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Direct torque control of doubly fed induction motor using threelevel NPC inverter
Protection and Control of Modern Power Systems volume 4, Article number: 17 (2019)
Abstract
This article presents the direct torque control (DTC) strategy for the doubly fed induction motor (DFIM) connected to two threelevel voltage source inverters (3LVSIs) with neutral point clamped (NPC) structure. This control method allows to reduce the torque and flux ripples as well as to optimize the total harmonic distortion (THD) of motor currents. The use of 3LVSI increases the number of generated voltage, which allows improving the quality of its waveform and thus improves the DTC strategy. The system modeling and control are implemented in Matlab/Simulink environment. The analysis of simulation results shows the better performances of this control, especially in terms of torque and flux behavior, compared to conventional DTC.
Introduction
In the mid − 1980s, the direct torque control strategy of induction machine was introduced by Takahashi to overcome the problems of conventional controls such as scalar control (SC) and field oriented control (FOC) [1, 2]. DTC is based on the direct regulation of electromagnetic torque and flux of the machine. This control is characterized by good torque dynamic response, high robustness and less complexity than other controls [3]. It allows minimizing the influence of parametric variations in the machine and calculating the control variables which are stator flux and electromagnetic torque from the stator current measurements without using mechanical speed sensors [4].
Recently, many authors have applied the DTC technique to the Doubly Fed Induction Motor connected to twolevel voltage source inverters (2LVSIs) [2, 5, 6]. The researchers have pointed out the remarkable dynamic performance of this technique as well as its robustness to parametric variations in the motor. However, DTC suffers from major disadvantages such as (a) high torque and flux ripples that generate mechanical vibrations and undesirable acoustic noise, (b) variable switching frequency which causes switching losses, (c) and the negligence of stator and rotor resistances lead problems at low speed.
Several solutions have been proposed to minimize the ripples and to keep the frequency at constant value, for example: fuzzy logic controller (FLC), artificial neural network (ANN), space vector modulation (SVM) technique and predictive control (PC) have been applied to improve the conventional DTC of DFIM [7,8,9,10]. Nevertheless, the practical implementation of these methods is more complicated.
The voltage inverter is the most essential part of the DTC. It is well known that increasing the levels number of the inverter is a better solution in DTC drives [11]. The threelevel voltage source inverter with NPC structure is more efficient in terms of its lower switching frequency, reduced stress across the semiconductors, less harmonic content, and lower voltage distortion compared to 2LVSI [12].
Although many studies about DTC for permanent magnet synchronous motors (PMSMs) and DTC for induction motors (IMs) using the multilevel inverter to increase the voltage vector number of switching table have been conducted individually [13, 14]. However, to the author’s knowledge, no study on DTC for doubly fed induction motor powered by threelevel inverters is available. This gives us the opportunity to propose and design a DTC based on the use of 3LVSI with NPC structure to control the doubly fed induction motor for the first time in the literature.
The main contributions of this work are as follows:

The new DTC switching tables of the DFIM connected to two 3LVSIs with NPC structure is designed to give better performance, while retaining the merits of the conventional DTC namely robustness and simplicity.

The torque and flux ripples are reduced and the inverter switching frequency is mastered to limit the different problems of DFIM (mechanical vibration, acoustic noises, heating, ageing…).

The performance of the DFIM connected to two 3LVSIs is compared to that of the DFIM connected to two 2LVSIs so as to illustrate the improvements made.
This paper is structured as follows: section 2 presents the dynamic modeling of DFIM. Section 3 introduces the mathematical model of the threelevel inverter with NPC structure and describes the DTC technique of DFIM based on two switching tables and hysteresis controllers. In section 4, the simulation results using the MATLAB/SIMULINK environment are presented and analyzed. Finally, Section 5 concludes the paper giving some comments and future directions.
Modeling of the DFIM
The power supply of the doubly fed induction motor is assured by two 3LVSIs [15]. Figure 1 illustrates the synoptic schema of the studied system.
In the literature, for a better representation of the behavior of DFIM, it is necessary to use a specific and simple model. The twophase model (α,β) given by the Concordia transformation is largely used for direct torque control [16].
The electric equations of DFIM in the reference frame (α,β) are given by [17]:

Stator voltages:

Rotor voltages:
The magnetic equations of DFIM in the reference frame (α,β) are expressed by:

Stator flux:

Rotor flux:
The electromagnetic torque expression of DFIM as a function of the stator flux and stator currents is written as follows [18, 19]:
The fundamental equation of dynamics is:
Direct torque control strategy
DTC strategy for the DFIM connected to two 2LVSIs
The principle of DTC is based on the direct regulation of the torque and flux of DFIM, by applying the different voltage vectors of inverters (towlevel) [5]. The choice of these vectors is made using two switching tables and the hysteresis regulators whose role is to control the electromagnetic torque and flux of the motor in a decoupled manner. The output of these switching tables determines the optimal voltage vector of inverter to be applied at each switching instant.
The vector voltage expression of each twolevel inverter can be given in the form below [2]:
With: S_{a}, S_{b}, S_{c} are switching logic states.
Figure 2 presents the set of voltage vectors delivered by each inverter.
In DTC, the accuracy of electromagnetic torque and flux estimation is very important to ensure satisfactory performance. The stator and rotor flux are estimated from the following eqs. [5]:
The electromagnetic torque is estimated from the measured stator currents:
With:
The positions of stator and rotor flux are determined by:
The estimated values of the electromagnetic torque and flux are compared respectively to their reference values; the comparison results form the inputs of hysteresis comparators [20]. The stator and rotor flux are controlled using the twolevel hysteresis comparators, while the electromagnetic torque is controlled using a threelevel hysteresis comparator. The flux space is divided into six sectors of 60° each. The selection of the appropriate voltage vector is based on the control table shown in Table 1 [7]. The inputs of this table are the flux sector number and the outputs of hysteresis comparators.
DTC strategy for the DFIM connected to two 3LVSIs
The development of speed control and DTC of doubly fed induction motors has favored the use of threelevel inverters. The increase in levels number of the latter proves to be a better solution in high power drives. The inverter is made up of switching cells, generally with transistors or GTO thyristors for large powers [21]. In this section, we present the study DFIM associated with two 3LVSIs with neutral point camped structure controlled by the DTC algorithm. Figure 3 illustrates the general schema of 3LVSI with NPC structure; it is one of the structures of threelevel inverter. It has a lot of advantages, such as the higher number of voltage vectors generated, less harmonic distortion and low switching frequency [22]. Each arm of the inverter consists of 4 switches: S_{k1}, S_{k2}, S_{k3}, S_{k4}. The S_{k1} and S_{k2} have complementary operation.
On the control side, this converter topology offers the following advantages: high number of freedom degrees compared to the twolevel inverter and reduced output current ripples.
The mathematical model of the 3LVSI is represented by the following matrix [23]:
With:
V_{a}, V_{b}, V_{c}: Phase voltages.
S_{ki}: Switching state.
U_{dc}: DC bus voltage.
Each arm of the threelevel inverter has three switching states shown in Table 2.
The set of voltage vectors delivered by a threelevel inverter are shown in Table 3, they are divided into 4 groups.
The 3LVSI produces 27 voltage vectors; some of them apply the same voltage vector. There are two possible configurations for each small vector and three for the zero vectors. Therefore, 19 different vectors are available in a threelevel inverter [22]. The distribution of these voltage vectors in the reference frame (α, β) is shown in Fig. 4.
The estimated values of the torque and flux are respectively compared to their reference values. The comparison results form the hysteresis regulators inputs. The stator and rotor flux are controlled using the threelevel hysteresis comparators, while the electromagnetic torque is controlled using a fivelevel hysteresis comparator (Fig. 5). The flux space is divided into 12 sectors of 30° each.
In order to realize the direct control of flux and torque of the DFIM connected to two threelevel voltage inverters with NPC structure, we need to develop the switching table that optimizes the inverter possibilities. The construction of this table (Table 4) depends on the choice of voltage vector applied to increase or decrease the flux modulus and electromagnetic torque value.
DTC scheme for the doubly fed induction motor connected to two 3LVSIs is illustrated in Fig. 6.
Simulation results and discusions
The direct torque control strategy of doubly fed induction motor was validated by numerical simulation using MATLAB/SIMULINK environment. The DFIM parameters used in the simulation are given in the Appendix.
The main features of this simulation are summarized as follows:

The widths of the hysteresis bands:
ΔT_{em1} = ±0.02 N.m, ΔT_{em2} = ±0.04 N.m, Δψ_{s} = ±0.001 N.m and Δψ_{r} = ±0.001 N.m.

The sampling frequency: f_{s} = 10 kHz.
The simulation results of the DTC strategy of DFIM powered by two 2LVSIs are shown in Fig. 7.
Figure 7a shows the motor rotation speed. The speed reference changes from zero to 100 rad/s with specific acceleration rate (500 rad/s^{2}), then it reduces to − 100 rad/s at t = 1 s. It can be seen that the speed reference has been properly tracked without any overshoot.
The load torque, torque reference and motor torque are represented in Fig. 7b. Here, the load torque is considered as disturbance, and the control method must track the speed reference independent of the load torque. The load torque changes from 0 Nm to 10 Nm at t = 0.5 s, then it decreases to 5 Nm at t = 1.5 s. The electromagnetic torque tracks its reference. Moreover, this torque has more ripples of 2.632 Nm.
Figure 7c and d show that the stator and rotor flux modulus follows perfectly its reference (1 Wb for stator flux, 0.5 Wb for rotor flux), as well as the evolution of these flux in (α,β) plan illustrated in Fig. 7e and f are perfectly circular.
Figure 7g represents the sectors repartition of stator and rotor flux in (α,β) plan, which shows that the DTC technique principle using 2LVSIs is ensured.
The stator and rotor currents of the DFIM are illustrated in Fig. 7h, the results show that the motor currents are sinusoidal. The harmonic spectra analysis of these currents is shown in Fig. 7i and j. Besides, the THD of stator current i_{sa} is equal to 8.75% and THD of rotor current i_{ra} is equal to 9.87%. The switching state of switch (S_{a}) of the twolevel inverter is given in Fig. 7k. The switching frequency is variable, its average value is equal to 4 kHz.
The simulation results of the DTC strategy of DFIM connected to two 3LVSIs are shown in Fig. 8.
The results show the high performance of proposed method. From Fig. 8a, it can be seen that the rotation speed track its reference without overshoot, with a very low relative fall during the torque inversion, the release time is equal to 50 ms.
Figure 8b clearly shows good torque dynamics which perfectly follow its steady state reference with a fast response time. Moreover, the torque has small ripples of 0.972 Nm. From the analysis of Fig. 8c and d it follows that the stator and rotor flux modulus follows perfectly its reference with less ripples, as well as the evolution of these flux in (α,β) plan shown in Fig. 8e and f are perfectly circular.
Figure 8g represents the sectors repartition of the stator and rotor flux in (α,β) plan, there are 12 sectors which shows that the proposed method is ensured.
The components of the stator and rotor currents in reference frame (a,b,c) are shown in Fig. 8h, the motor currents are sinusoidal with a frequency proportional to the reference speed. These currents respond effectively to the variations imposed by load torque. Furthermore, Fig. 8i and j present the harmonic spectra analysis of the stator and rotor currents absorbed by DFIM, the results indicate that the total harmonic distortions of these currents are considerably reduced compared to the results obtained by DTC using 2LSVI (THD = 1.57% for stator current i_{sa}, THD = 1.52% for rotor current i_{ra}). The switching state of threelevel inverter is given in Fig. 8k, the switching frequency is almost constant around 2.9 kHz, lower than that of DTC using 2LVSIs, which reduces switching losses.
Table 5 summarizes the comparative study between the two methods. The results of comparison show remarkable improvements obtained by DTC using 3LVSIs. These improvements include an important reduction in flux and torque ripples, as well as a minimization in the harmonics of the stator and rotor currents. Therefore, the proposed method provides better performance compared to DTC using 2LVSIs.
Conclusion
In this paper, we have presented the direct torque control for a doubly fed induction motor connected to two threelevel voltage source inverters with NPC structure. The objective is to improve the motor performance. The DFIM modeling and DTC technical using 3LVSIs is developed in detail. Simulation results of the proposed method are comparatively analyzed against conventional DTC using 2LVSIs to confirm the effectiveness and superiority of the proposed control. The results analysis shows that the DTC using 3LVSIs provides better performance in terms of minimization of torque and flux ripples and optimization of currents distortion. This provides an opportunity for motor operation under minimum switching loss and noise. The experimental validation of the proposed method on a dSPACE controller board is considered future work.
Methods/experimental
This study presents a method for improving the performance of the direct torque control. The doubly fed induction machine is used as a motor connected to two threelevel voltage source inverters. The system modeling and control are implemented in Matlab/Simulink environment. Comparison analysis of the proposed method with conventional DTC illustrates the advantages of this method.
Nomenclature
v_{s(α,β)},v_{r(α,β)} Stator and rotor voltages in the reference frame (α,β).
i_{s(α,β)}, i_{r(α,β)} Stator and rotor currents in the reference frame (α,β).
ψ_{s(α,β)}, ψ_{r(α,β)} Stator and rotor flux in the reference frame (α,β).
R_{s}, R_{r} Stator and rotor resistances.
L_{s}, L_{r} Stator and rotor inductances.
M Mutual inductance.
P Pole pair number.
ω_{s}, ω_{r} Stator and rotor pulsations.
ω Mechanical pulsation.
T_{r} Load torque.
T_{em} Electromagnetic torque.
Ω Rotation speed of the machine.
J Moment of inertia.
f Coefficient of viscous friction.
θ_{s}, θ_{r} Position of the stator and rotor flux.
U_{dc} DC bus voltage.
Availability of data and materials
Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.
Abbreviations
 2LVSI:

TwoLevel Voltage Source Inverter
 3LVSI:

ThreeLevel Voltage Source Inverter
 DFIM:

Doubly Fed Induction Motor
 DTC:

Direct Torque Control
 FOC:

Field Oriented Control
 IM:

Induction Motor
 NPC:

Neutral Point Clamped
 PMSM:

Permanent Magnet Synchronous Motor
 SC:

Scalar Control
 THD:

Total Harmonics Distortion
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Acknowledgements
The authors would like to thank the anonymous reviewers for their helpful and constructive comments that greatly contributed to improving the final version of the paper. They would also like to thank the Editors for their generous comments and support during the review process.
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The work is not supported by any funding agency. This is the authors own research work.
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NE, AD and AE performed the study of the direct torque control strategies, MT and YM corresponding, engaged in modifying the paper and submitted it to the PCMP. BB, KM and YM checked the grammar and writing of the paper. All authors read and approved the final manuscript.
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El Ouanjli, N., Derouich, A., El Ghzizal, A. et al. Direct torque control of doubly fed induction motor using threelevel NPC inverter. Prot Control Mod Power Syst 4, 17 (2019). https://doi.org/10.1186/s4160101901317
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Keywords
 Direct torque control
 Doubly fed induction motor
 Threelevel inverter
 Ripples
 Switching table