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Fuzzy Logic-Based Smart Control of a Wind Energy Conversion System Using Cascaded Doubly Fed Induction Generator

Amar Maafa¹, Hacene Mellah¹, Karim Benaouicha^{1, 2}, Badreddine Babes³, Abdelghani Yahioua², Hamza Sahraoui⁴

¹   Engineering Department, Faculty of sciences and applied sciences, University of Bouira, 10000 Bouira,    Algeria; omaafa@univ-bouira.dz (A.M.); h.mellah@univ-bouira.dz (H.M.)

²   Electrical systems engineering department, University of Boumerdes, Frantz fanon City, Boumerdes,     Algeria; k.benaouicha@yahoo.com (K.B.); abdelghani.yahiou@univ-bouira.dz (A.Y.)

³   Research Center in Industrial Technologies - CRTI P.O. Box 64, Cheraga 16014 Algiers, Algeria; elect_babes@yahoo.fr (B.B.)

⁴   Electrical systems engineering department, University of Boumerdes, Frantz fanon City, Boumerdes,    Algeria; hamzasahraoui@gmail.com (H.S.)

*   Correspondence: elect_babes@yahoo.fr (B.B.)

Abstract: This paper introduces a robust system designed to effectively manage and enhance the electrical output of Wind Energy Conversion System (WECS) using Cascaded Doubly Fed Induction Generator (CDFIG) connected to the power grid. We carried a comparison of three different types of controllers: the proportional integral (PI) controller, the fractional PID controller (FPID), and the fuzzy logic controller (FLC). It turns out that, according to the first results, the FLC performed optimally in terms of tracking and rejecting disturbances. The performance evaluation of the FLC includes analyzing the rise time, settling time, and peak overshoot of the transient response to a step input. The examination of total harmonic distortion (THD) is also employed to validate the superiority of the FLC. The solution that was investigated is a CDFIG that is based on a variable-speed wind power conversion chain. It is comprised of the electrical and mechanical connection of two DFIGs through their rotors. This system solves the problem by removing the requirement for sliding ring-brush contacts. Through the utilization of the MATLAB/Simulink environment, the effectiveness of this control and energy management approach is evaluated, thereby demonstrating its capacity to fulfil the objectives that have been set.

Keywords: Wind Energy Conversion System (WECS); Cascaded doubly fed induction generator (CDFIG); Fractional-order PID controller (FPID); fuzzy logic controller (FLC).

1. Introduction

The introduction of renewable energies, namely wind energy, into the power grid poses significant difficulties in terms of management and optimization. Wind Energy Conversion Systems (WECS) are challenging to manage because they are subject to uncertainties and variables caused by changing weather conditions [1-5]. Power control is crucial for effectively integrating WECS into smart and traditional grids, ensuring stability, reliability, and optimal electrical energy utilization. Due to the unpredictable characteristics of wind, it is crucial to control the energy generation of wind turbines in order to ensure constant and effective incorporation into the electrical grid. Modern power control techniques prioritize the optimization of energy generation while reducing disruptions in the electrical grid, such as fluctuations in frequency and voltage [6-8]. Recent approaches involve the utilization of sophisticated techniques like fuzzy logic, predictive controllers, and machine learning algorithms to improve the robustness and effectiveness of power control. These strategies enable improved adjustment to fluctuating wind conditions and more accurate control of wind energy integration into the power system [9-14].

Fuzzy controllers have emerged as an effective solution to improve the efficiency and stability of wind energy management systems [15-19]. FL controllers are being used more and more in wind power conversion systems to make them work better and more efficiently. FL controls are great at dealing with the highly unpredictable and nonlinear behavior of wind. They don't need exact mathematical models, which are often hard to understand or don't work well in the real world, so they can adapt to changing wind speeds and directions [9, 15].

The literature indicates that a number of advanced controls have been designed to offer improved solutions for difficulties that grid-connected WECS may face. The Fuzzy Logic Controller (FLC) proposed in [20] generate the rotor voltages necessary to ensure that the active and reactive power in the WECS achieve their target reference values. In this case, fuzzy controllers frequently call for modifications that are quite fine. The study in [21] presents a control law that combines sliding mode control and a single-input FLC to effectively and efficiently control a static synchronous compensator, enhancing both its performance and stability. The goal is to enhance the voltage profile and stability of an asynchronous WECS, even in the presence of wind speed and load fluctuations. However, an attractive choice is to experiment with an alternative form of FLC, specifically ones that modify the PI reference value. In paper [22], an adaptive controller that is based on the principle of fuzzy logic is proposed in order to limit the extracted power at its rated value while simultaneously enhancing its quality. Additionally, the pitch angle is adjusted in order to alleviate the loads that are applied to the turbine and the drive train when they are operating under full load conditions. In [23], a model for Load Frequency Control (LFC) is given, which combines the economic dispatching control with the frequency control problem. The need for frequency stability is crucial in both the short-term and long-term operation of power systems. In [24], the suggested LFC model examines the role of hydro-turbines in power systems with abundant wind energy. It also seeks to understand how hydro-turbines contribute to the secondary frequency control scheme using a PID controller. Current searches have additionally concentrated on comprehending the function of energy storage system (ESS), together with innovative control methods, in regulating the frequency of power systems mostly powered by wind. Using the cascaded dual FLC strategy, a robust and adaptive energy management system was developed in [25] with the purpose of mitigating the disturbances that were caused by varied solar irradiation, fluctuating wind speed, and even unexpected fluctuations in load. To achieve more stability, the suggested algorithm is able to govern the functioning of the batteries, the mode of the microgrid, and the management of the load. In [26], an adaptive fuzzy logic controller is proposed as a control system designed to maximize power output from a WECS equipped with a permanent magnet synchronous generator. Excessive overshooting of the results is observed whenever there is a sudden shift in the references. A novel single input variable (FLC) technique is proposed in [27] for a WT driven doubly fed induction generator (DFIG) that is equipped with a battery energy storage system and operates in autonomous mode. The fact that this type of command is dependent on the internal properties of the system makes it a fragile command. In [28], there is a lack of a comparison study for the purpose of validating the results of the control and administration of an energy conversion system within a microgrid setup that includes numerous renewable energy sources and a storage system.

This paper investigates a comparative study of three controllers, notably a novel FLC, a fractional-order PID controller (FPID), and a proportional-integral (PI) controller for a highly nonlinear and complex system in the first step. In the second step, we will use the suggested controllers for the production and management of a WECS chain based on CDFIG. This WECS configuration comprises a wind turbine (WT) that transforms wind's kinetic energy into mechanical energy, this latter will be transformed into electrical energy via two cascaded asynchronous machines, and an AC/AC converter that establishes the connection between the generator and the electrical network.

The brush-ring system in the DFIG, commonly employed in wind energy generation, reduces the machine's reliability. In order solve this problem, the electrical and mechanical connection of two DFIGs through their rotors is used to avoid the need for brush-ring sliding contacts. The complete system is referred to as a CDFIG [8, 13]. This machine will serve as a generator for the generation of electrical energy.

In order to establish a connection between the system and the network using a DC-link, we will utilize a power electronics transformer. The frequency converter comprises a rectifier on the machine side, which is responsible for managing and regulating the active and reactive powers transferred between the second stator and the grid. The grid-side inverter is controlled to ensure a constant DC-link.

2. Modeling and description of the energy conversion chain

CDFIG is a new area of research; but recently a lot of study has been published which concerns several areas. The cascade can be found in: wind power [29], small hydraulic power plants [30], and aviation [31].

The ring-brush system in the DFIG decreases its reliability; however, the electrical and mechanical coupling of two DFIGs via their rotors solves this issue by eliminating the need for sliding ring-brush contacts. The entire system is called CDFIG. In this case, succession coupling involves connecting the shafts and rotor windings in a reverse manner, resulting in the inversion of the rotor phases [32]. Figure 1 illustrates this coupling.

Figure 1. Connection of the CDFIG to the electrical network.

All equations are expressed in a frame of reference linked to the rotating field in the Park transform. The equations of the voltage and the flux of the two DFIGs are:

- The DFIM 1:

- The DFIM 2:

Modeling the electrical coupling of the two rotors depends on the type of coupling; the voltage and current equations will be:

The multivariable system can be represented by state-space equations. Multiple choices are possible for the state vector. Among these we will take the vector of the stator and rotor currents.

In order to obtain differential equations, we will need to replace the flux in the voltage equations. These differential equations is expressed as:

With:

2.1 Control powers of stator-1

By aligning the d-axis of the (dq) reference frame with the flux of the first stator φ_s1, the steady-state model of the CDFIG is simplified as:

Where v_ds2 and v_qs2 represent the two-phase voltage components of the second stator, which must be controlled to achieve the desired i_ds2 and i_qs2 current levels in the machine. The influence of coupling terms between the d and q axes in s.ωsLs2-C.Lm2  is minimal, and can be effectively compensated through proper regulator synthesis.

On the other hand, the term C.s.(Lm1Vs )/Ls1  represents an electromotive force that is dependent on the rotational speed. This term's influence is significant as it introduces a tracking error. Therefore, the control strategy must account for this error to ensure accurate system performance.

The powers of stator-1 can be controlled through the currents of stator-2 by the following system of equations:

With: s=s1.s2=ωs1-ωr1-ωr2ωs1=ωs1-Ω(p1+p2)ωs1,  and C=Lm2/(Lr1+Lr2-Lm12Ls1 )

Finally, we can control the active powers P_s1 and reactive powers Q_s1 exchanged between the network and stator-1 through the currents of stator-2 i_ds2 and i_qs2.

2.2 Modeling of the connection to the electrical network

The main objective is to maintain zero reactive power to ensure a unity power factor on the network side in order to optimize efficiency. Then adjust the active power sent to the network to its reference value and keep the DC bus voltage constant. The frequency converter (rectifier-inverter) and the CDFIG coupled to the network are shown in Figure 2.

Figure 2. Connection of the CDFIG to the electrical network via power converters.

The DC/AC converter, on the network side, is modeled as follows:

The current flowing through the grid side inverter is defined:

ig=f1iin1+f2iin2+f3iin3                                         (12)

The AC/DC converter can be modeled as follows:

The current flowing through the machine side rectifier is defined:

(f1, f2, f3) and (f1', f1', f1')  are logical connection functions of switches inverter and rectifier respectively.

The current which flows in the capacitor comes from the rectifier on the machine side and inverter from the network side:

 ic=im-ig                                   (15)

The temporal evolution of the DC link voltage is obtained from the integration of capacitive current:

The diagram in Figure 2 shows that the connection to the electrical network is made via an input filter. By applying the Park transformation, we can write:

With:

The reference power of the DC link:

The DC link voltage regulation block is resented in Figure 3.

Figure 3. DC link regulation scheme.

The active and reactive powers exchanged with the network are defined as follows:

We can derive the reference currents from equation (21):

The I_d current is used to regulate the DC link voltage. It is controlled using a regulator (PI). The I_q is used to regulate the reactive power transmitted. The regulation scheme for network currents is shown in Figure 4.

Figure 4. Network side current regulation scheme.

3. Design of the used controllers

3.1 PI-controller

The regulation of wind power systems with proportional-integral has been the subject of a great number of publications that have been published in the academic literature [33-38]. The PI controller, used in the CDFIG control, is simple and quick to implement while offering acceptable performance (dynamic, robustness and disturbance rejection). Figure 5 shows the closed-loop system, corrected by a classical PI controller, with its transfer function presented as follows:

Figure 5. Network side current regulation scheme.

The system's response time is approximately 10 milliseconds, which is sufficiently rapid for usage on WTs, where wind fluctuations are gradual and mechanical time constants are significant. Lowering the value may not enhance overall performance, but it could potentially result in disturbances during transient situations, resulting in undesired exceeds its and instabilities. We used the pole compensation method here for its speed; it is obvious that it is not the only valid method for the synthesis of the PI controller. The results of our calculations are as follows: k_p = 0.000118 and k_i = 0.00184.

3.2 Fractional-order PID controller

A PID fractional (Proportional-Integral-Derivative) is an extension of the classic PID controller, and has the form

Article

Fuzzy Logic-Based Smart Control of a Wind Energy Conversion System Using Cascaded Doubly Fed Induction Generator

Amar Maafa¹, Hacene Mellah¹, Karim Benaouicha^{1, 2}, Badreddine Babes³, Abdelghani Yahioua², Hamza Sahraoui⁴

¹   Engineering Department, Faculty of sciences and applied sciences, University of Bouira, 10000 Bouira,    Algeria; omaafa@univ-bouira.dz (A.M.); h.mellah@univ-bouira.dz (H.M.)

²   Electrical systems engineering department, University of Boumerdes, Frantz fanon City, Boumerdes,     Algeria; k.benaouicha@yahoo.com (K.B.); abdelghani.yahiou@univ-bouira.dz (A.Y.)

³   Research Center in Industrial Technologies - CRTI P.O. Box 64, Cheraga 16014 Algiers, Algeria; elect_babes@yahoo.fr (B.B.)

⁴   Electrical systems engineering department, University of Boumerdes, Frantz fanon City, Boumerdes,    Algeria; hamzasahraoui@gmail.com (H.S.)

*   Correspondence: elect_babes@yahoo.fr (B.B.)

Abstract: This paper introduces a robust system designed to effectively manage and enhance the electrical output of Wind Energy Conversion System (WECS) using Cascaded Doubly Fed Induction Generator (CDFIG) connected to the power grid. We carried a comparison of three different types of controllers: the proportional integral (PI) controller, the fractional PID controller (FPID), and the fuzzy logic controller (FLC). It turns out that, according to the first results, the FLC performed optimally in terms of tracking and rejecting disturbances. The performance evaluation of the FLC includes analyzing the rise time, settling time, and peak overshoot of the transient response to a step input. The examination of total harmonic distortion (THD) is also employed to validate the superiority of the FLC. The solution that was investigated is a CDFIG that is based on a variable-speed wind power conversion chain. It is comprised of the electrical and mechanical connection of two DFIGs through their rotors. This system solves the problem by removing the requirement for sliding ring-brush contacts. Through the utilization of the MATLAB/Simulink environment, the effectiveness of this control and energy management approach is evaluated, thereby demonstrating its capacity to fulfil the objectives that have been set.

Keywords: Wind Energy Conversion System (WECS); Cascaded doubly fed induction generator (CDFIG); Fractional-order PID controller (FPID); fuzzy logic controller (FLC).

1. Introduction

The introduction of renewable energies, namely wind energy, into the power grid poses significant difficulties in terms of management and optimization. Wind Energy Conversion Systems (WECS) are challenging to manage because they are subject to uncertainties and variables caused by changing weather conditions [1-5]. Power control is crucial for effectively integrating WECS into smart and traditional grids, ensuring stability, reliability, and optimal electrical energy utilization. Due to the unpredictable characteristics of wind, it is crucial to control the energy generation of wind turbines in order to ensure constant and effective incorporation into the electrical grid. Modern power control techniques prioritize the optimization of energy generation while reducing disruptions in the electrical grid, such as fluctuations in frequency and voltage [6-8]. Recent approaches involve the utilization of sophisticated techniques like fuzzy logic, predictive controllers, and machine learning algorithms to improve the robustness and effectiveness of power control. These strategies enable improved adjustment to fluctuating wind conditions and more accurate control of wind energy integration into the power system [9-14].

Fuzzy controllers have emerged as an effective solution to improve the efficiency and stability of wind energy management systems [15-19]. FL controllers are being used more and more in wind power conversion systems to make them work better and more efficiently. FL controls are great at dealing with the highly unpredictable and nonlinear behavior of wind. They don't need exact mathematical models, which are often hard to understand or don't work well in the real world, so they can adapt to changing wind speeds and directions [9, 15].

The literature indicates that a number of advanced controls have been designed to offer improved solutions for difficulties that grid-connected WECS may face. The Fuzzy Logic Controller (FLC) proposed in [20] generate the rotor voltages necessary to ensure that the active and reactive power in the WECS achieve their target reference values. In this case, fuzzy controllers frequently call for modifications that are quite fine. The study in [21] presents a control law that combines sliding mode control and a single-input FLC to effectively and efficiently control a static synchronous compensator, enhancing both its performance and stability. The goal is to enhance the voltage profile and stability of an asynchronous WECS, even in the presence of wind speed and load fluctuations. However, an attractive choice is to experiment with an alternative form of FLC, specifically ones that modify the PI reference value. In paper [22], an adaptive controller that is based on the principle of fuzzy logic is proposed in order to limit the extracted power at its rated value while simultaneously enhancing its quality. Additionally, the pitch angle is adjusted in order to alleviate the loads that are applied to the turbine and the drive train when they are operating under full load conditions. In [23], a model for Load Frequency Control (LFC) is given, which combines the economic dispatching control with the frequency control problem. The need for frequency stability is crucial in both the short-term and long-term operation of power systems. In [24], the suggested LFC model examines the role of hydro-turbines in power systems with abundant wind energy. It also seeks to understand how hydro-turbines contribute to the secondary frequency control scheme using a PID controller. Current searches have additionally concentrated on comprehending the function of energy storage system (ESS), together with innovative control methods, in regulating the frequency of power systems mostly powered by wind. Using the cascaded dual FLC strategy, a robust and adaptive energy management system was developed in [25] with the purpose of mitigating the disturbances that were caused by varied solar irradiation, fluctuating wind speed, and even unexpected fluctuations in load. To achieve more stability, the suggested algorithm is able to govern the functioning of the batteries, the mode of the microgrid, and the management of the load. In [26], an adaptive fuzzy logic controller is proposed as a control system designed to maximize power output from a WECS equipped with a permanent magnet synchronous generator. Excessive overshooting of the results is observed whenever there is a sudden shift in the references. A novel single input variable (FLC) technique is proposed in [27] for a WT driven doubly fed induction generator (DFIG) that is equipped with a battery energy storage system and operates in autonomous mode. The fact that this type of command is dependent on the internal properties of the system makes it a fragile command. In [28], there is a lack of a comparison study for the purpose of validating the results of the control and administration of an energy conversion system within a microgrid setup that includes numerous renewable energy sources and a storage system.

This paper investigates a comparative study of three controllers, notably a novel FLC, a fractional-order PID controller (FPID), and a proportional-integral (PI) controller for a highly nonlinear and complex system in the first step. In the second step, we will use the suggested controllers for the production and management of a WECS chain based on CDFIG. This WECS configuration comprises a wind turbine (WT) that transforms wind's kinetic energy into mechanical energy, this latter will be transformed into electrical energy via two cascaded asynchronous machines, and an AC/AC converter that establishes the connection between the generator and the electrical network.

The brush-ring system in the DFIG, commonly employed in wind energy generation, reduces the machine's reliability. In order solve this problem, the electrical and mechanical connection of two DFIGs through their rotors is used to avoid the need for brush-ring sliding contacts. The complete system is referred to as a CDFIG [8, 13]. This machine will serve as a generator for the generation of electrical energy.

In order to establish a connection between the system and the network using a DC-link, we will utilize a power electronics transformer. The frequency converter comprises a rectifier on the machine side, which is responsible for managing and regulating the active and reactive powers transferred between the second stator and the grid. The grid-side inverter is controlled to ensure a constant DC-link.

2. Modeling and description of the energy conversion chain

CDFIG is a new area of research; but recently a lot of study has been published which concerns several areas. The cascade can be found in: wind power [29], small hydraulic power plants [30], and aviation [31].

The ring-brush system in the DFIG decreases its reliability; however, the electrical and mechanical coupling of two DFIGs via their rotors solves this issue by eliminating the need for sliding ring-brush contacts. The entire system is called CDFIG. In this case, succession coupling involves connecting the shafts and rotor windings in a reverse manner, resulting in the inversion of the rotor phases [32]. Figure 1 illustrates this coupling.

Figure 1. Connection of the CDFIG to the electrical network.

All equations are expressed in a frame of reference linked to the rotating field in the Park transform. The equations of the voltage and the flux of the two DFIGs are:

- The DFIM 1:

- The DFIM 2:

Modeling the electrical coupling of the two rotors depends on the type of coupling; the voltage and current equations will be:

The multivariable system can be represented by state-space equations. Multiple choices are possible for the state vector. Among these we will take the vector of the stator and rotor currents.

In order to obtain differential equations, we will need to replace the flux in the voltage equations. These differential equations is expressed as:

With:

2.1 Control powers of stator-1

By aligning the d-axis of the (dq) reference frame with the flux of the first stator φ_s1, the steady-state model of the CDFIG is simplified as:

Where v_ds2 and v_qs2 represent the two-phase voltage components of the second stator, which must be controlled to achieve the desired i_ds2 and i_qs2 current levels in the machine. The influence of coupling terms between the d and q axes in s.ωsLs2-C.Lm2  is minimal, and can be effectively compensated through proper regulator synthesis.

On the other hand, the term C.s.(Lm1Vs )/Ls1  represents an electromotive force that is dependent on the rotational speed. This term's influence is significant as it introduces a tracking error. Therefore, the control strategy must account for this error to ensure accurate system performance.

The powers of stator-1 can be controlled through the currents of stator-2 by the following system of equations:

With: s=s1.s2=ωs1-ωr1-ωr2ωs1=ωs1-Ω(p1+p2)ωs1,  and C=Lm2/(Lr1+Lr2-Lm12Ls1 )

Finally, we can control the active powers P_s1 and reactive powers Q_s1 exchanged between the network and stator-1 through the currents of stator-2 i_ds2 and i_qs2.

2.2 Modeling of the connection to the electrical network

The main objective is to maintain zero reactive power to ensure a unity power factor on the network side in order to optimize efficiency. Then adjust the active power sent to the network to its reference value and keep the DC bus voltage constant. The frequency converter (rectifier-inverter) and the CDFIG coupled to the network are shown in Figure 2.

Figure 2. Connection of the CDFIG to the electrical network via power converters.

The DC/AC converter, on the network side, is modeled as follows:

The current flowing through the grid side inverter is defined:

ig=f1iin1+f2iin2+f3iin3                                         (12)

The AC/DC converter can be modeled as follows:

The current flowing through the machine side rectifier is defined:

(f1, f2, f3) and (f1', f1', f1')  are logical connection functions of switches inverter and rectifier respectively.

The current which flows in the capacitor comes from the rectifier on the machine side and inverter from the network side:

 ic=im-ig                                   (15)

The temporal evolution of the DC link voltage is obtained from the integration of capacitive current:

The diagram in Figure 2 shows that the connection to the electrical network is made via an input filter. By applying the Park transformation, we can write:

With:

The reference power of the DC link:

The DC link voltage regulation block is resented in Figure 3.

Figure 3. DC link regulation scheme.

The active and reactive powers exchanged with the network are defined as follows:

We can derive the reference currents from equation (21):

The I_d current is used to regulate the DC link voltage. It is controlled using a regulator (PI). The I_q is used to regulate the reactive power transmitted. The regulation scheme for network currents is shown in Figure 4.

Figure 4. Network side current regulation scheme.

3. Design of the used controllers

3.1 PI-controller

The regulation of wind power systems with proportional-integral has been the subject of a great number of publications that have been published in the academic literature [33-38]. The PI controller, used in the CDFIG control, is simple and quick to implement while offering acceptable performance (dynamic, robustness and disturbance rejection). Figure 5 shows the closed-loop system, corrected by a classical PI controller, with its transfer function presented as follows:

Figure 5. Network side current regulation scheme.

The system's response time is approximately 10 milliseconds, which is sufficiently rapid for usage on WTs, where wind fluctuations are gradual and mechanical time constants are significant. Lowering the value may not enhance overall performance, but it could potentially result in disturbances during transient situations, resulting in undesired exceeds its and instabilities. We used the pole compensation method here for its speed; it is obvious that it is not the only valid method for the synthesis of the PI controller. The results of our calculations are as follows: k_p = 0.000118 and k_i = 0.00184.

3.2 Fractional-order PID controller

A PID fractional (Proportional-Integral-Derivative) is an extension of the classic PID controller, and has the form

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