Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
Vol.
6, No. 4, Decem
ber
2015, pp. 797~
807
I
S
SN
: 208
8-8
6
9
4
7
97
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
Analysis of Impedance Source
In
vert
er T
o
pologies
for Grid
Integration of PV Inverters
A. Sangari
1
, R
.
Um
am
ahesw
a
ri
2
1
Departm
e
nt
of
Ele
c
tri
cal
and
E
l
ectrno
i
cs
Eng
i
neering, Rajalakshmi E
ngineering
College, India
2
Departm
e
nt
of
Ele
c
tri
cal
and
E
l
ectrno
i
cs
En
g
i
neering, Velammal Engin
eering
Co
lleg
e
, India
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
J
u
n 27, 2015
R
e
vi
sed Oct
4,
2
0
1
5
Accepted Oct 24, 2015
In this paper, th
e performance o
f
diffe
rent Impedance Source In
verter (ZSI)
topologies in implementing
s
i
ngle
stage po
wer conversion for grid
ingetertion of
PV power con
v
erters
is discu
ssed. Unlike th
e tradi
tiona
l
invert
ers
,
ZS
I em
plo
y
s
a dis
tinctiv
e
impedance network, there b
y
makin
g
shoot-through state is possible.
The inde
p
e
ndent control variables are shoot-
through duty
r
a
tio and modulation index.
Simple Boost Control pulse width
modulation tech
nique was used
in this
work to
var
y
the modulation index
.
Here the b
a
sic operation,
simple boost con
t
r
o
l method, ch
aracteristics,
requirem
e
nts
an
d
harm
onic anal
ys
is
of the clas
s
i
cal Z-S
ource
Inv
e
rter
(ZS
I),
TZ-Source Inv
e
rter (TZSI),
Trans-Z-
Source Inverter (Tr
a
ns-ZSI) and
Improved ZSI (IMZSI) topologi
es were compar
ed for interfacin
g
the wide
range var
i
abl
e
i
nput energ
y
to u
tili
t
y
suppl
y
s
y
st
em
. The perfo
r
m
ances were
compared based
on its MATLAB
/
SIMULINK
simulation model and featur
ed
results ar
e show
n to
confirm its
validity
.
Keyword:
Im
prove
d Z-s
o
urce
i
n
vert
er
Tot
a
l
ha
rm
oni
c di
st
o
r
t
i
o
n
Trans-Z
-
s
o
urc
e
inve
rter
TZ-s
o
urce i
nve
rter
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
:
A. San
g
a
r
i,
Depa
rt
m
e
nt
of
El
ect
ri
cal
and
and
El
ect
r
noi
c
s
En
gi
nee
r
i
n
g,
R
a
jal
a
ks
hm
i
Engi
neeri
n
g
C
o
l
l
ege.
Em
a
il: san
g
a
ri.a@raj
alak
sh
m
i
.edu
.in
1.
INTRODUCTION
In c
o
nve
nt
i
o
na
l
vol
t
a
ge s
o
urc
e
or c
u
rre
nt
so
urce
fe
d I
nve
rt
ers, t
h
e
m
a
i
n
ci
rcui
t
i
s
n
o
t
t
h
e sam
e
for
buc
k a
n
d boos
t
ope
rations. T
h
ey can
operat
e either as
bu
c
k
or
boost inverter a
nd ca
nnot operate as
a
buck-
bo
ost
m
ode,
W
hereas
ZS
I e
m
pl
oy
s a di
st
i
n
ct
i
v
e i
m
pedance
net
w
or
k a
n
d
i
t
al
l
o
ws s
h
o
o
t
t
h
ro
u
g
h
st
at
e i
n
i
nve
rt
er o
p
erat
i
on w
h
i
c
h
m
a
kes b
o
t
h
b
u
ck
an
d bo
ost
o
p
e
rat
i
ons
p
o
ssi
b
l
e
[1]
.
I
n
rece
nt
t
i
m
es,
i
t
has
bee
n
fo
u
nd t
h
at
ZS
I
co
ul
d
ove
rc
o
m
e t
h
e t
h
eoretical b
a
rriers / li
m
i
tatio
n
s
of t
h
e trad
itio
n
a
l
co
nv
erter an
d
d
e
v
e
l
o
p
in
to
a nov
el po
w
e
r
co
nv
ersio
n
pr
acti
ce [2]
-
[
4
]
.
W
i
t
h
i
t
s
uni
que
feat
u
r
e
s
, t
h
e ZS
I i
n
ve
rt
er p
r
ovi
des c
h
eape
r
,
si
m
p
ler, sing
le
stag
e ap
pro
a
ch fo
r
d
i
stribu
ted g
e
n
e
ration
i
n
teg
r
ation
[5
].
To dat
e
, m
a
ny
researche
r
s
aro
u
nd t
h
e
gl
obe
ha
ve re
po
rt
ed va
ri
o
u
s Z
S
I t
ech
ni
q
u
es.
Som
e
have
foc
u
se
d o
n
de
v
e
l
opi
n
g
t
h
e Z
S
I i
n
t
o
P
u
l
s
e-
wi
dt
h m
odul
at
i
o
n
st
rat
e
gi
es, ap
p
l
i
cat
i
ons [6]
,
c
ont
rol
an
d m
o
d
e
l
i
n
g
[7
]-[12
] and
a few h
a
v
e
work
ed
on
th
e
dev
e
lop
m
en
t o
f
ZSI top
o
l
o
g
i
es. Th
e m
a
j
o
r
d
i
fficu
lties related
to
vol
t
a
ge
so
urce
and c
u
rre
nt
so
urce i
nve
rt
ers
are re
duce
d
po
wer c
o
nve
rsi
o
n ef
fi
ci
ency
be
cause
of t
h
e t
w
o st
a
g
e
co
nfigu
r
ation,
redu
ced
reliab
i
lity an
d
th
eir
h
a
v
i
n
g
gr
eater v
o
l
u
m
e an
d
weigh
t
[1
3
]
.
Fo
r t
h
e wi
d
e
varyin
g
rene
wa
bl
e ener
gy
so
urces
, ZS
I has
bee
n
projected as a feas
ible buc
k-boos
t
inverter fo
r g
r
id-i
nterfa
cin
g
[1
4]
.
W
i
t
h
t
h
e d
e
vel
opm
ent
of
pr
o
p
er c
ont
rol
t
h
e
ZSI o
p
e
r
at
es at
any
desi
red
out
put
AC
v
o
l
t
a
ge [1
5]
,[
1
6
]
or a
s
bo
ost
e
r
du
ri
n
g
i
rreg
u
l
a
r
very
l
o
w
vol
t
a
ge
s. T
h
i
s
pap
e
r p
r
o
v
i
d
es pe
rf
orm
a
nce anal
y
s
i
s
by
com
p
ari
s
on
of
basi
c
ZSI,
Tra
n
s-
ZS
I, TZ
SI, a
n
d I
M
ZSI
based
o
n
t
o
t
a
l
ha
rm
oni
c di
st
ort
i
o
n
of
t
h
e cu
rre
nt
, i
n
duct
o
r i
n
r
u
s
h
c
u
r
r
ent
,
capaci
t
o
r
v
o
l
t
a
ge st
res
s
, m
i
s-gat
i
n
g
-
of
f,
rat
i
n
g
o
f
passi
ve
com
pone
nt
s, c
o
st
an
d
r
o
b
u
st
ness
part
i
c
ul
ar
l
y
for
gri
d
i
n
t
e
grat
i
o
n
of
re
newa
bl
e
ene
r
gy
s
o
urce
s.
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
.
4
,
D
ecem
b
er
2
015
:
79
7 – 807
79
8
In t
h
e di
st
ri
bu
t
i
on net
w
o
r
k i
n
t
e
g
r
at
i
on sy
st
em
s t
h
e ZSI,
basi
cal
l
y
t
h
e Z-S
o
u
r
ce
net
w
or
k wi
t
h
a
specific im
pedance acts as
an interface
bet
w
een the
re
ne
wa
ble ene
r
gy source
out
put a
n
d
three
phase inverter
[17
]
.
Here
six
IGBT
switch
e
s an
d
six
d
i
od
es are
u
tili
zed
. The o
u
t
p
u
t
v
o
ltage is co
n
t
ro
lled
u
s
ing
PWM con
t
ro
l
sig
n
a
l. Th
e switch
i
n
g
leg
s
m
a
y co
n
t
ain th
e ad
d
ition
a
l zero
state.
2.
VARIOUS Z
-
SOURCE INVERTER TOPOLOGIES
Th
e nor
m
a
l
Z
-
Sour
ce n
e
t
w
or
k
h
a
s two
in
du
ctor
s in
se
ries an
d
two
cap
a
cito
rs in
p
a
rallel ar
m
in
th
e
form
of a bridge network. In
TZSI t
h
e two i
n
ductors a
r
e re
placed
by tra
n
s
f
orm
e
rs. By changi
ng the turn ratio
o
f
t
h
e tran
sformers v
e
ry
h
i
gh
b
o
o
s
t
v
o
ltage in
v
e
rsio
n
abilit
y with
a
v
e
ry lo
w sh
oo
t-t
h
rou
g
h
d
u
t
y
ratio
is
at
t
a
i
n
ed. Tra
n
s
-
Z-s
o
urce i
n
ve
rt
er (TZS
I) i
s
bei
n
g deri
ve
d fr
om
t
h
e vol
t
a
ge/
c
u
rre
nt
fed
Z or q
u
asi
-
Z
-
S
o
u
r
ce
In
vert
e
r
s t
o
o
b
t
ai
n a hi
g
h
e
r
b
oost
gai
n
wi
t
h
t
h
e sam
e
sho
o
t
-
t
h
ro
u
g
h
d
u
t
y
rat
i
o
an
d m
odul
at
i
o
n i
n
de
x.
Lat
e
r
Im
prove
d
Z-s
o
urce
i
n
vert
er
i
s
de
ri
ve
d t
o
l
i
m
i
t
t
h
e cap
aci
t
o
r
vol
t
a
ge
st
ress
a
n
d
i
n
duct
o
r
i
n
r
u
sh
c
u
r
r
ent
.
2.
1.
Conve
n
ti
onal
Z
-
Source
I
n
ve
rter
A classical Z-s
o
urce
network
consis
ts of two id
en
tical ind
u
cto
r
s
(L
1
, L
2
) an
d two
id
en
tical cap
acitors
(C
1
, C
2
). The
Z-Source net
w
ork connects the inve
rter m
a
in
circu
it with
th
e v
a
riab
le vo
ltag
e
sou
r
ce as
sh
own
in
Fig
u
r
e
1. The Z-
Sour
ce In
ver
t
er
is
use
d
to reduce the volt
age stress a
nd
cur
r
ent
ri
ppl
es
.
The re
qui
rem
e
nt
of
inductor and capacitor s
h
ould be less
co
m
p
ared wi
t
h
vol
t
a
ge s
o
urce
i
nve
rters.
When the
value
s
of the
in
du
ctor
s (
L
1
an
d L
2
) are
sm
all and m
ove nea
r
zer
o,
t
h
e Z-S
o
u
r
ce net
w
or
k red
u
ces
the
num
ber of ca
paci
tors.
Fi
gu
re
1.
Z-
So
urce
I
nve
rt
er
Si
m
ilarly, wh
en
th
e
v
a
lu
es of th
e two
cap
a
cito
rs (C
1
and
C
2
) are sm
all a
n
d m
ove nea
r
zero, the Z
-
So
urce net
w
o
r
k red
u
ces t
o
t
w
o i
n
d
u
ct
or
s (
L
1
and L
2
) i
n
seri
es and
bec
o
m
e
s a t
r
adi
t
i
onal
cu
rre
nt
sou
r
ce
in
v
e
rter.
Th
e si
ze of th
e ind
u
c
to
r is
sm
al
ler th
an th
e con
v
e
ntio
n
a
l curren
t so
urce i
n
v
e
rters.
2.
2.
TZ
-Source Inverter
The T
Z
-S
o
u
rc
e i
nve
rt
er i
s
s
h
o
w
n i
n
Fi
g
u
r
e
2
where t
h
e
inductors i
n
th
e conv
en
tional ZSI
ar
e
repl
ace
d by
t
h
e t
r
ans
f
o
r
m
e
rs. It
co
nsi
s
t
s
o
f
one
di
o
d
e
(Di
n
), t
w
o ca
paci
t
o
rs (C
1
a
nd C
2
)
and t
w
o t
r
ans
f
orm
e
rs
(T
1
and T
2
). The tu
rn
s rati
o
o
f
th
e tran
sform
e
rs is d
e
fin
e
d
as
N
i
= N
i2
/ N
i1
, whe
r
e i
= 1 and 2 re
prese
n
t
s
T
1
and
T
2
.
Fi
gu
re 2.
TZ-
S
o
u
r
ce In
ve
rt
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
An
al
ysi
s
of
Im
ped
a
n
ce
So
urc
e
I
n
vert
e
r T
o
p
o
l
o
gi
es f
o
r
G
r
i
d
Int
e
grat
i
o
n
..
.. (
A
.
S
a
n
g
a
ri
)
79
9
In
TZ-
So
u
r
ce
I
nve
rt
er,
t
h
e
basi
c Z
-
Source im
peda
nce
network structure is
sam
e
as Z
-
Source
Inv
e
rter and
ad
d
ition
a
l two
t
r
an
sfo
r
m
e
rs are u
s
ed
to
v
a
ry
th
e bo
o
s
t fact
or. The bo
o
s
t facto
r
can
b
e
v
a
ried
b
y
vary
i
n
g t
h
e t
u
r
n
s rat
i
o
of t
h
e
t
r
ans
f
o
r
m
e
r.Th
e
m
o
re effi
ci
en
t
i
nput
cu
rre
nt
pr
ofi
l
e
wi
t
h
l
e
s
s
vol
t
a
ge st
re
ss
can
be at
t
a
i
n
e
d
by
ext
e
n
d
i
n
g t
h
e
TZ-S
o
urce
I
n
v
e
rt
er t
o
t
h
e
q
u
a
s
i
or
em
bedde
d Z
S
I.
Owi
ng
t
o
vol
t
a
ge a
n
d
cur
r
en
t
spi
k
es i
n
TZ
-S
ou
rce I
nve
rt
er,
t
h
e l
a
rge st
art
up re
so
na
nt
curre
nt
i
s
pro
duc
ed an
d i
t
m
a
y
dest
r
o
y
t
h
e devi
ces
.
This is the
m
a
jo
r p
r
o
b
lem
of TZ
-S
ou
rce
In
verte
r
. Th
e
current and voltage spi
k
es are ge
nerate
d by the
tran
sform
e
r’s
wind
ing
s
and
cap
acito
rs.
2.
3.
Trans-Z
-
Sour
ce Inverter
Fi
gu
re
3 sh
o
w
s t
h
e v
o
l
t
a
ge f
e
d Tra
n
s
-
Z-
So
urce
In
ve
rt
er.
It
has t
w
o
DC
i
n
d
u
ct
o
r
s w
h
i
c
h can
b
e
co
up
led or
separ
a
ted
.
A
l
so
it
h
a
s con
tin
uou
s in
pu
t cu
rr
en
t; th
e i
n
du
ctor
s
ar
e co
up
led as show
n in
Figu
r
e
3.
Owi
n
g
to
t
h
e mag
n
e
tic co
uplin
g
b
e
t
w
een
t
h
e two
i
n
du
ctors, th
e
v
o
ltag
e
acro
s
s th
e in
ducto
r L
1
is appe
ared t
o
th
e in
du
ctor L
2
. There
f
ore
,
any one of the ca
pacitors
, for e
x
a
m
ple C
2
, can be rem
oved
fr
o
m
t
h
e ci
rcui
t
.
Whe
n
th
e turn’s
ratio N
2
/N
1
is
ch
ang
e
d, th
en
t
h
e
vo
ltag
e
acro
ss
L
2
can
b
e
so ad
ju
sted
as t
o
be propo
rtion
a
l
to
th
e
vol
t
a
ge ac
r
o
ss
L
1
. Like the Z
-
Source Inve
rt
er, the T
r
ans-Z-Sour
ce Inve
rter has a
n
e
x
tra shoot-through ze
ro
state besides
the six active
states
and t
w
o traditional zero sta
t
es.
Vd
c
D
L2
L1
C1
n : 1
Fi
gu
re
3.
Tra
n
s
-
Z-
So
urce
I
n
ve
rt
er
2.
4.
Improved Z
-
Source
Inverte
r
Fig
u
re
4
shows th
e Im
p
r
ov
ed
Z-Sou
r
ce Inv
e
rter. In
th
e t
r
ad
ition
a
l in
v
e
rter, th
e i
n
v
e
rt
er bridg
e
is
co
nn
ected
in
parallel with
th
e Z-sou
r
ce
n
e
two
r
k
,
wh
ile in
th
e IMZSI, th
e in
v
e
rter bridg
e
is in
series wi
th
th
e
Z-S
o
u
r
ce net
w
o
r
k
.
A
not
her
di
ffe
rence i
s
t
h
at
t
h
e posi
t
i
ons o
f
t
h
e I
nve
rt
er B
r
i
d
ge
and t
h
e di
od
e are
in
terch
a
ng
ed an
d th
eir con
n
e
ctio
n
d
i
rection
is rev
e
rsed
.
The vo
ltag
e
po
larities o
f
th
e
Z cap
acito
rs are
sa
m
e
as
th
e in
pu
t vo
ltag
e
po
larity; th
erefo
r
e, th
e Z cap
acito
rs
vo
ltag
e
stresses are g
r
eatly redu
ced
and
th
e sam
e
b
o
o
s
t
v
o
ltag
e
is
p
r
o
d
u
ced acro
s
s th
e in
v
e
rter
bridge. Th
is top
o
l
o
gy h
a
s i
n
h
e
ren
t
i
n
ru
sh
-cu
r
ren
t
li
m
i
tatio
n
ab
ility.
Fi
gu
re 4.
Im
pr
ove
d Z-S
o
urce
I
nve
rt
er
Th
e i
m
p
act o
f
th
e p
h
a
se leg sh
oo
ts th
ro
ugh
is
analysed. After sim
p
lifica
tion the ave
r
age of the
vol
t
a
ge
acr
oss
a Z-s
o
urce i
n
d
u
ct
o
r
ove
r a
sw
i
t
c
hi
ng
pe
ri
o
d
(0
t
o
T
)
i
s
gi
ve
n
by
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
.
4
,
D
ecem
b
er
2
015
:
79
7 – 807
80
0
dc
V
T
T
T
L
V
0
1
1
(1)
B
i
s
a b
o
o
st
fa
ct
or,
T-
Swi
t
c
hi
ng
pe
ri
o
d
,
t
h
e i
m
pedance s
o
u
r
ce i
nve
rt
er
o
u
t
put
v
o
l
t
a
ge i
s
g
i
ven
by
2
.
2
dc
V
M
B
i
V
M
ac
V
In
t
h
e c
o
nve
nt
i
onal
c
o
nve
rt
er
,
2
.
dc
V
M
ac
V
,
Wh
ere, M is mo
du
latio
n ind
e
x
an
d V
dc
is DC in
pu
t
v
o
ltage
Th
e
ou
tpu
t
vo
l
t
ag
e can be
b
o
o
s
ted or
r
e
du
ced
b
y
selecting
an a
p
propriat
e
Buck –B
oost factor
M
B
B
B
.
,
(2)
Whe
r
e B
B
i
s
B
u
ck
B
o
ost
fact
or
va
ry
i
n
g
f
r
o
m
0 t
o
α
.
The
bo
ost
fact
or i
s
co
nt
r
o
l
l
e
d
by
t
h
e s
h
oot
t
h
r
o
u
g
h
ze
ro
st
at
e dut
y
cy
cl
e. The
m
odul
a
t
i
on i
n
d
e
x
d
e
term
in
es th
e
zero state p
e
riod
s.
Th
e m
a
g
n
e
tizin
g
indu
ctan
ce is v
e
ry im
p
o
r
tan
t
in
theTZ-So
urce
Inv
e
rter.
M
a
gnet
i
z
i
n
g In
duct
a
nce Desi
g
n
,
0
]
2
1
)[
1
(
2
)
1
(
2
1
P
ND
N
dc
TV
D
D
m
L
m
L
(3
)
In t
h
e case of
Trans-Z
-
Sourc
e
networ
k,
d
u
r
i
ng s
h
o
o
t
-
t
h
r
o
ug
h ze
ro st
at
e,
t
h
e pea
k
val
u
e of t
h
e p
h
ase
vol
t
a
ge
i
s
gi
ve
n by
2
.
2
dc
V
B
M
i
V
M
ph
V
,
(4)
Whe
r
e,
M
i
s
t
h
e m
odul
at
i
o
n
i
nde
x.
V
o
l
t
a
ge
gai
n
i
s
M
n
M
M
MB
G
2
3
1
)
1
(
(
5
)
If th
e turn
s ratio
is 1
,
th
en
th
e in
v
e
rter bo
ost g
a
in
o
f
DC link
vo
ltag
e
is same as th
at o
f
co
nv
en
tio
n
a
l
Z-So
urce In
v
e
rters, bu
t in
th
e new T
r
ans
-
Z
-
Source network, one capacitor
is sav
e
d
.
If th
e tu
rn
s ratio
is ab
ov
e
1, i
t
pro
d
u
ces t
h
e sam
e
AC
out
p
u
t
vol
t
a
ge a
s
Z-So
u
r
ce
Inverter and
it req
u
i
res a sm
a
ller sh
oo
t-throug
h d
u
t
y
rat
i
o
Ds
h.
Thi
s
i
s
t
h
e m
a
jor
adva
nt
a
g
e o
f
Tran
s-Z
-
S
o
u
r
c
e
In
vert
e
r
.
In i
m
prove
d Z-
So
urce
In
ve
rt
er
du
ri
n
g
sh
oo
t throug
h
m
o
d
e
, th
ere
will b
e
lin
ear increase in
t
h
e v
o
ltag
e
wh
ich
eq
u
a
tes
i
n
du
cto
r
v
o
ltag
e
and
th
e
cap
acito
r vo
ltag
e
.
Du
ri
n
g
shoo
t-throug
h th
e
cap
acito
r ch
ar
ges t
h
e inductors a
n
d curre
nt t
h
rough t
h
e ca
pacitor
equal
s
t
h
e c
u
r
r
e
nt
t
h
r
o
u
g
h
t
h
e
i
nduct
o
r
.
The
cal
cul
a
t
i
on o
f
i
n
d
u
ct
ance a
n
d capaci
t
a
nce pl
a
y
s a vi
t
a
l
rol
e
in t
h
e
d
e
s
i
gn
. T
h
er
e
f
o
r
e th
e
r
e
qu
ir
ed
ca
pacitance was found
to be
C
avg
L
V
T
I
C
0
)
(
(6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
An
al
ysi
s
of
Im
ped
a
n
ce
So
urc
e
I
n
vert
e
r T
o
p
o
l
o
gi
es f
o
r
G
r
i
d
Int
e
grat
i
o
n
..
.. (
A
.
S
a
n
g
a
ri
)
80
1
C
a
l
c
ul
at
i
on
of
req
u
i
r
e
d
i
n
d
u
ct
ance i
s
d
one
b
y
usi
n
g t
h
e f
o
r
m
ul
a,
L
C
I
V
T
L
0
(7
)
Tabl
e
1 a
n
d
Ta
bl
e 2
s
h
o
w
t
h
e
sim
u
l
a
t
i
on pa
r
a
m
e
t
e
r of i
n
t
e
r
f
aci
n
g
devi
ce
wi
t
h
t
h
e
va
ri
o
u
s
i
n
vert
ers
.
Tabl
e 1. So
urc
e
Param
e
t
e
rs
Para
m
e
ter Value
PV
Panel Voltage (
S
ingle)
16.
54
V
PV Panel Curr
ent (Single)
2.
25 A
Gr
id Voltage
415 V
No.
of Cells (
s
ingle PV Panel)
36 in ser
i
es
PV arr
a
y
size
14x2
PV arr
a
y
Voltage
230V
PV arr
a
y
Cur
r
e
nt
4.
5A
Tab
l
e 2
.
Param
e
ters
of d
i
fferen
t
inv
e
rter
topo
lg
ies
I
nver
t
er
topolo
g
y
I
nductance capacitance
No. of
Tran
sf
o
r
m
e
rs
ZSI
L
1
=L
2
=1nH C
1
=C
2
=2nF
NA
TZSI
NA
C
1
=C
2
=1nF
2
T
r
ans-
ZSI NA
C=320µF
1
IMZ
S
I
L
1
=L
2
=1nH C
1
=C
2
=2nF
NA
3.
PULSE
WIDTH MODUL
A
TION TECHNIQUE
Sim
p
l
e
bo
ost
c
ont
rol
P
W
M
t
e
chni
que
i
s
use
d
i
n
Z-S
o
urce
In
vert
e
r
,
whi
c
h a
dds
sh
o
o
t
t
h
r
o
ug
h i
n
al
l
the c
o
nve
n
tional zero states.
The
sim
p
le control m
e
thod i
s
illustrated in
Figure
5 in
which
only two straight
lin
es are
u
s
ed
to
id
en
tify the
sh
oo
t throug
h.
Th
e
pu
l
s
es f
o
r
t
h
e si
x s
w
i
t
c
h
e
s are s
h
o
w
n.
Sh
oot
t
h
r
o
u
g
h
dut
y
rat
i
o
(
D
o)
dec
r
eases wi
t
h
ri
si
ng
m
odul
at
i
o
n
i
nde
x
(M
).
0
0.
00
5
0.
0
1
0.
0
1
5
0.
02
0.
0
2
5
0.
0
3
-2
0
2
Ti
m
e
(
s
)
Fi
gu
re
5.
S
w
i
t
c
hi
n
g
se
q
u
ence
wi
t
h
Si
m
p
l
e
B
oost
C
o
nt
r
o
l
P
W
M
Tec
hni
qu
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
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-86
94
I
J
PED
S
Vo
l.
6
,
No
.
4
,
D
ecem
b
er
2
015
:
79
7 – 807
80
2
4.
SIM
U
LATI
O
N
RESULTS
AN
D DIS
C
US
SION
The Z-S
o
urce
t
o
p
o
l
o
gi
es wer
e
m
odel
e
d
a
n
d
pe
rf
orm
a
nce out
put
s
o
f
t
h
e sol
a
r
fe
d gri
d
con
n
ect
ed
Z
-
So
urce I
n
vert
e
r
s were st
u
d
i
e
d wi
t
h
t
h
ree
pha
se ful
l
bri
dge i
n
vert
e
r
u
s
i
ng P
W
M
sw
i
t
c
hi
ng t
ech
ni
que as
M
A
TLAB
/
S
I
M
U
LI
NK
m
odel
[1
8]
. I
n
gene
ral
t
h
e
out
put
s
of i
nve
rt
er a
r
e
con
n
ect
ed
t
o
t
h
e gri
d
by
m
eans of
L
an
d
C filter. Gri
d
is a v
o
ltag
e
sou
r
ce of in
fin
ite cap
ab
ility. Th
e v
a
riab
le en
erg
y
in
pu
t was m
o
d
e
led
as a
v
a
riab
le vo
ltage sou
r
ce. Th
e si
m
u
latio
n
ou
tpu
t
vo
ltag
e
s a
nd curre
n
ts we
re
obtaine
d
for al
l the four inverters.
Th
e cu
rren
t To
tal Harm
o
n
i
c Distortio
n
was calcu
lated
fo
r
al
l
i
nve
rt
er
t
o
p
o
l
o
gi
es
by
pe
rf
orm
i
ng F
o
u
r
i
e
r
an
alysis b
y
Fast Fou
r
ier Al
g
o
rith
m
(FFT).
The P
V
sy
st
em
was m
odel
l
e
d
usi
n
g si
ngl
e
di
ode
m
odel
as d
i
scusse
d i
n
[
1
9
]
. The a
rray
si
z
e
of
1
4
x
2
w
a
s used
t
o
obtain
th
e d
e
sir
e
d v
o
ltag
e
of
23
0 V
.
Th
e VP
and the
VI c
h
ara
c
teristics are shown in Fi
gure
s 6 (a
)
and (b) res
p
ect
ively.
(a)
(b)
Figu
re
6.
(a
)
V
-
P c
u
r
v
es
(
b
)
V
-I c
u
rves
o
f
s
o
l
a
r panel
fo
r var
i
ous
i
rra
di
at
i
o
n
s
Fi
gu
re
7 sh
o
w
s t
h
e si
m
u
l
a
t
e
d
ci
rcui
t
of
Z-S
o
u
r
ce I
n
vert
er
fed
gri
d
co
n
n
e
c
t
e
d PV sy
st
e
m
. The phas
e
t
o
p
h
ase
o
u
t
p
ut
v
o
l
t
a
ge a
n
d
cur
r
e
n
t
wa
vef
o
rm
s of Z
-
S
o
urce
I
nve
rt
er
are s
h
o
w
n i
n
Fi
gu
res
8
(a)
and
(
b
)
respectively.
Fi
gu
re
7.
Si
m
u
l
a
t
i
on ci
rc
ui
t
o
f
gri
d
co
n
n
ect
e
d
s
o
l
a
r
fe
d Z
-
S
o
u
r
ce
In
ve
rt
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
An
al
ysi
s
of
Im
ped
a
n
ce
So
urc
e
I
n
vert
e
r T
o
p
o
l
o
gi
es f
o
r
G
r
i
d
Int
e
grat
i
o
n
..
.. (
A
.
S
a
n
g
a
ri
)
80
3
(a)
(b
)
Fi
gu
re
8.
(a
) P
h
ase t
o
phase
v
o
l
t
a
ge
of
o
u
t
p
u
t
wave
f
o
rm
(b)
O
u
t
p
ut
p
h
ase
cur
r
ent
o
f
Z
-
S
o
u
r
ce
In
ve
rt
er
The i
n
rus
h
c
u
r
r
ent
an
d t
h
e ca
paci
t
o
r
vol
t
a
ge
st
ress of Z
-
S
o
urce i
n
ve
rt
er a
r
e sh
ow
n i
n
fi
gu
res 9
(a)
and (b) res
p
ect
ively.
0
0.
5
1
1.
5
2
0
10
00
20
00
30
00
40
00
Ti
m
e
(
s
)
C
ur
r
e
n
t
(A
)
0
0.
5
1
1.
5
2
-
600
0
-
400
0
-
200
0
0
Ti
m
e
(
s
)
Vol
t
a
g
e
(
V
)
(a)
(
b
)
Fi
gu
re
9.
Z-
So
urce
I
nve
rt
er
(
a
) I
n
rus
h
c
u
rre
nt
(
b
)
C
a
paci
t
o
r
vol
t
a
ge
st
ress
FFT a
n
al
y
s
i
s
o
f
Z
-
S
o
u
r
ce
In
v
e
rt
er i
s
s
h
ow
n i
n
Fi
gu
re
1
0
. T
h
e t
o
t
a
l
harm
oni
c di
st
ort
i
o
n
was
fo
u
n
d
t
o
be
1.
17
%.
Fig
u
r
es
11
(a
) a
n
d
(
b
)
sh
o
w
s th
e in
rus
h
c
u
rre
nt and ca
pacitor vol
t
age stre
ss
o
f
T
Z
-S
ou
rce
In
ve
r
t
er.
Figure 10. FFT
analysis
o
f
Z
-
So
urce
In
ve
rt
er
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
.
4
,
D
ecem
b
er
2
015
:
79
7 – 807
80
4
0
0.
5
1
1.
5
2
0
0.
05
0.
1
0.
15
0.
2
Ti
m
e
(
s
)
C
u
rr
en
t
(
A
)
0
0.
5
1
1.
5
2
0
500
1000
1500
2000
Ti
m
e
(
s
)
V
o
l
t
age
(
V
)
(a)
(
b
)
Figu
re
1
1
. T
Z
-
S
o
u
rce
I
nve
rte
r
(a
)
In
r
u
sh
cu
r
r
ent
(b
) Ca
paci
tor
v
o
ltage stre
ss
FFT a
n
aly
s
is o
f
TZ
-S
ou
rce
In
verter
fe
d gri
d
connected
PV syste
m
is
sh
ow
n in
Fi
g
u
r
e
12
. Th
e t
o
tal
harm
oni
c
di
st
o
r
t
i
o
n
was
f
o
un
d t
o
be
1
5
.
1
8
%.
Fig
u
r
e
12
.
FFT an
alysis of
TZSou
r
c
e In
v
e
r
t
er
Si
m
ilarly
th
e i
n
ru
sh
curren
t
an
d
the cap
acitor vo
ltag
e
st
ress
of Tra
n
s
-
Z-
So
urce
In
vert
e
r
are sh
ow
n
i
n
Figu
res 1
3
(a) and
(
b
)
res
p
ect
ively
.
0
0.
5
1
1.
5
2
0
5
10
15
x 10
4
Ti
m
e
(
s
)
C
u
r
r
e
n
t (A
)
0
0.
5
1
1.
5
2
0
200
0
400
0
600
0
800
0
Ti
m
e
(
s
)
Vo
l
t
a
g
e
(
V
)
(a)
(
b
)
Figu
re
13
. T
r
an
s-Z-
So
ur
ce I
n
v
e
rter
(a)
I
n
r
u
s
h
cu
rre
nt (
b
)
Ca
pacitor
v
o
ltage
stress
FFT analysis of Trans-Z
-
Source I
nve
rter fe
d grid connected syste
m
is sh
o
w
n
in
Figure 14
. Th
e to
tal
harm
oni
c
di
st
o
r
t
i
o
n
was
f
o
un
d t
o
be
0
.
9
4
%.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
An
al
ysi
s
of
Im
ped
a
n
ce
So
urc
e
I
n
vert
e
r T
o
p
o
l
o
gi
es f
o
r
G
r
i
d
Int
e
grat
i
o
n
..
.. (
A
.
S
a
n
g
a
ri
)
80
5
Fig
u
r
e
14
. FFT
an
alysis
of
T
r
ans-Z-Source
Inve
rter
Sim
i
l
a
rl
y
Fi
gur
es 1
5
(a
) a
nd
(
b
) s
h
ow
t
h
e i
n
r
u
sh
cu
rre
nt
a
n
d t
h
e ca
paci
t
o
r
vol
t
a
ge
st
ress
of
Im
pro
v
ed
Z-Source Inve
rter.
0
0.
5
1
1.
5
2
0
20
40
60
80
100
Ti
m
e
(
s
)
C
u
rr
en
t
(
A
)
0
0.
5
1
1.
5
2
-1
0
0
10
20
30
Ti
m
e
(
s
)
Vo
l
t
ag
e
(
V
)
(a)
(
b
)
Fig
u
r
e
15
.
I
m
p
r
ov
ed
Z-
So
ur
ce In
v
e
r
t
er
(
a
) In
ru
sh
cu
rr
en
t
(b
) Cap
acitor
vo
ltag
e
str
e
ss
FFT a
n
alysis of Tra
n
s
Z-Source Inve
rter fe
d gri
d
c
o
n
n
ect
e
d
sy
st
em
i
s
shown i
n
Fi
gu
re
1
6
. T
h
e t
o
t
a
l
harm
oni
c
di
st
o
r
t
i
o
n
was
f
o
un
d t
o
be
3
.
0
9
%.
Fig
u
r
e
16
. FFT
an
alysis
of
Im
pr
o
v
ed
Z-
So
ur
ce I
nve
rt
er
Fro
m
th
e sim
u
l
a
ted
resu
lts
wi
th
a co
m
p
arison
o
f
ZS
I,
TZS
I, T
r
a
n
s-Z
S
I
,
a
n
d
Im
pro
v
e
d
Z
S
I a
r
e
p
r
esen
ted in
Tab
l
e 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
.
4
,
D
ecem
b
er
2
015
:
79
7 – 807
80
6
Tabl
e
3. %
T
H
D
C
o
m
p
ari
s
on
s o
f
ZS
I, TZS
I,Trans-Z
S
I, and IMZS
I
INVER
TER TYP
E
Cu
rren
t
TH
D %
ZSI
1.
17
TZSI
8.
06
T
r
ans-
ZSI 0.
94
I
M
ZSI 3.
09
5.
CO
NCL
USI
O
N
The si
m
u
l
a
t
i
on of Z-
So
urce
, TZ-S
o
urce, a
n
d Tra
n
s-
Z-Source, and Im
proved Z
-
Source Inve
rters
was
carried
out
usi
n
g
M
A
T
L
AB/
S
IM
UL
I
N
K
s
o
ft
ware
an
d
ou
tpu
t
wav
e
form
s were ob
tain
ed. Fro
m
th
e THD
an
alysis, it was clear th
at for th
e sam
e
setu
p
and
filte
r circu
it, th
e Tran
s-Z-Sou
r
ce
Inverter (TZSI) had
less
harm
oni
c
di
st
u
r
ba
nce t
h
an
t
h
e basi
c
ZSI
,
T
Z
SI,
an
d
IM
Z
S
I.
The
m
a
xi
m
u
m
possi
bl
e b
o
o
s
t
gai
n
c
o
ul
d
be
obt
ai
ne
d i
n
Tr
ans-
Z S
o
u
r
ce I
nve
rt
er
when t
h
e tra
n
sform
e
r ratio wa
s grea
ter than
one. T
h
e capacitor
voltage
str
e
ss and
t
h
e in
ru
sh
cur
r
e
n
t
w
e
r
e
also
b
e
measu
r
ed
f
o
r
all th
e Z-Sou
r
ce In
v
e
r
t
er
t
o
po
log
i
es and
it w
a
s found
that the im
proved Z
-
Source Inverte
r
ha
d very less
in
ru
sh
cu
rren
t an
d
th
e cap
acito
r
v
o
ltag
e
stress wh
en
com
p
ared with
the othe
r
Z
-
So
urce
I
nve
rt
er t
o
p
o
l
o
gi
es.
ACKNOWLE
DGE
M
ENT
The a
u
t
h
or
s
wi
sh t
o
t
h
an
k
t
h
e M
a
nage
m
e
nt
of
R
a
jal
a
ks
hm
i
Engi
n
eeri
n
g C
o
l
l
e
ge
, C
h
e
n
nai
,
f
o
r
p
r
ov
id
ing
all t
h
e co
m
p
u
t
atio
n
a
l facilities to carry
ou
t th
is
work.
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