Paper Title (use style: paper title)
Journal of Renewable Energy and Sustainable Development (RESD) June 2015 - ISSN 2356-8569
30
RESD © 2015
http://apc.aast.edu
A review of Indirect Matrix Converter Topologies
Lazhar Rmili
1
, Salem Rahmani
1
, Kamal Al-Haddad
2
1
Laboratory of Biophysics and Medical Technology (BMT),
ISTMT of the University of Tunis El-Manar, Tunisia
Av. Dr. Zouhaier Essafi, 1006, Tunisia
rmili_lazhar@yahoo.fr, rsalem02@yahoo.fr
2
Canada Research Chair in Energy Conversion and Power Electronics CRC-ECPE,
École de Technologie Supérieure, 1100 Notre-Dame, Montréal, Québec H3C 1K3, Canada
kamal@ele.etsmtl.ca
I. INTRODUCTION
Matrix converter is a new generation of the direct
power converter controlling the output voltage,
amplitude and frequency. It has an adjustable
power factor to control the input, regardless of the
load. The absence of heavy and susceptible-to-
failure capacitors, matrix converters can perform
operations at high temperature, gain reliability,
control input and output current and adjust voltage
sine waves with an adjustable phase shift. These are
considered some advantages of this type of
converters. The controlling of output voltage,
amplitude and frequency represents one more
advantage over the previously mentioned
advantages and over other types of converters as
well. Those advantages promote the integration of
this new topology in several areas of industrial
applications. For example, aerospace industries
have a great interest in that converter [1], [2], marine
propulsion industries, electrical drive machines with
variable speed [3]-[10], embedded systems and
other fields of renewable energy which are based on
wind and fuel cells [11]-[14].
Various research works on the topologies of
matrix converters, led to the discovery of appropriate
structures that minimize the number of semi-
conductors. Two types of topologies for the matrix
converter have been established by researchers
including direct and indirect matrix converter
topologies [15]-[26]. It has been shown that the
indirect topology is handled easier. Other studies
have been published on the design of multilevel and
Z-Source Matrix Converters.
In previous work [24], authors showed the
primary concerns of the MCs on bidirectional
switches as well as the direct MC topologies and
associated modelling. In this paper, the indirect
topologies for MCs are investigated. Various
features of those topologies are studied and a brief
summary of the research will be shown at the end.
II. INDIRECT MATRIX CONVERTER
TOPOLOGY
A new topology, developed in the early 2000s,
can be proposed as an alternative to the matrix
converter. This configuration consists of a
combination of two conventional converters through
a fictitious intermediate floor without capacitive
storage element. It is called "double stage
converter". The first floor is a controlled rectifier
directly connected to the second floor, which
consists of a voltage inverter, traditionally used in
variable speed AC machines as presented in figure
1.
This indirect converter topology has two stages:
- Rectifier stage and inverter stage
The rectifier stage is formed of two switching
cells, denoted (R) and (R'), modeled by the (1). One
switch is closed at each switching time for both cells;
this condition is expressed by the relation (2).
(1) (1)
Where …. is the connection matrix of the
rectifier.
Abstract— Matrix Converter (MC) is a modern direct
AC/AC electrical power converter without dc-link capacitor.
It is operated in four quadrants, assuring control of
the output voltage, amplitude and frequency. The matrix
converter has recently attracted significant attention
among researchers and it has become increasingly
attractive for applications of wind energy conversion,
military power supplies, induction motor drives, etc.
Recently, different MC topologies, which have their own
advantages and disadvantages, have been proposed
and developed. Matrix converter can be classified as
direct and indirect structure. In this paper, the indirect
MCs are reviewed. Different characteristics of the
indirect MC topologies are mentioned to show the
strengths and weaknesses of such converter topologies.
Keywords— Matrix converter; AC/AC conversion;
topologies; bidirectional switches;
Journal of Renewable Energy and Sustainable Development (RESD) June 2015 - ISSN 2356-8569
31
RESD © 2015
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(2)
The operation of the rectifier is described by (3)
and (4).
(3)
(4)
The inverter stage of the indirect matrix converter
consists of three switching cells called a, b, c as
shown in figure 1. This floor is modeled by equation
(5) and satisfies the constraints described by (6).
(5)
Where … is the connection matrix of the
inverter stage.
p
o
ia
ib
ic
va
vb
vc
vp
vo
Udc
idc
-idc
SA SB SC
S’A S’B S’C
Sa Sb Sc
S’a S’b S’c
Cell
R
Cell
R’
Cell
a
Cell
b
Cell
c
vA
vB
vC
iA
iB
iC
Fig. 1. Dual-stage indirect matrix converter
Every rectifier switch may be one of the following
switches Fig. 2
(6)
The inverter operation is set by the relations (7)
and (8).
Transistors with common emetters
Transistors with common collectors
Transistor associated with a diode bridge RB-IGBT structure
(a) (b)
(e)
(c) (d)
:
(f )
(g) Hybride strcture
Transistor and diode in series Transistor and diode in series
Fig.2. Different topologies of the bidirectional switches
(7)
(8)
The connection matrix of two-stage matrix
converter named is obtained by the product of
the connecting matrices of the inverter and rectifier,
as shown in equation (9).
(9)
A tie between two matrices connections can be
established as shown in (10).
(10)
In the same manner as the direct matrix converter,
(9)
(10)
Journal of Renewable Energy and Sustainable Development (RESD) June 2015 - ISSN 2356-8569
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RESD © 2015
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a formulation based on modulation of the switches
may also be set for the dual stage matrix converter.
The equations described above in "connection
function" are transposed in "modulation function"
and the conversion matrices defined by the
modulation functions of each stage of "dual-stage"
matrix converter are described by (11), (12) for the
rectifier stage and (15), (16) for the inverter stage.
where represents the conduction time of
switch ( ) during the commutation period .
(11)
(12)
The laws of conversion of electrical values,
whatsoever voltage/voltage or current/current are set
by relations (13), (14) for the recovery block and
(17), (18) for the inverter stage.
(13)
(14)
(15)
(16)
(17)
(18)
Product conversion matrices of inverter and
rectifier stages are the conversion matrix of "double
stage" matrix converter, denoted It is
expressed by (19).
As explained before; there is a relationship
between "modulation functions" of the direct matrix
converter and the indirect matrix converter, which is
the equality of two conversion matrices according to
(20).
where represents the conduction time
of switch ( ) during the commutation period .
Matrix converter « dual-stage »
Ultra-sparseVery-sparseSparseIndirect With Inverter
stage
With IGBT switch
Two antiparallel
RB-IGBT
RB-IGBT and IGBT
in antiparallel
With RB-IGBT switch
Fig. 3. Different indirect MC topologies
This two-stage indirect matrix converter structure
developed by “J.W. Kollar” has a major advantage
which is the ability to minimize the number of power
transistors. The different topologies derived from
indirect dual-stage MC have been shown in figure 3.
Based on the two-stage indirect MC configuration,
the following topologies have been derived:
A. Indirect matrix converter:
The configuration shown in figure 4 includes a
rectifier stage comprising six bidirectional switches
connected to a common emitter or common
collector. This configuration generates less switching
and conduction losses compared to other
(19)
(20)
Journal of Renewable Energy and Sustainable Development (RESD) June 2015 - ISSN 2356-8569
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RESD © 2015
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configurations. It has a complex control for the
number of switches to handle. All this leads to the
development of other configurations with the aim of
reducing the number of required transistors which
facilitates the monitoring and control of the matrix
converter.
Inverter stageRectifier stage
Fig. 4. Indirect matrix converter (19)
B. Sparse matrix converter:
The configuration shown in figure 5, leads to
remove an IGBT from each arm of the rectifier, so
three components will be eliminated totally
compared to the previous configuration, which
facilitates the development of control algorithm of the
converter. Conduction losses will be greater than
those generated by the first configuration since three
transistors and diodes are working during the
feeding phase of the load as well as two transistors
and two diodes in the feedback phase to the
network.
Fig. 5. Sparse Matrix converter
C. Very-Sparse matrix converter:
The structure of this topology illustrated in figure 6
is based on the implementation of bidirectional IGBT
switches connected to a diode bridge, where the
number of the controlled components in the rectifier
is reduced compared to the two configurations
mentioned above. Each active element of the
rectifier requires the activation of a transistor with
two diodes in each commutation phase, the rectifier
requests two transistors and four diodes, bearing in
mind that conduction losses are then a matter of
importance.
Fig. 6. Very-Sparse Matrix Converter
D. Ultra-Sparse Matrix Converter:
In this configuration, the least number of switches
is employed. There is a single switch via input phase
as shown in figure 7. In each arm, one transistor and
two diodes are controlled. This structure generates
similar conduction losses to those produced by the
"Very- Sparse" structure. Yet, this configuration does
not allow bi-directional power flow which limits its
practical application.
Fig. 7. Ultra-Sparse matrix converter
E. Matrix Converter "to inverter stage"
The first stage of this configuration includes a
rectifier in cascade with an inverter circuit as shown
in figure 8. This structure has many controlled
components than the "Sparse" topology. It creates
additional switching losses and has a high
complexity level in control. Consequently, this
configuration will not be an objective study.
Fig. 8. Matrix converter with rectifier stage
F. Matrix Converter based on RB-IGBT:
The structure shown in figure 9 incorporates RB-
IGBTs into the rectifier stage with advantages like
reduction of conduction losses. The poor diode
recovery behavior of the RB-IGBT is of less concern
here than in a matrix converter because it is possible
Journal of Renewable Energy and Sustainable Development (RESD) June 2015 - ISSN 2356-8569
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RESD © 2015
http://apc.aast.edu
to switch the rectifier stage at zero current as soft
switching pattern. At low switching frequencies, a
matrix converter built with RB-IGBTs will be more
efficient than the one built with IGBTs.
Fig. 9. Matrix converter or rectifier unit switches are based on RB-
IGBT
G. Matrix Converter based hybrid switches:
The topology of matrix converter using hybrid bi-
directional switches in the rectifier stage (as shown
in figure 10), provides low conduction losses in
motoring operation as well as soft turn-on
commutation of the RB-IGBTs, whereas in the
rectifier stage the standard IGBTs and diodes
provide low switching losses in regenerative
operation.
Fig. 10. Matrix converter or rectifier unit switches are based on a
RB-IGBT on anti-parallel to an IGBT with a series diode
Table 1 shows the summary of the above-
mentioned MC topologies considering various points
including some elements such as a number of
components, power losses, control strategy
complexity and reversibility.
III. SIMULATION RESULTS
The SimPowerSystem toolbox of MATLAB has
been used as the simulation tool. The simulation
results before and after compensation of the three-
level sparse matrix converter feeding an RL load as
illustrated in Fig.11, also shown in Figs.12 to 17.
Table II gives the system parameters used in the
simulations.
va
vb
vc
Lin-f
Lo-f
cin-f co-f
Load
R-L
ie
vs is
Fig. 11. Three-level Sparse Matrix Converter
Table 1. Summary of the indirect topologies features
Figs.12 (a)-(b) show the phase a input current (ie)
and its harmonic spectrum, respectively. The input
current has a THD of 75.33%. The output voltage
(vs) of phase (a), and its harmonic spectrum (output
voltage THD of 92.21%) are shown in figs.13 (a)-(b),
respectively. Figs.14 (a)-(b) show the phase (a)
output current (is) and its harmonic spectrum. The
output current THD is 2.43%. An input and output LC
filters are necessary to compensate the high-
frequency ripple from the input currents and output
voltages. Thus, an LC filter is connected at the input
side to avoid overvoltage and to filter the high-
frequency ripple from the input currents. Similarly, on
the other side, an output LC filter is connected
between the converter and the load which allows
controlling the output voltage and mitigates its
harmonics. Figs. 15 (a) and (b) show the phase (a)
input current and its harmonic spectrum after
filtering. The measured THD of the input current in
phase (a) is reduced from 75.33% before
compensation to 1.78% after compensation. It is
important to notice that the input current is kept free
of harmonics.
Topology
Numbe
r of
transist
ors
Number
of
diodes
Energetic
losses
Reversibi
lity power
Control
Indirect
Matrix
18 18 low yes
fairly
complic
ated
Sparse 15 18 important yes
fairly
complic
ated
Very-
Sparse
12 12 low yes easy
Ultra-
sparse
9 18 low No easy
With Stage
inverter
14 14 important yes
complic
ated
Based on
RB-IGBT
18 18 low yes
fairly
complic
ated
Based-on
Hybrid
switches
18 18 average yes easy
Journal of Renewable Energy and Sustainable Development (RESD) June 2015 - ISSN 2356-8569
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RESD © 2015
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0.6 0.61 0.62 0.63 0.64 0.65 0.66 0.67
-20
0
20
Time (s)
ie
(
A
)
0 10 20 30 40 50 60 70 80 90 100
0
20
40
60
80
100
120
Harmonic order
Fundamental (50Hz) = 13.45 , THD= 75.33%
M
a
g
(
%
o
f
F
u
n
d
a
m
e
n
t
a
l)
(a)
0.6 0.61 0.62 0.63 0.64 0.65 0.66 0.67
-20
0
20
Time (s)
ie
(
A
)
0 10 20 30 40 50 60 70 80 90 100
0
20
40
60
80
100
120
Harmonic order
Fundamental (50Hz) = 13.45 , THD= 75.33%
M
a
g
(
%
o
f
F
u
n
d
a
m
e
n
ta
l)
(b)
Fig. 12. (a) Waveform of phase a input current (ie) of three-phase
three-level sparse matrix converter before filtering, (b) Harmonic
spectrum of input current.
0.6 0.61 0.62 0.63 0.64 0.65 0.66 0.67
-400
-200
0
200
400
Time (s)
V
s
(
V
)
0 10 20 30 40 50 60 70 80 90 100
0
20
40
60
80
100
120
Harmonic order
Fundamental (50Hz) = 205 , THD= 92.21%
M
a
g
(
%
o
f
F
u
n
d
a
m
e
n
ta
l)
(a)
0.6 0.61 0.62 0.63 0.64 0.65 0.66 0.67
-400
-200
0
200
400
Time (s)
V
s
(
V
)
0 10 20 30 40 50 60 70 80 90 100
0
20
40
60
80
100
120
Harmonic order
Fundamental (50Hz) = 205 , THD= 92.21%
M
a
g
(
%
o
f
F
u
n
d
a
m
e
n
ta
l)
(b)
Fig. 13. (a) Waveform of phase a output voltage (vs) of three-
phase three-level sparse matrix converter before filtering, (b)
Harmonic spectrum of output voltage
0.6 0.61 0.62 0.63 0.64 0.65 0.66 0.67
-20
0
20
Time (s)
i
s
(
A
)
0 10 20 30 40 50 60 70 80 90 100
0
20
40
60
80
100
120
Harmonic order
Fundamental (50Hz) = 19.56 , THD= 2.43%
M
a
g
(
%
o
f
F
u
n
d
a
m
e
n
t
a
l
)
(a)
0.6 0.61 0.62 0.63 0.64 0.65 0.66 0.67
-20
0
20
Time (s)
is
(
A
)
0 10 20 30 40 50 60 70 80 90 100
0
20
40
60
80
100
120
Harmonic order
Fundamental (50Hz) = 19.56 , THD= 2.43%
M
a
g
(
%
o
f
F
u
n
d
a
m
e
n
ta
l)
(b)
Fig. 14. (a) Waveform of phase a output current (is) of three-
phase three-level sparse matrix converter before filtering, (b)
Harmonic spectrum of output current.
0.6 0.61 0.62 0.63 0.64 0.65 0.66 0.67
-20
0
20
Time (s)
ie
(
A
)
0 10 20 30 40 50 60 70 80 90 100
0
20
40
60
80
100
120
Harmonic order
Fundamental (50Hz) = 26 , THD= 1.78%
M
a
g
(
%
o
f
F
u
n
d
a
m
e
n
ta
l)
0.6 0.61 0.62 0.63 0.64 0.65 0.66 0.67
-20
0
20
Time (s)
ie
(
A
)
0 10 20 30 40 50 60 70 80 90 100
0
20
40
60
80
100
120
Harmonic order
Fundamental (50Hz) = 26 , THD= 1.78%
M
a
g
(
%
o
f
F
u
n
d
a
m
e
n
ta
l)
(b)
Fig. 15. (a) Waveform of phase a input current of three-phase
three-level sparse matrix converter after filtering, (b) Harmonic
spectrum of input current.
The waveforms and harmonic spectra of output
voltage and current waveforms after filtering are
shown in (figs.16 and 17) respectively. The output
filter reduces the THD in the output voltage from
92.21% to 0.26%. The THD of the output current in
phase (a) is therefore reduced from 2.43% without
output filter to 0.15% after filtering. These results
show the output LC filter capability to compensate
harmonics of output voltages and output currents.
0.6 0.61 0.62 0.63 0.64 0.65 0.66 0.67
-200
0
200
Time (s)
V
s
(
V
)
0 10 20 30 40 50 60 70 80 90 100
0
20
40
60
80
100
120
Harmonic order
Fundamental (50Hz) = 265.3 , THD= 0.26%
M
a
g
(
%
o
f
F
u
n
d
a
m
e
n
ta
l)
(a)
0.6 0.61 0.62 0.63 0.64 0.65 0.66 0.67
-200
0
200
Time (s)
V
s
(
V
)
0 10 20 30 40 50 60 70 80 90 100
0
20
40
60
80
100
120
Harmonic order
Fundamental (50Hz) = 265.3 , THD= 0.26%
M
a
g
(
%
o
f
F
u
n
d
a
m
e
n
ta
l)
(b)
Fig.16. (a) Waveform of phase a output voltage of three-phase
three-level sparse matrix converter after filtering, (b) Harmonic
spectrum of output voltage
0.6 0.61 0.62 0.63 0.64 0.65 0.66 0.67
-20
0
20
Time (s)
is
(
A
)
0 10 20 30 40 50 60 70 80 90 100
0
20
40
60
80
100
120
Harmonic order
Fundamental (50Hz) = 25.31 , THD= 0.15%
M
a
g
(
%
o
f
F
u
n
d
a
m
e
n
t
a
l)
(a)
0.6 0.61 0.62 0.63 0.64 0.65 0.66 0.67
-20
0
20
Time (s)
is
(
A
)
0 10 20 30 40 50 60 70 80 90 100
0
20
40
60
80
100
120
Harmonic order
Fundamental (50Hz) = 25.31 , THD= 0.15%
M
a
g
(
%
o
f
F
u
n
d
a
m
e
n
ta
l)
(b)
Fig.17. (a) Waveform of phase a output current of three-phase
three-level sparse matrix converter after filtering, (b) Harmonic
spectrum of output current
(a)
Journal of Renewable Energy and Sustainable Development (RESD) June 2015 - ISSN 2356-8569
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Table 2. Specification Parameters
Circuit
Specifications
Value
Input side ,
Load ,
Input filter
, ,
Output filter
, ,
Output side ,
Ratio 0.825
Switching frequency
IV. CONCLUSION
This paper proves that the dual stage MC topology
has been studied and analyzed. Different topologies
based on dual stage configuration of MC have been
illustrated. The brief summary at the end shows
some facts and characteristics of the afore-
mentioned topologies which would be useful for
future applications on MC topologies and control
aspects. As mentioned before, MC has two main
topologies including direct and indirect ones. The
comparison between these two topologies made it
clear that the two-stage matrix converters have
advantages over the direct or conventional ones. For
example, the possibility of reducing the number of
switches forming the converter enables consumers
to reduce the switching power losses and
manufacturing cost as well. Less switching
difficulties occurs because switches of the input
stage (rectifier) can be turned on by the application
of the zero vector current. The second stage is
controlled as a standard inverter and the Clamp
circuit can be simplified only by a capacitor in series
with a diode which is not compatible with the direct
matrix converter topology. Simulation results for an
RL load supplied via a sparse matrix converter with
the PWM modulation show that output voltage is
controllable with corresponding improvements in
power quality and the unity displacement power
factor is achieved at the input stage. Eventually,
these studies offer a very wide field of research,
especially in the study of reliability, maintainability,
availability; faults tolerances and stability of these
types of converters.
REFERENCES
[1] Alesina, A. and Venturini, M. (April 1988) Intrinsic
Amplitude Limits and Optimum Design of 9-switches
direct PWM AC-AC converters, Proceedings of Power
Electronic Specialist Conference, vol. 2, pp. 1284 –
1291.
[2] Alesina, A. and Venturini, M. (January 1989) Analysis
and Design of Optimum Amplitude Nine-Switch Direct
AC- AC Converters, IEEE Transactions on Power
Electronics, vol. 4, no.1, pp. 101-112.
[3] Alesina, A. and Venturini, M. (1980) Generalised
Transformer: A New Bidirectional, Sinusoidal
Waveform Frequency Converter with Continuously
Adjustable Input Power Factor, IEEE Power
Electronics Specialists Conference, pp. 242-252.
[4] Rmili, L., Rahmani, S., Fnaiech, F. and Al-Haddad, K.
(2013) Space Vector Modulation Strategy for a Direct
Matrix Converter, In Proc.14th international
conference on Sciences and Techniques of Automatic
control & computer engineering - STA'2013, pp.1-6.
[5] Bradaschia, F., Cavalcanti, M., Neves, F. A. and
Helber, E. P. (April 2009) A Modulation Technique to
Reduce Switching Losses in Matrix Converters”, IEEE
Transactions on Industrial Electronics, vol. 56, no. 4,
pp. 1186-1195.
[6] Choi, J. and Sul, S. (1995) A New Compensation
Strategy Reducing Voltage/Current Distortion In PWM
VSI Systems Operating With Low Voltages”, IEEE IAS
Annual Meeting, vol.31, pp. 1001-1008.
[7] Kang, J., Yamamoto, E., Ikeda, M. and Watanabe, E.
(November 2011) Medium-Voltage Matrix Converter
Design Using Cascaded Single-Phase Power Cell
Modules, IEEE Transactions on Industrial Electronics,
vol. 58, no. 11, pp. 5007-5013.
[8] Garcés, A. and Molinas, M. (January 2012) A Study of
Efficiency in a Reduced Matrix Converter for Offshore
Wind Farms, IEEE Transactions on Industrial
Electronics, Vol. 59, no. 1, pp. 184-193.
[9] Klumpner, A. and Blaabjerg, F. (October 2003) Using
Reverse Blocking Igbts in Power Converters for
Adjustable Speed Drive, Proceedings of IEEE
Industry Applications Conference, vol. 3, pp. 1516 –
1523.
[10] Klumpner, A., Nielsen, P., Boldea, I. and Blaabjerg, F.
(April 2002) A New Matrix Converter Motor (Mcm) for
Industry Applications, IEEE Transactions on Industrial
Electronics, vol. 49, pp. 325 – 335.
[11] Changliang, X., Yan, Y., Song, P. and Tingna, S.
(January 2012) Voltage Disturbance Rejection for
Matrix Converter-Based PMSM Drive System Using
Internal Model Control, IEEE Transactions on
Industrial Electronics, vol. 59, no. 1, pp. 361-372.
[12] Ortega, C., Arias, A., Caruana, C., Balcells, J. and
Asher, G. M. (June 2010) Improved Waveform Quality
in the Direct Torque Control of Matrix- Converter-Fed
PMSM Drives, IEEE Transactions on Industrial
Electronics, vol. 57, no. 6, pp. 2101-2110.
[13] Daning, Z., Sun, K., Huang, L., and Sasagawa, K.
(2005) A Novel Commutation Method of Matrix
Converter Fed Induction Motor Drive Using RBIGBT,
Fourtieth. IEEE IAS Industry Applications Society
Annual Meeting, pp. 2347-2354.
[14] Casadei, D., Serra, G., Tani, A., Trentin, A. and Zarri,
L. (October 2005) Theoretical and Experimental
Investigation on the Stability of Matrix Converters,
IEEE Transactions on Industrial Electronics, vol. 52,
no. 5, pp. 1409-1419.
[15] Yue, F., Wheeler P., and Clare, J. (March 2006)
Relationship of Modulation Schemes for Matrix
Converters, 3rd IET International Conference on
Power Electronics, Machines and Drives, pp. 266-
270.
[16] Rodriguez, J., Rivera, M., Kolar, J. and Wheeler, P.
(January 2012) A Review of Control and Modulation
Methods for Matrix Converters, IEEE Transactions on
Industrial Electronics, vol. 59, no. 1, pp. 58-70,.
[17] Domes, D., Hofman, W.and Lutz, J. (September 11-
14, 2005) A First Loss Evolution Using a Vertical Sic-
JFET and a Conventional Sic-IGBT in the Bidirectional
Journal of Renewable Energy and Sustainable Development (RESD) June 2015 - ISSN 2356-8569
37
RESD © 2015
http://apc.aast.edu
Matrix Converter Switch Topology, European
Conference on power Electronics and Application.
[18] Hojabri, H., Mokhtari, H. and Chang, L. (March 2011)
A Generalized Technique of Modeling, Analysis, and
Control of a Matrix Converter Using SVD, IEEE
Transactions on Industrial Electronics, vol. 58, no. 3,
pp. 949-959.
[19] Mahlein, J. , Weigold , J. , and Simon,O. (November
29-december 2, 2001) New Concepts for Matrix
Converter Design, The 27th Annual conference of the
IEEE Industrial Electronics Society IECON, vol.2, pp
1044-1048.
[20] Ibarra, I., Kortabarria, J. , Andreu, I., Martin, M. L. and
Ibañez, P. (January 2012) Improvement of the Design
Process of Matrix Converter Platforms Using the
Switching State Matrix Averaging Simulation Method,
IEEE Transactions on Industrial Electronics, vol. 59,
no. 1, pp. 220-234.
Mahlein,J., Bruckmann , M., and Braun, M. (April
2002) Passive Protection Strategy for Drive System
with Matrix Converter and Induction Machine, IEEE
Transactions and Industrial Electronics, vol. 49, no. 2,
pp. 297-303,.
[21] Ishiguro, A., Furuhashi, T., and Okuma, S. (1991) A
Novel Control Method for Forced Commutated Cyclo-
converters Using Instantaneous Values of Input Line-
To-Line Voltage, IEEE Transactions on Industrial
Electronics, pp.166-172,.
[22] Schafmeister F. and Kolar, J. (January 2012) Novel
Hybrid Modulation Schemes Significantly Extending
the Reactive Power Control Range of All Matrix
Converter Topologies with Low Computational Effort,
IEEE Transactions on Industrial Electronics, vol. 59,
no. 1, pp. 194-210.
[23] Rmili, L., Rahmani, S., Vahedi, H. and Al-Haddad, K.
(June 2014) A Comprehensive Analysis of Matrix
Converters: Bidirectional Switch, Direct Topology,
Modeling and Control, In Proc. 23rd IEEE
International Symposium on Industrial Electronics,
IEEE-ISIE,
[24] Huang,X., Goodman, A., Gerada, C., Fang, Y. and
Lu, Q. (September 2012) A Single Sided Matrix
Converter Drive for a Brushless DC Motor in
Aerospace Applications, IEEE Transactions on
Industrial Electronics, vol. 59, no. 9, pp.3542-3552.
[25] Wheeler, P., Clare, J.C., Empringham, L., Apap, M.,
Bradley, K., Whitley C. and Towers, G. (June 2004) A
Matrix Converter Based Permanent Magnet Motor
Drive for an Aircraft Actuator System, Proceedings of
IEEE International Electric Machines and Drives
Conference, vol. 2, pp. 1295 – 1300.