Int
ern
at
i
onal
Journ
al of
P
ower E
le
ctr
on
i
cs a
n
d
Drive
S
ystem
s
(
IJ
PEDS
)
Vo
l.
12
,
No.
2
,
Jun
2021
,
pp.
886
~
901
IS
S
N:
20
88
-
8694
,
DOI:
10
.11
591/
ij
peds
.
v12.i
2
.
pp
886
-
901
886
Journ
al h
om
e
page
:
http:
//
ij
pe
ds
.i
aescore.c
om
Review
of DC
-
AC
co
nverters
for
photo
vo
l
taic co
nversion
chains
Mounir B
ou
z
gu
en
da
1
,
Tare
k S
el
mi
2
1
Depa
rtment of
El
e
ct
ri
al
Engi
n
e
eri
ng,
Coll
ege of
Engi
n
ee
ring
,
Ki
ng
Faisal Unive
r
sity
,
Saud
i
Arab
i
a
2
Univer
sity
of
T
unis E
l
-
Man
ar,
Faculty
of
Mathemat
i
cal, Phys
ic
a
l
and
Natur
al
S
cienc
es
of
Tun
is, La
bora
tory
of
Analysis
and
Proce
ss
ing
o
f
Signal
s,
E
le
c
trica
l
and
Ene
rgy
S
ystem
s, Tuni
sia
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
J
ul
6
,
20
20
Re
vised
Jan
11
, 20
2
1
Accepte
d
Fe
b
22
, 20
2
1
Thi
s
pap
er
is
de
vote
d
to
th
e
st
ate
of
the
art
in
p
hotovol
taic
(PV
)
conve
rsion
cha
ins
and
the
i
r
arc
h
itect
ur
es.
T
wo
ma
jor
ch
aract
er
isti
cs
are
co
nsidere
d
to
cl
assify
the
se
c
hai
ns.
The
se
ar
e
th
e
ga
lva
ni
c
i
solat
ion
and
the
numbe
r
of
stage
s;
ch
aract
e
risti
cs
gen
era
l
ly
lo
ca
l
ized
aro
u
nd
th
e
DC
-
AC
conv
erter
(inve
rt
er)
at
the
end
of
the
PV
c
onver
sion
ch
ai
n
.
The
r
efo
re
,
thi
s
pape
r
d
eals
with
a
com
pr
ehens
ive
rev
ie
w
of
the
d
iffe
r
ent
inv
ert
er
topol
og
ie
s
tha
t
ca
n
be
int
egr
at
ed
int
o
P
V
conve
rsion
ch
ai
ns,
dist
ingui
shi
ng
bet
wee
n
the
t
ran
sforme
r
base
d
and
the
t
ran
sforme
r
-
l
ess
conve
rsion
ch
ains
.
The
p
ape
r
d
em
onstra
tes
tha
t
to
th
is
da
te,
tra
nsform
er
-
ba
sed
inv
ert
ers
ar
e
v
ery
common
and
wide
ly
used,
hav
e
a
lon
g
rec
ord
of
a
cc
o
mpl
ishme
n
t
as
a
com
ponen
t
of
s
ola
r
ene
rgy
sys
te
ms,
in
par
t
ic
ul
ar
for
residentia
l
app
li
c
at
ion
s
bec
ause
of
th
ei
r
gr
ea
t
e
r
eff
icienc
y
,
smaller
size,
and
l
ower
costs.
Ne
ver
theless,
tr
ans
forme
r
-
l
ess
cha
ins
a
re
tout
e
d
with
some
pr
oble
ms
and
shortcom
ings
.
Mor
eove
r,
solar
ene
rgy
stor
age
d
evi
c
es,
wir
el
ess
cha
rging
sys
te
m
s
in
sta
ti
ons
and
al
ong
the
highways
req
uir
e
the
r
e
-
ex
am
in
at
ion
of
the
ex
i
sting
solar
PV
conve
rsion
cha
ins,
th
ei
r
ar
c
hit
e
ct
ure
s
and
p
oss
ibl
y
new
con
ver
sion
cha
ins
suita
bl
e
for
all
distri
bute
d
gen
er
at
ion
including
e
le
c
tri
c
c
ars
and
storage de
vi
ce
s.
Ke
yw
or
d
s
:
Conver
sio
n
c
ha
ins
DC
-
AC in
ver
te
r
Galva
nic isolat
ion
le
akag
e
cu
rr
e
nt
So
la
r
ph
otovo
l
ta
ic
Transf
ormer
-
le
ss in
ver
te
r
s
This
is an
open
acc
ess arti
cl
e
un
der
the
CC
BY
-
SA
l
ic
ense
.
Corres
pond
in
g
Aut
h
or
:
M
ou
nir
B
ouzg
uenda
Dep
a
rtme
nt of
Ele
ct
rial
En
gi
ne
erin
g
Coll
ege
of
En
gi
neer
in
g, Ki
ng
Faisa
l U
niv
er
sit
y
P.O. Bo
x 3
80, Al A
hs
a
PC
31982, Ki
ngdom
of Sa
ud
i
Ar
a
bi
a
Emai
l:
mbuzg
a
nd
a
@
kfu.
e
du.s
a
1.
INTROD
U
CTION
So
la
r
ra
diati
on
is
the
la
r
gest
f
low
of
ene
r
gy
enterin
g
t
he
ea
rth
s
ys
te
m
.
A
ft
er
re
flect
ion
an
d
a
bs
or
ption
in
the
at
mo
s
pher
e,
mu
c
h
of
it
can
be
c
onve
r
te
d
into
var
i
ous
f
orms
of
e
nerg
y
us
e
d
by
man
kind.
Nowad
a
ys,
accor
ding
t
o
[
1],
the
act
ual
powe
r
of
t
he
PV
sy
ste
m
is
le
ss
tha
n
60
-
75%
of
the
est
imat
ed
el
ect
rici
ty
pro
du
ct
io
n.
T
he
ALCE
N
C
orp
or
at
e
Fou
ndat
ion
f
or
E
ne
rgy
K
nowl
ed
ge
[2]
re
porte
d
t
hat
this
e
nerg
y
corres
ponds
t
o
nea
rly
6,0
00
ti
mes
the
ene
r
gy
c
on
s
um
e
d
by
the
e
ntire
world
po
pu
la
ti
on.
As
a
res
ult,
so
la
r
energ
y
has
the
po
te
ntial
to
de
velo
p
int
o
a
m
aj
or
c
omp
on
e
nt
of
the
s
us
ta
in
able
ene
r
gy
fa
mil
y.
T
his
renewable
energ
y w
as
us
e
d by ancie
nt ci
vili
zat
ion
s
for heat
ing wate
r,
desali
natio
n,
a
nd fo
od dry
i
ng.
a.
Since
the
nin
et
eenth
ce
ntury
,
so
la
r
e
nerg
y
ha
s
bee
n
the
sc
op
e
of
a
gro
wi
ng
num
ber
of
researc
h
project
s
and
de
velo
pme
nts.
Ke
y
an
d
de
vel
opments
are
t
he
disc
over
y
of
the
ph
otov
oltai
c
e
ff
e
ct
by
Be
querel
i
n
1839
[3].
b.
Disco
very
of t
he photoc
ondu
ct
ivit
y
of sele
ni
um
by W
il
lo
ughb
y
S
mit
h
in
1873.
c.
The de
velo
pme
nt of t
he
fi
rst
work
i
ng s
olar c
el
l by
C
har
le
s
Fr
it
ts wit
h a
1 perce
nt effic
ie
ncy in
1883.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
Revi
ew
o
f DC
-
AC co
nverters
for
photo
v
oltai
c co
nversio
n
c
ha
i
ns
(
M
ounir
Bo
uz
gue
nda
)
887
d.
The
dev
el
opm
ent
of
the
first
so
la
r
cel
l
with
an
ef
fici
enc
y
of
6
pe
rcen
t
i
n
1954.
This
wa
s
f
ollow
e
d
by
the
dev
el
opment
of
s
olar
cel
l
with
a
n
8
per
ce
nt
in
19
57,
14
pe
rcen
t
in
19
60,
32.
3
pe
rce
nt
i
n
1999
an
d
42
.8
per
ce
nt in
20
07.
e.
So
la
r
cell
s co
st
drop
ped f
rom
$76
i
n 197
7
to
$0.25 pe
r Wat
t i
n 201
7
.
f.
DC
to
AC
in
ve
rter
is
as
im
porta
nt
as
t
he
s
olar
pa
nels
a
nd
t
hey
at
the
hear
t
of
dome
sti
c
so
la
r
po
w
er
sy
ste
ms
,
co
nve
rting
t
he
DC
t
o
AC
.
I
nverte
rs
ha
ve
bee
n
e
xp
e
rienci
ng
c
onti
nu
e
d
de
velo
pm
e
nt
since
la
te
nin
et
eent
h
cen
tur
y.
I
n
2000
Sa
nd
ia
La
borator
ie
s
in
ve
n
te
d
t
he
mode
r
n
i
nv
e
rter
pa
ving
t
he
wa
y
t
o
reside
ntial
so
la
r
s
ys
te
ms
de
plo
yme
nt
g.
Ap
a
rt
f
rom
t
he
a
bove
de
ve
lop
me
nts,
th
e
wides
pread
smart
gr
i
ds
hav
e
bee
n
di
ct
at
ing
ad
diti
onal
requireme
nts
on
s
olar
P
V
in
ve
rters
su
c
h
a
s
auto
nomy,
a
da
ptivit
y,
co
oper
at
ion
,
pl
ug
-
an
d
-
play
f
unct
io
ns,
commu
nicat
io
n,
a
nd
sel
f
-
a
w
aren
es
s
[
4].
S
uch
re
quireme
nts
are
ex
pect
ed
to
af
fect
th
e
inv
e
rter
t
opol
ogy
and ph
ys
ic
al
pr
op
e
rtie
s. Ho
we
ver, these
addit
ion
al
require
m
ents ca
n be a
ddresse
d
in
a se
pa
rate stu
dy.
h.
Howe
ver,
the
global
producti
on
of
ph
otovo
l
ta
ic
energ
y
has
so
fa
r
remai
ne
d
l
ow
co
mp
a
re
d
t
o
the
po
te
ntial
of
this
res
ourc
e.
This
is
main
ly
due
to
the
hi
gh
pro
du
ct
i
on
cost
of
this
ene
rgy,
wh
ic
h
is
s
ti
ll
do
minate
d
by
that
of
f
os
sil
e
nerg
y.
As
a
res
ult,
the
mai
n
c
halle
ng
e
is
fi
ndin
g
l
ow
-
c
os
t
and
high
-
e
ff
ic
i
ency
s
olu
ti
ons
for
dev
el
op
i
ng ne
w photo
volt
ai
c pow
e
r
s
ys
te
m
s.
i.
Im
prov
i
ng
t
he
eff
ic
ie
nc
y
of
the
phot
ovoltai
c
gen
e
rator
by
i
nteg
rati
ng
new
cel
l
te
chnolo
gies
s
uc
h
a
s
orga
nic cel
ls o
r
li
ght
-
co
nce
nt
rati
on cell
s.
j.
Im
prov
i
ng
the
eff
ic
ie
nc
y
a
nd
c
os
t
of
t
he
e
ntire
s
ys
te
m
by
set
ti
ng
up
ne
w
ar
chite
ct
ur
es
of
photov
oltai
c
conve
rsion c
ha
ins.
Give
n
the
fact
that
the
globa
l
market
f
or
s
olar
P
V
grew
about
44
%
in
2019
[
5],
t
he
f
act
that
th
e
global
total
of
627
G
W
incl
udin
g
on
-
a
nd
off
-
gri
d
s
ys
te
ms
[5]
a
nd
the
fa
ct
that
the
s
olar
s
olar
ef
fici
en
cy
has
been
witnessin
g
mar
gin
al
im
pro
ving,
ot
her
al
te
rn
at
ives
shou
l
d
be
in
vestigat
ed
to
ma
xi
mize
the
powe
r
from
so
la
r
ph
otovo
l
ta
ic
sy
ste
ms
.
In
par
ti
cular
and
it
is
with
ou
t
do
ub
t
tha
t
the
a
rc
hitec
ture
of
the
D
C
-
A
C
conve
rsion c
ha
ins s
hall be e
va
luate
d,
a
nd it
is
in
this
context
that co
mes t
he
work
de
velo
pe
d
in
t
his
pa
per.
2.
PHO
T
OVO
LTAI
C C
O
NVERS
ION
CHAIN A
R
CHITEC
TU
RE
A
so
la
r
ph
otovo
lt
ai
c
co
nv
e
r
sion
c
hain
c
onsist
s
of
seve
ral
subsyst
ems
[6]
that
pro
vi
de
va
rio
us
functi
onal
it
ie
s
as
il
lustrate
d
in
Fi
gure
1.
S
uc
h
functi
ons
i
nc
lud
e
pro
duct
ion,
c
onve
rsion
,
a
nd
inter
face.
The
se
functi
ons
a
re
c
om
m
on
in
al
l
photov
oltai
c
conve
rsion
c
hai
ns
.
A
uxil
ia
ry
f
un
ct
io
ns
inclu
de
c
on
t
ro
l,
pr
ot
ect
ion
,
and
sto
rag
e
an
d
diff
e
r
from
on
e
chai
n
to
a
no
t
her.
Gr
id
c
onnected
co
nv
ersio
n
c
hains
do
not
r
eq
uire
stora
ge
batte
ries
as
th
e
conve
rsion
c
hain
i
s
fe
d
dir
ect
ly
from
the
so
la
r
pan
el
s
a
nd
pro
duce
al
te
rn
at
in
g
vo
lt
a
ge
an
d
su
pp
or
ts t
he
c
ust
om
er
loa
d.
Figure
1. Ge
ne
ral arc
hitec
ture
of s
olar p
ho
t
ovoltai
c c
onvers
ion
c
hain
s
So
la
r
P
V
chai
ns
ca
n
be
cl
assif
ie
d
by
dif
fer
e
nt
famil
ie
s
acc
ordi
ng
to
the
nu
m
be
r
of
powe
r
pr
ocessin
g
sta
ges,
t
he use
and of a
transf
ormer a
nd
oth
e
rw
ise
t
he
el
imi
nation a t
ra
nsf
ormer.
a.
The
galva
nic
i
so
la
ti
on
bet
we
en
the
s
ource
and
the
gri
d
c
on
sist
s
of
a
n
i
so
la
ti
on
tra
ns
f
ormer
desi
gn
e
d
a
t
high
fr
e
quenci
es
(
HF)
on
th
e
sou
rce
si
de
via
a
high
f
re
qu
e
nc
y
of
1
kHz
or
higher.
Alte
r
nativel
y,
a
trans
forme
r
is
placed
on th
e
gri
d
si
de
a
nd op
erates at
a l
ow
fr
e
qu
e
nc
y (LF
)
of
50 to 6
0H
z
.
b.
The
num
ber
of
sta
ges
in
the
chain.
In
one
hand,
the
c
onve
rsion
of
the
e
nerg
y
is
achie
ved
strai
gh
t
f
r
om
dire
ct
c
urre
nt
(
DC)
the
al
te
rnat
ing
c
urre
nt
(
AC).
Othe
rw
is
e,
the
c
onve
rsi
on
is
do
ne
t
hro
ugh
a
buck
-
boos
t
DC
-
DC stage
to reg
ulate
the
DC volt
age
b
e
f
or
e
the
DC to
AC c
onversi
on
.
c.
Additi
on
al
l
y,
so
la
r
phot
ovol
ta
ic
chains
ar
c
hitec
ture
is
c
ha
racteri
zed
by
co
ns
trai
nts
s
uc
h
as
e
ff
ic
ie
nc
y
impro
veme
nt,
the
in
put
powe
r
fluctuati
on
s
re
duct
ion,
pro
du
ct
i
on
op
ti
miza
ti
on
durin
g
ir
ra
diati
on
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
12
, N
o.
2
,
J
une
2021
:
886
–
901
888
intermit
te
ncy
a
nd
t
he
reli
abili
ty
imp
r
ov
e
ment
and
ex
te
ns
io
n
of
t
he
li
feti
me
of
k
e
y
co
mpo
ne
nts
su
c
h
as
t
he
el
ect
ro
lyti
c cap
aci
tors,
i
nduct
or
s
, etc.
As
a
res
ult,
va
rio
us
to
po
l
og
ie
s
of
phot
ovoltai
c
conver
si
on
chains
ha
ve
be
en
de
velo
pe
d
a
nd
re
porte
d
in
the
li
te
ratur
e
.
I
n
the
f
ollow
i
ng,
a
s
pecial
f
oc
us
w
il
l
be
g
iv
en
t
o
th
e
to
polog
ie
s
that ha
ve
cau
ght
the
at
te
ntion
of
m
os
t
res
ear
cher
s
in
the
fie
ld
o
f
phot
ovoltai
c
sy
ste
ms
.
T
his
stu
dy
fo
c
use
s
on
t
he
esse
ntial
functi
on
of
an
y
chain
wh
ic
h
is
the
“
co
nv
e
rsi
on
”
functi
on
a
s
well
as
the
aux
il
ia
r
y
f
un
ct
i
on
s
su
c
h
as
pr
otect
ion
,
c
onne
ct
ion
with the
grid
a
nd o
t
her
s
.
2.1.
Ga
lv
an
ic
c
onv
ersi
on
li
nes
of
high freq
uenc
y ty
pe
Galva
nic
isola
ti
on
is
e
nsure
d
by
mea
ns
of
a
c
ompact
H
F
tra
ns
f
ormer
.
H
ow
e
ve
r,
t
he
trans
f
or
me
r
exh
i
bits
ext
ra
losses
pe
naliz
ing
the
refor
e
the
e
ff
ic
ie
nc
y
of
the
c
onve
rs
ion
c
hai
n
[
7
]
-
[
10].
The
diagram
in
Figure
2
s
how
s
the
galva
nic
isolat
ion
pri
nci
ple.
T
his
t
yp
e
of
isolat
io
n
is
base
d
on
the
fl
yb
ac
k
a
ppr
oac
h
that
us
es
high v
al
ue
capacit
or
s at
the input stage
.
Th
is ap
proac
h t
end
s to si
gnif
ic
antly r
e
du
ce
the en
ti
re c
onve
rsion
chain
li
feti
me.
The
i
nput
volt
age,
ge
ne
rall
y
of
the
or
der
of
12V,
is
c
onve
r
te
d
int
o
ve
r
y
hi
gh
AC
volt
ag
e
(
HF
pulse
s
of
the
or
der
of
400V).
T
his
vo
lt
age
is
recti
fied
a
nd
filt
ered
to
pro
vid
e
a
hi
gh
DC
volt
age
t
hat
is
ap
plied
to
t
he
input
of
t
he
i
nverter
t
o
pro
duce
“
co
nsuma
ble
”
AC
volt
ages.
T
he
us
e
of
HF
gal
van
i
c
isolat
io
n
ap
plies
to
sy
ste
ms
h
a
ving
fe
w
PV
m
odules
in
series
pro
du
ci
ng
fe
w
hundr
ed
Watt
s.
T
he
c
urren
t
wav
e
f
or
m
s
are
quasi
-
sinu
s
oid
al
due
to the a
dopte
d con
t
ro
l st
rategi
es.
2.2.
Conv
ersi
on ch
ains with
lo
w
-
freque
ncy g
al
vanic i
so
l
at
io
n
The
sche
mati
c
dia
gr
a
m
of
s
uc
h
c
hai
ns
is
s
how
n
in
Fig
ure
3.
I
n
t
his
cas
e,
the
DC
i
nput
vo
lt
a
ge
i
s
conve
rted
i
nto
AC
volt
age
thr
ough
the
in
ver
t
er.
T
he
LF
tra
ns
f
ormer
am
plifie
s
this
vo
lt
a
ge
to
sta
ndar
d
value
s
(11
0/220V
,
50
-
60H
z).
T
his
typ
e
of
is
olati
on
is
t
he
le
ast
use
d
beca
us
e
of
their
relat
ively
hi
gh
pr
ic
es,
weig
ht
and size
c
omp
ared t
o
c
onve
rs
ion
with
HF t
ra
ns
f
ormer
s [7
]
-
[
10].
Figure
2. Gal
va
nic isolat
io
n u
sing HF
tra
ns
f
ormer
F
i
g
u
r
e
3
.
Gal
va
nic isolat
io
n u
sing LF t
ran
s
f
ormer
2.3.
Non
-
is
olated c
onversi
on ch
ai
ns
In
this
gal
van
i
c
isolat
io
n
c
ha
ins,
t
he
non
-
is
olate
d
dc
–
dc
c
onve
rters
a
re
de
sign
e
d
t
o
ste
p
-
up
or
ste
p
-
dow
n
the
volt
age.
As
a
res
ult,
the
siz
e,
the
weig
ht
an
d
the
vo
l
um
e
of
the
c
hain
s.are
com
pact
a
nd
the
conve
rsion e
ff
i
ci
ency
is
enha
nced.
2.3.1.
Non
-
is
olated
mono
-
s
t
ag
e
conversi
on
c
ha
i
ns
In
this
ca
se,
t
he
co
nversi
on
is
done
in
a
si
ngle
ste
p
with
ou
t
a
vo
lt
age
am
pl
ific
at
ion
sta
ge
.
A
s
s
how
n
in
Fig
ur
e
4,
m
any
phot
ovoltai
c
mo
dule
s
are
require
d
to
ge
ner
at
e
a
volt
ag
e
at
the
ou
tp
ut
of
the
i
nv
e
rter
that
is
su
f
fici
ently
hi
g
h,
cl
os
e
to
that
of
t
he
gr
i
d.
T
he
a
ddit
ion
al
f
un
ct
io
ns
(
M
P
P
T
an
d
pr
otect
ion)
a
re
al
l
inte
gr
at
e
d
in a si
ng
le
sta
ge
of the
con
versi
on ch
ai
n.
2.3.2.
Non
-
is
olated
t
wo
-
st
age c
onv
ersi
on
c
ha
ins
In
t
his
case
of
photov
oltai
c
sy
ste
ms,
t
he
c
onve
rsion
c
hain
consi
sts
of
tw
o
casca
ded
sta
ges.
T
he
first
sta
ge
is
a
DC
-
DC
co
nverter
to
boos
t
the
D
C
vo
lt
age
ge
ne
rated
by
the
photov
oltai
c
pa
nel
w
hile
the
seco
nd
sta
ge
is
DC
-
A
C
ty
pe,
al
lo
wing
t
he
ge
ner
at
i
on
of
a
n
AC
volt
age
to
inter
f
ace
the
phot
ovoltai
c
syst
em
with
the
gr
i
d
as
s
how
n
in
Fi
gure
5.
I
n
t
his
c
ase,
th
e
a
dd
it
io
nal
functi
ons
c
ould
be
distri
bu
te
d
betwee
n
the
D
C
-
D
C
conve
rter a
nd t
he DC
-
AC c
onver
te
r
.
F
i
g
u
r
e
4
.
Non
-
i
so
la
te
d
si
ng
le
-
sta
ge
str
uctu
re
Figure
5. N
on
-
isolat
ed
tw
o
-
sta
ges
st
ru
ct
ur
e
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
Revi
ew
o
f DC
-
AC co
nverters
for
photo
v
oltai
c co
nversio
n
c
ha
i
ns
(
M
ounir
Bo
uz
gue
nda
)
889
3.
CONFIG
U
R
ATIO
NS
OF
PHOTO
VOL
TAIC C
ONV
ERSIO
N CH
AINS
This
sect
io
n
re
views
t
he
var
i
ou
s
co
nfi
gurati
on
s
of
the
ph
ot
ovoltai
c
conv
ersio
n
c
hains
a
ccordin
g
t
o
their
DC
-
to
-
A
C co
nv
e
rsion s
ta
ge.
3.1.
Photov
olt
aic c
onversi
on ch
ai
ns b
ase
d
on c
entr
al inv
er
te
rs
The
ce
ntral
in
ver
te
r
co
nfi
gur
at
ion
s
ys
te
m
i
s
sho
wn
i
n
Fi
gure
6
[11
]
-
[
15]
.
It
is
fr
e
que
ntly
us
ed
f
or
high
po
wer
a
ppli
cat
ion
s.
I
n
this
ty
pe
of
c
onfig
ur
at
io
n,
phot
ovoltai
c
modul
es
are
m
ounte
d
in
rows
with
eac
h
end
of
a n
on
-
re
tur
n
di
od
e
.
T
he
rows
a
re
c
onnected
i
n
pa
ral
le
l
to
the
i
nput o
f
t
he
ce
ntral
inv
e
rter.
It
is
a simple
config
ur
at
io
n
char
act
e
rized
by
l
ow
instal
la
ti
on
a
nd
maint
enan
ce
cost.
H
ow
e
ve
r,
the
ce
ntral
in
ver
te
r
c
hain
is
pen
al
iz
e
d
by
losses
due
t
o
th
e
phen
ome
no
n
of
as
ymmet
ry,
al
so
kn
own
a
s
mismat
c
h
phenomen
on,
w
hi
ch
i
s
li
nk
ed
to
t
he
use
of
a
sin
gle
M
PP
T
strat
e
gy
implante
d
i
n
t
he
sai
d
in
ver
te
r.
In
ad
diti
on,
i
n
case
the
i
nv
e
rter
is
fau
lt
y,
t
he
e
ntire
c
onve
rsion
chain
is
is
olate
d,
an
d
no
co
ntinu
it
y
of
se
rv
ic
e
is
possible.
M
ore
ov
e
r,
the
us
e
of
long ca
bles c
onnecti
ng t
he p
ho
t
ov
oltai
c m
odules
comp
romise
s the e
ff
ic
i
ency o
f
t
he
c
onver
si
on ch
ai
n.
3.2.
Photov
olt
aic c
onversi
on ch
ai
ns b
ase
d
on s
tring
inver
ter
s
Nowa
day
s
,
as
per
t
he
“
s
ys
te
m
te
ch
no
l
ogy
for
photov
oltai
cs
”
[
16],
t
he
st
rin
g
in
ver
te
r
c
onfig
ur
at
io
n
the
m
os
t
us
e
d
sy
ste
m
c
onfi
gurat
io
n.
T
he
sc
hemati
c
diagra
m
of
t
his
c
onfi
gurati
on
is
give
n
in
Fi
gure
7
[
17
]
,
[
18]
. I
t i
nvolv
e
s conn
ect
i
ng
a
n
in
ver
te
r
to
ea
ch
r
ow
of
phot
ovoltai
c mod
ules and
par
al
le
li
ng the
outp
uts
of
t
he
diff
e
re
nt in
ver
t
ers.
The
i
nverters
need
ce
rtai
n
s
yn
c
hro
nizat
ion
to
a
void
a
ny
exch
a
nge
of
powe
r.
Eac
h
i
nverter
has
it
s
own
MPPT
w
hich
al
lows
be
tt
er
co
ntr
ol
of
the
powe
r.
I
n
add
it
io
n,
in
ca
se
of
fail
ure
of
an
in
ver
te
r,
only
th
e
row
a
sso
ci
at
e
d
with
it
is
is
ol
at
ed
wh
ic
h
al
l
ow
s
c
on
ti
nu
it
y
of
ser
vice.
Fi
nally,
s
uch
a
n
arr
a
ng
e
men
t
offe
rs
a
modu
la
rity that
all
ow
s
an easy
ch
ai
n exte
ns
io
n.
Figure
6. Bl
oc
k diag
ram of
th
e central i
nv
e
rt
er
sy
ste
m c
onfi
gurati
on
F
i
g
u
r
e
7
.
Strin
g
in
ve
rter s
ys
te
m con
fig
ur
at
io
n
3.3.
Multis
tring
system c
onfigur
at
i
on
The
e
ff
ic
ie
nc
y
an
d
reli
abili
ty
of
the
c
onve
rs
ion
c
hain
co
ul
d
be
imp
r
ov
e
d
by
co
nnect
in
g
the
DC
-
DC
conve
rter
to
ea
ch
r
ow
or
st
rin
g
[
19
]
,
[
20].
T
he
c
onver
te
rs’
ou
t
pu
ts
a
re
c
onnecte
d
in
pa
r
al
le
l
to
the
in
put
of
a
central
i
nv
e
rter
as
s
how
n
in
Fig
ur
e
8.
Thi
s
co
nfi
gurati
on
c
ombines
th
e
ad
va
ntages
of
the
cent
ral
inv
e
rte
r
config
ur
at
io
n
with
th
os
e
of
the
strin
g
in
ve
rter
co
nfi
gurat
ion
.
I
nd
ee
d,
t
he
maxim
um
powe
r
poi
nt
trackers
(MPPT
)
are
i
nt
egr
at
ed
at
t
he
conve
rter
le
ve
l,
wh
ic
h
ma
ke
s
it
po
ssi
ble
to
overc
om
e
the
loss
e
s
due
to
the
ph
e
nome
non
of
mismat
ch
.
T
his
c
onfig
urat
ion
is
certai
nl
y
more
ec
onomi
cal
tha
n
t
he
st
r
ing
co
nfi
gurati
on
but
cannot e
nsure
t
he
c
on
ti
nuit
y o
f
the
servic
e
offer
e
d by the lat
te
r
in case
of
f
ai
lure of
t
he
ce
ntral in
ver
te
r.
F
i
g
u
r
e
8
.
Mult
i
-
strin
g
i
nv
e
rter
conv
e
rsion c
ha
in
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
12
, N
o.
2
,
J
une
2021
:
886
–
901
890
3.4.
Int
e
grated
system c
onfigur
ati
on
This
cat
e
gory
include
s
the
f
ollow
i
ng
th
ree
co
nf
i
gurati
on
s,
namely
[
21
]
-
[
23]
,
i)
p
arall
el
conve
rter
config
ur
at
io
n,
ii
)
s
e
ries
conve
rter
c
on
fig
ur
at
io
n,
an
d
ii
i)
m
ic
r
oin
ve
rter
co
nfi
gurati
on.
The
th
r
ee
config
ur
at
io
ns
li
ste
d
above
are
res
pecti
vel
y
sho
wn
i
n
Fi
gure
9,
Fi
gure
10
a
nd
Fig
ur
e
11.
A
s
sho
wn
i
n
Figure
9,
eac
h
of
the
pa
rall
el
or
t
he
pa
rall
el
co
nverter
c
onfig
ur
at
io
n
s
how
n
i
n
Fig
ure
9,
e
ach
c
onve
rter
is
connecte
d
to
a
ph
otovo
lt
a
ic
modu
le
ha
ving
it
s
ow
n
M
P
PT
wh
ic
h
im
pro
ves
t
he
power
ge
ner
at
io
n
mana
geme
nt.
I
n
ad
diti
on,
this
config
ur
at
io
n
al
lows
a
m
or
e
pr
eci
se
c
on
t
ro
l
sy
ste
m
a
nd
a
qu
ic
k
res
ponse
in
the
even
t
of a
fau
lt
.
Howe
ver,
this
config
ur
at
io
n
r
equ
i
res
high
a
mp
li
ficat
ion
ga
in
of
the
volt
a
ge
to
matc
h
t
he
re
quire
d
vo
lt
age
at
the
i
nput
of
the
in
ve
rter,
wh
ic
h
sign
i
ficantl
y
inc
reases
the
los
s
es
and
t
hu
s
pe
naliz
es
the
eff
i
ci
ency
of the e
ntire c
onve
rsion c
hain
.
To
reduce
this
gain,
series
c
onve
rter
c
onfig
ur
at
io
n
s
how
n
in
Fig
ur
e
10
is
recomme
nd
e
d.
Indee
d,
t
hi
s
config
ur
at
io
n
al
lows
acce
s
s
to
the
pa
ral
le
l
conver
te
r
config
ur
at
io
n
op
ti
ons
exce
pt
that
the
ga
in
of
amplific
at
ion
is
reduce
d
as
t
he
num
be
r
of
conve
rters
inc
r
eases.
T
he
dra
wb
ac
k
of
t
his
config
ur
at
io
n
l
ie
s
in
connecti
ng se
ve
ral co
nverter
s
which
res
ults in the
d
e
pe
nd
e
nc
e of the
MPP
T of
diff
e
re
nt c
onve
rters.
Anothe
r
c
onfi
gurati
on
co
ns
i
der
e
d
in
t
he
l
it
eratur
e
is
th
e
microi
nv
e
rte
r
syst
em
de
sign
sho
wn
i
n
Figure
11.
Thi
s
co
nfi
gurati
on
c
onsist
s
in
c
onnecti
ng
t
he
inv
e
rter
directl
y
t
o
the
photovo
lt
ai
c
m
o
du
le
via
a
vo
lt
age
a
mp
li
f
ic
at
ion
sta
ge.
This
desi
gn
w
ou
l
d
re
du
ce
lo
sses
due
t
o
t
he
mismat
c
h
phe
nomen
on
an
d
would
al
low flexible
extensi
on thro
ugh
t
he
“
plug a
nd p
la
y
”
te
c
hn
i
qu
e
.
F
i
g
u
r
e
9
.
Parall
el
co
nve
rter c
onfi
gurati
on
F
i
g
u
r
e
1
0
.
Se
ries co
nverter
confi
gurati
on
F
i
g
u
r
e
1
1
.
M
ic
ro
i
nv
e
rter s
ys
t
em con
fig
ur
at
i
on
4.
INV
E
RTER
TOPOL
OGIE
S OF
PHOT
O
VOLTAI
C C
ONVERS
IO
N
C
H
AI
NS
4.1.
Cate
go
ri
es
of
inverters
The
in
ver
te
r
is
the
major
el
em
ent
of
a
ny
phot
ovoltai
c
c
onve
rsion
c
hai
n.
I
nverter
s
c
ould
be
cl
assifi
ed
into tw
o
cat
e
gories,
n
a
mely:
a.
“
Line
-
s
witc
he
d
”
in
ver
te
r
s
w
hich
a
re
usual
ly
of
hi
gh
pow
e
rs.
T
he
y
are
m
ade
of
th
yr
ist
ors
whose
s
witc
hi
ng
fr
e
qu
e
nc
y
is
c
on
t
ro
ll
ed
f
r
om
the
li
ne
c
urre
nt.
H
ow
e
ve
r,
the
t
hyristo
r
re
qu
i
res
f
or
ce
d
s
witc
hing
ci
rcu
i
ts
to
br
i
ng
t
he
c
urr
ent
to
ze
ro
t
o
tu
rn
t
hem
OF
F
.
I
n
a
dd
it
ion
,
i
n
ver
te
rs
made
up
of
t
hyristo
rs
re
quire
com
plica
te
d
fil
te
ring circ
uits.
Fo
r
these
r
eas
ons,
t
his ty
pe o
f i
nv
e
rter is
rar
el
y use
d
as
re
por
te
d
in t
he [2
4].
b.
“
Self
-
c
om
m
uta
te
d
”
in
ver
te
rs
that
are
based
on
powe
r
tra
nsi
stors
s
uc
h
as
bipolar
tra
ns
i
stors
,
fiel
d
e
ffec
t
transisto
rs
(
MOSFE
Ts)
a
nd
insu
la
te
d
gate
bipolar
tra
ns
ist
or
s
(IGBTs)
.
Those
in
ver
te
rs
are
c
on
t
ro
ll
ed
us
in
g
sim
ple
s
witc
hing
te
c
hniqu
es
impleme
nted
i
n
a
nalo
g
or
dig
it
al
inte
gr
at
e
d
ci
rc
uits
[25].
T
he
y
c
oul
d
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
Revi
ew
o
f DC
-
AC co
nverters
for
photo
v
oltai
c co
nversio
n
c
ha
i
ns
(
M
ounir
Bo
uz
gue
nda
)
891
be
vo
lt
age
c
on
trolle
d
cal
le
d
“
vo
lt
age
sou
rce
inv
e
r
te
r
”
(VSI
),
or
c
urre
nt
c
on
t
ro
ll
ed
c
al
le
d
“
c
urren
t
s
our
ce
inv
e
rter
”
(CSI)
.
c.
VS
I
i
nv
e
rters
are
the
m
os
t
use
d
beca
us
e
a
high
-
powe
r
fa
ct
or
co
uld
be
a
chieve
d
by
a
s
imple
pulse
wi
dth
modu
la
ti
on
(PW
M
).
d.
The
us
e
of
CS
I
in
ver
te
rs
is
ge
ner
al
ly
li
mit
ed
to
me
diu
m
a
nd
hi
gh
-
po
wer
ap
plica
ti
on
s.
CSIs
hav
e
a
se
ries
of
in
duct
ors
at
the
DC
bus
t
o
mainta
in
c
on
sta
nt
curre
nt.
These
in
ve
rter
s
hav
e
t
he
f
ollow
i
ng
a
dvanta
ges
[26]
,
i)
i
n
the
e
ven
t
of
a
sho
rt
-
ci
rcu
it
,
t
he
cu
rr
e
nt
remai
ns
l
imi
te
d
within
t
he
in
ver
te
r
w
hi
ch,
t
hanks
t
o
th
e
inducta
nces
of
the
DC
bus,
cannot
e
xcee
d
the
s
hort
-
ci
rc
uit
cu
rr
e
nt
of
the
P
V
pa
nel
,
and
ii
)
t
he
us
e
of
sens
or
s
is not
ne
cessar
y becau
se the c
onnecti
on of t
he
in
ver
t
er to t
he gri
d d
oes n
ot u
se
any
contr
ol lo
op.
4.2.
Inv
er
ter
s
peci
ficat
i
on
s
Fo
r
al
l
in
ve
rters
cat
e
gories,
there
are
te
ch
ni
cal
sp
eci
ficat
io
ns
t
hat
m
us
t
be
ta
ke
n
i
nto
c
onside
rati
on
wh
e
n
dev
el
op
i
ng
a
PV
c
onve
rsion
syst
em.
Among
the
se
s
pecifica
ti
ons,
t
he
total
ha
rm
onic
disto
rtion
(
THD)
and po
wer fact
or (
P
F)
a
re
reta
ined [
27].
The
“
929
-
1988
-
IEEE
Re
co
mmende
d
Pr
ac
ti
ce
for
Util
it
y
I
nterf
ac
e
of
Re
sidentia
l
an
d
In
te
rme
diate
Photo
vo
lt
ai
c
(
PV
)
S
ys
te
ms
(
1987)
”
[
28]
ha
s
sta
te
d
that
th
e
total
harmo
ni
c
disto
rtion
is
def
i
ned
as
the
rati
o
of
the
squar
e
r
oot
of
the
sum
of
the
s
quares
of
t
he
r
ms
va
lues
of
t
he
ana
lyzed
si
gn
al
t
o
the
rm
s
val
ue
of
it
s
fun
dame
ntal t
erm. This
v
al
ue i
s always gi
ve
n
in
p
e
rce
nt as
ind
ic
at
ed
in (1
)
.
(
%
)
=
100
√
∑
2
∞
=
2
1
(1)
wh
e
re H
n
is
th
e
rm
s v
al
ue
of the n
th h
a
rm
onic
an
d
H
1
is
t
he
rms value
of
t
he
fun
dame
nta
l
te
rm.
Accordi
ng
to
US
IE
EE
P
929
[
28],
the
T
H
D
of
t
he
c
urre
nts
mu
st
al
wa
ys
be
le
ss
tha
n
5%
.
Table
I
sh
ows
the
T
H
D
li
mit
s
adopted
by mo
st st
and
a
r
ds
[29].
Table
1
.
T
H
D
l
imi
t of
t
he
c
urr
ent acco
r
ding t
o
the
or
der
of t
he har
monics
Order
of
h
arm
on
ic
s
Li
mit of
the T
H
D
2
-
9
4%
10
-
15
2%
16
-
21
1.
5%
22
-
33
0.
6%
THD up
to
the 5
0
th
har
moni
c
5%
The
sec
ond
s
pe
ci
ficat
ion
is
the
po
wer
fact
or
w
hich
is
of
domina
nt
imp
or
ta
nce.
A
un
it
powe
r
fact
or
is
of
te
n
require
d
wh
e
re
it
is
as
so
ci
at
ed
with
l
ow
val
ues
of
c
urren
t.
T
his
re
s
ults
in
a
re
duct
ion
of
los
ses
w
it
hin
the ch
ai
n
a
nd c
on
s
eq
ue
ntly a bet
te
r profita
bi
li
ty o
f
the
phot
ovoltai
c co
nve
rsion.
The
e
ff
ect
ive
val
ue
of t
he
c
urr
ent is e
xpresse
d
as
(2)
.
=
√
∑
2
∞
=
1
(2)
Wh
e
re
I
n
is t
he
amp
li
tu
de of
the
harmo
nic
of ord
e
r n.
Simi
la
rly,
t
he r
ms
value of
curre
nt could
b
e
expresse
d
as
a
functi
on
of
TH
D
as
(
3)
.
=
1
√
1
+
2
(3)
In
a
ddit
ion
,
t
he
powe
r
facto
r
PF
is
desc
rib
ed
in
the
“
1547.
1
-
2005
-
IE
EE
Stan
dard
Conforma
nce
Test
P
ro
ce
dure
s
f
or
E
quip
me
nt
In
te
r
co
nnect
ing
Distri
bu
te
d
Re
sou
rces
wit
h
Ele
ct
ric
P
ow
er
Sy
ste
m
s
(20
11)
”
[30
]
,
[
31]
as
(4)
.
=
=
1
(4)
wit
h
is
t
he
back
-
ph
ase
s
hi
ft
of
the
c
urre
nt
fun
dame
ntal
te
rm
with
res
pect
t
o
t
he
f
undame
ntal
te
r
m
of
the
vo
lt
age
.
Re
wr
it
ing
(4)
wh
il
e
c
onside
r
ing
(
3),
ma
kes
it
possi
ble
t
o
express
the
power
fact
or
as
a
f
unct
ion
of
the T
HD as s
how
n
i
n (5)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
12
, N
o.
2
,
J
une
2021
:
886
–
901
892
=
√
1
+
2
(5)
In
a
dd
it
io
n
t
o
the
tw
o
s
pecifi
cat
ion
s
des
crib
ed
a
bove
,
an
y
photov
oltai
c
s
ys
te
m
is
c
har
a
ct
erized
by
furthe
r
sp
eci
ficat
ion
s
relat
e
d
to
secu
rity
an
d
co
upli
ng
t
o
the
gri
d.
T
hes
e
sp
eci
ficat
io
ns
are
dicta
te
d
by
t
he
fo
ll
owin
g
sta
ndar
ds
,
a)
IEC
6036
4
-
7
-
2005:
Ele
ct
rical
ins
ta
ll
at
ion
s
of
buil
dings
sect
io
n
712:
photov
oltai
c
powe
r
s
ys
te
m
s
(
2016)
[30],
b)
I
EEE
15
47
-
1
-
2005:
St
and
a
r
d
IEEE
conf
or
ma
nce
t
est
proce
dures
f
or
equ
i
pm
e
nt
co
nn
ect
in
g
distri
bu
te
d
s
ources
to
el
ect
rical
gr
i
ds
(
2011)
[
29],
c
)
IE
EE
929
-
20
00
:
P
r
act
ic
a
l
interfaci
ng
of
photov
oltai
c
sy
ste
ms
(20
00)
[32],
d)
I
EC
6172
7:
Photo
vo
lt
ai
c
sy
ste
ms:
char
act
e
risti
cs
of
t
he
interface
(20
04)
[33
],
a
nd
e
)
D
S
/
EN
61
000
-
3
-
2:
E
M
C
,
li
mit
s
fo
r
ha
rm
on
ic
emissi
on
s
(
Inp
ut
cu
r
ren
t
of
equ
i
pm
e
nt that
can wait
16
A
per p
hase
)
(
20
19) [34
].
Table
2
s
hows
a
c
omparis
on
of
f
ort
h
me
ntio
ned
sta
nd
a
r
ds
in
te
rms
of
c
urr
ent
i
nject
ed
int
o
t
he
gri
d.
The
VDE
0126
-
1
-
1
sta
ndar
d
is
the
on
l
y
one
that
imp
os
es
a
disc
onnecti
on
ti
me
from
t
he
gr
i
d
i
n
the
or
der
of
200
m
s
if
a
dir
ect
cur
r
en
t
gr
e
at
er
than
1A
is
injec
te
d
into
t
he
gri
d
[35
]
-
[
37]
.
This
sta
nda
rd
al
s
o
re
quire
s
the
disco
nnect
ion of
the
c
onve
rsi
on
s
ys
te
m
if
a
l
eakag
e
c
urren
t occurs,
as sho
wn
in
Table
3
[
38].
Co
ns
ide
ri
ng
the
te
chn
ic
al
s
pecifica
ti
on
s
of
photovo
lt
ai
c
s
ys
te
ms,
se
ve
ral
i
nv
e
rter
t
opologies
that
more
cl
os
el
y
meet
thes
e
sp
eci
ficat
io
ns
hav
e
bee
n
stu
di
ed
an
d
a
re
pr
e
sented
withi
n
t
his
pa
pe
r
that
mainly
f
ocu
se
s
on
,
a
)
i
nv
e
rter
s
with
galva
nic isolat
ion,
a
nd b) i
nv
e
rters
with
ou
t
ga
lvanic is
olati
on
.
Table
2.
In
je
ct
ed direct
c
urre
nt li
mit
f
or
dif
f
eren
t
sta
nd
a
rds
Stan
d
ard
DC in
jected
IE
C 6
1
7
2
7
≤1
% o
f
th
e ou
tp
u
t curre
n
t
VDE
0
1
2
6
-
1
-
1
≤1
A
IE
E
E
1
5
4
7
≤0
.5%
of the o
u
tp
u
t curre
n
t
EN
6
1
0
0
0
-
3
-
2
≤0
.22
A
IE
E
E
9
2
9
-
2000
≤0
.5%
of the o
u
tp
u
t curre
n
t
Table
3.
M
a
xi
mu
m
disc
onne
ct
ion
ti
me acc
ordi
ng to
VD
E
01
26
-
1
-
1
Leakag
e curr
en
t (
m
A)
Disco
n
n
ectio
n
tim
e (
s)
30
0
.30
60
0
.15
100
0
.04
4.3.
Fly
ba
ck m
ono
-
tr
an
sist
or
inv
erter
The
sc
hemati
c
diag
ram
of
t
his
to
po
l
ogy
i
s
show
n
in
Figure
12.
This
is
a
galva
nical
ly
isolat
ed
topolo
gy
usi
ng
a
hi
gh
f
reque
ncy
(
HF)
tra
nsfo
rme
r.
It
is
a
low
po
wer
i
nverter
(a
rou
nd
100W
)
ba
sed
on
a
sing
le
-
t
ran
sist
or
f
ly
bac
k
co
nv
erter
w
hose
outpu
ts
fee
d
a
mi
d
-
point
tran
sf
ormer
[
39
]
-
[
42
].
Both
out
pu
ts
of
t
he
trans
forme
r
a
r
e
co
nnect
ed
to
the
gri
d
th
roug
h
tw
o
diode
s,
tw
o
tra
ns
ist
or
s
a
nd
a
filt
er.
This
c
onfig
ur
at
io
n
al
lows
the
Flyb
ac
k
c
onve
rter
to
pro
vid
e
two
c
urre
nts
of
opposit
e
sign
s
.
T
he
tw
o
outp
ut
tra
nsi
stors
sy
nc
hro
nousl
y
switc
h
with
t
he
sin
gle
tra
nsi
stor
of
t
he
fl
yback
co
nverter
in
the
high
frequ
e
nc
y
re
gim
e.
The
Flyb
ac
k
co
nve
rter
operates
i
n
a
disc
on
ti
nuou
s
c
onduct
io
n
m
ode
(D
C
M
)
w
hich
im
plies
that
t
he
current
thr
ough the
tra
ns
f
ormer
r
eac
he
s zer
o bef
or
e
the start
of eac
h swit
chi
ng cy
cl
e.
The
major
disa
dv
a
ntage
of
t
his
topolo
gy
li
es
in
the
fact
tha
t
the
dec
ouplin
g
of
t
he
powe
r
in
par
al
le
l
with
the
ph
otovo
lt
ai
c
m
odule
is
ge
ner
al
ly
c
arr
ie
d
out
us
in
g
el
ect
r
oly
ti
c
c
apacit
or
s
of
hi
gh
val
ues.
Mor
eov
e
r,
the
tw
o
sta
ge
s
of
t
his
to
po
l
og
y
m
us
t
be
siz
e
d
f
or
a
power
equ
al
t
o
twic
e
the
nomi
nal
po
wer.
Finall
y,
a
no
t
her
dr
a
w
back o
f
th
is t
opolog
y
is t
he
lo
w p
ow
e
r f
act
or
due to
th
e existe
nce
of
a zer
o
-
c
ro
s
sin
g dist
ort
ion.
4.4.
Fly
ba
ck in
ver
ter
with
high
power dec
oup
li
ng
This
t
opolog
y
consi
sts
of
the
fl
ybac
k
i
nv
e
rt
er
with
a
bu
c
k
-
bo
os
t
c
onver
t
er
[43].
The
ci
rcu
it
of
this
topolo
gy is
give
n
in
Fig
ure
13.
F
i
g
u
r
e
1
2
.
Fl
yback mo
no
-
tra
nsi
stor
i
nv
e
rter
F
i
g
u
r
e
1
3
.
Fl
yback inve
rter
wi
th h
i
gh po
wer
decou
pling
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t J
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ys
t
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S
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88
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Revi
ew
o
f DC
-
AC co
nverters
for
photo
v
oltai
c co
nversio
n
c
ha
i
ns
(
M
ounir
Bo
uz
gue
nda
)
893
The
to
po
l
ogy
i
s
a
modifie
d
ve
rsion
of
the
one
prese
nted
i
n
Fig
ur
e
12
in
order
to
a
void
the
use
of
high
value
el
ect
ro
lyti
c
ca
pa
ci
tors.
I
nd
ee
d,
t
he
dec
oupl
ing
ca
pacit
or
is
el
imi
nated
us
i
ng
a
buc
k
-
boos
t
conve
rter.
T
his
is
a
to
polo
gy
wh
e
re
the
tra
nsi
stor
S
pv
,
the
diode
D
pv
,
the
pr
ima
ry
winding
of
the
tra
nsfo
rme
r,
the
f
reewheel
ing
di
od
e
of
the
transisto
r
S
DC
and
the
ca
pacit
or
C
DC
f
orm
t
he
buck
-
bo
os
t
c
onve
rter
op
e
rat
ing
i
n
the d
isc
onti
nuous c
onduct
io
n mo
de.
Each
c
ycle
be
gin
s
with
t
he
c
onduct
ion
of
t
he
tra
ns
ist
or
S
PV
wh
ic
h
res
ults
in
a
li
nea
r
in
crease
of
t
he
mag
netiz
at
ion
current.
W
he
n
this
c
urren
t
r
eaches
a
so
-
ca
ll
ed
ref
e
re
nce
value,
the
t
ransi
stor
S
PV
is
bl
ock
e
d
and
t
he
ene
r
gy
store
d
in
the
mag
netiz
at
ion
inducta
nce
is
t
ran
s
ferre
d
to
t
he
capaci
t
or
C
DC
.
The
tra
ns
is
tor
S
DC
mu
st
be
act
ive
wh
e
n
the
c
urr
ent
is
bein
g
di
scharge
d
to
th
e
capaci
tor
w
hi
ch
impli
es
the
sta
te
of
zer
o
volt
age
switc
hing.
In
a
ddit
ion,
one
of
t
he
tw
o
ou
t
pu
t
t
ran
sist
or
s
is
sim
ultan
eousl
y
act
ivate
d
with
the
t
ra
ns
ist
or
S
DC
.
Th
us
,
the
tra
nsi
s
tors
on
the
sec
onda
ry
si
de
of
t
he
in
ve
rter
switc
h
at
hi
gh
fr
e
quen
cy
re
gime
unl
ike
t
he
topolo
gy
of
th
e
Fly
bac
k
in
ve
rter.
T
he
mag
netiz
at
ion
cu
rrent
c
on
ti
nu
es
t
o
dec
rease
unt
il
reachi
ng
a
s
econd
ref
e
ren
ce
.
At
t
his
ti
me,
th
e
tr
ansisto
r
S
DC
will
tur
n
OFF
a
nd
t
h
e
ene
rgy
st
or
e
d
in
the
in
duct
or
is
tra
ns
fe
rr
e
d
t
o
the
sec
onda
r
y
side
of
t
he
tra
ns
f
ormer
a
nd
t
hen
to
t
he
gr
i
d.
T
he
di
od
e
D
PV
is
use
d
to
e
li
minate
the
re
ver
se
vo
lt
age
acr
os
s
the capa
ci
tor
C
PV
wh
e
n
t
he
e
ne
rgy
is
bein
g
t
r
ansf
e
rr
e
d
t
o
th
e seco
ndar
y
si
de.
4.5.
The mo
dified
“
SHI
MIZ
U
”
i
nv
er
ter
The
pre
vious
topolo
gy
sho
ws
volt
age
s
pik
es
at
t
he
le
aka
ge
in
duct
ance
in
cl
ud
e
d
in
the
t
ran
s
f
or
me
r
[44].
S
uch
volt
age
sp
i
kes
e
xist
betwee
n
the
te
rmin
al
s
of
t
he
tra
ns
ist
or
S
DC
du
ri
ng
it
s
tr
ansiti
on
t
o
the
OF
F
sta
te
.
Also
,
t
hi
s
topolo
gy
has
been
i
mpro
ve
d
by
rep
la
ci
ng
the
sin
gle
-
tra
nsi
stor
c
onver
te
r
with
a
bi
-
tra
ns
ist
or
conve
rter as
shown i
n
Fi
gure
14.
F
i
g
u
r
e
1
4
.
M
odifie
d
“
S
himizu
”
in
ve
rter
In
it
ia
ll
y,
the
i
nput
e
nerg
y
of
t
he
in
ver
te
r
is
c
onve
rted
us
in
g
the
bo
os
t
co
nverter
an
d
is
s
aved
in
t
he
interme
diate
capaci
tor
.
T
his
energ
y
is
the
n
conve
rted
us
in
g
the
Fly
bac
k
conve
rter.
Fina
ll
y,
the
e
ne
rgy
store
d
in the ma
gnet
i
zat
ion
in
duct
an
ce is retu
r
ned to the
grid
thro
ugh
t
he
tra
nsfo
rmer.
4.6.
The i
so
la
ted
inver
ter
with
p
ara
ll
e
l
-
p
ar
allel
co
n
figu
r
at
i
on
The
i
nv
e
rter
m
ade
in
the
pa
ra
ll
el
-
par
al
le
l
co
nf
i
gurati
on
is
s
how
n
in
Fig
ur
e
15.
It
deliver
s
a
power
of
the
orde
r
of
200W
[
45]
.
It
is
an
in
ver
te
r
t
hat
is
desig
ned
to
op
e
rate
in
the
disco
ntin
uous
c
onduct
io
n
m
od
e
,
DCM.
T
his
re
su
lt
s
in
a
discon
ti
nu
ous
cu
rrent
in
on
e
of
the
inducta
nce
s
L
pv
or
L.
Th
e
adv
a
nta
ge
of
thi
s
topolo
gy
li
es
in
the
fact
t
hat
the
disco
ntin
uous
c
onduct
i
on
m
od
e
is
ge
ner
al
ly
ass
ociat
ed
with:
a
)
a
simple
con
t
ro
l,
b)
a
reduce
d
siz
e
of
the
in
duct
ance
L
PV
,
a
nd
c)
a
c
urren
t
injec
te
d
i
nto
t
he
gri
d
f
ree
of
H
F
rip
ples/fluct
uat
ion
s
.
At
the
outp
ut
of
the
t
ran
s
f
ormer,
the
re
are
two
c
onve
rsion
sta
ges
whos
e
outp
uts
a
re
connecte
d
in
qu
a
si
-
pa
rall
el
.
On
e
sta
ge
is
re
sp
onsi
ble
f
or
pro
duci
ng
the
posit
ive
al
te
rn
at
ion
of
t
he
cu
rrent,
the
se
c
ond
sta
ge
is res
pons
ible
f
or the
ne
gative
alt
ern
at
io
n.
4.7.
The bi
-
transis
to
r
f
ly
ba
c
k in
vert
er
This
i
nv
e
rter
topolo
gy
is
s
how
n
in
Fig
ure
16.
Its
ou
t
pu
t
po
wer
is
a
r
ound
16
0W.
T
he
operati
ng
pr
i
nciple
is
det
ai
le
d
in
[
46].
At
the
be
ginni
ng
of
a
per
io
d
of
the
gri
d
cu
rrent,
t
he
tra
ns
ist
or
s
S
1
a
nd
S
4
(S
2
an
d
S
3
for
the
ne
ga
ti
ve
half
-
pe
riod)
are
act
ivat
ed.
T
his
will
ge
ner
at
e
a
cu
rr
e
nt
an
d
the
ene
rgy
pr
oduce
d
will
be
save
d
in
the
mag
netiz
at
ion
inducta
nce.
Wh
e
n
these
t
wo
tra
ns
ist
ors
are
deacti
vat
ed,
the
e
nerg
y
will
be
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
12
, N
o.
2
,
J
une
2021
:
886
–
901
894
trans
ferred
to
the
sec
onda
r
y
s
ide
of
the
tra
nsf
orme
r
a
nd
will
subse
qu
e
ntly
be
tr
ans
mit
te
d
to
the
gr
id
th
r
ough
the tra
ns
ist
or S
5
, th
e
fr
ee
w
hee
li
ng
diode
of th
e transist
or
S
6
and the
filt
er.
F
i
g
u
r
e
1
5
.
I
so
l
at
ed
in
ver
te
r w
it
h
pa
rall
el
-
paral
le
l
config
ur
at
io
n
Figure
16. In
ve
rter type
f
ly
bac
k bi
-
tra
ns
ist
or
4.8.
Iso
la
ted fly
back i
nv
er
ter in
pa
r
allel
-
seri
es connec
ti
on
The
to
polo
gy
i
s
show
n
in
Fig
ur
e
17.
It
is
buil
t
aro
und
t
wo
ind
e
pende
nt
fl
yb
ac
k
c
onve
rters
[
47].
I
n
this
case,
the
gri
d
is
co
nnect
ed
in
se
ries
with
the
outp
uts
of
the
tw
o
c
onve
r
te
rs
w
hile
the
photov
oltai
c
m
odule
is
connecte
d
i
n
par
al
le
l
with
t
he
in
pu
ts
of
th
e
conve
rters.
Pr
od
ucin
g
a
powe
r
of
160W,
the
in
ver
te
r
operates
in
co
ntin
uous
cond
uction
m
ode,
CC
M
,
w
hi
ch
resu
lt
s
i
n
a
more
c
ompli
c
at
ed
c
on
tr
ol.
I
t
pro
duces
a
n
outp
ut
vo
lt
age
of
AC
typ
e
by m
odul
at
ing
tw
o si
nus
oid
al
vo
lt
a
ges shifted
by 1
80
° across
the ca
pacit
or
s
C
1
an
d C
2
.
4.9.
Low
freq
uenc
y i
nv
erter
a
s
s
ocia
ted with
a fly
ba
c
k c
onve
rter
This
i
nverter
t
opolog
y
is
s
ho
wn
in
Fig
ur
e
18.
It
is
buil
t
ar
ound
a
Fly
bac
k
c
onve
rter
c
onnecte
d
to
a
thyrist
or
-
ba
sed
in
ver
te
r
.
It
is
de
dicat
ed
to
pro
du
ce
a
po
wer
of
ab
out
150W.
I
n
som
e
cases,
this
powe
r
is
li
mit
ed
to
100W.
T
he
us
e
of
thyrist
or
s
i
ns
te
ad
of
powe
r
tra
ns
ist
ors
can
ca
us
e
s
om
e
s
witc
hing
pr
ob
le
m
s
as
the
thyrist
or
s
are
c
urren
t c
ontr
olled
[48].
F
i
g
u
r
e
1
7
.
I
so
l
at
ed
f
l
yb
ac
k
i
nverter
in pa
rall
el
-
series
connecti
on
F
i
g
u
r
e
1
8
.
L
ow f
re
quenc
y
i
nverter ass
ociat
e
d
with a
f
ly
bac
k conve
rter
4.10.
Inv
er
ter
with
seri
es reso
nan
ce con
ver
ter
The
t
opolog
y
of
this
i
nv
e
rter
associat
e
d
to
a
co
nverter
is
sh
ow
n
i
n
Fi
gure
19.
It
is
bu
i
lt
around
a
series
res
onan
ce
co
nv
e
rter
c
onnected
to
a
high
f
reque
nc
y
gal
va
nical
ly
isolat
ed
in
vert
er.
It
is
desig
ned
t
o
pro
du
ce
a
pow
er
of
ab
out
11
0W
[
49]
an
d
c
an
reach
25
0W
in
s
om
e
ca
ses
[
5
0]
.
M
ore
ov
e
r,
the
t
ran
s
forme
r
le
akag
e
in
duct
ance
an
d
the
c
apacit
or
c
onne
ct
ed
i
n
series
f
orm
a
res
on
a
nc
e
ci
rcu
it
that
reduces
the
s
w
it
chin
g
losses
of the i
nverter
.
The
DC
-
DC
c
onve
rter
switc
hes
at
100K
Hz
with
a
duty
c
ycle
sli
gh
tl
y
le
ss
than
50%
a
nd
it
operat
es
with
a
fi
xed
c
onve
rsion
rati
o,
wh
ic
h
ma
ke
s
it
po
ssi
ble
to
overc
om
e
t
he
po
wer
dec
ouplin
g
be
twe
en
the
photov
oltai
c
modu
le
a
nd
the
gr
id
.
T
he
losses
within
the
co
nverter
are
quit
e
smal
l
wh
il
e
th
os
e
of
t
he
trans
forme
r
are
conside
rab
le
.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
Revi
ew
o
f DC
-
AC co
nverters
for
photo
v
oltai
c co
nversio
n
c
ha
i
ns
(
M
ounir
Bo
uz
gue
nda
)
895
The
i
nv
e
rter
use
s
tw
o
t
yp
e
s
of
switc
hing
frequ
e
nc
y:
high
fr
e
qu
e
nc
y
a
nd
low
f
reque
ncy.
I
nd
ee
d,
the
le
ft arm
of the i
nv
e
rter ope
rates at
f
re
qu
e
nci
es b
et
wee
n 20
and
80K
Hz wh
il
e the r
igh
t ar
m sw
it
ches t
o 100
Hz
.
In
this
case,
th
e
s
witc
hing
l
osse
s
a
re
halve
d
com
par
e
d
to
th
os
e
of
t
he
in
ve
rters
w
hose
t
w
o
a
rms
s
witc
he
s
at
high
fr
e
qu
e
nci
es.
F
i
g
u
r
e
1
9
.
I
nve
rter
with se
ries
r
es
on
a
nce c
on
ver
te
r
4.11.
H
-
brid
ge
in
ve
rter
This
in
ve
rter
i
s
w
hose
to
polo
gy
is
s
how
n
in
Fig
ur
e
20.
Ma
de
up
of
t
wo
transisto
r
a
rms
an
d
hav
i
ng
no
tran
sf
ormer
,
this
to
polo
gy
is
sat
isfact
ory
in
va
riable
s
peed
dri
ves
f
or
AC
mo
t
or
s
and
in
UP
S
.
Abo
ut
con
t
ro
l st
rateg
y,
dif
fer
e
nt P
W
M
tech
nique
s could
b
e
impl
emented
[5
1]
.
The
H
-
br
i
dge
inv
e
rter
is
c
har
act
erize
d
by
a
l
ow
ef
fici
ency
co
mp
a
re
d
to
ot
her
t
ra
ns
f
ormerless
topolo
gies
du
e
to
th
e
us
e
of
hi
gh
fr
e
quen
cy
PWM
c
ontrol
sign
al
s.
T
he
outp
ut
volt
age
of
the
in
ver
te
r
e
xh
i
bits
sign
ific
a
nt
flu
ct
uations
w
hic
h
a
re
at
the
or
igin
of
a
relat
ively
la
r
ge
le
ak
age
c
urre
nt
de
pendin
g
only
on
the
value
of
the
pa
rasit
ic
capaci
ta
nces
C
PV
-
G
that
ex
ist
bet
we
en
the
ph
otov
oltai
c
modu
le
and
the
gro
und.
O
ne
so
luti
on
f
or
re
du
ci
ng
t
he
le
a
kag
e
c
urre
nt,
i
n
the
case
of
bipolar
P
W
M
,
is
to
us
e
a
n
LCL
filt
er
w
hose
tw
o
inducto
rs
are
l
ocated
on
ei
the
r
si
de
of
the
lo
ad
a
s
sho
wn
in
Fig
ure
21.
S
uc
h
a
filt
er
mak
es
it
possible
to
so
l
ve
the
prob
le
m
of
le
aka
ge
c
urre
nt
f
or
the
bipo
la
r
P
W
M
H
-
B
rid
ge
in
ve
rter
pro
vid
e
d
that
the
t
wo
in
du
ct
ors,
on
ei
ther
side
of
the
l
oad,
a
re
pe
rf
ect
ly
s
ym
m
et
rical
.
Alt
hough
th
e
pro
ble
m
of
le
a
kag
e
current
is
so
l
ve
d,
the
energ
y
ef
fici
en
cy remai
ns
lo
w
co
m
pa
red to t
he
tra
nsfo
rme
rless to
po
l
og
ie
s
.
The
un
i
po
la
r
PWM
strat
e
gy
co
uld
al
s
o
be
ap
plied
to
H
-
Bridg
e
in
ver
te
r
to
po
l
ogy.
I
n
this
case,
t
he
vo
lt
age
of
the
inv
erte
r
ta
kes
three
di
ff
e
rent
values,
name
ly:
+
V
IN
,
0
a
nd
-
V
IN
.
Als
o,
the
filt
er
bec
om
es
simp
le
r
a
nd
t
he
fluctuati
ons
of
th
e
outp
ut
vo
lt
age
a
re
re
du
ce
d.
This
st
rateg
y
is
cha
r
act
erized
by
a
high
eff
ic
ie
nc
y.
H
oweve
r,
the
le
akag
e
c
urren
t
i
s
quit
e
high
s
o
th
at
the
H
-
Bridg
e
to
polo
gy
ca
nnot
be
us
e
d
f
or
trans
forme
rless to
po
l
og
ie
s.
Figure
20. H
-
B
rid
g
e in
ver
te
r
F
i
g
u
r
e
2
1
.
LC
L f
il
te
r
c
onfig
urat
ion f
or the
bipolar
PWM
H
-
Bri
dge in
vert
er
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