Dynamic Modeling and Robust Control by ADRC of Grid-Connected Hybrid PV-Wind Energy Conversion System

Aboudrar, Imad; El Hani, Soumia; Heyine, Mohamed Saleck; Naseri, Nisrine

doi:https://doi.org/10.1155/2019/8362921

Mathematical Problems in Engineering

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Abstract Introduction Results and Discussion Conclusion Appendix Data Availability Conflicts of Interest References Copyright Related Articles

Research Article | Open Access

Volume 2019 | Article ID 8362921 | https://doi.org/10.1155/2019/8362921

Dynamic Modeling and Robust Control by ADRC of Grid-Connected Hybrid PV-Wind Energy Conversion System

Imad Aboudrar,¹Soumia El Hani,¹Mohamed Saleck Heyine,¹and Nisrine Naseri¹

Academic Editor: Antonino Laudani

Received19 Jun 2019

Accepted13 Sept 2019

Published20 Oct 2019

Abstract

This work presents linear and nonlinear control strategies applied to a grid-connected multiple-source renewable energy system (wind and photovoltaic), in order to extract the maximum power and to enhance the control of the active and reactive powers. A new robust control strategy known as the active disturbance rejection control (ADRC) is proposed and applied to the hybrid renewable energy system (HRES), and it is based on the extended state observer (ESO) which allows us to estimate the internal and external disturbances such as modeling errors and parameter variations. The studied system consists of two conversion chains which are linked via a common DC bus and interconnected to the grid through a voltage source inverter (VSI); the first chain consists of a PV system and a DC-DC boost converter, and the second chain consists of a direct-driven wind turbine, permanent magnetic synchronous generator (PMSG), and of a AC/DC rectifier converter. The extraction of maximum power from the PV system and the wind energy conversion system is ensured by using the voltage based perturb and observe (VPO) and the optimal torque control (OTC) MPPT techniques, respectively. The ADRC technique is utilized to control the active and reactive powers by acting on the grid currents. In order to verify and validate the effectiveness of the proposed control strategy, a detailed model of the studied system is designed and evaluated under the MATLAB/Simulink software. The simulation results prove the effectiveness of the MPPT techniques in terms of maximum power extraction during the variation in the environmental conditions. Additionally, the regulation of active and reactive powers is ensured by ADRC, and the system is operating at a unity power factor. Moreover, it is demonstrated that the suggested strategy is efficient in terms of fast tracking and robustness to internal and external disturbances compared to the classical PI controller.

1. Introduction

Since the beginning of the century, global energy consumption has been growing very strongly in all regions of the world. It seems that, on a trend basis, energy consumption will continue to increase, driven by economic growth on the one hand and by the increase in per capita electricity consumption on the other hand, regardless of the scenarios considered [1]. For this reason, renewable energies appear today and in the long term as the solution that covers this energy requirement by reducing the major disadvantages of fossil fuels such as greenhouse emissions [2]. They have become an essential form of energy due to their flexibility, simplicity, use, and the multiplicity of fields of activity in which they are called upon to play a role. These modes of production, as well as the associated means of distribution, are subject to deep changes over the next few decades [3].

Available in quantities greater than humanity’s current energy needs, the resources of renewable energy also represent an opportunity for more than two billion people, living in remote areas, to have access to electricity. However, these renewable energy sources have a drawback that their output characteristic change becomes extreme because it significantly depends on climatic conditions, as solar irradiance and temperature in PV systems and wind speed in the wind turbines [4]. Consequently for better operation of these systems, maximum power point tracking (MPPT) algorithms are needed to improve the energy efficiency of both PV and wind systems. In this context, several research has been conduct in the literature, going from the utilization of classical algorithms such as perturb and observe (PO), incremental conductance (INC), and hill climbing search (HCS) [5, 6] for both PV and WECS applications, to those based on artificial intelligence as fuzzy logic and neural networks [7].

The grid-side converter is a necessary element in an electrical power generation system for obtaining sinusoidal waveforms with low total harmonic distortion. Nevertheless, the performance of the system depends largely on the control strategy applied by the grid-side converter [8]. Therefore, several control techniques for the voltage inverter have been discussed in the literature. Among them, in [9], the authors deals with a new nonlinear backstepping sliding mode control for photovoltaic- (PV-) based grid interactive voltage source converter (VSC) system, and a new small signal stability phenomenon is depicted by the multivariable dynamic model of the proposed PV-based grid converter system, where PV penetration as well as nonlinear control parameter optimization practices is considered in this paper. In [10], the authors presented different topologies and control strategies for grid-connected photovoltaic systems, and the following sections report, investigate, and present control structures for single-phase and three-phase inverters. Some solutions to control the power injected into the grid and functional structures of each configuration are proposed. Jain et al. in [11] presented a review for the control strategies applied to the grid-connected PMSG-based wind turbines, a comparative study of rotor flux-oriented control and direct torque control (DTC) techniques applied in the generator-side converter of PMSG wind turbine application, for grid-side converter, and various control schemes are developed mainly based on voltage-oriented control (VOC) or on direct power control (DPC). And authors in [12] have presented a sensorless maximum power point tracking (MPPT) method for a hybrid photovoltaic-wind system, which consists of photovoltaic (PV) system and doubly fed induction generator (DFIG) wind turbine (WT). The performance of the proposed method is demonstrated in the simulation study, and the three converters can work very well to handle the power flow under various operation scenarios, such as variations of mechanical power and irradiation, changes of DC-link voltage. Hence, the proposed system can be a cost-effective alternative of the two separated systems.

In general, the most commonly used control strategy to connect the power generation systems with the utility power grid is based on the proportional integrator controller due to its simple structure as presented in [13, 14]. Considering the internal and external disturbances of grid-connected multiple-source renewable energy systems such as a hybrid PV-wind system, the control objective becomes more difficult and ordinary controllers like PI and PR controllers are not sufficient. Therefore, several researchers have proposed and investigated nonlinear controllers to drive this system as in [15]. A control strategy based on the sliding mode control theory is proposed for the hybrid grid-connected PV-wind system where the obtained results are satisfactory and, nevertheless, this controller presents oscillations around its references due to the chattering phenomena. In [16], the authors have designed a backstepping controller for PV-wind hybrid system with grid interfacing and shunt active filtering functionality, but to ensure stability or the negativeness of the derivative of the every-step Lyapunov function, it usually requires the cancellation of the indefinite cross-coupling terms, while this cancellation results in the perfect-looking of the derivative of the Lyapunov function, and it does not necessarily mean that good performance is ensured. To overcome these problems, another controller was proposed in the last 10 years, and it is used in several areas for the control applications. This controller is known as the active disturbance rejection controller (ADRC), and it is proposed by Han in 2009 [17].

The prospective of ADRC as an effective new control strategy is evident in many case studies, where the technique is used to address a number of benchmark problems in diverse industry sectors, with promising results. However, to the author’s best knowledge, very few publications are available in the literature documenting the issue of controlling the hybrid PV-wind energy conversion systems but in a separate way. In [18], the authors have proposed a predictive ADRC to overcome the time delay in PMSG wind turbine systems, and in [19], control of active and reactive powers in a DFIG-based WECS by the ADRC technique has been discussed, and in [20], the author proposed an active disturbance rejection control to a solar PV DC-DC converter. The main advantages of this controller lies on the real-time rejection of internal and external disturbances based on an extended state observer (ESO) [21]. The variation of internal parameters or modeling errors as internal disturbances and the instability of the grid as external disturbances are caused either by voltage dips and frequency droops. As a result, this paper presents the application of a new linear ADRC to the hybrid PV-wind energy conversion system.

Our main contribution in this work lies on the development of a new robust control strategy for the grid-connected hybrid PV-wind energy conversion system by ADRC, in order to extract the maximum power available from the PV-wind system and to control the power delivery. The voltage based perturb and observe technique is used to extract the maximum power from the PV system, while the optimal torque control technique is used for the WECS. The linear ADRC is utilized to regulate the DC bus voltage and to ensure the control of active and reactive powers. For this purpose, this paper is structured as follows: Section 2 presents the overall architecture of the proposed system and its modeling components. Section 3 introduces the mathematical model of the active disturbance rejection controller. Section 4 gives the proposed control by ADRC for the hybrid system, while in Section 5, the simulation results of the wind energy conversion system are presented.

2. Mathematical Modeling and Architecture of the Proposed System

The proposed system as demonstrated in Figure 1 consists of a variable speed direct-driven wind turbine based on permanent magnetic synchronous generator (PMSG), a photovoltaic array, a DC/DC converter, an AC/DC converter, a common DC bus capacitor, and a grid interface inverter with an RL filter. The PV generator is controlled by the boost converter to track the maximum power point by using the MPPT technique. The WEC system which involves a wind turbine directly connected to the PMSG and is controlled by the AC/DC converter to extract the maximum power from the wind. These two energy sources are connected in parallel with a common DC link through their individual converters, where a voltage source inverter (VSI) is utilized to supply the total generated power into the grid while ensuring a unit power factor.

2.1. Mathematical Equivalent Model of PV Array

In order to set up the PV model, it is necessary to establish its equivalent electrical circuit. Indeed, the literature cites numerous mathematical models [22] representing the very strong nonlinear behavior of the PV model due to their design based on semiconductor junctions. These models differ from each other depending on the number of parameters involved in calculating the voltage and current delivered by the PV module. The single- and the double-diode models are generally used to model the solar cell behavior. The double-diode model is adopted in this paper [22], and its equivalent circuit is given in Figure 2. It consists of two diodes characterizing the junction, a current source characterizing the photocurrent, a series resistor representing the losses by the Joule effect, and a shunt resistor characterizing the leakage current.

The cell model can then be expressed bywhere and are the reverse saturation current of the diodes, are the ideality factors of diodes, and is the cell thermal voltage, , where T is the junction P-N temperature, k is Boltzmann’s constant , and q is the electron charge .

2.2. Wind Turbine Modeling

In any wind energy conversion system, the purpose of the turbine is to harness the wind kinetic energy and transform it into mechanical energy that rotates an electric generator. The modeling of a wind turbine consists in expressing the extracted aerodynamic power as a function of the incident wind speed V, and its expression is given by

Its aerodynamic torque is given by the following expression:where ρ is the air density, generally taken equal to 1.225 kg/m³.

The wind turbine aerodynamic efficiency is represented by a power factor called [23]. This coefficient depends on the turbine characteristics (speed ratio λ and pitch angle β). Figure 3 represents the C_p characteristics:where is the turbine rotational speed. The mechanical equation of the turbine shaft which is rigidly connected to the synchronous generator is given by [24]where J is the system total inertia, f is the friction coefficient, and represents the generator electromagnetic torque.

2.3. Permanent Magnet Synchronous Generator Modeling

Generally, to represent a state model, we define the state vector x, the input vector u, and the output vector y. This model is written in the following form:

For the PMSG, the input vector is composed of the stator voltages. The state vector consists of electrical quantities (currents) and mechanical quantities (speed and position). The nonlinear state model in the frame is described by the system below:where represents the stator resistance, and are the direct and quadrature inductances, and are the stator currents in the d-q frame, is the permanent magnet flux, ω is the PMSG speed, and it is given by , and are the pair poles [25].

The electromagnetic torque is given by

2.4. DC Link and Filter Modeling

The interconnection between the hybrid energy conversion system and the utility power grid is carried out via an RL filter (, ) as illustrated in Figure 4. This filter is used to prevent harmonic currents from spreading through the grid [26]:

Applying Park’s transformation, equation (11) becomes in d-q frame as follows:where and are the inverter voltage components, and are the grid voltages, and and are the filter currents.

The modeling of the DC-link bus is given bywhere C is the DC-link capacitor.

3. Proposed Control Strategy for the HRES by ADRC

The proposed control scheme for the grid-connected hybrid energy conversion system is given as follows:(i)VPO-MPPT based on ADRC is used to enhance the photovoltaic energy conversion system (PVECS) efficiency under irradiation changes(ii)OTC-MPPT based on ADRC is used to enhance the WECS efficiency under wind velocity changes(iii)VOC based on ADRC is used to control the DC-link voltage and to regulate the injection of the produced active and reactive powers into the grid

3.1. Mathematical Model of ADRC

Active disturbance rejection control (ADRC) is a robust control strategy proposed by Han [17]. The principal concept of this method is to treat the internal and external uncertainties as a “generalized disturbances,” try to estimate them in real time by using an extended state observer (ESO), and then use it in the feedback control law with the objective to compensate the disturbances rapidly. A first-order ADRC configuration is shown in Figure 5. It mainly consists of three parts: tracking differentiator (TD), extended state observer (ESO), and nonlinear state error feedback (NLSEF).

In Figure 5, is the input signal, is the input tracking signal, y is the system feedback signal, is the estimated tracking signal, is the total disturbance estimation, is the compensation factor, is the internal and external disturbance compensation, is the initial control object by NLSEF, and u is the final control signal after disturbance compensation.

For a first-order controlled object, its mathematical model of ADRC is set as [27]where the mathematical model of the TD is defined by using equation (14), the model of ESO is given by equation (15), and for NLSEF block, it is represented by equation (16). , , and are the output error factors, is the best function which is defined by using equation (17), δ is the filtering factor to ESO, and α is a nonlinear factor.

In practice, the ADRC needs to adjust a large number of parameters, and adjusting these parameters is complicated. So as to reduce the model complexity and the controller computational, a linear ADRC design method is proposed and applied to the hybrid PV-wind energy conversion system.

3.2. Linear ADRC Design

To illustrate the principle of ADRC [28], a nonlinear and time-varying dynamic system of is considered, with only a single input and an output, and it can be described by the following equation:where represents the model internal dynamics which is assumed to be unknown, represents the external disturbances, and represents the known system parameter.

The following terms are considered as all the internal and external disturbances affecting the system to be controlled.

Therefore, the system equation is rewritten in the following form:

Instead of looking for an explicit mathematical model of , ADRC offers another alternative that significantly reduces the dependence of the control on accurate system modeling, as the proposed strategy consists in estimating , and then to cancel it in real time using an appropriate control signal . To do so, an extended state observer is used. Let

Assume that f is differentiable and let . Then equation (19) can be written aswhere

A full-order Luenberger state observer can be designed aswhere is the observer gain vector.

The error between the actual value z and the estimated value by the observer can be written in the following form:

The dynamics of the estimation error is therefore expressed bywhere

In order to ensure asymptotic convergence of the estimation error ( when ) and therefore a good functioning of the observer, it is necessary that the parameters of the gain matrix L are chosen in such a way that forms a Hurwitz matrix; that is to say, the poles of its polynomial characteristic are all with strictly negative real parts:

The observer’s gains are generally determined by the pole placement technique. A compromise must be established between the speed at which the observer follows the states and his sensitivity to noise measurement. The faster the ESO is, the earlier the disturbance is estimated and cancelled by the corrector. This is achieved by placing the observer’s poles well to the left of the observed system poles the . This choice leads to the adoption of a large bandwidth for the extended state observer. However, it should be remembered that too much bandwidth can harm the system by promoting noise transmission [28].

Taking into account all these constraints, the cutoff pulse of the extended state observer is chosen to have a suitable stabilization time, and its poles are placed to :

The observer’s gains are then expressed as follows:

Therefore, when is asymptotically stable, will approximate and its derivatives (up to order ), and will approximate the generalized disturbance . Consequently, the estimated generalized disturbances can be applied in control to reject it more quickly.

If the control law is chosen asthen the system equation (19) becomes

If is a correct estimation of , then the system is reduced to an -order integral system:

Therefore, the final system can be controlled by the corresponding state-feedback control law:where is the reference signal.

Since is a correct estimation of , then the final control law can be approached aswhere

The linear active disturbance rejection controller can be summarized and designed by

The structure of the first-order LADRC is depicted in Figure 6.

4. Control of the Machine-Side Converter by ADRC

The control of the machine-side converter is obtained by using the linear ADRC, and it regulates the stator currents with its references, where is set to zero and is given by the optimal torque control OTC-MPPT [29] block as depicted in Figure 7.

4.1. MPPT Analysis for the Variable Speed Wind Turbine

To ensure maximum power extraction from the wind turbine, the rotational speed must be maintained at the optimum value of the tip speed ratio which makes the turbine operating at .

Considering the relationship between the wind speed V and the tip speed ratio λ in equation (5), the wind turbine power can be expressed as a function of the rotational speed :

Replacing λ by and placing in , the wind turbine maximum power can be expressed aswhere is a coefficient given by

So the torque reference is expressed as follows:

4.2. Linear ADRC Design for Machine-Side Converter

The zero direct axis control (ZDC) is used to obtain the references of currents used in control [29]. The three-phase stator currents are converted into axis frame using Park’s transformation technique, and then, the d-axis current is set to be zero and the q-axis current is set to be equal to the stator current :

Consequently, for , the electromagnetic torque can be controlled by :

Hence,

The stator current regulations are achieved by two ADRC, where the equations of and are adapted to the canonical from of ADRC:

For the d-axis current, we havewhereand for the q-axis, we have

5. Control of the DC-DC Converter by ADRC

To obtain the optimal exploitation of the PVECS during the change of environmental conditions, a two-stage control strategy is proposed and adopted here [30]. As illustrated in Figure 8, firstly, a PO-based voltage MPPT is used to generate the reference voltage V_mpp. After that, an improved cascaded loop based on linear ADRC is used to track the PV voltage and current in order to extract the maximum power from the PV array.

5.1. P and O-Based V-MPPT

The main aim of the VO-MPPT is to generate the reference voltage V_mpp corresponding to the maximum power point. For this purpose, P and O-based V-MPPT [30] technique is utilized due to its featuring effectiveness and simplicity as shown in Figure 9.

5.2. ADRC Design for the V-MPPT

Because of the almost zero variation in PV voltage at the MPP under irradiation changes, V-MPPT is considered as an effectiveness alternative. However, the efficiency of this method depends on the cascaded V/I control loop concept. In this section, a robust cascaded V/I control loop based on ADRC is proposed and demonstrated to track the MPP under weather changes.

The outer loop of the proposed strategy consists in controlling the voltage to its reference obtained by the V-MPPT. The dynamic of the voltage is expressed as follows:

Then, the ADRC for the outer loop can be designed as follows:

For the inner loop, it is used to regulate the current across the inductor. Its dynamics is presented below:

Then, the ADRC for the inner loop can be designed as follows:

6. Control of the Grid-Side Converter by ADRC

The grid-side control consists of two cascade control loops in which its main purpose is to stabilize the DC-link voltage and to control the active and reactive powers injected to the grid during variation in environmental conditions. The inner loop will control the filter currents, and the outer loop will control the DC bus voltage. The inner loop dynamics is settled to be faster than the outer one. The GSC can be controlled either by voltage-oriented control (VOC) or direct power control (DPC) technique. VOC is considered to be more efficient due to lower energy losses and to lower current distortion compared to DPC [31].

As illustrated in Figure 10, VOC is used to control the GSC and it involves a dual-loop control structure: an outer loop to control the DC-link voltage and an inner loop to control the grid currents.

The phase-locked loop (PLL) device is used to obtain the phase angle and frequency from the grid voltages [32]. The d-axis component of the synchronous reference frame is aligned with the grid voltage and the q-axis component was set to zero .

The active and reactive powers are then given by

This shows that the active and reactive powers will be controlled, respectively, by currents and .

6.1. DC Bus Voltage Control by LADRC

The power across the DC-link capacitor C can be expressed by

By substituting equation (13) with equation (55), we get

If all the losses in the filter, the power electronics converters, and in the capacitor are neglected, the exchanged powers on the DC bus are expressed bywhere , , and are the generator, PV system, and grid powers, respectively.

By taking into account equations (54)–(56), the DC bus voltage can be expressed byand we put :so we obtain

6.2. Control of Filter Currents by LADRC

The external voltage regulation loop makes it possible to maintain the voltage across the capacitor and to generate the current reference for the internal current loop.

For the current , it is calculated by the desired delivery of reactive power:

Then, similarly to the machine-side control, the filter currents are given in canonical form of ADRC.

For d-axis current,where

For q-axis current,where

7. Results and Discussion

7.1. Simulation Results

To validate the theoretical study and the effectiveness of the presented control strategy, a complete structure of HRES is designed and simulated under MATLAB/Simulink environment. The simulation parameters are given in appendix.

The applied wind speed profile is shown in Figure 11. Figures 11–18 present the simulations results of the proposed strategy for the WECS system.

As can be noticed in Figures 12 and 13, the mechanical speed and the extracted power take the same form as the wind profile, and it is also shown in Figure 14 that the power coefficient has been maintained at its optimal value () which shows the effectiveness of the MPPT strategy in terms of maximum power extraction.

The response of the ADRC shows good tracking characteristics as highlighted in Figures 15 and 16 where the direct axis current was maintained to be zero and the quadrature current tracks its references. The generated active power and stator currents are shown in Figures 17 and 18.

For the PVECS, the applied profile of the irradiation is illustrated in Figure 19 and the corresponding results are demonstrated in Figures 20–22.

As can be noticed in Figures 20 and 21, the voltage is regulated with its references that is obtained from the VPO-MPPT and the inductor current is also regulated to its references, which ensures the extraction of the maximum PV power as illustrated in Figure 22.

Figure 23 shows that the DC-link voltage V_dc is maintained at its reference with some fluctuations which are due to the stochastic nature of wind speed. Also we notice in Figures 24 and 25 that the linear ADRC regulates the grid currents to their references.

The control of the active and reactive powers is also achieved as shown in Figures 26–28 where the extracted power from the HECS was injected into the grid and the reactive power was set to zero to ensure a unit power factor.

In order to test the robustness of the proposed control strategy, another test was carried out in which we have changed the internal parameters of the PMSG, the stator resistance, and inductance , by an increase of 50% of their nominal value. The results obtained by LADRC are compared with the classical PI controller. The utilized wind speed profile is given in Figure 29. For the PV system, the irradiation was maintained at

As shown in Figure 30, both controllers regulate the current to zero, but the ADRC has a faster response compared to the PI controller.

It can be noticed in Figure 31 that the current was regulated to its reference and that the response of LADRC is better than the PI one. So as a closing statement, the simulation results have demonstrated that the proposed strategy is efficient in terms of stability, rapidity, accuracy, and robustness regarding the variation of the parameters of the machine.

7.2. Discussion: Benefits and Limitations

The proposed hybrid PV-wind system presents some benefits and limitations in terms of efficiency and control, and the main advantages of the used structure are as follows:(i)Continuous power supply: solar and wind energies are complimentary in nature, that is, when there is no sun, there is plenty of wind and vice versa.(ii)Reducing cost of the system: the cost of the hybrid system is reduced because the inverter and all the associated circuits are removed.(iii)Reducing power loss: the converter numbers in the proposed system are less than a separated system. Therefore, the power loss of the PV’s inverter is eliminated. A two-level inverter power loss is estimated to be around 0.015 pu [33]. This value is considerable in case of MW-level power plants. For the system limitations, we can mention the following:(i)Complicated controlling process: with different types of energy sources in use, the systems require some knowledge. The operation of different energy sources and their interaction and coordination must be controlled, and it can become complicated.(ii)Operations under grid faults: according to the new grid code, the wind power system and the PV system should not disconnect from the grid in case of voltage dips. Moreover, it is required to participate in ancillary services; therefore, the control structure needs to be adjusted.

8. Conclusion

In this article, we have studied the modeling of a hybrid energy conversion chain (wind and photovoltaic), followed by an overall control structure introducing the ADRC method and the extended state observer (ESO) which constitutes its core. Its generalized mathematical theory in the linear and nonlinear cases is discussed. It is then applied to the control of the two chains (photovoltaic and wind) in order to extract the maximum power on the one hand, and on the other hand, it is applied to the control of the grid-side converter by ensuring the stability of the DC bus voltage and the control of the active and reactive powers exchanged with the utility grid. To prove its robustness, a simulation is established by applying variations to the machine parameters; and the test results have demonstrated that the ADRC is largely independent of its variations unlike the classical PI regulator.

Appendix

A. PMSG Wind Turbine Parameters

(i)Radius: (ii)Nominal wind speed: (iii)Total inertia of the mechanical transmission: (iv)(v)(vi)Nominal power: (vii)Stator resistance: (viii)Stator inductance: (ix)Flux (x)Pair poles

B. PV System Parameters

(i)PV array system rated power: (ii)PV panel rated power: (iii)Open circuit voltage of the PV panel: (iv)Short circuit current of the PV panel: (v)MPP voltage of the PV panel: (vi)MPP current of the PV panel: (vii)Number of series connected panels per string: (viii)Number of PV panel strings:

C. Grid-Side Parameters

(i)DC bus voltage (ii)DC bus capacitor (iii)Filter resistance (iv)Filter inductance

Data Availability

No data were used to support this study.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

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Copyright © 2019 Imad Aboudrar et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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