Content uploaded by Sk. Moin
Author content
All content in this area was uploaded by Sk. Moin
Content may be subject to copyright.
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 48, NO. 2, MARCH/APRIL 2012 697
Space Vector PWM Technique for a
Three-to-Five-Phase Matrix Converter
Atif Iqbal, Senior Member, IEEE, Sk Moin Ahmed, Student Member, IEEE,and
Haitham Abu-Rub, Senior Member, IEEE
Abstract—Variable-speed multiphase (more than three phases)
drive systems are seen as serious contenders to the existing
three-phase drives due to their distinct advantages. Supply to
the multiphase drives is invariably given from a voltage source
inverter. However, this paper proposes an alternative solution for
supplying multiphase drive system using a direct ac–ac converter
called a matrix converter. This paper proposes the pulsewidth
modulation (PWM) algorithm for the matrix converter topology
with three-phase grid input and five-phase variable-voltage and
variable-frequency output. The PWM control technique developed
and presented in this paper is based on space vector approach.
This paper presents the complete space vector model of the three-
-to-five-phase matrix converter topology. The space vector model
yield 2
15
total switching combinations which reduce to 243 states
considering the imposed constraints, out of which 240 are active
and 3 are zero vectors. However, for space vector PWM (SVPWM)
implementation, only 90 active and 3 zero vectors can be used.
The SVPWM algorithm is presented in this paper. The viability of
the proposed solution is proved using analytical, simulation, and
experimental approaches.
Index Terms—Five-phase, matrix converter, pulsewidth modu-
lation (PWM), space vector.
I. INTRODUCTION
T
HE matrix converter is a bidirectional power flow con-
verter that uses semiconductor switches arranged in the
form of matrix array. The matrix converter has recently at-
tracted significant attention among researchers. Matrix convert-
ers offer some distinct advantages such as operation at unity
power factor for any load, controlled bidirectional power flow,
sinusoidal input and output currents, etc. A comprehensive
overview of the development in the field of matrix converter
research is presented in [1]. It is to be noted here that the
most common configuration of the matrix converter discussed
in the literature is three-phase to three-phase [2], [3]. Little
Manuscript received April 28, 2011; revised August 28, 2011; accepted
October 30, 2011. Date of publication December 23, 2011; date of current
version March 21, 2012. Paper 2011-IPCC-151.R1, presented at the 2010 IEEE
Energy Conversion Congress and Exposition, Atlanta, GA, September 12–16,
and approved for publication in the IEEE T
RANSACTIONS ON INDUSTRY AP-
PLICATIONS by the Industrial Power Converter Committee of the IEEE Industry
Applications Society. This work was supported by an NPRP grant (08-369-2-
140) from the Qatar National Research Fund (a member of the Qatar Founda-
tion). The statements made herein are solely the responsibility of the authors.
A. Iqbal is with Qatar University, 2713 Doha, Qatar, on academic leave from
Aligarh Muslim University, Aligarh, India (e-mail: atif.iqbal@qu.edu.qa).
S. M. Ahmed and H. Abu-Rub are with Texas A&M University, 23874 Doha,
Qatar (e-mail: moin.sk@qatar.tamu.edu; haitham.abu-rub@qatar.tamu.edu).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TIA.2011.2181469
attention has been paid on the development of matrix converter
with output more than three, except in [4]–[7]. The pulsewidth
modulation (PWM) technique presented in [4] for a generalized
three- to n-phase matrix converter topology is based on direct
duty ratio control. Space vector PWM (SVPWM) is discussed
in [5] for a three-to-five-phase matrix converter considering
only outer large length space vectors. In contrary, this paper
utilizes 93 space vectors for the implementation, offering better
voltage and current waveforms. Carrier-based PWM is elabo-
rated for a three-to-seven-phase matrix converter in [6] and for
a three-to-nine-phase matrix converter in [7].
The conventional structure for variable-speed drives consists
of a three-phase motor supplied by a three-phase power elec-
tronic converter. However, when the machine is connected to a
modular power electronic converter, such as a voltage source
inverter or a matrix converter, then the need for a specific
number of phases, such as three, disappears since simply adding
one leg increases the number of output phases. Nowadays, the
development of modern power electronics makes it possible to
consider the number of phases as a degree of freedom, i.e., an
additional design variable in electrical machines. Multiphase
motor drives have some inherent advantages over the traditional
three-phase motor drives, such as reducing the amplitude and
increasing the frequency of torque pulsations, reducing the
rotor harmonic current losses, and lowering the dc link current
harmonics. In addition, owing to their redundant structure,
multiphase motor drives improve system reliability. A five-
phase system has several salient features that are attractive for
industrial applications. The fault-tolerant property of a five-
phase system makes it a strong candidate for safety critical ap-
plications such as defense, hospitals, ship propulsions, traction
drive and aircraft applications, etc. The reduced volume of a
machine for higher phase number is another feature that can
be utilized in naval ship applications and mining applications
where the space requirement is stringent. Although a five-
phase system is still not used in industrial applications, it has
high potential of adoption by industries. A 15-phase induction
machine built by Alstom is now part of an electric drive system
of a British naval ship. The machine winding is reconfigurable
as five three-phase induction machines or three five-phase
induction machines. Detailed reviews on the development in
the area of multiphase (more than three phases) drive are
presented in [8]–[11]. The performance of power electronic
converters (ac to ac or ac–dc-ac) is highly dependent on their
control algorithms. Thus, a number of modulation schemes are
developed for voltage source inverters for three-phase [12],
[13] and multiphase outputs [14]–[16]. Modulation methods
0093-9994/$26.00 © 2011 IEEE
698 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 48, NO. 2, MARCH/APRIL 2012
Fig. 1. General power circuit topology of three-to-five-phase ac–ac matrix
converter.
of matrix converters are complex and are generally classified
in two different groups, called direct and indirect. The direct
PWM method developed by Alesina and Venturini [17] limits
the output to half the input voltage. This limit was subsequently
raised to 0.866 by taking advantage of third harmonic injection
[18], and it was realized that this is the maximum output that
can be obtained from a three-to-three-phase matrix converter
in the linear modulation region. Indirect method assumes a
matrix converter as a cascaded virtual three-phase rectifier and
a virtual voltage source inverter with imaginary dc link. With
this representation, the SVPWM method of VSI is extended to
a matrix converter [19]–[21]. SVPWM applied to a multilevel
matrix converter is also reported recently [22]. A carrier-based
PWM scheme is introduced recently for three-to-three-phase
matrix converter [23]–[25]. However, SVPWM is more suitable
for digital implementation.
In this paper, the SVPWM strategy is presented based on
the space vector model of the three-to-five matrix converter.
The complete space vector model is presented along with
the SVPWM algorithm. It is seen that the output voltage is
limited to 0.7886 of the input magnitude. Theoretically, this
is the maximum output magnitude that can be obtained in
this matrix converter configuration in the linear modulation re-
gion. Nevertheless, this limit can be further enhanced by using
overmodulation strategy at the expense of higher complexity.
This paper presents the simulation results which are further
validated using experimental investigation. The simulation and
experimental results match to a good extent.
II. T
HREE-TO-FIVE-PHASE MAT RIX CONVERTER
The general power circuit topology of a three-to-five-phase
matrix converter is shown in Fig. 1. There are five legs, with
each leg having three bidirectional power switches connected
in series. Each power switch is bidirectional in nature, with
antiparallel-connected IGBTs and diodes. The input is similar
to a three-to-three-phase matrix converter having LC filters,
and the output is five-phase with 72
◦
phase displacement be-
tween each phase.
The switching function is defined as S
jk
= {1 for closed
switch, 0 for open switch}, with j = {a, b, c} (input) and k =
{A, B, C, D, E} (output). The switching constraint is S
ak
+
S
bk
+ S
ck
=1.
The load to the matrix converter is assumed as a star-
connected five-phase ac machine.
III. S
PACE VECTOR MODULATION ALGORITHM
The space vector algorithm is based on the representation of
the three-phase input current and five-phase output line voltages
on the space vector plane. In matrix converters, each output
phase is connected to each input phase depending on the state
of the switches. For a three-to-five-phase matrix converter, the
total number of switches is 15.
With this number of switches, the total combination of
switching is 2
15
. For safe switching in the matrix converter, the
following rules should be observed.
1) The input phases should never be short circuited.
2) The output phases should never be open circuited at any
switching time.
Considering the aforementioned two rules, there are 3
5
, i.e.,
243, different switching combinations for connecting the output
phases to the input phases. These s witching combinations can
be analyzed in five groups.
The switching combinations are represented as {p, q, r},
where p, q, and r represent the number of output phases con-
nected to input phase A, phase B, and phase C, respectively.
1) p, q, r ∈ 0, 0, 5|p = q = r: All of the output phases are
connected to the same input phase. This group consists
of three possible switching combinations, i.e., either all
output phases connect to input phase A or input phase
B or input phase C. {5, 0, 0} represents the switching
conditions when all of the output phases connect to input
phase A. {0, 5, 0} represents the switching conditions
when all of the output phases connect to input phase B.
{0, 0, 5} represents the switching conditions when all of
the output phases connect to input phase C. These vectors
have zero magnitude and frequency. These are called zero
vectors.
2) p, q, r ∈ 0, 1, 4|p = q = r: Four of the output phases are
connected to the same input phase, and the fifth output
phase is connected to any of the other two input phases.
Here, 4 means four different output phases are connected
to input phase A. The number 1 means that one output
phase other than the previous four is connected to input
phase B and input phase C is not connected to any output
phase. As such, there exist six different switching states
({4, 1, 0}, {1, 4, 0}, {1, 0, 4}, {0, 1, 4}, {0, 4, 1}, and {4,
0, 1}). Out of these, one switching state can have further
five different combinations, i.e., every switching state
has
5
C
4
×
1
C
1
=5combinations. This group hence con-
sists of 6 × 5=30switching combinations in all. These
IQBA L et al.: SPACE VECTOR PWM TECHNIQUE FOR A THREE-TO-FIVE-PHASE MATRIX CONVERTER 699
vectors have a variable amplitude at a constant frequency
in space. It means that the amplitude of the output volt-
ages depends on the selected input line voltages. In this
case, the phase angle of the output voltage space vector
does not depend on the phase angle of the input voltage
space vector. The 30 combinations in this group deter-
mine ten prefixed positions of the output voltage space
vectors which are not dependent on α
i
. A similar condi-
tion is also valid for current vectors. The 30 combinations
in this group determine six prefixed positions of the input
current space vectors which are not dependent on α
o
.
3) p, q, r ∈ 0, 2, 3|p = q = r: Three of the output phases are
connected to the same input phase, and the two other
output phases are connected to any of the other two input
phases. As such, there exist six different switching states
({3, 2, 0}, {2, 3, 0}, {2, 0, 3}, {0, 2, 3}, {0, 3, 2}, and
{3, 0, 2}). Out of these, one switching permutation can
have further ten different combinations, i.e., every switch-
ing permutation has
5
C
3
×
2
C
2
=10combinations. This
group hence consists of 6 × 10 = 60 switching combi-
nations. These vectors also have a variable amplitude at
a constant frequency in space. The 60 combinations in
this group determine ten prefixed positions of the output
voltage space vectors which are not dependent on α
i
.A
similar condition is also valid for current vectors. The
60 combinations in this group determine six prefixed
positions of the input current space vectors which are not
dependent on α
o
.
4) p, q, r ∈ 1, 1, 3|p = q = r: Three of the output phases are
connected to the same input phase, and the two other
output phases are connected to the other two input phases,
respectively. As such, there exist three different switching
states ({3, 1, 1}, {1, 3, 1}, and {1, 1, 3}). Out of these,
each switching state can have further 20 different com-
binations, i.e., every switching permutation has
5
C
3
×
2
C
1
×
1
C
1
=20combinations. This group hence consists
of 3 × 20 = 60 switching combinations. These vectors
have variable-amplitude variable frequency i n space. It
means that the amplitude of the output voltages depends
on the selected input line voltages. In t his case, the phase
angle of the output voltage space vector depends on the
phase angle of the input voltage space vector. The 60
combinations in this group do not determine any prefixed
positions of the output voltage space vector. The locus
of the output voltage space vectors forms ellipses in
different orientations in space as α
i
is varied. A similar
condition is also valid for current vectors. For the space
vector modulation technique, these switching states are
not used in the matrix converter since the phase angle
of both input and output vectors cannot be controlled
independently.
5) p, q, r ∈ 1, 2, 2|p = q = r: Two of the output phases are
connected to the same input phase, the two other output
phases are connected to another input phase, and the fifth
output phase is connected to the third input phase. As
such, there exist three different switching states ({1, 2, 2},
{2, 1, 2}, and {2, 2, 1}). Each switching state can have
further 30 different combinations, i.e., every switching
permutation has
5
C
2
×
3
C
2
×
1
C
1
=30 combinations.
This group hence consists of 3 × 30 = 90 switching com-
binations. These vectors also have variable-amplitude
variable frequency i n space. That is, the amplitude of the
output voltages depends on the selected input line volt-
ages. In this case, the phase angle of the output voltage
space vector depends on the phase angle of the input
voltage space vector. The 90 combinations in this group
do not determine any prefixed positions of the output volt-
age space vector. The locus of the output voltage space
vectors forms ellipses in different orientations in space as
α
i
is varied. A similar condition is also valid for current
vectors. For the space vector modulation technique, these
switching states are also not used in the matrix converter
since the phase angle of both input and output vectors
cannot be controlled independently.
The active switching vectors used for the proposed SVPWM
of a three-to-five-phase matrix converter are the following.
Group 1: {5, 0, 0} consists of 3 vectors.
Group 2: {4, 1, 0} consists of 30 vectors.
Group 3: {3, 2, 0} consists of 60 vectors.
IV. S
PACE VECTOR CONTROL STRATEGY
The general topology of a three-to-five-phase matrix con-
verter is shown in Fig. 1. It consists of 15 bidirectional switches
which allow any output phase to be connected to any input
phase. Being the converter supplied by the voltage source, the
input phases could never be short circuited and, owing to the
presence of inductive loads, should not be interrupted. With
these constraints in three-phase input and five-phase matrix
converter, there are 243 permitted switching combinations.
However, the active switching vectors used for the matrix
converter modulation technique are 93. These active vectors are
divided into four groups.
Group 1: {5, 0, 0} consists of three vectors; these are called as
zero vectors.
Group 2: {4, 1, 0} consists of 30 vectors; these are called as
medium vectors.
Group 3: {3, 2, 0} consists of 30 vectors in which the two
adjacent output phases are connected to the same input
phase; these are called as large vectors.
Group 4: {3, 2, 0} consists of 30 vectors in which the two
alternate output phases are connected to the same input
phase; these are called as small vectors.
In the proposed SVPWM strategy for the t hree-to-five-phase
matrix converter, only the switching states of groups 1, 2, and
3 are utilized. The switching states in groups 4 and 5 are not
used since the corresponding switching space vectors (SSVs)
are rotating with time. Input current SSVs and output voltage
SSVs of each switching state in groups 2 and 3 are shown in
Figs. 2 and 3, respectively.
The large vectors and medium vectors are represented as “L”
and “M,” respectively. The small vectors are not considered
in this paper. The letters “L” and “M” refer to the large and
medium vectors, respectively, and the numbers in front of the
letters are the vector numbers.
700 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 48, NO. 2, MARCH/APRIL 2012
Fig. 2. Input current space vectors corresponding to the permitted switching
combinations for group 3: {3, 2, 0} (all vectors).
Fig. 3. Output voltage space vectors corresponding to the permitted switching
combinations for group 3: {3, 2, 0} (large and medium vectors).
For each combination, the input and output line voltages can
be expressed in terms of space vectors as
−→
V
i
=
2
3
V
ab
+ V
bc
· e
j
2π
3
+ V
ca
· e
j
4π
3
= V
i
· e
jα
i
(1)
−→
V
o
=
2
5
V
AB
+ V
BC
· e
j
2π
5
+ V
CD
· e
j
4π
5
+ V
DE
· e
j
6π
5
+V
EA
· e
j
8π
5
= V
o
· e
jα
O
. (2)
In the same way, the input and output line current space vectors
are defined as
−→
I
i
=
2
3
I
a
+ I
b
· e
j
2π
3
+ I
c
· e
j
4π
3
= I
i
· e
jβ
i
(3)
−→
I
o
=
2
5
I
A
+ I
B
· e
j
2π
5
+ I
C
· e
j
4π
5
+ I
D
· e
j
6π
5
+ I
E
· e
j
8π
5
= I
o
e
jβ
O
. (4)
α
i
and α
o
are the input and output voltage vector phase angles,
respectively, whereas β
i
and β
o
are the input and output current
vector phase angles, respectively. The SVM algorithm does
the following: 1) it selects appropriate switching states, and
2) it calculates the duty cycle for each switching state. During
one switching period T
s
, the switching states whose SSVs are
adjacent to the desired output voltage (input current) vector
should be selected, and the zero switching states are applied to
complete the switching period to provide the maximum output-
to-input voltage transfer ratio.
The aim of the proposed space vector control strategy is to
generate the desired output voltage vector with the constraint of
unity input power factor. For this purpose, let
−→
V
o
be the desired
output line voltage space vector and
−→
V
i
be the input line voltage
space vector at a given time. The input line to neutral voltage
vector
−→
E
i
is defined by
−→
E
i
=
1
√
3
−→
V
i
· e
−j
π
6
. (5)
In order to obtain unity input power factor, the direction of the
input current space vector
−→
I
i
has to be the same as that of
−→
E
i
.
Assume that
−→
V
o
and
−→
I
i
are in sector 1 (there are six sectors
at the input side and ten sectors at the output side as the input
side is three-phase and the output is five-phase). In Fig. 3, for
large and medium vector configurations,
−→
V
o
and
−→
V
o
represent
the components of
−→
V
o
along the two adjacent vector directions.
Similarly
−→
I
i
is resolved into components
−→
I
i
and
−→
I
i
along the
two adjacent vector directions. Possible switching states that
can be utilized to synthesize the resolved voltage and current
components (assuming that both input and output vectors are in
sector 1) are
−→
V
o
: ±10 L, ±11 L, ±12 L and ± 7M, ±8M, ±9M
−→
V
o
: ±1L, ±2L, ±3Land ± 13 M, ±14 M, ±15 M
−→
I
i
: ±3L, ±6L, ±9L, ±12 L, ±15 L and
± 3M, ±6M, ±9M, ±12 M, ±15 M
−→
I
i
: ±1L, ±4L, ±7L, ±10 L, ±13 L and
± 1M, ±4M, ±7M, ±10 M, ±13 M.
The output voltage and input current vectors can be synthesized
simultaneously by selecting the common switching states of the
output voltage components and input current components. The
common switching states are ±10 L, ±12 L, ±7M, ±9Mand
±1L, ±3L, ±13 M, ±15 M.
From two switching states with the same number but oppo-
site signs, only one should be used since the corresponding
voltage or current space vectors are in opposite directions.
Switching states with the positive signs are used to calculate the
IQBA L et al.: SPACE VECTOR PWM TECHNIQUE FOR A THREE-TO-FIVE-PHASE MATRIX CONVERTER 701
TABLE I
S
PACE VECTOR CHOICE FOR SVPWM IN DIFFERENT SECTORS
duty cycle of the switching state. If the duty cycle is positive,
the switching state with a positive sign is selected; otherwise,
the one with a negative sign is selected. The switching state
selection for implementing SVPWM can also be explained as
follows.
Owing to the small variation of the input voltage during the
switching cycle period, the desired
−→
V
o
can be approximated by
utilizing four (two medium and two large) switching configura-
tions corresponding to four space vectors in the same direction
of
−→
V
o
and one zero voltage configuration.
Among the six possible switching configurations, the two
giving the higher voltage values corresponding to large vectors
and the two giving the medium voltage values corresponding
to medium vectors with the same sense of
−→
V
o
are chosen.
In the same way, four different switching configurations and
one zero voltage configuration are used to define
−→
V
o
. With
reference to the example shown in Figs. 2 and 3, the input
voltage
−→
V
i
has a phase angle 0 ≤ α
i
≤ (π/3). In this case, the
line voltages V
AB
and −V
CA
assume the higher values. Then,
according to the switching table of large and medium vectors,
the configuration used to obtain
−→
V
o
is +10 L and −12 L f or
large vectors and +7 M and −9 M for medium vectors, while
those for
−→
V
o
are +1L,−3 L and +13 M, −15 M. These
eight space vector combination can be utilized to determine the
input current vector direction also as shown in Fig. 2. These
configurations are associated to the vector directions adjacent
to the input current vector position.
There are 60 switching combinations for different sector
combinations. These combinations for large and medium vec-
tors are shown in Table I.
Applying the space vector modulation technique, the on-
time ratio δ of each configuration can be obtained by solving
two systems of algebraic equations. In particular, utilizing the
configurations +10 L, −12 L and +7M,−9 M to generate
−→
V
o
and to set the input current vector direction, one can write
δ
+10 L
·|L|·V
ab
− δ
−12 L
·|L|·V
ca
+ δ
+7 M
·|M|·V
ab
− δ
−9M
·|M|·V
ca
= V
o
=
5
3
−−→
|V
o
|·|L + M|·sin
π
10
+ α
o
(6)
δ
+10 L
2
√
3
i
D
= I
i
=
−→
I
i
2
√
3
sin
π
6
−
α
i
−
π
6
(7)
δ
−12 L
2
√
3
i
D
= I
i
=
−→
I
i
2
√
3
sin
π
6
+
α
i
−
π
6
(8)
δ
+7 M
2
√
3
i
C
= I
i
=
−→
I
i
2
√
3
sin
π
6
−
α
i
−
π
6
(9)
δ
−9M
2
√
3
i
C
= I
i
=
−→
I
i
2
√
3
sin
π
6
+
α
i
−
π
6
. (10)
Considering a balanced system of sinusoidal supply voltages
expressed as
V
ab
= |
−→
V
i
|cos(α
i
)
V
bc
= |
−→
V
i
|cos
α
i
−
2π
3
V
ca
= |
−→
V
i
|cos
α
i
−
4π
3
. (11)
The solution of the system of (6), (7), (8), (9), and (10) gives
δ
+10 L
= q ·|L|·
10
3
√
3
sin
π
10
+ α
o
· sin
π
3
− α
i
δ
−12 L
= q ·|L|·
10
3
√
3
sin
π
10
+ α
o
· sin(α
i
)
δ
+7 M
= q ·|M|·
10
3
√
3
sin
π
10
+ α
o
· sin
π
3
− α
i
δ
−9M
= q ·|M|·
10
3
√
3
sin
π
10
+ α
o
· sin(α
i
) (12)
where q =
−−→
|V
o
|/|
−→
V
i
| is the voltage transfer r atio. L and M
correspond to large and medium vectors, respectively.
702 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 48, NO. 2, MARCH/APRIL 2012
With the same procedure, utilizing the configurations +1L,
−3 L and +13 M, −15 M to generate
−→
V
o
and to set the input
current vector direction yields
δ
+1 L
= q ·|L|·
10
3
√
3
sin
π
10
− α
o
· sin
π
3
− α
i
δ
−3L
= q ·|L|·
10
3
√
3
sin
π
10
− α
o
· sin(α
i
)
δ
+13 M
= q ·|M |·
10
3
√
3
sin
π
10
− α
o
· sin
π
3
− α
i
δ
−15 M
= q ·|M |·
10
3
√
3
sin
π
10
− α
o
· sin(α
i
). (13)
The results obtained are valid for −(π/10) ≤ α
o
≤ (π/10) and
for 0 ≤ α
i
≤ (π/3).
Applying a similar procedure for the other possible pairs of
angular sectors, the required switching configurations and the
on-time ratio of each configuration can be determined.
Note that the values of the on-time ratios (or duty cycle)
should be positive. Furthermore, the sum of the ratios must be
lower than or equal to unity. By adding (12) and (13), with the
aforementioned constraints, one can write
δ
+10 L
+ δ
−12 L
+ δ
+1 L
+ δ
−3L
+ δ
+7 M
+ δ
−9M
+δ
+13 M
+ δ
−15 M
≤ 1. (14)
The maximum value of the voltage transfer ratio can be de-
termined as q =0.7886 for a three-phase to five-phase matrix
converter. This value is the same with what was achieved in [5].
A. Maximum Output in n by m Matrix Converter
One can relate the maximum output voltage in an n-phase to
m-phase matrix converter with the maximum output achievable
in equivalent m-phase voltage source inverter and the length
of the largest space vector of n-phase voltage source inverter.
A general relationship is given as in the equation shown at
the bottom of the page. The maximum output expression for
the “n”by“m” phase matrix converter is correlated to the
“n” and “m” phase inverter. In an “n”by“m” phase matrix
converter, the input is n-phase, and the output is m-phase. It
can be reimaged as two inverters (one has an n-phase output,
and the other has an m-phase output) are connected back to
back. In case of an m-phase inverter, the maximum output in
the linear range can be written as [26]
1
{2. cos (pi/(2.m))}
.
The aforementioned term will be divided by the maximum
vector length of the n-phase inverter to obtain the maximum
output value for an “n”by“m” phase matrix converter in the
linear modulation range. The V
dc
is written in the formula of
Table II to show the exact vector length equation for an inverter.
In this case, V
dc
is equal to unity.
TABLE II
M
AXIMUM MODULATION INDEX FORMULATION
V. C OMMUTATION REQUIREMENTS
Once the phase angles of the input current and output line
voltage are known, the eight space vectors are required to
implement the SVPWM. These eight space vectors are utilized
until α
i
or α
o
will change the angular sector. One of the zero
space voltage vectors should be employed in each switching
cycle to obtain a symmetrical switching waveform. The se-
quence of switching of the resulting nine (eight active and one
zero) space vectors should be defined in order to minimize the
number of switch commutations.
With reference to the α
i
and α
o
values considered in Figs. 2
and 3, the available space vectors and their sequence of switch-
ing are listed in Table III, assuming both input and output
reference vectors in sector 1. The first column lists the different
space vectors that will be used for the SVPWM. The second
to sixth columns list the input and output phases that will be
connected during switching period. The capital letter denotes
the output phases (five-phase), and the small letter indicates the
input phases (three-phase). Sequence of application of space
vectors can be defined such that the number of switching in
Maximum possible output in n by m matrix converter =
maximum output in m-phase inverter in linear range
length of the largest space vector of n-phase inverter
IQBA L et al.: SPACE VECTOR PWM TECHNIQUE FOR A THREE-TO-FIVE-PHASE MATRIX CONVERTER 703
TABLE III
S
PACE VECTOR SWITCHING SEQUENCE
one sampling period is minimum. The switching sequence in
one sample period in s ector 1 (both input and output reference
vectors) is listed in Table III.
To obtain a symmetrical switching, at first, a zero vector
is applied, followed by eight active vectors in half sampling
period. The mirror image of the switching sequence is em-
ployed in the second half of the sampling period. The time
of applications of active and zero vectors is divided in two
portions; hence, the total time of application is also halved. It
is observed that, when applying vector +7 M after zero vector,
only one state is changed; input phase “a” is now connected to
output phase “C.” In the next transition from +7Mto+13 M,
two states are changed. Each change in switching is shown by
an elliptical shape.
It should be noted that, in this way, only 12 commutations are
required in each half sampling period. Once the configurations
Fig. 4. Output phase voltages at 70 Hz.
are selected and sequenced, the on-time ratio of each configura-
tion is calculated using (12) and (13) given for the appropriate
sector.
VI. I
NVESTIGATION RESULTS
A. Simulation Results
MATLAB/Simulink model is developed for the proposed
matrix converter control. The input voltage is fixed at 100 V
peak to show the exact gain at the output side, and the switching
frequency of the devices is kept at 6 kHz. The load connected
to the matrix converter is R−L with the parameter values
R =10Ω, L =3mH. The operation of the proposed topology
of the matrix converter is tested for a wide range of frequencies,
from as low as 6.7 Hz to higher frequencies (70 Hz) for deep
flux weakening operation. The output phase to neutral voltage,
adjacent and non-adjacent voltages are shown in Figs. 4–6. A
balanced five-phase output is observed. The spectrum of the
output voltage at 6.7-Hz output frequency is shown in Fig. 7.
The sinusoidal nature of the input current is another distinct
feature of the matrix converter. The input side current spectrum
shown in Fig. 8 (lower trace) yields a completely sinusoidal
waveform while completely eliminating the lower order har-
monics. The THD in the input current waveform is obtained as
3.67%, which is well within the tolerance limit of the specified
IEEE 19-1999 standard.
Similar results are obtainable for all operating frequencies,
showing a successful operation of the proposed matrix con-
verter PWM. The presented results clearly show a successful
phase transformation from three-phase input to five-phase out-
put. The input current will not show a significant change for
the change in the frequency for low inductive load, and thus,
only one trace for the input current is shown in Fig. 8(a) at
the 70-Hz output case only. The simulation results verify the
effectiveness of the proposed solution. Hence, the proposed
direct ac–ac converter can be employed for wide range speed
control of multiphase drive systems.
704 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 48, NO. 2, MARCH/APRIL 2012
Fig. 5. Output currents at 70 Hz.
Fig. 6. Output phase, adjacent-1, and adjacent-II voltages for 6.67 Hz.
Fig. 7. Frequency spectrum of the output phase voltage at 6.67 Hz.
Fig. 8. (a) Input voltage with filtered and unfiltered input currents. (b) Input
current spectrum.
Fig. 9. Block diagram of the experimental setup.
IQBA L et al.: SPACE VECTOR PWM TECHNIQUE FOR A THREE-TO-FIVE-PHASE MATRIX CONVERTER 705
Fig. 10. Output side five-phase waveform for 70 Hz: output phase voltages
(100 V, 5 ms/div).
B. Experimental Results
A prototype three-phase to nine-phase matrix converter is
developed, where the input is three-phase and the output can
be configured from single to nine phases. The proposed space-
vector-based modulation scheme is implemented for a three-
to-five-phase matrix converter. The block schematic of the
experimental setup is shown in Fig. 9. The power module is a
bidirectional switch FIO 50-12BD from IXYS and is composed
of a diagonal IGBT and fast diode bridge in ISOPLUS i4-PAC.
The voltage blocking capability of the device is 1200 V, and
the current capacity is 50 A. This comes in single chip with
five output pins: four for the diode bridge and one for the gate
drive of the IGBT. It controls bidirectional current flow by a
single control signal. The advantage of this bidirectional power
switch is the decreased number of IGBTs which is a major
issue for multiphase operation, but the major disadvantage is the
higher conduction losses and the two-step commutation. Extra
line inductances are used for safe operation during the overlap-
ping of current commutation. Dead-time compensation is done
along with snubbers and clamping circuit. The matrix converter
consists of 27 of such bidirectional power switches, of which
only 15 are used. The control platform used is the Spartan 3-A
DSP controller and Xilinx XC3SD1800A FPGA. Furthermore,
the modulation code is written in C and is processed in the
DSP. Logical tasks, such as A/D and D/A conversion, gate drive
signal generation, etc., are accomplished by the powerful FPGA
board. The FPGA board is able to handle up to 50 PWM signals.
Clamping diodes are used for protection purposes.
The input supply is given from an autotransformer and is
fixed at 100 V, 50 Hz. The switching frequency of t he bidirec-
tional power switch of the matrix converter is fixed at 6 kHz.
The value of the input LC filter used for this configuration is
200 µH, 10 A and 15 µF, 440 V, respectively. The developed
matrix converter is tested for a wide range of output frequen-
cies. A five-phase R−L load is connected at the output termi-
nals of the matrix converter, with R =10Ωand L =30mH.
The resulting output waveforms for the fundamental frequency
of 70 and 6.7 Hz are shown in Figs. 10–11, and 12, respectively.
The simulation and experimental results match to a good
extent. The output voltage THD is 4.83%. This proves the
viability of the proposed space vector modulation scheme for a
three-to-five-phase matrix converter. To further show the unity
power factor at the input side, one input phase voltage and one
input phase current are shown in Fig. 13. It is evident that
unity power factor is maintained at the input side. The five-
Fig. 11. Output side five-phase waveform for 70 Hz: output phase currents
(2 A, 5 ms/div).
Fig. 12. Output side five-phase waveform for 6.7 Hz. (Upper trace) Output
phase voltage (100 V, 25 ms/div) and output current (2 A, 25 ms/div). (Bottom
trace) Output Adj-2 line-to-line voltage (100 V, 25 ms/div).
Fig. 13. Input voltage (25 V, 10 ms/div) and current (2.0 A, 10 ms/div).
phase matrix converter feeds a five-phase squirrel cage 1.5-hp
induction motor at no load to observe the input current behavior
at light load condition. The filtered input current leads the input
voltage due to the capacitive nature of the input filter without
any input displacement factor correction. The phase angle
between the input phase current and voltage is 12
◦
.TheTHD
i
’s
of the input current and input power factor are 4.74% and 0.967,
respectively. A phase lag of 12
◦
is introduced for the input
706 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 48, NO. 2, MARCH/APRIL 2012
Fig. 14. Input voltage (25 V, 2.5 ms/div) and filtered input current (0.2 A,
2.5 ms/div).
displacement correction, which results in 6.97% THD
i
and
input power factor of 0.99. Both results are s hown in Fig. 14.
VII. CONCLUSION
A novel space vector control of a three-to-five-phase matrix
converter has been discussed in this paper. The input to the
matrix converter is a three-phase ac supply, and the output
is five-phase. This converter is useful in a five-phase motor
drive application. The output voltage magnitude is found to be
limited to 78.8% of the input voltage magnitude in the linear
modulation region. This is the limitation associated with this
type of ac–ac converter. The proposed SVPWM strategy is
derived from the analogy of the modulation of a voltage source
inverter. There are 243 possible space vectors, but only 93 are
useful in implementing the SVPWM. Symmetrical switching is
obtained by utilizing zero space vectors and active vectors, and
24 commutations are noted in one sampling period. The analyti-
cal findings are confirmed using simulation and an experimental
approach.
R
EFERENCES
[1] P. W. Wheeler, J. Rodriguez, J. C. Clare, L. Empringham, and
A. Weinstein, “Matrix converters: A technology review,” IEEE Trans. Ind.
Electron., vol. 49, no. 2, pp. 276–288, Apr. 2002.
[2] M. P. Kazmierkowaski, R. Krishnan, and F. Blaabjerg, Control in Power
Electronics-Selected Problems. New York: Academic, 2002.
[3] H. A. Toliyat and S. Campbell, DSP Based Electromechanical Motion
Control. Boca Raton, FL: CRC Press, 2004.
[4] S. M. Ahmed, A. Iqbal, and H. Abu-Rub, “Generalized duty ratio based
pulse width modulation technique for a three-to-k phase matrix con-
verter,” IEEE Trans. Ind. Electron., vol. 58, no. 9, pp. 3925–3937,
Sep. 2011.
[5] S. M. Ahmed, A. Iqbal, H. Abu-Rub, and M. R. Khan, “Space vector
PWM technique for a novel 3 to 5 phase matrix converter,” in Proc. IEEE
ECCE, Atalanta, 2010, pp. 1875–1880.
[6] S. M. Ahmed, A. Iqbal, and H. Abu-Rub, “Carrier-based PWM technique
of a novel three-to-seven-phase matrix converter,” presented at the Int.
Conf. Electrical Machine ICEM, Rome, Italy, Sep. 3–6, 2010, Paper RF-
004 944.
[7] S. M. Ahmed, A. Iqbal, H. Abu-Rub, J. Rodriguez, and C. Rojas, “Simple
carrier-based PWM technique for a three to n ine phase matrix converter,”
IEEE Trans. Ind. Elect., vol. 58, no. 11, pp. 5014–5023, Nov. 2011.
[8] M. Jones and E. Levi, “A literature survey of state-of-the-art in multiphase
ac drives,” in Proc. 37th Int. UPEC, Stafford, U.K., 2002, pp. 505–510.
[9] R. Bojoi, F. Farina, F. Profumo, and Tenconi, “Dual three induction ma-
chine drives control—A survey,” IEEJ Trans. Ind. Appl., vol. 126, no. 4,
pp. 420–429, 2006.
[10] E. Levi, R. Bojoi, F. Profumo, H. A. Toliyat, and S. Williamson, “Multi-
phase induction motor drives—A technology status review,” IET Elect.
Power Appl., vol. 1, no. 4, pp. 489–516, Jul. 2007.
[11] E. Levi, “Multi-phase machines for variable speed applications,” IEEE
Trans. Ind. Electron., vol. 55, no. 5, pp. 1893–1909, May 2008.
[12] J. Holtz, “Pulsewidth modulation—A survey,” IEEE Trans. Ind. Electron.,
vol. 39, no. 5, pp. 410–420, Oct. 1992.
[13] D. G. Holmes and T. A. Lipo, Pulse Width Modulation for Power
Converters: Principle and Practice. Piscataway, NJ: IEEE Press, 2003.
[14] D. Dujic, M. Jones, and E. Levi, “Generalized space vector PWM for sinu-
soidal output voltage generation with multiphase voltage source inverter,”
Int. J. Ind. Electron. Drives, vol. 1, no. 1, pp. 1–13, 2009.
[15] A. Iqbal and S. K. Moinuddin, “Comprehensive relationship between
carrier-based PWM and space vector PWM in a five-phase VSI,” IEEE
Trans. Power Electron., vol. 24, no. 10, pp. 2379–2390, Oct. 2009.
[16] O. Lopez, D. Dujic, M. Jones, F. D. Freijedo, J. Doval-Gandoy, and
E. Levi, “Multidimensional two-level multiphase space vector PWM al-
gorithm and its comparison with multi-frequency space vector PWM
method,” IEEE Trans. Ind. Electron., vol. 58, no. 2, pp. 465–475,
Feb. 2011.
[17] A. Alesina and M. Venturini, “Solid state power conversion: A Fourier
analysis approach to generalised transformer synthesis,” IEEE Trans.
Circuits Syst., vol. CAS-28, no. 4, pp. 319–330, Apr. 1981.
[18] A. Alesina and M. Venturini, “Analysis and design of optimum ampli-
tude nine-switch direct ac–ac converters,” IEEE Trans. Power Electron.,
vol. PEL-4, no. 1, pp. 101–112, Jan. 1989.
[19] D. Casadei, G. Grandi, G. Serra, and A. Tani, “Space vector control of
matrix converters with unity power factor and sinusoidal input/output
waveforms,” in Proc. EPE Conf., 1993, vol. 7, pp. 170–175.
[20] L. Huber and D. Borojevic, “Space vector modulated three-phase to three-
phase matrix converter with input power factor correction,” IEEE Trans.
Ind. Appl., vol. 31, no. 6, pp. 1234–1246, Nov./Dec. 1995.
[21] H. She, H. Lin, B. He, X. Wang, L. Yue, and X. An, “Implementation
of voltage-based commutation in space vector modulated matrix con-
verter,” IEEE Trans. Ind. Electron., vol. 59, no. 1, pp. 154–166, Jan. 2012.
DOI:10.1109/TIE.2011.2130497.
[22] L. M. Y. Lee, P. Wheeler, and C. Klumpner, “Space vector modulated
multi-level matrix converter,” IEEE Trans. Ind. Electron., vol. 57, no. 10,
pp. 3385–3394, Oct. 2010.
[23] B. Wang and G. Venkataramanan, “A carrier-based PWM algorithm for
indirect matrix converters,” in Proc. IEEE PESC, 2006, pp. 1–8.
[24] Y.-D. Yoon and S.-K. Sul, “Carrier-based modulation technique for matrix
converter,” IEEE Trans. Power Electron., vol. 21, no. 6, pp. 1691–1703,
Nov. 2006.
[25] P. C. Loh, R. Rong, F. Blaabjerg, and P. Wang, “Digital carrier modulation
and sampling issues of matrix converter,” IEEE Trans. Power Electron.,
vol. 24, no. 7, pp. 1690–1700, Jul. 2009.
[26] A. Iqbal, E. Levi, M. Jones, and S. N. Vukosavic, “Generalised sinusoidal
PWM with harmonic injection for multi-phase VSIs,” in Proc. IEEE-
PESC, 2006, pp. 1–7.
Atif Iqbal (M’09–SM’10) received the B.Sc. and
M.Sc. degrees in electrical engineering from Aligarh
Muslim University (AMU), Aligarh, India, in 1991
and 1996, respectively, and the Ph.D. degree from
Liverpool John Moores University, Liverpool, U.K.,
in 2006.
He has been a Lecturer in the Department of
Electrical Engineering, AMU, since 1991, where he
is currently working as an Associate. He is on acad-
emic assignment and is working at Qatar University,
Doha, Qatar. His principal areas of research interest
is power electronics and multiphase machine drives.
Dr. Iqbal was a recipient of the Maulana Tufail Ahmad Gold Medal for
standing first at the B.Sc. Engg. Exams in 1991 from AMU and a research
fellowship from EPSRC, U.K., for working toward the Ph.D. degree.
IQBA L et al.: SPACE VECTOR PWM TECHNIQUE FOR A THREE-TO-FIVE-PHASE MATRIX CONVERTER 707
Sk Moin Ahmed (S’10) was born in Hooghly, West
Bengal, India, in 1983. He received the B.Tech. and
M.Tech. degrees from Aligarh Muslim University
(AMU), Aligarh, India, in 2006 and 2008, respec-
tively, where he is currently working toward the
Ph.D. degree.
He is also pursuing a research assignment at Texas
A&M University, Doha, Qatar. His principal areas
of research are modeling, simulation, and control
of multiphase power electronic converters and fault
diagnosis using artificial intelligence.
Mr. Ahmed was a gold medalist in earning the M.Tech. degree. He was a
recipient of a Toronto fellowship funded by AMU. He also received the Best
Research Fellow Excellence Award from Texas A&M University, Qatar, for the
year 2010–2011.
Haitham Abu-Rub (M’99–SM’07) received the
Ph.D. degree from the Electrical Engineering De-
partment, Technical University of Gdansk, Gdansk,
Poland.
His main research focuses on electrical drive
control, power electronics, and electrical machines.
He is currently a Senior Associate Professor at Texas
A&M University, Doha, Qatar.
Dr. Abu-Rub has earned many prestigious inter-
national awards including the American Fulbright
Scholarship, the German Alexander von Humboldt
Fellowship, the German DAAD Scholarship, and the British Royal Society
Scholarship.
