Ahmed Abdelrehim Abstract—This paper discusses the indirect space vector modulation for a four-leg matrix converter. The four-leg matrix converter has been proven to be a reliable, cost-effective, and compact power electronic interface to supply unbalanced or nonlinear loads. However, the added fourth leg has shifted the inverter side modulation from simple two-dimension SVM into complex three-dimension. This paper employs a new technique to implement indirect 3D SVM in digital controllers with further simplification in the modulation process. Moreover, Simulink simulation using repetitive controller has been performed to regulate the output voltage for 400 Hz Power supplies.

1. Engineering, Technology & Applied Science Research Vol. 8, No. 2, 2018, 2847-2852 2847
www.etasr.com Abdelrehim et al.: Indirect 3D-Space Vector Modulation for a Matrix Converter
Indirect 3D-Space Vector Modulation for a Matrix
Converter
Ahmed Abdelrehim
Department of Electrical Engineering
Alexandria University
Alexandria, Egypt
ahmed.abdelrehim@siemens.com
Mohamed El-Habrouk
Department of Electrical Engineering
Alexandria University
Alexandria, Egypt
eepgmme1@yahoo.com
Samir Deghedie Erfan
Department of Electrical Engineering
Alexandria University
Alexandria, Egypt
deghedie@gmail.com
Karim Hassan Youssef
Department of Electrical Engineering
Alexandria University
Alexandria, Egypt
khmyoussef@yahoo.com
Abstract—This paper discusses the indirect space vector
modulation for a four-leg matrix converter. The four-leg matrix
converter has been proven to be a reliable, cost-effective, and
compact power electronic interface to supply unbalanced or
nonlinear loads. However, the added fourth leg has shifted the
inverter side modulation from simple two-dimension SVM into
complex three-dimension. This paper employs a new technique to
implement indirect 3D SVM in digital controllers with further
simplification in the modulation process. Moreover, Simulink
simulation using repetitive controller has been performed to
regulate the output voltage for 400 Hz Power supplies.
Keywords-repetitive controller; 3D SVM; four-leg matrix
converter
I. INTRODUCTION
The matrix converter is a static and direct AC to AC
converter with unique features of unity input power factor, high
power to volume ratio, high reliability and MTBF factor which
has gained interest in applications aiming to produce a
realization of a compact three-phase drive for military,
industrial and aerospace systems [1-3]. Moreover, researchers
utilized the matrix converter as an electronic interface layer
between all resources (wind, solar, storage, etc.) of the energy
matrix model and as an electronic transformer competing with
the traditional magnetic transformer. The added fourth leg is
placed to provide a return path for the zero-sequence current
during unbalancing and add the capability of supplying
different connected single-phase loads. Four-leg converters
have a superior ability to produce balanced output voltage
waveform even under severely unbalanced load or non-linear
load conditions [4]. A four-leg matrix converter topology is
shown in Figure 1. This paper investigates the indirect space
vector modulation which decouples the modulation into two
stages (rectifier + inverter) without intermediate energy
storage. This decoupling is efficient and allows separate control
to each stage, while as there is no intermediate energy storage,
a proper synchronization between the two stages is mandatory
to fulfill the power balance equation as instantaneous input
power shall be equal to the instantaneous output power for the
load [5]. At high-frequency applications with precise control
requirements as for naval and aerospace applications where the
115V-400Hz system is commonly used, traditional controllers
have failed to achieve a proper regulation, due to the limited
bandwidth so the repetitive controller is introduced as an
optimum solution for this control problem [6].
II. MATRIX CONVERTER MODEL
Matrix converter can be represented mathematically by
matrix M and switches are identified as , where X is the
output phase, Y is the input phase and S is the linking switch
between input and output. Rectifier switches are numbered
from to while inverter side switches are numbered from
to . The rectifier is represented in Figure 1. Governing
equations are:
Vout=M*Vin (1)
Iout=MT
*Iin (2)
Vout=Mi*VDC (3)
VDC=MR*Vin (4)
Vout=Mi*MR*Vin (5)
where , , , , , , , and are
output voltage, input voltage, output current, input current, DC
intermediate voltage, inverter side switching matrix, rectifier
side switching matrix, matrix converter switching matrix and
transposed matrix converter switching matrix respectively.
and Mi are described by (6) and (7) respectively:
=
1 3 5
2 4 6
(6)

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Fig. 1.
M =
S7 S8
S9 S1
S11 S1
S13 S1
M equals to M
M =
S7 S8
S9 S10
S11 S12
S13 S14
Equation (8)
=
S1 ∗ S7 S2
S1 ∗ S9 S2
S1 ∗ S11 S2
S1 ∗ S13 S2
=
SaA SaB
SbA SbB
ScA ScB
SnA SnB
In Figure 1 v
The mathema
Fig. 2.
III. INDIREC
Indirect spac
litting the mo
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hieve decoupl
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sumption of vi
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Schematic of a f
8
10
12
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Mi*MR:
8
0
2
4
*
S1 S3 S5
S2 S4 S6
can be further
∗ S8 S3 ∗ S7
∗ S10 S3 ∗ S9
∗ S12 S3 ∗ S11
∗ S14 S3 ∗ S13
SaC
SbC
ScC
SnC
voltages are: V
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CT SPACE VECT
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four-leg direct ma
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7 S4 ∗ S8 S
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(7)
(8)
into
S5 ∗ S7 S6 ∗ S8
5 ∗ S9 S6 ∗ S10
5 ∗ S11 S6 ∗ S1
5 ∗ S13 S6 ∗ S1
(9)
V =
V
V
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.
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rix converter
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Figures 6-7).
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en P=2
en P=3
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Vol. 8, No. 2, 20
al.: Indirect 3D
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300<θ<36
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018, 2847-2852
D-Space Vector M
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distributed into
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n P=5
n P=6, where θ
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witching vectors i
entification for 3D
tribution into each
ation is define
ection of sw
nearest referen
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alculate the du
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2849
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θ= tan
as shown in F
in αβγ coordinatio
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h prism
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witching vecto
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from Mi and MR
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fully develop
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irect 3D SVM
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igures
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A.
Vol. 8, No. 2, 20
al.: Indirect 3D
Source sys
Load syst
Switching freq
Input filter
Output filter
Repetitive Contr
Tracking con
Unbalanced
Balanced l
Nonlinear l
Non-Linear L
Fig. 12. FF
018, 2847-2852
D-Space Vector M
TABLE I.
tem
em
quency
(LC)
r (LC)
roller Q(z)
ntroller
d load 5Ω
load
load
Load
Fig. 10. O
(a) P
(b) P
(c) P
(d) N
Fig. 11. O
FT analysis for ou
2
Modulation for
SYSTEM PARAM
440V
115V-
1280
56Ω/0.8m
180uH+70
1.72377
1.663
1.868
Ω+5.5mH, 10Ω+6
5Ω +5
3phase diode
Output voltage
Phase A
Phase B
Phase C
Neutral
Output current
utput phase voltag
2850
r a Matrix Con
METERS
V-60Hz
-400Hz
00Hz
mH/10uF
0uH/100uF
2 1
76 0.75754
3 0.9914
8 0.8735
6.2mH, 20Ω+7.5m
5.5 mH
e bridge +50Ω
ge (THD=3.3%)
verter
mH

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Fig. 13.
Unbalanced
Fig. 17. Inp
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FFT analysis fo
Fig. 14.
Load
Fig. 15.
(a) P
(b) P
(c) P
(d)
Fig. 16. O
put current multip
y & Applied Sci
or output current
Error signal
Output voltage
Phase A
Phase B
Phase C
Neutral
Output Currents
plied by factor 50
ience Research
A
(THD=1.8%)
and input voltage
h V
Abdelrehim et a
e
C.
Vol. 8, No. 2, 20
al.: Indirect 3D
Fig. 19.
Fig. 20. FF
Non Linear L
F
Fig. 22.
018, 2847-2852
D-Space Vector M
Fig. 18.
FFT analysis fo
FT analysis for ou
Load
Fig. 21. Output
FFT analysis fo
2
Modulation for
Error signal
or input current (T
utput phase voltag
t voltage 115V/40
or input current (T
2851
r a Matrix Con
THD=48%)
ge (THD=3.3%)
00H
THD=48%)
verter

6. mo
bee
con
lim
(11
con
eff
rep
vo
[1]
[2]
[3]
[4]
[5]
[6]
[7]
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Fig
Fig. 25. Inp
This paper
odulation for
en implement
ntroller was s
mited bandw
15V/400Hz).
nditions (bal
fectiveness o
petitive contro
ltage in an exc
P. Zanchetta,
Empringham, “
AC power s
Electronics Sp
16, 2005
C. Klumpner,
process of th
Electronics Sp
1083–1088, Ju
D. Casadei, G
torque control
Electronics, Vo
F. Yue, P. W. W
space vector m
Electronics Co
R. Zhang, Hig
unbalanced loa
State Universit
R. Cárdenasa,
control system
Electric Power
T. Friedli, J.
evaluation of t
back-to-back
Electronics, Vo
ng, Technology
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Fig. 23.
. 24. Repetitive
put current multip
VI. C
introduced th
four-leg matri
ted and simu
selected to reg
width for
The simulat
anced, unbal
f the propos
oller showed t
cellent way.
REFE
J. C. Clare, P.
“Control Design
upply using ge
pecialists Confere
F. Blaabjerg, P
he matrix conve
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three-phase AC–A
converter system
ol. 59, No. 12, pp
y & Applied Sci
Output current
e controller outpu
plied by factor 50
CONCLUSION
he design of
ix converter, c
ulated in Sim
gulate the out
high-freque
tion results
lanced, nonlin
sed modulati
the ability to
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