Keywords: Abstract: This study proposes enhancing

induction motor (IM) drive systems by

developing a DTC-MC with SVPWM
Highlights:
• integration to reduce ripple. DTC-MC is
effective for precise torque control in AC
•
drives, offering high control accuracy by
•
isolating stator flux and torque. The

ARTICLE INFO method excels in sensor-less speed control,

Article history:
maintaining unity input power factor at low
Received 02 Feb. 2024
Received in revised form 08 Apr. 2024 speeds, and constant switching frequency
Accepted 18 Apr. 2024
Final Proofreading 05 Sep. 2024 for rapid torque adjustments. Combining
Available online 15 Oct. 2024
DTC-MC with SVPWM improves
© THIS IS AN OPEN ACCESS ARTICLE UNDER THE CC BY
LICENSE. http://creativecommons.org/licenses/by/4.0/
simplicity, dynamic behavior, and torque
response. The DTC-SVM approach further
Citation: Mahmood AT, Gaeid KS, Al Smadi TA. refines the torque response by correcting
Direct Torque Control Space Vector Modulation
flux and torque discrepancies.
for Induction Motor Driven by Matrix Converter.
Tikrit Journal of Engineering Sciences 2024; 31(4): 58- MATLAB/SIMULINK simulations
69.
http://doi.org/10.25130/tjes.31.4.6
validated the approach, showing a robust
dynamic response and significantly
Ayad T. Mahmood reduced motor torque ripple and control of
Department of Electrical Engineering, College of
Engineering, Tikrit University, Tikrit, Iraq. speed.

Tikrit Journal of Engineering Sciences Volume 31 No. 4 2024 Page 58

 Ayad T. Mahmood, Khalaf S. Gaeid, Takialddin A. Al Smadi / Tikrit Journal of Engineering Sciences 2024; 31(4): 58-69.

‫السيطرة على المحركات الحثية عن طريق محول المصفوفة باستخدام تعديل ناقل‬
‫الفضاء للتحكم المباشر في عزم الدوران‬
2
‫ تقي الدين الصمادي‬،1 ‫ خلف سلوم كَعيد‬،1 ‫اياد طارق محمود‬
.‫ العراق‬- ‫ تكريت‬/‫ جامعة تكريت‬/‫ كلية الهندسة‬/‫ قسم الهندسة الكهربائية‬1
.‫ األردن‬- ‫ جرش‬/‫ جامعة جرش‬/‫ كلية الهندسة‬2
‫الخالصة‬
DTC-MC ‫ يعتبر‬.‫ لتقليل التموج‬SVPWM ‫ مع تقنية‬DTC-MC ‫تقترح هذه الدراسة تعزيز أنظمة المحركات الحثية من خالل تطوير نظام‬
.‫ مما يوفر دقة تحكم عالية عن طريق عزل تدفق الجزء الثابت وعزم الدوران‬،‫فعاالً للتحكم الدقيق في عزم الدوران في محركات التيار المتردد‬
‫ وتردد التبديل الثابت‬،‫ والحفاظ على عامل طاقة اإلدخال الموحد عند السرعات المنخفضة‬،‫تتفوق هذه ا لطريقة في التحكم في السرعة بدون مستشعر‬
‫ على تحسين البساطة والسلوك الديناميكي واستجابة عزم‬SVPWM‫ و‬DTC-MC ‫ يعمل الجمع بين‬.‫إلجراء تعديالت سريعة على عزم الدوران‬
‫ أثبتت عمليات محاكاة‬.‫ على تحسين ذلك عن طريق تصحيح تباينات التدفق وعزم الدوران‬DTC-SVM ‫ يعمل نهج‬.‫الدوران‬
.‫ وأظهرت استجابة ديناميكية قوية وتقليل تموج عزم دوران المحرك بشكل كبير والتحكم في السرعة‬،‫ صحة هذا النهج‬MATLAB/SIMULINK
‫ التحكم المباشر في عزم‬،)SVM( ‫ تعديل ناقل الفضاء‬،)SVPWM( ‫ تعديل عرض نبض ناقل الفضاء‬،)MC( ‫ محول المصفوفة‬:‫الكلمات الدالة‬
.)IM( ‫ المحرك الحثي‬،)DTC( ‫الدوران‬
1.INTRODUCTION
In the last two decades, the need for improved interval, which results in higher switching
power supply quality and efficiency has frequencies [3]. Various endeavors have
catapulted the three-phase matrix converter enhanced the stable-state capabilities of DTC
into a prominent position as a contemporary techniques, including adopting Direct Self
energy converter, which has risen as a superior Control (DSC), utilizing SVM, incorporating
choice to traditional energy conversion multilevel inverters, integrating with Matrix
modules. Matrix converter-driven motor Converters, and implementing Predictive
systems surpass PWM inverter drives due to Torque Control. When the strengths of MCs are
their capacity for two-way power transfer, merged with those of DTC methods, it becomes
generation of sine-shaped input and outcome feasible to attain swift torque and flux
currents, and the flexibility to adjust the power responses over a broad speed range [4], as
factor at the input. Moreover, MCs facilitate explained in the following studies and research
small and efficiently organized designs by [5]. This article introduces a DTC scheme using
eliminating the necessity for components SVPWM for a five-phase IM powered by a 3 × 5
storing energy, such as capacitors in the DC- phase DMC. It focuses on eliminating the third
link. Nevertheless, the practical application of harmonic in the 𝑥𝑦 plane via SVPWM-VV and
matrix converters in vector control systems for volt-second balancing. SVPWM-VVs impact
(IM) has been constrained because the stator flux, torque, speed, and power factor,
modulation techniques and switching control reducing torque and stator current ripple while
require a higher quantity of intricate than those maintaining a consistent switching frequency.
employed in conventional PWM power It also employs a LUT to regulate input power
inverters [1]. Since the mid-1980s, the Direct factor and grid current harmonics at [6]. As a
Control (DTC) approach has become widely validation of the work presented in this paper,
accepted in variable-speed drive applications, the same results were obtained as shown in [7,
especially when achieving precise control over 8]. They developed a direct torque-controlled
torque is prioritized over speed regulation. matrix converter-fed induction motor drive
Typically, IMs can be controlled using two system based on the space vector modulation
methods, known as scalar and vector control technique (SVPWM) for ripple reduction. DTC-
(VC), which can be implemented as open or MC combination is an efficient way to get better
closed-loop systems. Vector control focuses on performance specifications in the industry. The
regulating the rotor flux and torque by direct torque control technique is used in AC
estimating the motor by speed and voltage, drive systems to obtain high-performance
which can be determined directly or indirectly. torque control. The DTC-SVM combination
An uncomplicated substitute for vector control method on the matrix converter has been
is the DTC [2]. DTC has several notable successfully used for the IM to reduce torque
benefits, including quick transient torque ripples. Since torque control and ripple
response and low computational demands. reduction were the main goals, the DTC-SVM
Nonetheless, traditional DTC has two distinct technique minimizes the torque and flux error.
drawbacks: variable switching frequencies that Constant switching frequency DTC-SVM
rely on hysteresis bands and motor speed, and schemes considerably improved the drive
it produces significant torque fluctuations, performance in reduced torque and flux
especially compared to the Field-Oriented pulsations and low-speed operation, well-
Control method. To mitigate torque defined radiated noise, and a harmonic
fluctuations in traditional DTC, the typical spectrum. The contribution of the present work
approach involves reducing the sampling can be explained as follows: controlling the

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 Ayad T. Mahmood, Khalaf S. Gaeid, Takialddin A. Al Smadi / Tikrit Journal of Engineering Sciences 2024; 31(4): 58-69.

matrix converter using DTC-SVM technology, The variables 𝑖𝑞𝑠 and 𝑖𝑑𝑠 represent the stator
controlling the speed of the IM, and reducing flux linkages in Weber for the q-axis and d-axis,
distortions in voltage and current using the and 𝜆𝑞𝑟 and 𝜆𝑑𝑠 represent the rotor flux
appropriate filter. The present work is linkages in Weber for the q-axis and d-axis,
organized as follows: section 1 studies the DTC respectively. The inverter's switch settings are
structure, section 2 explains the concept of determined by the disparities in torque and
space vectors, section 3 explains the DTC flux, which are determined by sector
Matrix Converter structure, section 4 shows identification, ensuring the estimated stator
clear LC input filters, and section 5 shows the flux and torque stay within their predetermined
simulation and result. thresholds, as shown in Fig. 2. During every
2.DTC STRUCTURE sampling interval, estimations for torque and
The fundamental framework of the DTC-IM stator flux are made and subsequently assessed
system is depicted in Fig. 1. The underlying by the hysteresis comparator against their
fundamental concept of the DTC method can be corresponding reference values [15].
explained as outlined below: Initially, the
system measures phase currents and voltages.
These measurements are sent for the flux and
torque estimation module, which calculates the
natural system flux and torque values. The
computed torque is subsequently contrasted to
its reference values in the torque controller,
Fig. 1 Block Diagram of DTC.
while the actual flux is contrasted against the
reference flux values in the controller. The
control signal for the IGBTs is generated using
the outputs from the stator flux and torque
controllers, serving as inputs for the DTC
switching look-up table [9]. This paper presents
an enhanced DTC approach where the
reference stator voltage vectors were generated
based on torque and flux errors, as indicated in
Eqs. (1) to (5) below. These reference stator (a) (b)
voltage vectors are then modulated using the Fig. 2 (a) Flux Hysteresis Comparison Module
SVPWM technique [10, 11]. The component (b) Torque Hysteresis Comparison Module.
related to the field is oriented along the d-axis, 3.THE CONCEPT OF SPACE VECTORS
while the torque component is allocated The idea of space vectors, originating in the
synchronized with the q-axis, and both rotating domain of IMs, finds application in the
components are mutually perpendicular to one modulation of inverter output voltage. In this
another. Stator voltage given in Eq. (1) and technique, the three-phase values are converted
rotor voltage given in Eq. (2): into their respective two-phase equivalents,
𝒅𝜸𝒔 either in a frame that rotates in synchrony or a
𝒗 𝒔 = 𝑹𝒔 𝒊 𝒔 + (1)
𝒅𝒕 stationary frame. The magnitude of the
𝒅𝜸𝒓 reference vector is expressed through these
𝒗 𝒓 = 𝑹𝒓 𝒊 𝒓 + − 𝒋𝒘𝒎 𝜸𝒓 (2)
𝒅𝒕 dual-phase constituents. Moreover, it is
The variables 𝜆𝑠 and 𝜆𝑟 represent the flux subsequently employed to modulate the
linkage of the stator and rotor, measured in inverter's output. The procedure for acquiring
Weber (Wb). The variables 𝑖𝑠 and 𝑖𝑟 represent the revolving spatial vector is elaborated in the
the current flowing through the stator and next section, focusing on the fixed reference
rotor, measured in Amperes (A). Similarly, 𝑅𝑠 frame. Within the fixed reference frame, the
and 𝑅𝑟 denote the resistance of the stator and trinary sinusoidal voltage element is assumed
rotor, measured in Ohms (Ω), respectively. The as [16]:
equation for stator flux and flux in the rotor are 𝑽𝒂 = 𝑽𝒎𝑺𝒊𝒏𝝎𝒕 (6)
as follows: 𝟐𝝅
𝝀 𝒔 = 𝒍 𝒎 𝒊 𝒓 + 𝑳𝒔 𝒊 𝒔 (3) 𝑽𝒃 = 𝑽𝒎𝑺𝒊𝒏(𝝎𝒕 − ( )) (7)
𝟑
𝝀 𝒓 = 𝒍 𝒎 𝒊 𝒔 + 𝑳𝒓 𝒊 𝒓 (4) 𝟒𝝅
𝑽𝒄 = 𝑽𝒎𝑺𝒊𝒏(𝝎𝒕 − ( )) (8)
where Mutual inductance is denoted in Henrys 𝟑
as 𝐿𝑚, and 𝐿𝑠 and 𝐿𝑟 represent the stator and When three-phase voltage is supplied to the AC
rotor inductances, respectively, also measured machine, it creates a rotating magnetic field in
in Henrys [12]. The torque developed by the the machine's air gap. This rotating magnetic
motor given from Eq. (5) [13, 14]: field can be expressed as a sole rotating voltage
𝟑𝒑 vector. Clark's Transformation is employed to
𝑻 = 𝟐 (𝜸𝒅𝒔 𝒊𝒒𝒔 −𝜸𝒒𝒔 𝒊𝒅𝒔) (5)
determine the magnitude and direction of this
rotating vector within the stationary reference

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 Ayad T. Mahmood, Khalaf S. Gaeid, Takialddin A. Al Smadi / Tikrit Journal of Engineering Sciences 2024; 31(4): 58-69.

frame. For implementing SVPWM, the voltage obtain the desired reference voltage vector,
equations in the 𝑎𝑏𝑐 reference frame are 𝑉𝑟𝑒𝑓, within the d-q plane from the desired
converted into the stationary dq reference output voltage. The primary objective of the
frame, comprising the horizontal (d) and SVPWM technique is to approximate 𝑉𝑟𝑒𝑓 by
vertical (q) axes [17], as depicted in Fig. 3, utilizing the eight switching patterns. A
illustrating the connection between these two straightforward approach to achieving this aim
reference frames in Eqs. (9) and (10). is to approximately ensure that the average
𝒍𝒅𝒒𝟎 = 𝑴𝒔 ∗ 𝒍 𝒂𝒃𝒄 (9) inverter output within a short time T matches
𝟏 − 𝟏⁄𝟐 − 𝟏⁄𝟐 𝑉𝑟𝑒𝑓 within an identical time frame [20].
𝟐
𝑴𝒔 = ∗
𝟑 𝟎 − √𝟑⁄𝟐 − √𝟑⁄𝟐 , 𝒍𝒅𝒒𝟎 =
𝟏 𝟏⁄ 𝟏⁄
[ ⁄𝟐 𝟐 𝟐 ]
𝑻 𝑻
[𝒍𝒅 𝒍𝒒 𝒍𝟎 ] , 𝒍𝒂𝒃𝒄 = [𝒍𝒂 𝒍𝒃 𝒍𝒄 ] (10)
Where 𝑙 represents an electrical variable, which
could be either a voltage or a current.

Fig. 3 SVPWM for 𝑑𝑞 and 𝑥𝑦 Axes [18]. Fig. 5 SVPWM Sectors and Switching Vectors
Representation.
The Park's conversion process involves
transforming αβ to dq coordinates, For the operation mode spanning 180 degrees,
simultaneously rotating α and β axes utilizing a there are six distinct switching states and a pair
predefined frequency. This reference frequency of additional states where either entirely upper
is conveyed via the input related to the phase or entirely lower arm switches are turned on.
(𝜔𝑡), as illustrated in Fig. 4 [19]. These eight states can be represented with three
bits in binary form (2^3 = 8). As upper and
lower switches consistently operate
complementary, it is sufficient to indicate the
upper bridge switch status. In this
representation, "1" indicates the switch is on,
and "0" indicates it is off. Table 1 tabulates
detailed information on these eight states’
phase and line voltages [21].
Table 1 Visualizes Voltage Space Vector
Switching Patterns About Phase and Line
Voltages.
Switching The line to Line-to-line
Fig. 4 Conversion of Coordinates from the α-β Vector vector neutral voltage voltage
𝒔𝟏 𝒔𝟐 𝒔𝟑 𝑽𝒂𝒏 𝑽𝒃𝒏 𝑽𝒄𝒏 𝑽𝒂𝒃 𝑽𝒃𝒄 𝑽𝒄𝒂
Frame to the d-q Frame 𝑈𝛼 𝑈𝛽 . V0 000 0 0 0 0 0 0
2 −1 −1
In Fig. 3, this transformation essentially V1 100 𝑉
3 𝑑𝑐
𝑉
3 𝑑𝑐 3 𝑑𝑐
𝑉 𝑉𝑑𝑐 0 −𝑉𝑑𝑐
projects [a b c]t orthogonally onto a two- V2 110
1
𝑉
3 𝑑𝑐
1
𝑉
3 𝑑𝑐
−2
𝑉
3 𝑑𝑐
0 𝑉𝑑𝑐 −𝑉𝑑𝑐
dimensional plane orthogonal to the vector [1 1 V3 010
−1
𝑉
3 𝑑𝑐 3 𝑑𝑐
2
𝑉
−1
𝑉
3 𝑑𝑐
−𝑉𝑑𝑐 𝑉𝑑𝑐 0
1]t, forming what is known as the d-q plane V4 011
−2
𝑉
1
𝑉
1
𝑉 −𝑉𝑑𝑐 0 𝑉𝑑𝑐
3 𝑑𝑐 3 𝑑𝑐 3 𝑑𝑐
within a spatial three-dimensional coordinate V5 001
−1
𝑉
−1
𝑉
2
𝑉 0 −𝑉𝑑𝑐 𝑉𝑑𝑐
𝑑𝑐 𝑑𝑐 3 𝑑𝑐
system. This transformation allows for the V6 101
3
1
𝑉
3
−2
𝑉
1
𝑉 𝑉𝑑𝑐 −𝑉𝑑𝑐 0
𝑑𝑐 𝑑𝑐 3 𝑑𝑐
existence of six nonzero vectors (V1 through V7 111 0
3 3
0 0 0 0 0
V6), which establish the vertices of a hexagonal
shape, as shown in Fig. 5, and are responsible 4.DTC MATRIX CONVERTER
for supplying power delivered to the load. The STRUCTURES
angle between each consecutive pair of these The various topologies of multiphase
nonzero vectors is 60 degrees. Additionally, two converters can be categorized as shown in Fig.6
zero vectors (V0 and V7) are at the origin, with [22]. On one hand, these configurations can be
zero voltage applied to the load. These eight categorized according to the power conversion
vectors are collectively referred to as the basic method, either as AC-DC-AC or AC-AC modes.
space vectors (V0, V1, V2, V3, V4, V5, V6, and AC-AC converters are called MCs and consist of
V7). A similar transformation is employed to direct and indirect types. Conversely,
considering the neutral point connections,

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multiphase configurations can be categorized configurations are detailed in Table 2, where

as open-winding or single-sided modes. In their associated output voltage and input
open-winding configurations, which lack a current vectors can be found. These switching
neutral point connection, both ends can receive arrangements can be categorized into three
power from either a single or two separate DC primary groups:
sources. Furthermore, single-ended topologies 1- Zero vectors labeled as 0a to 0c, which
might feature one or multiple central point’s have no magnitude.
[23]. 2- Rotating vectors with a consistent
magnitude but changeable direction
ranging from ±10 to ±12.
3- Active vectors with a fixed direction but
adjustable magnitude spanning from ±1
to ±9 [26].
Table 2 Eight Hexagon States, each Associated
with Specific Phase Voltages and Space.
State Mode On Switches 𝐯𝟎 ∝𝟎 𝐢𝐢 𝛃𝐢
0𝑎 𝐴𝐴𝐴 𝑆𝐴𝑎 𝑆𝐴𝑏 𝑆𝐴𝑐 0 - 0 -
0𝑏 𝐵𝐵𝐵 𝑆𝐵𝑎 𝑆𝐵𝑏 𝑆𝐵𝑐 0 - 0 -
0𝑐 𝐶𝐶𝐶 𝑆𝐶𝑎 𝑆𝐶𝑏 𝑆𝐶𝑐 0 - 0 -
Fig. 6 Categorization of Multiphase Converter +10 ABC 𝑆𝐴𝑎 𝑆𝐵𝑏 𝑆𝐶𝑐 𝑣𝑖𝑚𝑎𝑥 ∝𝑖 𝑖𝑜𝑚𝑎𝑥 𝛽𝑜
Configurations. -10 ACB 𝑆𝐴𝑎 𝑆𝐶𝑏 𝑆𝐵𝑐 𝑣𝑖𝑚𝑎𝑥 −∝𝑖 𝑖𝑜𝑚𝑎𝑥 −𝛽𝑜
𝛽𝑜
The matrix converter utilizes a configuration of +11 CAB 𝑆𝐶𝑎 𝑆𝐴𝑏 𝑆𝐵𝑐 𝑣𝑖𝑚𝑎𝑥 ∝𝑖 +
2𝜋
𝑖𝑜𝑚𝑎𝑥 2𝜋
3 + 3
9 switches that can be operated in both
−∝𝑖 −𝛽𝑜
directions, enabling the connection from any -11 𝐵𝐴𝐶 𝑆𝐵𝑎 𝑆𝐴𝑏 𝑆𝐶𝑐 𝑣𝑖𝑚𝑎𝑥 2𝜋 𝑖𝑜𝑚𝑎𝑥 2𝜋
+ 3 + 3
output phase to any input phase. The
𝛽𝑜
converter's input terminals are linked to a +12 BCA 𝑆𝐵𝑎 𝑆𝐶𝑏 𝑆𝐴𝑐 𝑣𝑖𝑚𝑎𝑥 ∝𝑖 +
4𝜋
3
𝑖𝑜𝑚𝑎𝑥
+ 3
4𝜋

voltage-fed system comprising three phases, −∝𝑖 −𝛽𝑜

typically sourced from the grid. On the other -12 CBA 𝑆𝐶𝑎 𝑆𝐵𝑏 𝑆𝐴𝑐 𝑣𝑖𝑚𝑎𝑥 4𝜋
+ 3
𝑖𝑜𝑚𝑎𝑥
+ 3
4𝜋

hand, the output connections are connected to 2 2 −𝜋

+1 𝐴𝐵𝐵 𝑆𝐴𝑎 𝑆𝐵𝑏 𝑆𝐵𝑐 𝑣 0 𝑖𝑎
a system where current is supplied consisting of 3 𝐴𝐵
−2
√3
−2
6
−𝜋
three phases, similar to what was employed in -1 𝐵𝐴𝐴 𝑆𝐵𝑎 𝑆𝐴𝑏 𝑆𝐴𝑐 3 𝐴𝐵
𝑣 0 √3
𝑖𝑎 6
2 2 𝜋
an IM [24]. The MC employs a one-stage +2 𝐵𝐶𝐶 𝑆𝐵𝑎 𝑆𝐶𝑏 𝑆𝐶𝑐 𝑣
3 𝐵𝐶
0 √3
𝑖𝑎 2
conversion unit that utilizes bidirectional -2 𝐶𝐵𝐵 𝑆𝐶𝑎 𝑆𝐵𝑏 𝑆𝐵𝑐
−2
𝑣
3 𝐵𝐶
0
−2
𝑖𝑎 𝜋
2
√3
switches instead of multiple conversion stages +3 𝐶𝐴𝐴 𝑆𝐶𝑎 𝑆𝐴𝑏 𝑆𝐴𝑐
2
𝑣 0
2
𝑖𝑎 7𝜋
3 𝐶𝐴
and energy storage components commonly −2
√3
−2
6
7𝜋
-3 𝐴𝐶𝐶 𝑆𝐴𝑎 𝑆𝐶𝑏 𝑆𝐶𝑐 𝑣 0 𝑖𝑎
found in conventional converters [25]. Figure 7 3 𝐶𝐴 √3
2
6
−𝜋
+4
2 2𝜋⁄ 𝑖𝑏
presents a simplified block diagram of the 𝐵𝐴𝐵 𝑆𝐵𝑎 𝑆𝐴𝑏 𝑆𝐵𝑐 𝑣
3 𝐴𝐵 3 √3 6
−2 −𝜋
matrix converter, known for its compact and -4 𝐴𝐵𝐴 𝑆𝐴𝑎 𝑆𝐵𝑏 𝑆𝐴𝑐
−2
3 𝐴𝐵
𝑣 2𝜋⁄
3 √3
𝑖𝑏 6
capacitor-free design. This configuration offers +5 𝐶𝐵𝐶 𝑆𝐶𝑎 𝑆𝐵𝑏 𝑆𝐶𝑐
2
𝑣 2𝜋⁄ 2
𝑖𝑏 𝜋
3 𝐵𝐶 3 √3 2
27 switching states, allowing 27 potential space -5 𝐵𝐶𝐵 𝑆𝐵𝑎 𝑆𝐶𝑏 𝑆𝐵𝑐
−2
𝑣 2𝜋⁄ −2
𝑖𝑏 𝜋

vectors to control the IM. These states are 3 𝐵𝐶 3 √3 2

2 2𝜋⁄ 2 7𝜋
+6 𝐴𝐶𝐴 𝑆𝐴𝑎 𝑆𝐶𝑏 𝑆𝐴𝑎 𝑖𝑏
grouped into three categories: Group I 3
𝑣𝐶𝐴
3 √3
−2
6
-6
−2 2𝜋⁄ 7𝜋
connected one input line to two output lines, 𝐶𝐴𝐶 𝑆𝐶𝑎 𝑆𝐴𝑏 𝑆𝐶𝑐 𝑣
3 𝐶𝐴 3 √3
𝑖𝑏
6
Group II linked all output lines to a common +7 𝐵𝐵𝐴 𝑆𝐵𝑎 𝑆𝐵𝑏 𝑆𝐴𝑐
2
3
𝑣𝐴𝐵 4𝜋⁄
3
2
√3
𝑖𝑐 −𝜋
6
input line, and Group III established -7 𝐴𝐴𝐵 𝑆𝐴𝑎 𝑆𝐴𝑏 𝑆𝐵𝑐
−2
𝑣 4𝜋⁄ −2
𝑖𝑐
−𝜋
3 𝐴𝐵 3 6
connections between each output line and a 2 4𝜋⁄
√3
2 𝜋
+8 𝐶𝐶𝐵 𝑆𝐶𝑎 𝑆𝐶𝑏 𝑆𝐵𝑐 𝑣𝐵𝐶 𝑖𝑐
distinct input line. 3
−2 4𝜋⁄
3 √3
−2
2
𝜋
-8 𝐵𝐵𝐶 𝑆𝐵𝑎 𝑆𝐵𝑏 𝑆𝐶𝑐 𝑣
3 𝐵𝐶 3 √3
𝑖𝑐 2
2 4𝜋⁄ 2 7𝜋
+9 𝐴𝐴𝐶 𝑆𝐴𝑎 𝑆𝐴𝑏 𝑆𝐶𝑐 3
𝑣𝐶𝐴
3 √3
𝑖𝑐
6
−2 4𝜋⁄ −2 7𝜋
-9 𝐶𝐶𝐴 𝑆𝐶𝑎 𝑆𝐶𝑏 𝑆𝐴𝑐 𝑣
3 𝐶𝐴 3 √3
𝑖𝑐
6
Consequently, Table 3 elucidates the
relationship between the DTC method’s voltage
vectors and switching states across different
voltage sectors [27].
Table 3 Matrix Converter Switching.
Voltage Voltage sector
vector 𝟏 𝟐 𝟑 𝟒 𝟓 𝟔
⃗⃗⃗1
v -3, +1 +2, -3 -1, +2 +3, -1 -2, +3 +1, -2
Fig. 7 Matrix Converts Schematic Diagram v⃗⃗⃗2 +9, -7 -8, +9 +7, -8 -9, +7 +8, -9 -7, +8
[6]. v⃗⃗⃗3 -6, +4 +5, -6 -4, +5 +6, -4 -5, +6 +4, -5
v⃗⃗⃗4 +3, -1 -2, +3 +1, -2 -3, +1 +2, -3 -1, +2
The matrix converter offers a total of 27 v⃗⃗⃗5 -9, +7 +8, -9 -7, +8 +9, -7 -8, +9 +7, -8
different switching configurations. These v⃗⃗⃗6 +6, -4 -5, +6 +4, -5 -6, +4 +5, -6 -4, +5

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 Ayad T. Mahmood, Khalaf S. Gaeid, Takialddin A. Al Smadi / Tikrit Journal of Engineering Sciences 2024; 31(4): 58-69.

Figure 8 illustrates the block diagram of DTC- employing a constant switching period, such as
MC-SVM. To provide a concise overview of the those utilizing Pulse Width Modulation, the
fundamental DTC principles when employing cut-off frequency is typically set slightly below
MCs, it can be summarized as follows: During the switching frequency. However, the DTC
each sampling interval, the appropriate algorithm operates with a variable switching
switching arrangement is chosen. This selection period, making the precise determination of its
enables the correction of immediate deviations value challenging. It is important to note that
in stator flux magnitude and torque while the inductance value significantly influences
adhering to the unity input power factor the size and cost of a coil. Considering these
constraint [14] and feeding the IM [28]. The factors, it is most advantageous to treat the
DTC (Direct Torque Control) employs a general inductance and cut-off frequency of the filter as
selection table represented by the sector arbitrarily chosen parameters. To calculate the
number "M" detailed in Table 4. In DTC, the third parameter, capacity, using transform the
null sequence vectors (V000 or V111) sustain formula given in Eq. (12):
rotational force consistency and are inactive 𝑪= 𝟐 𝟐
𝟏
(12)
within the switching duration. The DTC 𝟒𝝅 𝒇𝒄𝒖𝒕 𝑳

switching table enables selecting vector This kind of filter is responsible for the
positions to apply to the Motor Controller based suppression of high current and voltage
on the direct component (DC) of stator flux and harmonics introduced by the converter.
electromagnetic torque, as demonstrated in Without it, the MC cannot function stable [30,
Table 5. Observing Table 4, it becomes evident 31]. The transfer function H(s) for the
that the switching frequency of IGBTs. continuous-time input signal and output of the
(Insulated Gate Bipolar Transistors) utilized in filter given in Eq. (13), then the cut-off
this approach is variable. Controlling the frequency (fc=355.88 H), Quality factor
permissible ranges makes maintaining the =2.236, Damping ratio = 4.45, and poles =
average switching frequency at reference 355.88 Hz.
𝟏⁄
possible, thereby minimizing ripple current and 𝑯(𝒔) = 𝑹
𝑳𝑪
(13)
torque fluctuations [29]. 𝒔𝟐 + 𝒔+𝟏⁄𝑳𝑪
𝑳
6.SIMULATION MODEL AND RESULTS
In this study, the induction motor was
controlled using a matrix converter consisting
of 18 IGBTs, through which the SVM-DTC
technology was used, which is considered one
of the most influential and fast techniques for
solving problems. Thus, the signals of all IGBTs
are suppressed, ensuring no interference
between the electrical signals. An appropriate
Fig. 8 Diagram Illustrating the Operation of input filter was used to guarantee that the
DTC-MC-SVM. current and voltage signals entering the matrix
Table 4 Table for General Selection. converters were undistorted. Thus, the power
𝜳𝒔 in sector M Torque factor will be unity, as shown in the present
Increase Decrease study. The speed was precisely controlled, and
Increase Vm+1 V000 the response of the induction motor to all
Flux
Decrease Vm+2 V111
variables was swift due to using the SVM-DTC
Table 5 DTC-MC Switching Table. technology. To evaluate the effectiveness of the
Sector
1 2 3 4 5 6 suggested method, simulations were conducted
𝑑𝑇 = 0 𝑉0 𝑉7 𝑉0 𝑉7 𝑉0 𝑉7 using a sampling interval of 20 microseconds.
𝑑∅ = +1 𝑑𝑇 = +1 𝑉2 𝑉3 𝑉4 𝑉5 𝑉6 𝑉1 The closed-loop model used for system
𝑑𝑇 = −1 𝑉6 𝑉1 𝑉2 𝑉3 𝑉4 𝑉5 simulation is depicted in Fig. 9. The simulation
𝑑𝑇 = 0 𝑉7 𝑉0 𝑉7 𝑉0 𝑉7 𝑉0 employed a 4-kW squirrel-cage induction
𝑑∅ = +1 𝑑𝑇 = +1 𝑉3 𝑉4 𝑉5 𝑉6 𝑉1 𝑉2
𝑑𝑇 = −1 𝑉5 𝑉6 𝑉1 𝑉2 𝑉3 𝑉4
motor with three phases as the machine model:
Pi =2.5kW， 𝑉𝑛 =480V, Rs =0.6Ω, Rr =0.65Ω,
5.LC INPUT FILTERS
Ls =1.8mH, Lr =1.8mH， 𝐿𝑚 =65.33mH, J =0.
An analytical approach assessed the optimized
parameters' performance quality and defined 05kg.m2, and P =2. The best parameters
optimization constraints. The parameters of LC analytical and optimized of input filters were
filters are interrelated through the cut-off L=1 𝑚𝐻 and C=200 𝜇𝑓. Figure 10 illustrates the
frequency formula, also known as the input voltages and currents of phase-a during
resonance frequency given in Eq. (11). steady-state operation. The currents exhibited
𝟏 sinusoidal characteristics and maintained
𝒇𝒄𝒖𝒕 =
𝟐𝝅√𝑳𝑪
(11) phase alignment with the voltages, indicating a
From the formula above, it can be inferred that unity power factor using the appropriate LC
two of the three variables, namely 𝑓𝑐𝑢𝑡, L, and input filter. Figure 11 displays the desired speed
C, must be chosen arbitrarily. In systems setting and the corresponding speed tracking,

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 Ayad T. Mahmood, Khalaf S. Gaeid, Takialddin A. Al Smadi / Tikrit Journal of Engineering Sciences 2024; 31(4): 58-69.

which align perfectly as the speed command stator voltage for the dq axes, as shown in
transitions from 500 RPM to 700 RPM and Fig.17, refers to the voltage components in the
decreases back to 500 RPM and 0 RPM. During dq-axis coordinate system. These voltage
the initial phase of the loading process, components are typically expressed as 𝑉𝑑 and
noteworthy events concerning torque, 𝑉𝑞, representing the voltage in the direct (d)
particularly the torsional force, occurred. and quadrature (q) axes, respectively. In Fig.
Initially, the electrically generated torque began 18, the Flux rotor for dq axes illustrates the
at zero and gradually increased to +15 Nm, as concept used to analyze and control the
depicted in Fig. 12. This initial response magnetic field produced by the rotor of an
provides insight into the system's reaction to electric machine within the context of the dq
varying torque loads, ultimately finding reference frame, making designing, controlling,
equilibrium. Therefore, it follows the torque and optimizing electric drives and synchronous
reference to the induction motor. Figure 13 machines easier. Different parameters and
shows the stator current signal in the simulated speed references of the induction motor were
time domain. The stator current peaked at applied, illustrated in Fig.19. The bode gain and
about 28 A during startup, and the rotor speed phase plots provide a direct and accurate
decreased the moment the plate entered method to depict gain and phase-shift
operation; however, the speed was controlled properties in circuit and control theory. They
according to the input speed reference. Figures are valuable tools for frequency domain
14 and 15 illustrates the pulses generated by analysis, allowing a practical examination of
dtc- svm techniques to control of MC and also these aspects through experimental
achieve that is no interference signals. Figure 16 representation, as illustrated in Fig. 20.
illustrates that the adaptive observer can
estimate the stator flux well and truly. The

Fig. 9 The Simulation Model for (MC-DTC-IM).

(a)

(b)
Fig. 10 Input Voltage and Current of MC (a) Input Voltage of Phase a (b) Input Current of Phase a.

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 Ayad T. Mahmood, Khalaf S. Gaeid, Takialddin A. Al Smadi / Tikrit Journal of Engineering Sciences 2024; 31(4): 58-69.

Fig. 11 Speed Reference in (blue) and Actual Speed Response in (Red).

Fig. 12 Actual (red) and Reference Torque Dynamic (Blue).

Fig. 13 Stator Current with the Proposed DTC Scheme Phase a, b, and c.

Fig. 14 Nine Gate Signals from (DTC1 to DTC9) to the Gate Drive the Matrix Converter.

Tikrit Journal of Engineering Sciences Volume 31 No. 4 2024 Page 65

 Ayad T. Mahmood, Khalaf S. Gaeid, Takialddin A. Al Smadi / Tikrit Journal of Engineering Sciences 2024; 31(4): 58-69.

Fig. 15 Gate Signal of S11, S12, and S13 and Achieve Safe Switching Devices Commutation.

Fig. 16 Flux Stator for dq Axes Curve d-q axes.

Fig. 17 Stator Voltage for dq Axes dq-Axes.

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 Ayad T. Mahmood, Khalaf S. Gaeid, Takialddin A. Al Smadi / Tikrit Journal of Engineering Sciences 2024; 31(4): 58-69.

Fig. 18 Flux Rotor for dq Axes.

Fig. 19 Speed Reference in (blue) and Actual Speed Response in (red) at Speed References.

Fig. 20 LC-Filter Voltage Transfer Function.

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 Ayad T. Mahmood, Khalaf S. Gaeid, Takialddin A. Al Smadi / Tikrit Journal of Engineering Sciences 2024; 31(4): 58-69.

7.CONCLUSION Efficient Technologies for Sustainability,

The present study introduces the MC-DTC St Xavier's Catholic College of
approach for induction motors, incorporating Engineering, TamilNadu, India 5th to 7th
connecting DTC-MC with space vector April; 2018.
modulation. This method seamlessly merges [7] Badiee-Azandehi, A. Yousefi-Talouki, and
the benefits of DTC with SVM within the M. Rezanejad. Direct Torque Control
context of a matrix converter. A fresh switching Space Vector Modulation of Five-
table for DTC-SVM was proposed, offering Phase Interior Permanent Magnet
comprehensive control over the induction Synchronous Motor Using Matrix
motor requirements while maintaining the Converter. Australian Journal of
unity power factor at the input. Simulation Electrical and Electronics Engineering
results across a wide speed range validated the 2015;12(2): 113-124.
efficacy of this innovative control strategy. [8] De Klerk, Matthew Liam, Akshay Kumar
Moreover, the approach demonstrated Saha. Performance Analysis of DTC-
improved input current harmonic SVM in a Complete Traction Motor
characteristics and low-speed performance Control Mechanism for a Battery
compared to the traditional MC-DTC approach. Electric Vehicle. Heliyon 2022; 4(6):
The approach also ensured the stability and 10-12.
reduction of flux, torque, and speed control. [9] Malla M, Gudey SK, Sudha S. Transient
With its numerous advantages and promising and Steady State Characteristics of
prospects, further research is warranted. Induction Motor Drive Using Dtc-
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