A Novel Direct Active and Reactive Power Control Method Using Fuzzy Super Twisting Algorithms and Modified Space Vector Modulation Technique for an Asynchronous Generator-based Dual-rotor Wind Powers

This work presents a novel direct active and reactive powers command (DARPC) scheme based on fuzzy super twisting algorithms (FSTAs) of an asynchronous generator (ASG) integrated into dual-rotor wind power (DRWP) systems. The DRWP has two sets of blades. So it is more efficient for collecting power from wind in comparison to a traditional wind turbine. The scientific works indicate that a DRWP could extract additional 20-30% power compared to a traditional wind turbine. The conventional DARPC control scheme using the conventional integral-proportional (PI) regulators (DARPC-PI) has considerable reactive and active power oscillations. In order to guarantee an effective DARPC technique for the ASG-based DRWP system and minimize these oscillations, FSTAs are used in this work. Both DARPC strategies are presented and simulated from two tests using Matlab software. Simulation results showed the effectiveness of the designed DARPC control technique especially on the quality of the provided active and reactive power comparatively to the traditional DARPC control scheme with PI controllers.


INTRODUCTION 1
DARPC or direct active and reactive powers command is a technique to control asynchronous generators (ASGs) by utilizing stator active and reactive powers. But the reactive and active power oscillations are occurred in the traditional DARPC strategy [1]. The principle of the DARPC strategy is detailed in literature [2][3][4]. In addition, DPC offers many advantages include: simplicit y in calculations, robustness against ASG parameters, and fast dynamic response [5][6][7]. Although the DARPC strategy is getting more and more popular, it suffers fro m some drawbacks such as the large ripples of reactive and active powers. In order the overcome these disadvantages many researchers have been investigating on the DARPC strategy and they can be grouped under several headlines :  Using artificial intelligence methods (Neural networks and fuzzy logic) on different sections of the system; *Corresponding Author Email: habib0264@gmail.com (H. Benbouhenni)  Using different inverter topologies;  Using sliding mode controller (SMC).
In this work, a novel fuzzy super-twisting algorith m (FSTA) and modified space vector modulation (MSVM ) strategy has been designed to improve the stator active and reactive powers of the ASG on the DARP C technique.
The aim of this work is to improve the performance of the DARPC using FSTA controllers for ASG-based dual-rotor wind turbine (DRWT) system under variable speed wind and also to reduce fluctuations in reactive power, current, torque, and active power.
The FSTA method in the proposed technique rates active and reactive power errors and described the optimum space vector to reduce stator reactive and active power errors and oscillations. The simulation studies have been performed using Matlab logiciel board to effectiveness testing of the designed control strategy. In part II of this paper, the basic principles of the DARPC R2 technique with PI controllers are presented. In part III, detailed information about the proposed strategy is introduced. Part IV gives the simulation results of the proposed technique. In conclusion, we provided a summary of the work performed.

MATHEMATICAL MODELING OF DRWP SYSTEM
The DRWP system with ASG is shown in Figure 1. The DRWP consists of two wind powers. The mechanical power captured from the DRWP system is given by Benbouhenni [8]: where, PAT is the mechanical power of auxiliary turbine, and PMT is the mechanical power of auxiliary turbine. The torque of DRWP is given by: where, TAT is the torque of auxiliary turbine, and PMT is the torque of auxiliary turbine. Equations (3) and (4) represent the torque of the output main and auxiliary turbines [9].
where λAT, λMT : the tip speed ration of the main and auxiliary turbines, RMT, RAT: blade radius of the auxiliary and main turbines, ρ: the air density and wAT, wMT the mechanical speed of the auxiliary and main turbines. The tip speed ratios of the auxilliary and main turbines are given below: where ΩMT is the rotational speed of the main rotor, and ΩAT is the rotational speed of the auxiliary rotor.
The power coefficient CP equation is approximated using a non-linear function according to.
where, β is pitch angle. The wind speed on the main turbine is given below [10]: with Vx: is the velocity of the disturbed wind between rotors at point x and CT the trust coefficient, which is taken to be 0.9; x: the non-dimensional distance from the auxiliary rotor disk. So, with respect to x=15, the value of the Vx close to the main rotor is computable (rotors are located 15 meters apart from each other).

MODIFIED SVM TECHNIQUE
The proposed SVM technique named as modified SVM (MSVM) technique is an effective modulation technique for uncertain inverter and it overcomes the main disadvantages of the traditional SVM strategy. Figure 2 shows a block diagram representation of the MSVM technique approach for a two-level inverter in wind power. The principle of MSVM is detailed by Benbouhenni et al. [11]. This proposed strategy is based on calculation of the minimum and maximu m of threephase voltages. In this strategy, the sector and angle are not necessary to calculate. Modified SVM technique is used to minimize harmonic distortion (THD) in threephase output current waveform compared to PWM technique.
The MSVM modulation technique is used to generate gate pulses to the IGBT switches of the ASG-based DRWP systems. The proposed MSVM technique is a simple algorithm compared to the classical SVM method and is more robust compared to the traditional PWM strategy. Benbouhenni et al. [12] proposed the use of an MSVM technique applied to the four-level inverter of ASG. The fuzzy MSVM technique is proposed to reduces the active and reactive powers [13]. The simulatio n results have shown the superiority of the two-level fuzzy MSVM strategy. Mehedi et al. [14], have proposed an MSVM to control the five-phase inverter and the results indicate that the proposed MSVM strategy-based technique is good at minimizing the torque undulation, THD value of stator current, and stator flu x undulation.

DARPC STRATEGY WITH PI CONTROLLERS
In the DARPC-PI technique, the control of an ASG involves the direct command of the active and reactive powers by using two PI regulators [15]. This technique is a robust, easy, and simple technique. Stator active and reactive powers are estimated using Equations (9) and (10) [16].
These estimated values are compared to reference values and the resultant errors are applied to the PI regulators. Two PI controllers, as reactive and active PI regulators, generate other command parameters on the DARPC-MSVM technique or (DARPC-PI). The basic schematic representation of the DARPC-PI technique for ASG is shown in Figure 3.
The rotor flux can be estimated by: The rotor flux amplitude is given by: The reactive and active PI regulators gains (Ki and Kp) were found after performing simulations in Matlab logiciel. The gianes of PI regulator is stated in Table 1.

THE FSTA METHOD BASED DARPC METHOD
The DARPC scheme with PI controllers (DARPC-PI) offers some drawbacks associated with the large active and reactive powers ripples. In order to reduce these ripples, an STA technique with a fuzzy controller (FC) was designed. The origin of the DARPC-FSTA method is like to the DARPC-PI technique. The difference is using an FSTA algorithm to replace the conventional PI controllers. Also, the FLC is not dependent on the accurate mathematical model of the system [17]. It is based on 'IF…THEN' rules and experiences of human beings. In this work, using the advantage of FLC and STA, a DARPC method is presented.

A. Design of PI controller based on STA algorithm
The STA algorithm is based on the design of the discontinuous command signal that drives the system states toward special surfaces in state space [18]. Two  STA algorithms are selected for stator reactive and active power command. On the other hand, the STA algorith m is one of the robust techniques [19]. It is a particular operation mode of variable structure control systems. These techniques were used in numerous research works in the past years [20][21][22][23][24]. In the ASG command using the STA algorithm, the manifolds are chosen according to the error between the measured signals and the reference input signal. Considering that e1 and e2 are the errors of the stator active and the reactive power, we have the following: The expression of the manifolds has the followin g form.
The STA algorithms active and reactive power controllers are designed to respectively change the q and d-axis voltages as in Equations (17) and (18) [11]. (18) where, the constant gains k1 and k2 must check the stability conditions. Figure 4 shows the block diagram of STA algorithms of active and reactive powers.

B. Designe of FLC based on STA algorithm
FSTA algorithm is a merge between the STA algorith m and FLC technique, where the switching term, Sign(S(x)), has been replaced by the FLC technique. The proposal of an STA algorithm incorporating the FLC method helps in achieving minimized active and reactive powers oscillations, easy method, simple technique, and robust technique compared to vector command method. The proposed FSTA algorithm, which is proposed to command the active and reactive powers of the ASG is shown in Figure 5     The proprieties of our regulators are given in the Table 3.
The structure of the DARPC technique with the FSTA algorithms applied to the ASG-DRWP is illustrated in Figure 8.

SIMULATION RESULTS
To study the effectiveness of the designed DARPC DARPC-PI and DARPC-FSTA technique, the simulatio n of the system was accomplished using Matlab logiciel and  [27]. The ASG has the following mechanical parameters : J = 1000 Kg.m2, fr= 0.0024 Nm/s. From the simulation results are presented in Figures  9 and 10. It is apparent that the THD value of current for the DARPC-FSTA strategy is reduced (see Table 4).
From the system responses given in Figures 11 and  12 for DARPC-PI and DARPC-FSTA technique the stator active and reactive power tracks the reference powers without overshoot, with zero steady-state error. Figure 13 shows the torque of both techniques. Note that torque is related to active power.
From Figure 14 can be seen that the amplitudes of the stator phase currents depend on the state of the drive system and the value of the load active power.
The zoom in the active power, torque, and stator current are shown in Figures 15, 16 and 17, respectively. It can be seen that the DARPC control with FSTA algorithms minimized the undulations in active power, torque, and current compared to the DARPC strategy with PI controllers.    As it's shown by these figures, these variations present an apparent effect on the torque, current, active and reactive power curves, and that the effect appears more significant for the DARPC using PI controllers compared to DARPC using FSTA algorithms (See Figures. 24-26).
The THD value of the current in the DARPC using the FSTA algorithms has been minimized significantly (See Figures 22 and 23). Table 5 shows the THD value of both strategies. Thus it can be concluded that the proposed DARPC using FSTA algorithms is more robust than the DARPC using the PI controllers.   On the other hand, this designed technique reduced the THD value of current compared to other techniques (see Table 5). Based on the results above, it can be said that the DARPC-FSTA control technique has proven its efficiency in reducing ripples and chattering phenomena in addition to keeping the same advantages of the traditional DARPC method.