# A novel fuzzy-logic-improved direct power control strategy for DFIG-based wind turbine through real-time OPAL-RT validation

Karim Fathi Sayeh, Salah Tamalouzt, Djamel Ziane, Nabil Benyahia, Sofia Lalouni Belaid

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

## ► To cite this version:

Karim Fathi Sayeh, Salah Tamalouzt, Djamel Ziane, Nabil Benyahia, Sofia Lalouni Belaid. A novel fuzzy-logic-improved direct power control strategy for DFIG-based wind turbine through real-time OPAL-RT validation. International Journal of Electrical Power & Energy Systems, 2025, 172, 10.1016/j.ijepes.2025.111317. hal-05339544

HAL Id: hal-05339544

https://hal.science/hal-05339544v1

Submitted on 30 Oct 2025

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published 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_2.png" /></figure>
<figure><img src="image_3.png" /></figure>

# A novel fuzzy-logic-improved direct power control strategy for DFIG-based wind turbine through real-time OPAL-RT validation

Karim Fathi Sayeh<sup>a, b, c</sup>, Salah Tamalouzt<sup>a</sup>, Djamel Ziane<sup>a, b, *</sup>, Nabil Benyahia<sup>c, d</sup>,
Sofia Lalouni belaid<sup>a</sup>

## ARTICLE INFO

### Keywords:

RT-LAB

OPAL-RT

Fuzzy Logic Controller

Direct Power Control

DFIG

Wind Turbine

## ABSTRACT

Direct Power Control for doubly-fed induction generator-based wind turbines are a widely used strategy, but it inherently suffers from significant power ripples and high total harmonic distortion, which compromise grid power quality and can induce mechanical stress on the turbine's drivetrain. To address these critical issues, this paper introduces and validates a novel fuzzy-logic-improved direct power control strategy. The proposed method replaces the conventional hysteresis comparators and switching table with a single, parameter-free fuzzy logic controller that provides a more intelligent and smoother selection of rotor voltage vectors. The performance of this strategy was rigorously evaluated using comprehensive software simulations in MATLAB/Simulink under realistic, variable wind speed with local reactive powers compensation profiles, followed by real-time hardware-in-the-loop validation using an OPAL-RT simulator. The main results demonstrate substantial performance gains over the conventional approach, with the proposed controller achieving a 72.13 % reduction in generated active power ripples and accelerating the control system's response time by up to 31.71 %. Crucially, power quality was significantly enhanced, with the stator current's total harmonic distortion being reduced from 7.06 % to just 2.04 % during super-synchronous operation. The conclusion drawn from these results is that the fuzzy-logic-based approach is a simple and robust solution whose high effectiveness and practical feasibility have been successfully demonstrated in a real-time environment, making it a promising candidate for improving the grid integration of modern wind energy systems.

## 1. INTRODUCTION

Global energy demand has surged dramatically in recent times, driven by widespread use of electronic devices and appliances. Historically, this demand was primarily met by fossil fuels, which pose significant environmental threats, including global warming and pollution. Consequently, there has been a global shift towards clean, renewable energy sources. Among these, wind energy stands out as a highly promising option, harnessed through wind farms that often operate at variable speeds to optimize energy capture from the wind [1].

The doubly-fed induction generator (DFIG) is widely regarded as the furthermost suitable generator for these wind usages. Its ability to control both active/reactive power provides excellent operational flexibility across a broad range of speeds. The DFIG's rotor winding is

associated to the AC grid through an indirect AC/AC converter [2]. As a critical renewable energy source, wind power relies on sophisticated control techniques for the doubly-fed induction generators (DFIGs) employed in wind turbines. Significant advancements have been made by researchers over the years in developing improved DFIG control strategies.

Initial DFIG control methods utilized conventional vector control techniques [3]. While these offered acceptable performance, they suffered from notable drawbacks. For instance, flux-oriented vector control requires precise knowledge of generator parameters to tune PI controllers effectively. This reliance on machine models limits the system's ability to adapt to changing conditions, and the dynamic response was often considered marginal.

Direct torque control (DTC) was introduced in the 1980s [4] as a

<footnote><sup>a</sup> Université de Bejaia, Faculté de Technologie, Laboratoire de Technologie Industrielle et de l'Information (LTII), 06000 Bejaia, Algeria</footnote>

<footnote><sup>b</sup> Nantes Université, Institut de Recherche en Énergie Électrique de Nantes Atlantique, IREENA, UR 4642, F-44600 Saint-Nazaire, France</footnote>

<footnote><sup>c</sup> ESME Research Lab, 38 rue Molière 94200, Ivry-sur-Seine, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail addresses: karimfathi.sayeh@univ-bejaia.dz (K.F. Sayeh), salah.tamalouzt@univ-bejaia.dz (S. Tamalouzt), djamel.ziane@univ-nantes.fr (D. Ziane), nabil.benyahia@esme.fr (N. Benyahia), belaid@univ-bejaia.dz (S.L. belaid).</footnote>
means to overcome the limitations of flux-oriented vector control. DTC achieves direct regulation of torque and flux by selecting voltage vectors based on errors in these quantities, using a switching table. This method is known for its fast dynamic response. But the usage of hysteresis comparators within DTC typically results in significant torque ripple effects. For successful grid integration, controlling DFIG active and reactive power is essential. Direct power control (DPC) adapts the DTC concept to straight control active/reactive powers [5,6]. DPC selects voltage vectors using a switching table based on errors in power, also providing a fast response. Similar to DTC, the use of hysteresis comparators in DPC leads to considerable ripples in the power exchanged by the generator.

Initial efforts aimed at reducing these power ripples. Techniques like steady switching frequency DPC [7] and space vector modulation DPC (DPC-SVM), which utilized PI controllers instead of hysteresis comparators, were proposed [8,9]. Nevertheless, DPC-SVM presents challenges as it necessitates accurate system parameters for effective controller tuning and often lacks robustness. More sophisticated techniques have been suggested, including adaptive DPC [10], predictive DPC [11–13], parallel predictive [14] and predictive with active disturbance rejection active [15]. These methods determine voltage vectors based on power errors with the goal of minimizing ripples. However, they typically increase control complexity and require precise system models. Nonlinear control approaches like sliding mode DPC (SMC-DPC) [16], super-twisting SMC [17], second order SMC [18,19], SMC with extend state observer [20] and backstepping DPC (BC-DPC) [21,22] have also been proposed and applied. They utilize principles such as variable structure or backstepping to achieve strong transient and steady-state performance, but this again adds to the complexity.

Intelligent control methods, particularly fuzzy logic-based DPC, have gained traction in recent years. Early works improved switching decisions through rule-based inference [23] and extended the structure to 12 sectors [24]. Later studies introduced adaptive tuning of membership functions [25], fuzzy adjustment of hysteresis bands [26], and applications to reactive power compensation [27,28]. Other contributions replaced conventional hysteresis comparators entirely with fuzzy decision-making [29].

Neural network (NN)-based DPC has also been explored, with approaches replacing PI regulators [30], enhancing multilevel inverter dynamics [31]. Additional studies [32,33] combined neural networks with sliding mode and higher-order control schemes to strengthen dynamic performance. In another approach [34], three separate neural networks were introduced to substitute the conventional C-DPC framework. A later contribution [35] applied neural networks to refine the 12-sector DPC method, and in [36], two different neural networks, one dedicated to prediction and another to classification, were implemented in place of the C-DPC structure. These intelligent approaches were motivated by the desire to overcome the limitations of conventional DPC, offering more adaptive and responsive control of active and reactive power.

Despite these promising results, most prior studies only validated their methods under restricted conditions. These conditions were often limited to one or two operating modes or short simulation durations. The studies also ignored the advantages of the WT-DFIG system in relation to different operating modes and reactive energy compensation. However, real-world wind turbines experience highly variable wind speeds and frequent transitions between sub-synchronous, synchronous, and super-synchronous operation. Comprehensive evaluations of intelligent DPC across realistic operating profiles are limited. This study addresses this gap by proposing a twelve-sector DPC enhanced with fuzzy logic (F12-DPC) and validating its performance across the full operating range of a WT-DFIG under variable wind conditions and multiple local reactive power compensation modes through simulation and real-time OPAL-RT implementation.

A significant limitation observed in most DPC research is that performance demonstrations are often confined to one or two operating

modes over brief periods. Real-world conditions, however, involve fluctuating wind speeds and frequent transitions between modes. Consequently, very few studies have thoroughly evaluated DPC performance across the full operational envelope using realistic wind speed profiles.

Real-time simulation (RTS) models are becoming increasingly popular among researchers due to their ability to integrate hardware systems and improve simulation fidelity. The interaction between simulated models and physical devices in RTS produces more accurate and realistic outcomes. This advanced simulation technique is particularly valuable for testing and validating control systems. RTS offers a safe and controlled setting for evaluating novel control strategies before deployment in the real world. The practicality and cost-effectiveness of real-time solutions have also been factors in their increasing adoption [37,38].

This paper proposes a novel Direct Power Control (DPC) method enhanced with fuzzy logic (F12-DPC) to address the limitations of existing approaches. Its primary objectives are to reduce power fluctuations and improve current characteristics. The F12-DPC enables precise regulation of both local compensated reactive and active powers, thus enhancing the power exchange quality with the AC grid. The suggested method is designed to handle the changeable nature of wind across all operational modes of a WT-DFIG, in addition to different reactive power compensation. This study thus presents a comprehensive solution for improving WT-DFIG system performance and the quality of power provided to the grid. Furthermore, the suggested control system underwent validation through real-time simulation. The system was initially developed as a model in MATLAB software, then executed by the OPAL-RT in conjunction with the RT-LAB platform. Performance evaluation of the control system model was carried out by analyzing the results obtained from the real-time simulation. Specifically, the study employed the OP4512 simulator, which provides a versatile and economic environment for conducting real-time simulation testing of the control system.

The primary novelty presented in this manuscript is the suggested fuzzy logic-based direct power control (F12-DPC) scheme specifically designed for WT-DFIGs.

* The study integrates the OP4512 platform with a MATLAB/ Simulink-based model to enable simulation-in-the-loop (SIL) validation, ensuring a reliable assessment before real-world implementation.

* The study introduces a fuzzy logic-based direct power control (F12-DPC) scheme to overcome the limitations of conventional DPC. This new scheme provides accurate regulation of active and local compensated reactive powers under variable wind conditions.

* This method replaces the classical DPC's hysteresis comparators and switching tables with fuzzy logic rules, reducing power ripples and lowering the total harmonic distortion (THD) of grid-injected currents.

* The control system is validated under diverse wind speed variations and across all DFIG operating modes (sub-synchronous, synchronous, and super-synchronous), demonstrating robust performance in realistic scenarios.

* F12-DPC explicitly handles all reactive power compensation modes (generation, absorption, and unit power factor), improving the stability and reliability of power exchange with the AC grid.

* This control scheme improves grid interaction quality by mitigating power fluctuations, reducing THD, and optimizing reactive power support. Consequently, there are lower losses and higher overall WT-DFIG efficiency.

While fuzzy logic controllers (FLCs) have been previously applied to DFIG-based wind systems, most works remained limited to simulation studies or single operating modes. Moreover, their applicability in real-time environments has rarely been demonstrated. The novelty of this
<figure><img src="image_4.png" /><figcaption>Fig. 1. Overall schematic of the WT-DFIG system.</figcaption></figure>

paper lies not in the use of fuzzy logic itself, but in:

* The development of a 12-sector fuzzy logic direct power control (F12-DPC) using a single FLC, eliminating hysteresis comparators and switching tables.

* Comprehensive validation under sub-, super-, and synchronous operating modes with different compensation scenarios.

* Real-time execution on OPAL-RT OP4512, demonstrating feasibility beyond conventional simulation studies.

## 2. SYSTEM DESCRIPTION OF THE WT-DFIG

### 2.1. Overview of the WT-DFIG system configuration

As illustrated in Fig. 1, the WT-DFIG system comprises several principal components:

* Wind turbine: Converts wind energy into mechanical energy through the rotation of blades;

* Gearbox: Increases the rotational speed of the wind turbine shaft to match the operating DFIG speed;

* Doubly fed induction generator (DFIG): Converts mechanical energy into electrical energy;

* Two electronic power converters: Electronic devices that control the flow of powers between the DFIG, and the DC with AC grids.

### 2.2. Mathematical model of mechanical power

The mechanical power $P_m$ harnessed by the wind turbine, is calculated using the following [10,32]:

$$P_{mec} = 0.5 \rho \pi R^2 v^3 C_p(\lambda, \beta) \quad (1)$$

where

* $\rho$ represents the air density

* R denotes the rotor radius

* $v$ indicates the wind speed

* $C_p(\lambda, \beta)$ is the power coefficient

Equation (2) defines the power coefficient $C_p(\lambda, \beta)$, which incorporates parameters C1 through C6 [39].

$$ \begin{cases} C_p(\lambda, \beta) = C_1 \left[ C_2 \left( \frac{1}{\lambda_i} \right) - C_3\beta - C_4 \right] e^{\left( \frac{C_5}{\lambda_i} \right)} + C_6\lambda_i \\ \lambda_i = \left( \frac{1}{\lambda + 0.08\beta} - \frac{0.035}{1 + \beta^3} \right)^{-1} \end{cases} \quad (2) $$

### 2.3. DFIG model in the d-q reference frame

The generator model in the d-q reference frame is represented by Eqs. (3) and (4), which define the stator and rotor voltages ($v_{sd}$, $v_{sq}$, $v_{rd}$, $v_{rq}$) and currents ($i_{sd}$, $i_{sq}$, $i_{rd}$, $i_{rq}$). The parameters $R_s$, $R_r$, $L_s$, $L_r$, and M denote the stator and rotor resistances, leakage inductances, and mutual
<table><caption>**Table 1**
Switching Table OF The Conventional DPC [23].</caption><thead><tr><th>HQ<sub>AC</sub></th><th>HP<sub>s</sub></th><th>N<br>I</th><th>II</th><th>III</th><th>IV</th><th>V</th><th>VI</th></tr></thead><tbody><tr><td rowspan="3">+ 1</td><td>+ 1</td><td>V5</td><td>V6</td><td>V1</td><td>V2</td><td>V3</td><td>V4</td></tr><tr><td>0</td><td>V7</td><td>V0</td><td>V7</td><td>V0</td><td>V7</td><td>V0</td></tr><tr><td>-1</td><td>V3</td><td>V4</td><td>V5</td><td>V6</td><td>V1</td><td>V2</td></tr><tr><td rowspan="3">-1</td><td>+ 1</td><td>V6</td><td>V1</td><td>V2</td><td>V3</td><td>V4</td><td>V5</td></tr><tr><td>0</td><td>V0</td><td>V7</td><td>V0</td><td>V7</td><td>V0</td><td>V7</td></tr><tr><td>-1</td><td>V2</td><td>V3</td><td>V4</td><td>V5</td><td>V6</td><td>V1</td></tr></tbody></table>

inductance, respectively.

$$ \left\{ \begin{aligned} v_{sd} &= R_s i_{sd} + \frac{d\varphi_{sd}}{dt} - \omega_s \varphi_{sq} \\ v_{sq} &= R_s i_{sq} + \frac{d\varphi_{sq}}{dt} + \omega_s \varphi_{sd} \\ v_{rd} &= R_r i_{rd} + \frac{d\varphi_{rd}}{dt} - \omega_r \varphi_{rq} \\ v_{rq} &= R_r i_{rq} + \frac{d\varphi_{rq}}{dt} + \omega_r \varphi_{rd} \end{aligned} \right. \quad (3) $$

$$ \left\{ \begin{aligned} \varphi_{sd} &= L_s i_{sd} + M_i r_{rd} \\ \varphi_{sq} &= L_s i_{sq} + M_i r_{rq} \\ \varphi_{rd} &= L_r i_{rd} + M_i r_{sd} \\ \varphi_{rq} &= L_r i_{rq} + M_i sq \end{aligned} \right. \quad (4) $$

## 2.4. MPPT algorithm

The Maximum Power Point Tracking (MPPT) algorithm is applied to ensure the optimal capture of available wind power, particularly when the system operates below its nominal power [40]. This algorithm endlessly monitors wind situations and adjusts the DFIG's rotational speed to preserve synchronization with the maximum power point. By precisely controlling the DFIG's speed, the algorithm allows the wind turbine to achieve peak efficacy. This adaptive regulation of the system's operating parameters significantly contributes to improved overall energy yield, operational efficacy, and productive wind power production.

## 2.5. Converter control

The control strategies employed for the converters are essential for achieving the desired system performances. The rotor-side converter (RSC) is controlled using the Direct Power Control (DPC) approach, which facilitates precise regulation of active and reactive power flow. This control strategy significantly improves system responsiveness and efficiency. The grid-side converter (GSC), which interfaces with the AC grid and is typically a DC/AC converter as shown in Fig. 1, is controlled to maintain unity power factor operation, by ensuring zero reactive power exchange with the grid. Furthermore, it generates a sinusoidal current waveform at 50 Hz, synchronized with the standard grid frequency.

# 3. DIRECT POWER CONTROL

## 3.1. Overview and principle

Direct Power Control (DPC) primarily focuses on regulating the generated active power ($P_s$) and local reactive power compensation ($Q_{AC}$) within the WT-DFIG system. The core principle of this control strategy involves the choice and application of an ideal rotor voltage vector for RSC, led by the errors between the desired and measured both powers, as well as the angle of the rotor flux.

The expressions for $P_s/Q_{AC}$ powers are given by:

$$ \left\{ \begin{aligned} P_s &= (v_{sd} i_{sq} + v_{sq} i_{sd}) \\ Q_{AC} &= (v_{sd} i_{sd} - v_{sq} i_{sq}) \end{aligned} \right. \quad (5) $$

## 3.2. Power and flux Relationships

Produced $P_s/Q_{AC}$ exchanged between DFIG stator/grid expressed as functions of the rotor and stator flux [6,23].

$$ \left\{ \begin{aligned} P_s &= -\frac{M}{\sigma L_s L_r} \omega_s |\varphi_s| |\varphi_r| \sin\gamma \\ Q_{AC} &= \frac{\omega_s}{\sigma L_s} |\varphi_s| \left( \frac{M}{L_r} |\varphi_r| \cos\gamma - |\varphi_s| \right) \end{aligned} \right. \quad (6) $$

Here, $\gamma$ represents the angle between the rotor and stator flux vectors.

Changes in the magnitude of the rotor flux $|\varphi_r|$ and the angle $\gamma$ directly influence the values of $P_s/Q_{AC}$. Given that the stator is directly connected to the AC grid, as shown by Equation (6), regulation of the rotor flux linkage vector provides a means to control the flow of active and reactive power between the DFIG and the AC grid.

## 3.3. Rotor flux dynamics

The rotor flux ($\varphi_r$) is determined by integrating the voltage applied to the rotor circuit, as expressed by:

$$ \varphi_r(t) = \int_0^t (v_r - R_r i_r) dt \quad (7) $$

Analysis of rotor flux variations is simplified by neglecting the effect of rotor resistance. With this assumption, the dynamic behavior of the rotor flux can be described by:

$$ \varphi_r(t) = \int_0^t v_r dt \quad (8) $$

The change in the rotor flux can be approximated as:

$$ \Delta\varphi_r \approx v_r \Delta T \quad (9) $$

Based on the previously derived relationships, changes in the rotor flux $\varphi_r$ have a direct impact on $P_s$ and $Q_{AC}$. Consequently, by choosing an appropriate rotor voltage vector $v_r$ over consecutive intervals, the variation $\Delta\varphi_r$ in the rotor flux can be regulated, enabling the regulation of reactive and active powers flow as wanted.

## 3.4. Optimal voltage vector selection

In references [23,32], they graphically illustrate how using different rotor voltage vectors impacts the $P_s$ and $Q_{AC}$ power outputs.

Table 1 provides a summary of optimal rotor voltage vector selections intended to increase or decrease $P_s$ and $Q_{AC}$ powers based on their respective errors relative to the setpoints. This table serves as a lookup tool, mapping the $P_s$ error (evaluated with a 3-level hysteresis) and the $Q_{AC}$ error (evaluated with a 2-level hysteresis) to the appropriate rotor voltage vector needed to correct the errors in the desired direction.

By employing this $P_s$ and $Q_{AC}$ powers mapping in the mentioned references and the Table 1, a conventional direct power control (DPC) structure can choose a suitable rotor voltage vector. This approach forms the foundation of the conventional DPC strategy, enabling the independent regulation of $P_s$ and $Q_{AC}$.

## 3.5. Powers and rotor flux Estimation

### Reference Frame and Assumptions:

The analysis in this study is conducted using the d-q synchronous reference frame. This orientation simplifies the mathematical modeling and associated calculations. Furthermore, an infinite grid is presumed.

### Active and Reactive Powers Estimations:
<figure><img src="image_5.png" /><figcaption>Fig. 2. Control Flowchart of F12-DPC Strategy.</figcaption></figure>

<table><caption>**Table 2**

F12-DPC's fuzzy rule.</caption><thead><tr><th>δ<sub>r</sub></th><th colspan="3">eQ<sub>AC</sub></th><th colspan="3">P</th></tr><tr><th></th><th>N</th><th>eP<sub>s</sub></th><th></th><th>N</th><th>eP<sub>s</sub></th><th></th></tr><tr><th></th><th>N</th><th>Z</th><th>P</th><th>N</th><th>Z</th><th>P</th></tr></thead><tbody><tr><th>θ<sub>1</sub></th><td>V2</td><td>V0</td><td>V6</td><td>V3</td><td>V7</td><td>V5</td></tr><tr><th>θ<sub>2</sub></th><td>V2</td><td>V7</td><td>V6</td><td>V3</td><td>V0</td><td>V5</td></tr><tr><th>θ<sub>3</sub></th><td>V3</td><td>V0</td><td>V1</td><td>V4</td><td>V7</td><td>V6</td></tr><tr><th>θ<sub>4</sub></th><td>V3</td><td>V7</td><td>V1</td><td>V4</td><td>V0</td><td>V6</td></tr><tr><th>θ<sub>5</sub></th><td>V4</td><td>V0</td><td>V2</td><td>V5</td><td>V7</td><td>V1</td></tr><tr><th>θ<sub>6</sub></th><td>V4</td><td>V7</td><td>V2</td><td>V5</td><td>V0</td><td>V1</td></tr><tr><th>θ<sub>7</sub></th><td>V5</td><td>V0</td><td>V3</td><td>V6</td><td>V7</td><td>V2</td></tr><tr><th>θ<sub>8</sub></th><td>V5</td><td>V7</td><td>V3</td><td>V6</td><td>V0</td><td>V2</td></tr><tr><th>θ<sub>9</sub></th><td>V6</td><td>V0</td><td>V4</td><td>V1</td><td>V7</td><td>V3</td></tr><tr><th>θ<sub>10</sub></th><td>V6</td><td>V7</td><td>V4</td><td>V1</td><td>V0</td><td>V3</td></tr><tr><th>θ<sub>11</sub></th><td>V1</td><td>V0</td><td>V5</td><td>V2</td><td>V7</td><td>V4</td></tr><tr><th>θ<sub>12</sub></th><td>V1</td><td>V7</td><td>V5</td><td>V2</td><td>V0</td><td>V4</td></tr></tbody></table>

<table><caption>**Table 3**

Quantitative Comparison of P<sub>s</sub> and Q<sub>AC</sub> Performances.</caption><thead><tr><th>Performance Metrics</th><th></th><th>C-DPC</th><th>F12-DPC</th><th>Improvement Ratio (%)</th></tr></thead><tbody><tr><td rowspan="2">Ripples</td><td>P<sub>s</sub>(W)</td><td>197.82</td><td>55.14</td><td>72.13 %</td></tr><tr><td>Q<sub>AC</sub>(VAR)</td><td>177.42</td><td>49.03</td><td>72.37 %</td></tr><tr><td rowspan="2">Overshoot</td><td>P<sub>s</sub>(W)</td><td>62.85</td><td>16.14</td><td>74.32 %</td></tr><tr><td>Q<sub>AC</sub>(VAR)</td><td>65.33</td><td>16.17</td><td>75.25 %</td></tr><tr><td rowspan="2">Response time</td><td>P<sub>s</sub>(ms)</td><td>0.82</td><td>0.56</td><td>31.71 %</td></tr><tr><td>Q<sub>AC</sub>(ms)</td><td>0.81</td><td>0.45</td><td>44.44 %</td></tr><tr><td rowspan="2">SSE</td><td>P<sub>s</sub>(W)</td><td>112.81</td><td>31.27</td><td>72.28 %</td></tr><tr><td>Q<sub>AC</sub>(VAR)</td><td>91.54</td><td>24.24</td><td>73.52 %</td></tr></tbody></table>

Based on these assumptions, the estimated values for (P<sub>s</sub>) and (Q<sub>AC</sub>) are given by

$$ \left\{ \begin{array}{l} P_s = -\frac{M}{L_s} V_s i_{rq} \\ Q_{AC} = \left[ \frac{V_s^2}{L_s \omega_s} - V_s \frac{M}{L_s} i_{rd} \right] \end{array} \right. \qquad (10) $$

Where, V<sub>s</sub> is the magnitude of the stator voltage and ω<sub>s</sub> denotes synchronous pulsation.

**Magnitude of Rotor Flux Estimation:**

The magnitude of the rotor flux ϕ<sub>r</sub> is computed as:

$$ \left\{ \begin{array}{l} \varphi_{rd} = \left(1 - \frac{M^2}{L_s L_r}\right) L_r i_{rd} + \frac{M}{L_s} \\ \\ \varphi_{rq} = \left(1 - \frac{M^2}{L_s L_r}\right) L_r i_{rq} \end{array} \right. \qquad (11) $$

$$ |\varphi_r| = \sqrt{\varphi_{dr}^2 + \varphi_{qr}^2} \qquad (12) $$

**Rotor Flux Angle Estimation:**

The rotor flux parts ϕ<sub>dr</sub>, ϕ<sub>qr</sub> in the synchronous dq frame are obtained by transforming from the stationary αβ frame using the standard dq/αβ transformations.

The angle δ<sub>r</sub> of the rotor flux vector is then computed as:

$$ \delta_r = \tan^{-1} \left( \frac{\varphi_{rj}}{\varphi_{rat}} \right) \qquad (13) $$

This angle is utilized to determine the sector number of the rotor flux.

# 4. PROPOSED CONTROL

This section introduces a new direct power control (DPC) method using fuzzy logic (FL) named F12-DPC, as depicted in Fig. 3. It aims to improve upon the performances and limitations of the conventional C-DPC method. The F12-DPC control utilizes the errors of powers and angle of rotor flux as inputs and generates an optimum rotor voltage vector for the AC/DC converter (RSC converter), as depicted in Fig. 1, as output through the fuzzy logic control process.

## 4.1. Fundamental Features

* **Inspiration:** The design of this controller draws inspiration from the 12-sector DPC strategy detailed in [33].

* **Single FLC:** Unlike C-DPC, F12-DPC uses a single FLC instead of separate hysteresis controllers and a switching table.

* **Parameter-Free:** It does not involve knowledge of specific system parameters, making it adaptable.

* **Simple Implementation:** The controller's structure facilitates straightforward implementation.

## 4.2. Operation Steps

The proposed F12-DPC algorithm improves conventional DPC by embedding a fuzzy logic controller (FLC) that directly selects the optimal rotor voltage vector. The complete procedure can be described in three stages and is illustrated in the control flowchart of Fig. 2:
<figure><img src="image_6.png" /><figcaption>Fig. 3. Experimental Setup for Real-Time Validation of F12-DPC on WT-DFIG by OP4512.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Fig. 4. Illustration of the RTS system implementation in MATLAB.</figcaption></figure>

### 4.2.1. Fuzzification

Through the fuzzification phase, the FL's input variables, $eP_s$, $eQ_{AC}$, and $\delta_r$, are converted to linguistic variables by means of defined membership functions (MFs). The design choices for these MFs are critical for controller performance (See Table 2).

<figure><img src="image_8.png" /><figcaption>Fig. 5. Wind speed.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 6. Speed response of DFIG.</figcaption></figure>

* For the active power error ($eP_s$) input variable:

* N (Negative) and P (Positive) MFs: A **trapezoidal** shape was chosen to provide a wider range for large errors, ensuring a consistent control action and making the system less sensitive to minor overshoots.

* Z (Zero) MF: A **triangular** shape was selected to provide high sensitivity and a crisp response when the error is close to zero, which is crucial for minimizing steady-state ripple.
<figure><img src="image_10.png" /><figcaption>Fig. 7. $P_s$ power and its reference.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Fig. 8. $Q_{AC}$ power and its reference.</figcaption></figure>

* For the compensated local reactive power error ($eQ_{AC}$) input variable:

* N (Negative) and P (Positive) MFs: A **trapezoidal** shape was chosen.

* For the rotor flux angle ($\delta_r$) input variable:

* $\theta_{-1}$ to $\theta_{-12}$ MFs: The 360° flux space is divided into 12 sectors of 30°, each defined by a **triangular** membership function. This 12-sector approach provides finer control granularity than the conventional 6-sector method, while the triangular MFs ensure smooth transitions between sectors. This combination enables more precise voltage vector selection to significantly reduce power ripples.

### 4.2.2. Fuzzy inference

The controller's logic is encapsulated in a rule base of 72 rules, as

detailed in Table 3. These rules are not arbitrary; they are designed based on the fundamental principles of DPC theory. For instance, consider a scenario where the flux angle is in Sector 1 (θ1), the active power error is Positive (P), and the reactive power error is Negative (N). This means the controller needs to increase active power and decrease reactive power. The rule base maps this input combination to the voltage vector V3, which is known to produce this specific change in torque and flux for that sector. This underlying physical logic is applied to construct the entire rule base. The Mamdani inference method with a Max-Min decision process was selected due to its intuitive nature and its widespread successful application in control systems.

#### 4.3.3. Defuzzification

In the defuzzification stage, a single, decisive rotor voltage vector is selected from the fuzzy output. To achieve this efficiently, the output
<figure><img src="image_12.png" /><figcaption>Fig. 9. $i_{sabc}$ currents to the AC grid; a) via F12-DPC; b) $i_{sa}$ compared to both controls.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Fig. 10. $i_{rabc}$ currents; a) via F12-DPC; b) $i_{ra}$ compared to both controls.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>Fig. 11. Harmonic spectrum of $i_{sa}$ by C-DPC approach.</figcaption></figure>

variable is represented by **singleton** membership functions, which directly map to the discrete integer commands (0–7) for the eight voltage vectors ($V_0–V_7$). The “**Bisector**” method is then used to compute the crisp output.

## 5. REAL-TIME SIMULATION AND VALIDATION

RTS, or real-time simulation, has gained popularity as a method in various engineering disciplines for creating computer models that operate synchronously with real-world time. The OPAL-RT OP4512 serves as one such real-time digital simulator, enabling the simulation and testing of power electronics, control systems, and other embedded
<figure><img src="image_15.png" /><figcaption>Fig. 12. Harmonic spectrum of $i_{sa}$ by F12-DPC approach.</figcaption></figure>

<table><caption>**Table 4**
Comparison of C-DPC and F12-DPC Methods.</caption><thead><tr><th rowspan="2">Performances</th><th rowspan="2">Approaches</th><th colspan="3">Operating modes of the WT-DFIG</th></tr><tr><th>Synch</th><th>Super</th><th>Sub</th></tr></thead><tbody><tr><td rowspan="2">THDs (%)</td><td>C-DPC</td><td>4.67</td><td>7.06</td><td>4.88</td></tr><tr><td>F12-DPC</td><td>1.06</td><td>2.04</td><td>1.32</td></tr><tr><td>Improvement (%)</td><td></td><td>77.30 %</td><td>71.10 %</td><td>72.95 %</td></tr></tbody></table>

systems. The OPAL-RT OP4512 integrates with OPAL-RT's RT-LAB software platform, which acts as an interface between physical systems and MATLAB/Simulink models. RT-LAB permits operators to implement intricate control strategies developed within MATLAB/Simulink and execute them in real-time on the OPAL-RT OP4512, thereby facilitating real-time communication with real devices under test. Through the use of the RT-LAB and the OP4512, scientists may quickly develop and validate control systems using real-time hardware-in-the-loop applications [41,42].

The proposed F12-DPC control approach for the WT-DFIG was

confirmed by experimentation using the OPAL-RT OP4512 real-time digital simulator. As depicted in Fig. 3, the experimental test setup involved RT-Lab running on a host PC, with the OPAL-RT OP4512 simulator functioning as the target system. A model of the WT-DFIG system, including the proposed F12-DPC control scheme, was developed in MATLAB/Simulink. This model was then compiled on the host PC and subsequently deployed onto the OPAL-RT OP4512 simulator via an Ethernet TCP/IP connection using the RT-LAB. Real-time control plan execution by the OP4512 was followed by direct data collection utilizing a Digital Storage Oscilloscope (DSO) that was USB-connected to the simulator. This setup provided experimental justification of the F12-DPC strategy for WT-DFIG systems, leveraging OPAL-RT's advanced real-time simulation and rapid control prototyping capabilities.

To facilitate real-time simulation, the Simulink model was divided into subsystems: master and console, as demonstrated in Fig. 4. The master subsystem, which contains the electrical and mechanical models of the WT-DFIG system, runs on the processor cores of the OPAL-RT OP4512. The console subsystem operates in the background on the host PC and manages input/output operations and communication with the OPAL-RT OP4512. This configuration allows the F12-DPC control

<figure><img src="image_16.png" /><figcaption>Fig. 13. $P_s$ power response under parameter variations (Rs, Rr + 50%; Ls, Lr -10%).</figcaption></figure>
<figure><img src="image_17.png" /><figcaption>Fig. 14. $Q_{AC}$ power response under parameter variations (Rs, Rr + 50%; Ls, Lr -10%).</figcaption></figure>

loops and the WT-DFIG simulations to operate on the OP4512 in real time, while the host PC is utilized for monitoring and data collection. Employing separate master and console subsystems is a standard practice in OPAL-RT simulation-in-the-loop testing for allocating tasks between the host computer and the target simulator, which optimizes real-time performance. This approach facilitates accurate and fast simulation of complex systems. When the model is simulated in MATLAB/Simulink, code is automatically generated, compiled, and sent to RT-LAB.

The OPAL-RT OP4512 was operated at a 20 kHz sampling frequency. Control loops executed within 50 µsHI ensuring real-time feasibility. Data acquisition was carried out using RT-LAB console subsystems, with direct oscilloscope capture for current and power signals. The study was conducted in a simulation-in-the-loop (SIL) setup without physical power converters, which avoids hardware risks but faithfully reproduces real-world dynamics.

# 6. SIMULATION AND EXPERIMENTAL RESULTS

The performance of the F12-DPC approach was evaluated for the WT-DFIG. Evaluation was conducted with variable wind speed circumstances, covering all operating modes: sub, super, and synchronous. Also was tested across various local reactive power compensation modes, including unit power factor operation, reactive power absorption, and reactive power generation.

## 6.1. Simulation results with MATLAB/Simulink

MATLAB/Simulink was used for simulation evaluation, and the model is displayed in Fig. 1. The system parameters can be found in Reference [39].

To accurately simulate actual world wind circumstances, the wind speed was simulated to produce random variations over a fifty-second duration. This type of wind is crucial for the assessment of control approaches for wind energy conversion systems, as shown in Fig. 5. At the same time, Fig. 6 shows the DFIG's mechanical behavior and how well it functions in three different modes of operation.

Figs. 7 and 8 present a comparison of the performance of the C-DPC and F12-DPC control methods in regulating $P_s$ and $Q_{AC}$. Both methods are capable of tracking their respective reference values for both power components. However, the F12-DPC technique achieves markedly superior results in mitigating power fluctuations. This improvement is

clearly visible in the figures, where the power fluctuations are considerably reduced when using F12-DPC compared to C-DPC. This enhanced control over power leads to reduced pressure on the DFIG mechanisms and contributes to more steady and efficient operation of the entire wind energy conversion system.

To provide a more detailed and quantitative assessment of the performance improvements visually observed in Figs. 7 and 8, a comparative analysis of key dynamic and steady-state metrics was conducted. The results, summarized in Table 3, unequivocally demonstrate the advantages of the proposed F12-DPC strategy. The data reveals a remarkable reduction in both active power ripples (by 72.13%) and reactive power ripples (by 72.33%), which directly contributes to reduced mechanical stress on the turbine and improved grid power quality. Furthermore, the dynamic response of the system is significantly enhanced, with the F12-DPC reducing transient overshoot by approximately 75% and improving the response time by up to 31.71%. This faster and more precise response is also reflected in the steady-state error (SSE), which was reduced by nearly 73% for both power components. This comprehensive quantitative improvement is attributed to the F12-DPC's intelligent fuzzy logic core, which replaces the coarse switching of hysteresis comparators with a more nuanced and precise voltage vector selection process, leading to a smoother, faster, and more accurate control response.

The generated (stator) and rotor currents under F12-DPC control exhibit distinct characteristics. Fig. 9a displays the generated currents. The amplitude of these currents increases with generator speed, while the frequency remains at 50 Hz during mode transitions (as shown in the zoomed sections). Fig. 9b compares the current (isa) for both C-DPC and F12-DPC, clearly illustrating the smoother current waveform achieved with F12-DPC. Similarly, Fig. 10a shows the rotor currents observed under F12-DPC control. The amplitude of the rotor current varies with speed, and its frequency is related to the mechanical slip (visible in the zoomed areas). Fig. 10b compares the rotor current ($i_{ra}$) for both control methods, again demonstrating a smoother waveform with F12-DPC.

Figs. 11 and 12 present an analysis of the harmonic content in the generated current (phase A) using Fast Fourier Transform (FFT) across the three operating modes. The analysis discloses that the F12-DPC technique consistently achieves a minor Total Harmonic Distortion (THD) in every operating mode contrasted to the C-DPC method. This outcome indicates that the current waveform produced by the F12-DPC method resembles an ideal sine wave, effectively reducing harmonic
<figure><img src="image_18.png" /><figcaption>Fig. 15. $I_{sa}$ compared to both controls under parameter variations (Rs, Rr + 50%; Ls, Lr -10%); a) Overall, b) Zoomed c) THD by C-DPC approach, d) THD by F12-DPC approach.</figcaption></figure>

currents that can lead to inefficiencies and potential damage in the power grid. Table 4 provides a comprehensive comparison of the C-DPC and F12-DPC methods.

## 6.2. Robustness analysis

To evaluate the robustness of the proposed F12-DPC strategy, parameter variations were introduced in the DFIG model. In particular, the stator and rotor resistances (Rs, Rr) were increased by + 50%, while the stator and rotor inductances (Ls, Lr) were decreased by -10%, while the controller operated without knowledge of these changes. These variations emulate uncertainties and aging effects in machine parameters, which often degrade control performance in conventional methods.

The system's performance under these mismatched conditions was

evaluated over the same variable wind speed profile. The results of this robustness test are presented in Figs. 13 through 16.

As depicted in Figs. 13 and 14, even with significant parameter deviations, the F12-DPC controller continues to demonstrate exceptional performance. Both $P_s$ and $Q_{AC}$ powers precisely track their reference values. Crucially, the controller maintains its superior ability to suppress power ripples, with the F12-DPC waveform remaining significantly smoother than that of the C-DPC. This indicates that the control loop's stability and effectiveness are not compromised by the parameter inaccuracies.

The impact on power quality is further analyzed in Figs. 15 and 16. The stator and rotor current waveforms generated under F12-DPC control remain smooth and exhibit substantially lower ripple compared to the C-DPC.
<figure><img src="image_19.png" /><figcaption>Fig. 16. $i_{ra}$ compared to both controls under parameter variations (Rs, Rr + 50%; Ls, Lr -10%); a) Overall, b) Zoomed.</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>Fig. 17. Wind and DFIG speeds;</figcaption></figure>

The most compelling evidence of robustness is found in the harmonic spectrum analysis in Fig. 15 c and d. Despite the parameter mismatch, the F12-DPC consistently achieves a much lower Total Harmonic Distortion (THD) across all operating modes. For instance, in the super-synchronous mode, the F12-DPC maintains a THD of just 2.04 %, whereas the C-DPC’s THD is 7.05 %. Similarly, in the sub-synchronous mode, F12-DPC achieves a THD of 1.06 % compared to C-DPC’s 4.67 %.

These results powerfully underscore a fundamental advantage of the

F12-DPC’s design. Its reliance on a fuzzy logic inference system, which responds directly to real-time power errors and the rotor flux position, makes it inherently resilient to parametric uncertainties. Unlike model-based controllers that depend on accurate parameter knowledge for optimal performance, the F12-DPC’s decision-making process is adaptive and does not use a rigid mathematical model.

Therefore, this test provides strong empirical evidence that the F12-DPC is not only high-performing under nominal conditions but is also
<figure><img src="image_21.png" /><figcaption>Fig. 18. Power Responses using F12-DPC approach with RT-LAB; a) $P_s$ power and its reference, b) $Q_{AC}$ power and its reference.</figcaption></figure>

highly robust, making it a reliable and practical control solution for real-world DFIG applications where parameter drift is inevitable.

### 6.3. Experimental validation

To experimentally confirm the efficiency of the suggested F12-DPC scheme, a simulation-in-the-loop (SIL) setup is utilized based on the OP4512 and the RT-Lab. Fig. 3 illustrates the experimental test setup employed. The configuration involved a host PC running the RT-Lab software, connected to the OP4512 simulator, which served as the target system for execution.

The OP4512 simulator's real-time implementation successfully demonstrated the performance of the F12-DPC control strategy, as

evidenced by the results presented in Figs. 17 through 22. These figures collectively confirm the approach's performance when operating in a virtualized real-world setting. Fig. 17 displays the wind speed profile and the corresponding behavior of the DFIG mechanical. Fig. 18 effectively demonstrates the F12-DPC's capability to regulate both $P_s$ and $Q_{AC}$ powers, showing accurate tracking of their references.

Figs. 19 and 20 present a comprehensive view of the *i.s* current behavior with the F12-DPC method, illustrating the current responses in each of the different operating modes. Likewise, Figs. 21 and 22 present visions into the rotor current characteristics influenced by the F12-DPC strategy across these same operating modes.

The F12-DPC approach is robustly confirmed by the strong agreement between the experimental results from RTS by OP4512 and the
<figure><img src="image_22.png" /><figcaption>Fig. 19. Response of $i_{sabc}$ by the F12-DPC approach with RT-LAB.</figcaption></figure>

<figure><img src="image_23.png" /><figcaption>Fig. 20. Zoomed $i_{sa}$ by the F12-DPC approach in operating mode: a) Super, b) Sub, c) Synchronous.</figcaption></figure>

MATLAB simulations. This alignment suggests a high chance of successful translation to genuine physical WT-DFIG systems since it shows that the control method operates efficiently and consistently in a

replicated real-world environment.

The improved waveforms observed with F12-DPC are a direct consequence of the fuzzy inference mechanism. By replacing hysteresis
<figure><img src="image_24.png" /><figcaption>Fig. 21. Response of $i_{abc}$ by the F12-DPC approach with RT-LAB.</figcaption></figure>

<figure><img src="image_25.png" /><figcaption>Fig. 22. Zoomed $i_a$ by the F12-DPC approach in operating mode; a) Super, b) Sub, c) Synchronous.</figcaption></figure>

comparators with a rule-based fuzzy logic approach, the voltage vector selection becomes smoother, reducing abrupt switching and, consequently, power ripples. The reduction in THD confirms that the

generated grid currents are closer to sinusoidal, which reduces converter stress and ensures better compliance with grid codes. Furthermore, the alignment of real-time OPAL-RT results with MATLAB/Simulink
simulations indicates that the proposed method is both computationally efficient and practically implementable.

## 7. CONCLUSION

This paper introduces and validates a novel fuzzy logic-based strategy, F12-Direct Power Control (F12-DPC), designed to overcome the limitations of conventional methods and enhance the power quality of wind turbines equipped with doubly fed induction generators. The F12-DPC method was rigorously evaluated through both MATLAB/Simulink simulations and real-time hardware-in-the-loop testing on an OPAL-RT simulator. The results conclusively show that the proposed controller effectively reduces power ripples, provides accurate control of active and locally compensated reactive power, and significantly improves harmonic performance across all operating modes under variable wind speeds when compared to the conventional approach. Crucially, the strong correlation between the simulation and real-time test results confirms the practical feasibility of implementing the F12-DPC on physical wind energy systems. This validates its promise as a robust control solution for improving power quality and grid integration. Future work will explore the development of adaptive fuzzy or neuro-fuzzy approaches to further enhance controller adaptability under highly dynamic wind and grid conditions.

### CRediT authorship contribution statement

**Karim Fathi Sayeh:** Software, Methodology, Investigation, Formal analysis, Conceptualization.
**Salah Tamalouzt:** Visualization, Supervision, Conceptualization.
**Djamel Ziane:** Visualization, Validation, Supervision.
**Nabil Benyahia:** Visualization, Supervision.
**Sofia Lalouni belaid:** Visualization, Supervision.

### Funding

No specific funding was received for this work.

Research Ethics.

This study did not involve human participants or animals. All research procedures complied with ethical standards of the relevant institutional guidelines.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgements

The Nantes Atlantique Electrical Energy Research Institute (IREENA) laboratory at Nantes University, Saint-Nazaire, France, is well appreciated by the authors. They supplied the OPAL-RT (OP 4512) and the RT-LAB, which allowed us to test our proposed control method in RTS.

### Data availability

No data was used for the research described in the article.

### Data availability

No data was used for the research described in the article.

### References

[1] Kluger JM, Haji MN, Slocum AH. The power balancing benefits of wave energy converters in offshore wind-wave farms with energy storage. Appl Energy 2023; 331. https://doi.org/10.1016/j.apenergy.2022.120389.

[2] Muthuraj GS, Balaraman S, Raja P. DFIG-based Wind Energy Conversion System using Matrix Converter under Unbalanced and Harmonic Grid Conditions with Band Pass-FIR Filters. IETE J Res 2021;1-16. https://doi.org/10.1080/03772063.2021.1941331.

[3] Li S, Haskew TA, Williams KA, Swatloski RP. Control of DFIG Wind Turbine with Direct-Current Vector Control Configuration. IEEE Trans Sustainable Energy 2012; 3(1):1-11. https://doi.org/10.1109/tste.2011.2167001.

[4] Tamalouzt S, Ijdarene K, Rekioua T, Abdessemed R. Direct torque control of wind turbine driven doubly fed induction generator. Rev Roum Sci Technol Electrotechnol Energ 2016;61(3):244.

[5] Xu L, Cartwright P. Direct active and Reactive Power Control of DFIG for Wind Energy Generation. IEEE Trans Energy Convers 2006;21(3):750-8. https://doi.org/10.1109/tec.2006.875472.

[6] Sahri Y, Tamalouzt S, Belaid Lalouni S. Enhanced Direct Power Control strategy of a DFIG-Based Wind Energy Conversion System Operating under Random Conditions. Period Polytech Electr Eng Comput Sci 2021;65(3):196-206. https://doi.org/10.3311/PFee.16656.

[7] Zhi D, Xu L. Direct Power Control of DFIG with constant Switching Frequency and improved Transient Performance. IEEE Trans Energy Convers 2007;22(1):110-8. https://doi.org/10.1109/tec.2006.889549.

[8] Massoum S, Meroufel A, Massoum A, Wira P. A direct power control of the doubly-fed induction generator based on the SVM strategy. Elektrotechniski Vestnik 2017; 84(5):235-40.

[9] I. Yaichi, A. Semmah, P. Wira, and S. M. El-Amine, "An improved direct power control based on SVM strategy of the doubly fed induction generator," in 2019 7th International Renewable and Sustainable Energy Conference (IRSEC), 2019: IEEE, pp. 1-8.

[10] Mazouf F, Belkacem S, Colak I, Drid S, Harbouche Y. Adaptive direct power control for double fed induction generator used in wind turbine. Int J Electr Power Energy Syst 2020;114. https://doi.org/10.1016/j.ijepes.2019.105395.

[11] A. A. Z. Diab, "Model predictive direct power control of rotor side converter for DFIGs driven by variable speed wind turbines," in 2018 25th International Workshop on Electric Drives: Optimization in Control of Electric Drives (IWED), 2018: IEEE, pp. 1-6.

[12] F. S. Guedes, N. Rocha, A. M. Maciel, and A. J. S squarei Filho, "A Simple and Powerful Model Predictive Direct Power Control for DFIG," presented at the 2021 Brazilian Power Electronics Conference (COBEP), 2021.

[13] Yang X, Liu G, Li A, Dai LV. A Predictive Power Control Strategy for DFIGs based on a Wind Energy Converter System. Energies 2017;10:8. https://doi.org/10.3390/en10081098.

[14] Benzouaoui A, Khouidmi H, Bessedik B. Parallel model predictive direct power control of DFIG for wind energy conversion. Int J Electr Power Energy Syst 2021; 125. https://doi.org/10.1016/j.ijepes.2020.106453.

[15] Z. Di, W. Yanjun, Z. Jinlong, and Q. Hanhong, "A Novel Predictive Direct Power Control of Doubly Fed Induction Generator based on ADRC method," in 2019 22nd International Conference on Electrical Machines and Systems (ICEMS), 2019: IEEE, pp. 1-4.

[16] A. Daoud and N. Derbel, Direct power control of DFIG using sliding mode control approach, Modeling, Identification and Control Methods in Renewable Energy Systems, pp. (193-204), 2019.

[17] Djeriri Y, Wira P, Semmah A, Yaichi I. Super-twisting Sliding Mode Control of a Doubly-fed Induction Generator based on the SVM Strategy. Periodica Polytechnica Electrical Engineering and Computer Science 2019;63(3):178-90. https://doi.org/10.3311/PFee.13726.

[18] Mazen Alhato M, Bouallegue S, Rezk H. Modeling and Performance Improvement of Direct Power Control of Doubly-Fed Induction Generator based Wind Turbine through Second-Order Sliding Mode Control Approach. Mathematics 2020;8(11). https://doi.org/10.3390/math8112012.

[19] F. Mazouz, S. Belkacem, and G. Boukhalfa, "Second Order Sliding Mode Control Based DPC of DFIG Using SVM," in Artificial Intelligence and Heuristics for Smart Energy Efficiency in Smart Cities, (Lecture Notes in Networks and Systems, 2022, ch. Chapter 75, pp. 743-750.

[20] A. Shah and A. Mehta, Sliding Mode Direct Power Control of a Grid-Connected DFIG Using an Extended State Observer, Emerging Trends in Sliding Mode Control: Theory and Application, pp. (325-349), 2021.

[21] F. Mazouz, S. Belkacem, G. Boukhalfa, and I. Colak, "Backstepping Approach Based on Direct Power Control of a DFIG in WECS," presented at the 2021 10th International Conference on Renewable Energy Research and Application (ICRERA), 2021.

[22] Mensou S, Essadki A, Nasser T, Bououlid Idrissi B. A direct power control of a DFIG based-WECS during symmetrical voltage dips. Protect Control Mod Power Syst 2020;5:1. https://doi.org/10.1186/s41601-019-0148-y.

[23] Sayeh KF, Tamalouzt S, Sahri Y. Improvement of power quality in WT-DFIG systems using novel direct power control based on fuzzy logic control under randomness conditions. Int J Model Simul 2023;1-13. https://doi.org/10.1080/02286203.2023.2270757.

[24] Sayeh KF, Tamalouzt S, Ziane D, Deffal B, Lalouni Belaid S, Belkhier Y, et al. Fuzzy Logic-Enhanced Direct Power Control for Wind Turbines with Doubly Fed Induction Generators. Results Eng 2024;24. https://doi.org/10.1016/j.rineng.2024.103557.

[25] Heydari E, Rafiee M, Pichan M. Fuzzy-genetic algorithm-based direct power control strategy for DFIG. Iran J Electr Electron Eng 2018;14(4):353-61.

[26] S. Khateri-Abri, S. Tohidi, and N. Rostami, "Improved Direct Power Control of DFIG Wind Turbine by using a Fuzzy Logic Controller," in 2019 10th International Power Electronics, Drive Systems and Technologies Conference (PEDSTC), 2019: IEEE, pp. 458-463.
[27] Tamalouzt S. Performances of direct reactive power control technique applied to three level-inverter under random behavior of wind speed. Rev Roum Sci Technol Electrotechnol Energ 2019;64(1):33-8.

[28] Tamalouzt S, Belkhier Y, Sahri Y, Bajaj M, Ullah N, Chowdhury MS, et al. Enhanced Direct Reactive Power Control-based Multi-Level Inverter for DFIG Wind System under Variable Speeds. Sustainability 2021;13(16). https://doi.org/10.3390/su13169060.

[29] Sayeh KF, Tamalouzt S, Ziane D, Bekhiti A, Belkhier Y, Oyedepo SO. Utilizing Fuzzy Logic Control and Neural Networks based on Artificial Intelligence Techniques to Improve Power Quality in Doubly Fed Induction Generator-Based Wind Turbine System. Int J Energy Res 2025;2025(1). https://doi.org/10.1155/er/5985904.

[30] Benbouhenni H, Boudjema Z, Belaidi A. Power Control of DFIG in WECS using DPC and NDPC-NPWM Methods. Math Modell Eng Probl 2020;7(2):223-36. https://doi.org/10.18280/mmep.070208.

[31] Habib B. Robust Direct Power Control of a DFIG Fed by a Five-Level NPC Inverter using Neural SVPWM Technique. Tecnica Italiana-Italian J Eng Sci 2021;65(1): 119-28. https://doi.org/10.18280/ti-ijes.650118.

[32] Benbouhenni H, Boudjema Z, Belaidi A. Direct power control with NSTSM algorithm for DFIG using SVPWM technique. Iran J Electr Electron Eng 2021;17(1): 1-11.

[33] Yaichi I, Semmah A, Wira P. Neuro-second order sliding mode control of a DFIG based wind turbine system. J Electr Electron Eng 2020;13(1):63-8.

[34] Sahri Y, Tamalouzt S, Hamoudi F, Lalouni Belaid S, Bajaj M, Alharthi MM, et al. New intelligent direct power control of DFIG-based wind conversion system by using machine learning under variations of all operating and compensation modes. Energy Rep 2021;7:6394-412.

[35] Benbouhenni H. Twelve Sectors DPC Control based on Neural Hysteresis Comparators of the DFIG Integrated to Wind Power. Tecnica Italiana-Italian J Eng Sci 2020;64(2-4):347-53. https://doi.org/10.18280/ti-ijes.642-433.

[36] Sayeh KF, Tamalouzt S, Sahri Y, Lalouni Belaid S, Bekhiti A. Artificial intelligence-based direct power control for power quality improvement in a WT-DFIG system via neural networks: Prediction and classification techniques. J Franklin Inst 2025; 362(1). https://doi.org/10.1016/j.jfranklin.2024.107401.

[37] El Zerk A, Ouassaid M. Real-Time Fuzzy Logic based Energy Management System for Microgrid using Hardware in the Loop. Energies 2023;16(5). https://doi.org/10.3390/en16052244.

[38] Kumar P, Kashyap Y, Castelino RV, Karthikeyan A, M. S. K., Karmakar D, et al. Laboratory-Scale Airborne Wind Energy Conversion Emulator using OPAL-RT Real-Time Simulator. Energies 2023;16(19). https://doi.org/10.3390/en16196804.

[39] Tamalouzt S, Benyahia N, Rekioua T, Rekioua D, Abdessemed R. Performances analysis of WT-DFIG with PV and fuel cell hybrid power sources system associated with hydrogen storage hybrid energy system. Int J Hydrogen Energy 2016;41(45): 21006-21.

[40] S. Tamalouzt, T. Rekioua, and R. Abdessemed, "Direct torque and reactive power control of grid connected doubly fed induction generator for the wind energy conversion," in 2014 International conference on electrical sciences and technologies in Maghreb (CISTEM), 2014: IEEE, pp. 1-7.

[41] Roy B, Adhikari S, Datta S, Lalngaihawma S, Samanta S. Real-Time simulation of a Wind-Solar-Battery based Microgrid System. J Electr Eng Technol 2022;18(3): 2087-102. https://doi.org/10.1007/s42835-022-01292-z.

[42] Zouggar EO, Chaouch S, Abdelhamid L, Abdeslam DO. Real-Time Implementation of the MPPT Control Algorithms of a Wind Energy Conversion System by the Digital Simulator OPAL_RT. Eur J Electr Eng 2021;23(1):45-52. https://doi.org/10.18280/ejee.230106.