Super Twisting Algorithm Direct Power Control of DFIG using Space Vector Modulation

: This paper presents the super-twisting algorithm (STA) direct power control (DPC) scheme for the control of active and reactive powers of grid-connected DFIG. Simulations of 5 KW DFIG has been presented to validate the effectiveness and robustness of the proposed approach in the presence of uncertainties with respect to vector control (VC). The proposed controller schemes with fixed gains are effective in reducing the ripple of active and reactive powers, effectively suppress sliding-mode chattering and the effects of parametric uncertainties not affecting system performance.


Introduction
In recent years and with its economic and environmental benefits, wind energy has become more and more a source of energy for many countries, in addition, and because of its advantages, the dual feed induction generator (DFIG) is currently the generator of choice for driven wind turbines [1][2][3][4][5][6][7][8].
The vector control (VC) using conventional proportional-integral (PI) controllers allows decoupled control of the active and reactive powers typically applied for their simplicity [9][10]. However, the VC structure strongly count on the parameters of the machine and require exact knowleduses of the system model, therefore can not ensure the robustness of the system in the face of parameter variations and model uncertainties. Different strategies have been presented in the literature to remedy the aforementioned difficulties. Direct torque control (DTC) or direct power control (DPC) has been introduced in [11][12]. The application of DPC on the DFIG had many advantages over the classical VC method: no coordinate transformations, no current loops, less dependence on parameters. From its basic version the classical direct power control causes fluctuations in the currents, the reactive, active powers and the variable switching frequency because of the use of hysteresis regulators. Several approaches are suggested on the development of DPC techniques operating at a constant switching frequency. using space vector modulation [13][14][15][16]. its precaution is elimination of the hysteresis regulators and the switching table. The reduction of the power pulsation and the quality of the power has been achieved. These controllers are not robust to uncertain parameters.
The authors suggested the application of DPC in a DFIG-based wind turbine system under unbalanced grid voltage conditions [17][18]. The control strategy consists of a purely sinusoidal and balanced stator and GSC current injector, without the need to extract the negative sequence harmonics. The dual frequency pulses of the reactive power of the stator and the torque are completely eliminated when the torque / power is changed in transient and transient conditions when the voltage is unstable. Another technique is to use a second-order or higher sliding-mode command, such as super-twisting , which combines a MPPT using a fuzzy logic algorithm [24]. In [25][26][27][28], the authors propose controllers in second order sliding control.
The purpose of this paper is to use a second order continuous sliding mode control for a DFIG drive, this control strategy presents attractive features such as robustness to parametric uncertainties and attenuate chattering. The proposed strategy is compared with vector control.

WIND TURBINE MODELING
The relationship between the wind power and wind speed by the rotor blade of a wind turbine can be expressed as: The mechanical power expression as [30]: The tip speed ratio is described by: The aerodynamic torque is expressed by: The dynamic equation can be written as follows [31]:

MODELING OF THE DFIG
In the synchronous repository (d-q) we can highlight the DFIG dynamic equations as follows [4]: The flux equations are given by: The rotor voltages expression according to the rotor currents are obtained by the organization of the equations (7) and (8) Negligible stator resistance Rs and the stator flux is constant oriented along the axis, we can deduct from equation (7): The simplified diagram of the vector control is illustrated in Figure 3 Grid

DESIGN OF SECOND ORDRE SLIDING MODE CONTROL OF DFIG
The purpose of the SMC is to converge the system state trajectories to a predefined sliding variety.
The controller causes unwanted high frequency ripples. The second order sliding mode control is useful for reducing "chattering" as it applies to the second derivative of the system. This section introduces the Super Twisting algorithm. In order to reduce the chattering phenomenon, and maintaining the properties of robustness and convergence of the system in finite time. In this control, the sliding surfaces are chosen so as to be compatible with the errors in the powers of the stator.

1. Super Twisting Algorithm
The (STA) among the most popular second-order sliding mode algorithms. This algorithm only applies to systems of relative degree 1. Its interest lies in the reduction of chattering, due to the continuity of the control signal. This command breaks down into an algebraic and integral term. We can therefore consider this algorithm as a nonlinear generalization of a PI [25]. The Super-Twisting algorithm, like other algorithms of the same categorical, requires only the information on S and causes the cancellation of that one in a finite time; it also makes it possible to construct a differentiator called generally an exact differentiator [26]. The command law of fuper-twisting is formed of two parts; the first u1 is defined by its derivative with respect to time; while the second u2 is continuous and depending on the slip variable. The control law is suggested by [27]:  (17) where and are positive bounded constants.
The controller gains and should be over-estimated respecting to the system bounds with uncertainty in order to get a robust controller, as given in [28].

SIMULATION RESULTS
In order to validate the results obtained through the different approaches, it is necessary to make a comparison of the static and dynamic characteristics of the two control techniques under the same operating conditions and in the same simulation configuration. Simulation studies of the DFIG-based training system were performed using MATLAB / Simulink. The parameters of a wind turbine and a DFIG are presented in Table.2.

A. Simulation Results With Constant Speed
Simulations involving vector control and second order sliding mode control schemes. DFIG is used in a constant speed mode. Figures 5 and 6 compare the responses of the system during different active and reactive power steps for the two schemes, respectively. As these figures show, the robustness of the proposed controller scheme is also confirmed in terms of tracking aptitude compared to VC.
The stator phases current are shown in figures 7. It can be seen that the current waviness also has a noticeable reduction in the proposed algorithm compared to the classical algorithm.

B. Simulation Results with Variable Speed Wind Turbine
In order to test the influence of the variation of wind speed for both strategies. The reactive and active powers as well the stator current are illustrated in Figures (8 to 10), these results show that the suggested approach provides near-perfect performance in terms of system tracking performance relative to classical vector control. However, noticeable improvements have been recorded thanks to the new approach.  Further to investigate the performance of the proposed scheme, the stator current harmonic spectra with Ps = -5 kW and Qs = 0 kVar for different control strategies are obtained as shown in Fig. 11. It can be seen that traditional VC-SVM results in higher stator current harmonic distortion than those Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 26 July 2020 doi:10.20944/preprints202007.0628.v1 obtained by 2-SMC-SVM schemes.

2. Simulation Results With Parametric Uncertainty
To study the influence of the electrical parameter variation on the behavior of the DFIG, we also simulated the system for a +150% of the nominal rotor resistance and inductance at time t = 5.5s. The figure12 and 13 illustrates the evolution of the powers, we note from this result, the scheme (VC) has a slight variation due to the variations of Lr and Rr. The proposed method is robust against parameter variations and allows a fast and suitable dynamic response.

CONCLUSION
In this paper, second order sliding mode control for DFIG has been presented. The suggested control has been compared to the vector control. Simulation results demonstrate that the power ripples and total harmonics distortion (THD) are lower in second order sliding mode control compared with classical control. The effectiveness of the proposed controller was verified using simulation tests with a 5 KW DFIG. Moreover, the proposed controller was examined for DFIG parameter variations it has been demonstrated that the suggested algorithm gives better performance.
The advantages of the suggested algorithm are highlighted by the following points: 1. Good robustness against the machine's parameter 2. Improvements of the stator current spectrum.