Comparative Study of the Grid Side Converter’s Control during a Voltage Dip

e modeling and control of a wind energy conversion system based on the Doubly Fed Induction Generator DFIG is the discussed theme in this paper. e purpose of this system was to control active and reactive power converted; this control is ensured thanks to the control of the two converters. e proposed control strategies are controlled by PI regulators and the sliding mode technique. In the present work a comparison of the robustness of the 2 controls of the grid side converter (GSC) during a voltage dip is shown. e simulation is carried out using the Matlab/Simulink so ware with a 300 kW generator.


Introduction
In recent years, the wind energy has become the fastest growing renewable energy source in the world. is is mainly due to the fact that it has received thorough attention and has been considered as a way of fighting climate change. Control of the speed of the wind turbine is generally used to improve the energy production [1].
Several structures are used to control speed, structures based on asynchronous machine, synchronous machine and Doubly Fed Induction Generator known as DFIG. e DFIG's structure is the most used, thanks to the advantages it gives. is structure is composed of a wound rotor induction generator where its stator is directly connected to the grid and its rotor is connected to the grid through two power converters [2]. Several lines of research in literature shows the classical control of the power converters; the first one rotor side converter (RSC) controls the DFIG, and the second one grid side converter (GSC) controls the DC link's voltage. e control can be ensured using different techniques as the PI regulators, the Backstepping technique, direct power control, direct torque control and the control by sliding mode, which will be the object of this work [3,4].
In PI, control strategy has been investigated; the synthesis of this technique is purely algebraic and uses the pole compensation based on a numerical method [1], investigating a polynomial RST controller. is method is a sophisticated one and based on pole placement technique. Sliding Mode Control (SMC) controllers have been implemented in many areas because of their excellent properties, such as insensitivity to external perturbation and parameter variation [1]. ese wind generators, like most decentralized generators, are very sensitive to grid disturbances and tend to disconnect quickly. Indeed, faults in the power system, even very far from the generator, can result in short-term voltage disturbances, called voltage dips, which can lead to the disconnection of the wind system. e need to ensure the continuity of service of the WECS in the voltage dips event is all the stronger as the penetration rate in the network is high [5][6][7]. e aim of this paper is to compare the GSC's controls with PI and with the SM technique during a voltage dip.
Wind generators, like most decentralized generators, are very sensitive to network disturbances and tend to disconnect quickly during a voltage dip or when the frequency changes.
ese disconnections lead to production losses that can aggravate the situation on a network, already weakened by the incident and thus have negative consequences. It is therefore necessary to avoid this instability in the production of wind energy to ensure continuity of service [8].
e challenge is to satisfy the continuity of service during a voltage dip. is paper is structured as follows: first, the topology of the system studied is presented in the second section. en, the modeling of the turbine, the doubly fed induction generator, the power converters and the filter is shown in the third, fourth and fi h sections, respectively. e sixth, seventh and eighth sections present to the controllers of the power converters using the PI regulators and the sliding mode techniques. e ninth section shows the voltage dip types. e last section is dedicated to the simulation results carried out using the Matlab/Simulink so ware, followed by a conclusion.

The Topology of the Studied System
e most suitable technology is the one based on the double-feed asynchronous machine with wound rotor, whose speed variation is done by means of the power converters located at the rotor circuit and the stator, which is connected directly to the grid ( Figure 1).

Aerodynamic Conversion.
e wind velocity that passes through a surface is expressed as follows: where: : air density; : wind-swept turbine surface; its expression is as follow: e turbine power according to the Betz theory is given by: 퐶 훽, 휆 : aerodynamic efficiency of the turbine o en referred to as a power factor. It is a specific coefficient to each wind turbine; it depends on the specific speed and the orientation angle of the blades .
where e turbine torque is defined by: e role of the gear box is to adapt the rotation speed of the turbine to the rotation speed of the generator. Its gain is given by: Applying the fundamental relation of the dynamics, the generator tree is modeled by the following equation: : the total inertia given by:

The DFIG Modelling Used in a WECS
e schematic representation of a DFIG in the three-phase reference is given in Figure 3.
e DFIG is represented in the park frame by the following equations: e electrical equations are: e magnetic equations are: e active and reactive stator's powers are: For vector control of DFIG connected to a reliable grid (balanced three-phase system), the Park reference linked to the rotating field is chosen. By adopting the hypothesis of a stator resistance as negligible (given the power of the DFIG), and that the stator flux is constant (while is constant) and oriented along the axis [10].
Interaction with the wind Gear box I nteraction with the machine 3: Representation of the DFIG in three-phase plan [9].
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The RSC's Control Using the PI Regulator
It exists 2 methods exist using the PI regulator: is technique consists of directly and independently regulating the active and reactive stator powers produced to those of references, using a single regulator on each axis. e control is given by correcting the difference between the measured and the reference power, the regulator used is a PI controller.
(ii) Indirect control without power loop: is control does not consist in directly regulating the powers as the previous control but is based on the indirect regulation of the measured rotor currents which are controlled with the reference currents which are expressed as a function of the stator powers of reference imposed on the machine. (iii) Indirect vector control with power loop: is command consists in regulating the stator powers and the rotor currents in cascade, for this we will set up two control loops on each axis with an integral proportional regulator for each, one regulating the power and the other the current.
In this paper the last one was chosen and its principal scheme is illustrated by e sliding mode (SM) technique is developed from the variable structure control in order to solve the disadvantages of the other nonlinear control system designs namely the PI controller. Sliding mode is a technique that consists of initially defining a surface, the system that is controlled will be forced to that surface, and the system behavior is said to slide to the desired balance point. [7,[11][12][13].
e SM technique is mainly carried out in three complementary steps defined by:  (21) e control function will satisfy reaching conditions in the following form: where: is the equivalent or nominal control is determined by the system model. the sliding control: it consists of the sign function of the sliding surface 푆(푥), multiplied by a constant .    e main feature of this control as mentioned before is to drive the error to a "switching surface" 푠(푥). When the system is in "sliding mode", the system behavior is not affected by any modeling uncertainties and/or disturbances [14].

e Switching Surface Choice.
e sliding surface 푠(푥) can be chosen in general as a hyperplane passing through the origin of space for stabilization reasons, the sliding surface that is a scalar function should be chosen such that the variable to be adjusted slides on this surface. So its expression is as follows: (i) is positive gain that will interpret the bandwidth of the desired control. (ii) 푒(푥) is the variable's error to be regulated. (iii) is the relative degree; it is the smallest positive integer representing the number of times to derive in order to display the command.

e Control's Conditions for
Existence. e conditions of existence and convergence are the points that allow the different dynamics of the system to converge towards the sliding surface and to remain there independent of the perturbation. It exists 2 approaches: e direct approach: it consists on: e Lyapunov's approach, it consists of choosing a Lyapunov's candidate function 푣(푥) > 0 (scalar positive function) and a vector control that will decrease its derivative.

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We have to redo the same calculation to find the control vector of the reactive power.
A er all this calculation the RSC controller's principle scheme using the SM is illustrated by Figure 6, and more detailed in      (43) (ii) Control reference reactive power to zero to ensure a unit power factor.
In fact, controlling the GSC is like controlling the active power by keeping the DC link voltage constant, and setting the reference reactive power to zero so as not to impair the quality of the grid (unit grid power factor).

e GSC's Control Using PI Regulators.
is method is little used because of the disadvantages it brings, its Control scheme of the GSC using the SM controller. principle is illustrated in Figure 8. It consists of synthesizing PI regulators.

e GSC's Control Using the SM Technique.
is technique consists of developing a control law based on the sliding mode, so just follow the steps explained previously. e principle scheme is illustrated in Figure 9.
To elaborate the control laws of the two SMDC Link and SM Line current blocks, Equations (25) and (26) are used, and the same steps already explained before are followed.
Increasing currents can cause the over-size of the rotor side converter to support this extra current while the decrease of the voltage of the continuous bus can cause a disconnection of the wind turbine.

The Simulation Results
e simulation was carried out with MATLAB/Simulink, in order to validate the control strategies studied in this work. Simulation tests are realized with a 300 KW generator coupled to a 398 V/50 Hz grid and for a fixed wind speed because it is assumed that the duration of the fault is so short that the speed remains constant. e machine's parameters are given next in the Tables 1 and 2. e different quantities are expressed in reduced unit (P.U), as an example the power in reduced unit is expressed as follows:

The Voltage Dips
A grid fault is physically, a short circuit occurring somewhere in the network, a voltage dip (voltage dips) being the repercussion of this fault on the voltage. A voltage dip is a sudden decrease in the supply voltage to a value below a threshold value, followed by its recovery a er a short time [6].
ere are different types of voltage dips as shown in the  It can be observed that before the arrival of the default the voltage exactly follows its instruction for both types of commands, once the default has arrived the bus voltage is disturbed in both cases, except that for the command with PI, the voltage gives strong oscillations for a very deep default, that last as long as default is present. While for the control with SM the voltage is shi ed from that of reference-this shi , is even larger than the depth of the default, is important. e voltage dip is applied from 푡 = 500 ms and lasts up to 푡 = 1000 ms, for different depths: 20% and 40%. Figure 11 shows the stator voltages with the voltage dip at 푡 = 500 ms. Figure 12 represents the stator currents that increase at the onset of the fault (explained in part 8). Figure 13 shows the rotor currents for different depths: 20% for Figure 13(a) and 40% for Figure 13(b). It can be clearly noticed that the deeper the fault is, the higher the current increases.
(50) 푃 = 푃 푃 .   Figures 16 and 17 show the active power developed by the DFIG. It is assumed that the power set point changes at time 푡 = 600 ms and the remainder until the end of the simulation, it can be seen that for the control with PI the power is disturbed at the moment of the application of the hollow at significant depth, and the remainder until the disappearance of the latter, as for the command with SM with a very deep drop, we only notice spikes at the appearance and the disappearance of the drop, while the power perfectly follows his instructions.
A summary of the comparison results is presented in Tables 3 and 4. 11. Conclusion e purpose of this paper is to develop the control law using the sliding mode for both converters (GSC and RSC). e study is based on a comparison between a system whose GSC is based on a conventional PI controller and a second made by sliding mode taking into account the voltage dips to highlight the performance.
Finally, the simulation results showed that the control of the GSC using sliding mode, and during a voltage dip, is more efficient than the control using PI regulator.

Nomenclature
: turbine speed , : the axis stator voltages , : the axis stator current , : the stator and axis fluxes , : the dq axis rotor voltages , : the axis rotor current , : the rotor and axis fluxes , : stator and rotor resistances , : the supply and rotor angular frequency 푎,푏,푐 : are the single voltages from the converter 1,2,3 : are the MLI commands applied to the switches of the converter : is the DC voltage that comes from the DC link 푡1,2,3 : are the three-phase system of the source (the grid) 푎,푏,푐 : are the single voltages from the converter 푡1,2,3 : are the line currents coming from the source.
Data Availability e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.