Hybrid ANFIS-PI-Based Optimization for Improved Power Conversion in DFIG Wind Turbine

Abstract

Wind energy is essential for promoting sustainability and renewable power solutions. However, ensuring stability and consistent performance in DFIG-based wind turbine systems (WTSs) remains challenging due to rapid wind speed variations, grid disturbances, and parameter uncertainties. These fluctuations result in power instability, increased overshoot, and prolonged settling times, negatively impacting grid compliance and system efficiency. Conventional proportional-integral (PI) controllers are simple and effective in steady-state conditions, but they lack adaptability in dynamic situations. Similarly, artificial intelligence (AI)-based controllers, such as fuzzy logic controllers (FLCs) and artificial neural networks (ANNs), improve adaptability but suffer from high computational demands and training complexity. To address these limitations, this paper presents a hybrid adaptive neuro-fuzzy inference system (ANFIS)-PI controller for DFIG-based WTS. The proposed controller integrates fuzzy logic adaptability with neural network-based learning, allowing real-time optimization of control parameters. Implemented within the rotor-side converter (RSC) and grid-side converter (GSC), ANFIS enhances reactive power management, grid compliance, and overall system stability. The system was tested under a step wind speed signal varying from 10 m/s to 12 m/s to evaluate its robustness. The simulation results confirmed that the ANFIS-PI controller significantly improved performance compared with the conventional PI controller. Specifically, it reduced rotor speed overshoot by 3%, torque overshoot by 12.5%, active power overshoot by 2%, and DC link voltage overshoot by 20%. Additionally, the ANFIS-PI controller shortened settling time by 50% for rotor speed, by 25% for torque, by 33% for active power, and by 16.7% for DC link voltage, ensuring faster stabilization, enhanced dynamic response, and greater efficiency. These improvements establish the ANFIS-PI controller as an advanced, computationally efficient, and scalable solution for enhancing the reliability of DFIG-based WTS, facilitating seamless integration of wind energy into modern power grids.

1. Introduction

1.1. Research Background

Wind power has emerged as a key contributor to sustainable electricity generation, driven by the rising demand for eco-friendly energy solutions. Recognized for its availability and accessibility and as a sustainable substitute for non-renewable fuels, wind energy plays a significant role in lowering greenhouse gas emissions and combating environmental change. As of 2024, global wind energy capacity surpassed 117 GW [1], highlighting its growing significance in the energy sector. This capacity will expand further as nations pursue ambitious climate and renewable energy targets. Electricity is generated from wind energy using the wind turbine system (WTS), which operates through three fundamental stages: aerodynamic, mechanical, and electrical. Each stage is essential for the efficient conversion of wind energy into electricity.

• Aerodynamic stage: This stage captures the wind’s dynamic energy and converts it into rotational motion through turbine blades. The blades are aerodynamically optimized to maximize power extraction under different atmospheric conditions.
• Mechanical stage: The rotational energy is transmitted through a gear mechanism that optimizes speed for generator efficiency.
• Electrical stage: The generated energy is converted and conditioned for grid integration using advanced power electronic components, including AC–DC–AC converters and filters.

The most widely used generators for wind turbines with variable-speed operation employ doubly fed induction generators (DFIGs), permanent magnet synchronous generators (PMGSs), and synchronous machines with wound rotors [2]. Among the various generator technologies available for variable-speed wind turbines, the doubly fed induction generator (DFIG) is a preferred choice for its efficiency, versatility, and economic feasibility.

The DFIG offers several advantages over other generator types:

• It can regulate real and reactive power, improving grid compatibility and electrical performance.
• It minimizes mechanical load on turbine parts, prolonging their lifespan.
• Its partial-scale power electronic converter design allows operation over a broad range of wind speeds, making it suitable for regions with moderate wind conditions.
• It provides a cost-effective balance between performance and production costs compared with other advanced generator systems [3].

The DFIG system operates using two power electronic converters:

• The rotor-side converter (RSC) controls the rotor current and manages reactive power.
• The grid-side converter (GSC) maintains the DC link voltage stability and ensures compliance with grid requirements [4].

Despite its advantages, wind energy conversion faces challenges due to wind’s inherently variable nature, which affects the stability, efficiency, and reliability of power generation [5].

1.2. Motivation for the Research

DFIG-based WTSs are preferred for renewable energy due to their efficiency, cost-effectiveness, and power regulation capabilities. However, wind speed variability causes voltage fluctuations, frequency instability, and power quality issues, impacting grid reliability. While simple and effective in steady-state conditions, traditional PI controllers lack adaptability under dynamic changes. AI-driven controllers, such as fuzzy logic controllers (FLCs) and artificial neural networks (ANNs), offer improved adaptability but have limitations—FLCs require expert-defined rules, while ANNs demand extensive training data. To overcome these challenges, a hybrid intelligent control strategy integrating fuzzy reasoning with artificial neural adaptability is needed to improve dynamic response, stability, and real-time adaptability while maintaining computational efficiency.

1.3. Literature Review

Effective control of WTSs is essential for maximizing power extraction and maintaining grid reliability. Traditional PI (proportional-integral) regulators have historically been the primary choice for managing DFIG systems. PI controllers are praised for their simplicity, cost-effectiveness, and ability to eliminate steady-state deviations in controlled environments. These controllers rely on fixed tuning parameters to regulate system dynamics, making them relatively easy to implement and widely adopted in industrial applications [6,7,8,9]. However, the reliance on fixed parameters also serves as their primary limitation. In dynamic operating environments, such as those experienced in wind energy systems, fixed-parameter PI controllers struggle to adapt to external disturbances, grid variability, and fluctuating wind speeds. This can lead to overshoot, instability, and prolonged settling times, undermining the efficiency and dependability of the system. To overcome these limitations of conventional PI controllers in DFIG-driven wind turbine systems (WTSs), meta-heuristic optimization techniques have been applied for automatic calibration and adaptive tuning, enhancing system output response and robustness. These methods include the jellyfish search algorithm (JSA), beetle antennae search (BAS), ant colony optimization (ACO) [10], thermal exchange optimization (TEO), grasshopper optimization algorithm (GOA), water cycle algorithm (WCA) [11], cuckoo search algorithm (CS), dragonfly algorithm (DA), modified flower pollination algorithm (MFPA) [12], hunger games search (HGS), grey wolf optimizer (GWO), artificial bee colony (ABC), hybrid meta-heuristics [13], whale optimization algorithm (WOA), hawks optimization (HHO) [14], bat algorithm (BA), squirrel search algorithm (SSA) [15], and artificial fish-swarm algorithm (AFSA) [16]. Despite numerous advantages, meta-heuristic techniques have notable drawbacks. They often involve high computational costs due to iterative processes and complex algorithms, limiting real-time applicability in WTSs. Additionally, these methods may require extensive parameter tuning and initialization, and their performance can sometimes depend on problem-specific customization. In some cases, convergence to global optima is not guaranteed, and there is a risk of premature convergence, especially in dynamic and nonlinear systems like DFIG-based WTSs [17,18].

To further address these challenges, fuzzy logic controllers (FLCs) have gained popularity. Fuzzy logic controllers (FLCs) are increasingly utilized in DFIG-based wind turbine systems for their ability to handle nonlinearities and uncertainties without requiring exact mathematical models. Their rule-based decision-making enables adaptability to dynamic operating conditions, enhancing system stability and control precision. However, their performance depends on carefully designing membership functions and rules, which can be subjective and demand expert knowledge. Studies highlight their superior responsiveness and disturbance rejection compared with conventional PI [19]. Fuzzy logic-based control strategies have been extensively utilized in wind energy systems, particularly in DFIG-based systems, due to their ability to handle uncertainties and nonlinearities without requiring precise mathematical models. However, when compared with artificial neural networks (ANNs), fuzzy controllers present several limitations. One significant drawback is that FLCs heavily rely on expert knowledge to design membership functions and define rules, which can be subjective and time-consuming. Additionally, fuzzy controllers are typically less adaptive to changing dynamic conditions when compared with ANNs, which can learn and adjust their parameters based on real-time data through training.

ANNs, on the other hand, excel in handling large and complex datasets, can generalize well, and can adapt continuously to variations in operating conditions. Their learning capabilities make them more robust in optimizing the control of dynamic systems, such as DFIG-based wind power systems, under varying environmental and operational conditions. Moreover, ANNs can avoid the need for predefined rules, which can make them more flexible and scalable than fuzzy controllers in systems with uncertain or complex behavior [20]. However, while ANNs have these advantages, they come with challenges. They require substantial data for training and may be computationally intensive, especially when deployed in real-time applications. Furthermore, the training process can be lengthy, resulting in model overfitting if not adequately controlled. Neural networks contribute dynamic learning and adaptability, allowing for self-tuning capabilities in changing environments. Still, they demand significant training data and computational power, and their “black-box” nature can complicate interpretability [21]. Recent advancements in intelligent control techniques for DFIG-based WTSs have focused on improving power quality, grid compliance, and system efficiency. Researchers in [22] proposed a fuzzy logic-based neural network controller for power quality enhancement but required large datasets for training, leading to high computational overhead. The proposed ANFIS-PI controller minimizes the need for extensive training data while ensuring superior adaptability. The authors in [23] developed a direct power control method using fuzzy logic, achieving grid stability but encountering longer response times. The ANFIS-PI approach reduces settling time by 25%, ensuring faster and smoother responses. Furthermore, the authors of [24] implemented a model predictive direct torque control (MP-DTC) algorithm, which improved torque precision but suffered from high computational demand. The literature summary cited in

Table 1. Summary of the latest literature review on meta-heuristic techniques.

S#	Ref.	Control Technique Applied	Parameters Applied	Signal Applied	Merits	Demerits
1	[19]	PI controller	DC link voltage, wind turbine speed	Variable wind speed	Simple implementation, eliminates steady-state errors	Sudden overshoot, longer settling time
2	[3,4]	Particle swarm optimization (PSO)	Stator current, DC link voltage, active/reactive powers	Short circuit faults, variable wind speed	Enhances performance under faults, provides pitch angle regulation	High settling time, DC voltage instability under fluctuations
3	[5,6]	Genetic algorithm (GA)	Active/reactive powers	Rotor resistance variation	Smooth, reliable performance under variations	Difficulty in stopping criteria
4	[10]	Jellyfish search algorithm (JSA)	Power regulation parameters	Grid variations	Enhances stability, intense global search	High computational complexity
5	[11]	Grasshopper optimization algorithm (GOA)	DC link voltage, power factors	Grid variations	Fast execution, adaptive capabilities	Poor exploitation ability
6	[12]	Cuckoo search algorithm (CS)	Frequency and voltage control	Grid fluctuations	Strong global search ability	May get stuck in local optima
7	[13]	Grey wolf optimizer (GWO)	Power system stabilization	Grid disturbances	Adaptive behavior	Sensitive to initialization parameters
8	[14]	Whale optimization algorithm (WOA)	Reactive power optimization	Variable wind speed	Effective in multi-objective problems	Slower convergence
9	[15]	Bat algorithm (BA)	Stator and rotor control	Variable wind speed	Good exploration ability	High dependency on parameter tuning
10	[16]	Artificial fish-swarm algorithm (AFSA)	Grid synchronization parameters	Variable wind speed	Strong global optimization	Computational complexity
11	[22]	Fuzzy logic-based neural network	Power quality parameters	Grid disturbances	Handles nonlinearities, improves stability	Requires large datasets
12	[23]	Direct power control using fuzzy logic	Power control variables	Grid disturbances	Ensures grid stability	Longer response times
13	[24]	Model predictive direct torque control (MP-DTC)	Torque and flux parameters	Dynamic grid Variations	Improved torque precision	High computational demand
14	Proposed	Hybrid ANFIS-PI controller	RSC and GSC control parameters	Grid Variations	Superior adaptability with fuzzy learning and neural network-based optimization, reducing overshoot by 20% and improving settling time by 50%	Minimizes need for large datasets while maintaining real-time computational feasibility

concludes that the hybrid ANFIS-PI controller surpasses traditional PI controllers by significantly reducing overshoot, improving settling time, and enhancing dynamic adaptability.

Compared with meta-heuristic techniques, it provides a balanced trade-off between real-time adaptability and computational efficiency. Unlike purely heuristic methods, which often face convergence and tuning challenges, the hybrid ANFIS-PI controller integrates fuzzy logic adaptability with neural learning for superior robustness in dynamic wind energy systems.

1.4. Problem Statement

Despite advancements in PI, AI, and predictive control techniques, existing methods have significant limitations in real-time adaptability, computational efficiency, and stability under dynamic wind conditions. Conventional PI controllers fail to handle rapid wind fluctuations, while AI-driven methods often demand excessive computational resources. There is a need for a hybrid intelligent control system that balances adaptability, computational feasibility, and system robustness.

1.5. Aim of the Research

This research aimed to develop a hybrid ANFIS-PI controller that integrated fuzzy logic-based inference with neural network adaptability. The goal was to optimize DFIG-based WTS operations by improving real-time adaptability, reducing computational overhead, and ensuring stable power generation.

1.6. Objectives of the Research

The primary objectives of this research were as follows:

• Develop a hybrid ANFIS-PI controller to enhance power stability and grid compliance in DFIG-based WTSs.
• Reduce overshoot and improve settling time, ensuring better dynamic response under fluctuating wind speeds.
• Optimize RSC and GSC simultaneously, unlike previous works focusing on only one converter.
• Validate system performance by comparing it with conventional PI controllers and existing AI-based techniques.

1.7. Contribution

The significant contributions of this research are as follows:

• Introduction of a novel hybrid ANFIS-PI controller, integrating fuzzy reasoning adaptability with neuro-computational learning.
• Dual converter optimization, enhancing both RSC and GSC control mechanisms, ensuring improved power stability and grid compliance.
• Reduction in computational complexity, minimizing the need for large training datasets while maintaining superior real-time adaptability.
• Validated performance improvements, demonstrating lower overshoot (20%) and improved settling time (50%) over traditional PI controllers.

1.8. Novelty and Advantages of the Proposed Method

• Hybrid control approach: The research introduced a novel adaptive neuro-fuzzy inference system (ANFIS)-PI hybrid controller for the rotor-side converter (RSC) and grid-side converter (GSC) in a doubly fed induction generator (DFIG)-based wind turbine system (WTS). Unlike traditional fixed-parameter controllers, this hybrid structure combined fuzzy logic inference with neural network adaptability, allowing dynamic parameter tuning.
• Improved system adaptability: Unlike conventional proportional-integral (PI) controllers, which struggle with real-time adaptation to fluctuating wind speeds and grid disturbances, the ANFIS-based controller dynamically learned from operational conditions and adjusted the control parameters accordingly.
• Optimized computational efficiency: The model achieved lower training errors (~0.034) in just 25 training epochs, compared with the conventional AI-based controllers requiring double the dataset size and 50 epochs for similar results. This highlights superior computational efficiency without compromising accuracy.
• Dual-converter optimization: Most previous studies optimized the RSC or the GSC. This research enhanced both converters, ensuring improved rotor current regulation, DC link voltage stability, and active/reactive power management for grid compliance.
• Real-time feasibility: Unlike meta-heuristic algorithms (such as genetic algorithms, particle swarm optimization, and ant colony optimization), which are computationally expensive and may suffer from slow convergence, ANFIS ensures fast and adaptive control decisions, making real-time applications more feasible.

The proposed hybrid ANFIS-PI controller represents a DFIG-based wind turbine control breakthrough by combining AI-driven adaptability with classical control robustness. Its ability to reduce overshoot, enhance stability, minimize computational overhead, and improve grid compliance makes it a superior alternative to conventional PI and AI-based controllers.

The layout of this paper is structured as follows: Section 2 offers an overview of the system configuration and presents detailed mathematical modeling of its components. Section 3 discusses the development framework of the proposed ANFIS controller, highlighting its integration into the wind turbine system. Section 4 demonstrates the simulation outcomes, offering a comparative analysis of the proposed controller’s performance against conventional PI controllers and other advanced methods. Last, Section 5 concludes the paper by outlining the significant insights and contributions and suggesting possible directions for future research.

2. Proposed System Configuration and Modeling of WTS Components

The configuration and modeling of the hybrid ANFIS-PI controller, integrated within MATLAB R2023b/Simulation, along with various components of a horizontal axis wind turbine (HAWT) and double-fed induction generator (DFIG), are described as follows.

2.1. System Configuration

The wind turbine system is essential in driving the transition toward sustainable energy solutions, offering a clean alternative to fossil fuels. Through advanced mechanical and electrical techniques, WTSs harness wind energy to generate electricity efficiently and reliably [25]. These systems integrate aerodynamic modeling, advanced power converters, and grid connection strategies to maximize energy output and ensure stable operation. The designed system featured a variable-speed, direct-drive wind turbine with a power rating of 1.5 MW. It employed a doubly fed induction generator (DFIG). The DFIG model was designed in Simulink with parameter ratings as depicted in

Table 2. Parameters of DFIG-based wind turbine.

Notation	Parameter	Magnitude and Unit
P	Nominal power	1.5 MVA
V	Nominal L-L voltage	575
F	Grid frequency	60
p	No. of pole pairs	40
$V_{dc}$	DC link voltage	1.15 KV
$\mathbb{L}$	Line inductance	0.31 pu
$\mathcal{R}$	Line resistance	0.0032 pu

[26].

Figure 1 illustrates a DFIG-based wind turbine system (WTS) integrated with the grid. In this configuration, the stator is directly connected to the grid for direct power injection. At the same time, the rotor is linked to the grid via a power electronic converter, allowing variable-speed operation and bidirectional power flow, enhancing efficiency. The back-to-back power converter system includes the rotor-side converter (RSC), which regulates rotor currents and controls generator speed, and the grid-side converter (GSC), which maintains a constant DC link voltage and ensures smooth, stable power injection into the grid [27]. This paper employed a hybrid controller to enhance the control effectiveness of these B2B converters integrated within WECS.

2.2. Mathematical Representation of Wind Turbine

A turbine was created in the last century to transform aerodynamic power into electrical power. The wind’s kinetic energy is transformed into rotational energy to drive an electric generator. Although wind turbines can have two or three blades, three-bladed wind turbines are the most widely utilized on land and water. Equations can express the power output and rotational force exerted by a wind turbine. The mechanical power ($P_m$) generated by the wind turbine is represented by Equation (1).

$$P_m={\displaystyle \frac{1}{2}}\rho \pi {\mathcal{R}}^2{V}^3{\mathcal{C}}_p(\lambda ,\beta )$$

(1)

Here, $\rho$ denotes the atmospheric density in kg/m³, while $A$ signifies the rotor-swept region of the wind turbine blades; this swept area is equivalent to π${\mathcal{R}}^2$, where $\mathcal{R}$ denotes wind rotor radius, $V$ stands for the wind speed, and $\mathcal{C}$_p stands for the power coefficient of WT, and it is a function of $\lambda$ and $\beta$ as given in Equations (2) and (3). Here, β represents the blade pitch angle in degrees, which impacts the aerodynamic efficiency of the wind turbine and affects the power coefficient, whereas $\lambda$ is described by Equation (4).

$${\mathcal{C}}_p=f(\lambda ,\beta )$$

(2)

$${\mathcal{C}}_p={\mathcal{C}}_1({\displaystyle \frac{{\mathcal{C}}_2}{{\lambda }_i}}{-\mathcal{C}}_3\beta -{\mathcal{C}}_4)e^{-({\displaystyle \frac{\mathcal{C}5}{{\lambda }_i}})}+{\mathcal{C}}_6{\lambda }_i$$

(3)

Here, (${\displaystyle \frac{1}{{\lambda }_i}}$) = (${\displaystyle \frac{1}{\lambda }}+0.008\beta )-({\displaystyle \frac{0.035}{{\beta }^3}}+1)$, with empirical constants [28], while ${\mathcal{C}}_p$ depends on $V_{wind}$ and the rotational speed of the shaft ${\omega }_t$. This characteristic of the wind turbine can be depicted through the ${\mathcal{C}}_p$ curves presented in Figure 2.

$$\lambda ={\displaystyle \frac{{\omega }_t{\mathcal{R}}_T}{V_{wind}}}$$

(4)

Since the shaft of WT and the generator are directly connected, there is just one state variable in the system. The mechanical equation for the wind turbine is represented as

$$\mathrm{J}{\displaystyle \frac{{\mathrm{d}\mathsf{\omega }}_{\mathrm{m}}}{\mathrm{d}\mathrm{t}}}={\mathrm{T}}_{\mathrm{m}}-{\mathrm{T}}_{\mathrm{g}\mathrm{e}\mathrm{n}}-{\mathrm{B}}_{{\mathsf{\omega }}_{\mathrm{m}}}$$

(5)

Here, $\mathrm{J}$ represents the total moment of inertia in kilogram-square meters (kg ${\mathrm{m}}^2$) for the WT and generator. $T_m$ denotes the mechanical torque, $T_{gen}$ represents the electromagnetic torque, and the coefficient of viscous friction is defined as B and measured in kilogram-square meters per second (kg ${\mathrm{m}}^2$/s), which can be neglected in the case of small-scale WTs. Finally, ${\omega }_m$ represents the mechanical rotor speed. In this model, a 1.5 MW WT is connected with a DFIG that supplies alternating current (AC) power to the grid.

The mechanical power from WT can be controlled in the specified operating range of wind speed. The operating regions of WTS are classified into four regions [30] as shown in Figure 3. The WT operating range begins from cut-in speed to cut-out speed. The WTS does not produce any power in regions 1 and 4 because in region 1 the wind speed is too low for the turbine to generate power, while region 4 is the period of too-high wind speed, where the power of the wind is so high that it could be harmful to the turbine, so the turbine shuts down.

In region 2, the wind is needed such that the power output Cp is maximized for each wind speed. Meanwhile, in region 3, the WTS achieves its peak power generation capacity due to high wind speeds. This shows that the turbine has reached its maximum output capacity and cannot produce additional power, regardless of any further increase in wind speed. The power output becomes limited by the design capabilities of the turbine itself, not by the wind availability [31]. Therefore, it is evident that regions 2 and region 3 are extremely important. In these two regions, robust, rigorous, stable, fast, and accurate controllers are required for smooth and efficient operation of WTS.

2.3. Mathematical Model of DFIG

The DFIG consists of stator and rotor windings and slip rings. The stator has three-phase insulated windings linked to the grid via a three-phase transformer. Similarly, the rotor contains three-phase insulated windings, mirroring the design of the stator. A system of slip rings and brushes establishes a connection between the rotor windings and an external stationary circuit. These components allow for either injection into or absorption from the rotor windings of the control rotor current [32]. The dynamic model of the DFIG is represented using direct and inverse transformations. By applying space vector theory, the three-phase windings of the stator and rotor can be simplified into two equivalent windings: the stationary ab reference frame for the stator and the rotating dq reference frame for the rotor. The voltage vectors for both the stator and rotor are formulated as follows:

$$\overrightarrow{{\mathcal{u}}_{\mathcal{s}}}⟹\left\{\begin{array}{c}{\mathcal{u}}_{ds}={\mathcal{R}}_s{i}_{ds}+{\displaystyle \frac{d\psi ds}{dt}}-{\omega }_s\psi qs\\ {\mathcal{u}}_{qs}={\mathcal{R}}_s{i}_{qs}+{\displaystyle \frac{d\psi qs}{dt}}+{\omega }_s\psi ds\end{array}\right.$$

(6)

$$\overrightarrow{{\mathcal{u}}_{\mathrm{r}}}⟹\left\{\begin{array}{c}{\mathcal{u}}_{dr}={\mathcal{R}}_r{i}_{dr}+{\displaystyle \frac{d\psi dr}{dt}}-{\omega }_r\psi qr\\ {\mathcal{u}}_{qr}={\mathcal{R}}_r{i}_{qr}+{\displaystyle \frac{d\psi qr}{dt}}+{\omega }_r\psi dr\end{array}\right.$$

(7)

where ${\mathcal{u}}_{ds}$,${\mathcal{u}}_{qs}$,${\mathcal{u}}_{dr}$, and ${\mathcal{u}}_{qr}$ are the stator and rotor voltages and are represented in the reference frame of dq. Similarly, $i_{ds}$, $i_{qs}$, $i_{dr}$, and $i_{qr}$ denote the stator and rotor currents in the dq frame. ${\mathcal{R}}_r$, ${\mathcal{R}}_s$, ${\omega }_s$, and ${\omega }_r$ correspond to the stator and rotor phase resistances and angular velocities, respectively. Based on Equations (6) and (7), the equivalent dq electric circuit is illustrated in Figure 4.

The stator and rotor flux vectors are represented in Equations (8) and (9), respectively:

$$\overrightarrow{{\psi }_{\mathcal{s}}}⟹\left\{\begin{array}{c}{\psi }_{ds}={\mathbb{L}}_s{i}_{ds}+{\mathbb{L}}_m{i}_{dr}\\ {\psi }_{qs}={\mathbb{L}}_s{i}_{qs}+{\mathbb{L}}_m{i}_{qr}\end{array}\right.$$

(8)

$$\overrightarrow{{\psi }_{\mathrm{r}}}⟹\left\{\begin{array}{c}{\psi }_{dr}={\mathbb{L}}_m{i}_{ds}+{\mathbb{L}}_r{i}_{dr}\\ {\psi }_{qr}={\mathbb{L}}_m{i}_{qs}+{\mathbb{L}}_r{i}_{qr}\end{array}\right.$$

(9)

where $\overrightarrow{{\psi }_{\mathcal{s}}}\mathrm{a}\mathrm{n}\mathrm{d}\overrightarrow{{\psi }_{\mathrm{r}}}$ represent the flux vectors of the stator and rotor, respectively. ${\psi }_{ds}$ and ${\psi }_{qs}$ denote the flux components along the d–q axis of the stator, while ${\psi }_{dr}$ and ${\psi }_{qr}$correspond to the flux components along the d–q axis of the rotor. ${\mathbb{L}}_s$ and ${\mathbb{L}}_r$ represent the leakage inductances in the stator and rotor phases; ${\mathbb{L}}_m$ is the mutual inductance between the stator and the rotor; and p is the generator pole pair count [33].

The mathematical formulation of electromagnetic torque is given in the following equation:

$$T_{em}-{\displaystyle \frac{3}{2}}p{\displaystyle \frac{{\mathbb{L}}_m}{{\mathbb{L}}_s}}{(\psi }_{qs}{i}_{dr}-{\psi }_{ds}{i}_{qr})$$

(10)

The equations for active and reactive power in the stator and rotor are presented in Equations (11) and (12), respectively:

$$P_s={\displaystyle \frac{3}{2}}({\mathcal{u}}_{ds}{i}_{ds}+{\mathcal{u}}_{qs}{i}_{qs})$$

(11)

$$Q_s={\displaystyle \frac{3}{2}}({\mathcal{u}}_{qs}{i}_{ds}+{\mathcal{u}}_{ds}{i}_{qs})$$

$$P_r={\displaystyle \frac{3}{2}}({\mathcal{u}}_{dr}{i}_{dr}+{\mathcal{u}}_{qr}{i}_{qr})$$

(12)

$$Q_r={\displaystyle \frac{3}{2}}({\mathcal{u}}_{qr}{i}_{dr}+{\mathcal{u}}_{dr}{i}_{qr})$$

Here, $P_s$ and $Q_s$ represent the stator’s active and reactive power, respectively, while $P_r$ and $Q_r$ denote the rotor’s active and reactive power. $T_{em}$ refers to the electromagnetic torque.

The fundamental torque equation is provided in Equation (13):

$$T_{em}-T_{load}=J{\displaystyle \frac{d{\omega }_m}{dt}}$$

(13)

where $J$ represents the rotor’s inertia, $T_{load}$ denotes the load torque applied to the shaft, and ${\omega }_m$ refers to the rotor speed [34].

3. Proposed Hybrid ANFIS-PI Controller

ANFIS demonstrates exceptional efficiency in modeling complex and nonlinear systems, even with limited input and output training data. It surpasses other artificial intelligent control strategies like fuzzy logic controllers and artificial neural networks (ANNs) due to its hybrid structure. By combining the strengths of fuzzy inference systems (FISs) and ANNs into a unified model, ANFIS ensures faster convergence and is particularly suitable for modeling complex and unpredictable systems without relying on fully precise mathematical formulations. The ANFIS technique leverages system data and formulates rules directly from the data using ANN methods. To enhance system performance by minimizing overshoot and improving settling time, ANFIS was implemented in the wind turbine (WT) model, and its performance was evaluated in MATLAB/Simulink, using percentage overshoot and settling time as key metrics. The robustness of the ANFIS-based model was then compared with a conventional PI-based model.

ANFIS is an advanced intelligent control system built on the Takagi–Sugeno fuzzy inference framework. It integrates fuzzy logic concepts with neural network methodologies to form a hybrid model capable of learning and adapting to varying conditions. Using fuzzy logic rules, ANFIS generates input variables, which are then processed by a neural network to produce the corresponding control output. This capability allows it to learn from system data and progressively enhance its performance. Unlike the PI controller, ANFIS excels in managing dynamic system behavior and addressing nonlinearities, resulting in superior control outcomes. The ANFIS structure is composed of five core layers, as illustrated in Figure 5.

The initial layer, referred to as the input layer, allocates membership degrees to input data by mapping it into membership functions (MFs). In ANFIS, variables x and y represent the inputs, where x₁ and x₂ correspond to the membership functions of x, and y₁ and y₂ correspond to the membership functions of y. The second layer implements fuzzy logic rules to define the relationships between inputs and outputs. The third layer standardizes these outputs and forwards them to the fourth layer, where the output data are processed to generate the output membership function. Finally, the fifth layer aggregates these outputs into a single value. ANFIS is capable of managing multiple inputs. The flow chart in Figure 6 illustrates the implementation process of the hybrid controller. Training data are collected from the PI-controller-based model, using the error signal as the input and the control signal as the output. Fuzzification maps these inputs to fuzzy sets using membership functions. ANFIS is then trained using historical or simulated data to optimize membership functions and rule weights. As shown in Figure 5, the fuzzification layer converts crisp inputs into fuzzy terms. The rule base then connects these fuzzy inputs to the output through a set of if–then rules.

The flow chart incorporates two validation steps: one to ensure minimal output error and another to verify an improved dynamic response. Following the ANFIS training, the first check evaluates the output error. If the error does not meet the desired minimal threshold, the process loops back to retrain ANFIS with further iterations to reduce the error. Conversely, if the output error is minimized to the desired level, the process moves forward to export and saves the FIS (fuzzy inference system) file, which contains the optimized ANFIS model. The saved FIS undergoes a second evaluation to determine whether the system’s dynamic response has improved. If the response meets the required criteria, the process is finalized. However, if the dynamic response is inadequate, the process restarts at the relevant step in the flow chart.

In this case, adjustments are made to the membership functions and training epochs, and the system is re-evaluated. This iterative process continues until the desired dynamic response is achieved. The parameters utilized in the designed simulation model are outlined in

Table 3. Parameters configured in the proposed simulation model.

Parameters	Value
Proportion constant, Kp (RSC)	2.25
Integral constant, Ki (RSC)	14
Proportion constant, Kp (GSC)	0.73
Integral constant, Ki (GSC)	2.85
Dataset (input–output pairs)	4,000,001
Test signal applied (Vwind) at 10 s	From 10 m/s to 12 m/s
No. of inputs	01
No. of outputs	01
No. of membership functions	08
Type of membership functions	Constant
Nos. of epochs/iterations	25

.

In wind turbine systems (WTSs), a hierarchical control framework is commonly utilized for both the rotor-side converter (RSC) and the grid-side converter (GSC). This hierarchical control strategy divides the task into multiple control loops, improving the control precision, stability, and response time by decoupling objectives. The cascade control system consists of two primary loops: the machine control loop, which features an inner loop for torque regulation and an outer loop for rotor speed control, and the grid control loop, which includes an inner loop for active power management and an outer loop for DC link voltage regulation. These control loops ensure stable rotor speed, regulated current flow, and proper voltage levels, thereby facilitating smooth wind turbine integration and efficient operation. Ultimately, this hierarchical control approach enhances the system’s reliability, performance, and robustness.

Implementation of Proposed Hybrid Controller in WECS Model

This study introduced a hybrid controller into the cascade control framework, where ANFIS controllers were deployed in the outer loops, and conventional PI controllers were utilized in the inner loops of the RSC and GSC converters in WTS. This method sought to attain greater reliability and efficiency. Figure 7 depicts the integration of the proposed hybrid control approach into the RSC converter. In this setup, the ANFIS controller in the outer loop ensured the desired rotor speed, while the inner loop employed a PI controller to manage mechanical torque, resulting in improved performance of the RSC converter.

Similarly, when the proposed hybrid ANFIS-PI control approach was implemented in the GSC converter, as shown in Figure 8, the ANFIS controller in the outer loop ensured the desired DC voltage level across the capacitor, while the inner loop utilized a PI controller to manage current regulation, resulting in improved performance of the GSC converter.

Figure 9 and Figure 10 illustrate the error reduction obtained throughout the learning process of the adaptive neuro-fuzzy inference system (ANFIS) applied to both the rotor-side controller (RSC) and the grid-side controller (GSC) in a doubly fed induction generator (DFIG)-based wind turbine system (WTS). The training process, conducted over 25 epochs using the hybrid optimization method, demonstrated a steady decrease in error for both controllers. For the RSC, the error reduced progressively to approximately 0.0657 by the 25th epoch, while the GSC achieved a final error value of approximately 0.0344. The fuzzy inference system was generated using the grid-partitioning approach. The findings confirmed the efficiency of the ANFIS model in achieving precise control, minimizing deviations, and enhancing the overall stability and efficiency of both controllers under varying operating conditions.

The proposed model demonstrated significant advancements over [2] in terms of computational efficiency, accuracy, and system complexity. With a dataset of 4,000,001 input–output pairs and only 25 training epochs, the model achieved a lower training error (~0.034), as shown in Figure 9, compared with the higher error (~0.094) in [2], which used a larger dataset of 8,000,001 pairs and was trained for 50 epochs. By employing 8 membership functions instead of 10, the proposed model reduced computational complexity while maintaining performance. Additionally, the replacement of PI controllers in both the outer loops of RSC and GSC enhanced the stability of the wind turbine power generation system, whereas [2] modified the controller for only one converter. These improvements underline the proposed model’s superior design and practical applicability.

After completing the training, an ANFIS structure was generated for eight membership functions, as shown in Figure 11, which clearly illustrates the distribution of input/output membership functions and the associated rule set. The blue dots represent AND operation while the red dot and green line are associated with hidden layers.

The test signals of wind speed (V_wind) illustrated in Figure 12 are given at 10 s by varying the wind speed from 10 m/s to 12 m/s to evaluate the performance and robustness of the WTS.

4. Simulation Results and Discussion

The proposed hybrid ANFIS-PI model was designed in MATLAB Simulation by applying a step wind speed signal for simulation conditions, with the wind velocity varying from 10 m/s to 12 m/s, as outlined in Figure 11. This evaluated the system’s dynamic response under changing wind regimes. Regarding dataset partitioning, the collected data were divided into three subsets:

• The training set (70%) was used for training the ANFIS model by adjusting membership functions and rule parameters.
• The validation set (15%) was applied for refinement and prevent overfitting, ensuring the model generalizes well.
• The testing set (15%) was used to assess the overall model accuracy and compare it against the PI controller for validation.

By following this structured approach, we ensured that the ANFIS model was trained effectively using a well-defined dataset derived by applying step wind signal in the model as a wind turbine operating condition, enabling robust performance comparisons with conventional PI control strategies. The efficiency of the proposed hybrid ANFIS-PI controller and the conventional PI controller was evaluated under dynamic wind speed conditions, focusing on key performance indicators (KPIs) such as maximum overshoot and settling time, as well as overall system stability. The comparison evaluated electromechanical and power control variables, including the rotor speed, electromagnetic torque, active power, and DC link voltage. The hybrid ANFIS-PI controller consistently demonstrated superior performance across all these parameters, establishing itself as a more robust and adaptable solution for wind turbine control systems. The simulation results of both comparing controllers are illustrated in Figure 13, Figure 14, Figure 15 and Figure 16.

In Figure 13, the rotor speed performance of the wind turbine model is presented over time, comparing the responses of the traditional PI controller and the developed hybrid ANFIS-PI controller. The PI controller showed significant undershoot (~0.65 rad/s) and overshoot (1.05 rad/s, 5% deviation), with a settling time of ~2 s and oscillations, indicating less stability. In contrast, the hybrid ANFIS-PI controller achieved a reduced undershoot (0.75 rad/s), minimal overshoot (1.02 rad/s, 2% deviation), and faster stabilization within 1 s, ensuring smoother and more robust performance under dynamic wind conditions.

Similarly, Figure 14 displays the time-dependent response of electro-mechanical torque for both PI and hybrid controllers. The PI controller showed a maximum overshoot of 1.15 N·m (43.75% deviation) with a settling time of 4 s, alongside oscillatory behavior. In contrast, the hybrid ANFIS-PI controller achieved a reduced overshoot of 1.05 N·m (31.25% deviation) and a faster settling time of 3 s, with a smoother and more stable response. This highlights the hybrid ANFIS-PI controller’s superior adaptability and robustness, making it a more effective control strategy for wind turbines.

The response of active power (in per unit) over time under the control of both the proposed hybrid ANFIS-PI and the traditional PI controller is depicted in Figure 15. The PI controller showed a larger undershoot (~17.5%) and longer stabilization time (~10 s), with higher overshoots (~9%) and settling times (~4.5 s). In contrast, the hybrid ANFIS-PI controller had a smaller undershoot (~11%), stabilized faster (~6 s), and achieved lower overshoots (~7%) with shorter settling times (~3 s). This highlights the hybrid controller’s superior adaptability, stability, and efficiency, making it a more effective wind turbine power generation strategy.

The DC link voltage response, depicted in Figure 16, demonstrated the hybrid controller’s enhanced performance in regulating system voltage. The conventional PI controller exhibited significant overshoot, peaking at 1800 V, and took approximately 12 s to stabilize. Such high overshoot and extended settling times could increase the system components’ stress, potentially reducing their lifespan and increasing maintenance costs. In contrast, the hybrid controller effectively limited the overshoot to 1600 V and stabilized within 10 s. By maintaining tighter control over the DC link voltage, the hybrid controller reduced the risk of component degradation and enhanced the overall system reliability. The responses of rotor speed, torque, active power, and DC bus voltage parameters when subjected to test signals for both PI and hybrid controllers are presented in

Table 4. PI and hybrid ANFIS-PI controllers’ responses across parameters.

S. No.	Parameters	Control Scheme	Rise Time (s)	Overshoot (%)	Settling Time (s)	Steady State Error
1	Rotor speed	PI	1.2	5	2	0.88
		ANFIS-PI	0.8	2	1	0
2	Torque	PI	1	43.75	4	0.9
		ANFIS-PI	0.7	31.25	3	0
3	Active power	PI	0.56	9	4.5	0.83
		ANFIS-PI	0.55	7	3	0
4	DC bus Voltage	PI	0.8	50	12	0.9
		ANFIS-PI	0.7	30	10	0

.

As illustrated in Table 3, the results emphasized the notable enhancements introduced by the hybrid ANFIS-PI controller in the simulation. Across all evaluated parameters, the hybrid controller consistently outperformed the conventional PI controller, showcasing its ability to adapt to dynamic wind speed variations with lower overshoot, faster stabilization, and improved stability. These attributes enhanced the overall dynamic response and contributed to robustness and reliability, making the hybrid controller a more effective solution for wind turbine control applications.

Limitations of the Proposed Method

While the proposed hybrid ANFIS-PI controller offers superior adaptability, improved dynamic response, and reduced computational complexity, it has certain drawbacks that should be acknowledged:

• Initial training complexity: The ANFIS model requires an initial training phase, during which membership functions and rules must be optimized. Although it requires fewer training data than standalone ANN models, the training process still demands careful tuning to ensure stability and accuracy.
• Dependence on membership function design: The fuzzy logic component in ANFIS relies on well-defined membership functions. Suboptimal membership function selection can lead to degraded performance, requiring expert knowledge or additional optimization techniques for fine-tuning.
• Computational load during implementation: While ANFIS-PI is computationally more efficient than purely ANN-based or model predictive controllers, it still requires more processing power than traditional PI controllers. Implementing real-time control on low-cost embedded systems may require optimized hardware (e.g., DSP or FPGA) for efficient execution.
• Limited generalization for different wind turbine configurations: The proposed ANFIS-PI controller was designed for DFIG-based WTS, meaning its direct applicability to other types of wind turbines (e.g., PMSG-based systems) may require modifications in control strategies and parameter tuning.
• Additional computational cost for real-time adaptation: Since ANFIS continuously adapts control parameters, real-time adaptation in highly dynamic environments increases computational demand, potentially impacting performance in large-scale wind farms without adequate processing resources.

Despite these drawbacks, the proposed ANFIS-PI controller maintains a strong balance between adaptability, efficiency, and real-time feasibility, making it a more practical solution than existing AI-based and conventional control strategies.

5. Conclusions

This study presents a hybrid ANFIS-PI controller for the rotor-side converter (RSC) and grid-side converter (GSC) in wind turbine systems (WTSs), addressing the limitations of conventional PI controllers in handling nonlinear wind variations. The proposed methodology significantly enhances system performance by integrating the adaptability of ANFIS with the effectiveness of PI control. The simulation results confirmed that the ANFIS-PI controller significantly improved performance compared with the conventional PI control. Specifically, it reduced rotor speed overshoot by 3% (from 5% to 2%), torque overshoot by 12.5% (from 43.75% to 31.25%), active power overshoot by 2% (from 9% to 7%), and DC link voltage overshoot by 20% (from 50% to 30%). Additionally, the ANFIS-PI controller shortened settling time by 50% (from 2 s to 1 s) for rotor speed, by 25% (from 4 s to 3 s) for torque, by 33% (from 4.5 s to 3 s) for active power, and by 16.7% (from 12 s to 10 s) for DC link voltage, ensuring faster stabilization, enhanced dynamic response, and greater efficiency. These improvements demonstrated that the hybrid ANFIS-PI controller effectively mitigated the adverse effects of wind fluctuations, ensuring stable and reliable WTS operation. By optimizing power delivery, enhancing reliability, and improving dynamic response, this study contributes to advancing wind power technologies and their efficient assimilation into contemporary electrical networks. The results emphasize the effectiveness of AI-driven control strategies in renewable energy systems, opening new avenues for future research on intelligent and adaptive wind turbine system (WTS) control techniques.