Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
V
o
l.
4, N
o
. 1
,
Mar
c
h
20
14
pp.
61
~
6
9
I
S
SN
: 208
8-8
6
9
4
61
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
/
IJPEDS
Comparative Evaluati
on of Ge
neralized Multicell Impedance
Source Inverter for Drives
V Raghaven
d
r
a Rajan, CS
Ajin Sekh
ar,
R
He
manth
a
Kum
a
r, M Sasikumar
Jeppiaar
Engineering Co
lleg
e
, Anna Un
iversity
,
Chennai – 600
1
19, India
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Nov 12, 2013
Rev
i
sed
D
ec 28
, 20
13
Accepte
d
Ja
n 19, 2014
V
o
ltag
e
-Source I
nverter
is lim
it
e
d
b
y
its
only
vo
ltage step-d
own operation. I
n
adding with
ex
tra boosting
the
flexibilit
y
is k
e
pt activ
e for
the number of
semiconductors
which is un
ch
anged,
voltage-
t
y
p
e Z-source inverter
was
earl
i
er
proposed
.
Th
is n
e
w
clas
s of
inver
t
er
is
gen
e
rall
y
less
sensitive to
electromagnetic noi
ses.
However
,
their
boosting
capab
ilities
ar
e an
y
how less
with high comp
onent stresses and poorer
spectr
al perfo
rmances
caused
b
y
low modulation
index
ratios.
Their boosting
g
a
ins
ar
e, th
erefor
e, r
e
stricted
in
practice.
T
o
overcome th
ese we use
the gen
e
raliz
ed switched-inductor
Z-
source inv
e
rter is proposed, B
y
comp
aring with P
W
M techniqu
e and SPWM
techn
i
que, whose extr
a boos
ting
abilities and other
advan
t
ag
es have been
verified in
simulation
analy
s
is an
d exper
i
ment.
Keyword:
Mu
lticell
P
W
M
t
e
c
hni
qu
e
S
P
W
M
te
chn
i
qu
e
Sw
itch
e
d
I
nducto
r
Z-s
o
urce Inverter
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
:
V R
a
gha
ve
nd
r
a
R
a
ja
n
Depa
rt
m
e
nt
of
El
ect
ri
cal
and
El
ect
roni
cs
E
n
gi
nee
r
i
n
g,
Jeppiaar E
n
gineering Colle
ge,
R
a
ji
v Ga
nd
hi
s
a
l
a
i
,
C
h
en
nai
– 60
0 11
9,
I
n
di
a
Em
ail:
ragh
aven
draraj
an.89@gm
ail
.
com
1.
INTRODUCTION
M
ode
rn el
ect
ri
cal
sy
st
em
s li
ke di
st
ri
b
u
t
e
d
g
e
nerat
o
rs
, p
o
w
er co
n
d
i
t
i
oner
s
, an
d i
n
dust
r
i
a
l
dri
v
es ha
ve
rai
s
ed
t
h
e i
m
port
a
nce
of
dc
–
ac i
n
vert
ers
,
t
h
ro
u
g
h
w
h
i
c
h
e
n
er
gy
i
s
a
p
pr
o
p
ri
at
el
y
co
ndi
t
i
one
d.
Al
t
h
o
u
g
h
wel
l
estab
lish
e
d
n
o
w, ex
isting
pop
u
l
ar in
v
e
rter to
po
log
i
es s
till
h
a
v
e
so
m
e
c
o
n
s
t
r
ain
t
s to
reso
lv
e with
the first
bei
n
g t
h
ei
r i
n
f
l
exi
b
l
e
vol
t
a
ge
or cu
rre
nt
co
nve
rsi
o
n ra
n
g
e
s
. To be m
o
re
preci
se, exi
s
t
i
ng v
o
l
t
a
ge
-so
u
rce
in
v
e
rter (VSI) can
on
ly p
e
rfo
rm
v
o
ltag
e
st
ep
-do
w
n
op
eratio
n
.
Vo
ltag
e
an
d
cu
rren
t step
-up
flex
i
b
ilit
y can
surel
y
be a
d
d
e
d
by
c
o
n
n
ect
i
ng
ap
pr
o
p
ri
at
e dc
–
d
c c
o
n
v
e
r
t
e
rs t
o
t
h
e t
r
adi
t
i
onal
i
nve
r
t
ers,
whi
c
h
pr
oba
bl
y
would be
the
m
o
st co
mm
erc
i
ally viable approac
h
becaus
e
of its sim
p
licity. Z source
inve
rter als
o
finds
i
n
ap
p
lication
in
electric v
e
h
i
cles wh
ere driv
e v
o
ltag
e
stress an
d
con
t
ro
llab
ility is
a
maj
o
r fact
o
r
[11
]
. Ind
e
ed,
researc
h
in Z-s
o
urce inverters
has progres
s
e
d
actively
with their
m
odulation
[2],
m
odelling
[3], control
[4],
[5], c
o
m
pone
nt
sizing and a
pplicati
ons,
[7]–[9] now
being a
d
dresse
d.
Recen
tly, anothe
r intere
st has
surfa
ced,
an
d
th
at is to
ad
dress th
e li
m
i
ted
p
r
actical con
v
e
rsion
ra
n
g
e
s
of t
h
e Z-s
o
ur
ce i
nvert
ers. T
h
e Z source inverters
with
in
tellig
ent co
n
t
ro
l and
ren
e
wab
l
e sou
r
ce fo
r m
a
x
i
m
u
m
o
u
t
p
u
t
h
a
v
e
also
b
e
en
an
area
o
f
i
n
terest for
r
e
sear
ch
ers [10
]
. A
ltho
ugh
co
nv
er
sion
g
a
i
n
s of
th
e Z-
sou
r
ce inv
e
rters
are th
eoretically in
fin
ite, p
r
actical
issues like
hi
ghe
r sem
i
conductor stresse
s
and poore
r
s
p
ectral performances ca
n c
o
nstrain thei
r hi
ghe
st
achieva
ble limits. These c
o
nstraint
s are
und
en
iab
l
y lin
k
e
d
to
t
h
e trad
e
o
f
f b
e
t
w
een
mo
du
latio
n ratios and
sho
o
t
t
h
ro
u
gh
du
rat
i
o
n ex
pe
r
i
enced
by
t
h
e
Z-s
o
u
r
ce i
n
ver
t
ers. Eac
h
t
ech
ni
q
u
e ha
s i
t
s
o
w
n a
d
vant
a
g
es
an
d
d
i
sadv
an
tag
e
s
th
at
m
i
g
h
t
b
e
tter su
it certain
ap
p
lication
s
. Th
e fin
a
l d
ecisi
o
n
o
n
wh
ich
to
select is, th
erefo
r
e,
depe
n
d
ent
on t
h
e p
r
o
b
l
e
m
s
unde
r co
nsi
d
era
t
i
on, i
n
di
vi
dual
ju
dgm
ent
s
, p
r
efere
n
ces. T
h
e
bel
i
e
f m
i
ght
ha
ve l
e
d
to the
de
velopm
ent of va
rious dc
–ac i
nve
rters found
i
n
t
h
e literature. Am
ong them
, the m
o
st noticeable at
prese
n
t
m
i
ght
be t
h
e
vol
t
a
ge
Z-s
o
u
r
ce i
nve
r
t
er,
wh
ose
l
a
y
out
s
are
sh
o
w
n
i
n
Fi
g
u
re
1
[
1
]
.
cha
r
act
eri
s
t
i
c
s suc
h
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 4,
No
.
1,
Mar
c
h
2
014
:
61
–
6
9
62
as b
i
d
i
rection
a
l en
erg
y
fl
o
w
cap
ab
ility, it p
r
ov
id
es si
n
u
soid
al in
pu
t an
d o
u
t
p
u
t
wav
e
fo
rm
with
m
i
n
i
m
u
m
hi
g
h
or
de
r
har
m
oni
cs and
n
o
s
u
b
harm
oni
cs, T
h
e
speci
a
l
Z-
net
w
or
k,
c
o
m
p
ri
si
ng
t
w
o
capaci
t
o
rs a
n
d t
w
o
in
du
ctor
s, co
nn
ected
to
t
h
e w
e
ll k
now
n
thr
ee ph
ase br
idg
e
, as sh
own
in
Figu
r
e
1
,
allo
w
s
wo
rk
ing
in
bu
ck
or
b
o
o
s
t m
o
d
e
s usin
g
th
e
ST state. Th
e ZSI adv
a
n
t
ag
eou
s
ly
utilizes th
e ST states to
b
o
o
s
t th
e d
c
- lin
k
v
o
l
t
a
g
e
b
y
gat
i
ng
o
n
bot
h
t
h
e u
ppe
r a
nd l
o
we
r s
w
i
t
c
hes
of a
p
h
ase l
e
g
.
In a
d
di
t
i
on, a
S
T
st
at
e caused
by
El
ect
rom
a
gnet
i
c
Interfere
n
ce (E
MI) noise does
not dest
roy the circuit. Therefore a
m
o
re
reliable single stag
e powe
r conve
rter
fo
r
bot
h
buc
k a
n
d
b
o
o
st
po
we
r c
o
n
v
er
si
o
n
i
s
obt
ai
ne
d.
Fig
u
r
e
1
.
Topolo
g
y
o
f
vo
ltag
e
typ
e
SL Z-Sour
ce Inv
e
r
t
er
2.
GENERALIZ
E
D
MULTICELL SL TOPOLOGY
Th
e
SL topo
log
y
is
g
e
n
e
ralized
in Figure
2
,
wh
ere
th
e
g
e
neric cell id
en
ti
fied
is
shown
at th
e lower
r
i
gh
t co
rn
er. I
t
co
n
s
ists of
one in
du
cto
r
Ln
and t
h
ree
di
o
d
e
s
D
3
n
−
1
,
D
3
n
−
2
, and
D
3
n
fo
r
th
e
n
th
cell. Th
is cell
can be duplicat
ed 2
N
tim
e
s (where
N
i
s
an i
n
t
e
ger
)
, di
vi
de
d equal
l
y
bet
w
ee
n t
h
e up
pe
r an
d l
o
we
r dc rai
l
s
, and
connected as in Figure 2.
Note th
at in
du
ctors
L
2
N
+1
and
L
2
N
+2
are not
i
n
cl
ude
d i
n
t
h
e
gene
ri
c cel
l
s
,
but
ca
n
rath
er b
e
v
i
ewed
as t
h
e
o
r
i
g
in
al two
indu
cto
r
s fo
und
in Fig
u
re 1 fo
r th
e trad
ition
a
l voltag
e
-typ
e Z-so
urce
in
v
e
rter. It thus ap
p
e
ars th
at th
e style o
f
fo
rmin
g
th
e g
e
n
e
ric cell al
lo
ws th
e g
e
n
e
ralized
SL to
po
log
y
to
b
e
viewe
d
as
addi
ng ext
r
a cells t
o
the
origi
n
al
two induct
o
rs
rather t
h
an to
re
place them
[12].
Fig
u
r
e
2
.
Topolo
g
y
o
f
g
e
n
e
r
a
l
i
zed
vo
ltag
e
typ
e
SL Z-
So
ur
ce In
v
e
r
t
er
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
C
o
m
p
a
r
at
i
ve E
v
al
u
a
t
i
o
n
of
G
e
ner
a
l
i
z
ed M
u
l
t
i
cel
l
Impe
da
n
ce S
o
u
r
ce I
n
ve
rt
er …
(
V
Ra
g
have
n
dr
a R
a
j
a
n)
63
Th
ese cells m
u
st in
trod
u
ce add
itio
n
a
l ind
u
c
t
o
rs i
n
p
a
rallel d
u
ring
sh
oo
t-t
h
rou
g
h
ch
arg
i
ng
and
m
o
re
in
du
ctor
s in
ser
i
es d
u
r
i
ng
non
shoo
t-
thro
ugh d
i
sch
a
rg
ing
.
Featu
r
es and
exp
r
essi
on
s f
o
r
th
e tw
o
p
r
o
cesses ar
e
summ
arized as follows
Sho
o
t
-Thro
ugh: In
itiated
b
y
tu
rn
ing
on
two sw
itch
e
s fro
m
th
e sam
e
p
h
a
se leg
o
f
t
h
e V
S
I
b
r
i
d
ge.
That
cau
ses di
ode
s D a
n
d D
3n
to
tu
rn
OFF, wh
ile d
i
od
es D
3n-1
and D
3n-
2
co
ndu
ct. A
l
l
in
du
ctors are
the
n
ch
arg
e
d
in p
a
rallel b
y
th
e two
Z-so
urce capacito
rs,
g
i
v
i
ng
rise to
a co
mmo
n ind
u
c
tive
vo
ltag
e
o
f
V
L
= V
C
.
Non
s
h
o
o
t
-Thro
ugh
: Rep
r
esen
ted
b
y
on
e
of th
e trad
itio
nal activ
e o
r
nu
ll VSI states. In
t
h
is state,
diodes D
and D
3n
co
nd
uct
,
w
h
i
l
e
di
o
d
es D
3n
-
1
and D
3n-2
b
l
o
c
k. All ind
u
cto
r
s th
en
d
i
scharg
e i
n
series
to
th
e
external ac load, whose com
m
on i
nductive
voltage is written as V
L
=(V
dc
−
V
C
)/
(N + 1
)
,
whe
r
e N + 1 is the
num
ber o
f
i
n
d
u
ct
o
r
s i
n
t
h
e u
ppe
r o
r
l
o
we
r cascade
d
bl
oc
k.
Avera
g
i
ng V
L
ove
r a swi
t
c
hi
n
g
peri
o
d
t
o
zer
o t
h
e
n
gi
ves
t
h
e
fol
l
o
w
i
n
g
gene
ri
c e
x
p
r
essi
ons
f
o
r
go
ve
rni
n
g
t
h
e
gene
ral
i
zed
SL
Z-s
o
urce i
nve
r
t
er.
1
– d
ST
V
dc
V
C
=
(1
)
1
−
(
N
+ 2
)
d
ST
1 +
Nd
ST
V
dc
V
i
=
(2
)
1
−
(
N
+ 2)
d
ST
M
[1
+
Nd
ST
]
V
dc
V
ac
=
(3
)
1
−
(
N
+ 2)
d
ST
2
The b
o
o
st
fact
or i
s
gi
ve
n by
B
= (1 +
Nd
ST
)/(1
−
(
N
+ 2)
d
ST
), w
h
i
c
h ca
n b
e
m
a
de hi
ghe
r t
h
an any
o
f
the earlier gai
n
s by adding
m
o
re generic
cells. The desi
red
gai
n
i
s
al
so ar
ri
ve
d
at a r
e
du
ced
shoo
t-th
ro
ugh
du
rat
i
o
n,
wh
os
e l
i
m
i
t
i
s
gi
ven
d
ST
<
1/
(
N
+
2
)
i
s
de
ri
ve
d
by
set
t
i
ng t
h
e
de
nom
i
n
at
or
of
(
3
) t
o
be
great
e
r
t
h
a
n
zero. Th
at allows a
h
i
gh
er mo
du
latio
n ratio to
be used
since
M
≤
1.
1
5
(
1
−
d
ST
). Better
u
tilizatio
n
of t
h
e
d
c
-
l
i
nk, l
o
we
r c
o
m
ponent
st
res
s
es, a
nd
bet
t
e
r sp
ect
ral
pe
rf
orm
a
nce l
i
nke
d t
o
a
hi
gh
M
can, there
f
ore
,
be
achieve
d.
With these c
h
aracte
r
istics,
t
h
e
ge
n
e
ral
i
zed SL
t
o
pol
ogy
i
s
l
i
kel
y
t
o
fi
nd
ap
pl
i
cat
i
ons i
n
re
ne
wabl
e
or
ot
h
e
r cl
ea
n
ene
r
gy
i
n
d
u
st
ry
, w
h
e
r
e
hi
g
h
bo
ost
i
n
g
gai
n
f
o
r
gri
d
i
n
t
e
rfaci
n
g
i
s
us
u
a
l
l
y
needed
[
1
3]
. A
p
r
ob
ab
le ex
amp
l
e is g
r
i
d
-tied
pho
tov
o
ltaic (PV) sy
stem
,
who
s
e im
p
l
emen
tatio
n
will u
s
u
a
lly inv
o
l
v
e
th
e
sensi
n
g o
f
ˆ
v
i
di
rect
l
y
or i
n
d
i
rect
l
y
t
h
rou
g
h
m
easuri
ng i
s
gi
ven
by
V
C
(since ˆ
v
i
= 2
V
C
−
V
dc
du
r
i
ng
th
e
no
ns
ho
ot
-t
hr
o
u
g
h
st
at
e).
The m
easure
d
ˆ
v
i
can t
h
en
be
reg
u
l
a
t
e
d c
o
n
s
t
a
nt
by
a
d
j
u
st
i
ng
M
with
i
n
t
h
e
u
p
p
e
r li
m
it
o
f
1
.
15
(1
−
d
ST
), while
rese
rvi
ng
d
ST
f
o
r t
r
a
c
ki
n
g
t
h
e m
a
xi
m
u
m
powe
r
p
o
i
nt
of t
h
e PV s
o
u
r
ce. T
h
i
s
c
o
nt
r
o
l
arra
n
g
em
ent
i
s
standa
rd for P
V
system
s,
m
e
aning that
unforeseen com
p
lication is
unli
k
ely
to
surface wi
th
th
e
g
e
n
e
rali
zed
SL
i
nve
rt
er[
1
4]
. W
i
t
h
i
t
s
ˆ
v
i
regu
lated
con
s
tan
t
, selectin
g a suitab
l
e vo
ltag
e
ratin
g
for its semico
n
d
u
c
tors i
s
thu
s
q
u
ite straigh
t
forward
as lon
g
as th
ey h
a
v
e
the in
stan
ta
n
e
o
u
s cap
acity to
c
a
rry th
e p
e
ak
sh
oo
t-
t
h
ro
ugh
cu
rr
en
t.
Othe
r passive com
pone
nt sizi
ng wise can
be approac
h
e
d
base
d on the
s
a
m
e
sizing requirem
ents outlined in
[6
]
for th
e trad
itio
n
a
l Z-sou
r
ce in
v
e
rter.
3.
THREE PHASE VOLT
AGE
SOURCE INVE
RTER
The ci
rc
ui
t
di
a
g
ram
for t
h
ree
-
p
h
ase
VSI t
o
pol
ogy
i
s
s
h
o
w
n i
n
Fi
g
u
re
3 an
d t
h
e ei
gh
t
val
i
d
swi
t
c
h
st
at
es are
gi
ve
n i
n
Ta
bl
e 1
.
A
s
i
n
si
ngl
e
-
pha
se VS
Is,
t
h
e
s
w
i
t
c
hes
of
any
l
e
g o
f
t
h
e i
n
ver
t
er (S
1
and S
4
, S
3
and
S
6
, or S
5
a
nd S
2
) cannot be s
w
itched
on si
m
u
ltaneously because th
is woul
d res
u
lt in a short circuit across t
h
e
dc l
i
nk
v
o
l
t
a
ge
sup
p
l
y
. Si
m
i
l
a
rl
y
,
i
n
o
r
de
r t
o
avoi
d u
n
d
efi
n
ed st
at
es i
n
t
h
e
VSI
,
an
d t
h
us
un
de
fi
ne
d ac o
u
t
p
ut
lin
e v
o
ltag
e
s, th
e switch
e
s of
an
y leg
of th
e i
n
v
e
rter ca
n
n
o
t
b
e
switch
e
d
o
f
f sim
u
ltan
e
o
u
s
ly as th
is will r
e
su
lt
in
vo
ltag
e
s th
at will d
e
p
e
n
d
up
on
th
e
resp
ect
iv
e lin
e curren
t
p
o
l
arity. Duri
n
g
t
h
e states 7
& 8
(in
tab
l
e
1) th
e
ac curre
nt free
wheel through
either
t
h
e u
ppe
r or l
o
we
r com
p
o
n
e
n
t
whi
c
h
pr
o
duces ze
ro
ac l
i
n
e vol
t
a
ge
s. The
rem
a
i
n
i
ng st
at
es (1 t
o
6 i
n
Ta
bl
e 1)
pr
o
duce
no
nze
r
o ac
out
put
v
o
l
t
a
ges
.
T
h
e i
n
vert
er m
oves f
r
om
one s
t
at
e t
o
an
o
t
h
e
r t
o
g
e
nerate a requ
ired
vo
ltag
e
wav
e
form
. Th
u
s
th
e resu
lting
ac ou
tpu
t
lin
e vo
ltag
e
s con
s
ist of
d
i
scret
e
val
u
es
o
f
v
o
l
t
a
ges t
h
at
a
r
e V
s
, 0,
an
d
-Vs
f
o
r t
h
e t
o
p
o
l
o
gy
sho
w
n i
n
Fi
g
u
r
e 4
.
T
h
e m
odul
at
i
ng t
e
c
hni
q
u
e i
s
use
d
to ens
u
re
the valid states
. In t
h
i
s
we
al
s
o
e
xpl
ai
n
i
n
va
ri
o
u
s m
odes.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
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:
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94
I
J
PED
S
Vo
l. 4,
No
.
1,
Mar
c
h
2
014
:
61
–
6
9
64
Figu
re
3.
Circu
it diagram
fo
r
Voltage
S
o
u
r
c
e
I
nve
rter
Tab
l
e 1
.
Valid
switch
stat
es
for a three-phas
e VSI
State Switch
V
ab
V
bc
V
ca
No.
States
S1
,
S2
,
1 100
Vs
0
-
V
s
S3
o
n
S2
,
S3
,
2 110
0
Vs
-
V
s
S1
o
n
S3
,
S4
,
3 010
-
V
s
Vs
0
S2
, o
n
S4
,
S5
,
4 011
-
V
s
0
Vs
S3
o
n
S5
,
S6
,
5 001
0
-
V
s
Vs
S4
o
n
S6
,
S1
,
6 101
Vs
-
V
s
0
S5
o
n
S1
,
S3
,
7
111
0
0
0
S5 on
S4
,
S6
,
8
000
0
0
0
S2 on
Th
e lin
e to
n
e
u
t
ral vo
ltag
e
m
u
st b
e
d
e
termin
ed
to
fi
nd t
h
e line (or pha
s
e) curre
nt. T
h
ere are t
h
ree
m
odes of
o
p
e
ration
in a
h
a
lf
–
cycle and
th
e expression
for each
m
o
de will b
e
g
i
v
e
n b
e
low,
Du
rin
g
M
ode
I
:
(0
<
t <
/3
)
/
,
2
/3
(4
)
Du
ri
n
g
M
ode
I
I
:
(
/3
<
t <
2
/3
)
,
2
/3
(5
)
Du
rin
g
M
ode
I
II:
(2
/3
<
t <
)
/
,
2
/3
(6
)
In t
h
i
s
c
o
n
s
eq
uence
,
t
h
e s
h
a
p
e o
f
t
h
e m
odul
at
i
on i
n
de
x
m
of th
e power con
v
e
rter is
v
e
ry sim
i
lar to
th
e grid vo
ltage w
a
v
e
fo
rm
. Th
e
o
u
t
pu
t vo
ltag
e
o
f
th
e converter can
b
e
written
as
V
ou
t
=
mV
dc
. De
pe
ndi
ng
o
n
the m
odulation inde
x
value
,
t
h
e
power converter
will be
driven by diffe
re
nt
P
W
M
st
rate
gies.
As a m
a
tter of
fact, it is possi
ble to ide
n
tify four
operating zone
s
(see Figure 3),
and fo
r each zone
[15], the output voltage
lev
e
ls of th
e
p
o
wer conv
erter
will b
e
d
i
fferen
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
C
o
m
p
a
r
at
i
ve E
v
al
u
a
t
i
o
n
of
G
e
ner
a
l
i
z
ed M
u
l
t
i
cel
l
Impe
da
n
ce S
o
u
r
ce I
n
ve
rt
er …
(
V
Ra
g
have
n
dr
a R
a
j
a
n)
65
4.
PULSE WIDTH
MODUL
A
TION
P
W
M
i
s
a ver
y
effi
ci
ent
way
of pr
ovi
di
n
g
i
n
t
e
rm
edi
a
t
e
am
ount
s of el
ect
ri
cal
powe
r
b
e
t
w
een f
u
l
l
y
o
n
an
d
fu
lly o
f
f. A sim
p
le p
o
wer switch
wit
h
a typ
i
cal p
o
wer so
urce prov
id
es fu
ll po
wer on
ly, wh
en
switch
e
d
on. PWM is a
com
p
aratively recent tec
hni
que, m
a
de
practic
al by m
odern e
l
ectronic
powe
r s
w
itches
[3].
Figu
re
4.
P
W
M
fo
r t
h
e
DC line side
co
n
v
er
ters
Fi
gu
re 4
prese
n
t
s
t
h
e de
pen
d
ence
of t
h
e
con
v
e
r
t
e
r i
n
pu
t
vol
t
a
ge o
n
t
h
e m
odul
at
i
o
n
i
ndex
wi
t
h
resp
ect to
t
h
e DC-link
vo
ltag
e
. Th
e m
o
du
latio
n
b
a
ndwid
th
is g
e
n
e
rally d
i
v
i
d
e
d
i
n
t
o
th
e lin
ear an
d
t
h
e
no
nl
i
n
ea
r ran
g
e
. The l
i
m
i
t
a
t
i
on
of t
h
e m
odul
at
i
o
n re
gi
o
n
t
o
t
h
e l
i
n
ear
range i
s
su
ffi
ci
ent
for t
h
e
pr
o
p
er
o
p
e
ration
o
f
th
e
PWM rectifier. Yet for
t
h
e
ex
cellen
t
dyn
amic p
e
rf
orman
ce of
t
h
e
syn
c
hr
ono
us rectif
ier
du
ri
n
g
t
h
e t
r
a
n
si
ent
s
t
h
e
op
erat
i
on i
n
t
h
e
ove
r m
odul
at
i
on ra
n
g
e m
u
st
be pr
o
v
i
d
e
d
[
8
]
.
H
o
we
v
e
r t
h
i
s
tech
n
i
qu
e in
tro
d
u
ces th
e lin
e cu
rren
t d
i
sto
r
tion
s
du
e its n
o
n
linearity an
d
m
a
y
b
e
in
ad
v
i
sab
l
e in
th
e
applications of the DC conve
r
ters
im
proving the electrical power quality
. The issue of the m
odulation
inde
x
and the m
odul
ation ra
nge for the basic P
W
M techniques will
be prese
n
ted in detail in the ne
xt sections of this
pape
r
5.
SINU
SIODAL
PU
LSE WID
T
H M
O
DULA
T
ION
There
are
th
ree
sin
u
soi
d
al re
fe
rence
wa
ves
(
V
ra
, V
rb
, a
n
d
V
rc
) each s
h
ifted by
120
o
. A carrier
wave
is
com
p
ared
wi
t
h
t
h
e
refe
ren
ce
si
gnal
c
o
rres
p
on
di
n
g
t
o
a
p
h
a
se t
o
ge
nerat
e
t
h
e
gat
i
n
g si
gnal
s
f
o
r
t
h
at
pha
se.
Com
p
aring the
carrier si
gnal
V
cr
with the
re
fere
nce
phases
V
ra
, V
rb
, an
d
V
cr
pr
od
uces
S
1
a
n
d
S
3
res
p
e
c
t
i
v
el
y
as sh
o
w
n i
n
Fi
gu
re
5b
. T
h
e i
n
st
ant
a
neo
u
s l
i
ne
– t
o
– l
i
n
e
out
put
v
o
l
t
a
ge
i
s
V
ab
=
V
s
(
S
1
– S
3
)
.
T
h
e
o
u
t
p
ut
vol
t
a
ge as sh
o
w
n i
n
Fi
g
u
r
e 5d i
s
ge
nerat
e
d by
el
im
i
n
at
ing t
h
e co
n
d
i
t
i
on t
h
at
t
w
o s
w
i
t
c
hi
n
g
de
vi
ces i
n
t
h
e
sam
e
ar
m
cannot
co
nd
uct
at
t
h
e sam
e
tim
e.
The n
o
r
m
a
li
zed car
ri
er f
r
eq
u
e
ncy
m
f
shoul
d be
od
d m
u
l
t
i
pl
e of
t
h
ree.
Th
us
, a
l
l
phase
–
v
o
l
t
a
ge (
V
an
, V
bn
, and
V
cn
) a
r
e
identical,
but
120
o
ou
t of
p
h
a
se w
i
t
h
ou
t
ev
en
h
a
rm
o
n
i
cs; m
o
reov
er,
h
a
rm
o
n
i
cs at
frequ
encies m
u
ltip
le o
f
three are i
d
en
tical in
am
p
litu
d
e
and
ph
ase in
all
pha
ses.
Fo
r i
n
s
t
ance, i
f
t
h
e
ni
nt
h
ha
rm
oni
c v
o
l
t
a
ge i
n
p
h
ase
‘a’
i
s
V
an
9
(t) =
v
9
si
n.9
t.
(7)
The
ni
nt
h
har
m
oni
c i
n
p
h
ase
b
n
will
b
e
,
V
bn
9
(t) =
v
9
Si
n
(9(
t-1
2
0
o
)) (
8
)
= v
9
Si
n
(9
t
-
108
0
o
) (
9
)
= v
9
Si
n9
t (1
0)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 4,
No
.
1,
Mar
c
h
2
014
:
61
–
6
9
66
6.
SIMULATION &
RESULT
S
C
o
m
p
arat
i
v
e anal
y
s
i
s
i
s
do
ne
by
usi
ng M
a
t
l
ab/
S
im
ul
i
nk
m
odel
for P
W
M
and
SP
W
M
i
n
t
e
rm
s of
TH
D fo
r Mo
tor
lo
ad
Fi
gu
re
6.
TH
D
f
o
r R
o
t
o
r c
u
r
r
e
nt
wi
t
h
P
W
M
Tech
ni
q
u
e
Th
e sim
u
latio
n
resu
lts for PWM Techn
i
que is d
e
ter
m
in
ed
with
THD An
alysis fo
r
which
th
e ro
t
o
r
cu
rren
t
it h
a
s 13
.4
4%.
Fi
gu
re 7.
TH
D
f
o
r
S
t
a
t
or
cu
rr
en
t w
ith PW
M
T
e
c
h
n
i
qu
e
Th
e abo
v
e
simu
latio
n
resu
lts
for PWM Techn
i
qu
e is
d
e
termin
ed
with THD
An
alysis
for
th
e stato
r
current 13.11%.
Im
pl
em
ent
a
ti
on of Si
nus
oi
d
a
l
PW
M
t
ech
ni
que i
n
t
h
e t
h
re
e phase i
n
vert
e
r
fo
r t
h
e i
n
d
u
c
t
i
on dri
v
e i
s
shown in the Figure 8. T
h
e re
sults for the sa
me are sh
own
in
th
e fo
llo
wi
ng
sectio
ns. Bo
t
h
th
e circu
its differ
onl
y
by
t
h
e P
W
M
t
ech
ni
q
u
e
use
d
. T
h
e
har
m
oni
cs red
u
ct
i
on i
s
t
h
e m
a
jor
reaso
n
s
be
hi
n
d
u
s
i
n
g t
h
e si
n
u
soi
d
al
P
W
M
.
T
h
e i
m
pr
o
v
em
ent
i
n
the pe
rf
orm
a
nc
e of t
h
e i
n
d
u
ct
i
on m
o
t
o
r i
s
t
hus ac
hi
ev
ed
. Fi
gu
re 9 s
h
ow
n t
h
e
rot
o
r c
u
r
r
ent
p
e
r p
h
ase a
nd t
h
e ha
rm
oni
c cont
e
n
t
an
d i
n
Fi
gu
re 1
0
har
m
oni
c cont
ent
i
n
t
h
e st
at
or c
u
r
r
ent
i
s
analyzed a
n
d s
h
own.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
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8-8
6
9
4
C
o
m
p
a
r
at
i
ve E
v
al
u
a
t
i
o
n
of
G
e
ner
a
l
i
z
ed M
u
l
t
i
cel
l
Impe
da
n
ce S
o
u
r
ce I
n
ve
rt
er …
(
V
Ra
g
have
n
dr
a R
a
j
a
n)
67
Fi
gu
re
8.
Si
m
u
l
a
t
i
on f
o
r
M
o
t
o
r l
o
a
d
wi
t
h
SP
WM
Tec
hni
qu
e
Fi
gu
re
9.
TH
D
f
o
r R
o
t
o
r C
u
r
r
e
nt
wi
t
h
SP
W
M
Tech
ni
q
u
e
Fi
gu
re
1
0
. T
H
D f
o
r St
at
o
r
C
u
r
r
ent
wi
t
h
SP
WM
Tec
hni
qu
e
The a
b
ove
Si
m
u
l
a
t
i
on re
sul
t
s sh
ow
n
f
o
r
r
o
t
o
r c
u
r
r
ent
a
n
d
st
at
or
c
u
r
r
e
nt
,
wh
ose
r
o
t
o
r
cu
rre
nt
i
s
9.
84
% a
n
d
st
at
or
cu
rre
nt
has
10
.0
5%
wi
t
h
S
i
nus
oi
dal
Pul
s
e
W
i
dt
h M
o
d
u
l
a
t
i
on Tec
h
ni
q
u
e
. T
h
e i
n
p
u
t
v
o
l
t
a
ge
ap
p
lied fo
r PWM Techn
i
qu
e an
d SPW
M
Tech
n
i
q
u
e
is
4
40vo
lts.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
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:
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-86
94
I
J
PED
S
Vo
l. 4,
No
.
1,
Mar
c
h
2
014
:
61
–
6
9
68
7.
CO
NCL
USI
O
N
Th
is p
a
p
e
r h
a
s d
eals with
a
Mu
lticell with
Z-So
ur
ce inver
t
er
so
lu
tion
f
o
r
Th
r
ee
p
h
a
se I
ndu
ctio
n
m
o
t
o
r. The
P
W
M
st
rat
e
gy
was c
hose
n
i
n
or
der t
o
obt
ai
n
t
h
e m
i
nim
u
m
num
ber
of c
o
m
m
u
t
a
t
i
ons t
o
m
a
xim
i
ze
effi
ci
ency
. T
h
e
pr
o
pose
d
s
o
l
u
t
i
on
wa
s com
p
ared
with the
PW
M techni
q
u
e an
d S
P
W
M
t
echni
que
. B
y
us
i
n
g
P
W
M
Ha
rm
oni
cs are
m
o
re. To o
v
erc
o
m
e
t
h
is di
sad
v
ant
a
ge
SP
W
M
t
echni
que i
s
use
d
by
usi
n
g t
h
i
s
swi
t
c
hi
n
g
losses a
r
e c
o
ntrolled and ha
rm
onics are
reduced c
o
m
p
ared
to PWM m
e
th
od
. Fin
a
lly th
e PWM and
SPWM
co
n
t
ro
lled Mu
l
ticell Z-So
urce Inv
e
rter is an
alyzed
b
y
Sim
u
latio
n
resu
lts are ob
tain
ed and
resu
lting
in stab
ilit
y
im
provem
ent.
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ES
[1]
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rce
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t
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E
EE Trans. Ind
.
Appl
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: 504–510.
[2]
PC Loh, DM Vi
lathg
a
muwa, YS Lai,
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l
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EE
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[3]
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y
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y
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e
r
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rt
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ase photovoltaic s
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r
ans. Power El
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[10]
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b
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ontroller in Z-S
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[13]
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ies
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c
. I
E
EE Int. Con
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erg
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r
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r
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[15]
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Z
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n
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rans
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.
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E
E
E
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r
ans. Power El
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.
BIOGRAP
HI
ES OF
AUTH
ORS
V Raghavendr
a
Rajan
receiv
ed the Bachelor
deg
r
ee
in E
l
e
c
tri
c
a
l
and
Ele
c
tron
ics
Engin
eering
from
Aurora’s
Seeth
a
iah
engin
e
e
r
ing col
l
eg
e, J
a
wa
harlal Nehru
University
, H
y
d
e
rabad
,
India in
2011. Pursuing Master of Engineer
ing in Po
wer Electronics and Drives
from Jeppiaar
Engineering Co
lleg
e
, Anna Un
iversity
, India.
M
y
ar
ea of
int
e
res
t
in
cludes
i
n
the fi
eld of
Renewable
Ener
g
y
and
PW
M
techniques in conv
erters.
CS
Ajin S
e
khar
has
receiv
e
d the
B.E degre
e
in El
ectr
i
ca
l and El
ec
tronics
Engin
eer
ing from
S
RR
engineering Co
lleg
e
, Anna U
n
iversity
, Chen
na
i 2012, Ind
i
a. He
is pursuing Master of
Engineering in
Power Electro
nics and Driv
es from Jeppiaar Engineer
ing College, Anna
Univers
i
t
y
, Indi
a. His
area of
inter
e
s
t
includ
e
s
in the field
of Renewabl
e Energ
y
, P
o
wer
Converters, AC-
A
C Converters
and PWM techniques.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
C
o
m
p
a
r
at
i
ve E
v
al
u
a
t
i
o
n
of
G
e
ner
a
l
i
z
ed M
u
l
t
i
cel
l
Impe
da
n
ce S
o
u
r
ce I
n
ve
rt
er …
(
V
Ra
g
have
n
dr
a R
a
j
a
n)
69
R Hem
a
ntha Ku
m
a
r has
rec
e
ive
d
the B
ach
elor d
e
gree
in
Ele
c
tri
c
al and
El
ec
troni
cs
Engine
ering
from Thangavelu Engineering C
o
lleg
e
, Anna Un
iver
sity
, India in
2011. He is pur
suing Master of
Engineering in
Power Electro
nics and Driv
es from Jeppiaar Engineer
ing College, Anna
University
, India. His area of in
terest in
cludes
in the field of Power Converters for Renewable
Energ
y
, PWM techniques
and M
u
ltil
evel
Conver
t
ers.
M
S
a
s
i
kum
ar has
receiv
e
d the B
ache
l
or degr
ee i
n
Ele
c
tri
cal
and
Ele
c
troni
cs
Eng
i
neer
ing from
KS Rangasamy
College of Tec
hnolog
y
,
Madras University
, In
dia in 1999, an
d the M Tech
degree in Power
Electron
ics fro
m VIT Universi
ty
, in
2006. He
has obtain
e
d his
Ph.D. degr
ee
from Sath
y
a
b
a
ma University
, Ch
ennai
in 2011. C
u
rre
ntly
h
e
is w
o
rking as a Prof
essor and Head
in J
e
ppi
aar
Engi
neering
Coll
ege
,
Chenna
i T
a
m
i
l
n
adu, Ind
i
a
.
His
are
a
of
int
e
res
t
includ
es
in
the
fields of wind
energ
y
s
y
stems, H
y
brid s
y
stems and Power convert
ers and
Soft-Switching
techn
i
ques
.
He
is
a
lif
e m
e
m
b
er o
f
IS
TE.
Evaluation Warning : The document was created with Spire.PDF for Python.