PSO-optimized sensor-less sliding mode control for variable speed wind turbine chains based on DPIG with neural-MRAS observer

Abstract

This research introduces a resilient Sensor-Less 1st Sliding Mode (SL-FOSM) approach employing a novel observer, the Artificial Neural Network with Model Reference Adaptive System-Adaptive (Neural-MRAS), for wind turbine chains. The proposed model is implemented on a Doubly Powered Induction Generator (DPIG) operating under genuine variable speed conditions in the Adrar region in Algeria. The control objective is to independently regulate the active and reactive power of the DPIG stator, achieved through decoupling using the field-oriented control technique and control application via FOSM-C. Notably, this methodology reduces both the control scheme cost and the DPIG size by eliminating the need for a speed sensor (encoder). To enhance the MRAS-PI, an Artificial Neural Network (ANN) is suggested to replace the typical classical Proportional-Integral (PI) controller in the adaptation mechanism of MRAS. The rotor position estimation is scrutinized and discussed across various load conditions in low, zero, and high-speed regions. Optimal controller parameters are determined through particle swarm optimization (PSO). The results demonstrate that the proposed observer (Neural-MRAS) exhibits compelling attributes, including guaranteed finite time convergence, robust performance in response to speed variations, high resilience against machine parameter fluctuations, and adaptability to load variations when compared to the MRAS-PI. Consequently, the estimated rotor speed converges to its actual value, showcasing the capability to accurately estimate position across different speed regions (low/zero/high).

Keywords

Sensor-less 1st sliding mode (SL-FOSM-C)Model reference adaptive system-PI (MRAS-PI)Particle swarm optimization (PSO)Artificial neural network with model reference adaptive system (Neural-MRAS) observer

Introduction

In the contemporary era, wind energy stands as a pivotal player among renewable energy sources, offering an environmentally friendly alternative compared to traditional energy sources that contribute to environmental pollution. The ubiquity of wind, available worldwide makes it a viable resource for harnessing clean energy, while traditional wind turbine systems operate at fixed speeds, the trend toward variable-speed turbines has gained momentum due to their numerous advantages (Cherifi et al., 2023; Saihi et al., 2023a). Doubly Powered Induction Generators (DPIGs) have become integral components of variable-speed wind turbine systems, providing substantial benefits in the conversion of wind energy (Cherifi et al., 2023; Djilali et al., 2022; Saihi et al., 2023a).

The control landscape for DPIG systems encompasses various schemes, with the 1st Sliding Mode control (FOSM-C) emerging as a nonlinear and advanced strategy designed to ensure controlled dynamics follow a specified sliding surface until equilibrium is reached (Djilali et al., 2022; Saihi et al., 2023c). In Benbouhenni et al. (2023), a synergetic control based on fractional order control theory is proposed for multi-rotor wind power (MRWP) systems to avoid the chattering effect of traditional synergetic control. Two schemes are compared: traditional direct power control (DPC) and DPC with fractional-order synergetic controllers, with the latter showing superior performance in Matlab simulations. In Chojaa et al. (2023), a control strategy for a grid-connected WECS with battery storage is presented. Using Integral Sliding Mode Control (ISMC), it manages DFIG power and battery charging/discharging, addressing system variations and non-linearities, validated through simulations. Furthermore, Dahiya (2024) presents a DFIG in a WECS using a Direct Matrix Converter (DMC) for AC-AC transmission, reducing converter costs and enhancing reliability, with IGBT switches commonly used in various control and modulation techniques.

The pursuit of Sensor-Less control for DPIGs necessitates the acquisition of rotor speed and position information traditionally obtained through mechanical sensors or encoders that, unfortunately, escalate the cost and size of DPIGs, compromise system performance, and render them susceptible to disturbances. Furthermore, the requirement for a shaft poses a limitation for smaller machines (Saihi et al., 2023b; Saihi and Boutera, 2017).

In response to these challenges, Sensor-Less (SL) strategies have garnered increased attention from researchers, exploring various techniques to control speed and position (mechanical parameters) (Saihi et al., 2023b). Utilizing state observers, such as the Model Reference Adaptive System (MRAS), to infer unmeasured states from electrical parameters, has been a prominent avenue for Sensor-Less (SL) control and the estimation of rotor speed/position (Saihi et al., 2023b; Saihi and Boutera, 2017). However, the classical MRAS-PI exhibits instability during speed variations (high/zero/low) and variation parameters, with undesired transients affecting precision during varying loads, ultimately compromising the overall control system’s performance. To enhance wind turbine system efficiency, this study employs artificial intelligence techniques based on neural networks (ANN) instead of traditional Proportional-Integral (PI) controllers in the adaptation mechanism of MRAS-PI. This innovative approach effectively addresses control challenges, reducing the estimated error’s speed of MRAS-PI and enabling accurate position of rotor estimation across different speed regions of the DPIG under varying wind speeds.

Various methodologies have been proposed for assessing mechanical parameters, specifically the position and speed of the DPIG rotor, utilizing measurable electrical quantities such as current and voltage. In Mbukani et al. (2023), a sliding mode control-based model reference adaptive system (SMC-MRAS) estimator is introduced for sensor-less control of DFIG systems in wind turbines. This study emphasizes the superior estimation performance of the SMC-MRAS estimator compared to the PI-MRAS estimator, particularly in the presence of machine parameter variations. However, the chattering effect created by the discontinuous part of SMC affects the quality of power. Furthermore, Pourjafari and Fallah Choolabi (2023) presents a novel sensor-less vector control approach for standalone DFIGs, featuring an open-loop flux and speed estimator to enhance system robustness. Although sensitive to machine parameters, the introduced Particle Swarm Optimization (PSO), implemented in a digital signal processor, mitigates this sensitivity for parameter identification. Simulation and experimental results confirm the efficacy of the proposed method, especially in preserving sinusoidal load voltage amplitude and frequency. However, it does not demonstrate the ability to accurately estimate position across diverse speed regions (low/zero/high).

In Bahlouli et al. (2023), an Interconnected High Gain Observer (IHGO) is introduced for estimating electromagnetic torque, speed, and position in a DFIG-based wind turbine, relying solely on voltage, current, and wind speed measurements. The IHGO is designed to be robust against parameter uncertainties, but global efficacy under various conditions such as parameter uncertainties, power and speed variations, grid voltage dips, and current sensor noise is not validated. Additionally, in Gayen (2022), the paper focuses on an improved rotor position/speed estimation technique for DFIGs using a MRAS, with the stator-side reactive current as the primary variable. The experimental results obtained align consistently with the expected performances outlined in the theoretical analysis. Another study (Mbukani and Gule, 2023) explores an Adaptive Sliding Mode Observer (ASMO) coupled with a Phase-Locked Loop (PLL) for Sensor-Less control of a rotor-tied DFIG. The primary contribution is the introduction of a PLL-based ASMO estimator, aiming to improve estimation precision by reducing the chattering effect, but it does not address or eliminate this effect, impacting the quality of power.

In Khanh and Anh (2022), an advanced Fuzzy Model Reference Adaptive System (Fuzzy MRAS) is proposed to reduce chattering in SL control of Permanent Magnet Synchronous Motors (PMSM), improving rotor speed regulation by minimizing errors between actual and calculated stator currents. Matlab/Simulink simulations show that Fuzzy MRAS outperforms conventional MRAS and MRAS with Fuzzy PI control. In Ammar (2021), an improved sensorless direct flux and torque control for induction motor drives integrates the super twisting control approach to reduce chattering and enhance robustness. A load torque observer improves speed regulation and disturbance rejection, verified through MATLAB/Simulink simulations and dSpace 1104 experiments. Additionally, Guedida et al. (2024) presents a fractional-order adaptive MRAS for sensorless direct torque control of a five-phase induction motor, using a PSO-optimized FOPI controller to enhance speed estimation. The proposed MRAS-PSO/FOPI shows superior performance compared to conventional MRAS-PI and PSO-based MRAS-PI. In Jitendra et al. (2023), a Sensor-Less direct torque control (DTC) scheme for induction motors using a MRAS estimator estimates speed based on rotor flux, input current, and voltage, with PI controllers for torque, flux, and speed control. Simulink results demonstrate the effectiveness of sensorless DTC, comparing it with sensored DTC. All these strategies face limitations at low and high rotor speeds and lack robustness against parameter variations.

Implementing SL control presents a significant challenge, so this study aims to address several limitations associated with SL control, including machine parameter variations under varying wind speeds, sensitivity during parameter identification, the chattering effect, response time, observer complexity, and estimation across low, medium, and high rotor speeds. To overcome these challenges, the proposal introduces Sensor-Less 1st Sliding Mode (SL-FOSM-C) coupled with a hybrid approach integrating an ANN and a MRAS observer, and for determining optimal parameters, the PSO tuning algorithm is used. The resulting methodology is characterized by its user-friendly nature, reliability, and applicability to complex optimization challenges. The overarching objective is to enhance wind turbine efficiency and mitigate output fluctuations.

This research unfolds in five sections. Firstly, it delves into the modeling of both the mechanical and electrical components. Secondly, it introduces the robust 1st Sliding Mode Control (FOSM-C) designed for a chain’s wind energy featuring a DPIG operating under genuine variable speed conditions in the Adrar region of Algeria, and thirdly, introduces a novel approach, combining a MRAS with ANN, used for estimating rotor position and speed, the parameter gains of this proposed controller undergo meticulous fine-tuning through the PSO algorithm. results of the simulation validate the efficacy of the Sensor-Less FOSM-C for DPIGs with the Neural-MRAS observer, affirming superior dynamic performance compared to classical MRAS-PI.

Key contributions:

a- Mitigation of Speed’s Wind Variability and Parameter Changes in PI Regulator:

• Alleviation of the impact of speed of wind changings and variation parameters in the PI, enhancing the stability and performance of the control system under dynamic conditions.

b- Cost Reduction in DPIG Control Scheme:

• Significantly reduced costs by eliminating the need for mechanical sensors, thereby simplifying the control scheme, and enhancing reliability.

• Decreased complexity contributes to a more economically viable and streamlined DPIG system.

c- Introduction of Neural-MRAS Observer:

• Introduction of a MRAS coupled with an ANN to estimate the position and speed of the rotor.

• Enhancement of the MRAS-PI by incorporating advanced artificial intelligence techniques, improving accuracy in rotor position and speed estimation.

d- Accomplishing Control Goals without the Use of a Speed Sensor:

• Successful attainment of control objectives without reliance on a speed sensor.

• Elimination of the need for a speed sensor enhances system robustness, reduces hardware costs, and simplifies system design.

These contributions collectively address critical challenges in the field of wind energy, promoting cost-effectiveness, reliability, and precision in the control of DPIG within variable-speed WTCS.

Model of wind energy chain

Figure 1 depicts a wind energy chain employing a DPIG, as referenced in Cherifi et al. (2023) and Saihi et al. (2023c):

Figure 1.

Chain of WTCS based on DPIG.

Mechanical part modelling of WT

The equation describes the mechanical power generated by a wind turbine (Cherifi et al., 2023; Saihi et al., 2023c):

P_{t} = \frac{1}{2} ρ S V^{3} C_{p} (λ, β)

(1)

The power coefficient, given by:

C_{p} (λ, β) = \frac{1}{2} (\frac{116}{λ_{i}} - 0.4 β - 5) e^{- (\frac{21}{λ_{i}})}

(2)

The ratio of speed $λ$ can be given by (Djilali et al., 2022; Saihi et al., 2023a):

λ = \frac{R_{t} Ω}{V}

(3)

The definition of the turbine torque is outlined as follows, as indicated in Saihi et al. (2023b) and Saihi and Boutera (2017):

T_{t} = \frac{1}{2 λ} ρ π R_{t}^{3} V^{2} C_{p} (λ, β)

(4)

The equation representing the mechanical shaft system is as follows, as mentioned in Cherifi et al. (2023) and Saihi et al. (2023c):

J_{T} \frac{d Ω}{d t} = T_{t} - T_{e m} - f Ω

(5)

Electrical part modelling of DPIG

Two static converters, positioned on either side of a continuous bus, are supplied by the rotor winding of the DPIG, with the DPIG stator linked to the grid. This arrangement enables operation across a broad spectrum of wind speeds, optimizing power extraction from variable wind conditions (Cherifi et al., 2023; Saihi et al., 2023c):

The model for the DPIG is characterized by the following set of matrices, as detailed in Djilali et al. (2022) and Saihi et al. (2023b).

[\begin{matrix} {\overset{\cdot}{φ}}_{d s} \\ {\overset{\cdot}{φ}}_{q s} \\ {\overset{\cdot}{φ}}_{d r} \\ {\overset{\cdot}{φ}}_{q r} \end{matrix}] = [\begin{matrix} - R_{s} & 0 & 0 & 0 \\ 0 & - R_{s} & 0 & 0 \\ 0 & 0 & - R_{r} & 0 \\ 0 & 0 & 0 & - R_{r} \end{matrix}] [\begin{matrix} i_{d s} \\ i_{q s} \\ i_{d r} \\ i_{q r} \end{matrix}] + [\begin{matrix} 0 & ω_{s} & 0 & 0 \\ - ω_{s} & 0 & 0 & 0 \\ 0 & 0 & 0 & (ω_{s} - ω_{r}) \\ 0 & 0 & (ω_{s} - ω_{r}) & 0 \end{matrix}] [\begin{matrix} φ_{d s} \\ φ_{q s} \\ φ_{d r} \\ φ_{q r} \end{matrix}] + [\begin{matrix} v_{d s} \\ v_{q s} \\ v_{d r} \\ v_{q r} \end{matrix}]

(6)

The equations governing the flux linkage are as follows, as referenced in Cherifi et al., 2023; Saihi et al., 2023c):

[\begin{matrix} φ_{d s} \\ φ_{q s} \\ \begin{matrix} φ_{d r} \\ φ_{q r} \end{matrix} \end{matrix}] = [\begin{matrix} l_{s} & 0 & \begin{matrix} l_{m} & 0 \end{matrix} \\ 0 & l_{s} & \begin{matrix} 0 & l_{m} \end{matrix} \\ \begin{matrix} l_{m} \\ 0 \end{matrix} & \begin{matrix} 0 \\ l_{m} \end{matrix} & \begin{matrix} \begin{matrix} l_{r} \\ 0 \end{matrix} & \begin{matrix} 0 \\ l_{r} \end{matrix} \end{matrix} \end{matrix}] [\begin{matrix} i_{d s} \\ i_{q s} \\ \begin{matrix} i_{d r} \\ i_{q r} \end{matrix} \end{matrix}]

(7)

Equation for electromagnetic torque (Cherifi et al., 2023; Saihi et al., 2023c):

[T_{e m}] = p [\begin{matrix} - φ_{q s} & φ_{d s} \end{matrix}] [\begin{matrix} i_{d s} \\ i_{q s} \end{matrix}]

(8)

Equations for stator powers were derived (Cherifi et al., 2023; Saihi et al., 2023c):

[\begin{matrix} P_{s} \\ Q_{s} \end{matrix}] = [\begin{matrix} v_{d s} & v_{q s} \\ v_{q s} & - v_{d s} \end{matrix}] [\begin{matrix} i_{d s} \\ i_{q s} \end{matrix}]

(9)

Converter control

In the frame of d-q reference, aligning the stator vector flux $φ_{d s}$ along axis $d$ results in stationary electrical voltages and currents in permanent mode. Thus $φ_{d s} = φ_{s}$ , $φ_{q s} = \frac{d φ_{q s}}{d t} = 0$ .

Electromagnetic torque is given by (Cherifi et al., 2023; Saihi et al., 2023c):

[T_{e m}] = - p \frac{l_{m}}{l_{s}} [φ_{s}] [i_{q r}]

(10)

DPIG control focuses on regulating the powers of stator (active, and reactive) through the rotor side converter (RSC) as follows (Cherifi et al., 2023; Saihi et al., 2023c):

[\begin{matrix} P_{s} \\ Q_{s} \end{matrix}] = [\begin{matrix} 0 & - v_{s} \frac{l_{m}}{l_{s}} \\ - v_{s} \frac{l_{m}}{l_{s}} & 0 \end{matrix}] [\begin{matrix} i_{d r} \\ i_{q r} \end{matrix}] + [\begin{matrix} 0 \\ \frac{{v_{s}}^{2}}{l_{s} ω_{s}} \end{matrix}]

(11)

Active and reactive powers of stator are regulated by the rotor currents in the DPIG. The rotor currents are represented as (Cherifi et al., 2023; Saihi et al., 2023c):

[\begin{matrix} {\overset{\cdot}{i}}_{d r} \\ {\overset{\cdot}{i}}_{d r} \end{matrix}] = [\begin{matrix} \frac{- R_{r}}{l_{r} σ} & g ω_{s} \\ - g ω_{s} & \frac{- R_{r}}{l_{r} σ} \end{matrix}] [\begin{matrix} i_{d r} \\ i_{q r} \end{matrix}] + [\begin{matrix} v_{d r} \\ v_{q r} \end{matrix}] + [\begin{matrix} 0 \\ - g \frac{l_{m} v_{s}}{l_{s} l_{r} σ} \end{matrix}]

(12)

Sensor-less control of DPIG

In the realm of addressing challenges related to performance and stability in complex systems, 1st Sliding Mode Control (FOSM-C) stands out as a promising approach. This method is extensively applied in the regulation of DPIG due to its robustness against variable parameters, designed to enforce controlled dynamics on a specific trajectory system until reaching equilibrium (Djilali et al., 2022; Saihi et al., 2023c).

The FOSM-C methodology, in essence, involves a three-step process (Bakou et al., 2023; Karami et al., 2023; Yessef et al., 2022):

Establishing the Sliding Surface $S (P, Q)$ : The initial phase involves carefully selecting the sliding surface.

Establishment of Conditions for Existence: The second vital phase revolves around identifying the circumstances in which the sliding mode (SM) exists, ensuring the efficiency of the control mechanism.

Developing Control Laws for Sliding Mode: The concluding stage involves creating control laws for the SM, a task that lays the groundwork for the comprehensive control strategy.

This method, succinctly referred to as FOSM-C for DPIG, reflects a collective endeavor to improve control accuracy and stability within complex systems. The diagram of the FOSM-C is illustrated in Figure 2:

Figure 2.

FOSM-C organigram.

MRAS type observer

Various methods, such as utilizing a sensor’s speed (encoder) or employing a basic open-loop estimator’s speed, can be utilized to acquire the rotor speed and position signal. The former method faces challenges related to mechanical coupling and incurs higher costs due to the use of sensors and cables. In contrast, the accuracy of speed estimation in an open-loop estimator heavily depends on machine parameters (Saihi et al., 2023b; Saihi and Boutera, 2017). Several software-based approaches for data processing have been explored for rotor speed and position estimation. Among these, the MRAS has become widely popular due to its simple implementation, high precision, and stability (Mbukani et al., 2023; Saihi et al., 2023c).

The MRAS procedure involves employing two separate models. The first model, known as the model’s reference, is utilized to ascertain the direct and quadrature currents components through direct measurements of currents. The second model, termed the model’s adjustable, is used to estimate these components of current using both currents and voltages measurements (Saihi et al., 2023c; Saihi and Boutera, 2017). By reducing the error between these two models, the dynamic rotor speed can be effectively observed. This error acts as the input for the PI regulator, functioning as the adaptive mechanism (Figure 3).

Figure 3.

MRAS observer configuration.

Neural-MRAS type observer

An ANN strategy is a specific control system that utilizes the computational capabilities of ANN (Bakou et al., 2023; Djilali et al., 2022). These networks draw inspiration from the complex structure and functioning of the human brain. ANNs comprise interconnected processing units, typically arranged in layers, demonstrating an impressive ability to undergo training to recognize and adapt to complex patterns and relationships within data (refer to Figure 4) (Shankar et al., 2022; Sami et al., 2022).

Figure 4.

Neuron configuration.

In this part, we applied the Neural-MRAS observer under the varied speeds of wind conditions, encompassing low, medium, and high regimes, a drawback of the MRAS-PI observer was its less-than-optimal accuracy in estimating. To address this limitation and improve the overall performance of the observer, we innovatively replaced the traditional PI with an ANN. This novel observer method resulted in enhanced performance and robustness in speed estimation compared to the MRAS-PI, proving effective against parameter variations accompanying changes in the speed of wind (high, medium, low). Furthermore, it has the potential to improve the quality of power, enhance distribution grid stability, and optimize the performance of DPIG wind power production. The configuration of the Neural-MRAS observer is illustrated in Figure 5:

Figure 5.

Neural-MRAS observer diagram.

Algorithm of particle swarm optimization (PSO)

In 1995, Kennedy and Eberhart presented Particle Swarm Optimization (PSO), a population-based optimization method inspired by the collective behavior observed in birds and fish (Alloui and Fetha, 2017). The primary goal of PSO is to identify the maximum or minimum value of a function while adhering to specific constraints. The algorithm operates by managing a population of particles, each possessing its own best position (Pbest) and fitness value. Additionally, there is a global best position (Gbest) that represents the optimal solution discovered across the entire search space. During each time step, particles are directed toward their Pbest and Gbest positions through weighted random adjustments, emulating the cooperative movement observed in natural systems (Alloui and Fetha, 2017; Kafazi et al., 2023).

This core mechanism is fundamental to the functioning of PSO, and its detailed operation is elucidated in Alloui and Fetha (2017), providing a visual representation and a comprehensive breakdown of the PSO algorithm. In the present context, PSO is applied to optimize the parameters of the FOSM-C and the Neural-MRAS observer, showcasing its versatility in enhancing the performance and convergence of these control systems (Gouabi et al., 2023; Kafazi et al., 2023).

The main difficulty in implementing the FOSM-C based on the Neural-MRAS observer lies in determining the optimal parameters. To address this challenge, PSO was utilized to fine-tune the gains of the global controller. The focus of PSO was on improving the output power of variable-speed wind turbines by adjusting the gains specifically within the FOSM-C based on the Neural-MRAS framework. The PSO tuning method is favored for its rapid convergence (Gouabi et al., 2023). The diagram of PSO is illustrated in Figure 6:

Figure 6.

Diagram of PSO algorithm.

Integrated system employing SL-FOSM controller and neural-MRAS observer

The illustrated control system, featuring a robust Sensor-Less Sliding Mode Controller (FOSM-C) coupled with a hybrid Neural-MRAS observer, incorporates parameter optimization through the PSO algorithm. This system is tailored for wind turbine applications, particularly those utilizing a DPIG. Its primary objective is to regulate the stator powers of the DPIG and estimate the mechanical speed and position of the DPIG rotor. The conceptual representation of this integrated control approach is visually depicted in Figure 7.

Figure 7.

Global sensor-less FOSM-C based on a neural-MRAS.

Site and data and location

The Adrar province is highlighted in Figure 8(a), recognized for its notably high average annual wind speed within Algeria, reaching approximately 6.3 m/s (Oulimar et al., 2024). The data for this research were obtained from the meteorological and radiometric station associated with the Renewable Energy Research Unit in the Saharan Environment (URER/MS) located in Adrar, Algeria, as depicted in Figure 8(b) (Oulimar et al., 2024):

Figure 8.

The site location and the data. (a) The geographic location of Adrar, Algeria. (b) The MR station installed in the URER-MS, Adrar, Algeria.

Figure 9 illustrates the daily wind speed data recorded at the meteorological and radiometric (MR) station in Adrar, spanning from 00:00 to 24:00 on April 8th, 2021.

Figure 9.

The wind speed recorded from MR station in Adrar region.

Results of simulation

To evaluate the efficacy of power control in the Sensor-Less 1st Sliding Mode Control, using the observer of Neural-MRAS with optimized parameter values obtained through the PSO algorithm, a series of simulations were performed in Matlab/Simulink. These simulations simulated a wind turbine chain driving a DPIG under real varying wind speeds.

Tables 1 and 2 outline the specific parameters for the mechanical (wind turbine) and electrical (DPIG) components, respectively. Basic parameter values for the PSO optimization algorithms are provided in Table 3, and the parameter values of the proposed controller (Ka, Kb, Kc, Kd, Ke, Kf, Kg, Ks) for the PSO algorithm are illustrated in Table 4.

Table 1.

Parameter values of wind turbine chain.

Parameters	Values
$R_{t}$ : Wind turbine radius	35.25 m
$Ω$ : Nominal rotational speed	10 m/s
$N_{b}$ : Blades number	3
$f$ : Dry friction torque	953 N.m
$C_{p} (λ, β)$ : Power coefficient	8.1
$ρ$ : Air density	1.225 kg/m³
$J_{T}$ : Mechanical inertia	50 kg.m2

Table 2.

Parameter values of DPIG.

Parameters	Values
$f_{r}$ : Frequency	50 Hz
$V$ : Source voltage	698 V
$p :$ Pole pairs number	2
$L_{d}$ : Inductance (D-axis)	0.0136 H
$L_{m}$ : Mutual inductance	0.0135 H
$L_{q}$ : Inductance (Q-axis)	0.0137 H
$R_{s}$ : Resistance of stator	0.012 $Ω$
$R_{r}$ : Resistance of rotor	0.021 $Ω$

Table 3.

PSO parameter values.

Parameters	PSO
No of iterations	100
Size of population	42
Dimension	8
Upper bound	[120 6e3 13e3 2000 8e3 755 1500 89]
Lower bound	[0 0 0 0 0 0 0 0]

Table 4.

SL-FOSM-C based on neural-MRAS parameters values using PSO.

Parameters	1	2	3	4	5	6	7	8
PSO algorithm	90	3000.9	4000	1004.046	4637.2	500.1	1232	37

Figure 10 illustrates the real speed of wind profile in the Adrar, Algeria, expressed in meters per second (m/s), and applied to a mechanical element, specifically a wind turbine. This profile spans from +5.5 to +14.5 m/s and encompasses the timeframe from 10:00 to 18:00 on April 8th, 2021.

Figure 10.

The actual wind speed recorded at the Adrar region, Algeria from 10:00 to 18:00 on April 8th, 2021.

Tracking test

The primary objective of this assessment was to evaluate the capability of the SL-FOSM-C/Neural-MRAS with PSO in accurately following the desired reference values for the real powers (active and reactive) of the DPIG stator. In Figure 11, the dynamics of the stator’s active power are depicted, with the controlled trajectory shown in black, achieved through the proposed controller scheme. The figure distinctly demonstrates the superior performance of the FOSM-C using the PSO algorithm (red curve) compared to the classical PI controller (blue curve).

Figure 11.

Active power (Watt) using the sensor-less FOSM-C.

Moving to Figure 12, the dynamics of the reactive power are illustrated, with the DPIG’s generation of reactive power shown in red (FOSM-C). The desired trajectory is represented by the black curve, while the PI controller is indicated by the blue curve. These comprehensive visuals underscore the effectiveness of the SL-FOSM-C in regulating and sustaining the desired system performance.

Figure 12.

Reactive power (Var) using the sensor-less FOSM-C.

Figure 13 provides a graphical illustration of the stator currents, prominently presenting their accurate sinusoidal waveform. Furthermore, the torque of the electromagnetic system is depicted in these illustrations. These comprehensive visuals aim to emphasize the efficiency of the SL- FOSM-C based on Neural-MRAS using the PSO algorithm in controlling and sustaining the desired system performance.

Figure 13.

Electromagnetic torque and currents of stator and using the sensor-less FOSM-C.

The results indicate that the proposed controller successfully met the control objectives by ensuring that the active power followed a time-varying reference derived from the mechanically captured power, while maintaining the reactive power at a constant value of zero. It is noteworthy that changes in real wind speed did not significantly impact the controlled system. Overall, the FOSM-C exhibited superior control performance compared to PI controller.

Proceeding to the segment on Sensor-Less control employing the Neural-MRAS observer, the assessment of the wind turbine chain, incorporating a DPIG, will be executed using an industrial benchmark, as illustrated in Figure 14. This benchmark covers a variable speed range ranging from [+120 to +9 (rad/s)]. This comprehensive testing regimen is designed to evaluate both the efficacy and resilience of the proposed Neural-MRAS, drawing comparisons with MRAS-PI.

Figure 14.

Industrial benchmark configuration.

In Figure 15, a thorough comparison is provided between the speed estimations attained by the novel Neural-MRAS and the MRAS-PI. Remarkably, the dynamics of velocity estimation showcase variances when compared to the measured and reference velocities. However, it is important to highlight that the errors associated with the Neural-MRAS are considerably minimal compared to those observed with the classical MRAS-PI.

Figure 15.

Dynamics of speed estimations using novel neural-MRAS and MRAS-PI.

Specifically, the measured reference speed and error were almost zero for the suggested observer. Conversely, the speed estimated by the MRAS-PI displayed an error of 60 rad/s, notably apparent during the focused rotation speed around 0.5 and 0.7 second when subjected to the application of load torque. This convincing outcome serves as robust affirmation of the durability and enhanced performance provided by the Sensor-Less strategy system incorporating the robust Neural-MRAS.

Figure 16 offers a comprehensive overview of tracking and observation errors, specifically in the presence of load torque application at distinct time instances, namely t = 0.5 seconds, t = 2 seconds, and t = 3.5 seconds, with cancelations occurring at t = 1.5 seconds and t = 3 seconds. This figure vividly demonstrates the exceptional robustness and outstanding performance of the proposed observer (Neural-MRAS), establishing a clear contrast with the MRAS-PI.

Figure 16.

Errors of tracking and observation using neural-MRAS, and MRAS-PI.

These outcomes are distinctly evident through the representation of observation errors (Observation Error = Vmes − Vest) and tracking errors (Tracking Error = Vmes − Vref). The proposed Neural-MRAS observer consistently demonstrates its capacity to mitigate errors and effectively track the desired values, showcasing its superior resilience and performance compared to the MRAS-PI.

As a result, the devised Sensor-Less control strategy for the DPIG successfully attained the control objectives by effectively tracking time-varying active power while maintaining constant reactive power, even in the presence of varying speeds. Furthermore, the implemented observer accurately estimated the real mechanical rotor speed and position, enabling the elimination of mechanical sensors and consequent reduction in controller costs.

Robustness test

The robustness test involved evaluating the Sensor-Less control of DPIG under varying parameters influenced by physical conditions such as:

Inductance Saturation: As the inductances approach saturation, the magnetic flux density in the core reaches its maximum, leading to nonlinear behavior. This affects the dynamic response, causing longer response times and increased transient oscillations.

Resistor Heating: The heating of resistors, typically due to prolonged operation or excessive current, alters their resistance values. This variation impacts the current flow, resulting in deviations in the expected performance, such as slower response times and higher oscillation amplitudes.

Changes in resistances and inductances were examined to determine their impact on response time and the amplitude of transient oscillations

The Table 5 provided details the specific parameter changes and visually represents the resultant performance curves, illustrating how the DPIG system’s response is influenced under these varying conditions.

Table 5.

Variation parameters of DPIG.

Parameter	Variation
Stator resistance	150% Rs
Rotor resistance	150% Rr
Inductance in d-axis	50% Ld
Inductance in q-axis	50% Lq

The simulation results of the robustness test are presented in Figures 17 to 20, illustrating the following observations:

Observation Error Analysis: The comparison of the estimated speed with the actual speed using the Neural-MRAS, and MRAS-PI methods was conducted under conditions of DPIG parameter variations. This comparison highlighted the observation errors for each method for superior results in Neural-MRAS compared to MRAS-PI.

Neural-MRAS Performance: For the Neural-MRAS observer, a slight static discrepancy was noted between the measured and estimated speeds under abnormal conditions, such as variations in rotor and stator resistances (Rr, Rs) and inductances (Lr, Ls), compared to normal conditions. Despite this, the Neural-MRAS observer demonstrated effective estimation of the DPIG rotor mechanical speed.

MRAS-PI Performance: In contrast, the MRAS-PI method yielded unsatisfactory results in terms of speed estimation accuracy under the same varying parameter conditions.

Figure 17.

Influence of a 150% change in rotor and stator resistance (Rr, Rs) on rotational speed.

Figure 18.

Influence of a 150% change (Rq, Rd) on errors of tracking and observation using neural-MRAS, and MRAS-PI.

Figure 19.

Influence of a 50% change in rotor and stator inductance (Lq, Ld) on rotational speed.

Figure 20.

Influence of a 50% change (Lq, Ld) on errors of tracking and observation using neural-MRAS, and MRAS-PI.

The study concludes that the SL-FOSM-C control scheme shows robustness to parameter variations, maintaining reliable control and tracking of stator active and reactive powers even amidst disturbances. Moreover, the Neural-MRAS observer displayed outstanding performance in estimating DPIG speed and position under varying parameter conditions, proving to be an excellent choice for such applications.

Conclusion

This research presents an innovative Sensor-Less 1st Sliding Mode Controller (SL-FOSM-C) designed for a wind turbine system featuring a Doubly Powered Induction Generator (DPIG), addressing both ideal conditions and real-world scenarios. The FOSM-C is applied to control stator powers (active and reactive) and estimate the speed/position of the DPIG rotor utilizing Neural-MRAS, finely tuned and optimized through the PSO algorithm. The objective of the research is to elevate the performance of the MRAS-PI observer.

The primary objective of the study is to decrease the size and cost of the DPIG by eliminating the encoder and introducing the Neural-MRAS. Simulation results validate the robustness and high-speed estimation accuracy of the DPIG rotor across various speed ranges. The proposed innovative Neural-MRAS observer demonstrates low sensitivity and exceptional disturbance rejection compared to the MRAS-PI. In summary, this research highlights the potential benefits of deploying the Neural-MRAS observer in DPIG-based wind turbine systems, including cost reduction, enhanced robustness, and improved speed estimation accuracy under diverse operating conditions. These findings provide valuable insights for the design and optimization of wind power chains.

Potential limitations of the Sensor-Less strategy using the MRAS observer include estimation errors at low and high rotor speeds, as well as reduced robustness under varying parameter conditions. Future work could focus on addressing these limitations by enhancing the accuracy and robustness of the Neural-MRAS observer. This could involve developing advanced algorithms to improve performance across a broader range of operating scenarios and further optimizing the system for greater reliability in diverse conditions.

Footnotes

Appendix

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iDs

Lakhdar Saihi

Fateh Ferroudji

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