MATLAB implementation of dual synergetic control for multi-rotor wind turbine systems

Habib Benbouhenni; Adil Yahdou; Z M S Elbarbary; Ilhami Colak; Saad F Al-Gahtani

doi:10.1038/s41598-025-04040-1

. 2025 May 30;15:18995. doi: 10.1038/s41598-025-04040-1

MATLAB implementation of dual synergetic control for multi-rotor wind turbine systems

Habib Benbouhenni ^1,^✉, Adil Yahdou ², Z M S Elbarbary ^3,⁴, Ilhami Colak ⁵, Saad F Al-Gahtani ^3,⁴

PMCID: PMC12125305 PMID: 40447712

Abstract

Synergetic control (SC) is a technique that is easy to apply and has a fast dynamic response for managing the power generated by a doubly-fed induction generator. However, using this strategy in a power system does not yield satisfactory results regarding energy quality and performance. This research proposes using the dual SC (DSC) technique in conjunction with the modified space vector modulation to enhance performance and increase the robustness of the studied power system. Multi-rotor wind turbines are used to convert wind power into mechanical power. This work investigates the impact of inverter levels on the power quality and competence of the energy system. The designed regulator was applied to the direct power control approach using MATLAB, where some different tests were used. The efficacy and competence of the designed method were compared with the strategy based on the SC controller. The simulated results confirmed the efficacy and strength of the designed control based on DSC regulators compared to the approach based on the SC, where the value of total harmonic distortion was minimized by an estimated ratio of 7.17% and 24.36%. The suggested method in the case of a variable wind speed test reduces the active power ripples by an estimated 40% compared to the control based on the SC. Also, the suggested method in the case of durability testing reduces the value of response time and overshoot of active power by approximately 46.11% and 42.29%, respectively. These results show the efficiency of the suggested method in enhancing the quality of energy and current, which will be of interest in the future.

Keywords: Dual synergetic control, Multi-rotor wind turbine, Modified space vector modulation, Doubly-fed induction generator

Subject terms: Energy science and technology, Engineering

Introduction

Dual-rotor wind turbines (DRWTs), which are sometimes called multi-rotor wind turbines (MRWTs) or counter-rotating wind turbines (CRWTs) in different studies, offer notable advantages over traditional horizontal-axis wind turbines (HAWTs) when it comes to energy efficiency. The design of DRWTs allows them to capture wind energy (WE) more effectively, leading to better overall performance. For instance, the research mentioned in¹ shows that adding a second rotor can significantly enhance how much WE these turbines can capture, resulting in a noticeable improvement compared to wind turbines (WTs) with just one rotor. Another study² looked into how DRWTs handle aerodynamic factors and found that while the shadow from the tower doesn’t significantly affect average performance, it can cause fluctuations that might impact the stability of energy output. On the other hand, traditional HAWTs often face more serious aerodynamic issues, like shadowing from the tower and blade deformation, which can reduce their efficiency under changing wind conditions³. Because of these benefits, DRWTs appear to be a promising option for increasing energy production in WE applications.

WTs remain a promising and reliable solution for electricity generation. Relying on these WTs reduces reliance on conventional energy sources and thus reduces toxic gas emissions⁴. Reducing toxic gases helps mitigate global warming, a growing concern for governments. Furthermore, the use of WTs reduces electricity imports, potentially boosting the economy for governments in non-petroleum-producing countries⁵. In his work⁶, the author argues that the Indian electricity market is now more oriented toward renewable energy sources to meet growing energy demands at affordable prices. He also argues that the Indian WE industry has grown from a marginal activity to a multi-billion-dollar business due to its relatively safer and more favorable environmental features. On the other hand, the author conducted an evaluation study of 14 WE plants in India during the period 2016–2017 to 2019–2020 in terms of relative operational efficiency. The analytical study showed that 14% of India’s WE plants operated at their highest levels of productivity during the observed period (2016–2017 to 2019–2020). The analytical study also showed that the lifetime of WTs negatively impacts production efficiency. However, site elevation has a positive impact on the operational efficiency of WE plants. This analytical study may help stakeholders and decision-makers identify the key factors affecting WE plant performance and improve operational strategies and policies. In⁷, subsynchronous resonance is considered one of the most prominent problems in wind farms based on induction generators. This problem can be overcome by using a static synchronous compensator. The Bacteria Search Optimization Algorithm (BFOA) was used to select the controller gain values used in a static synchronous compensator control scheme. The proposed approach was applied to a 500 MW IG-based wind farm subjected to a three-phase LLL-G fault near the point of common coupling. MATLAB was used to implement the designed approach in three different cases: without a static synchronous compensator, with a basic static synchronous compensator, and with the proposed BFOA-optimal static synchronous compensator. Simulation results demonstrate the effectiveness of the proposed BFOA-optimal static synchronous compensator in mitigating potential subsynchronous resonance, allowing for increased wind farm performance. Another work in⁸ addressed the problem of subsynchronous resonance, which creates several drawbacks in wind farms. In this work, the Whale Optimization Algorithm (WOA) was proposed to mitigate low-frequency torsional oscillations. The WOA algorithm was used to control the pitch angle and the external resistance attached to the rotor. The effectiveness of the proposed WOA-based controller was examined using a time-domain approach based on the dynamic response (DR) of various components of the test system. MATLAB was used to implement the designed approach. Simulation results reveal the potential of the proposed WOA-based controller in damping low-frequency torsional oscillations, making it a promising solution for future applications. In work⁹, a WE system was integrated with a photovoltaic system to generate electricity. Also, a static synchronous compensator was used in this proposed hybrid system to dampen and control the overall chaotic oscillations in a dual-zone power system. Two proportional-integral (PI) controllers were used to regulate the AC and DC currents of the static synchronous compensator module. A hybrid swarm-based particle swarm optimization-BFOA optimizer and a molecular heuristic optimizer were used to optimize and control the PI controller parameters. This studied energy system was implemented in MATLAB under various operating conditions. Simulation results reveal the potential of the hybrid wind photovoltaic farm as a two-PI controller in mitigating global chaotic oscillations. The author sees in¹⁰ that the widespread use of renewable energy systems, especially wind farms, and their integration into existing transmission systems are facing challenges. These challenges are represented in the reliability of the power system due to sudden interruptions in WE and stability, so it is necessary to set strong network requirements. These challenges have received great attention from decision-makers and researchers. Fault ride-through is considered one of the most prominent requirements for integrating WE into the grid. A study is presented on the development criteria for fault ride-through for any wind farm connected to the high-voltage transmission grid, as well as the impacts on various types of protection due to high WE penetration depending on the type of wind generator technology. This study is conducted on the Egyptian case as a model, which is characterized by a high concentration of wind resources in a specific area and the absence of conventional power plants. These wind farms also feature a long transmission line connected to the load. Combined modeling of various WT technologies was performed at wind farms, using the DIgSILENT-Power Factory simulation software to achieve the study objective under various disturbance scenarios. The study results demonstrated the importance of developing fault ride-through criteria to improve the operational performance of wind farms. With the increasing complexity of the power system and the presence of hundreds of lines involved due to the spread of renewable and traditional energy sources to meet the increasing load demand, the author¹¹ argues that transmitting power over long distances of up to hundreds of kilometers makes it difficult to locate the fault in the network. Therefore, it is necessary to develop appropriate algorithms to accurately locate faults in the presence of a large number of transmission lines. A new method based on the wavelet artificial neural network was developed to detect faults, thereby increasing performance and reducing costs. In this proposed strategy, detailed coefficients (D1 coefficients) obtained from current signals are used to train and test the artificial neural network (ANN). Fault location was performed in the presence of renewable energy sources at different distances and fault impedances on a four-bus connected transmission system. The MATLAB environment was used to implement the system, and the proposed wavelet-based algorithm was tested for all fault conditions in the presence of renewable energy sources with different power ratings at different distances. The obtained results highlight the effectiveness and efficiency of the proposed method in detecting and mitigating faults.

In the field of WE, several generators are used to generate electrical power. These generators convert the mechanical energy generated by WTs into electrical energy. The most prominent generators used in WE systems are permanent magnet synchronous generators¹² and doubly fed induction generators (DFIGs)¹³. In¹⁴, the resilience of both the permanent magnet synchronous generator and the DFIG to potential grid disturbances, such as symmetrical and asymmetrical short circuits and voltage dips, was studied. The MATLAB environment was used to implement the systems based on both the permanent magnet synchronous generator and the DFIG, under the same grid conditions and wind speed (WS). This study aims to determine which generator achieves the greatest benefit in power quality under phase short circuit conditions. The results obtained showed that the DFIG-based power system reached its nominal effective power faster than the permanent magnet synchronous generator-based WT system. Furthermore, the frequency converter of the permanent magnet synchronous generator-WT system was more susceptible to power grid failures than the DFIG-based WE system, resulting in a significant increase in the DC bus voltage. This work provides an incentive to focus on the use of DFIG in power systems, as this generator was used in this work. On the other hand, the variable nature of WSs significantly impacts electricity generation, and the integration of large wind farms into the grid can lead to electricity quality problems. According to the work done in¹⁵, the DFIG is more suitable for variable WSs than the permanent magnet synchronous generator, due to the ability to control the output power through the rotor feed. Furthermore, the increasing number of WTs connected to the grid leads to electricity quality issues, including voltage instability and difficulties controlling reactive power and frequency. Therefore, power quality is one of the most significant drawbacks limiting the deployment of these energy systems. Therefore, it is essential to address power quality in DFIG-based systems.

Researchers have explored various methods for controlling DFIGs in WT systems to enhance performance, particularly in reference tracking and robustness. These approaches generally fall into two kinds: linear control and nonlinear approach. Implementing field-oriented control (FOC) with PI regulators in DFIG-based WTs poses several challenges. One major issue is the time-consuming nature of traditional PI tuning approaches, which often rely on error and trial, leading to suboptimal performance¹⁶. Additionally, DFIG systems can struggle to manage power effectively under unbalanced grid voltage scenarios, resulting in torque oscillations. Furthermore, this type of control tends to be less robust when internal or external disturbances occur¹⁷. In¹⁸, the authors propose both direct and indirect methods based on PI regulators to regulate the stator power of DFIG using a storage unit. The results demonstrate good reference tracking when the indirect method is applied. However, the robustness test was not studied in this research, and ripple effects can be observed in the power and torque curves. Table 1 presents selected published papers that show improved performance compared to the PI controller applied to power control of DFIG-based WTs.

Table 1.

Selected published papers addressing the limitations of the PI controller applied to power control in WTs.

References	Techniques	Contributions	Limitations
¹⁹	Direct torque control (DTC)	New modified switching table for WT-DFIG system Efficiency analysis of 12-sectors of DTC under variable WS Performance comparison of 12-DTC and conventional DTC (C-DTC)	Torque and flux ripples for C-DTC High total harmonic distortion (THD) value observed when C-DTC was applied
²⁰	Direct power control (DPC)	Novel DPC approach with artificial neural network Experimental validation of intelligent DPC technique using dSPACE	Ripple in torque of the generator Lack of guarantee for maximum energy due to power oscillations
²¹	Improved DTC	Improved DTC with fuzzy estimator for wind system stability	Impact of parametric variations on DTC technique Sensitivity of control to variations in resistance (R_s) highlighted
²²	Modified DTC	DTC based fuzzy super-twisting sliding mode controllers (STSMCs)	High ripples current, torque, rotor flux Slow response
²³	Improved DTC	Fuzzy logic-based 5-level DTC technique is employed to enhance DR performance and reduce torque and flux fluctuations	Complexity High current THD High flux and torque fluctuations
²⁴	Robust DTC	This paper suggests implementing second-order continuous sliding mode DTC for a DFIG	High THD value of current for C-DTC (2.57%) Complexity

Open in a new tab

Sliding mode control (SMC) of active and reactive power control is a nonlinear strategy proposed in²⁵ to overcome the shortcomings and problems of the PI-based approach. The SMC approach is used to generate voltage reference values, and two different strategies are used to convert these reference values into pulses to operate the machine’s inverter. This approach was implemented in MATLAB, and the results showed that the SMC approach based on space vector modulation (SVM) reduces the THD of current by approximately 26.83% compared to the SMC approach based on pulse width modulation (PWM). Furthermore, the SMC approach based on the SVM technique significantly improves power quality and increases robustness. However, the drawbacks of this approach are complexity and the presence of chattering, which causes several network problems. In²⁶, Active Disturbance Rejection Control (ADRC) was proposed to control the power of a DFIG. This strategy was compared with the PI approach, and MATLAB was used to implement this approach. Simulation results showed that the ADRC approach significantly reduces power ripples and overshoot compared to the PI approach. The author argues²⁷ that the widespread use of WTs has prompted electrical engineering researchers to consider improving the quality of power supply, given that it is the most promising energy source for our needs. To increase the efficiency of WE systems, points must be exploited more precisely. Therefore, maximum power requires the use of highly efficient maximum power point trackers (MPPTs), which are essential for WE systems by improving energy production. Furthermore, the use of power control is highly robust and highly effective in reducing power fluctuations. Fuzzy logic control was applied to continuously and independently control the reactive and active power generated by the DFIG of a flow-oriented WE system. This designed strategy was implemented in the MATLAB environment, with performance compared to the PI approach. Simulation results demonstrated the effectiveness of using the fuzzy approach in improving the operational performance of the studied power system compared to the PI approach. However, using the fuzzy approach has drawbacks, as it relies heavily on experience, requiring multiple iterations to obtain satisfactory results. In²⁸, the ANN approach was used to overcome the limitations of the PI control scheme. These limitations are a result of the nonlinearity of the DFIG model. Furthermore, the use of the PI control scheme requires the use or reliance on machine parameters, which reduces robustness in the event of a fault. The use of the ANN approach significantly improves the transient response of the DFIG system, while also reducing its computation time. This designed approach is implemented in the MATLAB environment, and its performance is comparable to that of a traditional PI controller-based approach. Simulation results show that the proposed ANN approach significantly improves the transient behavior of active and reactive power on the rotor side, and reactive power and DC bus voltage on the grid side, compared with the conventional control scheme. Using the ANN approach is passive, as it relies on experience. There are no rules that facilitate determining the required number of internal layers and number of cells to achieve optimal results. As is well known, the ANN approach relies heavily on experience and experimentation, requiring effort and time to achieve satisfactory results. The fuzzy second-order sliding mode (FSOSM) approach is the proposed solution in²⁹ to replace the traditional DPC controllers for DFIG. Using this controller allows for a significant increase in the performance and efficiency of the DPC approach, as it is characterized by high robustness and the ability to reduce current/power ripples compared to the traditional approach. This designed controller is used in conjunction with the SVM strategy. This designed controller was implemented using MATLAB, where variable WSs were used to study behavior and performance, and the results were compared with the traditional approach. Simulation results showed that using the DPC-FSOSM approach reduces the THD value by 19.42% compared to the second-order SMC approach. However, using an FSOSM controller has drawbacks, as it increases complexity and makes the DPC strategy expensive and difficult to implement. Furthermore, using an FSOSM controller increases the number of gains, making it difficult to control the DR of the power. Therefore, it is necessary to search for an approach that is simple, easy to implement, and effective in reducing power fluctuations in the DFIG. Four different strategies were proposed in³⁰ to control the DFIG power. These strategies are PI, SMC, RST, and fuzzy supervisory controllers (FSCs). After presenting mathematical models for each controller, these strategies were implemented in MATLAB using various tests. The simulation results demonstrate the superior performance of FSCs compared to other strategies in terms of robustness and reference traceability. Furthermore, the use of FSCs significantly improves the DR of power compared to other strategies. Despite the high performance of the FSC approach, some drawbacks limit its widespread adoption. The most significant drawback is the lack of a rule that facilitates determining the best value for the fuzzy rules to achieve satisfactory results. In³¹, the use of a neural network-based indirect FOC strategy was proposed. This strategy is characterized by a fast DR and high robustness due to the use of neural networks. This strategy was implemented using real tools, and the results demonstrated the effectiveness and efficiency of the designed approach in improving the quality of power and current. This approach also significantly reduces the THD value compared to the traditional approach. In³², a variable-speed WE conversion system based on a DFIG, in which the stator is directly connected to the electricity grid, was investigated. Direct control of the DFIG was implemented using a variable structure based on an ANN algorithm. The ANN algorithm was used to improve performance and replace traditional PI regulators in directly controlling the active and reactive power of the DFIG. The performance of this designed approach has been tested and validated through simulation under various operating conditions. Simulation results reveal superior performance of the designed approach compared to the PI approach in terms of current and power quality. However, despite this performance, the designed approach has a drawback: its reliance on a mathematical model of the machine, renders the designed approach unsatisfactory in the event of a system failure.

In the world of nonlinear control, backstepping control (BC) has emerged as a favored method for managing electrical machines^33,34. BC technique stands out due to its structured approach, where the control design is broken down into a series of smaller, more manageable steps. This method works by gradually stabilizing each subsystem of a complex system, effectively ‘backstepping’ from the desired outcome to the initial control inputs. As a result, the BC technique significantly boosts the stability and overall performance of electrical power systems, especially when navigating the complexities of nonlinear dynamics and uncertainties^35,36. By methodically addressing these control challenges, the BC technique enhances both the resilience and adaptability of electrical machines, making it applicable across a wide range of scenarios.

In³⁷, BC strategy and PI controller techniques were applied in the outer and inner regulation loops of the rotor-side converter (RSC) in a WT based on DFIG. The results of this paper show the efficient suppression of disturbances, with the BC approach exhibiting faster convergence properties compared to the PI controller. In³⁸, a model combining vector control and a nonlinear BC approach is developed to control the rotor currents and mechanical speed of DFIG. This proposed approach aims to extract the maximum generated power. This designed approach has high performance and great robustness compared to the conventional approach. This designed approach was implemented in a MATLAB environment and compared to a PI controller. The comparison was made in terms of reference tracking and its robustness to changes in DFIG parameters. Simulation results reveal the validity and effectiveness of the proposed control strategies compared to the PI approach in terms of reducing power fluctuations and increasing robustness. However, this approach has drawbacks, including its high degree of complexity and the presence of a significant number of gains, which makes it difficult to control the DR. In³⁹, the performance of the BC strategy of the DFIG was compared with the sliding mode control (SMC) approach. These strategies were used to control both the RSC and the grid-side converter (GSC). The BC strategy has asymptotic stability in the context of Lyapunov theory. This comparison was performed in MATLAB using different scenarios. The simulation results showed good system performance under these proposed control strategies. Compared with the BC strategy, the SMC approach shows the best performance. Numerical results show that the SMC approach reduces the response time for stator flux, velocity, and rotor flux by 10.32%, 1.69%, and 12.54%, respectively, compared to the BC approach. However, in terms of static errors, the approach yielded similar results to the SMC approach.

In reference⁴⁰, an integral BC (IBC) technique was proposed for a WT using a DFIG to enhance the MPPT technique. The overall system stability was analyzed using Lyapunov candidate functions, integrated throughout various stages of the BC technique design process. Additionally, a robust IBC technique-based DPC strategy was introduced for a DFIG-based WT system, aimed at enhancing the control system’s performance under conditions of distorted grid voltage⁴¹. Furthermore, in⁴², the authors proposed a nonlinear BC strategy for the RSC of a DFIG, with the primary goal of improving torque reference tracking facilitated by the MPPT technique. However, the conventional BC method does not account for external uncertainties, disturbances, or variations in system parameters during the design process^43–46. Moreover, designing a BC system requires accurate parameter values of the regulated system to effectively meet the desired control objectives^47,48.

In the field of control, a simpler approach than the BC approach has been designed. This approach is called synergetic control (SC)⁴⁹. This strategy is described by its ease of realization and the lack of use of a mathematical model (MM) of the system under study, which gives it a pros in robustness testing⁵⁰. According to the work done in⁵¹, the SC approach has a fast DR which makes it a prominent solution in industrial fields compared to other regulators such as PI or SMC technique. This strategy has been widely used in the field of renewable energy due to its pros, as it has been used in the field of WE⁵² and photovoltaics⁵³.

The work done in⁵⁴ shows that the SC approach has a strong and effective performance compared to the SMC technique in enhancing the features of a power system based on the use of DFIG. According to this work, the SC approach reduced the overshoot and steady-state error (SSE) of active power (P_s) by 67.74% and 78.01% times, respectively, compared to the SMC technique. The current THD was also reduced by a factor of 50 compared to the SMC technique. Therefore, the SC offers significant performance that can be relied upon in other industrial applications. In⁵⁵, a comparison was made between the SC approach and the super-twisting algorithm (STA) to demonstrate which strategy has the highest performance. These strategies were applied to the DPC approach of DFIG. Simulation results showed that the SC minimized P_s fluctuations by 66.66% and 50% compared to the PI and STA regulators, respectively. On the other hand, the SC approach improves the current THD by 56.05% and 40% compared to the PI and STA regulators, respectively. These results demonstrate the efficacy and robustness of the SC approach compared to both PI and STA controllers, and these results can be used in other applications.

In the field of control, several different approaches have been designed for the SC technique, most of which are combinations of other control approaches. The most prominent of these proposed approaches is the SC-SMC presented in the work⁵⁶. This strategy was used in conjunction with the PWM approach to defeat the cons of the DPC approach of DFIG. Using this suggested approach allows for ripple reductions of 41.17% and 94% for the P_s and reactive powers (Q_s), respectively, compared to the DPC technique. Furthermore, the SC-SMC reduces the current THD by 54.47% compared to the traditional controller. These figures highlight the effectiveness and robustness of the approach in enhancing power and current quality (54.47%). Another improved strategy was proposed for the SC technique in⁵⁷ to enhance the efficacy of the photovoltaic system, using a simplified STA controller. The obtained approach is described by simplicity and strong performance. Results showed that the suggested approach has a faster DR compared to the PI approach, reducing the battery charging time by an estimated 51.43%. Also, this suggested approach reduced the fluctuations of photovoltaic system power, battery power, and load power by 97.03%, 96.25%, and 93.03%, respectively compared to the PI controller. SC technique is integrated with the PI controller to defeat the cons of the DPC technique of DFIG-MRWT systems⁵⁸. This algorithm has high performance and robustness as demonstrated by simulation results compared to the usual strategy and some related works. A genetic algorithm (GA) is used to calculate the gain values of this proposed strategy. This strategy reduces ripple values by 34%, 22.95%, 44%, and 36.93% for torque, P_s, current, and Q_s, respectively. In⁵⁹, an integral-synergetic controller (ISC) was suggested as a solution to replace the use of SC controllers in the control domain. This proposed ISC strategy was used to defeat the drawbacks of the DPC technique of DFIG-MRWT. Fast DR, high robustness, and excellent performance are the most prominent features of the ISC approach compared to the SC technique. Using the ISC method does not require knowledge of the MM of the system under consideration, and it gave satisfactory results in all tests performed compared to the SC controller and some related works. The fractional-order SC (FOSC) technique is an optimum solution proposed in⁶⁰ to defeat the problems of the DPC strategy of DFIG-MRWT. This approach was compared with the conventional algorithm, where variable WS was used for the study. Results showed that using the FOSC technique reduces both SSE and overshoot of P_s by 94.55% and 85%, respectively, compared to the conventional approach. However, in the robustness test, it was observed that the FOSC technique was affected by the change in DFIG parameters, which is undesirable. In⁶¹, a SC technique was proposed to improve the power quality of distributed generation systems. The SC approach was used to maintain the DC link voltage. The SC approach was compared with an adaptive lizard algorithm (ALA)-based PI controller, a fuzzy logic controller, an adaptive fuzzy logic controller, and a SMC technique. This study was conducted in the MATLAB environment, comparing the strategies in terms of THD. Simulation results show that the ALA-based PI controller performed better than the SC approach and other strategies. These results show that the SC approach gave unsatisfactory results in terms of THD of current. The FOSC strategy was also used in⁶² to control the operation of a filter, where it gave excellent results in terms of DR and power ripple reduction compared to the PI approach and some related works. Terminal synergetic control (TSC) strategy has been suggested as a suitable solution that can replace the SC strategy in the field of renewable energy⁶³. This strategy is described by high competence and great robustness, as it relies on the use of a terminal sliding surface instead of a linear error. The effectiveness of the TSC technique was confirmed using MATLAB, where various tests were proposed. All of the obtained results highlight the significant superiority of the TSC technique over the conventional controller in terms of reducing the current THD, fluctuations, and overshoot of DFIG power. However, in the robustness test, it was noted that this TSC controller was significantly affected by changes in DFIG parameters, which is undesirable.

In contrast to prior research, this paper focuses on the control of Q_s and P_s in a variable-speed DFIG-MRWT, utilizing a smooth and robust control strategy based on the modified SVM (MSVM) technique. This method, integrated with the dual SC (DSC) strategy, is designed to enhance the competence and longevity of the energy system under study. Therefore, the DSC controller is the first major contribution of this paper. This regulator is described by simplicity, low gain, low cost, and ease of realization. This regulator is used in this paper to overcome the problems and drawbacks of the DPC technique of DFIG-MRWT. Therefore, the proposed DPC-DSC approach with a two-level MSVM technique is the second major contribution of this paper. This algorithm is an improvement over the usual approach, featuring a fast DR. The MSVM technique was adopted due to its simplicity and high performance compared to both SVM and PWM. Furthermore, the MSVM technique is easy to implement, making the proposed system less expensive. Figure 1 represents a schematic diagram of the proposed DSC-based technology. This figure provides a simplified overview of the basic steps for implementing this proposed approach. The implementation of this proposed algorithm achieves several objectives, which can be described as follows:

Ensuring robustness and accurate reference tracking compared to the DPC-SC approach.
Overcoming the problems of the traditional strategy.
Significantly improving power and current quality compared to the DPC-SC technique.
Significantly improving the current THD value.
Improving the DR of the power compared to the DPC-SC approach and some related work.

The approach based on DSC controllers was compared with the DPC-SC technique, using MATLAB to implement the control. A variable WS profile was used to investigate the effectiveness and efficiency of the DPC-DSC technique in terms of minimizing fluctuations, current THD, overshoot, and reference tracking. Furthermore, the proposed DPC-DSC technique was compared with related works in terms of power response time.

The paper is structured as follows: “Proposed DSC controller” section outlines the design of the DSC model, emphasizing its key features. “Proposed DPC-DSC-MSVM approach” section examines the DPC model based on DSC techniques, detailing its disadvantages and advantages. “Results” section presents simulation results for the designed DPC-DSC technique using a variable WS profile. Finally, “Conclusions” section summarizes the conclusions drawn from this work and provides a brief overview of future directions.

Proposed DSC controller

This section discusses a new controller based on the SC regulator. This proposed controller is named the DSC technique. The SC strategy is described by its simplicity, small gains, and ease of realization⁶⁴. Using this approach does not require complex calculations, making it easy to use in complex systems⁶⁵. According to the work done in⁶⁶, using the SC approach does not require precise data on the MM, which makes it less affected by changes in the parameters of the system under study. The design procedure of the SC technique is based on a macro-variable as a function of the state variables, φ = φ(x). Depending on the work⁶⁷, the SC controller can be expressed by Eq. (1).

where, φ is the macro variable and T is the convergence speed.

The nonlinear SC technique will compel the system to slide and operate onto the manifold φ = 0 operation.

Equation (2) represents the derivation of macro variables^63,65.

where, x denotes the state vector.

Equation (3) is a solution to Eq. (1)⁶⁶.

where, t is the time.

Figure 2 represents the SC technique. This figure gives an insight into the simplicity and ease of applying this algorithm to control. Furthermore, this strategy is easy to adjust due to its small number of gains, making it one of the most reliable solutions.

According to the⁶⁸, the SC technique gave unsatisfactory results compared to the modified SC approach in terms of response time and reduction of energy and current ripples for the DFIG. Moreover, several solutions were proposed to defeat the drawbacks of the SC strategy. The most prominent of these solutions was proposed in the works^57–62. These solutions gave somewhat satisfactory results. It is noted that the most prominent of these proposed solutions increased the complexity of the SC technique. Also, some of the proposed solutions made the SC approach dependent on the MM of the system under study.

This work proposes a solution based on the use of the two SC approaches, as shown in Fig. 3. This figure provides a clear picture of the proposed solution to defeat the cons of the SC technique, where simplicity, high robustness, and excellent competence are the most prominent features of this solution.

The DSC controller can be represented mathematically by Eq. (4). This controller is a modification and development of the SC controller using two controllers with the same parameters.

where, T > 0.

DSC controller parameters can be calculated using trial and error simulation, a strategy that doesn’t require complex software or extensive calculations. Smart algorithms can also be used to calculate DSC controller parameters. Using smart algorithms, such as Grey Wolf optimization, requires writing a program. These strategies sometimes don’t yield satisfactory results, requiring repeated iterations to obtain better gain values with improved performance. On the other hand, this paper relies on experimentation and simulation to obtain the gain values of the proposed approach. This method does not require writing complex programs. Furthermore, it does not require significant effort or time. The values that yielded good results in terms of power ripples and THD of current are taken (Supplementary Information).

This regulator is used in this paper to defeat the shortcomings of the DPC technique of DFIG-MRWT. In the following section, this proposed approach to power control is discussed, highlighting its main features.

Proposed DPC-DSC-MSVM approach

The DPC-DSC technique with a two-level MSVM technique is the approach designed in this work to replace the DPC technique. This strategy is a new approach that differs from the DPC technique in that it does not use a switching table. Using this approach overcomes the problems and cons of the DPC technique, such as low robustness and power fluctuations. This designed algorithm was applied to the machine’s inverter only to demonstrate its robustness and effectiveness without the need to control the grid inverter. In this work, an uncontrolled inverter (using diodes) was used to embody the grid inverter. Using an uncontrolled inverter allows for simplifying the system and reducing costs. Furthermore, using an uncontrolled inverter makes the system under study easier to implement.

This suggested method differs from the above literature in terms of structure, simplicity, robustness, number of gains, and ease of realization. The proposed approach relies on the Park transform and power estimation. Furthermore, the MPPT strategy is used to determine the reference value of the active power.

The DPC-DSC technique proposed in this work is an evolution of the DPC technique. Figure 4 illustrates the principle and structure of the DPC-DSC technique. From this figure, it is evident that the approach is simple, easy to implement, inexpensive, and easy to adjust. Furthermore, this approach does not require precise data on the MM of the system under study, which enables it to yield satisfactory results in robustness testing. A two-level inverter is used to embody the machine’s inverter, chosen for its ease of implementation and control. Using a two-level inverter reduces system complexity and costs. This inverter is controlled using the MSVM strategy.

Fig. 4 — Proposed DPC-DSC technique of DFIG.

The DPC-DSC approach is a DPC method that replaces the usual hysteresis comparators with DSC controllers. These controllers convert power errors into reference voltage values. These reference values are used to generate pulses to operate the inverter. On the other hand, the switching table of the DPC method is also replaced by the MSVM approach. The use of the MSVM approach allows for better control of the inverter and significantly simplifies the system. The MSVM strategy was chosen due to its simplicity and ease of realization compared to the SVM approach.

The MSVM strategy was discussed in detail in the work⁶⁹, where its advantages over the SVM approach were mentioned. In work⁷⁰, the MSVM strategy was implemented experimentally using dSPACE 1104, and the experimental results were compared with each of the PWM, neural SVM, and traditional SVM techniques. The experimental results showed the high performance of the MSVM strategy compared to other strategies in terms of improving the current quality. Based on the work done in⁷⁰, the two-level MSVM strategy used in the designed approach is shown in Fig. 5.

The proposed approach is less computationally complex, as the use of a DSC controller does not require complex calculations. The experimental design approach can be implemented using the dSPACE 1104 or the HIL test.

The DPC-DSC approach with the MSVM technique relies on the use of the MPPT strategy with PI controller to determine the reference value of the P_s. Using the MPPT approach protects the turbine from strong winds and makes the current and torque values dependent on the variations in WS. In this proposed strategy, the reference value of the Q_s is set to 0 VAR to achieve a power factor of 1.

The DPC-DSC approach with the MSVM technique uses the same estimation equations as the conventional DPC technique. In this designed strategy, both P_s and Q_s are estimated, requiring voltage and current measurements to estimate the power. Furthermore, to estimate the power, the flux must first be estimated.

To estimate the stator flux, Eq. (5) can be used. This flux is related to the resistance, current, and voltage of the stator⁷¹.

With: Inline graphic .

According to the work⁷² the rotor flux estimate is made by Eq. (6).

With: Inline graphic .

Based on the work⁷³ the P_s is estimated according to Eq. (7). The P_s is estimated based on the quadrature rotor flux.

With:

To estimate the Q_s, Eq. (9) is used. The estimation of the Q_s is related to the direct rotor flux⁷⁴.

In this proposed strategy, there are Ps errors and Qs errors. These errors are listed in Eq. (10).

where, ε_Ps is the P_s error and ε_Qs is the Q_s error.

In this proposed approach, a single DSC controller is used to command both the P_s and Q_s and Eq. (4) is used for this purpose. Using Eq. (4), the reference voltage values according to the proposed strategy are calculated using Eqs. (11) and (12).

Using Eq. (11) allows the calculation of the reference value of the quadrature rotor voltage based on the P_s error.

Equation (12) is used to calculate the reference value of a direct rotor voltage, where this value is related to the Q_s error.

The DSC controllers used in the DPC strategy for power control are represented in Fig. 6. This diagram illustrates the simplicity of these controls. These controls do not require complex calculations or programming. They can be easily implemented in complex systems, where all it takes is knowing the error or surface.

Table 2 compares the designed approach with some existing strategies such as DPC, SMC, and DPC-SC. This table highlights the similarities and differences between the designed approach and some existing strategies. The most notable similarity between the designed approach and these strategies is the use of the same control parameters (Qs and Ps). Also, the same power estimation equations are used in other strategies such as DPC-SC and DPC. The designed approach is similar to the SMC approach in that it does not use a switching table or hysteresis comparator. However, the designed approach differs from SMC and other approaches in that it uses the MSVM strategy to control the inverter of the machine. Furthermore, it significantly reduces power fluctuations and THD of current. Compared to the SMC approach, the designed approach is free of chattering, making it a promising solution for the future. Moreover, the use of the designed approach does not depend on the MM of the system under study, which makes it less affected by changes in machine parameters and more robust than other strategies such as DPC.

Table 2.

Compared to other strategies.

	DPC	SMC22	DPC-SC	DPC-DSC
Switching table	Yes	No	No	No
PI controller	No	No	No	No
Hysteresis comparator	Yes	No	No	No
Chatterring phenomenon	No	Yes	No	No
MSVM technique	No	No	No	Yes
Complexity	Low	Medium	Low	Medium
Using the system parameters studied	No	Yes	No	No
Dynamic response	Very quick	Fast	Fast	Very quick
Number of controller gains	Low	Medium	Low	Medium
PWM technique	No	Yes	Yes	No
Impacted by changes in system parameters	High	Medium	Low	Low
Power ripples	High	Medium	Medium	Low
MPPT technique	Yes	Yes	Yes	Yes
Current THD	High	Medium	Medium	Low

Open in a new tab

The gain values of the DSC regulator of DFIG power can be calculated using smart strategies, in this case, the genetic algorithm or the Grey Wolf optimization algorithm. Using this algorithm requires writing a program, and sometimes satisfactory results are not obtained immediately, requiring multiple iterations. An easy and painless method, using experimentation and simulation, is used in this work to calculate the gain values of the DSC controller of DFIG power. This technique does not require writing programs and is reliable, as the values that yielded satisfactory results in terms of power and current quality were taken.

The stability of the designed approach can be proven using the Lyapunov theorem. This method relies on calculating the derivative to prove stability. Calculating the derivative makes the Lyapunov theorem somewhat complex and labor-intensive. However, there is another method for proving stability that is simpler and does not require complex calculations. This method is the Bode curve, where both magnitude (dB) and phase (deg) are extracted to prove stability. The Bode curve method is a graphical method based on the use of MATLAB, which makes it inexpensive and does not require complex calculations. This method depends on extracting the value of both the gain margin and phase margin.

According to the Bode curve method, a control strategy is stable if both the phase margin and gain margin are positive. In this paper, the Bode curve is used to prove the stability of the DPC-DSC approach due to the absence of complex calculations and the ease of obtaining accurate and reliable results.

Figure 7a represents the Bode curve for the DPC-SC approach. From this figure, it is noted that the values of both phase (deg) and magnitude (dB) change with frequency, taking negative values. The magnitude (dB) value varies from 2 to − 250 dB, while the phase (deg) value varies from 0 to − 450 degrees. If the magnitude (dB) value is 0, the phase value is approximately − 135 degrees. Therefore, the phase margin value is approximately 45 degrees. Furthermore, if the phase (deg) value is 180 degrees, the magnitude (dB) value is approximately − 4 dB, which means that the gain margin value is 4 dB. Therefore, both the gain margin and phase margin values are positive, and thus the DPC-SC approach is stable.

Figure 7b represents the Bode curve for the DPC-DSC approach. From this figure, it is noted that the Magnitude (dB) value varies from + 2 to − 230 dB, while the Phase (deg) value varies from 0 to − 450 degrees. Therefore, the Phase (deg) value when Magnitude (dB) equals 0 is approximately − 45 degrees. Therefore, the Phase Margin value for the DPC-DSC approach is approximately 135 deg. On the other hand, when Phase (deg) equals 180 degrees, the Magnitude (dB) value is approximately − 9 dB. Therefore, the Gain Margin value is 9 dB. Since both Phase Margin and Gain Margin are positive, the DPC-DSC approach is stable.

The DPC-DSC strategy was implemented in this paper using MATLAB and compared to the DPC-SC technique, and the results obtained are presented in the next section.

Results

In this section, the DPC-DSC technique is implemented using simulations using MATLAB 2014. The competence and effectiveness of the DPC-DSC technique are compared with those of the DPC-SC. The DPC-DSC technique is also compared with related work in terms of reducing the response time of the power and the current THD. In this work, two different WSs (variable and step forms) are assumed to study the performance of the designed approach. Furthermore, the resistance values are increased by 100%, and the inductance values are decreased by 50% to perform the durability test. In tests one through three, the MPPT strategy is required to determine the reference value of the Ps. However, in the fourth test, the MPPT strategy is not required to determine the reference value of the Ps. In the fourth test, two different values are required for the reference value of the Ps to study the performance and effectiveness of the designed approach.

The system parameters are listed in Table 3.

Table 3.

System parameters.

Parameter		Values
DFIG	R _s	12 mΩ
	P _sn	1500 kW
	L _r	13.6 mH
	p	1
	R _r	21 mΩ
	J	1000 g.m²
	L _s	13.7 mH
	L _m	13.5 mH
	f _r	0.0024 Nm/s
	Vs	398 V
	fs	50 Hz
MRWT	R ₁	13.2 m
	fr	0.0024 Nm/s
	r _g	0.75 m
	r ₁	1 m
	r ₂	0.5 m
	J ₁	500
	J ₂	1000
	R ₂	25.5 m

Open in a new tab

Figure 8 represents the DPC-DSC technique in MATLAB. This figure provides the structure of the proposed approach, illustrating all the elements that make up the proposed approach. A figure illustrating the two controls together in MATLAB is also included. Figure 8 provides a clear picture of the validity of the DPC-DSC technique.

First test

The first test uses variable WS to investigate the efficiency of the DPC-DSC technique in improving current and power quality compared to the DPC-SC approach (Fig. 9). Figure 10 represents the WS variation profile used in the first test. The results of this test are presented in Figs. 10 and 11. Also, numerical results were obtained for the ripple response time, overshoot, and SSE of the DFIG energy. These numerical results are presented in Table 4.

Fig. 11 — Zoom in the results of the first test.

Table 4.

Ratios of response time, SSE, overshoot, and energy fluctuations of both techniques.

		P_s (W)	Q_s (VAR)
DPC-SC	Ripples	10,000	12,950
	SSE	4000	6000
	Overshoot	3800	2920
	RT (ms)	1.05	1.05
DPC-DSC	Ripples	6000	8529
	SSE	1130	4098
	Overshoot	800	435.50
	RT (ms)	0.650	0.68
Ratios (%)	Ripples	40	34.14
	SSE	71.75	31.70
	Overshoot	78.95	85.09
	RT (ms)	38.10	35.24

Open in a new tab

Figure 10a,b represent the DFIG power outputs using two controls. These figures show that these power outputs track the references well, with a rapid DR to the two controls. Waves are also observed across these power outputs. According to Fig. 10a, the P_s take the form of changes in WS as a result of using the MPPT, with negative values indicating that the machine is generating power and feeding it to the grid. However, the Q_s (Fig. 10b) remain constant throughout the simulation period and are not affected by changes in WS.

Figure 10c represents the current for the two controllers. According to Fig. 10c, this current varies with the change in WS due to the use of the MPPT approach. Also, ripples are observed in this current when using two controllers. This stream has a sinusoidal shape.

Figure 10d represents the torque for the two controllers. From this shape, the torque value changes with the change in WS, as the shape of this torque is the same as the shape of the P_s. This torque has a negative value. Also, ripples are observed when using two controllers.

The THD value of current using both controls is shown in Fig. 10e,f. These figures show that the THD value was estimated to be 2.51% for the DPC-SC technique and 2.33% for the DPC-DSC technique. These values highlight that the THD value is lower in the case of using the DPC-DSC technique compared to the DPC-SC technique. Therefore, the proposed approach reduced the THD value by 7.17% compared to the DPC-SC technique. On the other hand, Fig. 10e,f show that the fundamental signal (50 Hz) amplitude was estimated to be 411.30 A and 412.40 A for DPC-SC and DPC-DSC, respectively. These values indicate that the amplitude is higher in the case of using the DPC-DSC approach, where this amplitude improvement was estimated to be 0.26%. These ratios indicate that the current quality is higher when using the DPC-DSC technique. This ratio also highlights the efficiency, effectiveness, and power of the proposed DPC-DSC technique in improving current quality, making it a prominent and reliable solution for the future of control.

Figure 11 represents a zoomed-in view of the results of the first test. From this figure, it is noticeable that the proposed DPC-DSC technique produced lower ripples in power, torque, and current compared to the DPC-SC technique. The torque ripples in this test were estimated at 52 Nm for the DPC-SC technique and 27.20 Nm for the proposed approach. Based on these values, the DPC-DSC technique reduced the torque ripples by 47.69%. Furthermore, the current ripples were 14 A and 5 A for the DPC-SC and DPC-DSC approaches, respectively. These values indicate that the DPC-DSC technique reduced the current fluctuations by 64.29% compared to the DPC-SC technique. These graphical results highlight the superiority of the DPC-DSC approach and its significant ability to enhance current and power quality. This performance is attributed to the use of a DSC controller, making it a promising solution for the future.

Table 4 represents the reduction ratios obtained from the first test. This table demonstrates the competence and efficiency of the DPC-DSC compared to the DPC-SC approach. Examining this table reveals that the approach performs remarkably well in enhancing the response time, ripples, overshoot, and overshoot of DFIG power. This superior performance is evident in the reduction ratios listed in this table. The DPC-DSC technique in the case of Q_s reduced the fluctuations, response time, overshoot, and SSE by 34.14%, 35.24%, 85.09%, and 31.70%, respectively, compared to the DPC-SC technique. In the P_s scenario, the DPC-DSC technique reduces ripple, SSE, response time, and overshoot by 40%, 71.75%, 38.10%, and 78.95%, respectively, compared to the DPC-SC technique. These reductions are achieved by using the proposed DSC controller. These results demonstrate that the DSC controller has high performance, high efficiency, and high effectiveness, making it a promising solution for other industrial applications.

Second test

The second test is different from the first. However, the same WS as in the first test is used. In this test, the robustness of the proposed DPC-DSC technique under varying DFIG parameters is studied, and the results are compared with the DPC-SC technique. In this test, the resistance values are multiplied by 2 and the inductance values are divided by 2. Figures 12 and 13 present the graphical results of this test. Table 5 also presents the numerical results for the two controls in this test.

Fig. 13 — Zoom in the results of the test 2.

Table 5.

Ratios of SSE, overshoot, response time, and power ripple of DPC-SC and DPC-DSC approaches.

		P_s (W)	Q_s (VAR)
DPC-SC	Ripples	20,000	26,350
	SSE	7000	12,838
	Overshoot	8600	2782.50
	Respponse time (ms)	0.592	0.056
DPC-DSC	Ripples	6000	18,000
	SSE	4040	4698.05
	Overshoot	2130	2500
	Respponse time (ms)	0.319	0.291
Ratios (%)	Ripples	70	31.69
	SSE	42.29	63.41
	Overshoot	75.23	10.15
	Respponse time (ms)	46.11	− 80.75

Open in a new tab

The powers of the two controllers are shown in Fig. 12a,b. Despite the change in the DFIG parameters, the powers continue to track the meadow well, with a fast DR for the two regulators. Furthermore, the P_s continue to vary with changing WS (Fig. 12a), taking on negative values, which is the same as the first test result. Furthermore, the Q_s remain constant despite the change in DFIG parameters and are unaffected by changes in WS and the presence of undulations (Fig. 12b).

Figure 12c represents the current when the DFIG parameters are changed to the two controls. This current continues to vary with the change in WS, taking on a sinusoidal form for both controls. Furthermore, ripples are observed in the current when using the two controls. The results of this test are almost identical to those of the first test.

Figure 12d represents the torque variation for the two regulators. It is noted that changing the DFIG parameters significantly affects the torque ripples, with the ripples increasing when using the two controls. Also, the torque keeps taking negative values with its value depending on the way the WS changes.

The current THD for the two-regulator model is shown in Fig. 12e,f. From these figures, the THD value was estimated to be 3.49% for the proposed DPC-DSC and 2.64% for the DPC-SC strategy. Based on these values, the DPC-DSC approach yielded a better THD value than the DPC-SC technique. Therefore, the DPC-DSC method reduced the THD value by 24.36% compared to the DPC-SC technique. On the other hand, it is noted that the amplitude values of the fundamental (50 Hz) current signal were 425.70 A and 427.80 A for both DPC-SC and DPC-DSC, respectively. Therefore, the DPC-DSC approach yielded a higher amplitude value than the DPC-SC approach despite the change in the machine parameters. This improvement was estimated at 0.49%. These results demonstrate the competence and robustness of the proposed DPC-DSC technique in enhancing the characteristics of the studied power system.

Figure 13 represents a zoomed-in view of the results of the second test. Despite the DFIG parameters being changed, the DPC-DSC approach, as shown in this figure, significantly reduced the power, current, and torque fluctuations compared to the DPC-SC. The torque ripples were estimated at 100 Nm for the DPC-SC and 44 Nm for the DPC-DSC. Thus, the DPC-DSC reduced torque ripples by 56% compared to the DPC-SC. Furthermore, current fluctuations were estimated at 25 A and 15 A for the DPC-SC technique and DPC-DSC method, respectively. Therefore, the DPC-DSC minimized current fluctuations by an estimated 40% compared to the DPC-SC strategy. These results highlight the competence and efficiency of the proposed DPC-DSC technique, making it a suitable solution for other industrial applications, such as photovoltaic systems.

Table 5 presents the reduction values and ratios for the fluctuations, overshoot, response time, and SSE of the DFIG power when using both controls. Table 5 highlights the effectiveness and efficacy of the DPC-DSC technique compared to the DPC-SC strategy, as demonstrated by the reduction percentages. In the case of the P_s, the DPC-DSC reduced the ripples, SSE, response time, and overshoot by 70%, 42.29%, 46.11%, and 75.23%, respectively, compared to the DPC-SC.

In the case of Q_s, the DPC-DSC minimized the overshoot, fluctuations, and SSE of DFIG power by 10.15%, 31.69%, and 63.41%, respectively, compared to the DPC-SC technique. These high ratios demonstrate the robustness, efficacy, and competencies of the DPC-DSC technique in enhancing the properties of the studied system. Despite this high performance, the DPC-DSC technique yielded unsatisfactory results compared to the DPC-SC technique in terms of response time to Q_s. This drawback can be attributed to the proposed controller’s gain values. This drawback could be defeated in the future by using other approaches, such as neural networks. Overall, these illustrative results make the DPC-DSC technique a promising future solution.

Table 6 presents a study of the influence of current THD, torque ripples, fundamental signal (50 Hz) amplitude, and current ripples between the first and second tests. From this table, it is noted that the current THD value increased in the second test compared to the first test due to the change in machine parameters. This increase in current THD value was estimated to be 28.08% and 11.74% for DPC-SC and DPC-DSC, respectively. Therefore, the DPC-DSC approach presented a lower current THD influence than the DPC-SC approach. It is also noted that the torque ripple values for both controls increased in the second test, a change attributed to the machine parameter changes. Therefore, the change in machine parameters caused an increase in torque ripples. The torque ripple increases were estimated to be 48% and 38.18% for DPC-SC and DPC-DSC, respectively. These ratios indicate that the DPC-DSC approach presented a lesser impact than the DPC-SC approach. The amplitude of the fundamental signal (50 Hz) in the second test increased significantly in both control conditions. This increase was due to the change in the instrument parameters, which suggests that the change in instrument parameters increases the amplitude value. This increase in amplitude was estimated to be 3.38% and 3.59% for DPC-SC and DPC-DSC, respectively. The DPC-DSC approach showed the largest amplitude change, highlighting its effectiveness compared to the DPC-SC approach. On the other hand, it is noted that the current ripples increased significantly in the second test compared to the first test for both controls. This increase in current ripples is due to the change in machine parameters, which can be said to also cause an increase in current ripples. The difference in current ripples between the second and third tests was estimated at + 11 A and + 10 A for DPC-SC and DPC-DSC, respectively. Therefore, the DPC-DSC approach showed the least difference compared to the DPC-SC approach, demonstrating its effectiveness and strength in improving current quality. The study presented in this table highlights the positive and effective use of the DPC-DSC approach, making it a reliable solution for other industrial applications.

Table 6.

Effect study change of torque ripples, fundamental signal (50 Hz) amplitude, current ripples, and current THD in the second test compared to the first test.

		DPC-SC approach	DPC-DSC approach
Torque ripples (Nm)	Test 1	52	27.20
	Test 2	100	44
	Test 2–Test 1	+ 48	+ 16.80
	Ratios (%)	48	38.18
Amplitude of fundamental signal (50 Hz)	Test 1	411.30	412.40
	Test 2	425.70	427.80
	Test 2–Test 1	+ 14.40	+ 15.40
	Ratios (%)	3.38	3.59
Current ripples (A)	Test 1	14	5
	Test 2	25	15
	Test 2–Test 1	+ 11	+ 10
	Ratio (%)	44	66.66
THD (%)	Test 1	2.51	2.33
	Test 2	3.49	2.64
	Test 2–Test 1	+ 0.98	+ 0.31
	Ratios (%)	28.08	11.74

Open in a new tab

Third test

In this test, the effectiveness and efficiency of the DPC-DSC approach in improving the properties of the studied system compared to the DPC-SC approach is studied, as the WS takes the form of steps, as shown in Fig. 14. This test differs from the tests above. The results of this test are presented in Figs. 15 and 16. The numerical results of this test are also presented in Table 7.

Fig. 16 — Zoom in the results of the first test.

Table 7.

Ratios of response time, overshoot, SSE, and energy ripple of DPC-DSC and DPC-SC approaches.

		P_s (W)	Q_s (VAR)
DPC-SC	Ripples	11,300	12,960
	SSE	4700	5525
	Overshoot	3110	94.31
	Respponse time (ms)	0.0966	0.0959
DPC-DSC	Ripples	3100	7424
	SSE	3400	2195
	Overshoot	1170	491.62
	Respponse time (ms)	0.0597	0.0657
Ratios (%)	Ripples	72.56	42.71
	SSE	27.65	60.27
	Overshoot	62.37	− 80.81
	Respponse time (ms)	38.19	31.49

Open in a new tab

Figure 15a,b represent the power changes for the two controllers. These powers track the reference well, with a fast DR, similar to the results from previous tests. Also, ripples in the power levels are observed when using two controllers. Furthermore, the Ps remains negative, with the pattern of its change being the same as the WS change resulting from the MPPT strategy (Fig. 15a). In Fig. 15b, it is noted that the Qs of the two controllers do not change with the change in WS, as its value remains constant and equal to 0 VAR to obtain a power factor equal to 1.

Figure 15c represents the variation of the current for the two controls. This current varies with the change in WS, with its value rising and falling as the WS increases and decreases. Furthermore, this current remains sinusoidal for both controls, with the DPC-DSC approach showing an advantage in quality over the DPC-SC approach.

Figure 15d represents the torque variation for the two controllers. From this figure, it is noticeable that the torque takes on negative values due to the power generation with ripples. Also, it is noted that the torque variation pattern is the same as the Ps variation resulting from the use of the MPPT strategy.

Figure 15e,f represent the current THD values for the two controllers. From these figures, it is observed that the current THD values were estimated to be 0.61% and 0.41% for DPC-SC and DPC-DSC, respectively. These values indicate that the DPC-DSC approach significantly reduced the current THD value compared to the DPC-SC approach, as this reduction was estimated to be 32.78%. On the other hand, it is observed from the figures that the amplitude of the fundamental signal (50 Hz) for the DPC-SC approach was estimated to be 1055 A and for the DPC-DSC approach it was estimated to be 1056 A. These values indicate that the amplitude is higher in the case of using the DPC-DSC approach than in the DPC-SC approach. These results highlight the effectiveness and efficiency of the DPC-DSC approach in improving the quality of the current and the system as a whole, making it a promising future solution in other energy systems such as photovoltaic systems.

Figure 16 represents a zoomed-in test of the results for the third test of two controllers. It is observed that the ripples for torque, power, and current are lower in the DPC-DSC approach compared to the DPC-SC strategy. In the DPC-DSC approach, the torque and current ripples were estimated to be 28.38 Nm and 3.31 A, respectively. In the DPC-SC approach, the current and torque ripples were estimated to be 14.75 A and 52.18 Nm, respectively. Based on these values, it is observed that the DPC-DSC approach significantly reduced both torque and current ripples compared to the DPC-SC approach, with reductions estimated at 77.55% and 45.61% for current and torque, respectively. These figures highlight the robustness and effectiveness of the DPC-DSC approach in improving current and torque quality. The performance obtained in this test confirms the previous test results, making it a reliable solution for other energy applications.

Table 7 presents the numerical values (reduction ratios) for the third test using both controls. This table demonstrates the superiority and effectiveness of the DPC-DSC approach in reducing the ripples, response time, overshoot, and SSE of DFIG power compared to the DPC-SC approach. From this table, the DPC-DSC approach reduces the ripples, response time, SSE, and overshoot of Ps by 72.56%, 38.19%, 27.65%, and 62.37%, respectively, compared to the DPC-SC approach.

In the case of Qs, the DPC-DSC approach reduces ripple, response time, and SSE by 42.71%, 31.49%, and 60.27%, respectively, compared to the DPC-SC approach. These results highlight the effectiveness of the DPC-DSC approach in improving system properties. Despite this performance, it is noted that the DPC-DSC approach produces unsatisfactory results in terms of overshoot of Qs compared to the DPC-SC approach. Therefore, the overshoot value of the Qs can be considered a drawback of the DPC-DSC approach in this test. This drawback can be attributed to the DSC controller parameters, which can be overcome in the future using the Grey Wolf optimization algorithm.

Table 8 represents a study of the changes in current THD, torque ripples, fundamental amplitude, and current ripples for the two controls between the third and first tests. This table aims to determine the effect of changing the WS profile on torque/current ripples, current THD, and fundamental amplitude. Torque ripples increased significantly in the third test compared to the first test for both controls. This increase was estimated at 0.18% and 1.18% for DPC-SC and DPC-DSC, respectively. The DPC-SC approach showed less impact on the ripple variations compared to the DPC-DSC approach. The THD value was significantly reduced in the third test compared to the first test for both controls, suggesting that stepwise WS significantly reduces the THD value compared to random WS. The THD variations between the two tests were estimated to be 75.69% and 82.40% for DPC-SC and DPC-DSC, respectively. These values indicate that the DPC-DSC approach significantly improves the THD value compared to the DPC-SC approach.

Table 8.

Effect study change of current THD, fundamental signal (50 Hz) amplitude, current ripples, and torque ripples in the third test compared to the first test.

		DPC-SC approach	DPC-DSC approach
Torque ripples (Nm)	Test 1	52	27.20
	Test 3	52.18	28.38
	Test 3–Test 1	+ 0.18	+ 1.18
	Ratios (%)	+ 0.34	+ 4.15
Amplitude of fundamental signal (50 Hz)	Test 1	411.30	412.40
	Test 3	1055	1056
	Test 3–Test 1	+ 643.70	+ 643.6
	Ratios (%)	+ 61.01	+ 60.94
Current ripples (A)	Test 1	14	5
	Test 3	14.75	3.31
	Test 3–Test 1	+ 0.75	− 1.69
	Ratios (%)	+ 5.08	− 33.80
THD (%)	Test 1	2.51	2.33
	Test 3	0.61	0.41
	Test 3–Test 1	− 1.9	− 1.92
	Ratios (%)	− 75.69	− 82.40

Open in a new tab

Table 8 shows that the amplitude value increased significantly in the third test compared to the first test for both controls. Therefore, the steps WS significantly improved the amplitude value compared to the random WS, with the percentage change in amplitude value estimated at 61.01% and 60.94% for DPC-SC and DPC-DSC, respectively. Therefore, the DPC-SC approach provided the largest percentage change in amplitude compared to the DPC-DSC approach. On the other hand, it is noted that the value of current ripples increased significantly in the third test compared to the first test in the case of using the DPC-SC approach. This increase was estimated at 5.08%, indicating that the DPC-SC approach was significantly affected by the changing WS profile. However, when using the DPC-DSC strategy, the current ripples decreased significantly in the third test compared to the first. This decrease was estimated at 33.80%, demonstrating the effectiveness and power of the DPC-DSC approach in improving current quality despite the changing WS profile. Therefore, it can be concluded from this table that the shape of the WS has a major role in improving the value of each of the current THD, torque/current ripples, and fundamental amplitude.

Forth test

In this test, the effectiveness of the proposed approach is studied in the case of not using the MPPT strategy, where in the first case a fixed reference value for the Ps is used and in the second case a variable value in steps for the Ps is used.

First case

In this case, the reference Ps is used as a constant value of 1200 kW, and the reference Qs is set to 0. The graphical results for this case are shown in Figs. 17 and 18. The numerical results for this case are shown in Table 9.

Fig. 17 — First case of fourth test results.

Fig. 18 — Zoom in the results of the first case of forth test.

Table 9.

Ratios of SSE, overshoot, response time, and power ripple of DPC-DSC and DPC-SC approaches.

		P_s (W)	Q_s (VAR)
DPC-SC	Ripples	10,000	12,691.30
	SSE	5000	5758.326
	Overshoot	1700	269.80
	Respponse time (ms)	1.91	1.89
DPC-DSC	Ripples	3400	7961.41
	SSE	1600	2071.41
	Overshoot	1600	642.50
	Respponse time (ms)	1.12	1.29
Ratios (%)	Ripples	66	37.26
	SSE	68	64.02
	Overshoot	5.88	− 58
	Respponse time (ms)	41.36	31.74

Open in a new tab

Figure 17a,b represent the power outputs of the controllers proposed in this work. These power outputs still follow the reference outputs well despite not using the MPPT strategy and the presence of ripples. Moreover, these powers have a rapid DR.

Figure 17c represents the change in current over time for the two controls. This current remains sinusoidal, with its value related to the shape of the Ps change, similar to the observations made in the tests above. Also, ripples are observed in this current when using both controls.

Figure 17d represents the torque variation for the two controllers. This torque continues to take the form of Ps variation even when the MPPT strategy is not used. Also, note that this torque has a negative value, indicating that the machine is in power generation mode, with ripples in this torque level even when both controllers are used.

Figure 17e,f represent the current THD values for the two controllers. The current THD values were estimated to be 1.09% and 0.69% for the DPC-SC and DPC-DSC, respectively. These values highlight that the DPC-DSC approach reduced the current THD value by 36.69% compared to the DPC-SC approach. On the other hand, the amplitude of the fundamental signal (50 Hz) was estimated to be 2011 A and 2012 A for the DPC-SC and DPC-DSC, respectively. Therefore, the DPC-DSC approach achieved a higher amplitude than the DPC-SC approach. These results highlight the robustness and effectiveness of the DPC-DSC approach despite not using the MPPT strategy.

Figure 17 represents the zoomed-in graph results for the first case of the fourth test. It is observed that the torque, power, and current ripples are lower in the DPC-DSC approach compared to the DPC-SC approach. The torque ripples were estimated to be 43.11 Nm and 16.50 Nm for DPC-SC and DPC-DSC, respectively. Therefore, the DPC-DSC approach reduced the torque ripples by 61.72% compared to the DPC-SC approach. Furthermore, the current ripples were estimated to be 14.69 A and 2.75 A for DPC-SC and DPC-DSC, respectively. Therefore, the DPC-DSC approach reduced current ripples by 81.22% compared to the DPC-SC technique. These results confirm the effectiveness of the DPC-DSC approach in improving current and power quality compared to the DPC-SC approach. These results make the DPC-DSC approach a topic of interest for the future.

Table 9 presents the numerical results for the first case of the fourth test for the two controllers. This table demonstrates the superior performance of the DPC-DSC approach compared to the DPC-DSC approach in terms of ripple reduction, response time, SSE, and overshoot. In the case of Ps, the DPC-DSC approach reduces ripple, response time, overshoot, and SSE by 66%, 41.36%, 5.88%, and 68%, respectively, compared to the DPC-SC approach.

In the case of Qs, the ripple, response time, overshoot, and SSE values are significantly lower in the DPC-DSC approach compared to the DPC-SC approach. This reduction is estimated to be 37.26%, 64.02%, and 31.74% for ripple, SSE, and response time, respectively, compared to the DPC-SC approach. Despite this performance, the DPC-DSC approach yields unsatisfactory results in terms of overshoot of Qs compared to the DPC-SC approach. Therefore, the overshoot value remains negative for the DPC-DSC approach in this case of the fourth test. This negativity can be attributed to the DSC controller gain values. In the future, this negativity could be overcome by using intelligent strategies such as genetic algorithms to calculate DSC controller gain values.

Second case

In the second case, the reference Ps value is used, taking values in steps. The graphical results for this case are shown in Figs. 19 and 20. The numerical results with reduction ratios are shown in Table 10.

Fig. 19 — Fourth test (Second case) results.

Fig. 20 — Zoom in the results of the fourth test (second case).

Table 10.

Ratios of SSE, response time, overshoot, and power ripple of DPC-SC and DPC-DSC approaches.

		P_s (W)	Q_s (VAR)
DPC-SC	Ripples	8740	12,674.40
	SSE	4690	6117
	Overshoot	1700	269.8
	Respponse time (ms)	1.919	1.89
DPC-DSC	Ripples	6110	8847.30
	SSE	2350	2000
	Overshoot	1600	642.50
	Respponse time (ms)	1.128	1.29
Ratios (%)	Ripples	30.09	30.19
	SSE	49.89	67.30
	Overshoot	5.88	− 58
	Respponse time (ms)	41.21	31.74

Open in a new tab

Figure 19a,b represent the changes in Ps and Qs for the two controllers. These powers remain closely aligned with the reference values, with fluctuations in these powers. Also, these powers have a fast DR to two controls, where the Ps remain negative and the Qs remain constant at 0 VAR to obtain a power factor of 1.

Figure 19c represents the current change for the two controllers. This current remains in the form of a change in Ps with ripples. This current also has a sinusoidal form for the two controllers, which is the same as the test results above.

Figure 19d represents the torque change for the two controllers. This torque remains negative with ripples when using two controllers. Furthermore, the value of this torque decreases and increases with the decrease and increase of the Ps value.

Figure 19e,f represent the current THD values for the two controllers. From these figures, the THD values were 0.61% and 0.57% for DPC-SC and DPC-DSC, respectively. Therefore, the DPC-DSC approach significantly reduced the THD value compared to the DPC-SC approach. This reduction was estimated at 50%. It is also noted that the fundamental signal (50 Hz) amplitude for the two controllers in this case was the same (2011 A). These results highlight the effectiveness and efficiency of the approach in improving current quality despite not using the MPPT approach, making it a promising solution for the future.

Figure 20 represents the Zoom results for the second case test. This figure demonstrates the effectiveness and robustness of the proposed approach in reducing torque, current, and power ripples compared to the DPC-SC approach. The torque ripples were estimated to be 46.26 Nm and 12.58 Nm for the DPC-SC and DPC-DSC methods, respectively. Therefore, the DPC-DSC method reduced torque ripples by 61.72% compared to the DPC-SC method. Furthermore, current ripples were estimated at 9.27 A and 5.47 A for the DPC-SC and DPC-DSC methods, respectively. These values indicate that the DPC-DSC method reduced current ripples by 81.22% compared to the DPC-SC technique. Therefore, the DPC-DSC method has the great ability to reduce current and torque ripples significantly compared to the DPC-SC method, which makes it a reliable solution in the future in the field of control.

Table 10 presents the numerical values for the two controls in the second case of the fourth test. From this table, it is noted that the DPC-DSC approach yielded better values than the DPC-SC approach. The DPC-DSC approach reduced the values of ripples, response time, overshoot, and SSE of Ps by 30.09%, 41.21%, 5.88%, and 49.89%, respectively, compared to the DPC-SC approach. On the other hand, the DPC-DSC approach reduced the values of ripples, response time, and SSE of Qs by 30.19%, 31.74%, and 67.30%, respectively, compared to the DPC-SC approach. These ratios highlight the high operational performance of the DPC-DSC approach in improving system properties. However, despite this performance, the DPC-DSC approach yielded unsatisfactory results in terms of overshoot of Qs compared to the DPC-SC approach. Therefore, this value can be considered negative in this test. This disadvantage can be overcome in the future by employing intelligent strategies for calculating DSC controller gains.

Table 11 presents a study of the influence of current/torque ripple, fundamental (50 Hz) signal amplitude, and current THD values between the second and first cases of the fourth test. From this table, it is noted that the torque ripples increased in the second case compared to the first case in the case of the DPC-SC approach. This increase was estimated at 6.80%. However, in the case of the DPC-DSC approach, the torque ripples decreased significantly in the second case compared to the first case. This decrease was estimated at 3.92%, highlighting the strength of the DPC-DSC approach in improving the torque quality compared to the DPC-SC approach. Table 11 shows that the amplitude value of the fundamental signal (50 Hz) decreased in the second case using the DPC-DSC approach, while in the DPC-SC approach the amplitude value remained unchanged between the two cases. Furthermore, it is noted that the ripple value increased in the second case compared to the first case using the DPC-DSC approach. This increase was estimated at 47.30%. In the DPC-SC approach, the ripple value decreased significantly in the second case compared to the first case. This decrease was estimated at 36.89%. These results show that the DPC-DSC approach is significantly affected by the use of a step Ps reference value compared to a fixed reference value.

Table 11.

Effect study change of fundamental signal (50 Hz) amplitude, current ripples, current THD, and torque ripples in the second case compared to the first case.

		DPC-SC approach	DPC-DSC approach
Torque ripples (Nm)	Case 1	43.11	16.50
	Case 2	46.26	12.58
	Case 2–Case 1	+ 3.15	− 3.92
	Ratios (%)	6.80 +	− 23.75
Amplitude (A) of fundamental signal (50 Hz)	Case 1	2011	2012
	Case 2	2011	2011
	Case 2–Case 1	0	− 1
	Ratios (%)	0	− 0.049
Current ripples (A)	Case 1	14.69	2.75
	Case 2	9.27	5.47
	Case 2–Case 1	− 5.42	+ 2.72
	Ratios (%)	− 36.89	+ 47.30
THD (%)	Case 1	1.09	0.69
	Case 2	0.51	0.46
	Case 2–Case 1	− 0.58	− 0.23
	Ratios (%)	− 53.21	− 33.33

Open in a new tab

Table 11 also shows that the THD value decreased significantly in the second control case. This decrease in THD value was estimated at 33.33% and 53.21% for the DPC-DSC and DPC-SC, respectively. Therefore, the DPC-SC approach yielded a greater THD reduction than the DPC-DSC approach, demonstrating its significant impact on the step Ps reference value. This table demonstrates that the operational performance of the DPC-DSC approach is higher when the Ps reference value is fixed than when the step Ps reference value is used.

The DPC-DSC technique with the MSVM technique is compared with several existing strategies in related literature in terms of dynamic power response. Table 12 represents a comparison of the dynamic power response of the suggested approach with related literature. From this table, it is observed that the DPC-DSC technique with the MSVM technique has a much better power response time than some approaches. In the case of the DPC-DSC technique (Test 1), the P_s response time was estimated to be 0.650 ms, while in the work⁷⁶ this time was estimated to be 1.78 ms and in⁸³ it was 15 ms. Therefore, these values demonstrate the competence and efficiency of the DPC-DSC technique with MSVM technique in improving response time to power compared to other strategies. This comparison makes the DPC-DSC technique with the MSVM technique a reliable solution for other industrial applications.

Table 12.

A comparison between the DPC-DSC and some papers in terms of response time.

References			Response time (ms)
References			Ps (W)	Qs (VAR)
⁵⁴	SMC technique		2.7	0.85
⁵⁴	SC approach		4.3	1.18
⁶⁰	Fractional-order SC technique-based DPC		6.58	6.57
⁷⁵	Vector control with additional resonant controller		5	4
⁷⁶	Improved DPC		2.2	0.90
⁷⁷	SC technique		1.78	8.50
⁷⁸	Test 1		0.9	2.10
	Test 2		2.50	3
	Test 3		2.65	3.25
	Test 4		4.80	5.40
⁷⁹	DPC		17	18
⁷⁹	Nonlinear DPC		9	5
⁸⁰	Test 1		12.15	10.08
	Test 2		11.25	9.85
	Test 3		11.85	10.05
⁸¹	Test 1		1.70	1.85
⁸¹	Test 2		1.34	1.183
⁸²			–	28
⁸³			33.8	34.5
⁸⁴			15	80
⁴¹			1.50	0.80
⁸⁵	Test 1		3.87	2.58
⁸⁵	Test 2		1.29	0.46
Designed approach (DPC-DSC-MSVM)	Test 1		0.650	0.680
	Test 2		0.319	0.291
	Test 3		0.0597	0.0657
	Test 4	Case 1	1.12	1.2
	Test 4	Case 2	1.128	1.29

Open in a new tab

Table 13 compares the current THD value with relevant literature. From this table, it is observed that the designed approach yielded better THD values in all tests than several existing control strategies in the literature. Taking the first test values, the designed approach reduced the THD value by 50.31% compared to the SMC-SVM strategy²⁵. Also, the designed approach reduced the THD value by 75.47% compared to the fuzzy second-order SMC-based DPC-SVM approach²⁹. Compared to the incremental algorithm-based model predictive control approach⁸⁷, the designed approach reduced the THD value by an estimated 22.33%. Thus, the designed approach yielded better THD values than several control strategies, demonstrating its high performance and robustness in improving current quality. This comparison makes the designed approach a potential target for future applications.

Table 13.

Comparison with related works in terms of THD.

References			THD (%)
²⁰	DPC		2.62
²⁰	Neural DPC		2.22
²⁴	DTC		2.57
²⁴	Second-order SMC-based DTC		0.98
²⁵	SMC-PWM		6.41
²⁵	SMC-SVM		4.69
²⁸	PI control		5.40
²⁸	ANN control		3.88
²⁹	Second-order SMC-based DPC-SVM		11.79
²⁹	Fuzzy second-order SMC-based DPC-SVM		9.50
⁷¹			14.21
⁷¹			8.26
^7,3	Rotor flux estimation-based DPC		2.56
^7,3	Stator flux estimation-based DPC		0.79
⁷⁴	Five-level DPC		2.46
⁷⁴	Five-level neural DPC		0.71
⁷⁶			9
⁷⁷	SC technique54		7.51
⁷⁷	Nonlinear SC technique		2.10
⁷⁹	DPC		53.97
⁷⁹	Neural second-order SMC		45.03
⁴¹	Vector control with additional resonant controller		9.30
	LUT-DPC		12.55
	BC-DPC		10.97
⁸⁶	Neural tuning method-based PI controller		8.17
⁸⁶	Neural tuning method-based PI controller		8.23
⁸⁷	Traditional model predictive control		3
	Incremental algorithm-based model predictive control		3
	Different sampling time-based model predictive control		2.5
	Proposed model predictive control		2.8
Proposed technique	Test 1		2.33
	Test 2		2.64
	Test 3		0.41
	Test 4	Case 1	0.69
	Test 4	Case 2	0.46

Open in a new tab

Table 14 represents a comparison of the designed approach with other strategies in the literature in terms of Ps ripple reduction ratios. This table gives a clear picture of the superiority of the designed approach over several related works in terms of reduction ratio. It is noted that the Ps ripple reduction ratio in the case of the designed approach was 72.56% (third test) and 70% (second test). These ratios are higher than those presented in the work²⁸, which was estimated at 22.95%. Moreover, the ratio provided by the designed approach is higher than the ratio provided by the work⁹⁰, which was 21.75%. Therefore, the designed approach gave higher Ps ripple reduction ratios than several strategies in the literature, which can be said that the designed approach has a strong and effective performance in improving power quality. This comparison will make the designed approach a promising solution in the field of control in the future.

Table 14.

Comparison in terms of power ripples minimization rates.

Referances		Ratios (%)
Referances		Ps (W)
⁸⁸		22.95
⁸⁹	Intelligent control approach	36
⁵⁸		37.50
⁹⁰	Modified super-twisting control	19.11
⁹⁰	Super-twisting control	21.75
Proposed technique DPC-DSC-MSVM	Test 1	40
	Test 2	70
	Test 3	72.56

Open in a new tab

Conclusions

In this study, the competence and efficacy of the DPC-DSC technique in enhancing the power quality and reducing the THD of current for a power system based on an MRWT are investigated. A SC controller was developed to defeat the shortcomings of the DPC approach. This algorithm was applied to the machine’s inverter only, using the MSVM to control the inverter operation. The DPC-DSC technique was compared with the SC controller-based DPC technique. Furthermore, the DPC-DSC technique was compared with related works in terms of power response time. Simulation results under variable wind speed conditions demonstrated the significant superiority of the proposed approach over the SC regulator-based DPC technique in terms of ripple reduction, current THD, SSE, and overshoot.

Under variable wind speed conditions, the proposed approach reduces the response time, SSE, ripples, and overshoot of P_s by 38.10%, 71.75%, 40%, and 78.95%, respectively, compared to the conventional approach. The stream THD is also reduced by 7.17% compared to the SC-based DPC technique. Moreover, the suggested approach demonstrated excellent performance under varying system parameters compared to the SC controller-based DPC technique. The proposed approach maintained stable performance under parameter variation tests, confirming its reliability. In this test, the DPC-DSC reduced fluctuation, response time, overshoot, and SSE of active power by 70%, 46.11%, 75.23%, and 42.29% compared to the DPC-SC technique. Furthermore, the THD value was reduced by 24.36%. These results confirm the competence of the DPC-DSC technique in improving the reliability and stability properties of the studied system. These results (Minimization ratios) demonstrate that the suggested approach is a suitable solution for wind-based energy systems and can also be relied upon in other energy systems, such as photovoltaic systems. In addition, this work highlights the robustness of the DSC in ensuring operational efficiency while significantly improving power quality and current. We recommend further experimental research using real instruments or the OPAL-RT simulation platform, and we anticipate that the continued development of the proposed DSC controller will further improve power quality, especially in renewable energy applications. The proposed DSC controller emerges as a promising tool for enhancing performance, reducing power fluctuations, maintaining stable operation, and improving reliability in renewable energy systems.

Supplementary Information

Supplementary Information.^{(176.2KB, docx)}

Acknowledgements

This research was supported by King Khalid University, Research Project RGP.2/641/46.

Abbreviations

SC: Synergetic control
DRWT: Dual rotor wind turbine
WE: Wind energy
CRWT: Counter-rotating wind turbine
WT: Wind turbine
GA: Genetic algorithm
ISC: Integral synergetic control
TSC: Terminal synergetic control
PI: Proportional-integral controller
DFIG: Doubly fed induction generator
DTC: Direct torque control
RSC: Rotor side converter
SSE: Steady-state error
DR: Dynamic response
STA: Super-twisting algorithm
DSC: Dual synergetic control
THD: Total harmonic distortion
Ps: Active power
MRWT: Multi-rotor wind turbine
HAWT: Horizontal-axis wind turbine
FOSC: Fractional-order synergetic control
MSVM: Modified space vector modulation
FOC: Field-oriented control
DPC: Direct torque control
WS: Wind speed
BC: Backstepping control
SMC: Sliding mode control
MPPT: Maximum power point tracking
C-DTC: Conventional direct torque control
Qs: Reactive power

Author contributions

Conceptualization:Habib Benbouhenni, Adil Yahdou, Zakaria Mohamed Salem Elbarbary methodology:Habib Benbouhenni, Adil Yahdou, Zakaria Mohamed Salem Elbarbary software: Habib Benbouhenni, Adil Yahdou, Ilhami Colak validation:Habib Benbouhenni formal analysis:Habib Benbouhenni, Adil Yahdou, Zakaria Mohamed Salem Elbarbary, Ilhami Colak, Saad Al-Gahtani investigation:Habib Benbouhenni, Adil Yahdou, Zakaria Mohamed Salem Elbarbary, Ilhami Colak, Saad Al-Gahtani resources:Habib Benbouhenni, Adil Yahdou data curation:Habib Benbouhenni, Adil Yahdou writing—original draft preparation:Habib Benbouhenni, Adil Yahdou writing—review and editing:Habib Benbouhenni, Adil Yahdou, Zakaria Mohamed Salem Elbarbary, Ilhami Colak, Saad Al-Gahtani visualization:Habib Benbouhenni, Adil Yahdou, Zakaria Mohamed Salem Elbarbary, Ilhami Colak, Saad Al-Gahtani supervision:Habib Benbouhenni, Adil Yahdou, Zakaria Mohamed Salem Elbarbary, Ilhami Colak, Saad Al-Gahtani project administration:Habib Benbouhenni, Ilhami Colak funding acquisition: Habib Benbouhenni, Zakaria Mohamed Salem Elbarbary, Saad Al-Gahtani All authors have read and agreed to the published version of the manuscript.

Data availability

Data available on request from the authors. The datasets used and/or analysed during the current study available from the corresponding author on reasonable request. In the event of communication, the fist author (Habib Benbouhenni, E-mail: habib.benbouhenni@enp-oran.dz) will respond to any inquiry or request.

Declarations

Competing interests

The authors declare no competing interests.

Footnotes

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-025-04040-1.

References

1.Salah, D. A. H., Nosier, M. A. R. & Hamed, A. M. Investigation of the performance of a horizontal-axis dual rotor wind turbine. Sci. Rep.14, 6208. 10.1038/s41598-024-55844-6 (2024). [DOI] [PMC free article] [PubMed] [Google Scholar]
2.Ercan, E., Selim, S. & Fevzi, C. B. Analysis model of a small scale counter-rotating dual rotor wind turbine with double rotational generator armature. Int. J. Renew. Energy Res. IJRER8(4), 1849–1858. 10.20508/ijrer.v8i4.8235.g7549 (2018). [Google Scholar]
3.Wenyan, L. et al. The aerodynamic performance of horizontal axis wind turbines under rotation condition. Sustainability15(16), 12553. 10.3390/su151612553 (2023). [Google Scholar]
4.Mahmoud, Z., Saeed, M. & Vahdat, N. Coordinating the participation of energy sources and wind units in micro-grid frequency control by delaying micro-grid parameter measurement systems. Int. J. Smart Grid-ijSmartGrid8(2), 81–97. 10.20508/ijsmartgrid.v8i2.323.g354 (2024). [Google Scholar]
5.Yasser, E., Naggar, H. S. & Abdalhalim, Z. Assessing wind energy conversion systems based on newly developed wind turbine emulator. Int. J. Smart Grid-ijSmartGrid4(4), 139–148. 10.20508/ijsmartgrid.v4i4.133.g101 (2020). [Google Scholar]
6.Kumar, R., Khetrapal, P., Badoni, M. & Diwania, S. Evaluating the relative operational performance of wind power plants in Indian electricity generation sector using two-stage model. Energy Environ.33(7), 1441–1464. 10.1177/0958305X211043531 (2022). [Google Scholar]
7.Rajeev, K., Rajveer, S. & Haroon, A. Stability enhancement of induction generator–based series compensated wind power plants by alleviating subsynchronous torsional oscillations using BFOA-optimal controller tuned STATCOM. Wind Energy23(9), 1846–1867. 10.1002/we.2521 (2020). [Google Scholar]
8.Rajeev, K., Rajveer, S., Haroon, A., Sudhir, K. S. & Manoj, B. Power system stability enhancement by damping and control of Sub-synchronous torsional oscillations using Whale optimization algorithm based Type-2 wind turbines. ISA Trans.108, 240–256. 10.1016/j.isatra.2020.08.037 (2021). [DOI] [PubMed] [Google Scholar]
9.Rajeev, K. et al. An intelligent Hybrid Wind–PV farm as a static compensator for overall stability and control of multimachine power system. ISA Trans.123, 286–302. 10.1016/j.isatra.2021.05.014 (2022). [DOI] [PubMed] [Google Scholar]
10.Mohamed, A. E., Sayed, H. E. & Dalal, H. H. Maintaining system stability with high penetration of wind energy via fault ride through (FRT) criteria development (system operator perspective). Int. J. Renew. Energy Res. IJRER14(4), 867–878. 10.20508/ijrer.v14i4.14460.g8962 (2024). [Google Scholar]
11.Savarapu, Ch. S., Muthamizhan, T., Mohammad, A. & Chandra, S. D. Wavelet-ANN based detection of fault location of hybrid renewable energy sources connected power transmission system. Int. J. Renew. Energy Res. IJRER14(3), 551–562. 10.20508/ijrer.v14i3.14396.g8921 (2024). [Google Scholar]
12.Abdelhakim, B., Ilhami, C., Korhan, K. & Ramazan, B. Modeling of a permanent magnet synchronous generator in a power wind generation system with an electrochemical energy storage. Int. J. Smart Grid-ijSmartGrid2(4), 197–202. 10.20508/ijsmartgrid.v2i4.26.g25 (2018). [Google Scholar]
13.Mohammed, F., Ahmed, E., Mohamed, N. & Tamou, N. Control and optimization of a wind energy conversion system based on doubly-fed induction generator using nonlinear control strategies. Int. J. Renew. Energy Res. IJRER9(1), 44–45. 10.20508/ijrer.v9i1.8812.g7619 (2019). [Google Scholar]
14.Hüseyin, C., Ahmet, D. & Yuksel, O. Investigation of dynamic behavior of double feed induction generator and permanent magnet synchronous generator wind turbines in failure conditions. Int. J. Renew. Energy Res. IJRER11(2), 721–729. 10.20508/ijrer.v11i2.11837.g8193 (2021). [Google Scholar]
15.Tarek, B., Islam, A. S. & Doaa, K. I. Performance enhancement of doubly-fed induction generator-based-wind energy system. Int. J. Renew. Energy Res. IJRER3(1), 311–325. 10.20508/ijrer.v13i1.13649.g8685 (2023). [Google Scholar]
16.Fahal, N. A. M. & Zheng, T. Control of DFIG-based wind power generation system under unbalanced grid voltage conditions. Nat. Appl. Sci. Int. J. (NASIJ)5(1), 92–112. 10.47264/idea.nasij/5.1.7 (2024). [Google Scholar]
17.Yahdou, A., Boudjema, Z., Taleb, R. & Djilali, A. B. Backstepping sliding mode control of a dual rotor wind turbine system. In: 2018 International Conference on Electrical Sciences and Technologies in Maghreb, CISTEM, 2018, 1–5. 10.1109/CISTEM.2018.8613409.
18.Boyette, A., Saadate, S., Poure, P. Direct and indirect control of a Doubly Fed Induction Generator wind turbine including a storage unit. In: IECON 2006-32nd Annual Conference on IEEE Industrial Electronics, Paris, France. 06–10 November, 2006. 10.1109/IECON.2006.347300.
19.Younes, S. et al. Effectiveness analysis of twelve sectors of DTC based on a newly modified switching table implemented on a wind turbine DFIG system under variable wind velocity. Ain Shams Eng. J.14(11), 102221. 10.1016/j.asej.2023.102221 (2023). [Google Scholar]
20.Chojaa, H. et al. A novel DPC approach for DFIG-based variable speed wind power systems using dspace. IEEE Access11, 9493–9510. 10.1109/ACCESS.2023.3237511 (2023). [Google Scholar]
21.Ikni, D. & Raducan, E. Stability analysis of a wind turbine controlled by direct torque control. Energies17, 2488. 10.3390/en17112488 (2024). [Google Scholar]
22.Benbouhenni, H. Stator current and rotor flux ripples reduction of DTC DFIG drive using FSTSMC algorithm. Int. J. Smart Grid3(4), 226–234. 10.20508/ijsmartgrid.v3i4.82.g72 (2019). [Google Scholar]
23.Benbouhenni, H. Five-level DTC control of induction machine drive using fuzzy logic controller for low torque ripple. Acta Tech. Corviniensis-Bull. Eng.12(2), 91–96 (2019). [Google Scholar]
24.Boudjema, Z., Taleb, R., Djeriri, Y. & Yahdou, A. A novel direct torque control using second order continuous sliding mode of a doubly fed induction generator for a wind energy conversion system. Turk. J. Electr. Eng. Comput. Sci.25(2), 965–975. 10.3906/elk-1510-89 (2017). [Google Scholar]
25.Youcef, B. & Djilani, B. A. Comparison study between SVM and PWM inverter in sliding mode control of active and reactive power control of a DFIG for variable speed wind energy. Int. J. Renew. Energy Res. IJRER2(3), 471–476. 10.20508/ijrer.v2i3.269.g6047 (2012). [Google Scholar]
26.Mohammed, A., Ahmed, E., Tamou, N. & Haitam, C. Comparative analysis of ADRC & PI controllers used in wind turbine system driving a DFIG. Int. J. Renew. Energy Res. IJRER7(4), 1816–1824 (2017). [Google Scholar]
27.Rayane, L. & Lekhchine, S. Fuzzy logic controller-based power control of DFIG based on wind energy systems. Int. J. Smart Grid-ijSmartGrid8(1), 74–80. 10.20508/ijsmartgrid.v8i1.334.g346 (2024). [Google Scholar]
28.Sanjeev, K. G., Sundram, M. & Madhu, S. Performance enhancement of DFIG based grid connected SHPP using ANN controller. Int. J. Renew. Energy Res. IJRER9(3), 1165–1179. 10.20508/ijrer.v9i3.9427.g7694 (2019). [Google Scholar]
29.Mazouz, F., Sebti, B. & Ilhami, C. DPC-SVM of DFIG using fuzzy second order sliding mode approach. Int. J. Smart Grid5(4), 174–182. 10.20508/ijsmartgrid.v5i4.219.g178 (2021). [Google Scholar]
30.Bekhada, H. et al. Comparative study of PI, RST, sliding mode and fuzzy supervisory controllers for DFIG based wind energy conversion system. Int. J. Renew. Energy Res. IJRER5(4), 1174–1185. 10.20508/ijrer.v5i4.2915.g6705 (2015). [Google Scholar]
31.Boris, D., Bane, P., Dragan, M., Vladimir, K. & Djura, O. Artificial intelligence based vector control of induction generator without speed sensor for use in wind energy conversion system. Int. J. Renew. Energy Res. IJRER5(1), 299–307. 10.20508/ijrer.v5i1.2030.g6498 (2025). [Google Scholar]
32.Samir, M., Mohamed, H., Nadir, K. & Selman, K. Neural network based field oriented control for doubly fed induction generator. Int. J. Smart Grid-Ijsmartgrid2(3), 183–187. 10.20508/ijsmartgrid.v2i3.18.g18 (2018). [Google Scholar]
33.Xiaoming, Y. & Ming-Hsien, C. Backstepping-based direct power control for dual-cage rotor brushless doubly fed induction generator. IEEE Trans. Power Electron.38(2), 2668–2680. 10.1109/TPEL.2022.3214331 (2023). [Google Scholar]
34.Mostafa, A., Abdelilah, A., Rachid, A. & Jamal, B. Backstepping control of a switched reluctance motor with inter-turn short-circuit. Adv. Electr. Electron. Eng.20(3), 250–259. 10.15598/aeee.v20i3.4326 (2022). [Google Scholar]
35.Abderrahmen, K., Said, G. & Youcef, S. Improved sensorless backstepping controller using extended Kalman filter of a permanent magnet synchronous machine. Bull. Electr. Eng. Inf.11(2), 658–671. 10.11591/eei.v11i2.3560 (2022). [Google Scholar]
36.Marcin, M., Patryk, S., Arkadiusz, L., Jaroslaw, G. & Filip, W. Feedback control of multiphase induction machines with backstepping technique. IEEE Trans. Ind. Electron.67(6), 4305–4314. 10.1109/TIE.2019.2931236 (2022). [Google Scholar]
37.Nadour, M., Essadki, A. & Nasser, T. Comparative analysis between PI & backstepping control strategies of DFIG driven by wind turbine. Int. J. Renew. Energy Res.7(3), 1307–1316. 10.20508/ijrer.v7i3.6066.g7163 (2017). [Google Scholar]
38.Sara, M., Ahmed, E., Tamou, N. & Badr, B. I. An efficient nonlinear backstepping controller approach of a wind energy conversion system based on a DFIG. Int. J. Renew. Energy Res. IJRER7(4), 1520–1528. 10.20508/ijrer.v7i4.6112.g7192 (2017). [Google Scholar]
39.Adel, K., Nihel, K. & Mohamed, F. M. Wind energy conversion system using DFIG controlled by backstepping and sliding mode strategies. Int. J. Renew. Energy Res. IJRER2(3), 421–430. 10.20508/ijrer.v2i3.249.g6040 (2012). [Google Scholar]
40.Patel, R., Hafiz, F., Swain, A. & Ukil, A. Nonlinear rotor side converter control of DFIG based wind energy system. Electr. Power Syst. Res.198, 107358. 10.1016/j.epsr.2021.107358 (2021). [Google Scholar]
41.Xiong, P. & Sun, D. Backstepping-based DPC strategy of a wind turbine-driven DFIG under normal and harmonic grid voltage. IEEE Trans. Power Electron.31(6), 4216–4225. 10.1109/TPEL.2015.2477442 (2015). [Google Scholar]
42.Mechter, A., Kemih, K. & Ghanes, M. Backstepping control of a wind turbine for low wind speeds. Nonlinear Dyn.84(4), 2435–2445. 10.1007/s11071-016-2655-y (2016). [Google Scholar]
43.Trabelsi, R., Khedher, A., Mimouni, M. F. & M’sahli, F. Backstepping control for an induction motor using an adaptive sliding rotor-flux observer. Electr. Power Syst. Res.93, 1–15. 10.1016/j.epsr.2012.06.004 (2012). [Google Scholar]
44.Roy, T. K., Mahmud, M. A. & Oo, A. M. Robust adaptive backstepping excitation controller design for higher-order models of synchronous generators in multimachine power systems. IEEE Trans. Power Syst.34(1), 40–51. 10.1109/TPWRS.2018.2868783 (2018). [Google Scholar]
45.Yin, W., Wu, X. & Rui, X. Adaptive robust backstepping control of the speed regulating differential mechanism for wind turbines. IEEE Trans. Sustain. Energy10(3), 1311–1318. 10.1109/TSTE.2018.2865631 (2018). [Google Scholar]
46.Kasbi, A. & Rahali, A. MPPT performance and power quality improvement by using fractional-order adaptive backstepping control of a DFIG-based wind turbine with disturbance and uncertain parameters. Arab. J. Sci. Eng.48, 6595–6614. 10.1007/s13369-022-07474-1 (2023). [Google Scholar]
47.Wang, J. et al. Adaptive back-stepping control for a permanent magnet synchronous generator wind energy conversion system. Int. J. Hydrogen Energy44(5), 3240–3249. 10.1016/j.ijhydene.2018.12.023 (2019). [Google Scholar]
48.Kasbi, A. & Rahali, A. Performance improvement of modern variable-velocity wind turbines technology based on the doublyfed induction generator (DFIG). Mater. Today Proc.45, 5426–5432. 10.1016/j.matpr.2021.02.114 (2021). [Google Scholar]
49.Justo, J. J., Mwasil, F., Lee, J. & Jung, J.-W. AC-microgrids versus DC-microgrids with distributed energy resources: A review. Renew. Sustain. Energy Rev.24, 387–405 (2013). [Google Scholar]
50.Mushenko, A. et al. Modeling a single-channel synergetic observer for chaos-based secure communication system applications. Mathematics12, 2764. 10.3390/math12172764 (2024). [Google Scholar]
51.Brahim, D., Hamoudi, F., Habib, B., Slimane, M. & Naamane, D. Synergetic control for three-level voltage source inverter-based shunt active power filter to improve power quality. Energy Rep.10, 1013–1027. 10.1016/j.egyr.2023.07.051 (2023). [Google Scholar]
52.Habib, B. & Bizon, N. A synergetic sliding mode controller applied to direct field-oriented control of induction generator-based variable speed dual-rotor wind turbines. Energies14, 4437. 10.3390/en14154437 (2021). [Google Scholar]
53.Al-Hussein, A.-B.A., Tahir, F. R. & Pham, V.-T. FPGA Implementation of synergetic controller-based MPPT algorithm for a standalone PV system. Computation13, 64. 10.3390/computation13030064 (2025). [Google Scholar]
54.Habib, B. Comparative study of sliding mode control with synergetic control for rotor side inverter of the DFIG for multi-rotor wind power systems. Majlesi J. Mechatron. Syst.11(2), 29–37 (2023). [Google Scholar]
55.Habib, B. & Gasmi, H. Comparative study of synergetic controller with super twisting algorithm for rotor side inverter of DFIG. Int. J. Smart Grid-ijSmartGrid6(4), 144–156. 10.20508/ijsmartgrid.v6i4.265.g228 (2022). [Google Scholar]
56.Habib, B., Mehedi, F. & Soufiane, L. New direct power synergetic-SMC technique based PWM for DFIG integrated to a variable speed dual-rotor wind power. Automatika63(4), 718–731. 10.1080/00051144.2022.2065801 (2022). [Google Scholar]
57.Debdouche, N. et al. Synergetic simplified super-twisting algorithm control for stability enhancement of PV/BESS-based DC microgrid. Sci. Rep.15, 7392. 10.1038/s41598-025-92042-4 (2025). [DOI] [PMC free article] [PubMed] [Google Scholar]
58.Benbouhenni, H. et al. Synergetic-PI controller based on genetic algorithm for DPC-PWM strategy of a multi-rotor wind power system. Sci. Rep.13, 13570. 10.1038/s41598-023-40870-7 (2023). [DOI] [PMC free article] [PubMed] [Google Scholar]
59.Habib, B., Bizon, N., Thounthong, P., Colak, I. & Mungporn, P. A new integral-synergetic controller for direct reactive and active powers control of a dual-rotor wind system. Meas. Control57(2), 208–224. 10.1177/00202940231195117 (2024). [Google Scholar]
60.Habib, B. et al. Fractional-order synergetic control of the asynchronous generator-based variable-speed multi-rotor wind power systems. In IEEE Access11, 133490–133508. 10.1109/ACCESS.2023.3335902 (2023). [Google Scholar]
61.Srikanth, G. & Rajesh, G. N. Power quality enhancement in PV fed UPQC using adaptive lizard algorithm. Int. J. Smart Grid-ijSmartGrid9(1), 31–42. 10.20508/ijsmartgrid.v9i1.407.g378 (2025). [Google Scholar]
62.Deffaf, B., Debdouche, N., Benbouhenni, H., Hamoudi, F. & Bizon, N. A new control for improving the power quality generated by a three-level T-type inverter. Electronics12, 2117. 10.3390/electronics12092117 (2023). [Google Scholar]
63.Habib, B. & Bizon, N. Terminal synergetic control for direct active and reactive powers in asynchronous generator-based dual-rotor wind power systems. Electronics10, 1880. 10.3390/electronics10161880 (2021). [Google Scholar]
64.Mayilsamy, G., Natesan, B., Joo, Y. H. & Lee, S. R. Fast terminal synergetic control of PMVG-based wind energy conversion system for enhancing the power extraction efficiency. Energies15, 2774. 10.3390/en15082774 (2022). [Google Scholar]
65.Babes, B. et al. Experimental investigation of an adaptive fuzzy-neural fast terminal synergetic controller for buck DC/DC converters. Sustainability14, 7967. 10.3390/su14137967 (2022). [Google Scholar]
66.Dalal, Z., Youcef, B. & Habib, B. Robust synergetic-sliding mode-based-backstepping control of induction motor with MRAS technique. Energy Rep.10, 3665–3680. 10.1016/j.egyr.2023.10.035 (2023). [Google Scholar]
67.Erenturk, K., Draou, A. & AlKassem, A. Design and comparison of different types of synergetic controllers for islanded DC microgrids. Sustainability14, 8792. 10.3390/su14148792 (2022). [Google Scholar]
68.Habib, B. Neuro-scond order sliding mode field oriented command for DFIG based wind turbine. Int. J. Smart Grid-Ijsmartgrid2(4), 209–217. 10.20508/ijsmartgrid.v2i4.25.g27 (2018). [Google Scholar]
69.Benbouhenni, H., Bizon, N. & Colak, I. A brief review of space vector modulation (SVM) methods and a new svm technique based on the minimum and maximum of the three-phase voltages. Iran. J. Electr. Electron. Eng.18(3), 54–72 (2022). [Google Scholar]
70.Habib, B., Bizon, N., Ilhami, C., Mohamed, I. M. & Mourad, Y. Direct active and reactive powers control of double-powered asynchronous generators in multi-rotor wind power systems using modified synergetic control. Energy Rep.10, 4286–4301. 10.1016/j.egyr.2023.10.085 (2023). [Google Scholar]
71.Reza, G., Ali, M. & Alireza Davari, S. A new control algorithm method based on DPC to improve power quality of DFIG in unbalance grid voltage conditions. Int. J. Renew. Energy Res. IJRER8(4), 2228–2238. 10.20508/ijrer.v8i4.8583.g7527 (2018). [Google Scholar]
72.Zhou, P., He, Y. & Sun, D. Improved direct power control of a DFIG-based wind turbine during network unbalance. IEEE Trans. Power Electron.24(11), 2465–2474. 10.1109/TPEL.2009.2032188 (2009). [Google Scholar]
73.Seyed, M. T., Mohammad, A. P. & Mohammad, R. Z. Comparison between different DPC methods applied to DFIG wind turbines. Int. J. Renew. Energy Res. IJRER3(2), 446–452. 10.20508/ijrer.v3i2.680.g6162 (2013). [Google Scholar]
74.Habib, B. Application of five-level NPC inverter in DPC-ANN of doubly fed induction generator for wind power generation systems. Int. J. Smart Grid-IJSMARTGRID3(3), 128–137. 10.20508/ijsmartgrid.v3i3.66.g59 (2019). [Google Scholar]
75.Ramos, C. J., Martins, A. P. & Carvalho, A. S. Rotor current controller with voltage harmonics compensation for a DFIG operating under unbalanced and distorted stator voltage. In: IECON 2007. 33rd Annual Conference of IEEE, 5–8 (2007).
76.Wei, F., Zhang, X., Vilathgamuwa, D. M., Choi, S. S. & Wang, S. Mitigation of distorted and unbalanced stator voltage of stand-alone doubly fed induction generators using repetitive control technique. IET Electron. Power Appl.7(8), 654–663 (2013). [Google Scholar]
77.Ardjal, A., Bettayeb, M., Mansouri, R. & Mehiri, A. Nonlinear synergetic control approach for dc-link voltage regulator of wind turbine DFIG connected to the grid. In: 2018 5th International Conference on Renewable Energy: Generation and Applications (ICREGA), Al Ain, United Arab Emirates, 2018, 94–97. 10.1109/ICREGA.2018.8337639 (2018).
78.Yahdou, A. et al. Application of backstepping control with nonsingular terminal sliding mode surface technique to improve the robustness of stator power control of asynchronous generator-based multi-rotor wind turbine system. Electr. Power Compon. Syst.10.1080/15325008.2024.2304688 (2024). [Google Scholar]
79.Ibrahim, Y., Semmah, A. & Patrice, W. Neuro-second order sliding mode control of a DFIG based wind turbine system. J. Electr. Electron. Eng.13(1), 63–68 (2020). [Google Scholar]
80.Benbouhenni, H. et al. Hardware-in-the-loop simulation to validate the fractional-order neuro-fuzzy power control of variable-speed dual-rotor wind turbine systems. Energy Rep.11, 4904–4923. 10.1016/j.egyr.2024.04.049 (2024). [Google Scholar]
81.Yessef, M. et al. Experimental validation of feedback PI controllers for multi-rotor wind energy conversion systems. IEEE Access12, 7071–7088. 10.1109/ACCESS.2024.3351355 (2024). [Google Scholar]
82.Hamid, Ch. et al. Integral sliding mode control for DFIG based WECS with MPPT based on artificial neural network under a real wind profile. Energy Rep.7, 4809–4824. 10.1016/j.egyr.2021.07.066 (2021). [Google Scholar]
83.Echiheb, F. et al. Robust sliding-backstepping mode control of a wind system based on the DFIG generator. Sci Rep.12, 11782. 10.1038/s41598-022-15960-7 (2022). [DOI] [PMC free article] [PubMed] [Google Scholar]
84.Alami, H. E. et al. FPGA in the loop implementation for observer sliding mode control of DFIG-generators for wind turbines. Electronics11(1), 116. 10.3390/electronics11010116 (2022). [Google Scholar]
85.Yahdou, A., Djilali, A. B., Bounadja, E. & Habib, B. Using neural network super-twisting sliding mode to improve power control of a dual-rotor wind turbine system in normal and unbalanced grid fault modes. Int. J. Circuit Theory Appl.52(9), 4323–4347. 10.1002/cta.3960 (2024). [Google Scholar]
86.Hete, R. R. et al. Design and development of PI controller for DFIG grid integration using neural tuning method ensembled with dense plexus terminals. Sci. Rep.14, 7916. 10.1038/s41598-024-56904-7.(2024) (2024). [DOI] [PMC free article] [PubMed] [Google Scholar]
87.Aria, Y., Sajjad, T. & Mohammad, R. F. An improved long-horizon model predictive control for DFIG in WECS with variable sampling-time. IET Renew. Power Gener.16(3), 517–531. 10.1049/rpg2.12357 (2022). [Google Scholar]
88.Benbouhenni, H., Gasmi, H. & Colak, I. Backstepping control for multi-rotor wind power systems. Majlesi J. Energy Manag.11(4), 8–15 (2023). [Google Scholar]
89.Habib, B., Gasmi, H. & Colak, I. Intelligent control scheme of asynchronous generator-based dual-rotor wind power system under different working conditions. Majlesi J. Energy Manag.11(3), 8–15 (2022). [Google Scholar]
90.Ravikiran, H. & Tukaram, M. Modified super twisting algorithm based sliding mode control for LVRT enhancement of DFIG driven wind system. Energy Rep.8, 3600–3613. 10.1016/j.egyr.2022.02.235 (2022). [Google Scholar]

Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

Supplementary Information.^{(176.2KB, docx)}

Data Availability Statement

[CR1] 1.Salah, D. A. H., Nosier, M. A. R. & Hamed, A. M. Investigation of the performance of a horizontal-axis dual rotor wind turbine. Sci. Rep.14, 6208. 10.1038/s41598-024-55844-6 (2024). [DOI] [PMC free article] [PubMed] [Google Scholar]

[CR2] 2.Ercan, E., Selim, S. & Fevzi, C. B. Analysis model of a small scale counter-rotating dual rotor wind turbine with double rotational generator armature. Int. J. Renew. Energy Res. IJRER8(4), 1849–1858. 10.20508/ijrer.v8i4.8235.g7549 (2018). [Google Scholar]

[CR3] 3.Wenyan, L. et al. The aerodynamic performance of horizontal axis wind turbines under rotation condition. Sustainability15(16), 12553. 10.3390/su151612553 (2023). [Google Scholar]

[CR4] 4.Mahmoud, Z., Saeed, M. & Vahdat, N. Coordinating the participation of energy sources and wind units in micro-grid frequency control by delaying micro-grid parameter measurement systems. Int. J. Smart Grid-ijSmartGrid8(2), 81–97. 10.20508/ijsmartgrid.v8i2.323.g354 (2024). [Google Scholar]

[CR5] 5.Yasser, E., Naggar, H. S. & Abdalhalim, Z. Assessing wind energy conversion systems based on newly developed wind turbine emulator. Int. J. Smart Grid-ijSmartGrid4(4), 139–148. 10.20508/ijsmartgrid.v4i4.133.g101 (2020). [Google Scholar]

[CR6] 6.Kumar, R., Khetrapal, P., Badoni, M. & Diwania, S. Evaluating the relative operational performance of wind power plants in Indian electricity generation sector using two-stage model. Energy Environ.33(7), 1441–1464. 10.1177/0958305X211043531 (2022). [Google Scholar]

[CR7] 7.Rajeev, K., Rajveer, S. & Haroon, A. Stability enhancement of induction generator–based series compensated wind power plants by alleviating subsynchronous torsional oscillations using BFOA-optimal controller tuned STATCOM. Wind Energy23(9), 1846–1867. 10.1002/we.2521 (2020). [Google Scholar]

[CR8] 8.Rajeev, K., Rajveer, S., Haroon, A., Sudhir, K. S. & Manoj, B. Power system stability enhancement by damping and control of Sub-synchronous torsional oscillations using Whale optimization algorithm based Type-2 wind turbines. ISA Trans.108, 240–256. 10.1016/j.isatra.2020.08.037 (2021). [DOI] [PubMed] [Google Scholar]

[CR9] 9.Rajeev, K. et al. An intelligent Hybrid Wind–PV farm as a static compensator for overall stability and control of multimachine power system. ISA Trans.123, 286–302. 10.1016/j.isatra.2021.05.014 (2022). [DOI] [PubMed] [Google Scholar]

[CR10] 10.Mohamed, A. E., Sayed, H. E. & Dalal, H. H. Maintaining system stability with high penetration of wind energy via fault ride through (FRT) criteria development (system operator perspective). Int. J. Renew. Energy Res. IJRER14(4), 867–878. 10.20508/ijrer.v14i4.14460.g8962 (2024). [Google Scholar]

[CR11] 11.Savarapu, Ch. S., Muthamizhan, T., Mohammad, A. & Chandra, S. D. Wavelet-ANN based detection of fault location of hybrid renewable energy sources connected power transmission system. Int. J. Renew. Energy Res. IJRER14(3), 551–562. 10.20508/ijrer.v14i3.14396.g8921 (2024). [Google Scholar]

[CR12] 12.Abdelhakim, B., Ilhami, C., Korhan, K. & Ramazan, B. Modeling of a permanent magnet synchronous generator in a power wind generation system with an electrochemical energy storage. Int. J. Smart Grid-ijSmartGrid2(4), 197–202. 10.20508/ijsmartgrid.v2i4.26.g25 (2018). [Google Scholar]

[CR13] 13.Mohammed, F., Ahmed, E., Mohamed, N. & Tamou, N. Control and optimization of a wind energy conversion system based on doubly-fed induction generator using nonlinear control strategies. Int. J. Renew. Energy Res. IJRER9(1), 44–45. 10.20508/ijrer.v9i1.8812.g7619 (2019). [Google Scholar]

[CR14] 14.Hüseyin, C., Ahmet, D. & Yuksel, O. Investigation of dynamic behavior of double feed induction generator and permanent magnet synchronous generator wind turbines in failure conditions. Int. J. Renew. Energy Res. IJRER11(2), 721–729. 10.20508/ijrer.v11i2.11837.g8193 (2021). [Google Scholar]

[CR15] 15.Tarek, B., Islam, A. S. & Doaa, K. I. Performance enhancement of doubly-fed induction generator-based-wind energy system. Int. J. Renew. Energy Res. IJRER3(1), 311–325. 10.20508/ijrer.v13i1.13649.g8685 (2023). [Google Scholar]

[CR16] 16.Fahal, N. A. M. & Zheng, T. Control of DFIG-based wind power generation system under unbalanced grid voltage conditions. Nat. Appl. Sci. Int. J. (NASIJ)5(1), 92–112. 10.47264/idea.nasij/5.1.7 (2024). [Google Scholar]

[CR17] 17.Yahdou, A., Boudjema, Z., Taleb, R. & Djilali, A. B. Backstepping sliding mode control of a dual rotor wind turbine system. In: 2018 International Conference on Electrical Sciences and Technologies in Maghreb, CISTEM, 2018, 1–5. 10.1109/CISTEM.2018.8613409.

[CR18] 18.Boyette, A., Saadate, S., Poure, P. Direct and indirect control of a Doubly Fed Induction Generator wind turbine including a storage unit. In: IECON 2006-32nd Annual Conference on IEEE Industrial Electronics, Paris, France. 06–10 November, 2006. 10.1109/IECON.2006.347300.

[CR19] 19.Younes, S. et al. Effectiveness analysis of twelve sectors of DTC based on a newly modified switching table implemented on a wind turbine DFIG system under variable wind velocity. Ain Shams Eng. J.14(11), 102221. 10.1016/j.asej.2023.102221 (2023). [Google Scholar]

[CR20] 20.Chojaa, H. et al. A novel DPC approach for DFIG-based variable speed wind power systems using dspace. IEEE Access11, 9493–9510. 10.1109/ACCESS.2023.3237511 (2023). [Google Scholar]

[CR21] 21.Ikni, D. & Raducan, E. Stability analysis of a wind turbine controlled by direct torque control. Energies17, 2488. 10.3390/en17112488 (2024). [Google Scholar]

[CR22] 22.Benbouhenni, H. Stator current and rotor flux ripples reduction of DTC DFIG drive using FSTSMC algorithm. Int. J. Smart Grid3(4), 226–234. 10.20508/ijsmartgrid.v3i4.82.g72 (2019). [Google Scholar]

[CR23] 23.Benbouhenni, H. Five-level DTC control of induction machine drive using fuzzy logic controller for low torque ripple. Acta Tech. Corviniensis-Bull. Eng.12(2), 91–96 (2019). [Google Scholar]

[CR24] 24.Boudjema, Z., Taleb, R., Djeriri, Y. & Yahdou, A. A novel direct torque control using second order continuous sliding mode of a doubly fed induction generator for a wind energy conversion system. Turk. J. Electr. Eng. Comput. Sci.25(2), 965–975. 10.3906/elk-1510-89 (2017). [Google Scholar]

[CR25] 25.Youcef, B. & Djilani, B. A. Comparison study between SVM and PWM inverter in sliding mode control of active and reactive power control of a DFIG for variable speed wind energy. Int. J. Renew. Energy Res. IJRER2(3), 471–476. 10.20508/ijrer.v2i3.269.g6047 (2012). [Google Scholar]

[CR26] 26.Mohammed, A., Ahmed, E., Tamou, N. & Haitam, C. Comparative analysis of ADRC & PI controllers used in wind turbine system driving a DFIG. Int. J. Renew. Energy Res. IJRER7(4), 1816–1824 (2017). [Google Scholar]

[CR27] 27.Rayane, L. & Lekhchine, S. Fuzzy logic controller-based power control of DFIG based on wind energy systems. Int. J. Smart Grid-ijSmartGrid8(1), 74–80. 10.20508/ijsmartgrid.v8i1.334.g346 (2024). [Google Scholar]

[CR28] 28.Sanjeev, K. G., Sundram, M. & Madhu, S. Performance enhancement of DFIG based grid connected SHPP using ANN controller. Int. J. Renew. Energy Res. IJRER9(3), 1165–1179. 10.20508/ijrer.v9i3.9427.g7694 (2019). [Google Scholar]

[CR29] 29.Mazouz, F., Sebti, B. & Ilhami, C. DPC-SVM of DFIG using fuzzy second order sliding mode approach. Int. J. Smart Grid5(4), 174–182. 10.20508/ijsmartgrid.v5i4.219.g178 (2021). [Google Scholar]

[CR30] 30.Bekhada, H. et al. Comparative study of PI, RST, sliding mode and fuzzy supervisory controllers for DFIG based wind energy conversion system. Int. J. Renew. Energy Res. IJRER5(4), 1174–1185. 10.20508/ijrer.v5i4.2915.g6705 (2015). [Google Scholar]

[CR31] 31.Boris, D., Bane, P., Dragan, M., Vladimir, K. & Djura, O. Artificial intelligence based vector control of induction generator without speed sensor for use in wind energy conversion system. Int. J. Renew. Energy Res. IJRER5(1), 299–307. 10.20508/ijrer.v5i1.2030.g6498 (2025). [Google Scholar]

[CR32] 32.Samir, M., Mohamed, H., Nadir, K. & Selman, K. Neural network based field oriented control for doubly fed induction generator. Int. J. Smart Grid-Ijsmartgrid2(3), 183–187. 10.20508/ijsmartgrid.v2i3.18.g18 (2018). [Google Scholar]

[CR33] 33.Xiaoming, Y. & Ming-Hsien, C. Backstepping-based direct power control for dual-cage rotor brushless doubly fed induction generator. IEEE Trans. Power Electron.38(2), 2668–2680. 10.1109/TPEL.2022.3214331 (2023). [Google Scholar]

[CR34] 34.Mostafa, A., Abdelilah, A., Rachid, A. & Jamal, B. Backstepping control of a switched reluctance motor with inter-turn short-circuit. Adv. Electr. Electron. Eng.20(3), 250–259. 10.15598/aeee.v20i3.4326 (2022). [Google Scholar]

[CR35] 35.Abderrahmen, K., Said, G. & Youcef, S. Improved sensorless backstepping controller using extended Kalman filter of a permanent magnet synchronous machine. Bull. Electr. Eng. Inf.11(2), 658–671. 10.11591/eei.v11i2.3560 (2022). [Google Scholar]

[CR36] 36.Marcin, M., Patryk, S., Arkadiusz, L., Jaroslaw, G. & Filip, W. Feedback control of multiphase induction machines with backstepping technique. IEEE Trans. Ind. Electron.67(6), 4305–4314. 10.1109/TIE.2019.2931236 (2022). [Google Scholar]

[CR37] 37.Nadour, M., Essadki, A. & Nasser, T. Comparative analysis between PI & backstepping control strategies of DFIG driven by wind turbine. Int. J. Renew. Energy Res.7(3), 1307–1316. 10.20508/ijrer.v7i3.6066.g7163 (2017). [Google Scholar]

[CR38] 38.Sara, M., Ahmed, E., Tamou, N. & Badr, B. I. An efficient nonlinear backstepping controller approach of a wind energy conversion system based on a DFIG. Int. J. Renew. Energy Res. IJRER7(4), 1520–1528. 10.20508/ijrer.v7i4.6112.g7192 (2017). [Google Scholar]

[CR39] 39.Adel, K., Nihel, K. & Mohamed, F. M. Wind energy conversion system using DFIG controlled by backstepping and sliding mode strategies. Int. J. Renew. Energy Res. IJRER2(3), 421–430. 10.20508/ijrer.v2i3.249.g6040 (2012). [Google Scholar]

[CR40] 40.Patel, R., Hafiz, F., Swain, A. & Ukil, A. Nonlinear rotor side converter control of DFIG based wind energy system. Electr. Power Syst. Res.198, 107358. 10.1016/j.epsr.2021.107358 (2021). [Google Scholar]

[CR41] 41.Xiong, P. & Sun, D. Backstepping-based DPC strategy of a wind turbine-driven DFIG under normal and harmonic grid voltage. IEEE Trans. Power Electron.31(6), 4216–4225. 10.1109/TPEL.2015.2477442 (2015). [Google Scholar]

[CR42] 42.Mechter, A., Kemih, K. & Ghanes, M. Backstepping control of a wind turbine for low wind speeds. Nonlinear Dyn.84(4), 2435–2445. 10.1007/s11071-016-2655-y (2016). [Google Scholar]

[CR43] 43.Trabelsi, R., Khedher, A., Mimouni, M. F. & M’sahli, F. Backstepping control for an induction motor using an adaptive sliding rotor-flux observer. Electr. Power Syst. Res.93, 1–15. 10.1016/j.epsr.2012.06.004 (2012). [Google Scholar]

[CR44] 44.Roy, T. K., Mahmud, M. A. & Oo, A. M. Robust adaptive backstepping excitation controller design for higher-order models of synchronous generators in multimachine power systems. IEEE Trans. Power Syst.34(1), 40–51. 10.1109/TPWRS.2018.2868783 (2018). [Google Scholar]

[CR45] 45.Yin, W., Wu, X. & Rui, X. Adaptive robust backstepping control of the speed regulating differential mechanism for wind turbines. IEEE Trans. Sustain. Energy10(3), 1311–1318. 10.1109/TSTE.2018.2865631 (2018). [Google Scholar]

[CR46] 46.Kasbi, A. & Rahali, A. MPPT performance and power quality improvement by using fractional-order adaptive backstepping control of a DFIG-based wind turbine with disturbance and uncertain parameters. Arab. J. Sci. Eng.48, 6595–6614. 10.1007/s13369-022-07474-1 (2023). [Google Scholar]

[CR47] 47.Wang, J. et al. Adaptive back-stepping control for a permanent magnet synchronous generator wind energy conversion system. Int. J. Hydrogen Energy44(5), 3240–3249. 10.1016/j.ijhydene.2018.12.023 (2019). [Google Scholar]

[CR48] 48.Kasbi, A. & Rahali, A. Performance improvement of modern variable-velocity wind turbines technology based on the doublyfed induction generator (DFIG). Mater. Today Proc.45, 5426–5432. 10.1016/j.matpr.2021.02.114 (2021). [Google Scholar]

[CR49] 49.Justo, J. J., Mwasil, F., Lee, J. & Jung, J.-W. AC-microgrids versus DC-microgrids with distributed energy resources: A review. Renew. Sustain. Energy Rev.24, 387–405 (2013). [Google Scholar]

[CR50] 50.Mushenko, A. et al. Modeling a single-channel synergetic observer for chaos-based secure communication system applications. Mathematics12, 2764. 10.3390/math12172764 (2024). [Google Scholar]

[CR51] 51.Brahim, D., Hamoudi, F., Habib, B., Slimane, M. & Naamane, D. Synergetic control for three-level voltage source inverter-based shunt active power filter to improve power quality. Energy Rep.10, 1013–1027. 10.1016/j.egyr.2023.07.051 (2023). [Google Scholar]

[CR52] 52.Habib, B. & Bizon, N. A synergetic sliding mode controller applied to direct field-oriented control of induction generator-based variable speed dual-rotor wind turbines. Energies14, 4437. 10.3390/en14154437 (2021). [Google Scholar]

[CR53] 53.Al-Hussein, A.-B.A., Tahir, F. R. & Pham, V.-T. FPGA Implementation of synergetic controller-based MPPT algorithm for a standalone PV system. Computation13, 64. 10.3390/computation13030064 (2025). [Google Scholar]

[CR54] 54.Habib, B. Comparative study of sliding mode control with synergetic control for rotor side inverter of the DFIG for multi-rotor wind power systems. Majlesi J. Mechatron. Syst.11(2), 29–37 (2023). [Google Scholar]

[CR55] 55.Habib, B. & Gasmi, H. Comparative study of synergetic controller with super twisting algorithm for rotor side inverter of DFIG. Int. J. Smart Grid-ijSmartGrid6(4), 144–156. 10.20508/ijsmartgrid.v6i4.265.g228 (2022). [Google Scholar]

[CR56] 56.Habib, B., Mehedi, F. & Soufiane, L. New direct power synergetic-SMC technique based PWM for DFIG integrated to a variable speed dual-rotor wind power. Automatika63(4), 718–731. 10.1080/00051144.2022.2065801 (2022). [Google Scholar]

[CR57] 57.Debdouche, N. et al. Synergetic simplified super-twisting algorithm control for stability enhancement of PV/BESS-based DC microgrid. Sci. Rep.15, 7392. 10.1038/s41598-025-92042-4 (2025). [DOI] [PMC free article] [PubMed] [Google Scholar]

[CR58] 58.Benbouhenni, H. et al. Synergetic-PI controller based on genetic algorithm for DPC-PWM strategy of a multi-rotor wind power system. Sci. Rep.13, 13570. 10.1038/s41598-023-40870-7 (2023). [DOI] [PMC free article] [PubMed] [Google Scholar]

[CR59] 59.Habib, B., Bizon, N., Thounthong, P., Colak, I. & Mungporn, P. A new integral-synergetic controller for direct reactive and active powers control of a dual-rotor wind system. Meas. Control57(2), 208–224. 10.1177/00202940231195117 (2024). [Google Scholar]

[CR60] 60.Habib, B. et al. Fractional-order synergetic control of the asynchronous generator-based variable-speed multi-rotor wind power systems. In IEEE Access11, 133490–133508. 10.1109/ACCESS.2023.3335902 (2023). [Google Scholar]

[CR61] 61.Srikanth, G. & Rajesh, G. N. Power quality enhancement in PV fed UPQC using adaptive lizard algorithm. Int. J. Smart Grid-ijSmartGrid9(1), 31–42. 10.20508/ijsmartgrid.v9i1.407.g378 (2025). [Google Scholar]

[CR62] 62.Deffaf, B., Debdouche, N., Benbouhenni, H., Hamoudi, F. & Bizon, N. A new control for improving the power quality generated by a three-level T-type inverter. Electronics12, 2117. 10.3390/electronics12092117 (2023). [Google Scholar]

[CR63] 63.Habib, B. & Bizon, N. Terminal synergetic control for direct active and reactive powers in asynchronous generator-based dual-rotor wind power systems. Electronics10, 1880. 10.3390/electronics10161880 (2021). [Google Scholar]

[CR64] 64.Mayilsamy, G., Natesan, B., Joo, Y. H. & Lee, S. R. Fast terminal synergetic control of PMVG-based wind energy conversion system for enhancing the power extraction efficiency. Energies15, 2774. 10.3390/en15082774 (2022). [Google Scholar]

[CR65] 65.Babes, B. et al. Experimental investigation of an adaptive fuzzy-neural fast terminal synergetic controller for buck DC/DC converters. Sustainability14, 7967. 10.3390/su14137967 (2022). [Google Scholar]

[CR66] 66.Dalal, Z., Youcef, B. & Habib, B. Robust synergetic-sliding mode-based-backstepping control of induction motor with MRAS technique. Energy Rep.10, 3665–3680. 10.1016/j.egyr.2023.10.035 (2023). [Google Scholar]

[CR67] 67.Erenturk, K., Draou, A. & AlKassem, A. Design and comparison of different types of synergetic controllers for islanded DC microgrids. Sustainability14, 8792. 10.3390/su14148792 (2022). [Google Scholar]

[CR68] 68.Habib, B. Neuro-scond order sliding mode field oriented command for DFIG based wind turbine. Int. J. Smart Grid-Ijsmartgrid2(4), 209–217. 10.20508/ijsmartgrid.v2i4.25.g27 (2018). [Google Scholar]

[CR69] 69.Benbouhenni, H., Bizon, N. & Colak, I. A brief review of space vector modulation (SVM) methods and a new svm technique based on the minimum and maximum of the three-phase voltages. Iran. J. Electr. Electron. Eng.18(3), 54–72 (2022). [Google Scholar]

[CR70] 70.Habib, B., Bizon, N., Ilhami, C., Mohamed, I. M. & Mourad, Y. Direct active and reactive powers control of double-powered asynchronous generators in multi-rotor wind power systems using modified synergetic control. Energy Rep.10, 4286–4301. 10.1016/j.egyr.2023.10.085 (2023). [Google Scholar]

[CR71] 71.Reza, G., Ali, M. & Alireza Davari, S. A new control algorithm method based on DPC to improve power quality of DFIG in unbalance grid voltage conditions. Int. J. Renew. Energy Res. IJRER8(4), 2228–2238. 10.20508/ijrer.v8i4.8583.g7527 (2018). [Google Scholar]

[CR72] 72.Zhou, P., He, Y. & Sun, D. Improved direct power control of a DFIG-based wind turbine during network unbalance. IEEE Trans. Power Electron.24(11), 2465–2474. 10.1109/TPEL.2009.2032188 (2009). [Google Scholar]

[CR73] 73.Seyed, M. T., Mohammad, A. P. & Mohammad, R. Z. Comparison between different DPC methods applied to DFIG wind turbines. Int. J. Renew. Energy Res. IJRER3(2), 446–452. 10.20508/ijrer.v3i2.680.g6162 (2013). [Google Scholar]

[CR74] 74.Habib, B. Application of five-level NPC inverter in DPC-ANN of doubly fed induction generator for wind power generation systems. Int. J. Smart Grid-IJSMARTGRID3(3), 128–137. 10.20508/ijsmartgrid.v3i3.66.g59 (2019). [Google Scholar]

[CR75] 75.Ramos, C. J., Martins, A. P. & Carvalho, A. S. Rotor current controller with voltage harmonics compensation for a DFIG operating under unbalanced and distorted stator voltage. In: IECON 2007. 33rd Annual Conference of IEEE, 5–8 (2007).

[CR76] 76.Wei, F., Zhang, X., Vilathgamuwa, D. M., Choi, S. S. & Wang, S. Mitigation of distorted and unbalanced stator voltage of stand-alone doubly fed induction generators using repetitive control technique. IET Electron. Power Appl.7(8), 654–663 (2013). [Google Scholar]

[CR77] 77.Ardjal, A., Bettayeb, M., Mansouri, R. & Mehiri, A. Nonlinear synergetic control approach for dc-link voltage regulator of wind turbine DFIG connected to the grid. In: 2018 5th International Conference on Renewable Energy: Generation and Applications (ICREGA), Al Ain, United Arab Emirates, 2018, 94–97. 10.1109/ICREGA.2018.8337639 (2018).

[CR78] 78.Yahdou, A. et al. Application of backstepping control with nonsingular terminal sliding mode surface technique to improve the robustness of stator power control of asynchronous generator-based multi-rotor wind turbine system. Electr. Power Compon. Syst.10.1080/15325008.2024.2304688 (2024). [Google Scholar]

[CR79] 79.Ibrahim, Y., Semmah, A. & Patrice, W. Neuro-second order sliding mode control of a DFIG based wind turbine system. J. Electr. Electron. Eng.13(1), 63–68 (2020). [Google Scholar]

[CR80] 80.Benbouhenni, H. et al. Hardware-in-the-loop simulation to validate the fractional-order neuro-fuzzy power control of variable-speed dual-rotor wind turbine systems. Energy Rep.11, 4904–4923. 10.1016/j.egyr.2024.04.049 (2024). [Google Scholar]

[CR81] 81.Yessef, M. et al. Experimental validation of feedback PI controllers for multi-rotor wind energy conversion systems. IEEE Access12, 7071–7088. 10.1109/ACCESS.2024.3351355 (2024). [Google Scholar]

[CR82] 82.Hamid, Ch. et al. Integral sliding mode control for DFIG based WECS with MPPT based on artificial neural network under a real wind profile. Energy Rep.7, 4809–4824. 10.1016/j.egyr.2021.07.066 (2021). [Google Scholar]

[CR83] 83.Echiheb, F. et al. Robust sliding-backstepping mode control of a wind system based on the DFIG generator. Sci Rep.12, 11782. 10.1038/s41598-022-15960-7 (2022). [DOI] [PMC free article] [PubMed] [Google Scholar]

[CR84] 84.Alami, H. E. et al. FPGA in the loop implementation for observer sliding mode control of DFIG-generators for wind turbines. Electronics11(1), 116. 10.3390/electronics11010116 (2022). [Google Scholar]

[CR85] 85.Yahdou, A., Djilali, A. B., Bounadja, E. & Habib, B. Using neural network super-twisting sliding mode to improve power control of a dual-rotor wind turbine system in normal and unbalanced grid fault modes. Int. J. Circuit Theory Appl.52(9), 4323–4347. 10.1002/cta.3960 (2024). [Google Scholar]

[CR86] 86.Hete, R. R. et al. Design and development of PI controller for DFIG grid integration using neural tuning method ensembled with dense plexus terminals. Sci. Rep.14, 7916. 10.1038/s41598-024-56904-7.(2024) (2024). [DOI] [PMC free article] [PubMed] [Google Scholar]

[CR87] 87.Aria, Y., Sajjad, T. & Mohammad, R. F. An improved long-horizon model predictive control for DFIG in WECS with variable sampling-time. IET Renew. Power Gener.16(3), 517–531. 10.1049/rpg2.12357 (2022). [Google Scholar]

[CR88] 88.Benbouhenni, H., Gasmi, H. & Colak, I. Backstepping control for multi-rotor wind power systems. Majlesi J. Energy Manag.11(4), 8–15 (2023). [Google Scholar]

[CR89] 89.Habib, B., Gasmi, H. & Colak, I. Intelligent control scheme of asynchronous generator-based dual-rotor wind power system under different working conditions. Majlesi J. Energy Manag.11(3), 8–15 (2022). [Google Scholar]

[CR90] 90.Ravikiran, H. & Tukaram, M. Modified super twisting algorithm based sliding mode control for LVRT enhancement of DFIG driven wind system. Energy Rep.8, 3600–3613. 10.1016/j.egyr.2022.02.235 (2022). [Google Scholar]

PERMALINK

MATLAB implementation of dual synergetic control for multi-rotor wind turbine systems

Habib Benbouhenni

Adil Yahdou

Z M S Elbarbary

Ilhami Colak

Saad F Al-Gahtani

Abstract

Introduction

Table 1.

Fig. 1.

Proposed DSC controller

Fig. 2.

Fig. 3.

Proposed DPC-DSC-MSVM approach

Fig. 4.

Fig. 5.

Fig. 6.

Table 2.

Fig. 7.

Results

Table 3.

Fig. 8.

First test

Fig. 9.

Fig. 10.

Fig. 11.

Table 4.

Second test

Fig. 12.

Fig. 13.

Table 5.

Table 6.

Third test

Fig. 14.

Fig. 15.

Fig. 16.

Table 7.

Table 8.

Forth test

Fig. 17.

Fig. 18.

Table 9.

Fig. 19.

Fig. 20.

Table 10.

Table 11.

Table 12.

Table 13.

Table 14.

Conclusions

Supplementary Information

Acknowledgements

Abbreviations

Author contributions

Data availability

Declarations

Competing interests

Footnotes

Supplementary Information

References

Associated Data

Supplementary Materials

Data Availability Statement

ACTIONS

PERMALINK

RESOURCES

Similar articles

Cited by other articles

Links to NCBI Databases