1

Submitted on 6 Feb 2026

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons CC BY 4.0 - Attribution - International License
<figure><img src="image_2.png" /></figure>

ifip

International Federation for Information Processing

This document is the original author manuscript of a paper submitted to an IFIP
conference proceedings or other IFIP publication by Springer Nature. As such, there
may be some differences in the official published version of the paper. Such
differences, if any, are usually due to reformatting during preparation for publication or
minor corrections made by the author(s) during final proofreading of the publication
manuscript.
<figure><img src="image_3.png" /></figure>

# MPPT Control in an Offshore Wind Turbine
## Optimized with Genetic Algorithms
## and Unsupervised Neural Networks

Eduardo Muñoz-Palomeque<fnref n="1" />(✉) ID, Jesús Enrique Sierra-García<fnref n="1" /> ID,
and Matilde Santos<fnref n="2" /> ID

**Abstract.** In this work, a control operation of a 1.5 MW offshore wind turbine (WT) for maximum power point tracking (MPPT) when wind speed is below rated, is studied. The implemented controller is designed using the general Direct Speed Control (DSC) scheme in which artificial neural networks (ANN) are incorporated to close the control loop. The neural controller acts in an unsupervised mode updating its weights with the incorporation of a learning algorithm. The optimal configuration parameters of the controller are determined by genetic algorithms. With this intelligent control strategy, the generator speed is regulated by varying the electromagnetic torque while adapting to the external phenomena in real time. Then, the output power, through the power coefficient ($C_p$), reaches the maximum wind power generation in that region. The offshore WT model is subjected to external loads due to wind and waves, which increase the system complexity and produce tower vibrations, negatively impacting the control efficiency. Despite that, it is shown that the proposed controller is able to operate with satisfactory results in terms of power generation and even reducing vibration, and it has been compared to the OpenFAST embedded torque control for the same WT providing better results.

**Keywords:** DSC · Neural Networks · Learning Algorithm · MPPT · Offshore
Wind Turbine · Genetic Algorithms

## 1 Introduction

With the increasing energy requirements, renewable sources have been gaining importance. Among them, wind turbine [1] and photovoltaic systems [2] are two promising technologies. Focusing on the wind turbines, the high energy capacity, low environmental impact, affordable cost, and ease of installation have made these systems to be essential in clean energy production. Considering these benefits of the WT, and with the aim of taking advantage of the wider free of obstacles area in coastal and deep waters, offshore wind turbines have become profitable alternatives.

<footnote n="1">¹ Electromechanical Engineering Department, University of Burgos, Burgos, Spain
emp1016@alu.ubu.es, jesierra@ubu.es</footnote>

<footnote n="2">² Institute of Knowledge Technology, Complutense University of Madrid, Madrid, Spain
msantos@ucm.es</footnote>
To exploit these wind energy converters, the control of offshore wind turbines is a must to guarantee proper operation and efficient power generation. Therefore, some of the common goals in WT control systems are the maximization of the output power, the regulation of the blades angle, reduction of noise and vibration, among others [3, 4], which are of particular importance in the offshore scenarios.

The maximum power point tracking (MPPT) control in wind turbines, when the wind speed is below the nominal conditions, is one of these goals. The system must face the nonlinear loads that directly influence its operation and efficiency. In addition, for offshore WT, these nonlinear effects are increased and the complexity of the optimal control is directly affected by the waves and movement of the structure.

In fact, the mechanical stress and power fluctuations are some of the most negative effects that offshore wind turbines experience due to the harsh conditions to which they may be subjected to [5].

Taking into account all these factors that make the offshore wind turbine control more complex and strongly nonlinear, the importance of effective and more robust controllers is evident. In this context, neural networks have been proved very efficient to deal with these kinds of real systems.

In the MPPT WT operating region, the maximum power extraction is the main target. The power coefficient curve, $C_p$ with which the power is related, must be tracked in order to reach the highest energy level. This is achieved by using a speed controller to regulate the velocity of the generator and thus, the turbine. This assures the largest wind power is captured and converted into electrical energy. In this process, the angle of the blades maintains a specific position that corresponds to the lowest value with which the maximum wind flow is captured.

To address the MPPT problem, conventional as well as intelligent control methods have been studied and applied separately and also complementing each other. For instance, some conventional strategies include the hill-climb searching (HCS) technique, power signal feedback (PSF), tip-speed ratio (TSR), or indirect speed control (ISC) [6–9]. On the other hand, artificial intelligent controllers with different approaches have been also proposed in the literature. In [10] fuzzy logic is applied to enhance the sliding mode control, or in [11, 12] the MPPT problem is faced implementing the fuzzy control under the direct speed control (DSC) scheme. Neural networks (NN) have been also used for the MPPT control [13]. In [14], NN and FLC have been used for maximum voltage estimation and DC-DC boost converter control in a wind turbine. In [15], a backpropagation NN (BPNN) is applied for indirect current control in a wind generator microgrid. In [16], a cascade NN approach is presented for maximum power control.

In this work, the use of an artificial control technique, such as neural networks with learning capability for unsupervised operation, is implemented for the MPPT control of a 1.5 MW offshore wind turbine. The controller is adapted to the DSC control frame to obtain a reference generator speed. Then the NN controller obtains the electromagnetic torque ($T_{em}$) and the generator speed, tracking the $C_p$ and adapting to the changing environmental conditions that influence its dynamics. The use of genetic algorithms is important in this study to define the optimal configuration of the control scheme, including the neural network and the learning criteria.
As a summary, the main contribution of this article is the use of an online learning control based on neural networks that adapts to disturbances in the MPPT control in an offshore WT, instead of using static offline control algorithm. Also, the use of another artificial intelligent method such as genetic algorithms to enhance the controller finding the best neuro-control configuration shows the efficiency of the hybridization of several techniques.

After this introduction, the model of the WT is described in Sect. 2. Section 3 explains the intelligent neuro-control proposed. Results are discussed in Sect. 4. The paper ends with the conclusions and future works.

# 2 Wind Turbine Model

## 2.1 Offshore Wind Turbine

The wind turbine used in this work is a semi-submersible model with 3 blades, adapted from OpenFAST. In this system, the tower height is 92.39 m, and the distance measured from the level sea to the center of mass of the platform is 8.6 m. The platform is anchored to the seabed with a mooring system composed of 3 lines. The WT incorporates a 1.5 MW doubly fed induction generator (DFIG) with a nominal speed of 1200 rpm that is connected to the grid.

## 2.2 Aerodynamic Model

The wind turbine system captures the energy of the input wind through the blades. This causes the movement of the turbine, and that energy is converted into mechanical energy to move the generator.

In this first stage, the mechanical power that is extracted during the wind turbine operation can be expressed mathematically as [11, 17]:

$$P = \frac{1}{2} C_p A \rho V_w^3 \quad (1)$$

where $V_w$ is the wind speed (m/s), $\rho$ is the density of the air (Kg/m³), $A$ is the area covered by the blades (m²), and $C_p$ is the power coefficient.

The power coefficient is described as a function of two elements: the tip speed ratio (TSR) $\lambda$ and the blades angle $\beta$. The $C_p$ coefficient denotes the efficiency in power extraction and can be approximated by Eq. (2) [18]. As a result, the $C_p$ forms different curves according to the system features reflected in the coefficients $c_1 - c_6$ and the values of TSR and $\beta$.

$$C_p = c_1 \left( \frac{c_2}{\lambda_i} - c_3\beta - c_4 \right) e^{-\frac{c_5}{\lambda_i}} + c_6\lambda \\ \frac{1}{\lambda_i} = \frac{1}{\lambda + 0.08\beta} - \frac{0.035}{\beta^3 + 1} \quad (2)$$

TSR relates the velocity of the tip blade with the wind speed as expressed in (3).

$$\lambda = \frac{\omega_r R}{V_w} \quad (3)$$
where $\omega_r$ is the turbine rotor speed (rad/s) and $R$ is the blade length (m).

For the wind turbine model used in this work, the maximum $C_p$ is 0.48 and the optimal TSR is 7.1. The blades angle is fixed at 2° in the below rated operating region.

## 2.3 Mechanical Model

The mechanical process in the wind generator system is given by the gearbox. This mechanism generates the two zones of transmission of speed and torque. They are: the low-speed shaft (LSS) and, after the gearbox, the high-speed shaft (HSS). Expression (4) [19] shows the mathematical relation.

$$T_r = \dot{\omega}_r (N^2 J_g + J_r) + N T_{em} \quad (4)$$

where $\dot{\omega}_r$ is the rotor angular acceleration (rad/s²), $N$ is the gearbox ratio, $J_g$ and $J_r$ are the generator and rotor moments of inertia ($K_g \cdot m^2$), respectively, and $T_r$ is the aerodynamic torque (Nm). The rotor acceleration can also be described in terms of the generator acceleration $\dot{\omega}_g$ as: $\dot{\omega}_r = \dot{\omega}_g/N$.

## 2.4 Electrical Generator Model

The generator type adapted to the wind turbine model for this study corresponds to a DFIG machine. Its representation can be made with the voltages and fluxes using the Park transform, and the expressions are then denoted in the d-q frame [20]. Equations in (5) present this mathematical model. Each term is expressed in the stator (s) or rotor (r) side.

$$ 
\begin{aligned}
V_{ds} &= R_s i_{ds} + \frac{d\psi_{ds}}{dt} - \omega_e \psi_{qs} & \psi_{ds} &= L_s i_{ds} + M \cdot i_{dr} \\
V_{qs} &= R_s i_{qs} + \frac{d\psi_{qs}}{dt} + \omega_e \psi_{ds} & \psi_{qs} &= L_s i_{qs} + M \cdot i_{qr} \\
V_{dr} &= R_r i_{dr} + \frac{d\psi_{dr}}{dt} - \omega_{sl} \psi_{qr} & \psi_{dr} &= L_r i_{dr} + M \cdot i_{ds} \\
V_{qr} &= R_r i_{qr} + \frac{d\psi_{qr}}{dt} + \omega_{sl} \psi_{dr} & \psi_{qr} &= L_r i_{qr} + M \cdot i_{qs}
\end{aligned}
\quad (5) $$

where $V$ is the voltage (V); $\psi$ is the flux (Wb); $i$ is the current (A); $R$ is the resistance ($\Omega$); $L$ is the inductance and $M$ is the mutual inductance, both in (H); $\omega_e$ is the angular speed (rad/s) and $\omega_{sl}$ is the slip angular speed (rad/s).

# 3 Neural Networks for MPPT Control

Neural networks are applied in the DSC control scheme to address the MPPT problem. Figure 1 illustrates the control strategy that is detailed in this section.

First, the conventional DSC control scheme of a WT consists in obtaining the electromagnetic torque, that is determined from a pre-computed velocity signal, in order to achieve the optimum generator speed so to guarantee the maximum power extraction.
<figure><img src="image_4.png" /><figcaption>Fig. 1. Control scheme based on DSC and Unsupervised Neural Networks (Color figure online).</figcaption></figure>

According to [21], the reference speed for DSC (7) can be expressed as the relation between the gearbox ratio $N$, a computed rotor torque $T_r$ obtained from (4), and a constant value $K_{opt}$ (6) calculated in terms of the optimal $C_p$ and TSR.

$$K_{opt} = \frac{\rho\pi}{2} C_{p\_opt} \frac{R^5}{\lambda_{opt}^3} \qquad (6)$$

$$\omega_{g\_rf} = N \sqrt{\frac{T_r}{K_{opt}}} \qquad (7)$$

Then, the artificial neural network is designed to match the generator speed with the most suitable electromagnetic torque and thus to track the maximum power generation. The network used in this study is a radial basis neural network. In this controller, an unsupervised learning algorithm is used. This way, the neuro-controller updates its weights so to reduce the error speed signal over time.

To complete this process, the generator speed error $E\omega_g$ and the derivative generator speed error $E\dot{\omega}_g$ are calculated using the reference speed (7). These errors are connected to the neural network as inputs. The network produces the electromagnetic torque signal that is used as the reference for the MPPT control.

## 3.1 Radial Basis Neural Network

Breaking down the neuro-control scheme (yellow square of Fig. 1), it is possible to see two modules, the radial basis neural network and the learning algorithm. The RBNN is defined in a discretized plane whose dimensions are defined by the error speed inputs. This space is equally gridded in both dimensions, creating a dependency between the speed error and its derivative value. The centers of the neurons ($o_{ix}$, $o_{iy}$) are located on the vertices of the grid. Thus, the number of neurons that form the neural space is related
to the number of divisions on the $E\omega_g$ and $E\dot{\omega}_g$ axes, as follows:

$$N_{neu} = div_x * div_y \qquad (8)$$

where $N_{neu}$ is the total number of neurons in the network and $div_x$ and $div_y$ are the number of divisions of the error speed axis and the derivative error speed axis, respectively. Therefore, the number of cells in the neural space for each dimension is:

$$\begin{aligned} N_{cellx} &= div_x - 1 \\ N_{celly} &= div_y - 1 \end{aligned} \qquad (9)$$

Once the control space for the neural network is structured, the mapping operation takes place to calculate an approximate output corresponding to the electromagnetic torque of the MPPT control. The radial basis function is governed by the distances measured at each control instant $T_c$, between the center of the neurons and the Cartesian point described by the input speed errors ($E\omega_g$, $E\dot{\omega}_g$). For this purpose, a normalized distance is determined as follows:

$$nrmDst = \sqrt{\frac{(o_{ix} - E\omega_{gen})^2}{E\omega_{gmax}} + \frac{(o_{iy} - E\dot{\omega}_g)^2}{E\dot{\omega}_{gmax}}} \qquad (10)$$

The radial basis function that represents the output signal of the network is described in (11). This function specifies the neural principle of the applied radial basis neural network in terms of a sum of exponentials.

$$T_{em\_rf} = -\sum_{i=1}^{N_{neu}} W_i \cdot e^{-\left(\frac{nrmDst(o_{ix}, o_{iy}, E\omega_g, E\dot{\omega}_g)}{\delta}\right)} \qquad (11)$$

where $W$ is the neuron weight and the width of the RBF neuron is $\delta$.

The second module of the intelligent controller is the unsupervised learning algorithm. This function is in charge of modifying the weights of the neurons in order to reach the proper output and reduce the generator speed error. With these variations, the controller automatically adapts to the current conditions of the WT system in real-time.

The updating of weights is managed by the level of impact the errors have on the process. The learning algorithm is also determined by an exponential function and the distance between the neurons and the input errors. This factor is important because the influence of a neuron in the output signal varies in terms of this distance.
The learning operation is described in (12), where $K_p$ and $K_d$ are constants that specify the weight of the speed error and its derivative, respectively, in the learning process, and $\mu$ indicates the learning rate.

$$W_j(t_i) = W_j(t_{i-1}) + \mu \cdot (K_p E \omega_g(t_i) + K_d \dot{E} \omega_g(t_i)) \cdot e^{-(\frac{nmDst}{\delta})} \quad (12)$$

## 3.2 Control Configuration Parameters

The RBF-NN and the learning algorithm are defined by different parameters, including $K_p$, $K_d$, $\mu$, $\delta$, $N_{neu}$ and $T_c$. The correct definition of these parameters is essential to guarantee the controller operates as desired. In order to determine this set of parameters, genetic algorithms are used. The genetic algorithm works with a population size of 200 individuals randomly initialized. Each individual is composed of 6 chromosomes corresponding to the control parameters. To reduce the speed error, the cost function (13) that is minimized corresponds to the mean squared error metric of the speed ($MSE_{vel}$):

$$F_{costGA} = MSE_{vel} \quad (13)$$

where the $MSE_{vel}$ is calculated as follows:

$$MSE_{vel} = \frac{1}{n} \sum_{i=1}^{n} (E\omega_g)^2 \quad (14)$$

And $n$ is the number of elements of the $E\omega_g$ vector.

While the speed error is reduced, the optimal response of the WT for the current conditions is achieved. This means an increment of the power efficiency. The turbine operates at the speed with which the maximum energy of the wind is captured and transformed into electrical energy. Thus, the output power is optimized.

## 4 Results

Once the controller is designed, it is implemented in Matlab/Simulink, linked to a realistic offshore WT model in OpenFAST. Simulation is performed with random wind speed (Fig. 2) and wave inputs (Fig. 3) that replicate an actual WT system. Wind speed adopts values below the nominal speed 11.5 m/s value to operate in the MPPT region. The proposed control strategy is evaluated in terms of the MSE of the generator speed, output power, power coefficient, structural movement, and comparison with the OpenFAST torque control.

The optimal configuration of the controller is found with the genetic algorithms, obtaining the parameters presented in Table 1.
<figure><img src="image_5.png" /><figcaption>Fig. 2. Wind speed for the MPPT WT operation (Color figure online).</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 3. Waves elevation (Color figure online).</figcaption></figure>

<table><caption>**Table 1.** Parameters of the controller configuration</caption><thead><tr><td>Parameter</td><td>Value</td></tr></thead><tbody><tr><td>K<sub>p</sub></td><td>4.578686</td></tr><tr><td>K<sub>d</sub></td><td>0.196675</td></tr><tr><td>μ</td><td>0.136155</td></tr><tr><td>δ</td><td>0.446839</td></tr><tr><td>N<sub>neu</sub></td><td>25</td></tr><tr><td>T<sub>c</sub></td><td>0.098 seg</td></tr></tbody></table>

Each variable of the MPPT process will be analyzed. In Fig. 4, the MSE of the generator speed is presented. It shows the big reduction of the speed error obtained with the neuro-control strategy (red line). That is, the WT speed is closer to the reference than the one obtained with OpenFast (blue line), which allows it the maximum power generation.
<figure><img src="image_7.png" /><figcaption>**Fig. 4.** MSE of the speed in the MPPT WT operation (Color figure online).</figcaption></figure>

In Fig. 5, the output power generated is presented. It experiences quick adjustments in response to the applied torque obtained with the control process, facing the existing nonlinear dynamics. The power level with the neuro-controller achieves higher values, near the nominal value, with an average of 1.1374 MW (red line) in contrast to the average of 1.0488 MW with the OpenFAST controller (blue line). This means an increment of 8.45% in power extraction though it is noisier. These fluctuations result from a quick change in the electromagnetic torque to achieve the optimal relation between torque and speed for maximum energy production. This more oscillatory signal is common during the electric energy generation process. In addition, it can be managed in a later process to balance the power that is introduced in the grid.

<figure><img src="image_8.png" /><figcaption>**Fig. 5.** Output power in the MPPT WT operation (Color figure online).</figcaption></figure>

With the torque regulation, the generator speed (Fig. 6) is controlled. This variable oscillates to keep the speed-torque relation for the best system operation. It can be seen that the speed takes values around the nominal generator velocity during maximum energy conversion.
<figure><img src="image_9.png" /><figcaption>Fig. 6. Generator speed in the MPPT WT operation (Color figure online).</figcaption></figure>

It can be pointed out that the radial basis analysis in the neuro-control space with an even neuron distribution provides a suitable environment to constantly compute a reference torque with quick updates related to the WT dynamics. Thus, the output signal is used to achieve the zero-speed error, resulting in a better speed response, as shown in the figure. The optimized parameters of the network architecture improve the efficiency of the response and the adaptive learning process. At each iteration the electromagnetic torque responds to the rotational speed produced by the variations that the wind, waves, and other involved phenomena cause.

As an indicator of the efficiency of the MPPT control, the power coefficient (Fig. 7) is measured. The tracking of the optimal $C_p$ is more accurate with the neuro-controller and therefore, the maximum power curve, so the optimal power point is successful.

<figure><img src="image_10.png" /><figcaption>Fig. 7. Power coefficient in the MPPT WT operation (Color figure online).</figcaption></figure>

Finally, it is also important to consider the structural response of the WT. The movement of the tower is shown in Fig. 8. It can be noticed that with the designed control technique, a slightly bigger displacement of the tower top is generated in contrast with the embedded OpenFAST torque control (blue line).

On average, this indicator is 0.24330 m with the DSC-NN controller and 0.23201 m with the OpenFAST control. This may be due to the higher generator speed, that has a bigger effect of the masses of the system, inertia, and faster variations in the variables for tracking better the $C_p$. Nevertheless, the variations are very small and are justified with the increase in the power extracted.
<figure><img src="image_11.png" /><figcaption>Fig. 8. Tower displacement in the MPPT WT operation (Color figure online).</figcaption></figure>

On the other hand, to relate the effects of vibrations in the WT structure, the accelera-
tion on the tower top is considered. The mean squared acceleration in the wind direction
is calculated. A decrement of 0.0045 (m/s²)² in the MSE value of the acceleration is
finally obtained with the use of the neuro-controller, that is 0.05002 (m/s²)² with the
intelligent control strategy and 0.054505 (m/s²)² with the OpenFAST controller. The
small reduction contributes to the decrement of the vibration effects on the wind tur-
bine tower and can be extended to the diverse mechanical elements of the wind turbine,
including the platform. Thus, the vibrations in the device floating foundation are also
slightly reduced.

**5 Conclusions and Future Works**

An intelligent control strategy for the MPPT region of an offshore wind turbine system has been developed, based on the conventional DSC control and using an unsupervised neural network with autonomous learning and genetic algorithms.

The incorporation of this control strategy has given positive results in this type of non-
linear and complex system. The controller has been able to face and constantly adapt
to the nonlinear behaviour of the device and to the external loads that are presented
in offshore WTs. The intelligent controller maximizes the output power. In terms of
vibrations, a slight increase in the tower movements has been caused, but it can be
considered negligible taking into account the efficiency of the energy generation. Despite
this condition, the acceleration of the top of the tower has been reduced, decreasing the
negative effects of vibrations on the structure.

As future works, this control strategy could be applied to a floating offshore wind
turbine, and to a real prototype.

**Acknowledgement.** This work was partially supported by the Spanish Ministry of Science, Innovation and Universities under MCI/AEI/FEDER Project no. PID2021-123543OB-C21.
References

1. Chaoui, H., Miah, S., Oukaour, A., Gualous, H.: Maximum power point tracking of wind turbines with neural networks and genetic algorithms. In IECON 2014–40th Annual Conference of the IEEE Industrial Electronics Society, pp. 197–201. IEEE (2014)

2. Saxena, V., Kumar, N., Singh, B., Panigrahi, B.K.: A spontaneous control for grid integrated solar photovoltaic energy conversion systems with voltage profile considerations. IEEE Trans. Sustain. Energy **12**(4), 2159–2168 (2021). https://doi.org/10.1109/TSTE.2021.3084103

3. Sierra-García, J.E., Santos, M.: Deep learning and fuzzy logic to implement a hybrid wind turbine pitch control. Neural Comput. Appl. **34**(13), 10503–10517 (2021). https://doi.org/10.1007/s00521-021-06323-w

4. Sierra-García, J.E., Santos, M.: Redes neuronales y aprendizaje por refuerzo en el control de turbinas eólicas. Revista Iberoamericana de Automática e Informática industrial **18**(4), 327–335 (2021)

5. Pustina, L., Lugni, C., Bernardini, G., Serafini, J., Gennaretti, M.: Control of power generated by a floating offshore wind turbine perturbed by sea waves. Renew. Sustain. Energy Rev. **132**, 109984 (2020)

6. Thongam, J.S., Ouhrouche, M.: MPPT control methods in wind energy conversion systems. In: Carriveau, R. (ed.) Fundamental and Advanced Topics in Wind Power. InTech (2011)

7. Pozo, A., Ayala, E., Simani, S., Muñoz, E.: Indirect speed control strategy for maximum power point tracking of the DFIG wind turbine system. Revista Técnica "energía" **17**(2), 92–101 (2021). https://doi.org/10.37116/revistaenergia.v17.n2.2021.426

8. Ayala, E., Simani, S.: Perturb and observe maximum power point tracking algorithm for permanent magnet synchronous generator wind turbine systems. In: Conte, G. (ed.) Proceedings of 15th European workshop on advanced control and diagnosis – ACD. Lecture notes in control and information sciences. Alma Mater Studiorum, University of Bologna, pp. 1–11. Springer, Bologna (2019). https://doi.org/10.1007/978-3-030-85318-1_59

9. Pande, J., Nasikkar, P., Kotecha, K., Varadarajan, V.: A review of maximum power point tracking algorithms for wind energy conversion systems. J. Marine Sci. Eng. **9**(11), 1187 (2021)

10. Malobe, P., Djondine, P., Eloundou, P., Ndongo, H.: A novel hybrid MPPT for wind energy conversion systems operating under low variations in wind speed. Energy Power Eng. **12**(12), 716–728 (2020)

11. Muñoz, E., Ayala, E., Pozo, N., Simani, S.: Fuzzy PID control system analysis for a wind turbine maximum power point tracking using FAST and Matlab Simulink. In: Iano, Y., Sao-tome, O., Kemper, G., Mendes, A.C., de Seixas, G., de Oliveira, G. (eds.) Proceedings of the 6th Brazilian Technology Symposium (BTSym'20). SIST, vol. 233, pp. 905–917. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-75680-2_100

12. Muñoz, E., Ayala, E., Pozo, N.: Estrategia de Control Fuzzy PI en una Turbina Eólica con Generador de Inducción Doblemente Alimentado para Maximizar la Extracción de Potencia en Presencia de Perturbaciones. Revista Técnica energía **18**(1), 1–10 (2021). https://doi.org/10.37116/revistaenergia.v17.n2.2021.428

13. Muñoz-Palomeque, E., Sierra-García, J.E., Santos, M.: Wind turbine maximum power point tracking control based on unsupervised neural networks. J. Comput. Des. Eng. **10**(1), 108–121 (2023). https://doi.org/10.1093/jcde/qwac132

14. El Aissaoui, H., El Ougli, A., Tidhaf, B.: Neural networks and fuzzy logic based maximum power point tracking control for wind energy conversion system. Adv. Sci. Technol. Eng. Syst. J. **6**(2), 586–592 (2021)

15. Pathak, G., Singh, B., Panigrahi, B.K.: Back-propagation algorithm-based controller for autonomous Wind–DG microgrid. IEEE Trans. Ind. Appl. **52**(5), 4408–4415 (2016)
16. Chandrasekaran, K., Mohanty, M., Mallikarjuna Golla, A., Venkadesan, S.P.: Dynamic MPPT controller using cascade neural network for a wind power conversion system with energy management. IETE J. Res. **68**(5), 3316–3330 (2020). https://doi.org/10.1080/03772063.2020.1756934

17. Magdi, M., Mojeed, O.: Adaptive and predictive control strategies for wind turbine systems: a survey. IEEE J. Autom SINICA **6**, 364–378 (2019)

18. Yang, B., Zhang, X., Yu, T., Shu, H., Fang, Z.: Grouped grey wolf optimizer for maximum power point tracking of doubly-fed induction generator based wind turbine. Energy Convers. Manage. **133**, 427–443 (2017)

19. Semrau, G., Rimkus, S., Das, T.: Nonlinear systems analysis and control of variable speed wind turbines for multiregime operation. J. Dyn. Syst. Measur. Control **137**(4), 041007 (2015). https://doi.org/10.1115/1.4028775

20. Sahri, Y., Tamalouzt, S., Belaid, S.L.: Direct torque control of DFIG driven by wind turbine system connected to the grid. In: 2018 International Conference on Wind Energy and Applications in Algeria (ICWEAA), pp. 1–6. IEEE (2018)

21. Abad, G., Lopez, J., Rodriguez, M., Marroyo, L., Iwanski, G.: Doubly Fed Induction Machine: Modeling and Control for Wind Energy Generation. John Wiley & Sons (2011)