Switching Strategies of Three Phase Matrix

Converter fed Induction Motor Drive

R. A. Gupta, Rajesh Kumar, Virendra Sangtani and Ajay Kr. Bansal
Department of Electrical Engineering, M. N. I. T., Jaipur-302017 (India)
Email: ragmnit@gmail.com, rkumar.ee@gmail.com, virendrasangtani@rediffmail.com, ajayb007@rediffmail.com

Abstract— The operation of Matrix converter is based upon the increased up to 0.866 by adding the third harmonics of the
switching pattern of all nine switches. The input of three phase input and output voltages to the desired output voltage
induction motor is basically output of three phase matrix waveform [3, 4].
converter. The performance of three phase matrix converter fed
induction motor drive is analyzed by the switching pattern II. MATRIX CONVERTER THEORY
obtained by matrix converter and than three phase currents,
motor d axis and q axis current, motor torque and speed The topology of three-phase matrix converter fed induction
characteristics can be obtained. In this paper, simulation, design
motor is shown in Fig1(a). The input of three phase matrix
converter are phase voltages Vi1, Vi2,Vi3, which are basically
and implementation of three-phase to three-phase matrix
120 degree phase displaced with each other and its outputs are
converter and its switching pattern are obtained using Venturini
the voltages Vo1, Vo2, Vo3 ,which are applied to three phase
algorithm have been presented and after that the output of
induction motor. The matrix converter switches (S11. S12 …..
matrix converter is applied to three phase induction motor.
S33) represents nine bi-directional switches, which are capable
of blocking voltage in both directions. These nine bi
Index Terms— Matrix converter, switching pattern, Duty
directional switches are assumed as ideal.
cycle
I. INTRODUCTION
Matrix converter basically consists of nine bidirectional
switches, arranged into three groups of three switches, each
group being associated with an output phase. This arrangement
of bidirectional switches connects any of the input lines to any
of the output lines. Basically the array of 3*3 switches of
matrix converter produces total 512 combinations of switching
states, but only 27 switching states are permitted if two basic
rules are applied to operate on matrix converter safely i.e. not
to connect two different input lines to the same output line
(short-circuit of the main causes overcurrent) and does not
disconnect the output line currents. Matrix converter is capable
for performing frequency conversion with sinusoidal output
voltages and currents at desired output frequency and it also
allows bi-directional power flow. The converter offers the
advantages as sinusoidal input and output waveforms,
bidirectional power flow capability, minimum energy storage (a)
components, controllable input power factor and compact size.
Different modulation strategies are invented by many
researchers on matrix converters and main idea of modulation
algorithms for controlling the output voltage as to chop the
three-phase input voltages at the proper instant. Since there are
a number of switches in the power circuit, control algorithms
should be able to perform all processes with a minimum
switching frequency. This is important from the point of
switching losses [2, 3]. In order to calculate the target output
voltages, it is necessary to know the instantaneous input
voltages. One of the modulation algorithms which is mostly
used in matrix converters is Venturini control algorithm. In (b)
this technique, the output voltage amplitude is restricted to the Fig: 1. The topology of matrix converter fed induction motor
half of input voltage amplitude. However, this rate can be drive (a) and topology of bi-directional switch (b).
The input three phase voltages of the converter are given by: as:

 vi1   cos(i t )  1 2 2q 
    TBa  Ts   2 VoBVia  sin(imt )sin(3imt ) 
v  V cos( t  2 / 3)
 i2 
v 
i  i
 cos( t  4 / 3) 
  3 3Vim 9qm  … (8)
 i 3  i  ... (1)
1 2 2q 2 
The required first harmonic of the output phase voltages of TBb  Ts   2 VoBVib  sin(imt  )sin(3imt ) 
the unloaded matrix converter is:  3 3Vim 9 qm 3  … (9)
 vo1   cos(ot ) 
    1 2 2q 4 
 vo 2   Vo  cos(ot  2 / 3)  TBc  Ts   2 VoBVic  sin(imt  )sin(3imt ) 
v 
 o3 
 cos( t  4 / 3) 
   3 3Vim 9qm 3    … (10)
o
... (2)
Similarly the duty cycle for switch connected between the
The problem is stated as that with input voltages as equation input phase a, b and c and output phase C can be represented
(1), switching angles of the matrix converter will be as:
formulated such that the first harmonic of the output voltages
will represented as equation (2). 1 2 2q 
TCa  Ts   2 VoCVia  sin(imt )sin(3imt ) 
III. SWITCHING ALGORITHM  3 3Vim 9qm    … (11)
The switching algorithm is basically based upon the duty cycle
of all nine bidirectional switches. The duty cycle for switch 1 2 2q 2 
TCb  Ts   2 VoCVib  sin(imt  )sin(3imt ) 
connected between the input phase β and output phase γ as per
 3 3Vim 9qm 3     … (12)
Venturini algorithm is defined as:
1 2 2q 4 
1 2 2q  TCc  Ts   2 VoCVic  sin(imt  )sin(3imt ) 
T  Ts   2 Vo Vi  sin(it )sin(3imt  B )sin(3it )   3 3Vim 9qm 3   … (13)
 3 3Vim 9q m  ... (3)
The three phase output voltages for matrix converter are given
 as:
Where B is 0, 2  /3, 4  /3 corresponds to the input phases a,
q q
b and c, respectively, qm is the maximum voltage ratio (0.866), VOA  qVim cos  omt   Vim cos  3omt   Vim cos  3omt 
q is the desired voltage ratio, V im is the input voltage vector 6 4qm … (14)
magnitude and Vo  is represented as:
 2  q q
 q q  VOB  qVim cos  omt    Vim cos  3omt   Vim cos  3omt 
Vo  Ts qVim cos(ot   )  Vim cos(ot )  Vim cos(3it )   3  6 4 qm    …(15)
 6 4qm     ... (4)
 4  q q
VOC  qVim cos  omt    Vim cos  3omt   Vim cos  3omt 

is 0, 2  /3, 4  /3 corresponds to the output
 3 6 4qm    …(16)
Where;

phases A, B and C, respectively and

o is angular output IV. SIMULATION AND IMPLEMENTATION OF MATRIX
frequency. CONVERTER FED IM DRIVE
The equations, which was presented by Venturini algorithm
The duty cycle for switches connected between the input phase
a, b and c and output phase A, can be represented as: (3-4) has been used for calculation of duty cycle of
bidirectional switches. Fig.2 shows Simulink model of the
1 2 2q  three phase matrix converter fed induction motor drive with
TAa  Ts   2 VoAVia  sin(imt )sin(3imt )  Venturini algorithm. It basically consists of three main parts.
 3 3Vim 9 qm  … (5)
First part contains the supply voltage blocks, which is three
phase supply i.e. 120 degree phase displaced at each other.
1 2 2q 2 
TAb  Ts   2 VoAVib  sin(imt  )sin(3imt )  Second part contains generation of the duty cycles of nine
 3 3Vim 9 qm 3  … (6) bidirectional devices and finally third part consists of nine
bidirectional switches and three phase input voltages, by which
1 2 2q 4  output voltages of matrix converter can be found. Switching of
TAc  Ts   2 VoAVic  sin(imt  )sin(3imt )  all nine switches of matrix converter are calculated by
 3 3Vim 9qm 3      … (7)
equations (5) to (13).
Similarly the duty cycle for switches connected between the
input phase a, b and c and output phase B can be represented
 VA

t VB

Clock
Va
VC
speed
TBa
Subsystem
V0A
TCa
0 1

TAa V0A
Constant

Vb

TAb

TAa TBb V0B V0B

Cl ock1
Vab 2
TCb
TAb
VAB Vim 2
cons tant
clock
TAc
VBC wimt
Vc
3
Subsystem1 TBa
0.8 Vim2
TCc V0C

Constant2 V0C
TBb
TBc
wimt
TBc
TAc

2*pi*fout
TCa Subsystem2
q
Constant1
TCb

womt
TCc

Subsystem11

Fig.2:Simulink model of the matrix converter with Venturini calculated as:

algorithm
4
Vim  Vab 2  Vbc 2  VabVbc 
2

The duty cycle for switch connected between the input phase 9 ... (17)
β and output phase γ are calculated at every sampling period
with updated values to calculate the duty cycles for the Vbc
switches. For implementation of matrix converter fed i t  arctan
2 1 
induction motor drive, it is essential to measure any two of 3  Vab  Vbc 
 3 3  ... (18)
three input line-to-line voltages. Then,
Vim and i t are
where Vab,Vbc are the instantaneous input line voltages.

1
Va 2 3
4
5 TBa TCa
TAa
Vb
Switch3 Switch6
Switch 1 2
3
V0A V0B
V0C
6 7 8
TAb 0 TBb TCb
9 Switch1 0
Constant3 Switch4 Switch7
constant Constant4
10 Add Add1
Add2
Vc
11
12
13 TCc
TAc TBc

Switch5 Switch8
Switch2

Fig.3: Simulink Implementation of output voltage of matrix converter using Venturini algorithm
Hence, the duty cycle of all nine switches, which connects The instantaneous output voltages are obtained by simulink
each input phase to one output phase during one switching implementation, which is shown in Fig.3 and then these
period can be evaluated using Equations (3) and (4) (for voltages are applied to three phase induction motor.
instance these times will be tAa, tAb, tAc for output phase, A).
 V. SIMULATION RESULTS 1

S w itching State
0.8
In this paper, matrix converter fed induction motor drive using
0.6
Venturini algorithm have been simulated and implemented.
0.4
The switching of all nine bidirectional switches are shown in
0.2
Fig.4 to Fig.12. The Three phase instantaneous output voltages
0
using Venturini algorithm has been shown in Fig. 13 to 15. it 0 0.002 0.004 0.006 0.008 0.01 0.012
Time (Sec)
0.014 0.016 0.018 0.02

The proper switching of all nine bidirectional switches are

obtained at every instant as total 172 combinations of Fig.8: Switching pattern for TBb
switching has been produced to obtain instantaneous voltages 0.02
by this technique in only one cycle. The output of the three

Switching State
0.015
phase matrix converter are applied to the three phase induction
motor and the output of the simulation are given as three phase 0.01

currents, d axis and q axis current and finally motor speed in

0.005
Fig 16-18 respectively.
0
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02
1 Time (Sec)
Switching State

0.8

0.6
Fig.9: Switching pattern for TBc
0.4 1
0.2
0.8

Switching State
0
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 0.6
Time (Sec)

0.4
Fig.4: Switching pattern for TAa 0.2

1 0
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02
Time (Sec)
Switching State

0.8

0.6

0.4
Fig.10: Switching pattern for TCa
0.2 1

0
Switching State

0.8
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02
Time (Sec)
0.6

0.4
Fig.5: Switching pattern for TAb
0.2
1
0
0.8 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02
Switching State

Time (Sec)
0.6 Fig.11: Switching pattern for TCb
0.4
1
0.2
0.8
Switching State

0
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 0.6
Time (Sec)
0.4

0.2
Fig.6: Switching pattern for TAc
0
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02
1 Time (Sec)
Fig.12: Switching pattern for TCc
S w itching S tate

0.8

0.6
300
0.4
200
0.2
100
V a (V olts )

0
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 0
Time (Sec)
-100

Fig.7: Switching pattern for TBa -200

-300
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Time (sec)

Fig.13: Phase voltage A

 300 obtained from the simulation study can be applied to the
200 practical control of the matrix converter directly, which has
100 great value in practices.
V b (V olts )

0
VII. REFERENCES
-100

-200
[1] A. Alesina and M. Venturini, “ Analysis and Design of
optimum-amplitude nine switch direct AC-AC
-300
0 0.1 0.2 0.3 0.4 0.5
Time (sec)
0.6 0.7 0.8 0.9 1
converters,” IEEE Trans. Power electron., vol. 4, pp. 101-
Fig.14: Phase voltage B 112,Jan 1989.
300
[2] Ebubekir Erdem, Yetkin Tatar, Sedat Sunter, “Effects of
200 Input Filter on Stability of Matrix Converter Using
100 Venturini Modulation Algorithm, ” International
V c (V o lt s )

0
Symposium on Power Electronics, Electrical Drives,
-100
Automation and Motion, Speedam 2010, pp 1344-1349.
-200 [3] A.Zuckerberger,D.Weinstock,A.Alexandrovitz,”Simulatio
-300
n of three thase loaded matrix converter” 1EE Proc.-
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Time (sec)
Elecrr. Power Appl., Yol. 143, No. 4,J uly 1996,pp.294-
Fig.15: Phase voltage C 300.
40

30
[4] L.Gyugyi and B. Pelly, Static power frequency changers:
20 Theory, Performance and Application. New York: Wiley-
Interscience, 1976.
Current (Amp)

10

-10
[5] L.zhang, C Watthanasam and W. Shepherd, “Application
-20 of Matrix Converter for a variable- speed Wind- Turbine
-30
driving a double_ fed induction Generator,” IECON
-40
0 0.1 0.2 0.3 0.4 0.5
Time (sec)
0.6 0.7 0.8 0.9 1 Proceedings, V2.1997, pp:906-911.
Fig.16: Induction motor three phase current [6] MATLAB for Microsoft Windows (The Math Works,
40 Inc., 1993).
30

[7] C. Klumper, P. Nilesan, I. Boldea, and F. Blaabjerg, “New

C u rre n t (A m p )

20

10 steps toward a low-cost power electronic building for

0
matrix converters,” in Conf. Rec IEEE-IAS Annu.
-10
Meeting, vol. 3, Rome, Italy, Oct. 8-12,2000, pp. 1964-
1971.
-20

-30

-40
0 0.1 0.2 0.3 0.4 0.5
Time (sec)
0.6 0.7 0.8 0.9 1
[8] Lin Yong, He Yikang, “The modeling and Simulation of a
Fig.17: Induction motor dq current three-phase Matrix Converter” IEEE Trans. On Ind. App.,
350
Vol 28 No. 3, May/June, 1992, pp. 546-551.
300 [9] R. A. Gupta, R. Kumar, V. Sangtani and A. K. Bansal, “
Comparative analysis of three phase matrix converter fed
S p e e d (ra d /s e c )

250

200
induction motor drive”IEEE conference on computing,
150
communication and applications., Feb,2012,pp1-6.
100

50 [10] Neft, C.L., and Schauder,C.D., :”Theory and design of a

0 30-hp Matrix Converter ,“ . Proceedings of IEEE/IAS
-50
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
annual meeting confrence record, 1988, pp. 934.
Time(sec)

Fig.18: Induction motor speed [11] P. Ziogas, S. Khan, and M. Rashid, “Some improved force
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[12] P. WOOD, “General theory of switching power
Matrix converter modeling and simulation using Venturini
converters,” in Proc. IEEE-PESC 79,Vol. 1, pp. 3-10.
algorithm have been done. It gives the proper switching
instants of all nine bidirectional switches of matrix converter
so output of this technique is applied to three phase induction VIII BIOGRAPHIES
motor and analysis of three phase currents, d axis and q axis R. A. Gupta received B.E. and M.E. in Electrical
current, and the induction motor speed can be done. It is Engineering from MBM Engineering College, Jodhpur
clearly seen from the simulation results that the output of the (India) in 1980 and 1984 respectively. He obtained his
induction motor is same as if when three phase input applied is Ph.D. degree from IIT Roorkee, India (formerly
sinusoidal to three phase induction motor. In this paper, it was University of Roorkee) in 1996. Presently he is
observed that the most important is that the switching pattern Professor, Department of Electrical Engineering MNIT,
Jaipur. He has 27 years of teaching and research
experience. His area of specialization includes Power Electronics, Electrical
Drives & Control. He is guiding several Ph.D. & M. Tech. students in
Electrical Engineering. He has published/presented more than hundred and
seventy articles in International and National Journals/Conferences. He is
Advisor of various international journals. He has organized many conferences
& short term training programmes sponsored by AICTE/ISTE, New Delhi and
completed two research & development projects of MHRD/AICTE. He is
fellow member of the Institute of Engineers (INDIA) and member of Board of
Studies, RTU, Kota (India) and member of Board of Studies for P.G., JNV
University, Jodhpur. Dr. Gupta is Member IEEE, Fellow Member IE (INDIA),
and life member of ISTE. 

Rajesh Kumar is Associate Professor in the Department

of Electrical Engineering at the Malaviya National
Institute of Technology (MNIT), INDIA. He was Post
Doctorate in the Department of Electrical and Computer
Engineering at the National University of Singapore
(NUS), SINGAPORE. He has been active in the research
and development of Intelligent Systems and applications
more than ten years, and is internationally known for his
work in this area. Dr. Kumar has published over a hundred
and fifty articles on the theory and practice of intelligent
control, evolutionary algorithms, bio and nature inspired
algorithms, fuzzy and neural methodologies, power
electronics, electrical machines and drives. He has received the Career Award
for Young Teachers in 2002 from Government of India. Dr. Kumar is a senior
Member of IEEE, Member of IE (INDIA), Fellow Member IETE, Senior
Member IEANG and Life Member of ISTE.

Virendra Sangtani is Associate Professor in the Depart-

ment of Electrical Engineering at Anand International
College of Engineering Jaipur. He holds a M. Tech. in
Power systems from Malaviya National Institute of
Technology(MNIT), Jaipur. Presently, he is a research
scholar in Department of Electrical Engineering of MNIT,
Jaipur (INDIA). He has published more than fifteen
research paper publications in national & international
conferences. He is Life Member of Indian Society of
Technical Education (ISTE). His field of interest includes
power electronics, electric drives and control.
Ajay Kumar Bansal is Director and Associate
Professor in the Department of Electrical Engineering at
the Poornima Institute of Engineering & Technology,
Jaipur. He holds a M. Tech. in Power systems from
Malaviya National Institute of Technology(MNIT),
Jaipur. Presently, he is a research scholar in Department
of Electrical Engineering of MNIT, Jaipur (INDIA). He
has been active in the research and development of
Power Electronics drives and hybrid energy systems for
more than five years. Mr. Bansal has published more than twenty research
paper publications in national & international journals/ conferences. He is
Member of IEEE, Associate member of Institute of Engineers (INDIA) and
Life Member of Indian Society of Technical Education (ISTE). His field of
interest includes power electronics, drives, intelligent control, neural networks
and hybrid energy systems.