Sliding mode performance control applied to a DFIG system for a wind energy production

Received Jun 29, 2019 Revised May 28, 2020 Accepted Jun 9, 2020 This project presents a strategy of field control then sliding mode control put in to the conversion process of wind energy containing an asynchronous generator with double fed (DFAG; DFIG). A model was developed for each component of the wind turbine (turbine, DFAG and cascade rectifierinverter). MPPT device must be introduced in order to obtain maximum energy efficiency so that PI-MPPT method is made. The objective is to apply this command to control independently the active and reactive powers generated by the asynchronous generator uncoupled by orientation from the flow. The results of digital simulations obtained show the improvement of the performances of the sliding control compared to the field control, also it has provided information on the commands available techniques as reference tracking and robustness.


INTRODUCTION
Wind energy is one of the rapid growth renewable energy in the world. This energy is inexhaustible, clean and do not create greenhouse gases [1,2]. Conventional techniques were used to adjust the wind, but assuming the wind operation in balanced conditions [3]. Advances in technology of wind led to the design of a more powerful drive to improve their behaviors and make it more robust and reliable [4]. The generation of electrical energy by means of double-fed asynchronous machine is one of the current areas of research, using driving means such as wind power incorporated into a wind energy system, the function can DFIG on wide range of wind speed and get the maximum possible power for each wind speed [5].
In this article we demonstrate the modeling, the simulation and the comparison of the wind turbine driven doubly-fed induction generator performances of using at the same time the command of the PI control and sliding mode control [6,7]. A strategy for controlling the sliding mode has been put in place to control two powers and also achieve maximum wind energy [8,9]. The results of simulation show that this strategy has rapid dynamic response also a good robustness and low dependence parameters on the model [10].

MODELING AND CONTROL OF THE WIND TURBINE
The device, which is studied here, consists of a wind turbine including of the blades length R actuating a generator through a speed-increasing gear of profit G. Figure 1 describes a chain of conversion of wind energy [5,11].

Model of the wind turbine
Mechanical power available on the shaft of a wind turbine is expressed by [6,7,12]: The torque of aerodynamic is directly determined by [1]: The mathematical modeling of the multiplier is given by the following equations: and G mec turbine The aerodynamic efficiency of the wind turbine is represented by the power factor ) , turbine is a complex model, however simple mathematical models are often used aerodynamic system. The expression of power coefficient that we will use in our study is given by [3,13,14]: The Figure  We determine the evolution of the mechanical speed by the fundamental equation of dynamics [6]: The diagram block related to this modeling of the turbine is represented on Figure 3.

Control of the wind turbine
An electromagnetic torque control strategy adjusting to the mechanical speed to be presented in this part in order to maximize the electrical power generated [15][16][17][18]. This principle is known as terminology (MPPT). We are interested in controlling the electromagnetic torque servo mechanical speed using a conventional PI controller [19]. For this study, we assume that the electric machine and its drive are ideal and therefore, the electromagnetic torque develops at all times equal to its reference value, regardless of the power generated. For this study, we assume that the electric machine and its drive are ideal and therefore, the electromagnetic torque develops at all times equal to its reference value, regardless of the power generated. The maximum power extraction techniques include determining the speed of the turbine, which provides maximum power generated [17,18].
The structure of control consists in regulating the couple appearing on the turbine shaft so as to fix its speed at a reference. Therefore, we obtain the following relation [5]:

MODEL OF DFIG
The double fed asynchronous generator DFIG is modeled in the reference mark of park, under its equations [3] and are represented by the Figure 4.
Electromagnetic torque is expressed in terms of currents and flux:

Power control
By putting the equations which connect the values, we can easily control the production of the wind and also realize an independent control of the active and reactive power [20]. A referential d-q; related to the rotating field and a stator flow aligned on the axis were adopted, For obvious reasons of simplification. Therefore: The flow equations (19) are becoming: Based on a few considerations, we obtain: The adaptation of these equations gives simplifying assumptions: It should be noted that the powers and tensions are linked by a transfer function of the first order. Due to the low value of the slip, it is possible to establish vector control because the influences of the couplings remain weak and the d and q axes can be ordered separately with their own regulators. The method used in the power control is to neglect the coupling terms and to set up an independent regulator in each axis to control the active and reactive power independently. This method is called the direct method because the power controllers directly control the rotor tensions [2]. The block diagram representation is shown on the Figure 5.

CONTROL ACTIVE AND REACTIVE POWERS
This section as objective to introduce control algorithms based on two regulators PI and Sliding mode controllers to regulate a statoric powers to a DFIG system for a wind energy production [21][22][23].

PI controller design
The Figure 6 shows a closed loop system corrected by a PI regulator with a transfer function. The gains of the controllers are voluntarily chosen to be symmetrical, in order to preserve the property of symmetry of the open-loop: The closed loop is expressed by this function transfer:

Sliding mode control
The sliding Mode Control, is well known for its robustness against internal uncertainties (variations in machine parameters), and external (disturbance due to load), and phenomena having been omitted in the modeling, while having a very good response dynamic [24,25]. In summary, a sliding mode control is divided into three parts.

Control active power
The surface of the control of the active power is given by: The derivative of surface is: We replace the expression of the power becomes: We draw the expression from the current of the equation of the Vqr tension: By replacing the expression of Vqr by Vqreq+Vqr n the command appears clearly in the following equation: During the sliding mode and in permanent mode, we have We extract from the preceding equation the equivalent manipulated variable Vqreq that is written: During the mode of convergence, so that the condition 0 ) ( ) (   P S P S that is to say checked one poses: Consequently, the term of commutation is given by: To check the stability condition of the system, the parameter K must be positive.

Control of the reactive power
The surface of control of reactive power is: The derivative of surface is: We replace the expression of the power becomes: We draw the expression from the current of the equation of the Vqr tension: By replacing the expression of Vdr by Vdreq+Vdr n: In permanent mode, we have: We extract from the preceding equation the equivalent manipulated variable Vqreq that is written: During the mode of convergence, so that the condition 0 that is to say checked one poses: Consequently, the term of commutation is given by: To verify the stability condition of the system, the parameter K must be positive. The Figures 7 and 8 represent the block diagram of the control structure.

RESULTS AND DISCUSSION
In order to show and compare efficiently the two proposed controllers, a set of simulation tests have been carried using Matlab/Simulink. The both regulaters performances are tested and compared using two different specifications, the tracking of the references representing the robustness and the tracking based on changes of the system's parameters. The parameters of the wind turbine and DFIG are mentioned on the Table 1. Figure 9 shows the wind speed, Figure 10 shows the average output power as a function of wind speed.

Reference tracking
Different step inputs for an active and a reactive power were applied and we observed the response obtained with both PI control and Sliding mode control. Results are presented in the following Figures 11 and 12.

Robustness
In order to test the robustness of the two controllers, the nominal value of Rr is doubled value, and the value of mutual inductance Lm is decreased by 10% of its nominal value. Figures 13-16 shows the effect of parameters variation on the active and reactive power response for the two controllers.

Discussion
With the sliding mode control the results show that the response time is considerably reduced, a small overshoot and the oscillations are damped more quickly compared to the PI controller. The system in transient state with the sliding mode is better than the PI control.

CONCLUSION
This article presented a wind energy conversion system based on the wound rotor induction generator. Direct vector control of the active and reactive power of the stator was performed using Matlab/Simulink. The results shown illustrate that mathematical modeling based on knowledge of voltages and currents can be used to control powers. The comparative study of active and reactive power control reveals that the PI and Sliding Mode controllers work fairly well under ideal conditions when there is no disturbance or variation of parameters.