Enhancement of Direct Power Control by Using Artificial Neural Network for a Doubly Fed Induction Generator-Based WECS: An Experimental Validation

Abstract

Direct power control (DPC) is among the most popular control schemes used in renewable energy because of its many advantages such as simplicity, ease of execution, and speed of response compared to other controls. However, this method is characterized by defects and problems that limit its use, such as a large number of ripples at the levels of torque and active power, and a decrease in the quality of the power as a result of using the hysteresis controller to regulate the capacities. In this paper, a new idea of DPC using artificial neural networks (ANNs) is proposed to overcome these problems and defects, in which the proposed DPC of the doubly fed induction generators (DFIGs) is experimentally verified. ANN algorithms were used to compensate the hysteresis controller and switching table, whereby the results obtained from the proposed intelligent DPC technique are compared with both the classical DPC strategy and backstepping control. A comparison is made between the three proposed controls in terms of ripple ratio, durability, response time, current quality, and reference tracking, using several different tests. The experimental and simulation results extracted from dSPACE DS1104 Controller card Real-Time Interface (RTI) and Matlab/Simulink environment, respectively, have proven the robustness and the effectiveness of the designed intelligence DPC of the DFIG compared to traditional and backstepping controls in terms of the harmonic distortion of the stator current, dynamic response, precision, reference tracking ability, power ripples, robustness, overshoot, and stability.

1. Introduction

Nowadays, energy is a necessity because it is the strongest indicator of any kind of socio-economic development of countries. However, the massive exploitation of fossil fuels is causing an irreversible damage to the ecosystem [1,2,3]. The major factor that has contributed to these problems is the use of oil-dependent energy resources which are not environmental friendly, but are less expensive and more competitive compared to green resources [4]. Faced with the dilemma of increasing power demand and environmental protection, renewable energies cost reduction is becoming the first objective of both scientists and industrials.

Wind power is one of the most competitive power vectors due to its availability and practicability compared to other forms of energy [5,6]. To exploit wind power, wind turbines (WTs) are used, which can be divided into horizontal axis WTs and horizontal axis WTs. However, variable-speed WTs are the predominant installed machine in the market, since they exceed the fixed speed wind turbine by 5–10% in both aerodynamic and electrical efficiency, thanks to their ability to extract the kinetic energy of wind in wind speed ranges compared to fixed speed wind turbines [7,8]. In addition, their sophisticated power electronic system make their integration into the grid safe and profitable [9,10]. This is thanks to the benefits of the efficiency and reliability of the doubly fed induction generator (DFIG) and also their energy electronic equipment, which only consumes a maximum of 30% of the system total energy to operate at a variable speed and to obtain an optimum production of energy [11,12,13].

In the field of wind energy, several generators can be used to generate electric current; asynchronous generators [14], synchronous generators [15], DC generators [16], and DFIG [17] can be used. However, DFIG remains the most important and most widely used of these types as a result of its ease of command, low cost, durability, and low maintenance compared to some other generators. In addition, in the case of variable wind speed, DFIG is considered one of the most reliable solutions in generating electric power. Moreover, several control techniques, such as field-oriented control (FOC) using conventional proportional-integral (PI) controllers, have been designed for DFIG in the literature [18,19]. These strategies are applied to both grid-side converters and as rotor-side converters to realize a fully decoupled reactive and active power control. This is achieved with the PI current controllers. This control technique is broadly used in electric induction motor drives control [20]. However, the main disadvantage of these kinds of controller is their sensitivity to the machine parameters’ variations, inadequate internal disturbance rejection, and load variations [21,22]. To overcome the above drawbacks, many authors have proposed improvements such as adaptive controllers based on artificial intelligence strategies, such as fuzzy logic control (FLC) [23]. This latter is an effective control technique in terms of stability and robustness to external disturbances. However, one drawback with this technique is that the complexity increases with the increase in the number of inputs [24]. Moreover, fuzzy logic is applied without mathematical rules, which is not desirable, as there is no mathematical rule that specifies the number of rules that can be used. As is well known, the larger the number of rules in fuzzy logic, the higher the degree of complexity and the slower the system [25].

Direct torque control (DTC) is among the linear controls that have been put to widespread use and were put forward in the 1980s to compensate for and overcome the defects and problems of the FOC strategy [26]. This control has several advantages, such as simplicity, durability, fast response dynamic, and ease of implementation [27]. In DTC strategy, there is no need for the blocks’ current pulse width modulation (PWM) technique or internal current regulation loops, no requirements for coordinate transformation, and less machine parameter dependency, making the system more robust [28,29,30]. Compared to the FOC strategy, DTC provides better results in terms of energy quality and ripple value of current/power of the DFIG-WTs [31]. Another linear control that was proposed in the 1990s has the same characteristics as the DTC strategy and is similar in principle, idea, and degree of complexity. This control is called direct power control (DPC) [32]; durability, simplicity, and ease of implementation are among the biggest advantages of this method [33]. The differences between the DTC and DPC techniques can be found in the references used, where in the DTC strategy, both flux and torque are used as references, while in the DPC, both reactive and active power are used as references. In [34], the DPC was proposed to command the 3-phase PWM rectifiers. The first configuration of the DPC strategy was proposed by T. Neghouchi in 1998 [35], for the direct control of the instantaneous reactive and active powers of the 3-phase PWM rectifier without network voltage sensors. Then, this technique was developed and different configurations were proposed by [36]. The key objective of DPC is to keep machine powers (reactive and active powers) in the optimal band. Regarding the technological aspect, two hysteresis are used for switching instantaneously to the optimal vector, which ensures output voltage vector regulation [37,38]. In addition, the DPC ensures the sampling of sinusoidal currents while guaranteeing a unitary energy factor with a decoupled control of reactive and active powers. The different configurations of the DPC, defined in the literature, can be divided into two kinds: DPC using voltage vector [39] and DPC using virtual flux technique [40,41]. The DPC technique is based on the selection of a voltage vector in such a way that the errors between the reference and measured quantities are minimized and kept within the hysteresis bands [42,43]. In [44], the DPC strategy has a quick time response and is not affected much by changing the system parameters, as is the case in both the vector control and FOC strategy. However, the major disadvantage of this command is the energy ripples and current harmonics distortion, due to the variable switching frequency [45].

Because of the ease of implementation and simplicity, the DPC strategy was proposed as the best solution for controlling electric generators, as this interest appears in a number of research papers published in the field of renewable energies [46,47,48,49]. In [50], the DPC is designed to control DFIG, where a classical WT is used to convert wind power into mechanical power. Numerical results showed the efficiency of the DPC strategy in minimizing energy ripples compared to the FOC. In [51], the synchronous generator was controlled by the DPC strategy. Through the two references [50,51] and several other studies, the use of the DPC strategy leads to a reduction of potential ripples and an improvement in the quality of the electric current, but these ripples are not completely overcome. Among the solutions that have been proposed to increase the efficiency and characteristic of the DPC is to combine this control with several other controllers, such as nonlinear controllers and artificial intelligence algorithms. In [52], the author combined DPC and backstepping control to improve the output current quality of DFIG. Using a backstepping controller increases DPC complexity and difficulty in execution. However, it significantly improves the characteristics of the DPC strategy compared to the DPC. In addition, a sliding mode controller (SMC) has been proposed as a solution to overcome the drawbacks of the DPC [53]. In this proposed nonlinear strategy, both hysteresis controllers and switching tables are dispensed, which leads to a significant improvement in current quality and an increase in complexity, as the DPC strategy becomes experimentally expensive. In [54], both fuzzy logic and genetic algorithm are used in order to minimize the power ripples and improve the dynamic response of the DPC of DFIG-WTs. Simulation results show how effective smart methods are in improving DPC features. Vector control and DPC strategy are combined to command the DFIG-WTs [55]. Numerical results show a higher performance of the designed DPC based on vector control compared to the DPC. Artificial neural networks (ANNs) have been used to compensate for both hysteresis comparators and switching table of the DPC [56], where the use of the ANN strategy improved the dynamic response and significantly minimized current and torque ripples compared to the traditional DPC.

In wind farms, there is a mutual effect between the wind farm and the network, where this effect is at the level of system fluctuations. As is well known, it is necessary to regulate reactive power and network frequency due to technological advancement [57]. In addition, the stability of the system of power generation from wind farms is of great importance to minimize the problems that may occur in the future. Therefore, transmission system operators have created some special network codes to connect wind farms based on the damping system oscillations capacity (damping power system oscillations and internal wind turbine oscillations) [57,58]. Therefore, the ripples of current and power must be overcome to reduce network defects and affect electrical devices in general. The quality of the energy is one of the necessary things that must be focused on and given great importance, as the higher the quality of the energy, the longer the life of the devices, and the less periodic maintenance is required, thus reducing the industrial cost.

To overcome the defects of the DPC, both neural networks and the PWM technique are used. A PWM strategy was used to avoid system complexity, whereby space vector modulation (SVM) can be used to control the RSC. The SVM strategy is more complex and difficult to implement than the PWM strategy. Complexity and difficulty of achievement are not desirable in the field of control. The proposed intelligent DPC strategy using the PWM is used to control the RSC, and for the GSC an ordinary uncontrolled inverter is used (the use of a diode).

In this work, an experimental study of the intelligent DPC strategy based on ANN controllers is carried out on DFIG using dSPACE DS1104 Controller card Real-Time Interface, whereby the obtained results are compared with both the traditional strategy and the backstepping control. The literature has not yet taken into account the experimental work of backstepping control and DPC based on ANN controllers of DFIG-based wind turbines. However, the designed intelligent DPC technique is a simple structure, and more robust and easier compared to other controls. In addition, a simulation study is carried out between intelligent DPC, traditional DPC, and backstepping control in terms of ripple reduction ratio, reference tracking, durability, and current quality. Thus, the main contribution of this paper lies in the completion of an experimental comparative study of three different methods (traditional DPC, intelligent DPC, and backstepping control) using 1.5 KW DFIG, whereby a comparison is made between these proposed controls in terms of the value of current and power ripples, durability, reference tracking, current quality, overshoot, and steady-state error. To simplify the work carried out in the paper, a simple schematic diagram is given, represented in Figure 1, which is called the design diagram. Through this diagram, the stages of design, testing, comparative study, and experimental validation of the designed method are illustrated. On the other hand, the main objectives of this paper can be clarified in the following points:

• Experimental validation of the designed intelligent DPC strategy.
• Minimization of reactive and active powers ripples, mainly caused by the parametric uncertainties of DFIG and the nonlinearities due to the nature of the controller (powers estimators, hysteresis comparators), as noticed by Aroussi in [27].
• Improve the current quality of the DFIG-WT by using the intelligent DPC method.
• Comparing study between backstepping control, traditional and intelligent DPC techniques.
• Improve dynamic response for both torque and power.
• Overcoming the disadvantages and problems of the DPC.

The work is ordered as follows. The mathematical modeling of the WT system is described in Section 2. The traditional DPC strategy of the rotor side converter of the DFIG is described in Section 3. Backstepping control is covered in detail in Section 4. The designed control using ANN controllers is explained in Section 5. In Section 6, the numerical simulation results are presented. In Section 7, the experimental results and discussion are presented. Finally, conclusions are presented in Section 8.

2. WT System

The wind turbine system is a group of elements that are used to obtain electrical energy from a renewable source that is wind energy, where each element has a specific function in the generation system. These elements are placed in series in the generation system. These elements are the turbine, generator, transformers, filters, and inverter. The advantage of this system is that it is simple and does not affect the environment, but rather helps to overcome the emission of toxic gases, which are produced by traditional energy sources.

Wind turbines are among the most important components of the system, as they are responsible for converting WT into mechanical power. The latter is used to rotate the generator to obtain electric current. The mechanical power generated by the turbine can be expressed by relation (1) [7,59,60].

$$P_t=C_p\left(\lambda ,\beta \right)P_w=\frac{1}{2}{C}_p\left(\lambda ,\beta \right)\rho S{v}^3$$

(1)

where, $\rho \left(kg·m^{-3}\right)$ is the density of air, $v \left(m·s^{-1}\right)$ is the wind velocity, $R \left(m\right)$ denotes the radius of the WT rotor, and $C_P\left(\lambda ,\beta \right)$, illustrated in Figure 2, is the wind turbine power coefficient given by (2) as follows [9]:

$$\left\{\begin{array}{c}Cp \left(\lambda , \beta \right)=0.5\left(\frac{116}{\lambda i}-0.4\beta -5\right)exp\left(\frac{-21}{\lambda i}\right)+0.0068 \lambda \\ \frac{1}{\lambda i}=\frac{1}{\lambda +0.08\beta }-\frac{0.035}{{\beta }^3+1}\end{array}\right.$$

(2)

with:

$$\lambda =\frac{{\Omega }_{t}R}{V}$$

(3)

where $\beta$ is the blade pitch angle (in degrees), $\lambda$ denotes the tip-speed-ratio, and 𝛺_t is the angular speed of the WT rotor (in rad·s⁻¹) [9].

The gearbox is necessary to adapt the rotor speed and torque of the WT to that of the DFIG as given in the following equations [11]:

$$\left\{\begin{array}{c}{T}_m=\frac{T_{aer}}{G}\\ {\Omega }_m=G{\Omega }_t\end{array}\right.$$

(4)

where $G$ denotes the gear-ratio coefficient, ${\Omega }_m \left(\mathrm{Rad}·{\mathrm{s}}^{-1}\right)$ is the mechanical rotational speed of the DFIG, and $T_m\left(\mathrm{N}·\mathrm{m}\right)$ is the wind torque driven the DFIG shaft.

The mechanical equation of the WT generator system is given by [59]:

$$J\frac{d{\Omega }_g}{dt}=T_g-T_{em}-T_f$$

(5)

where $, T_f \left(\mathrm{N}·\mathrm{m}·\mathrm{s}·{\mathrm{rad}}^{-1}\right)$ denotes the friction torque and $J \left(\mathrm{kg}·{\mathrm{m}}^2\right)$ represents the total rotor inertia.

In addition to the turbine, DFIG is used, as this generator is characterized by simplicity, low cost, durability, and ease of control compared to other types [50,53]. In order to use this generator in wind energy, two different inverters are used to feed the DFIG rotor. The model of DFIG in the Park frame can be represented by the expressions of the rotor, stator voltages, and flux components as follows:

• Voltage equations:

$$\left\{\begin{array}{c}\begin{array}{c}{V}_{dr}=R_r{I}_{dr}+\frac{d}{dt}{\Psi }_{dr}-w_r{\Psi }_{qr}\\ V_{qr}=R_r{I}_{qr}+\frac{d}{dt}{\Psi }_{qr}+w_r{\Psi }_{dr}\end{array}\\ \begin{array}{c}{V}_{ds}=R_s{I}_{ds}+\frac{d}{dt}{\Psi }_{sd}-w_s{\Psi }_{qs}\\ V_{qs}=R_s{I}_{qs}+\frac{d}{dt}{\Psi }_{qs}+w_s{\Psi }_{ds}\end{array}\end{array}\right.$$

(6)

where, ω_s, and ω_r are the stator and rotor pulsation.

Equation (7) represents the relationship between both stator pulsation and rotor pulsation [1,9]:

$${\omega }_s={\omega }_r+p·{\Omega }_g$$

(7)

• Flux equations:

$$\left\{\begin{array}{c}{\mathsf{\Psi }}_{sd}=L_s{I}_{sd}+L_m{I}_{rd}\\ {\mathsf{\Psi }}_{sq}=L_s{I}_{sq}+L_m{I}_{rq}\\ {\mathsf{\Psi }}_{rd}=L_r{I}_{rd}+L_m{I}_{sd}\\ {\mathsf{\Psi }}_{sq}=L_r{I}_{rq}+L_m{I}_{sq}\end{array}\right.$$

(8)

• Power equations:

$$\left\{\begin{array}{c}{P}_s=\frac{3}{2}\left(+V_{qs}{I}_{qs}+V_{ds}{I}_{ds}\right)\\ Q_s=\frac{3}{2}\left(+V_{qs}{I}_{ds}-V_{ds}{I}_{qs}\right)\end{array}\right.$$

(9)

The torque is expressed as [1,9]:

$$T_e=\frac{3}{2}p\frac{M}{L_s}\left({\Psi }_{sq}{I}_{rd}-{\Psi }_{sd}{I}_{rq}\right)$$

(10)

The MPPT strategy allows the adjustment of the torque of the generator, which forces the generator speed to evaluate closely to its reference Ω_{g_ref} given by Equation (11). For a given operating point, the maximum power extracted can be achieved only if the aerodynamic power coefficient $C_p\left(\lambda ,\beta \right)$ achieves its maximum value. Moreover, this can be achieved when the λ reaches its optimum value λ_opt [1,9]:

$${\Omega }_{gref}=G\frac{{\lambda }_{opt}}{R}V$$

(11)

Figure 3 shows the scheme of the used MPPT technique, where the rotor speed is controlled by the reference torque T_emref. The PI speed control loop described in Figure 4 is established from the dynamics equation of rotating bodies.

Equation (12) represents the closed-loop transfer function of the speed regulator.

$$\frac{{\Omega }_{g\left(s\right)}}{{\Omega }_{g^{*}\left(s\right)}}=\frac{2\xi .{\omega }_n.s+{\omega }_n^2}{s^2+2\xi .{\omega }_n.s+{\omega }_n^2}=\frac{\frac{K_i+K_p.S}{J}}{s^2+\frac{K_p.f_v}{J}.s+\frac{K_i}{J}}$$

(12)

The parameters $K_p$ and $K_i$ of the PI regulator are expressed as follows:

$$\left\{\begin{array}{c}{K}_p=2\xi ·{\omega }_n·J-f_V\\ K_i=J·{\omega }_n^2\end{array}\right.$$

(13)

3. DPC Strategy for RSC

The DPC strategy is one of the linear methods that have experienced a recent upsurge in use in the field of renewable energies due to its ease of implementation and simplicity [53,56]. This control scheme has the same idea and working principle as direct torque control, but the difference between them lies in the references used. In this control, we need high-accuracy measuring devices to measure current and voltage [23]. In this control, two hysteresis controllers are used to regulate both the reactive and active power of the DFIG-WT. In addition, the switching table is used to generate control signals in the inverter transistors. The advantage of the DPC is that it does not need block current PWM modulation. To achieve the switching table, each of the reactive power, sectors, and active power are estimated, whereby the power estimation is used to calculate each of the errors in the active and reactive power [52]. There are three entrances to the switching table: active power error, sectors, and reactive power error, and three exits. The exits are used to control the inverter [45].

Figure 5 shows the structure of the DPC of the DFIG-WT, where the ease of implementation is the best advantage of this strategy.

To estimate the capacities, we need to know the rotor flux. Equation (14) is used to calculate the quadrature and direct rotor fluxes of the DFIG.

$$\left\{\begin{array}{c}{\mathsf{\Psi }}_{r\alpha }={{\displaystyle \int }}_0^{\mathrm{t}}(v_{r\alpha }-R_r·i_{r\alpha })dt\\ {\mathsf{\Psi }}_{r\beta }={{\displaystyle \int }}_0^{\mathrm{t}}(v_{r\beta }-R_r·i_{r\beta })dt\end{array}\right.$$

(14)

Equation (15) is used to calculate the rotor flux amplitude value from the quadrature and direct values.

$${\mathsf{\Psi }}_r=\sqrt{{{\mathsf{\Psi }}_{r\alpha }}^2+{{\mathsf{\Psi }}_{r\beta }}^2}$$

(15)

The relationship between rotor flux and rotor voltage is expressed by (16), such as:

$$\left|\overline{{\mathsf{\Psi }}_r}\right|=\frac{\left|\overline{{\mathrm{V}}_r}\right|}{{\omega }_r}$$

(16)

The rotor flux angle presented by Equation (17) is used to calculate the areas of the presence of the reference ray of voltage as follows:

$${\theta }_r={\tan }^{-1}\left(\frac{{\mathsf{\Psi }}_{r\beta }}{{\mathsf{\Psi }}_{r\alpha }}\right)$$

(17)

Equations (18) and (19) are used to estimate the capacities of DFIG.

$$P_s=-\frac{3L_m}{2\sigma L_s{L}_r}.V_s.{\mathsf{\Psi }}_{r\beta }$$

(18)

$$Q_s=-\frac{3V_s}{2}\left(\frac{{\mathsf{\Psi }}_{r\beta }}{\sigma L_s}-\frac{L_m{\mathsf{\Psi }}_{r\alpha }}{\sigma L_r{L}_s}\right)$$

(19)

where, $\sigma =1-\frac{{L_m}^2}{L_s{L}_r}$ is the dispersion coefficient of the DFIG.

The Qs and Ps are estimated through Equations (18) and (19). The digitized signals H_P and H_Q are then obtained according to the errors between the estimated and the desired powers ∆Qs and ∆Ps. The switching states for driving the main circuit are selected through the predefined switching table on the basis of HP, HQ, and N [45]. The errors of Qs and Ps and the work sector “sector (N)” are summarized in

Table 1. Switching tables of DPC based hysteresis controller.

∆Ps	∆Qs	Sector
		1	2	3	4	5	6
1	0	V6 (101)	V7 (111)	V1 (100)	V0 (000)	V2 (110)	V7 (111)
	1	V7 (111)	V7 (111)	V0 (000)	V0 (000)	V7 (111)	V7 (111)
0	0	V6 (101)	V1 (100)	V1 (100)	V2 (110)	V2 (110)	V3 (010)
	1	V1 (100)	V2 (110)	V2 (110)	V3 (010)	V3 (010)	V4 (011)

.

4. Backstepping Control for RSC

Traditionally, backstepping control is one of the methods characterized by complexity and difficulty in achieving, especially in the case of complex systems [52]. however, the backstepping approach was proposed in 1990 by Krstic Kanella kopoulos and Kokotovic [61]. It consists of a nonlinear control technique based on the Utkin strategy for law synthetizing and Lyapunov stability theorem. The advantage of backstepping compared with other techniques lies in its design flexibility, and the stability robustness, since the controller depends only on the dynamic of sliding surface after the reaching phase, which make it independent from system dynamics itself [1,2]. The use of backstepping control to control the capacities leads to a significant improvement in the quality of the power while reducing the ripples of torque and active power. Besides, this method improves the dynamic response compared to the classical techniques. The negative of this method is that it is related to the mathematical form of the system, which reduces its robustness in case the system parameters change, and this is undesirable. In order to apply this control we need error in reactive and active power of the DFIG-WT system.

The errors between the reference and the measured signals of reactive and active powers defined by Equation (20), such as [40]:

$$\left\{\begin{array}{c}{e}_1=P_s^{ref}-P_s\\ e_2=Q_s^{ref}-Q_s\end{array}\right.$$

(20)

Their derivate is given as:

$$\left\{\begin{array}{c}{\dot{e}}_1={\dot{P}}_s^{ref}+\frac{V_s·L_m}{\sigma .L_r·L_s}\left(V_{rq}-R_r·i_{rq}-\sigma ·L_r·{\omega }_r·i_{rd}+g·\frac{L_m·V_s}{{\omega }_s·L_s}\right)\\ {\dot{e}}_2={\dot{Q}}_s^{ref}+\frac{V_s·L_m}{\sigma ·L_r·L_s}\left(V_{rd}-R_r·i_{rd}+\sigma ·L_r·{\omega }_r·i_{rq}\right)\end{array}\right.$$

(21)

We chose the Lyapunov function defined by:

$$\left\{\begin{array}{c}{V}_{(e_1)}=\frac{1}{2}{e}_1^2\\ V_{(e_1,e_2)}=\frac{1}{2}{e}_1^2+\frac{1}{2}{e}_2^2\end{array}\right.$$

(22)

Substituting Equation (21) into Equation (22), we obtain the following:

$$\left\{\begin{array}{c}{\dot{V}}_{(e_1)}=e_1·{\dot{e}}_1=e_1·\left({\dot{P}}_s^{ref}+\frac{V_s·L_m}{\sigma ·L_r·L_s}\left(V_{rq}-R_r·i_{rq}-\sigma ·L_r·{\omega }_r·i_{rd}+g·\frac{L_m·V_s}{{\omega }_s·L_s}\right)\right)\\ {\dot{V}}_{(e_2)}=e_1·{\dot{e}}_1+e_2·{\dot{e}}_2=-K_1·e_1^2+e_2\left({\dot{Q}}_s^{ref}+\frac{V_s·L_m}{\sigma ·L_r·L_s}\left(\begin{array}{c}{V}_{rd}-R_r·i_{rd}\\ +\sigma L_r·{\omega }_r·i_{rq}\end{array}\right)\right)\end{array}\right.$$

(23)

The control voltages of the proposed backstepping controller which the bloc diagram is illustrated in Figure 6 is given by Equation (24), as follows:

$$\left\{\begin{array}{c}{V}_{rq}^{ref}=-\frac{\sigma .L_s.L_r}{V_s.L_m}.{\dot{P}}_s^{ref}+R_r{i}_{rd}+{\omega }_r.\sigma .L_r.i_{rd}-g.\frac{L_m.V_s}{{\omega }_s.L_s}-\frac{\sigma .L_s.L_r}{V_s.L_m}.K_{e_1}.e_1\\ V_{rd}^{ref}=-\frac{\sigma .L_s.L_r}{V_s.L_m}.{\dot{Q}}_s^{ref}+R_r{i}_{rd}-{\omega }_r.\sigma .L_r.i_{rq}-\frac{\sigma .L_s.L_r}{V_s.L_m}.K_{e_2}.e_2\end{array}\right.$$

(24)

where, $K_{e_1}$ and $K_{e_2}$ are positives constants.

5. Intelligent DPC Strategy for RSC

Considering the objective of overcoming the drawbacks of the traditional DPC strategy, a new intelligent DPC (DPC-ANN) is proposed in the present paper.In this section, an ANN controller is used to improve the current quality and overcome the defects of the DPC of DFIG. ANN was proposed because of its ease of use and accuracy compared to other methods [62]. Moreover, the use of ANN means the system has a faster dynamic speed, and greatly increases its robustness [63]. In [64], an ANN strategy was used to control the torque of the induction motor. The use of ANN led to a significant increase in the efficiency of the asynchronous motor compared to the DPC. The intelligent DPC in this part is used to command the RSC, while the GSC inverter is used as an uncontrolled two-level inverter in order to simplify the power generation system and focus on the effectiveness of the designed strategy in improving the quality of the torque and electric energy.

The novelty of the presented technique in this section can be summarized in the three following points:

• The proposed intelligent DPC strategy overcomes the artificial nonlinearities due to hysteresis switching operations, which required an infinite commutation frequency, which is still at the present impossible.
• Data have been collected from a genetic algorithm optimized controller and then used for training purposes, which ensures data accuracy with the optimal dynamic of the system.
• The use of an ANN controller and PWN strategy can be qualified as a novel combination according to the existingliterature.
• A new intelligent DPC strategy of DFIG is presented and compared to traditional DPC strategy and backstepping control.
• The intelligent strategy is robust/simple, and its implementation is technologically well-mastered.

The designed intelligent DPC strategy, which is proposed to control the torque and power of the variable-speed DFIG-WT, is shown in Figure 7. This proposed intelligent DPC strategy is a different work compared to published works in [47,52,53,55].

Compared with the classical control, the designed intelligent DPC is different, as both the hysteresis controller and switching table are dispensed with. Two ANN controllers were used to regulate the current and power and to control the converter the PWM technique was used because of its simplicity and ease of implementation. In this proposed intelligent DPC strategy, estimation or calculation sectors are not used. With regard to capacity estimation, the same capacity estimation equations are used as in the traditional strategy (Equations (18) and (19)) are used. Also, MPPT strategy is used to calculate the reference value of Ps.

In this proposed strategy, a feed-forward artificial neural network, mathematically identified by Equation (25) was used to command the Ps/Qs. As is known, this strategy is among the most popular artificial intelligence systems. Its high mapping ability ensures a high-quality produced current and power, and reduces the fluctuations of the Ps/Qs and torque thanks to the nonlinear nature of the sigmoidal transfer function of ANN. as a result a minimum value of THD value of stator current can be obtained [41,65].

$$Y_j^l=f\left({\displaystyle \sum }_i^{nl}{W}_{ji}^l{\mathsf{{\rm X}}}_i+b_j^l\right)$$

(25)

where, ${\mathsf{{\rm X}}}_i$: inputs vector, $W_{ji}^l$: synaptic weights of neuron j in layer l and $b_j^l$: bias input.

A static MLP network is envisaged in the present manuscript, the architectural schemes of the used (MLPs) are illustrated in Figure 8. The two MLP controllers used consisted of an input layer with 2 neurons representing power active error (${\xi }_{Ps}$) and its derivative ($\dot{{\xi }_{Ps}}$), and power reactive error (${\xi }_{Qs}$) and its derivative ($\dot{{\xi }_{Qs}}$) successively, two hidden layers, and an output layer with one neuron representing the rotor voltage reference components $V_{rq\_ref}$ and $V_{rd\_ref}$ successively [9]. The parameters of the ANN controllers used in this paper are shown in

Table 2. Switching tables of traditional DPC strategy.

ANN Parameters	Value/Methods
	ANN-Ps	ANN-Qs
Neural network	Multi-Layer Perceptron network
MLP training process	Levenberg Marquardt algorithm
Proposed structure	2-5-5-5-1	2-5-5-5-1
Number of iterations	100	100
Input layer (two neurons)	${\xi }_{Ps}$ and $\dot{{\xi }_{Ps}}$	${\xi }_{Qs}$ and $\dot{{\xi }_{Qs}}$
Output layer (one neuron)	$V_{rq\_ref}$	$V_{rd\_ref}$
Activation functions	Tansig	Tansig
Adaption learning function	Trainlm	Trainlm

.

Figure 9a and Figure 10a show the ANN training progress of active and reactive powers controller and its evolution training. As can be noted, the proposed architectures (2-5-5-5-1) used for the Ps and Qs controllers converge quickly to the best solution as of the 30th and the 50th iteration successively. Figure 9b and Figure 10b show the evolution of the Mean Square Error (MSE) as a function of the number of iterations for the reactive and active powers controllers successively. As can be noted, a small value of the MSE is observed for both controllers, achieving 3.62 × 10⁻⁴ and 3.69 × 10⁻⁴ for each controller successively at the 100th iteration. Finally, and for clarification purposes, the Figure 11 demonstrates the structure for the entire studied system.

In

Table 3. Comparison of the proposed methods.

	DPC Strategy	Intelligent DPC Technique	Backstepping Control
Simplicity	Yes	Yes	No
Switching table	Yes	No	No
Hysteresis controller	Yes	No	No
Nonlinear control	No	Yes	Yes
Linear control	Yes	No	No
Current quality	Low	High	Medium
Power ripple	High	Low	Medium
Robustness	Low	High	High
Sectors estimation	Yes
Power estimation	Yes	Yes	Yes
MPPT technique	Yes	Yes	Yes
References	Ps/Qs	Ps/Qs	Ps/Qs
Response dynamic	Low	Fast	Fast
Total harmonic distortion of current	High	Medium	Medium
Steady-state performance	High	Medium	Medium
Implementation	Easy	Easy	Difficult
Affected by changing system parameters	High	Medium	High

, a comparison is given between the three controls designed in this experimental work in terms of the degree of complexity, ease, robustness, references used and the method of controlling the inverter, etc. From this table, it can be said that the intelligent DPC is the best solution that can be proposed for controlling DFIG because of its simplicity and the results obtained experimentally and using simulations.

6. Results

To evaluate the efficiency of the designed intelligent DPC (DPC-ANN) compared to the DPC and backstepping controls, the parameters of a 1.5 KW DFIG-WT system have been used, which are given in

Table A1. Parameters of Simulations.

Parameters of WT and Generator
Parameters	Value	Parameters	Value
Number of blades	3	Irn (A)	8.5
R (m)	1	p	2
G	2	fs (Hz)	50
$f$(N·m·s/rad)	0.0027	Rs (Ω)	1.18
$J$(kg·m2)	0.04	Rr (Ω)	1.66
Pn (kW)	1.5	Ls (H)	0.20
Vs (V)	220/380	Lr (H)	0.18
Isn (A)	5.2	M (H)	0.17

(see Appendix A). A comparison is made between the three proposed methods in terms of complexity, current quality, robustness, reference tracking, dynamic response, ripple value, etc.

In the first step, a series of simulations have been carried about based on a realistic wind speed profile and step wind speed profile in presence of parametric uncertainties using Matlab/Simulink software. Then, the tuned controller was tested on a DSpace card in order to evaluate its implementation issues for eventual future field tests.

6.1. Realistic Wind Speed Scenario (Al Hoceima City)

To study the behavior of the designed intelligent DPC, we used the wind speed profile of the Moroccan City of Al Hoceima, as shown in Figure 12. The results obtained are shown in Figure 13, Figure 14, Figure 15, Figure 16, Figure 17, Figure 18, Figure 19, Figure 20 and Figure 21. Figure 13 represents the mechanical speed of the DFIG rotor. By this figure, speed is variable and takes the form of wind change. In addition, the maximum rotor speed is about 1550 rpm and the minimum speed is 1250 rpm. On the other hand, the power coefficient $C_p\left(\lambda ,\beta \right)$ is shown in Figure 14. It can be said that the $C_p\left(\lambda ,\beta \right)$ value is approximately 0.5, which is approximately variable. This value is affected by the change in wind speed, as it is noted that the behavior of $C_p\left(\lambda ,\beta \right)$ change is the same as the behavior of wind speed change. Figure 15 represents the tip speed ratio of the turbine. From this figure, the tip speed ratio is variable and takes the form of wind change. In addition, the maximum tip speed ratio is about 8.40 and the minimum speed is about 6.50. The Ps and Qs of the DFIG are shown in Figure 16a,b, respectively. With these two forms, the reactive and the active power perfectly follow the references. The Qs takes the form of a change in wind speed, and it is noted that the value of the Ps increases with the increase in wind speed and vice versa. As for the Qs, it is zero, and this is because we chose a zero reference for the reactive power. Additionally, the Qs is not affected by the change in wind speed, but the Ps has the highest value, around 1500 W, and the lowest value is 500 W. Figure 17 shows the direct and quadrature rotor currents. The direct rotor current has a fixed value and is estimated at 2.4 A, and the quadrature rotor current has a variable value, where the highest value is 4.2 A and the lowest value is about 1.78 A. Thus, the value of the direct rotor current is related to the Qs, while the quadrature rotor current is related to the Ps. The value of the power factor is about 1 and there are some ripples, as depicted in Figure 18. These ripples are caused by a change in wind speed and the system itself. The THD value of the stator current generated by DFIG is illustrated in Figure 18. The value of THD is about 2.22% (respect the IEEE-519 Std), when the proposed intelligent DPC strategy technique is adopted. This value of THD is low, which indicates that the quality of the current obtained is acceptable, and compared to other strategies, it is very good. The three-phase stator and rotor currents behavior in the three proposed tests are illustrated in Figure 19a, Figure 20a, Figure 19b, Figure 20b, Figure 19c and Figure 20c, respectively. The value of the rotor/stator currents is related to both the system and the reference value of the Ps, where there is a rapid dynamic response to the change in active power, which shows the characteristics of the designed strategy. Figure 21 describes the THD of current obtained under the 3 controllers. DPC exhibited the highest waveform deformation with a THD of 2.62%, followed by backstepping control, which had 2.45%. The best waveform conformity was obtained under the intelligent DPC strategy, with an acceptable THD of 2.22%.

The comparison between the three controllers is presented in

Table 4. Comparison between DPC, Backstepping control, and intelligent DPC strategy.

Performance	DPC	Backstepping Control	Intelligent DPC Strategy	Improvement (%)
Response time (s)	0.401	0.37	0.21	43.24
Rise time (s)	0.251	0.184	0.125	32.06
THD of the Current $I_{sa}$(%)	2.62	2.45	2.22	9.38
Overshoot (%)	Important (≈18%)	Medium (≈9%)	Neglected (≈5%)	44.44
Set-point tracking	Medium	good	Very good	/
Precision	Medium	High	High	/

. This table shows remarkable improvements obtained by the intelligent DPC strategy (DPC-ANN) in term of optimization of the dynamics response, rise time, reduction in ripples, and the minimization in the harmonics in the current.

A comparative study with previous works in terms of the THD of the stator current is carried out and illustrated in

Table 5. Comparison between the intelligent DPC strategy and those utilized in some existing papers.

References	Strategies	THD (%)
[66]	DPC-PI	2.59
[67]	SMC	3.05
[68]	Fuzzy DTC	2.40
[69]	DTC strategy	2.57
[70]	FOC based on type 2 fuzzy logic	1.14
[71]	DPC control using L-filter	10.79
	DPC control using LCL-filter	4.05
[72]	DTC control	7.83
	DTC with neural algorithm	3.26
Proposed Strategy	DPC-ANN	2.22

. Through this table, it is clear that the designed strategy gave a better value for the THD compared to some of the proposed controls, leading to the best improvement compared to other technics by a measured THD of 2.22%.

6.2. Step Wind Scenario (Robustness Test)

The test we carried out consists of varying the parameters of the used DFIG, since in reality they are subjected to variations caused by different physical phenomena such as saturation of the inductances, overheating of the resistances, etc. This test is based on the robustness test of the designed controls, where a study of the influence of parametric variations of the DFIG on their performances is conducted. In this test, the following parameters have been varied:

• Dividing resistances 𝑅_𝑠 and 𝑅_𝑟 by 2, (−50% of nominal R_s);
• Dividing inductances L_s, L_r, and M_sr by 2;
• Steps reactive and active power are imposed as reference to evaluate the system response under rapid variation of operating point.

Figure 22 shows the Ps and Qs of both techniques. The tested control laws, namely traditional DPC strategy, backstepping control, and the proposed intelligent DPC strategy, present a strong robustness and ensure good performances in presence of parametric variations and external disturbances. However, one can see that the ANN performs well compared to the traditional control and backstepping controller with a smooth transient state, even if some rapidity is lost compared to the backstepping control when acting harder when moving from an operation point to another, since all sliding mode controllers have mainly two phases: reaching phase and steady phases. Such a response can be justified by the effect of the chattering phenomenon, which occurred because of the discontinuous part of the control law governing the reaching phase. Such a variable structure controller is theoretically free of chattering in the case of infinite commutation frequency. Regarding traditional control in transient space, we observe that it fails against nonlinearities, presenting a spectacular overshooting compared to backstepping and ANN, since its tuning is carried out around a specific operating point. In the steady state, we note an enhancement of stability and precision compared to backstepping controller and traditional control, respectively.

In the next subsection, the proposed control will be experimentally implemented using DSPACE, thus confirming its applicability.

Figure 23 shows, respectively, the direct rotor current (I_rd) and the quadrature rotor current (I_qr) influencing directly the Ps and Qs. In terms of controller performances and response analysis in both transient and steady states, the same observations are concluded with a relatively high oscillation. Such results can be justified by the coupling effect between the two control axes, d and q.

7. Implementation of the Proposed Strategy

To accomplish the designed control and achieve it, a computer containing the program Matlab 2020, is used, where the proposed control is sent to the DS1104 R&D controller Board developed by dSPACE. The latter sends the necessary signals to IGBTs of the inverter, as shown in Figure 24. In this figure, it is shown how dSPACE communicates with a WT system based on DFIG. As part of the proposed strategy, experimental validation and tests were carried out using the dSPACE card and the real-time workshop tool. By accomplishing this work, it can be said that this strategy is easy to achieve and inexpensive, and does not require effort or specialists or a complex program, unlike some strategies. This makes the proposed control able to be more widely used in the future.

The results obtained from this experimental work are shown in Figure 23. This test is used to prove the tracking efficiency and regulation following a fluctuations wind profile. The first observation that can be observed through these experimental results is that these experimental results are the same as the results obtained from the numerical simulation. Almost the same behavior is obtained in the case of the experimental and numerical study. The mechanical angular speed curves follow perfectly the tracks tracked for the wind profiles in the tests. Figure 23a illustrates the wind speed profiles. Figure 23b represents the power coefficient. From these figures, we can see that an energy value is related to the change in wind speed profile. The tip speed ratio of the WT is shown in Figure 25d, and this is in the case of variable wind speed profiles, where we find that the shape of the tip speed ratio signal is related to the shape of the wind speed. With these two figures, the largest value for the tip speed ratio is about 8.5 and the lowest value is about 6. Figure 25e clearly shows the Ps tracking with its mechanical reference. The finding is based on the DFIG power quality with a low undulations rate. Figure 25f illustrates the Qs forms with their reference Qref = 0 VAR. It is clearly remarkable that the Qs value is reasonable low in comparison with the total power generated.

8. Conclusions

This paper proposed an experimental work for a DPC strategy based on neural networks for a DFIG-WT system. This intelligent strategy was proposed using the PWM strategy to control the RSC of the DFIG, and neural networks were used in order to control the capacities.Simplicity and ease of achievement are among the biggest advantages of this designed intelligent control. The behavior of the designed intelligent control is studied in comparison with both the DPC and the backstepping control. Hence, the designed control architecture greatly helps to overcome the ripples of torque, active power, current, and reactive power caused by the discrete nature of hysteresis regulators, but also improves the current quality, stability, and robustness of the system. In addition, at different operating speed ranges, the robustness of the designed intelligent strategy against perturbation of the active power has been demonstrated extensively.

In general, the experimental results agree with the obtained simulation results and demonstrate the superiority of the proposed control over both the DPC and the backstepping control. Thus, the proposed intelligent control has a major role in improving the quality of the current and in reducing power ripples compared to the classic DPC strategy and backstepping control, which makes it the best solution in the future for controlling electric generators. For future studies, other experimental work complementary to this paper will be carried out using other intelligent strategies, such as fuzzy logic and particle swarm optimization. Furthermore, DPC strategy demo work can be accomplished through other variants, such as using synergetic control and sliding mode control or exploiting intelligent DPC control in controlling other generators, as well as in controlling water pumps.