Internati
o
nal Journal
of App
lied Power E
n
gineering
(IJAPE)
V
o
l.
3, N
o
. 1
,
A
p
r
il
201
4, p
p
.
51
~66
I
S
SN
: 225
2-8
7
9
2
51
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJAPE
A Survey on Quality Changes
in Positi
ve, Negative and
Combined Switching Strategies
in Control of Three Phase
Ma
tr
ix Co
nver
te
r
Mohammad S
a
rvi,
Im
an
Sol
t
ani
,
Hossein
Far
a
marz
i
F
acult
y
of
Tech
nica
l and
Eng
i
ne
ering,
Im
am
K
homeini International Univ
ersity
,
Qazvin, Iran
Article Info
A
B
STRAC
T
Article histo
r
y:
Received 23 Oct,
2012
Rev
i
sed
O
c
t 25
, 20
13
Accepte
d
Mar 8, 2014
In this pap
e
r us
es positive
,
n
e
g
a
tiv
e an
d
com
b
i
n
ed switching
st
rateg
i
es for
three phas
e
ac/ac matrix conver
t
er .th
e
author co
mpares these strateg
i
es. Th
e
performance co
mparison of these three
strategies is
made under balan
ced
operation. Th
e simulation of th
ree phase
matrix converter f
e
eding a three
phas
e
lo
ad was
ac
com
p
lis
hed
b
y
m
e
an
s of th
e m
a
tl
ab/sim
uli
nk software
.
After th
e sim
u
lation
the
com
p
arison of th
e
waveform
s THD in thre
e
switching sequ
ence
is done. I
t
must be
mentio
ned th
at
the duty
cy
cle of th
e
whole switches
in th
e conv
e
r
te
r is
according to Ventur
in
i
switching
algorithm.
Keyword:
Three
Phase M
a
trix Converte
r
Switch
i
ng
strateg
i
es
THD
Copyright ©
201
4 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Im
an
So
ltan
i
,
Faculty of Tec
hnical a
n
d E
n
gineering,
Im
a
m
Kh
o
m
ei
n
i
In
tern
ation
a
l Un
iv
ersity, Qazv
in
, Iran.
Em
a
il: i_
so
ltan
i
@ik
i
u
.
ac.ir
1.
INTRODUCTION
AC-AC conve
r
ters are frequency
co
nv
erters. They p
r
o
d
u
ce an
AC vo
ltag
e
in
wh
ich
bo
th
t
h
e
fre
que
ncy
an
d vol
t
a
ge ca
n be
vari
e
d
di
rect
l
y
fr
om
t
h
e AC
l
i
ne v
o
l
t
a
ge, e.
g,
from
a 60-o
r
5
0
Hz so
urce
. T
h
ere
ar
e two
m
a
j
o
r
classes of
A
C
-A
C,
o
r
so-
called
d
i
r
ect static fr
equ
e
n
c
y conver
t
er
s:
C
y
cl
ocon
vert
e
r
, w
h
i
c
h i
s
c
o
nst
r
uct
e
d
u
s
i
ng
nat
u
ral
l
y
com
m
ut
ed t
hyri
s
t
o
rs
. T
h
e c
o
m
m
ut
at
i
on
v
o
ltag
e
is
en
su
red
b
y
su
pp
ly voltag
e
. Th
ese
are so-cal
led line
commuted converters.
2
.
Matr
ix conver
t
er
,
wh
ich
ar
e con
s
tru
c
ted
u
s
ing
fu
ll-
co
n
t
r
o
lled static d
e
v
i
ces, such
as tran
sist
o
r
s or
GTOs.Matrix co
nv
erter
wit
h
b
i
-d
irection
a
l
on
/o
ff
c
o
nt
r
o
l
s
w
i
t
c
hes ca
n
pr
o
v
i
d
e
i
n
d
e
pen
d
e
n
t
c
ont
rol
o
f
m
a
gni
t
ude
a
n
d
fre
q
u
ency
o
f
gene
rat
e
d
o
u
t
p
ut
v
o
l
t
a
ge
as
w
e
l
l
as si
n
u
soi
d
al
m
odul
at
i
o
n
of
o
u
t
p
ut
vol
t
a
ge a
n
d
cu
rr
en
t [3
],
[6
],
[
7
].
2.
MAT
R
I
X
CO
NVE
RTER
2.
1.
Definiti
on
The m
a
t
r
i
x
conve
rt
er i
s
a si
ngl
e st
a
g
e di
r
ect
ac-ac co
n
v
ert
e
r
,
w
h
i
c
h
has a
n
ar
ray
of m
×
n bi
-
d
i
rection
a
l power
switch
e
s th
at can d
i
rectl
y
connect a
n
m
-
phase voltage s
o
urce to a
n
n-pha
se loa
d
. A t
h
ree
p
h
a
se
m
a
trix
co
nv
erter co
n
s
i
s
t o
f
9
b
i
-d
irectio
n
a
l switc
h
e
s th
at allo
w an
y p
h
a
se of
the load to be c
o
nnected
to
an
y
ph
ase
of inpu
t vo
ltag
e
, e.g
,
t
h
e zero
v
a
lu
e
of th
e load
p
h
a
se
v
o
ltag
e
is m
a
in
tain
ed
b
y
con
n
ect
in
g
all
l
o
ad
p
h
ases t
o
t
h
e sam
e
i
nput
pha
se [
5
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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252
-87
92
IJA
P
E Vol
.
3
,
No
. 1, A
p
ri
l
20
14
:
51
–
6
6
52
2.
2.
Ad
va
nt
age
s
•
In
here
nt
fo
u
r
qua
d
r
ant
o
p
era
t
i
on an
d rege
n
e
rat
i
on ca
pabi
l
i
t
y
due t
o
t
h
e
use o
f
bi
di
rect
i
onal
swi
t
c
h a
n
d
hence
i
t
can
be
use
d
as
an
al
t
e
rnat
i
v
e
t
o
n P
W
M
i
nve
rt
er
dri
v
e f
o
r t
h
ree
p
h
a
s
e f
r
eq
ue
ncy
c
ont
rol
.
•
It
o
ffe
rs si
nu
so
i
d
al
i
n
p
u
t
a
n
d
out
put
wa
vef
o
r
m
s
•
It
has
bi
-di
r
ect
i
onal
swi
t
c
hes
,
so
i
t
ca
n of
fer bi
di
rect
i
o
nal
p
o
we
r fl
o
w
•
I
npu
t pow
er
f
a
cto
r
i
n
th
is
c
o
n
v
ert
e
r
i
s
c
ont
r
o
l
l
a
bl
e an
d
di
spl
ace
m
e
nt factor is unity
•
It
has
a c
o
m
p
act
desi
g
n
a
n
d
h
i
gh
d
r
i
v
e
perform
ance and lo
n
g
lif
e [1
],
[5
].
2.
3.
Di
sad
v
an
ta
ge
s
•
matrix
conve
rt
ers require
t
h
e use of
num
e
rous
switch
e
s and
well-estab
lish
e
d con
t
ro
l m
e
th
od
s
•
fo
r t
h
e
safe
co
m
m
u
t
a
t
i
on of
t
h
e s
w
i
t
c
hes,
s
o
m
e
el
em
ent
s
l
i
ke s
n
ub
ber
ci
rc
ui
t
an
d cl
am
p ci
rcui
t
are
re
qui
red
•
Ac
out
put
v
o
l
t
a
ge ca
nn
ot
e
x
c
eed t
h
e
ac i
n
p
u
t
vol
t
a
ge;
us
ual
l
y
i
t
s
m
a
xim
u
m
i
s
cl
ose t
o
t
h
e i
n
p
u
t
vol
t
a
ge
.
•
bot
h
bi
di
rect
i
o
nal
s
w
i
t
c
hes
of
any
pha
se l
e
g
can
neve
r
be t
u
rne
d
o
n
at
t
h
e
s
a
m
e
case
These
disa
dva
ntages
of m
a
trix c
o
nv
erters p
r
ev
en
t
t
h
eir u
s
e in
ind
u
strial application
[1],[5].
Th
e m
a
in
p
u
rp
o
s
e of th
is
pap
e
r is t
o
sh
ow th
at
three
phase m
a
trix conv
er
ter
th
at i
s
p
r
odu
cing
v
a
riab
le ou
tpu
t
vo
ltag
e
s
with
p
o
s
itiv
e,
n
e
g
a
t
i
v
e
and co
m
b
in
ed
switch
i
ng
strateg
i
es, h
a
s o
u
t
p
u
t
curren
t
s
th
at
are n
o
t
sy
m
m
e
t
r
i
cal
. There
f
or
e t
h
e i
n
p
u
t
a
n
d
out
put
c
u
r
r
ent
s
co
nsi
s
t
of s
o
m
e
unde
si
rabl
e
harm
oni
cs, al
s
o
t
h
e
THD for i
n
pu
t
an
d
o
u
t
p
u
t
qu
an
tities are
h
i
gh. it m
u
st b
e
no
ticed
th
at t
h
e
un
d
e
sirab
l
e cu
rren
t
h
a
rm
o
n
i
cs cau
se
m
a
ny
pro
b
l
e
m
s
, suc
h
as he
at
i
ng an
d re
d
u
ct
i
on
of l
i
f
e
i
n
t
r
ans
f
o
r
m
e
rs an
d i
n
d
u
c
t
i
on m
achi
n
es an
d
deg
r
a
d
at
i
o
n
o
f
sy
st
em
vol
t
a
ge
wav
e
f
o
rm
. Thi
s
pa
per
co
m
p
ares t
h
e T
H
D
of
t
h
e
wa
ve
fo
rm
s i
n
t
h
e i
n
put
an
d
out
put
si
des o
f
con
v
e
r
t
e
r.
3.
SWITCHING
STRATEGIE
S
The
basic power circ
uit of a three
p
h
ase m
a
tri
x
c
o
n
v
e
r
t
e
r i
s
sh
ow
n i
n
Fi
g
.
1;
i
t
i
s
com
p
o
s
ed
of
ni
ne
b
i
d
i
rection
a
l switch
e
s.
The t
h
ree
phas
e input
volta
ge
s of
th
e conv
erter
ar
e
g
i
ven by:
Fig.1
. t
h
ree
phase m
a
trix converter
The
i
n
p
u
t
a
n
d
out
put
v
o
l
t
a
ge vect
o
r
s of
t
h
e m
a
t
r
i
x
co
nve
rt
er
ca
n be gi
ve
n
by
:
Whe
r
e
i
and
o
are t
h
e
f
r
eq
ue
nc
i
e
s of
i
n
put
a
n
d
out
put
v
o
l
t
a
g
e
s o
f
m
a
t
r
i
x
co
nve
rt
er
res
p
ect
i
v
el
y
.
W
i
t
h
ni
ne
bi
-
d
i
r
ect
i
onal
swi
t
ches t
h
e m
a
t
r
ix co
nve
rt
er ca
n t
h
eo
ret
i
cal
l
y
assum
e
512 (
2
9
) di
ffe
rent
sw
itch
i
ng
state co
m
b
in
atio
n
s
. Bu
t n
o
t
all o
f
th
em
can
b
e
u
s
ef
u
lly e
m
p
l
o
y
ed
. Reg
a
r
d
less t
o
th
e con
t
ro
l
method
u
s
ed
, th
e ch
o
i
ce o
f
m
a
trix
co
nv
erter
switch
i
ng
state co
mb
in
ation
to
b
e
u
s
ed
m
u
st com
p
l
y
with
two b
a
sic
ru
les. Tak
i
ng
i
n
to
accou
n
t
that th
e co
nv
erter is sup
p
lied by a vo
ltag
e
sou
r
ce and
u
s
u
a
l
l
y f
eed
an
i
n
du
ctiv
e
l
o
ad, t
h
e i
n
put
pha
ses sh
o
u
l
d
neve
r b
e
sh
ort
-
ci
rcui
t
e
d a
nd t
h
e o
u
t
p
ut
cu
rre
nt
s sh
o
u
l
d
not
be i
n
t
e
r
r
u
p
t
e
d
.
Thi
s
(1)
(2)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
APE
I
S
SN
:
225
2-8
7
9
2
A
Survey on Quality
Change
s in Positive, Ne
gative
and C
o
mbi
n
ed Sw
itchi
ng Strategies (
M
ohammad
Sarvi
)
53
can be
ac
hi
e
v
e
d
by
usi
n
g Ve
nt
u
r
i
n
i
M
o
d
u
l
a
t
i
on Al
g
o
ri
t
h
m
.b
y
u
s
i
n
g th
is
alg
o
rith
m
,
in
a th
ree
p
h
a
se to th
ree
p
h
a
se m
a
trix
co
nv
erter 27
are th
e p
e
rm
itted
switch
i
ng
co
m
b
in
atio
n
s
, in
th
is p
a
p
e
r th
ree switch
i
ng
states are
e
m
p
l
o
y
ed
.
Th
ese states are
positiv
e, n
e
g
a
tiv
e and
co
m
b
in
ed
switch
i
ng
st
rateg
i
es.
3
.
1
.
Venturini switching
a
l
go
rithm
Th
e Ven
t
urin
i
alg
o
r
ith
m
co
n
t
ro
ls th
e th
e switch
e
s S
11
, S21, S31 accordi
ng to the desired output
voltage
and
output
fre
que
ncy. The
sw
itche
s
on each output
pha
se are
cl
ose
d
se
quentially and re
petitively.
9-
d
u
ri
n
g
a
n
y
i
t
h
se
q
u
ence
, t
h
e
sam
p
l
i
ng pe
ri
od
, T
i
s
, will b
e
d
i
v
i
d
e
d
t
o
t
h
ree-ti
m
e
in
terv
al
s t
i
1
,t
i
2
and
t
i
3
as sh
ow
n i
n
Fi
g.
2,a
n
d
T
i
s
is related
with
t
h
ese ti
m
e
in
tervals as fo
llows:
T
i
s=
t
i
1
+t
i
2
+ t
i
3
(3
)
Fig.2
. sam
p
ling
p
e
ri
o
d
in
t
h
ree ph
ase m
a
trix
co
nv
erter
Th
is
p
a
p
e
r
p
r
esen
ts three swi
t
ch
in
g strateg
i
es fo
r
produ
cing ou
tpu
t
vo
ltag
e
s:
•
th
e po
sitiv
e switch
i
n
g
strategy
•
th
e n
e
g
a
tiv
e switch
i
ng
strateg
y
•
th
e co
m
b
in
ed
switch
i
ng
strateg
y
3.
2.
T
h
e posi
t
i
ve
sw
i
t
chi
n
g stra
te
gy
The output
voltage
can be s
y
nthesized
by switc
hing t
h
e
input voltage
according t
o
t
h
e algorithm
sho
w
n i
n
Fi
g.
3
.
Th
is algorith
m h
a
s th
ree ru
les:
During
tim
e in
terv
al t
i
1,p
:S
11
,S
22
and S
33
m
u
st
be
o
n
, a
n
d t
h
e
rem
a
i
n
i
ng swi
t
ches m
u
st
be
o
ff.
During
tim
e in
terv
al t
i
2,p
:S
12
,S
23
and S
31
m
u
st
be
o
n
, a
n
d t
h
e
rem
a
i
n
i
ng swi
t
ches m
u
st
be
o
ff.
During
tim
e in
terv
al t
i
3,p
:S
13
,S
21
and S
32
m
u
st b
e
on
an
d th
e
rem
a
in
in
g
swit
ch
es m
u
st b
e
off.
Fig.4
. switch
e
s co
mm
an
d
s
fo
r po
sitiv
e switch
i
ng
strateg
y
.
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6
6
54
B
y
defi
ni
ng
t
h
e f
o
l
l
o
wi
ng
sw
i
t
c
h pat
t
e
r
n
s:
P
1
=
,
(
4
)
P
2
=
,
(
5
)
P
3
=
,
(
6
)
In
ex
pressi
o
n
o
f
the relatio
n b
e
tween
inp
u
t an
d
o
u
t
p
u
t
qu
an
tities, a matrix
is d
e
fi
ned
as low freq
u
e
n
c
y
tran
sfer m
a
trix
and
it is
g
i
v
e
n
b
y
33
32
31
23
22
21
13
12
11
)
(
m
m
m
m
m
m
m
m
m
t
M
(7
)
m
kj
(t) is th
e
d
u
ty cycle o
f
switch
S
kj
,it is sp
ecified
as
m
kj
(t)=t
kj
/T
s
, switch
can acce
pt the
following
values:
=M(t).
(8
)
=M(t)
T
.
(9
)
m
kj
(t) can acce
pt the
followi
ng
values:
0< m
kj
(t)<1 k={1,
2
,3}
, j={1,2,
3
}
(1
0)
In d
e
fin
ition
o
f
th
e switch
p
a
ttern
s we can assu
m
e
th
at:
P
1
=m
11
(1
1)
P
2
=m
3
1
(1
2)
P
3
=m
2
1
(1
3)
It is obv
iou
s
t
h
at:
m
11
+m
31
+m
21
=1
(14)
(1
5)
f
s
=
s
T
1
(16)
whe
r
e f
s
is th
e switch
i
n
g
freq
u
e
n
c
y wh
ich sh
ou
ld
b
e
20 ti
mes h
i
g
h
e
r th
an
th
e ou
tput frequ
en
cy so as to
have
l
o
w
harm
oni
c
co
nt
ent
i
n
t
h
e
o
u
t
p
ut
vo
l
t
a
ge.
3
.
3
.
The negativ
e
switching strateg
y
The output
voltage
can be s
y
nthesized
by switc
hing t
h
e
input voltage
according t
o
t
h
e algorithm
sho
w
n i
n
Fi
g.
5
.
Th
is algorith
m h
a
s th
ree ru
les:
During
tim
e in
terv
al t
i
1,n
:S
11
,S
22
and S
33
m
u
st
be
o
n
, a
n
d t
h
e
rem
a
i
n
i
ng swi
t
ches m
u
st
be
o
ff.
During
tim
e in
terv
al t
i
2,n
:S
12
,S
23
and S
31
m
u
st
be
o
n
, a
n
d t
h
e
rem
a
i
n
i
ng swi
t
ches m
u
st
be
o
ff.
During
tim
e in
terv
al t
i
3,n
:S
13
,S
21
and S
32
m
u
st
be
o
n
, a
n
d t
h
e
rem
a
i
n
i
ng swi
t
ches m
u
st
be
o
ff.
Ts
m
T
m
T
m
T
s
s
s
21
31
11
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2
A
Survey on Quality
Change
s in Positive, Ne
gative
and C
o
mbi
n
ed Sw
itchi
ng Strategies (
M
ohammad
Sarvi
)
55
Fig.5
. switch
i
ng
p
a
ttern in
n
e
g
a
tiv
e switch
i
ng
strateg
y
Fi
g.
6 s
h
ows
t
h
e swi
t
c
hes
com
m
ands
d
u
ri
n
g
i
t
h
e sam
p
l
i
ng
peri
od
.
Fig.6
. s
w
i
t
c
hes
com
m
ands f
o
r
ne
gat
i
v
e s
w
i
t
c
hi
n
g
st
rat
e
gy
B
y
defi
ni
ng
t
h
e f
o
l
l
o
wi
ng
sw
i
t
c
h pat
t
e
r
n
s:
N
1
=
,
(17)
N
2
=
,
(1
8)
N
3
=
,
(1
9)
In d
e
fin
i
ng
t
h
e
switch
p
a
ttern
s we can
assu
m
e
th
at:
N
1
=m
13
(20)
N
2
=m
23
(2
1)
N
3
=m
3
3
(2
2)
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6
6
56
It is obv
iou
s
t
h
at:
m
13
+m
23
+m
33
=1
(23)
3.4.
The c
o
m
b
ined switchi
n
g s
t
r
a
te
gy
Sin
ce
p
o
sitiv
e
an
d n
e
g
a
tiv
e switch
i
ng
strateg
i
es
p
r
o
d
u
ce i
n
g
e
n
e
ral, t
h
e
sam
e
o
u
t
p
u
t
vo
ltag
e
s, th
ese
vol
t
a
ge
s ca
n
b
e
f
o
rm
ed by
a
n
y
com
b
i
n
at
i
on
of
t
h
ese
swi
t
c
h
i
ng
st
rat
e
gi
es.
Fi
g.
7 s
h
ows
t
h
e swi
t
c
hi
ng
pat
t
ern
s
for co
m
b
in
ed
po
sitiv
e and
n
e
gativ
e switch
i
ng strateg
i
es. As it can
b
e
seen,
th
e ou
tpu
t
can
b
e
estab
lish
e
d
fro
m
p
a
rt of
p
o
sitiv
e strateg
y
an
d
part
of
ne
gat
i
v
e
st
rat
e
gy
.
Fig.7
. switch
e
s co
mm
an
d
s
fo
r co
m
b
in
ed
swit
ch
ing
strateg
y
4.
SOFTWARE
IMPLEME
N
TATION
OF THR
EE PHASE AC/AC
MA
TRI
X
CONVERTER
The m
a
t
r
i
x
co
n
v
ert
e
r
s
h
o
w
n i
n
Fi
g.
1
has
bee
n
si
m
u
l
a
t
e
d by
m
a
t
l
a
b soft
w
a
r
e
. t
h
e m
a
i
n
pa
r
a
m
e
t
e
rs of
th
e m
a
trix
co
nv
erter are listed
in tab
l
e
1
.
Ta
ble
1
. Main p
a
ram
e
ters o
f
th
e m
a
trix
co
nv
erter
par
a
m
e
ter value
V
im
311
V
V
om
155.
5
V
f
i
50
Hz
f
o
60
Hz
f
s
10
KHz
R 10
Ω
L
30
m
H
C
f
100
µf
L
f
.1
m
H
R
s
30
Ω
C
s
3
m
f
.5
.5
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A
Survey on Quality
Change
s in Positive, Ne
gative
and C
o
mbi
n
ed Sw
itchi
ng Strategies (
M
ohammad
Sarvi
)
57
The m
a
trix conve
rter re
quire
s
nine
bi-di
r
ec
tiona
l switches
with capa
b
ility of bl
ocki
ng
voltage a
nd
co
ndu
ctin
g
cu
rren
t in
bo
th
d
i
rectio
n
s
. T
h
ere
are seve
ral arra
ngem
e
nt can be used to c
r
eate such
bi-di
r
ec
tional
switch. Fig.8 presents
a num
b
er
of
these c
onnections. T
h
e a
dva
ntage
s
and
disadva
n
tages
of eac
h structure are
refe
rre
d i
n
re
fre
nce.
1.
wi
t
h
con
s
i
d
eri
ng
o
f
t
h
ese adva
n
t
ages and
di
sadva
nt
age
s
, t
h
e com
m
on em
i
t
t
e
r
con
f
i
g
urat
i
o
n
i
s
oft
e
n p
r
ef
er
red t
o
cre
a
t
e
t
h
e m
a
t
r
i
x
conve
rt
er
bi
-
d
i
r
e
c
t
i
onal
swi
t
c
h.
So
we c
h
oos
e t
h
i
s
co
nfigu
r
ation to
u
s
e i
n
th
e pro
p
o
s
ed
m
a
trix
co
nv
erter.
Fig.8
.
bi
-
d
i
r
ect
i
onal
s
w
i
t
c
h t
o
pol
ogi
es:
a
)
di
ode
em
bedde
d:
b
)
c
o
m
m
on em
i
t
t
e
r (C
E):
c
)
com
m
on col
l
ect
or
(CC)
4.
1.
Co
ntr
o
l Al
g
o
r
i
thm
The re
q
u
ire
d
v
o
ltage tra
n
sfe
r
ratio (q
),i
n
p
u
t
fre
que
ncy
(f
i
),
out
put
f
r
e
que
n
c
y
(f
o
)
,
ma
x
i
m
u
m t
r
a
n
s
f
e
r
ratio
(q
m
),i
n
put
an
d
out
put
v
o
l
t
a
ges are
t
h
e i
n
put
req
u
i
r
e
d
fo
r cal
cul
a
t
i
o
n
of
t
h
e
dut
y
cy
cl
e m
a
t
r
i
x
M
.
t
h
e
dut
y
cycle calculations
for voltage
tran
sfer ratio o
f
.5
is
realized
in th
e
form o
f
m
-file in
matlab
. th
e switch
i
ng
tim
e
for the s
w
itch conne
cted
betwee
n the
input
phase
an
d out
put
p
h
ase
is;
)]
3
sin(
)
sin(
9
2
2
3
2
3
1
[
t
i
t
i
m
q
q
im
V
i
V
o
V
Ts
T
(
2
4)
whe
r
e
is
0
,
3
2
,
3
4
co
rresp
ond
ing
to
th
e
i
n
pu
t phases
A,B,C, resp
ectiv
ely
q
m
i
s
t
h
e
ma
x
i
mu
m
v
o
ltag
e
ratio(0
.8
66).
re
prese
n
ts output phase
a,b,c, a
n
d
re
presents
input phase A,B or
C.
4.
2.
Sys
t
em simul
a
tion
The si
m
u
l
a
t
e
d
m
odel
of l
o
ade
d
m
a
t
r
i
x
co
nve
rt
er
usi
n
g M
A
TLAB
/
SIM
U
L
I
N
K
i
s
s
h
ow
n i
n
Fi
g.
9
Fig.9
. t
h
e sim
u
lated
m
o
d
e
l o
f
p
h
a
se m
a
trix
co
nv
erter.
5.
SIM
U
LATI
O
N
RESULTS
AN
D DIS
C
US
SION
Th
e sim
u
latio
n
of m
a
trix
con
v
e
rter is carri
ed
ou
t
usi
n
g P
o
we
r sy
st
em
bl
ock set
.
Li
ke
wi
se t
o
t
h
e
out
put
v
o
l
t
a
ge
s, t
h
e
i
n
put
c
u
rre
nt
s are
di
re
ct
l
y
generat
e
d
by
t
h
e
o
u
t
p
ut
cur
r
ent
s
, sy
nt
h
e
si
zed
by
se
qu
ent
i
a
l
piecewise sam
p
ling of t
h
e
out
put c
u
rre
nt wa
veform
s .t
he si
m
u
la
tion re
sult
s ar
e shown
in Fig.10-18.
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,
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. 1, A
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6
6
58
Fi
g.
10
.
o
u
t
p
u
t
lin
e vo
ltag
e
s i
n
po
sitiv
e switch
i
ng
strateg
y
.
Fi
g.
11
. o
u
t
p
u
t
cu
rren
ts
in
po
sitiv
e
switch
i
ng
strateg
y
.
Fi
g.
12
. inpu
t cu
rren
ts in
po
sitiv
e switch
i
ng
strateg
y
.
V
a
b
V
bc
Vca
Ib
I
c
I
a
I
a
I
b
I
c
I
b
Ia
I
c
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
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I
S
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:
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2-8
7
9
2
A
Survey on Quality
Change
s in Positive, Ne
gative
and C
o
mbi
n
ed Sw
itchi
ng Strategies (
M
ohammad
Sarvi
)
59
Fi
g.
13
.
out
put
l
i
n
e v
o
l
t
a
ges i
n
ne
gat
i
v
e s
w
i
t
c
hi
n
g
st
rat
e
gy
.
Fi
g.
14
. out
put
cur
r
ent
s
i
n
ne
g
a
t
i
v
e
swi
t
c
hi
ng
st
rat
e
gy
.
Fi
g.
15
. inpu
t cu
rren
ts in
n
e
g
a
tiv
e switch
i
n
g
strateg
y
.
Vab
Vbc
Vca
I
c
I
b
I
a
I
a
I
b
I
c
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:
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E Vol
.
3
,
No
. 1, A
p
ri
l
20
14
:
51
–
6
6
60
Fi
g.
16
.
o
u
t
p
u
t
lin
e vo
ltag
e
s i
n
co
m
b
in
ed
swit
ch
ing
strateg
y
.
Fi
g.
17
.
out
put
cur
r
ent
s
i
n
c
o
m
b
i
n
ed swi
t
c
hi
ng
st
rat
e
gy
.
Fi
g.
18
.
inpu
t cu
rren
ts in
co
mb
in
ed
switch
i
ng
strateg
y
.
Al
so ,t
hese fi
g
u
res s
h
ow
, t
h
e
out
put
vol
t
a
ge
.
i
t
C
a
n be seen
, i
n
al
l
st
rat
e
gi
es t
h
e o
u
t
p
ut
c
u
r
r
ent
i
s
not
sym
m
et
ri
cal
and i
t
has a co
nsi
d
e
r
abl
e
dc com
pone
nt
. T
h
ere
f
o
r
e ,i
n t
r
ansf
o
r
m
e
r app
l
i
cat
i
ons i
t
m
a
y
cause
sat
u
rat
i
o
n
of
t
r
ansf
o
r
m
e
r .t
he
fre
que
ncy
s
p
ec
t
r
um
s of t
h
e i
n
put
a
n
d
out
put
cur
r
ent
s
are
sh
ow
n i
n
Fi
g.
19
-
3
6
.
Vbc
Vca
Vab
Ia
I
b
I
c
I
a
I
b
I
c
Evaluation Warning : The document was created with Spire.PDF for Python.