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.
6, N
o
. 3
,
Sep
t
em
b
e
r
2015
, pp
. 63
6
~
64
7
I
S
SN
: 208
8-8
6
9
4
6
36
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
New Hybrid Structure Based on
Improved Switched Inductor
Z-Source and Parall
el In
vert
er
s for Renewable Energy Systems
Al
i
Z
a
keri
an,
Dar
y
oos
h Naz
a
rp
our
Department o
f
Electrical and Co
mputer E
ngin
eer
ing, Urm
i
a
Univ
ers
i
t
y
,
Urm
i
a,
Ir
an
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Apr 12, 2015
Rev
i
sed
Ju
l 24
,
20
15
Accepted Aug 15, 2015
Nowaday
s
, mor
e
and more distributed
g
e
ner
a
tions and renewable ener
g
y
sources, such as
wind, solar
and tidal
power
,
are connected
to the public
gr
id
b
y
the means of
power inv
e
rters. Th
ey
of
ten
for
m
microgrids before being
connected to th
e public grid
. Due to
the availability
of
high cur
r
e
nt power
ele
c
troni
c devic
e
s
, it is inevitabl
e
to use
several inverters in
parallel for high-
power and/or low-cost applications.
So, inv
e
r
t
ers should beconnected in
parallel to
pro
v
ide s
y
s
t
em r
e
dunda
ncy
and high
reliab
ility
,
which are
im
portant for cr
itic
al custom
ers.
In th
is paper, t
h
e m
odeling, de
signing and
s
t
abili
t
y
an
al
ys
i
s
of parall
el-
c
o
nnect
ed thr
ee-p
h
as
einver
t
ers
ar
e deriv
e
d for
a
ppl
ic
a
t
i
on i
n
re
ne
wa
ble
e
n
e
r
gy
sy
ste
m
s.
T
o
e
n
l
a
rge
volt
a
ge
adj
u
st
a
b
ility
,
the proposed in
verter
emplo
y
s
an
improved switched inductor Z-source
impedance network to coup
le the ma
in
circuit
and th
e po
wer source.
Compared with the classical
Z-source
inver
t
er (
Z
SI) and switched inducto
r
Z-source inverter (SL-ZSI), the
proposed
inverter significan
tly
in
creases th
e
voltag
e
boost
in
version ab
ility
and also
can
incr
ease the
power capacity
an
d
the reliability
of inverter s
y
st
ems. The proposed topology
and its
perform
ances
ar
e va
lida
t
ed usin
g sim
u
lation
res
u
lts which
are
obtain
e
d in
Matlab/Sim
u
link
.
Keyword:
Mo
du
latio
n ind
e
x
Parallel op
erati
o
n
Sw
itch
e
d
inducto
r
Vol
t
a
ge
gai
n
Z-s
o
urce inve
rter
Copyright ©
201
5 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
:
Ali Zak
e
rian,
Depa
rtem
ent of Electrical a
nd Co
m
p
u
t
er
Engin
eer
ing
,
Urm
i
a Un
iv
ersity,
Urm
i
a, Ira
n.
Em
a
il: zak
erian
.
alii@g
m
ail.c
o
m
1.
INTRODUCTION
In s
o
m
e
renewabl
e ener
gy
ut
i
l
i
zat
i
on appl
i
cat
i
ons, t
h
e i
n
p
u
t
po
wer s
o
ur
ce i
s
a DC
vol
t
a
ge sou
r
ce
whi
c
h
has a
wi
de
v
o
l
t
a
ge
vari
at
i
o
n ra
n
g
e
, suc
h
as
t
h
e gri
d
-t
i
e
d
p
h
o
t
o
vol
t
a
i
c
ge
n
e
rat
i
on a
n
d
fu
el
cel
l
g
e
n
e
ration
.
In
t
h
ese
cases,
an
in
v
e
rter with
bo
o
s
t
cap
ab
ility
is requ
ired
t
o
gen
e
rate electricity at lo
w inp
u
t
DC
vol
t
a
ge
. Di
f
f
e
r
ent
i
n
vert
er t
o
p
o
l
o
gi
es m
e
et
i
ng t
h
e re
qui
rem
e
nt
can be fo
un
d an
d
cl
assi
fi
ed i
n
t
o
t
w
o
categories: the isolated inve
rters and
no
n-
iso
l
ated
in
ver
t
ers.
The isolated inverters ar
e u
s
ual
l
y
equi
p
p
e
d
wi
t
h
a step
-u
p
tr
an
sf
or
m
e
r
w
h
ich
mak
e
s th
e syste
m
b
u
l
k
y
and
lo
w
eff
i
cien
cy
w
h
ile th
e non-
iso
l
ated
inv
e
rter
is
considere
d
high efficiency and hi
gh
powe
r density [1]. T
h
e
r
e are typically
tw
o
p
opu
lar
no
n-
iso
l
ated
t
o
po
log
y
can
d
i
d
a
tes
for
th
ese ap
p
licatio
n
s
.
On
e is t
h
e trad
ition
a
l t
w
o-stag
e boo
st
-bu
c
k
inv
e
rt
er
(BBI), an
d th
e o
t
h
e
r
one
i
s
t
h
e
ne
wl
y
pr
o
pose
d
Z-s
o
u
r
ce i
nve
rt
er
(ZS
I)
[
2
]
.
The ZSI prese
n
ts a ne
w singl
e
-stage structure to ac
hi
eve t
h
e v
o
l
t
a
ge
bo
o
s
t
/
buc
k cha
r
acter in a single
po
we
r co
nve
rs
i
on st
age
,
w
h
i
c
h has
been r
e
po
rt
ed i
n
a
ppl
i
cat
i
ons t
o
re
ne
wabl
e ene
r
gy
sy
st
em
s. The ZSI has
g
a
in
ed
p
opu
larity as a sing
le-stag
e
bu
ck-bo
o
s
t i
n
vert
er
t
o
p
o
l
o
gy
am
on
g m
a
ny
re
searchers
.
Howe
ver,
its
b
o
o
s
ting
cap
abilit
y co
u
l
d
b
e
l
i
m
i
ted
an
d
th
erefore it
m
a
y n
o
t b
e
su
itab
l
e fo
r so
m
e
ap
p
licatio
n
s
requ
iring
v
e
ry
hi
g
h
bo
ost
de
m
a
ndi
n
g
of
ca
scadi
n
g ot
he
r dc-
d
c bo
ost
c
o
nve
rt
ers
.
T
h
i
s
coul
d
l
o
se
t
h
e effi
ci
ency
a
n
d
dem
a
nd
m
o
re sen
s
ing
fo
r con
t
ro
llin
g th
e ad
d
e
d
n
e
w stag
es.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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94
I
J
PED
S
Vo
l.
6, No
. 3, Sep
t
em
b
e
r
2
015
:
63
6 – 647
63
7
Ove
r
the
recent years, m
a
ny r
e
searche
r
s
have give
n
their
focus in m
a
ny
direc
tions to
develop ZSI t
o
ach
iev
e
d
i
ff
er
en
t obj
ectiv
es
[3
]-
[8
].
In
[9
]-
[1
2
]
,
th
e
f
o
cu
s
is o
n
im
p
r
o
v
i
ng
th
e boo
st f
a
cto
r
o
f
th
e
ZSI
.
For
i
n
st
ance,
[
9
]
-
[
11]
a
d
d
i
n
duct
o
rs
, ca
paci
t
o
rs
,
an
d
di
o
d
es t
o
t
h
e Z
-
i
m
pend
ence
net
w
or
k t
o
pr
od
uce a
hi
gh
dc
-
l
i
nk v
o
l
t
a
ge f
o
r t
h
e m
a
i
n
powe
r
ci
rc
ui
t
fr
om
a very
l
o
w i
n
p
u
t
dc
vo
l
t
a
ge. In
[1
2]
,
t
w
o i
n
duct
o
rs
of t
h
e
im
pedance Z
-
network a
r
e re
pl
aced by a tra
n
s
f
orm
e
r with a
turn ratio
of 2:
1 to obta
in
hi
gh voltage gain.
T
h
ese
to
po
log
i
es su
it
so
lar cell an
d fu
el cell ap
p
licatio
n
s
th
at can
req
u
i
re h
i
gh v
o
ltag
e
g
a
in
to
m
a
tch
th
e so
urce
vol
t
a
ge
di
ffe
re
nce.
Applying s
w
i
t
ched-capacitor, sw
itched-
in
du
ctor
, h
ybrid
sw
itch
e
d
-
cap
acito
r
/
sw
itched
-
i
n
du
ctor
st
ruct
u
r
es,
vol
t
a
ge-l
i
f
t
t
echni
que
s, an
d v
o
l
t
a
ge m
u
l
t
i
p
l
i
e
r cel
l
s
[13]
-[
1
5
]
t
o
dc–d
c con
v
ersi
on
pr
ovi
d
e
s t
h
e
high boost in cascade a
n
d trans
f
or
m
e
rl
ess st
ruct
ures
wi
t
h
hi
gh e
ffi
ci
ency
and
hi
gh
p
o
we
r de
n
s
i
t
y
. A
success
f
ul com
b
ination of the
ZSI an
d switched-i
n
ductor structure, calle
d the switche
d induct
o
rZ
SI (SL
-
ZSI)
[
9
],
pr
ov
id
es st
r
ong
step-u
p inv
e
r
s
i
o
n to
ov
er
co
m
e
th
e b
o
o
s
t
li
m
i
tatio
n
of t
h
e classical ZSI.
On t
h
e
ot
he
r h
a
nd
, m
a
ny
i
n
d
u
st
ri
al
sy
st
em
s dem
a
nd a rel
i
abl
e
po
we
r su
ppl
y
.
O
n
e way
t
o
i
n
crease
th
e reliab
ility i
s
to
in
crease the n
u
m
b
e
r of sou
r
ces. An
o
t
h
e
r way to
in
crease th
e reliab
ility is to
h
a
v
e
p
a
rallel
in
v
e
rters and
th
is wou
l
d
i
n
crease th
e
redund
an
cy as w
e
ll
as th
e m
a
in
tain
ab
ility o
f
th
e i
n
v
e
rters. M
o
reov
er, th
e
p
a
rallel conn
ected
inv
e
rters
effectiv
ely
o
ffer a si
g
n
i
ficantly h
i
g
h
e
r lev
e
l o
f
av
ailab
ility th
an
conv
entio
n
a
l
approaches
. Commercially a
v
ailable ratings
range from
sev
e
r
a
l kVA
to
hu
ndr
ed
s
o
f
kVA
.
Par
a
llel co
nn
ectio
n
t
echni
q
u
es f
o
r i
nve
rt
ers ha
ve been
gai
n
i
n
g i
n
creasi
ng at
t
e
n
t
i
ons i
n
m
o
t
o
r-
dri
v
e sy
st
em
s, con
v
ert
e
r sy
st
em
s,
and
di
st
ri
but
e
d
ge
nerat
i
o
n sy
s
t
em
s [16]
-
[
19]
.
Paralleled inverters can
be built in num
erous
ways
. Firs
t and the m
o
st obvi
ous way
is to have
in
d
e
p
e
nd
en
t in
v
e
rters with
sep
a
rate d
c
so
urces [20
]
an
d
th
e o
t
h
e
r po
ssi
b
ility is
to
co
n
n
ect th
e in
v
e
rters i
n
to
a
com
m
on dc s
o
urce
[
21]
.
Fi
rst
m
e
t
hod
i
s
co
m
m
on as i
t
i
s
sim
p
l
e
. H
o
we
v
e
r, i
t
re
q
u
i
r
es
m
o
re t
h
an
on
e
p
o
we
r
source. In the
context
of
Z
-so
u
r
ce i
n
vert
er, t
h
i
s
m
e
t
hod re
q
u
i
r
es m
o
re t
h
a
n
one
i
nde
pe
nde
nt
Z
-s
o
u
r
ce
im
pedance
net
w
o
r
k
.
T
h
ere
f
o
r
e, t
h
i
s
pape
r p
r
o
p
o
ses a ne
w
hy
bri
d
st
ruct
u
r
e base
d o
n
i
m
prove
d SL Z
-
so
ur
ce
im
pedance
net
w
o
r
k
an
d
paral
l
el
i
nvert
er
s w
h
i
c
h s
h
a
r
e o
n
e
dc-i
np
ut
v
o
l
t
a
g
e
t
o
i
n
c
r
easet
h
e
o
u
t
p
ut
v
o
l
t
a
g
e
i
n
a
wi
de
ra
nge
,
us
abl
e
i
n
re
newa
bl
e en
er
gy
sy
s
t
em
s. M
o
re
ove
r,
beca
use
of
t
h
e
di
vi
ded
o
u
t
put
c
u
rre
nt
am
on
g
p
a
rallel inv
e
rters, t
h
e
p
r
op
o
s
ed
topo
log
y
h
a
s
th
e ab
ility o
f
su
pp
lyin
g h
i
g
h
lo
ad curren
t
s.
The rem
a
i
nder
of t
h
i
s
pape
r
i
s
orga
ni
ze
d as fol
l
o
ws. T
h
e next
sect
i
o
n
i
s
dev
o
t
e
d t
o
a det
a
i
l
e
d
t
o
p
o
l
o
gy
anal
y
s
i
s
of t
h
e i
m
prove
d SL Z
-
so
u
r
ce im
pedance
net
w
o
r
k. O
p
er
at
i
ng p
r
i
n
ci
pl
e
s
and t
h
e e
qui
val
e
n
t
ci
rcui
t
o
f
t
h
e
pr
o
pose
d
t
o
p
o
l
ogy
a
r
e p
r
ese
n
t
e
d i
n
sect
i
o
n
3. Sect
i
on
4
p
r
esent
s
t
h
e si
m
u
l
a
t
i
on res
u
l
t
s and
fin
a
lly, con
c
lusio
n
s
are in
clud
ed in
Section
5
.
2.
CIR
C
U
IT AN
ALYS
IS OF THE
IMP
R
O
V
ED SL
Z
-
S
O
U
RCE IM
P
E
DA
NCE
NE
TWOR
K
As illu
strated
i
n
Figu
re 1
,
t
h
e p
r
o
p
o
s
ed
im
p
r
ov
ed
SL Z-sou
r
ce im
p
e
d
a
n
c
e n
e
two
r
k
co
nsists o
f
si
x
inductors, two
capacito
rs
and twelve
diodes
. The c
o
m
b
ination of
1
2
3
1
23
456
,
,
,
,
,
,
,
,
L
LL
D
D
DD
DD
and
th
e co
m
b
in
ation
of
4
5
6
7
8
9
10
11
12
, ,
,
,
,
,
,
,
L
LL
D
D
D
D
D
D
p
e
rform
s
th
e fun
c
tion
of th
e top
SL cell an
d
th
e
b
o
tto
m
SL cell
,
resp
ectiv
ely.
Bo
th
o
f
th
ese t
w
o SL cells
are use
d
t
o
st
ore
and tra
n
s
f
er the e
n
ergy
from
the
cap
acito
rs to the d
c
bu
s
un
d
e
r
th
e switch
i
ng
actio
n
o
f
th
e m
a
in
circu
it.
dc
V
in
V
in
D
4
D
2
D
6
D
10
D
9
D
12
D
2
L
5
L
3
L
6
L
1
C
2
C
3
D
1
D
1
L
5
D
8
D
11
D
7
D
4
L
Fig
u
r
e
1
.
Topolo
g
y
o
f
th
e im
p
r
ov
ed
SL-
Z
SI
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
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4
N
e
w
Hyb
r
i
d
St
ruct
ure
B
a
sed
on
I
m
p
r
ove
d
S
w
i
t
c
hed I
n
du
ct
or Z
-
So
urce
a
n
d
P
a
r
a
l
l
e
l
…
(Ali Za
kerian
)
63
8
From
t
h
e
vi
e
w
p
o
i
n
t
o
f
t
h
e
swi
t
c
hi
ng
st
a
t
es o
f
th
e m
a
i
n
circu
it co
nnected
with
SL im
p
e
d
a
n
c
e
net
w
or
k, t
h
e
o
p
erat
i
o
n p
r
i
n
ci
pl
es of t
h
i
s
i
m
peda
nce net
w
o
r
k are si
m
i
l
a
r
t
o
t
hose o
f
t
h
e
cl
assi
cal
Z-source
im
pedance
net
w
o
r
k
.
F
o
r t
h
e
con
v
e
n
i
e
n
ce
of analysis, the
equi
valent circ
uit of t
h
e improved
SL Z
-
s
o
urce
im
pedance
net
w
o
r
k
vi
e
w
ed
f
r
om
t
h
e dc b
u
s
i
s
sho
w
n i
n
Fi
gu
re
2(a
)
i
n
w
h
i
c
h a
vi
rt
ual
act
i
v
e swi
t
c
h
S
and a
passi
ve s
w
i
t
c
h
o
D
are in
trod
u
c
ed
to
sim
u
late
t
h
e p
r
actical s
h
oo
t-t
h
ro
ugh
actio
n
s
of th
e to
p
and
bo
tto
m
arm
s
.Therefore
, the s
u
b-states of t
h
is im
pedance net
w
or
k
are classified i
n
to the
shoot-through state and t
h
e
non-shoot-through state, res
p
ectively.
2.
1. Sh
oo
t-T
h
r
ou
gh St
ate
During
th
is sub
-
state,
S
is ON, wh
ile b
o
t
h
in
D
and
o
D
are OFF.For i
n
ductor
s
of
t
h
e t
op
b
r
anc
h
,
fo
ur di
odes
12
3
, ,
DD
D
a
nd
4
D
are ON, while
two diodes
5
D
and
6
D
are OFF. T
h
en, three induct
o
rs
12
3
, ,
L
LL
are c
o
nnect
e
d
i
n
paral
l
e
l
a
n
d c
h
ar
ge
d
by
c
a
paci
t
o
r
1
C
. For
i
n
du
ctor
s
of
the bo
tto
m
b
r
an
ch
,
fo
ur
di
o
d
es
78
9
, ,
DD
D
and
10
D
are ON,
wh
ile two d
i
o
d
e
s
11
D
and
12
D
are
OFF. T
h
ree
induct
o
rs
45
6
, ,
L
LL
are c
o
nnected in
parallel and c
h
arge
d
by capa
c
itor
2
C
. Th
e eq
u
i
v
a
len
t
cir
c
u
it is show
n in
Figu
r
e
2(
b)
.
2.
2. N
o
n-
Sh
oo
t-T
hr
ou
gh St
a
t
e
This state corresponds t
o
the six active states
and two
zero states
of the m
a
in circuit and t
h
e
equi
val
e
nt
ci
rc
ui
t
i
s
sh
ow
n i
n
Fi
gu
re
2(c
)
.
D
u
r
i
n
g t
h
i
s
s
u
b
-
st
at
e,
S
is OFF, wh
ile bo
th
in
D
and
o
D
are
ON.
Fo
r
indu
ctor
s o
f
th
e top
br
anch
, fo
ur
d
i
o
d
e
s
12
3
, ,
DD
D
and
4
D
are OFF, while two di
odes
5
D
and
6
D
are
ON. T
h
en, three inductors
12
3
, ,
L
LL
are connected
in series a
n
d s
t
ore
d
en
erg
y
is tran
sferred
to
inv
e
rter
cir
c
u
it. Fo
r
i
n
du
ctor
s of
th
e
bo
tto
m
b
r
an
ch
,
fo
ur
d
i
od
es
78
9
, ,
DD
D
and
10
D
are OF
F,
wh
i
l
e
t
w
o di
odes
11
D
and
12
D
are ON. T
h
en, three i
n
ductors
45
6
, ,
L
LL
are connected in series
and st
ore
d
ene
r
gy
i
s
t
r
ansfe
rre
d t
o
inve
rter circ
uit.
in
V
dc
V
in
D
o
D
S
dc
V
in
V
5
L
3
L
6
L
1
C
2
C
1
L
4
L
2
L
dc
V
in
V
2
L
5
L
3
L
6
L
1
C
2
C
1
L
4
L
(a)
(b
)
(c)
Fi
gu
re 2.
Eq
ui
val
e
nt
ci
rc
ui
t
s
. (a) Im
pro
v
ed
S
L
-ZS
I
vi
ewe
d
fr
om
t
h
e
dc-l
i
n
k bus
.
(b
) S
h
oot
-thr
o
u
g
h
ze
r
o
state.
(c
)
No
n-
sh
oo
t-th
ro
ugh
zero
state.
Ass
u
m
i
ng t
h
at
t
h
e si
x i
n
d
u
ct
ors
(
12
3
4
5
, ,
, ,
L
LL
LL
and
6
L
) ha
ve t
h
e
sam
e
i
nduct
a
nce (
L
) a
n
d
two
cap
acito
rs(
1
C
and
2
C
) ha
ve the sam
e
capacitance (
C
).
As aresu
lt, th
e
n
e
tw
o
r
k bec
o
m
e
s
sym
m
e
t
r
i
cal
.
Fro
m
sy
mm
e
t
rical circu
it, th
e vo
ltag
e
ac
ros
s
the ca
pacitors
an
d
i
n
duct
o
rs
becom
e
:
12
CC
C
VV
V
(1
)
1
2
3456
L
LL
LL
L
L
vv
v
v
v
v
v
(2
)
From
Fi
g
u
re
2
(
b)
t
h
at
s
h
o
w
s
t
h
e e
qui
val
e
nt
c
i
rcui
t
o
f
t
h
e s
h
oot
-t
hr
o
u
g
h
st
at
e:
L
C
vV
,
0
in
v
(3
)
No
w c
o
nsi
d
e
r
no
n
-
sh
o
o
t
-
t
h
ro
ug
h st
at
e.
Fr
o
m
Fi
gure
2(c
)
,
t
h
e v
o
l
t
a
gee
q
u
a
t
i
ons ca
n
be
o
b
t
a
i
n
ed:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
6, No
. 3, Sep
t
em
b
e
r
2
015
:
63
6 – 647
63
9
3
L
dc
C
vV
V
(4
)
32
in
C
L
C
d
c
vV
v
V
V
(5
)
From
the fact that the a
v
era
g
e
voltages acr
os
s t
h
e i
n
duct
o
rs
du
ri
n
g
eac
h s
w
i
t
c
hi
ng cy
cl
e
T
are zero,
t
h
e f
o
l
l
o
wi
n
g
e
quat
i
o
n ca
n
be
deri
ved:
00
()
(
)
3
0
dc
C
C
LL
VV
TV
T
T
Vv
T
(6
)
Whe
r
e,
0
T
is th
e
sh
oo
t-t
h
rou
g
h
ti
m
e
in
terv
al ov
er a switch
i
ng
cycle,
o
r
0
(/
)
TT
D
is th
e sh
oo
t-
th
ro
ugh
d
u
t
y
ratio
.
From
(6
),
1
14
Cd
c
D
VV
D
(7
)
Th
erefo
r
e, th
e
p
eak d
c
-link
vo
ltag
e
acro
ss t
h
e inv
e
rter
b
r
i
d
g
e
can b
e
written
:
12
ˆ
32
14
in
C
L
C
d
c
d
c
D
vV
v
V
V
V
D
(8
)
Th
us, t
h
e
bo
ost
fact
o
r
B
i
s
ex
pre
ssed as:
0
10
0
12
(
)
12
14
14
(
)
TT
D
BB
B
DT
T
(9
)
Whe
r
e,
0
B
and
1
B
a
r
e d
e
f
i
n
e
d
as t
h
e bo
o
s
t f
act
o
r
o
f
th
e classical Z-
sou
r
ce and sw
itch
e
d
inducto
r
Z-
so
ur
ce im
p
e
d
a
n
c
e n
e
t
w
orks, r
e
sp
ectiv
ely. Th
eir expr
essi
o
n
s
ar
e g
i
v
e
n by [
9
] as:
0
0
11
12
1
(
)
B
DT
T
,
0
1
0
1(
)
1
13
13
(
)
TT
D
B
DT
T
(1
0)
Fo
r th
e
co
m
p
arison
o
f
t
h
e i
n
d
i
v
i
du
al
b
o
o
s
t
ab
ility, th
e curv
es
o
f
th
e
bo
ost factor
B
vers
us
t
h
e
dut
y
ratio
D
for im
proved SL Z
-
s
o
urce, SL Z
-
s
o
urce and cla
ssical Z-source impeda
nce
networks a
r
e s
h
own in
Fig
u
re 3. A
s
sh
own
in
Figu
re
3
,
th
e boost ab
ility
o
f
th
e i
m
p
r
ov
ed
SL Z-so
urce im
p
e
d
a
n
ce n
e
t
w
ork
is
significa
ntly increased com
p
a
r
ed
with SL
Z-source a
n
d clas
sical Z-source
im
pedance
net
w
orks.
Fig
u
re
3
.
Boo
s
t ab
ility co
m
p
a
r
ison
0
0.
0
5
0.1
0.15
0.2
0
5
10
15
20
S
h
o
o
t
-thr
o
u
g
h D
u
t
y
Rat
i
o
(
D
)
Bo
o
s
t
F
a
c
t
o
r
(
B
)
C
o
nv
e
n
ti
o
n
a
l
Z
-
S
o
ur
c
e
SL
Z
-
S
o
urce
I
m
prov
ed
SL
Z
-
S
o
urce
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
N
e
w
Hyb
r
i
d
St
ruct
ure
B
a
sed
on
I
m
p
r
ove
d
S
w
i
t
c
hed I
n
du
ct
or Z
-
So
urce
a
n
d
P
a
r
a
l
l
e
l
…
(Ali Za
kerian
)
64
0
3.
THE PROPOSED TOPOL
OGY
Paral
l
e
l
o
p
erat
i
o
n
o
f
i
n
ve
rt
ers
has m
a
ny
adva
nt
ages
suc
h
as
m
odul
ari
t
y
, ease o
f
m
a
i
n
t
e
nance,
(1
)
n
redun
d
a
n
c
y, hig
h
reliab
ility an
d
m
a
n
y
o
t
hers [2
2-2
4
]
. In
add
itio
n
t
o
th
ese, ou
tpu
t
cu
rren
t ri
p
p
l
e
o
f
the
paral
l
e
l
e
d i
nve
rt
er ca
n
be re
d
u
ced
si
g
n
i
f
i
can
t
l
y
by
vi
rt
ue
o
f
i
n
t
e
rl
eavi
n
g
ef
fect
[
25]
.
The
basi
c c
once
p
t
of t
h
e
pr
o
pose
d
i
m
pr
ove
d
SL Z
-
s
o
u
r
ce i
m
pedance
net
w
or
k
wi
t
h
N-
paral
l
e
l
i
n
ve
rt
ers i
s
sh
o
w
n
i
n
Fi
gu
re
4.
It
i
s
assum
e
d t
h
at
al
l
i
nve
rt
er
s sha
r
e t
h
e sam
e
dc
bus t
h
at
i
s
fed
fr
om
im
prove
d s
w
i
t
c
he
d
i
n
d
u
ct
o
r
Z-
sou
r
ce i
m
peda
nce
net
w
or
k.
S
i
nce t
h
e
v
o
l
t
a
ge at
t
h
e
p
o
i
n
t
o
f
c
o
m
m
o
n
c
o
n
n
ect
i
o
n
i
s
deri
ved
f
r
o
m
t
h
e
switching of diffe
rent powe
r
sem
i
conductors, an i
n
term
odule reactor is
a
b
sol
u
tely nece
ssary to interc
onnec
t
the di
ffe
rent i
n
verter
s.
As
d
e
scri
b
e
d in
[3
], t
w
o
PWM co
n
t
ro
l m
e
t
h
od
s, term
ed
as th
e sim
p
le bo
o
s
t con
t
ro
l meth
od
an
d the
m
a
xim
u
m
boo
st
cont
r
o
l
m
e
t
h
od
ha
ve bee
n
e
xpl
ore
d
,
whi
c
h
resul
t
i
n
t
h
e
di
ffe
rent
rel
a
t
i
o
n
s
hi
ps
of t
h
e v
o
l
t
a
ge
boost i
nve
rsion a
b
ility vers
us
the
give
n m
odulation i
nde
x
M
. Si
nce t
h
e a
f
o
r
em
ent
i
one
d t
w
o m
e
t
hods
can
be
rega
rde
d
as the theoretical basis of va
rious
adva
nced
PWM strategies such as
t
h
e t
h
i
r
d-
harm
oni
c i
n
j
ect
i
on
m
e
thod a
n
d t
h
e space
vect
or
P
W
M m
e
thod, the
propose
d
s
t
ructure unde
r the
cond
ition of these
two m
e
thods
will b
e
exp
l
ored in
t
h
e
follo
wing
d
i
scussio
n
s
,
resp
ectiv
ely. Fo
r t
h
e con
v
en
ien
c
e of illu
stration
,
t
h
e
wave
f
o
rm
s and
swi
t
c
hi
ng
st
rat
e
gi
es
of a
f
ore
m
ent
i
oned
t
w
o
m
e
t
hod
s are
s
h
o
w
n t
o
get
h
e
r
i
n
Fi
g
u
r
e
5.
1
b
L
1
a
L
1
c
L
2
a
L
2
b
L
2
c
L
aN
L
bN
L
cN
L
dc
V
in
V
Fi
gu
re
4.
Paral
l
el
im
prove
d
S
L
Z-s
o
urce
i
n
v
e
rt
ers
a
v
b
v
c
v
1
T
3
T
5
T
4
T
6
T
2
T
Fi
gu
re
5.
W
a
v
e
fo
rm
s and s
w
i
t
chi
n
g
st
rat
e
gi
es o
f
t
w
o basi
c P
W
M
co
nt
rol
m
e
t
h
o
d
s
It is seen
fro
m
Fig
u
re 5
t
h
a
t in th
e si
m
p
le b
o
o
s
t con
t
ro
l, a
straig
h
t
lin
e eq
u
a
l to
or greater th
an
t
h
e
peak val
u
e of t
h
e three
phase
refe
rences
is e
m
ployed.
The obt
ai
na
bl
e dut
y
rat
i
o
o
f
the s
h
oot-t
h
rough s
t
ate can
be
rega
r
d
ed
as
a co
nst
a
nt
val
u
e, an
d
i
t
s
m
a
xim
u
m
val
u
e i
s
l
i
m
i
t
e
d t
o
(1
)
M
. T
h
e
vol
t
a
ge
c
o
n
v
er
si
on
rat
i
o
o
f
the whole inve
rter
G
can be
e
x
p
r
esse
d by
:
ˆ
2
out
dc
v
GM
B
V
(1
1)
Whe
r
e,
ˆ
ou
t
v
is th
e p
eak
v
a
lu
e
o
f
th
e
ou
tpu
t
p
h
a
se
vo
ltage. Th
erefo
r
e,
th
e m
a
x
i
m
u
m v
o
ltage
co
nv
er
sion
r
a
tio
ma
x
G
ve
rsus
a
n
y
d
e
si
red m
o
d
u
l
a
t
i
on i
nde
x
M
ca
n
be e
x
p
r
esse
d
b
y
:
max
1
0
1
(3
2
)
43
s
s
DM
MM
GM
B
G
G
M
(1
2)
Whe
r
e,
0
s
G
and
1
s
G
ar
e de
fi
ne
d as t
h
e m
a
xim
u
m
vol
t
a
ge co
nve
rsi
o
n rat
i
o
of t
h
e cl
assi
cal
ZSI a
n
d
SL-Z
SI, res
p
ec
tively. Their expressi
o
n
sare
gi
ven
by
[
9
]
as f
o
l
l
o
w
s
:
0
21
s
M
G
M
,
1
(2
)
32
s
M
M
G
M
(1
3)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
6, No
. 3, Sep
t
em
b
e
r
2
015
:
63
6 – 647
64
1
For t
h
e m
a
xim
u
m
boost
c
ont
rol
m
e
t
hod as
sho
w
n i
n
Fi
g
u
r
e 5
,
t
h
e
key
p
o
i
n
t
i
s
t
h
at
al
l
zero st
at
es
n
eed
to
b
e
tu
rned
in
to
th
e shoo
t-throug
h
stat
e so
as to
m
a
k
e
th
e d
u
t
y ratio
as larg
e
as possible. The
r
efore, the
shoot-t
h
rough
duty cycle
vari
es in eac
h
cy
cl
e. A
s
descri
be
d i
n
[
3
]
,
t
h
e a
v
erage
d
u
t
y
rat
i
o
of
t
h
e
sh
o
o
t
-
t
h
r
o
ug
h
zero state,
D
is express
e
d by:
0
23
3
2
T
M
D
T
(1
4)
Sub
s
titu
tin
g (14
)
in
to (9
),
we
can
g
e
t th
e equ
i
v
a
len
t
boo
st
facto
r
B
un
d
e
r t
h
e co
nd
ition
o
f
v
a
riab
le
dut
y
rat
i
o
s:
12
6
6
3
14
12
3
6
DM
B
D
M
(1
5)
There
f
ore, t
h
e
m
a
xim
u
m
vol
t
a
ge con
v
e
r
si
o
n
rat
i
o
ma
x
G
versus
any
desi
red
m
odul
at
i
on i
n
dex
M
ap
pro
x
i
m
a
tes t
o
:
ma
x
1
0
(6
6
3
)
12
3
6
mm
MM
GM
B
G
G
M
(1
6)
Whe
r
e,
0
m
G
and
1
m
G
are
defi
ned
as t
h
e
m
a
xim
u
m
vol
t
a
ge
c
o
nve
r
sion ratio of the classical Z
S
I
and
SL
-ZS
I
,
re
spect
i
v
el
y
.
T
h
e
i
r ex
pre
ssi
o
n
sa
re
gi
ve
n
by
[
9
]
as f
o
l
l
o
ws
:
0
33
m
M
G
M
,
1
(4
3
3
)
93
4
m
M
M
G
M
(1
7)
Fi
gu
re
6
(
a)
sh
ows
t
h
e
m
a
xi
m
u
m
obt
ai
nabl
e v
o
l
t
a
ge c
o
nv
ersi
o
n
rat
i
o
s
v
e
rsus
t
h
e
gi
ve
n m
o
d
u
l
a
t
i
o
n
inde
x unde
r the sim
p
le boost
control
condit
i
on.
It is shown that the vo
ltage boost ability is unavailable at
1
M
.
H
o
w
ev
er
,
if
1
M
, with
t
h
e decre
a
sing
of
M
, t
h
e
v
o
ltag
e
b
o
o
s
t i
n
v
e
rsion ab
ility o
f
th
e pro
posed
inve
rter be
com
e
s m
u
ch stronger t
h
an
SL-Z
SI a
nd classi
ca
l ZSI.
It m
eans that for a
give
n voltage c
o
nversion
rat
i
o
, a
hi
g
h
er
m
odul
at
i
on i
nde
x ca
n
be
use
d
i
n
t
h
e p
r
o
p
o
sed
i
n
vert
er t
o
i
m
pro
v
e
t
h
e i
n
vert
er
out
put
per
f
o
r
m
a
nce.
Fi
gu
re
6(
b)
s
h
ows
t
h
e m
a
xi
m
u
m
obt
ai
nabl
e v
o
l
t
a
ge c
o
n
v
e
rsi
o
n rat
i
os
v
e
rsus
t
h
e
gi
ve
n m
odul
at
i
o
n
in
d
e
x
un
d
e
r the
m
a
x
i
m
u
m
b
o
o
s
t co
n
t
ro
l co
nd
itio
n. It is sh
own
th
at th
e v
o
ltag
e
boo
st
in
v
e
rsi
o
n
ab
ilities o
f
theseinverters
have
bee
n
e
nhanced to a
wi
der ra
nge
by
th
i
s
m
e
th
o
d
. Sim
i
lar to
th
e ob
serv
atio
n in
Figu
re 6
(
a),
th
e pro
p
o
s
ed
i
n
v
e
rter exh
i
b
i
t
s
its adv
a
n
t
ag
e of stron
g
e
r
voltag
e
boo
st inversion
ab
ility at th
e low m
o
dulatio
n
i
nde
x.
(a)
(b
)
Fig
u
re
6
.
Max
i
m
u
m
v
o
ltag
e
co
nv
ersion
ratio. (a)
Und
e
r th
e
si
m
p
le b
o
o
s
t co
n
t
ro
l con
d
ition
.
(b
)
Un
de
r t
h
e
m
a
xim
u
m
bo
o
s
t
co
nt
rol
c
o
nd
i
t
i
on.
0.
7
0.75
0.
8
0.
85
0.9
0.
9
5
1
0
5
10
15
20
M
o
du
lat
i
on
I
n
d
e
x (
M
)
V
o
l
t
age
C
o
n
v
e
r
s
i
on
R
a
t
i
o
(
M
*B
)
Con
v
e
n
t
i
ona
l
ZSI
SL
-Z
S
I
P
r
op
os
ed
T
o
p
o
l
ogy
0.91
0.
9
2
0.93
0.94
0.95
0.
96
0.97
0.98
0.9
9
1
0
5
10
15
20
M
o
dul
a
t
i
o
n I
n
d
e
x
(M
)
Vo
l
t
a
g
e
Co
n
v
e
r
s
i
o
n
Ra
t
i
o
(
M
*
B
)
C
o
n
v
e
n
t
i
on
al Z
S
I
SL
-
Z
SI
P
r
opos
e
d
T
o
pol
o
gy
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
N
e
w
Hyb
r
i
d
St
ruct
ure
B
a
sed
on
I
m
p
r
ove
d
S
w
i
t
c
hed I
n
du
ct
or Z
-
So
urce
a
n
d
P
a
r
a
l
l
e
l
…
(Ali Za
kerian
)
64
2
Fi
gu
re 7 s
h
o
w
s
a sim
p
l
i
f
i
e
d equi
val
e
nt
ci
rcu
i
t
of t
h
e sy
st
em
il
l
u
st
rat
e
d i
n
Fi
gu
re 4. It
i
s
assum
e
d t
h
at
each inverter
develops a bala
nced t
h
ree
pha
se voltage
a
n
d
its inter
m
odule
reactor c
o
nsis
ts of ide
n
tical pha
se
i
n
d
u
ct
o
r
s.
H
o
weve
r,
di
f
f
ere
n
ces m
a
y
exi
s
t
bet
w
een
di
f
f
ere
n
t
i
n
vert
er
m
odul
es
,
bot
h i
n
vol
t
a
ge
an
d
rea
c
t
a
nce.
Und
e
r su
ch
assu
m
p
tio
n
s
, th
e eq
u
i
v
a
len
t
circu
it illu
strated
i
n
Figu
re 7,
m
a
y b
e
fu
rth
e
r sim
p
l
i
fied
in
t
o
a p
h
as
or
eq
ui
v
a
l
e
nt
ci
rcui
t
s
h
ow
n i
n
Fi
g
u
re
8.
He
re, eac
h
i
nve
rt
er
i
s
re
pr
e
s
ent
e
d
by
i
t
s
i
n
t
e
rnal
pha
so
r
v
o
l
t
a
ge
sou
r
ce,
an
d
o
n
e
i
n
d
u
ct
o
r
a
n
d
one
resi
st
or
re
prese
n
t
i
n
g
t
h
e
equi
val
e
nt
se
ri
es resi
stance
of the circ
uit.
A
I
B
I
C
I
1
A
I
1
B
I
1
C
I
2
A
I
2
B
I
2
C
I
AN
I
B
N
I
CN
I
A
V
B
V
C
V
1
A
V
2
A
V
AN
V
2
B
V
1
C
V
1
B
V
2
C
V
B
N
V
CN
V
O
1
A
L
1
B
L
1
C
L
2
A
L
2
B
L
2
C
L
AN
L
B
N
L
CN
L
1
I
2
I
N
I
C
V
L
I
1
L
2
L
N
L
1
R
2
R
N
R
1
V
2
V
N
V
O
Fi
gu
re
7.
Si
m
p
l
i
f
i
e
d eq
ui
val
e
nt
ci
rc
ui
t
Fi
gu
re
8.
Si
m
p
l
i
f
i
e
d p
h
as
or
m
odel
In
vert
e
r
p
o
l
e
vol
t
a
ge
an
d c
u
r
r
ent
vect
o
r
s
can
be
defi
n
e
d as
12
(
...
)
T
N
VV
V
and
12
(
.
..
)
T
N
II
I
respectively, corresp
onding to the labels illustra
ted in
Figure
8. Now, t
h
e thevenin im
p
e
dance of
th
i
inve
rter
,
i
Z
may be identifi
e
d to be:
,
=
1
,
2
,
.
.
.
,
ii
i
Z
Rj
L
i
N
(1
8)
An
d t
h
e e
qui
va
lent thev
eni
n
i
m
pedance o
f
al
l inve
rters i
n
p
a
rallel,
TH
Z
, m
a
y be determ
ined as:
12
Z.
.
.
TH
N
Z
ZZ
(1
9)
Furt
herm
ore,
the
voltage
at th
e com
m
on
coupling point
can be calculated t
o
be:
1
()
N
j
CT
H
L
j
j
V
VZ
I
Z
(2
0)
No
w,
the
o
u
tp
ut cu
rre
nt
of
th
e
th
i
inve
rter can
be
e
v
aluate
d
as
:
1
(
)
,
N
j
TH
i
T
H
iL
j
ii
j
j
V
ZV
Z
I
Ii
ZZ
Z
Z
(2
1)
From
equatio
n
21 a
n
d Fig
u
re
6, it can be
de
rive
d
the p
r
op
ose
d
struct
ure
can achie
ve hi
ghe
r v
o
ltag
e
than t
h
e p
r
e
v
ious
co
n
v
erter
s
an
d also
, be
ca
use
of
divi
din
g
the
o
u
tp
ut c
u
r
r
ent
betwee
n
parallel in
vert
ers, t
h
e
probable dam
a
ges to the switches whic
h can be caused
by high
currents are preventabl
e
and t
h
is will increase
the reliability of the system
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN:
2
088
-86
94
I
J
PEDS
Vo
l.
6,
No
. 3,
Sep
t
em
b
e
r
2
015
:
63
6 – 647
64
3
It m
a
y
be obse
r
ve
d f
r
om
(21)
, that va
rio
u
s
i
Z
play
an im
porta
nt r
o
le in
determining the sharing
of
current
bet
w
ee
n the
diffe
re
nt
m
odules.
In order to
qua
n
tify this
phenom
enon, the
se
nsitivity of the
current to
the the
v
eni
n
i
m
pedance,
i
Z
can be
determ
ined to
be:
22
3
2
,
iL
i
T
H
TH
i
ii
i
i
II
V
Z
Z
Vi
ZZ
Z
Z
(2
2)
There
f
ore,
sm
all deviatio
ns
in eq
uivale
nt t
h
eve
n
in
im
pedances
of
in
ver
t
ers can
res
u
lt
in
une
ve
n
cu
rr
en
t d
i
str
i
bu
tio
ns as su
ggested
b
y
(
2
1
)
.Fr
o
m
(
2
2)
,
we
can also obse
r
ve that, if
the thevenin im
pedance is
increase
d
, the
depe
ndence
of output cu
r
r
e
n
t on the o
u
tp
u
t
im
pedance is
also decrease
d
leading to better
cur
r
ent distri
bu
tion.
4.
SIMULATION RESULTS
Extensi
v
e c
o
m
pute
r
sim
u
latio
n u
s
in
g M
A
TL
AB
-Sim
ulink
has
been
pe
rf
o
r
m
e
d to pr
o
v
e
per
f
o
r
m
a
nce
of t
h
e
pr
o
pose
d
in
verte
r
. T
h
e
sim
u
lation sc
hem
a
tic for
th
e pr
o
p
o
s
ed t
o
p
o
lo
gy
is sh
o
w
n in
Fig
u
re
9a
nd
the
selected pa
ra
m
e
ters are:
36
V
dc
V
,
1
23456
1m
H
LL
L
L
L
L
,
12
10
00
F
CC
, Switching
f
r
e
q
u
e
n
c
y = 10
kHz,
1m
H
a
n
d
2
2
.
5
F
ff
LC
(Three-phase ou
tput filter), Three-phase resistive
load =
10/
pha
se. I
n
the sim
u
lation,
all com
ponen
t
s are assum
e
d
ideal. The pr
op
ose
d
top
o
lo
gy
is co
m
p
are
d
to the
othe
r to
pol
ogie
s
whic
h
have
b
een p
r
op
ose
d
in [
2
]
an
d [
9
]
,
u
nde
r the sim
p
le bo
ost c
ontr
o
l
m
e
thod
(case
1) a
n
d
the m
a
xim
u
m
bo
ost c
o
ntrol
m
e
thod
(case
2
)
wit
h
the
sam
e
sh
oot
-th
r
o
u
g
h
duty
ratio.
in
V
dc
V
1
C
2
C
Figu
re
9.
Sc
he
m
a
tic of tw
o
p
a
rallel inve
rter
s base
d
o
n
im
pro
v
e
d
SL
Z-
so
urce
im
pedanc
e netw
o
r
k
4.
1.
Si
mpl
e
B
o
ost
C
o
n
t
rol
Th
e
p
r
op
osed syste
m
wo
rk
s
with
shoo
t-
thr
oug
h du
ty r
a
tio
0.
2
D
and
m
odulatio
n
inde
x
0.
8
M
.
We obtain
7
B
and
5.
6
G
usin
g m
e
ntione
d eq
uatio
n
s
.Fig
ure
10 s
h
owst
he sim
u
lation res
u
lts fo
r the
pr
o
pose
d
t
o
p
o
l
ogy
whic
h a
r
e
volta
ge acr
oss
the in
verter
s (
in
V
),
voltage of capacitors (
C
V
), output
voltage,
cu
rr
en
t wav
e
for
m
s
o
f
th
e up
an
d
down
inv
e
r
t
e
r
s
an
d a
l
s
o
th
e
lo
ad
cu
rr
en
t
wa
veform
, respectively. It is
seen
that the steady-state perform
a
nce in the
sim
u
lation
is identically
m
a
tching to
the theoreti
cal analysis.
In
orde
r to c
o
m
p
are the propose
d structure
with
pr
e
v
ious structures,
we a
pply the
sam
e
values
of
D
and
M
to the classical ZSI and SL-ZSI
, and
the boost invers
ion ability
will be
decr
eased sharply. The
corresponding param
e
ters are
1.67
B
,
1.
33
6
G
for the classical ZSI and
3
B
,
2.4
G
for the SL-
ZSI,
whic
h are
m
u
ch lowe
r than those ac
hieved
by th
e p
r
op
ose
d
in
verte
r
. The sim
u
lation
results f
o
r t
h
ese
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
S
SN:
208
8-8
6
9
4
N
e
w
Hyb
r
id
St
ructure
B
a
sed
on
I
m
p
r
ove
d
S
w
itched I
n
du
ctor Z
-
So
urce
a
n
d
P
a
r
a
llel …
(Ali Zakerian)
64
4
str
u
ctur
es ar
e
sh
own
in
Figur
es 11
and
12
, r
e
spectiv
ely. By com
p
arison between simulation
results, it is
com
p
letely
obvio
u
s t
h
at the
p
r
o
p
o
sed
str
u
ctu
r
e ca
n tra
n
sfe
r
hig
h
er
p
o
w
er t
h
an
the
othe
r t
o
p
o
lo
gies.
Figure 10. Simulation results of
th
e
p
r
op
osed
topo
log
y
(
c
ase 1)
Figure 11. Simulation results of
the
ZSI
(case
1)
Figure 12. Simulation results
of the
SL-Z
SI (case 1)
4.
2.
Ma
xi
mum
B
o
ost
C
o
n
t
rol
Unde
r the condition of the
m
a
xim
u
m
boost c
ontrol, according to (14-16), we c
o
nsider
0.
96
7
M
.
There
f
ore, we
obtain
0.
2
D
,
7
B
and
ma
x
6.
76
9
G
. The sim
u
lation results
fo
r the
pr
o
pos
ed t
o
p
o
l
og
y
are plotted i
n
Figu
re 1
3
,
wh
ich
are voltage across the i
nve
rters (
in
V
),
vo
ltage of cap
ac
itors (
C
V
), o
u
tp
ut
voltage
, c
u
r
r
en
t wave
fo
rm
s of the
up a
n
d d
o
w
n
in
ve
rters
and als
o
the l
o
ad cu
rre
nt w
a
v
e
fo
rm
, respectively
.
Because the duty ratio varie
s
peri
odically, a
s
m
all
oscillation has
bee
n
introduce
d
into
in
V
and
C
V
. All
sim
u
lation res
u
lts com
p
ly
with the
eq
uatio
ns
de
rive
d in
sect
ions
2
an
d
3.
0
0.
05
0.
1
0.
15
0.
2
0.
25
-100
0
100
200
300
Ti
m
e
(
S
)
(a
)
V
in
(V
)
0
0.
0
5
0.
1
0.
15
0.
2
0.
2
5
0
50
100
150
200
Ti
m
e
(
S
)
(b
)
V
C
(V
)
0
0.
05
0.
1
0.
15
0.
2
0.
25
-5
0
5
Ti
m
e
(
S
)
(d
)
I
in
v
e
r
t
e
r
1
(A
)
0
0.
0
5
0.
1
0.
15
0.
2
0.
2
5
-5
0
5
Ti
m
e
(
S
)
(e)
I
in
v
e
r
t
e
r
2
(A
)
0
0.
0
5
0.
1
0.
15
0.
2
0.
2
5
-10
-5
0
5
10
Ti
m
e
(
S
)
(f)
I
Lo
a
d
(A
)
0
0.
0
5
0.
1
0.
15
0.
2
0.
2
5
-150
-100
-50
0
50
100
150
Ti
m
e
(
S
)
(c)
V
ou
t
(V
)
-5
0
0
50
100
150
V
in
(V
)
0
50
100
V
C
(V
)
-5
0
0
50
V
ou
t
(V
)
0
0.
0
5
0.
1
0.
1
5
0.
2
0.
2
5
-5
0
5
Ti
m
e
(
S
)
I
Lo
a
d
(A
)
-1
0
0
0
10
0
20
0
V
in
(V
)
0
50
10
0
V
C
(V
)
-5
0
0
50
V
ou
t
(V
)
0
0.
05
0.
1
0.
1
5
0.
2
0.
25
-5
0
5
Ti
m
e
(
S
)
I
Loa
d
(A
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN:
2
088
-86
94
I
J
PEDS
Vo
l.
6,
No
. 3,
Sep
t
em
b
e
r
2
015
:
63
6 – 647
64
5
For t
h
e case
of the classical ZSI a
nd
SL-ZSI,
when
M
is taken as
0.
967
, the boost inversi
on
ability is still
very
weak. The corresponding
param
e
ters are:
1.
66
8
B
,
ma
x
1.
6
1
3
G
for the cl
assical ZSI
and
3
B
,
ma
x
2.
90
1
G
fo
r the
S
L
-ZS
I
. T
h
e si
m
u
lation res
u
lts fo
r the
s
e str
u
ctures a
r
e s
h
o
w
n i
n
Fi
gu
res
1
4
and 15
respectively.
Figure 13. Simulation results of
th
e
p
r
op
osed
topo
log
y
(
c
ase 2)
Figure 14. Simulation results of
the
ZSI
(case
2)
Figure 15. Simulation results
of the
SL-Z
SI (case 2)
The im
pro
v
e
d
switche
d ind
u
c
t
or Z-s
o
urce struct
ure
is extensible for the fu
rt
her de
velo
p
m
ent usin
g
the coupled induct
o
r techni
ques a
nd other potential
i
m
provi
ng
techniques.
Additionally, in conditions where
the load re
quires higher c
u
r
r
e
n
t, in o
r
de
r to
pre
v
e
n
t the pr
oba
ble da
m
a
ges to the switches, by increasi
ng the
num
ber
of
in
ve
rters i
n
parallel we ca
n
su
p
p
ly
the loa
d
by
de
sired c
u
rre
nt.
0
0.
0
5
0.
1
0.
15
0.
2
0.
25
-100
0
100
200
300
400
Ti
m
e
(
S
)
(a
)
V
in
(V
)
0
0.
05
0.
1
0.
15
0.
2
0.
25
0
50
10
0
15
0
20
0
Ti
m
e
(
S
)
(b
)
V
C
(V
)
0
0.
05
0.
1
0.
15
0.
2
0.
25
-15
0
-10
0
-50
0
50
10
0
15
0
Ti
m
e
(
S
)
(c
)
V
ou
t
(V
)
0
0.
0
5
0.
1
0.
15
0.
2
0.
25
-5
0
5
Ti
m
e
(
S
)
(
d
)
I
in
v
e
r
t
e
r
1
(A
)
0
0.
05
0.
1
0.
15
0.
2
0.
25
-5
0
5
Ti
m
e
(
S
)
(
e
)
I
in
v
e
r
t
e
r
2
(A
)
0
0.
05
0.
1
0.
15
0.
2
0.
25
-15
-10
-5
0
5
10
15
Ti
m
e
(
S
)
(
f
)
I
Lo
a
d
(A
)
-5
0
0
50
100
150
V
in
(V
)
0
50
100
V
C
(V
)
-5
0
0
50
V
ou
t
(V
)
0
0.
0
5
0.
1
0.
15
0.
2
0.
25
-5
0
5
Ti
m
e
(
S
)
I
Lo
a
d
(A
)
-1
00
0
10
0
20
0
V
in
(V
)
0
50
10
0
V
C
(V
)
-5
0
0
50
V
ou
t
(V
)
0
0.
05
0.
1
0.
15
0.
2
0.
2
5
-5
0
5
Ti
m
e
(
S
)
I
Lo
a
d
(A
)
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