Received: December 22, 2020. Revised: February 26, 2021. 177

Improved Direct Control of Doubly Fed Using Space Vector Modulation

Mohammed El Mahfoud1* Badre Bossoufi1 Najib El Ouanjli2 Mahfoud Said2 Mohammed Taoussi2

1Laboratory of engineering Modeling and Systems Analysis, SMBA University Fez, Morocco 2Technologies and Industrial Services Laboratory, SMBA University Fez, Morocco * Corresponding author’s Email: [email protected]

Abstract: This research paper deals with the improved direct torque control (DTC) of a doubly fed induction machine (DFIM) operating in motor mode. The conventional DTC is a powerful tool to ensure robustness and good torque dynamics. However, the variable switching frequency as well as the presence of torque and flux ripples due to the use of hysteresis controllers are the major drawbacks of this strategy. For this purpose, the control by space vector Modulation (SVM) is developed to improve DTC performance, by replacing hysterisis controllers by PI controllers to reduce electromagnetic flux ripple and torque ripple in order to minimize mechanical vibration and acoustic noise while maintaining the benefits of DTC control. The proposed control algorithm is simulated and tested in MATLAB/Simulink. A comparative analysis between this technique and conventional DTC is carried out, highlighting the efficiency of the proposed improvement approach. The performance indexes and comparative results show the effectiveness of the proposed control in reducing torque ripple and and flux ripple by up to 43%, 42% and 31%, respectively, resulting in Total Harmonic Distortion (THD%) 61% lower, in addition the switching frequency is controlled, and the Rejection Time is improved by more than 76%. Keywords: Direct torque control, Space vector modulation, Doubly fed induction motor, Inverter, Switching table.

machine. The invention of the Field Oriented Control 1. Introduction (FOC) algorithm in the 1972s has revived the applications of high-performance variable speed Over the past few decades, drive systems have drives [6]. FOC provides decoupling between torque been used regularly in a number of applications, such and machine flux and makes the DFIM like a DC as marine propulsion, rail traction, pumping and machine [7]. This decoupling gives fast torque electric vehicles [1], as well as in hydroelectric and response, a wide speed control range and high wind power conversion systems [2]. Among these efficiency over a wide load variation range. But this drives, the Doubly Fed Induction Machine (DFIM) control presents a high sensitivity to the parametric presents great robustness, high efficiency, reliability variations of the machine and a great complexity and longevity. Increasing interest is being given to caused by the presence of coordinate transformations DFIM [3]. and the use of several control variables [8]. In Despite its advantages, yet DFIM is still opposition to FOC, Direct Torque Control (DTC) is complicated and difficult to control particularly when known by its simple decoupled scheme which allows good performance is required in various operating controlling the electromagnetic flux and torque. DTC conditions [4]. This is because DFIM is a non-linear offers advantages such as fast response and less system, multivariable, time-varying and subject to dependence on machine parameters. In addition, it perturbations. In addition, some of its state variables, does not require any transformation of coordinates or like flux are not measurable [5]. These constraints current regulator loops [5]. The DTC has been made require more powerful algorithms to control this International Journal of Intelligent Engineering and Systems, Vol.14, No.3, 2021 DOI: 10.22266/ijies2021.0630.16

Received: December 22, 2020. Revised: February 26, 2021. 178 by TAKAHASHI [9]. It is based on the direct this purpose, the DTC-SVM control strategy (without application of a control sequence to the switches of the use of hysteresis controllers) is recommended, in the inverter placed before the induction order to obtain a selection table allowing the best machine {Formatting Citation}. The choice of this choice of the voltage vector sequence to be applied to sequence is based on the use of a switching table and the motor, while respecting the constraints on flux hysteresis controllers which have the role of and electromagnetic torque [15]. This allows us to controlling and regulating the electromagnetic torque directly control the torque without using hysteresis and flux of the machine. However, this technique controllers and therefore a significant reduction in the causes [5]: ripple of the control quantities as well as a control of • Undesirable flux and torque ripples. the switching frequency. The behavior of the DFIM • High and uncontrollable switching frequency. controlled by DTC-SVM is evaluated and compared • Acoustic noise and mechanical vibration of the with that of the conventional DTC to highlight the motor. effectiveness of the proposed improvement approach. • Problems at low speeds. This article is divided into six major sections as In recent years, research has been conducted to follows: Section 2 presents a brief modeling of the overcome the drawbacks previously mentioned [1, doubly fed induction machine. Section 3 is devoted 11-13]. In [11], A DTC improved by the sliding mode to the study of the direct torque control of the DFIM command is studied. This technique provides a good and the explanation of the principle of flux control, improvement and guarantees robustness against electromagnetic torque and the general structure with external disturbances and parametric variations of the two switch tables. The modifications made to the motor, but there is the problem of the chattering DTC control and the principle of space vector phenomenon which is degrading the performance of modulation is described in section 4. Section 5 shows the system. The paper [1] presents direct torque the results of the simulation of the proposed control control of a DFIM by a PI controller tuned using a techniques, the comparative study between these two genetic algorithm. the GA is a particular class of control structures is given and discussed. Finally, evolutionary algorithms using techniques inspired by section 6 presents the conclusion and perceptual evolutionary biology, which has become a tool for the considerations. optimization of nonlinear problems, the major advantage of GA focuses on the optimization of the 2. Modeling of the DFIM variable parameters of the system, but which requires The system studied is composed of a doubly a large number of iterations for the system to fed induction motor associated with two variable converge towards optimal solutions. Another method frequency power supply systems; one is connected to of improving DTC is proposed in [12]. New the stator and the other one to the rotor [16]. Fig. 1 switching tables are developed using fuzzy logic shows the DFIM power supply scheme. controllers (FLC) to control the switching frequency. The stator and rotor voltage of DFIM in Furthermore, the authors of [13] are proposed another synchronously rotating reference frame (훼, 훽) can be structure of DTC based on the artificial neural expressed as [17]: network (ANN) to have fast responses of flux and torque with less distortion. However, these last two 푣푠훼 푅 0 0 0 푖푠훼 solutions present a high complexity of design and 푠 푣푠훽 0 푅 0 0 푖푠훽 implementation. For the FLCs, The design and choice [ ] = [ 푠 ] + 푣푟훼 0 0 푅 0 푖 of structure is difficult due to the lack of a clear 푟 푟훼 푣푟훽 0 0 0 푅푟 [푖푟훽] methodology. These techniques of artificial 휓 0 intelligence are not recommended for optimizing 푠훼 휓 0 excessively complex or very large problems, and 푑 푠훽 푑휃 [−휓 ] (1) requires much time to fine tune all parameters. 푑푡 휓푟훼 푑푡 푟훽 Our contribution in this work consists of [휓푟훽] 휓푟훼 proposing an improvement of the performances of the classical DTC control for a DFIM operating in motor mode, while keeping its advantages. They are as The expression of stator and rotor flux in diphase follows: robustness, simplicity and good speed reference frame (훼, 훽): tracking. The integration of the SVM to the classical DTC is a very attractive solution to guarantee an optimal regulation of the motor under study [14]. For

International Journal of Intelligent Engineering and Systems, Vol.14, No.3, 2021 DOI: 10.22266/ijies2021.0630.16

Received: December 22, 2020. Revised: February 26, 2021. 179

3.2 Application of DTC control to the DFIM

The control must always be asynchronous so at too able to regulate both stator and rotor flux; this means adjusting the torque supplied by the DFIM [12]. The flux expressions are:

푡 휓푠(푡) = ∫ (푉푠 − 푅푠퐼푠)푑푡 + 휓푠0 { 0 (5) ( ) 푡 휓푟 푡 = ∫0 (푉푟 − 푅푟퐼푟)푑푡 + 휓푟0

Figure.1 Power system of the DFIM The terms 푅 퐼 and 푅 퐼 are considered 푠 푠 푟 푟 negligible in front of the 푉푠and 푉푟. During a 휓푠훼 sampling period Te, the logic control states (푆퐴, 푆퐵 휓푠훽 = and 푆퐶) remain fixed. Thus, Eq. (5) becomes: 휓푟훼 [휓푟훽] 훥휓 = 휓 (푘 + 1) − 휓 (푘) = 푉 푇 { 푠 푠 푠 푠 푒 (6) 퐿 0 푀 푐표푠 휃 −푀 푠푖푛 휃 푖푠훼 푠 훥휓푟 = 휓푟(푘 + 1) − 휓푟(푘) = 푉푟푇푒 0 퐿 푀 푠푖푛 휃 푀 푐표푠 휃 푖푠훽 [ 푠 ] 푀 푐표푠 휃 푀 푠푖푛 휃 퐿푟 0 푖푟훼 With: −푀 푠푖푛 휃 푀 푐표푠 휃 0 퐿푟 [푖푟훽] 휓(푘 + 1): Flux vector (stator or rotor flux) at the next (2) sampling step.

휓(푘) : Flux vector (stator or rotor) at the current The electromagnetic torque can be determined from: sampling step. 3 푃푀 훥휓 : Variation of the flux vector (휓(푘 + 1) − 푇푒푚 = (휓푠훽휓푟훼 − 휓푠훼휓푟훽) (3) 2 휎퐿푠퐿푟 휓(푘)).

푑훺 푇푒 : Sampling period. With: 푇 = 푇 + 퐽 + 푓. 훺 (4) 푒푚 푟 푑푡 From Eq. (6), it can be noticed that over a 3. Direct torque control strategy sampling interval [0. 푇푒], the extremity of the flux vector moves on a straight line whose direction is 3.1 Principe of the DTC given by the selected voltage vector 푉 for a period 푇푒, through choosing an appropriate sequence of the The DTC aims directly at controlling the torque voltage vector of the inverter over successive and flux produced by the machine, without current sampling periods of duration 푇푒 . This allows the control, as is the case in the FOC. DTC has many tracking of the extremity of the flux vector 휓 advantages such as less dependence on machine according to the desired trajectory as shown in Fig. 2. parameters, simpler implementation and a relatively The torque expression can be presented as follows: faster dynamic torque response to field-oriented rotor control [18]. Direct torque control allows decoupled control of 푇 = 퐾‖휓⃗⃗⃗⃗ ‖. ‖휓⃗⃗⃗⃗ ‖. 푠푖푛훾 (7) flux and electromagnetic torque in the reference 푒푚 푠 푟 frame (훼, 훽 ). It uses a switching table for the With: 퐾 constant depends on motor parameters selection of a suitable voltage vector [5]. The 3 푃푀 퐾 = selection of the switching states is directly related to 2 휎퐿푠퐿푟 the variation of the flux and torque of the motor. ⃗⃗⃗⃗ 2 2 Therefore, the selection is made by limiting both the ‖휓푠‖ = √휓푠훼 + 휓푠훽 flux and torque amplitudes in two hysteresis bands. (8)

These controllers provide separate control of these ‖휓⃗⃗⃗⃗ ‖ = √휓2 + 휓2 { 푠 푠훼 푠훽 two magnitudes. The inputs of the hysteresis controllers are flux and torque errors, and their 훾 = 휃 − 휃 (9) outputs determine the appropriate voltage vector for 푠 푟 each switching period.

International Journal of Intelligent Engineering and Systems, Vol.14, No.3, 2021 DOI: 10.22266/ijies2021.0630.16

Received: December 22, 2020. Revised: February 26, 2021. 180

Figure. 3 Electromagnetic torque evolution

Table 1. Choice of voltage vector Increase Decrease 휓s or 휓r Vi+1, Vi-1 Vi+2, Vi-2 Tem Vi+1, Vi+2 Vi-1, Vi-2

general, when the flux (stator or rotor) is in the Si sector, the torque and flux control can be done as presented in Table 1. Figure.2 Flux vector evolution The selection of the voltage vector is deduced from the estimated torque and flux deviations from 휓 휃 = ∠휓⃗⃗⃗⃗ = 푎푟푐푡푔 ( 푠훽) their references, as well as the sector or position 푠 푠 휓 { 푠훽 (10) where the flux vector was located. 휓푟훽 휃푟 = ∠휓⃗⃗⃗⃗푟 = 푎푟푐푡푔( ) a) Flux controller: 휓푟훽 The objective of this controller is to keep the extremity of the flux vector within a circular band as This equation shows that the electromagnetic shown in Fig. 4. Two-level hysteresis comparators torque depends on the amplitude of the two flux are used for the correction of stator and rotor flux. vectors (휓푠 and 휓푟 ) and their relative position 훾 . The output of each comparator must indicate the When stator and rotor flux are kept constant, by direction of evolution of the flux module, to select the limiting the flux in hysteresis bands around its set- corresponding voltage vector. points, the electromagnetic torque will be a function of the angle of phase shift 훾 between these fluxes. In order to act on this angle, the position of the stator flux vector in the frame (훼, 훽) must be varied via applying an appropriate tension vector. In this way, to maximize the value of the torque, it suffices to apply a voltage whose vector is in advanced quadrature with respect to the stator flux vector. Conversely, a reduction of the motor torque in algebraic value can be obtained quickly by applying a voltage vector having a strong delay quadrature component Fig. 3). The different selection strategies for each voltage vector 푉 are developed from the rules for the evolution of the flux modulus and the electromagnetic torque of the doubly fed induction machine, taking into account information on the position of the flux vector in the complex plane (훼, 훽). To delimit the flux space, a partition into six zones (sectors) of 60˚ of this space is necessary. In Figure. 4 Flux trajectories International Journal of Intelligent Engineering and Systems, Vol.14, No.3, 2021 DOI: 10.22266/ijies2021.0630.16

Received: December 22, 2020. Revised: February 26, 2021. 181

Figure. 5 General structure of DTC of the DFIM

The error between the reference flux and the Table 2. Switching table estimated flux is injected into a two-level hysteresis Flux 0 1 controller which generates at its output the boolean Torque -1 0 1 -1 0 1 variable 퐻휓, this variable directly indicates whether 1 V5 V0 V3 V6 V7 V2 2 V6 V7 V4 V1 V0 V3 the flux amplitude should be increased (퐻휓 = 1) or 3 V1 V0 V5 V2 V7 V4 decreased ( 퐻휓 = 0 ) in order to keep the error 4 V2 V7 V6 V3 V0 V5 between the estimated and reference flux within a Sectors 5 V3 V0 V1 V4 V7 V6 hysteresis width 훥휓 and the inequation |휓푟푒푓 − 6 V4 V7 V2 V5 V0 V1 휓푒푠푡| ≤ 훥휓 should be checked. If 휀 > 훥휓 or 휀˂ − 훥휓, it means the flux is coming out of the hysteresis sampling instant according to the state of the boolean band. In the first case, it is necessary to impose a variables (퐻휓 et 퐻푇푒푚) at the output of the two flux voltage vector which increases the flux modulus. In correctors and the electromagnetic torque, as well as the second case, a voltage vector is imposed which the 푆푖 sector giving information on the position of the reduces the flux modulus. flux vector in the reference frame (훼, 훽) , it is b) Electromagnetic torque controller: presented in Table 2. For torque correction, a three-level hysteresis Fig. 5 illustrates the general structure of direct comparator is used to control the machine in both torque control of the doubly fed induction motor directions of rotation. Its role is to keep the connected by two voltage inverters. electromagnetic torque within the limits |푇푒푚푟푒푓 −

푇푒푚푒푠푡 | ≤ 훥푇푒푚. The error 휀(푇푒푚, between esteemed 4. Direct torque control based on space and reference torque is introduced into a three-level vector modulation hysteresis comparator, the latter generates at its 4.1 Principe of the DTC output the boolean variable 퐻푇푒푚 , this variable directly indicates whether the torque amplitude must The main disadvantages of conventional direct be increased in absolute value ( 퐻 = 1 for a 푇푒푚 torque control are the variable switching frequency positive set-point and 퐻 = −1 for a negative 푇푒푚 and the high level of ripples. Consequently, they setpoint) or decreased ( ). 퐻푇푒푚 = 0 cause high current harmonics, acoustic noise and The two voltage inverters supplying the doubly degrade the performance of the control particularly at fed induction motor are controlled by a control law low speed [19]. The ripples are proportionally generated from two switching tables. Each table is affected by the width of the hysteresis band. However, used to select the appropriate voltage vector at each even when choosing lower bandwidth values, the ripples remain large due to the discrete nature of International Journal of Intelligent Engineering and Systems, Vol.14, No.3, 2021 DOI: 10.22266/ijies2021.0630.16

Received: December 22, 2020. Revised: February 26, 2021. 182 hysteresis controllers. In addition, very small Table 3. Inverter switch control signals bandwidth values increase the switching frequency of Sector1 푇1 = −푍, 푇2 = 푋 the inverter [12]. Sector2 푇2 = 푌, 푇3 = 푍 DTC-SVM for DFIM control powered by two Sector 3 푇3 = 푋 ,푇4 = −푌 inverters includes three PI controllers for regulating Sector 4 푇4 = 푍 , 푇5 = −푋 torque and stator and rotor flux. The torque PI Sector 5 푇5 = −푌, 푇6 = −푍 controller generates the quadratic stator and rotor Sector 6 푇6 = −푋, 푇1 = 푌 voltage 푉 ,thus the output of the two other PI 푞 The application time for each vector can be controllers in the flux loop gives the voltages obtained by vector calculations and the rest of the directs푉푑.Once 푉푑and 푉푞 are obtained, they must be time period will be spent by applying the zero vector transformed to a fixed reference (훼, 훽) which are both [23]. inputs delivered to space the vector modulator When the reference voltage is in sector 1 (Fig. 7), (SVM),which generates switching signals SA, SB, SC the reference voltage can be obtained by synthesis for the power transistors of the inverters [20]. using the vectors V1, V2 and V0 (zero vector). The volt-second principle for sector 1 can be expressed 4.2 Application of DTC control to the DFIM by: The SVM is different from conventional pulse- width modulation (PWM). It is based on the vectorial 푉푟푒푓푇푒 = 푉1푇1 + 푉2푇2 + 푉0푇0 (11) spatial representation of the inverter output. There are no separate modulators for each phase. The reference 푇푒 = 푇1 + 푇2 + 푇0 (12) voltages are given by the spatial voltage vector (i.e. the components of the voltage vector in the complex T1, T2 and T0 are the corresponding application times plane) [21]. The principle of SVM is the prediction of of the voltage vectors. the inverter voltage vector by projecting the reference The determination of the times 푇1 and 푇2 which correspond to the voltage vectors is obtained by vector Vref between adjacent vectors corresponding to two non-zero switching states [22]. For a two-level simple projections: inverter, the switching vector diagram forms a 푇푒 푇1 = (√6푉훽 − √2푉훼) (13) hexagon divided into six sectors, each expanded by 2푉푑푐 60° as shown in Fig. 6. 푇푒 푇2 = √2푉훼 (14) 푉푑푐

The method already presented for Vref between V1and V2is redone for the sectors. Table 3 shows the different application times of the state vectors for the different sectors (S1 to S6 ) from the values of the following variables X, Y and Z: With:

푇푒 푋 = √2푉훼 (15) 푉푑푐

푇푒 Figure. 6 Diagram of voltage space vector 푌 = (√6푉훽 + √2푉훼) (16) 2푉푑푐

푇푒 푍 = (√2푉훼 − √6푉훽) (17) 2푉푑푐

Figure. 7 Reference vector as a combination of adjacent

vectors at sector 1 Figure. 8 Switching times of sector 1 International Journal of Intelligent Engineering and Systems, Vol.14, No.3, 2021 DOI: 10.22266/ijies2021.0630.16

Received: December 22, 2020. Revised: February 26, 2021. 183

Figure. 9 Block diagram DTC-SVM scheme for DFIM drive

25 The calculation of the switching times (duty T (Conventional DTC) 2 em 20 cycles) is expressed as follows: T (DTC-SVM) 0 em 푇 −푇 −푇 Zoom 푒 1 2 T -2 푇푎표푛 = (18) 15 r 2 0.7 0.8 0.9 1 10 Time (s) 푇푏표푛 = 푇푎표푛 + 푇1 (19) 5 12 10 0 Zoom 8 푇푐표푛 = 푇푏표푛 + 푇2 (20) Electromagnetic torque (N.m) -5 6 0 0.5 1 1.5 2 2.5 3 3.5 4 2.4 2.5 2.6 2.7 Time (s) The carrier wave generated by the SVM model is Time (s) Figure. 11 Electromagnetic torque symmetrical. An example for this wave with a period 푇푒 in sector 1 is illustrated in Fig. 8. 1.4  (Conventional DTC)  (DTC-SVM)  Fig. 9 illustrates the general structure of DTC- 1.2 s s s-ref SVM control of the doubly fed induction motor 1 0.8 connected by two voltage inverters. 1.05 0.6 1

Stator flux (Wb) 0.4 5. Simulation results 0.95 0.2 2 2.5 3 0 In this section, the conventional DTC and SVM- 0 0.5 1 1.5 2 2.5 3 3.5 4 DTC controls of the doubly fed induction motor have Time (s) been tested by simulation under the Figure. 12 Stator flux

MATLAB/Simulink environment. The motor 0.7  (Conventional DTC)  (DTC-SVM)  parameters are mentioned in the appendix. 0.6 r r r-ref

0.5 200 158 0.4  (DTC-SVM) 157 0.51  (Conventional DTC) 0.3 100 156  Zoom 0.5

ref 155 Rotor flux (Wb) 0.2

0.48 0.5 0.52 0.54 0.49 0 0.1 Time (s) 2 2.5 3 158 0 0 0.5 1 1.5 2 2.5 3 3.5 4 -100 Time (s)

156 Rotation Speed (Rad/s) Zoom Figure. 13 Rotor flux -200 154 0 0.5 1 1.5 2 2.5 3 3.5 4 0.95 1 1.05 Time (s) Time (s) Figure. 10 Rotation speed International Journal of Intelligent Engineering and Systems, Vol.14, No.3, 2021 DOI: 10.22266/ijies2021.0630.16

Received: December 22, 2020. Revised: February 26, 2021. 184

1.5 0.8 (Classic DTC) (DTC-SVM)  (Classic DTC)  (DTC-SVM) s s r r 0.6 1 0.4 0.5

0.2

 r

s 0 0

 

-0.2 -0.5 -0.4 -1 -0.6

-1.5 -0.8 -1.5 -1 -0.5 0 0.5 1 1.5 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6   s r 1.05 0.51 1 0.5

0.49 Zoom Zoom 0.95 0.48 0.9 0.47 -0.4 -0.2 0 0.2 0.4 -0.2 -0.1 0 0.1 0.2 Figure.14 Stator flux evolution Figure.15 Rotor flux evolution

20 20 i i i i i i sa sb sc ra rb rc 10 10

0 0 -10

-10 Rotor currents (A) Stator currents (A) -20 -20 0 1 2 3 4 0 1 2 3 4 Time (s) Time (s)

10 10

0 0

Zoom Zoom -10 -10

0.9 0.95 1 1.05 1.1 0.8 0.9 1 1.1 1.2 Time (s) Time (s)

10 10

0 0

Zoom Zoom -10 -10

1.9 2 2.1 2.2 2.3 2.4 2 2.2 2.4 2.6 2.8 Time (s) Time (s) Figure. 16 Stator and rotor current by conventional DTC

20 20 i i i i i i ra rb rc sa sb sc 10 10

0 0 -10 -10

Rotor currents (A) -20 Stator currents (A) -20 0 1 2 3 4 0 1 2 3 4 Time (s) Time (s)

10 10

0 0

Zoom Zoom -10 -10 0.9 0.95 1 1.05 1.1 0.8 0.9 1 1.1 1.2 Time (s) Time (s)

10 10

0 0

Zoom Zoom -10 -10

1.9 2 2.1 2.2 2.3 2.4 2 2.2 2.4 2.6 2.8 Time (s) Time (s) Figure. 17 Stator and rotor current by DTC-SFM

The following figures show the simulation results tracking dynamic. The rotation speed relatively obtained for a trapezoidal speed set-point with follows its reference (Fig. 10). The reference torque, reversal of rotation direction. By applying a load load torque and the motor torque are shown in Fig. torque of 10 N.m and 5 N.m to 푡1 = 1푠 and 푡2 = 3푠. 11. In this case, the load torque is considered a disturbance. As the startup is empty, the motor torque 6. Discussion returns practically to zero at the end of the transient regime. However, at the instant of overloading the The results obtained show that the DTC-SVM motor, a drop in speed is caused; this disturbance is control presents satisfactory results with a good quickly rejected (10ms for DTC-SVM and for 42ms International Journal of Intelligent Engineering and Systems, Vol.14, No.3, 2021 DOI: 10.22266/ijies2021.0630.16

Received: December 22, 2020. Revised: February 26, 2021. 185

Fundamental (48.79Hz) = 5.131 , THD= 12.65% Fundamental (48.49Hz) = 5.122 , THD= 4.87% 100 100 5 80 80 5

60 60 0 40 40 0 2000 4000 0 0 2000 4000

20 20

Mag Mag (% of Fundamental) Mag Mag (% of Fundamental) 0 0 0 1000 2000 3000 4000 5000 0 1000 2000 3000 4000 5000 Frequency (Hz) Frequency (Hz)

(a) (b) Figure. 18 Harmonic analysis of rotor current spectra by control: (a) conventional DTC and (b) DTC-SVM

1.5 1.5

1 1

0.5 0.5

0 0

Switching state Switching state

-0.5 -0.5 4.005 4.0055 4.006 4.0065 4.005 4.0055 4.006 4.0065 Time (s) Time (s) (a) (b) Figure. 19 Switching stats Sa by control: (a) conventional DTC and (b) DTC-SVM

Table 4. Comparison between conventional DTC and DTC-SVM Performance Conventional DTC DTC-SVM Improvement (%) Torque ripple (N.m) 2.92 1.64 43.83 Stator flux ripple (Wb) 0.089 0.051 42.69 rotor flux ripple (Wb) 0.0175 0.012 31.42 THD of the phase current isa (%) 12.65 4.87 61.50 Speed rejection time 42ms 10 ms 76.19 Variable frequency of Almost constant Switching frequency is Switching frequency 8.66 kHz frequency of 5.62KHz mastered

Table 5. Comparison of our proposal with some published controls strategy Publication Response time Torque Ripple Method Complexity Robustness reference (s) (N.m) [24] Sliding mode control 0.19 2.40 high Not robust [1] GA based DTC 0.18 0.16 Very high Robust [12] Fuzzy based DTC 0.28 1.14 Very high Robust Proposal DTC-SVM 0.16 1.64 Medium Robust Method conventional DTC). Moreover, the electromagnetic total harmonic distortion (THD) of phase current by torque by DTC-SVM presents fewer ripples the DTC-SVM control is considerably reduced compared to that of conventional control. compared to conventional DTC. Figs.12 and 13 show that the stator and rotor flux Fig. 19 illustrates the switching state of the "푆푎" modules follow its references (1Wb for the stator flux switch for the two control strategies. The switching and 0.5Wb for the rotor flux). But these flux by frequency obtained by DTC-SVM is lower than that conventional DTC have ripples compared to DTC- of conventional DTC, and so reducing switching SVM due to the use of hysteresis comparators, they losses. are not affected by the variation in load and speed Table 4 summarizes the comparative study (Figs. 14 and 15). The components of the rotor and between the two controls in terms of speed tracking, stator currents for both techniques are presented in torque ripples, flux ripples and spectral harmonic Figs. 16 and 17. They respond well to the variations analysis of currents and switching frequency. imposed by the load torque. They have a sinusoidal A comparison between the proposed technique shape. and some published control strategies is presented in Furthermore, Fig. 18 shows the spectral analysis Table 5. It should be noted that they do not refer to of the stator current "isa" absorbed by the DFIM. The the same conditions since it is very difficult to find

International Journal of Intelligent Engineering and Systems, Vol.14, No.3, 2021 DOI: 10.22266/ijies2021.0630.16

Received: December 22, 2020. Revised: February 26, 2021. 186 several works carried out under the same conditions. NOMENCLATURES:

Therefore, if we compare the proposed works with 휓r(α, β), 휓r(α,β):Rotor and stator flux in (α,β) reference. the sliding mode [24], our solution has a faster Vr(α,β),vs(α,β) :Rotor and stator voltages in (α,β) reference. response and reduced torque ripples. In addition, our ir(α,β), is(α,β) :Rotor and stator currents in (α,β) reference. system is insensitive to load torque variations, which SA , SB, SC : Switching states. demonstrates a high level of robustness a high level Rr, Rs : Rotor and stator resistances. of robustness. Thus, DTC using PI controller tuned M : Mutual inductance. using genetic algorithm presented by [1] and the Lr, Ls : Rotor and stator inductances. fuzzy DTC presented by [12] presents less torque J : Moment of inertia. ripples than our proposal, but these controls are very f : Coefficient of viscous friction. complex for this reason fast processors are used, p : Number of pole pair. which leads to an increase in the cost of the system. ωr, ωs : Rotor and stator pulsations. ω : Mechanical pulsation. 7. Conclusion Ω : Rotation speed. This paper has presented a direct torque control Tr , Tem : Load and Electromagnetic torque. scheme based on space vector modulation for doubly θr, θs : Position of the rotor and stator flux. fed induction motor powered by two voltage inverters. VDC : DC bus voltage. The objective is to improve the performance of γ : Angle between the two rotor and stator flux conventional DTC. The dynamic model of DFIM and vectors. the principle of DTC strategies have been presented. Te : Sampling period.

The control technique DTC based on space vector modulation is developed in detail. After testing the ABBREVIATIONS: system controls using MATLAB/SIMULINK, the key findings of this work are as follows: ANN : Artificial Neural Network • Space Vector Modulation (SVM) is an efficient DTC : Direct Torque Control. method of improving DTC. Flux and torque DFIM : Doubly Fed Induction Machine. ripples are minimised by 43% and 42% FOC : Field Oriented Control. respectively. Consequently, fewer problems for FLC : Fuzzy Logic Controller DFIM are caused, such as ageing, mechanical SVM : Space Vector Modulation. vibrations, heating… THD : Total Harmonics Distortion. • Compared to traditional DTC, the proposed technique optimises the harmonic distortion of the Conflicts of Interest rotor and stator currents by 61%. The authors declare no conflict of interest. • The fast response, torque dynamics and robustness merits of the classic DTC are preserved. The future work will address the experimental Author Contributions validation of DTC-SVM control using the dSPACE Conceptualization by Mohammed El Mahfoud DS1104 platform. and Najib El Ouanjli; methodology, Mohammed Taoussi; software, Mahfoud Said; validation, APPENDIX resources, and formal analysis by Badre Bossoufi; PARAMETERS OF THE DFIM writing—original draft preparation, Mohammed El Variable Symbol Value (unit) Mahfoud and Mahfoud Said; writing—review and Nominal power Pm 1.5 kW editing, Najib El Ouanjli and Mohammed Taoussi; Frequency f 50 Hz visualization, supervision and project administration Pair pole number P 2 by Badre Bossoufi. Stator resistance Rs 1.75 Ω Rotor resistance Rr 1.68 Ω References Mutual inductance M 0.165 H [1] A. Zemmit, S. Messalti, and A. Harrag, “A new Stator self-inductance Ls 0.295 H Rotor self-inductance Lr 0.104 H improved DTC of doubly fed induction machine Total inertia J 0.01 Kg.m² using GA-based PI controller”, Ain Shams Total viscous frictions f 0.0027 Engineering Journal, Vol. 9, No. 4, 1877-1885, Kg.m²/s 2018.

International Journal of Intelligent Engineering and Systems, Vol.14, No.3, 2021 DOI: 10.22266/ijies2021.0630.16

Received: December 22, 2020. Revised: February 26, 2021. 187

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International Journal of Intelligent Engineering and Systems, Vol.14, No.3, 2021 DOI: 10.22266/ijies2021.0630.16