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I
SS
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c
o
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v
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n
ti
o
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a
l
e
n
e
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g
y
so
u
rc
e
s,
p
h
o
to
v
o
lt
a
ic
sy
ste
m
i
n
teg
ra
ti
o
n
in
to
th
e
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tri
c
a
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rid
is
b
e
c
o
m
in
g
m
o
re
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ru
c
ial.
It
is
a
d
v
ise
d
t
o
e
m
p
lo
y
a
d
o
u
b
le
-
sta
g
e
g
ri
d
-
c
o
n
n
e
c
ted
P
V
sy
ste
m
.
Th
is
c
a
n
b
e
e
m
p
lo
y
e
d
with
th
e
m
a
in
p
a
rts
b
o
o
st
c
o
n
v
e
r
ter,
wh
ich
h
e
lp
s
to
b
o
o
st
th
e
DC
o
u
tp
u
t
fr
o
m
t
h
e
P
V
c
h
a
n
n
e
ls.
An
d
n
e
x
t
o
n
e
is
t
h
e
sp
a
c
e
v
e
c
t
o
r
p
u
lse
wid
t
h
m
o
d
u
lati
o
n
(S
VPW
M
)
in
v
e
rte
r
wh
ich
c
a
n
p
ro
v
id
e
b
e
tt
e
r
h
a
rm
o
n
ic
p
e
rfo
rm
a
n
c
e
a
n
d
h
i
g
h
e
r
e
fficie
n
c
y
c
o
m
p
a
re
d
to
tra
d
it
i
o
n
a
l
P
W
M
m
e
th
o
d
s.
Th
e
S
VPW
M
tec
h
n
i
q
u
e
is
e
m
p
lo
y
e
d
to
m
o
d
u
late
th
e
in
v
e
rt
e
r
o
u
tp
u
t,
g
e
n
e
ra
ti
n
g
a
sin
u
so
i
d
a
l
AC
wa
v
e
fo
rm
th
a
t
m
a
tch
e
s
t
h
e
g
ri
d
fre
q
u
e
n
c
y
a
n
d
v
o
lt
a
g
e
.
B
y
a
d
ju
sti
n
g
th
e
p
u
lse
wi
d
th
to
a
c
h
iev
e
e
ffe
c
ti
v
e
a
n
d
tr
u
stw
o
rth
y
g
rid
in
teg
ra
ti
o
n
.
T
o
m
a
x
imiz
e
p
o
we
r
e
x
trac
ti
o
n
tak
e
s
p
lac
e
b
y
u
sin
g
m
a
x
imu
m
p
o
we
r
p
o
i
n
t
trac
k
i
n
g
(M
P
P
T).
T
h
e
S
VPW
M
i
n
v
e
rter
is
c
ru
c
ial
i
n
c
o
n
v
e
rt
in
g
DC
p
o
we
r
t
o
AC
p
o
we
r
a
n
d
e
n
a
b
li
n
g
g
rid
c
o
n
n
e
c
ti
o
n
.
Util
izin
g
S
VPW
M
a
ll
o
ws
e
x
a
c
t
c
o
n
tr
o
l
o
f
v
o
l
tag
e
m
a
g
n
it
u
d
e
,
fre
q
u
e
n
c
y
,
a
n
d
p
h
a
se
a
n
g
le
to
p
r
o
v
i
d
e
h
i
g
h
-
q
u
a
li
t
y
si
n
u
s
o
id
a
l
AC
o
u
t
p
u
t
v
o
lt
a
g
e
.
T
h
e
p
o
we
r
q
u
a
li
ty
o
f
th
e
e
lec
tri
c
it
y
p
u
m
p
e
d
i
n
to
th
e
g
ri
d
is
im
p
ro
v
e
d
b
y
t
h
i
s
p
re
c
ise
m
a
n
a
g
e
m
e
n
t,
wh
ich
a
lso
e
n
su
re
s
a
d
h
e
re
n
c
e
t
o
g
ri
d
sta
n
d
a
rd
s
a
n
d
re
d
u
c
e
s
h
a
rm
o
n
ic i
n
terfe
re
n
c
e
.
K
ey
w
o
r
d
s
:
Gr
id
I
GB
T
in
v
er
ter
MPPT
PV c
ell
SVP
W
M
tech
n
iq
u
e
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
An
k
ath
i M
an
ju
la
Dep
ar
tm
en
t o
f
E
lectr
ical
an
d
E
lectr
o
n
ics E
n
g
in
ee
r
i
n
g
,
Sath
y
ab
am
a
I
n
s
titu
te
o
f
Scien
ce
an
d
T
ec
h
n
o
lo
g
y
C
h
en
n
ai,
T
am
il Na
d
u
,
I
n
d
ia
E
m
ail:
m
an
ju
.
an
k
ath
i7
0
8
@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
As
th
e
wo
r
ld
s
ee
k
s
to
tr
an
s
itio
n
to
war
d
s
clea
n
er
an
d
m
o
r
e
s
u
s
tain
ab
le
en
er
g
y
s
o
u
r
ce
s
,
p
h
o
to
v
o
ltaic
s
o
lar
s
y
s
tem
s
h
av
e
em
er
g
ed
as
a
p
r
o
m
in
en
t
s
o
lu
tio
n
f
o
r
elec
tr
icity
g
en
er
atio
n
[
1
]
-
[
2
]
.
Gr
id
-
co
n
n
ec
ted
p
h
o
to
v
o
ltaic
s
y
s
tem
s
ef
f
icie
n
tly
u
tili
ze
s
o
lar
en
er
g
y
b
y
in
teg
r
atin
g
it
i
n
to
t
h
e
ex
is
tin
g
elec
tr
ical
g
r
id
in
f
r
astru
ctu
r
e.
T
u
s
in
g
a
b
o
o
s
t
co
n
v
er
ter
in
a
d
o
u
b
le
-
s
tag
e
g
r
id
-
co
n
n
ec
ted
p
h
o
to
v
o
ltaic
s
y
s
tem
in
n
o
v
ativ
el
y
en
h
an
ce
s
th
e
s
y
s
tem
'
s
g
r
id
co
m
p
atib
ilit
y
an
d
p
er
f
o
r
m
a
n
ce
[
3
]
.
T
h
is
in
tr
o
d
u
ctio
n
p
r
o
v
id
es
an
o
v
e
r
v
iew
o
f
th
is
ad
v
an
ce
d
s
o
lar
en
er
g
y
s
o
lu
tio
n
[
4
]
.
A
d
o
u
b
le
-
s
tag
e
g
r
id
-
c
o
n
n
ec
ted
PV
s
y
s
tem
w
ith
a
s
p
ac
e
v
ec
to
r
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
SVPW
M
)
in
v
er
ter
is
a
s
o
p
h
is
ticated
s
o
lar
en
er
g
y
s
etu
p
th
at
m
ax
im
izes
en
er
g
y
ex
tr
ac
tio
n
f
r
o
m
PV
ar
r
ay
s
an
d
en
s
u
r
es
ef
f
icien
t
i
n
teg
r
atio
n
with
th
e
elec
tr
ical
g
r
id
[
5
]
-
[
6
]
.
I
t
o
f
f
er
s
n
u
m
er
o
u
s
ad
v
an
tag
es
in
ter
m
s
o
f
en
er
g
y
ef
f
icien
c
y
,
g
r
id
s
u
p
p
o
r
t,
an
d
e
n
v
ir
o
n
m
en
tal
s
u
s
tain
ab
ilit
y
,
m
ak
in
g
it
a
v
a
lu
ab
le
s
o
lu
tio
n
f
o
r
r
en
ewa
b
le
en
er
g
y
g
en
er
atio
n
a
n
d
g
r
id
s
tab
ilit
y
[
7
]
-
[
8
]
.
A
DC
-
DC
co
n
v
er
ter
is
f
r
eq
u
en
tly
em
p
lo
y
ed
in
a
d
o
u
b
le
-
s
tag
e
s
y
s
tem
to
m
ax
im
ize
en
er
g
y
ex
tr
ac
tio
n
f
r
o
m
th
e
PV
ar
r
a
y
[
2
]
-
[
5
]
.
T
h
is
co
n
v
e
r
ter
ef
f
ici
en
tly
ad
ju
s
ts
v
o
ltag
e
an
d
cu
r
r
en
t
lev
els
to
m
ee
t
th
e
r
eq
u
ir
em
en
ts
o
f
s
u
b
s
eq
u
en
t
s
ta
g
es.
I
t
m
ay
in
c
o
r
p
o
r
ate
f
ea
tu
r
e
s
s
u
ch
as
m
ax
im
u
m
p
o
wer
p
o
in
t
tr
ac
k
in
g
(
MPPT)
to
o
p
tim
ize
th
e
PV
ar
r
ay
'
s
p
o
wer
o
u
tp
u
t
[
9
]
.
T
h
e
SVPW
M
in
v
er
ter
is
a
v
ital
co
m
p
o
n
en
t
in
th
e
s
y
s
tem
,
co
n
v
er
tin
g
t
h
e
d
i
r
ec
t
cu
r
r
en
t
o
u
tp
u
t
f
r
o
m
th
e
PV
ar
r
a
y
in
to
alter
n
atin
g
c
u
r
r
en
t
th
at
is
co
m
p
atib
le
with
g
r
id
c
o
n
n
ec
ti
o
n
[
1
0
]
.
SVPW
M
is
a
s
o
p
h
is
tic
ated
co
n
tr
o
l
tech
n
i
q
u
e
u
s
ed
in
i
n
v
er
ter
s
to
g
en
er
at
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
Gri
d
-
co
n
n
ec
ted
d
o
u
b
le
-
s
ta
g
e
P
V
s
ystem
w
i
th
s
p
a
ce
ve
cto
r
P
WM
in
ve
r
ter a
n
d
MPP
T
(
A
n
ka
th
i Ma
n
ju
la
)
901
h
ig
h
-
q
u
ality
s
in
u
s
o
id
al
AC
wav
ef
o
r
m
s
with
m
in
im
al
h
ar
m
o
n
ic
d
is
to
r
tio
n
an
d
h
i
g
h
ef
f
icie
n
cy
[
1
1
]
.
I
t
ass
u
r
es
g
r
id
c
o
m
p
atib
ilit
y
a
n
d
m
ax
im
i
ze
s
th
e
u
s
e
o
f
DC
p
o
wer
th
at
i
s
alr
ea
d
y
a
v
ailab
le
[
1
2
]
-
[
1
3
]
.
T
h
e
g
r
id
-
co
n
n
ec
ted
,
d
o
u
b
le
-
s
tag
e
PV
s
y
s
tem
u
s
es
a
co
n
tr
o
ller
to
en
s
u
r
e
e
f
f
icien
t
o
p
er
atio
n
.
T
h
e
MPPT,
v
o
ltag
e
r
eg
u
latio
n
,
an
d
g
r
id
s
y
n
ch
r
o
n
izatio
n
alg
o
r
ith
m
s
o
f
th
is
co
n
tr
o
ller
ar
e
s
tan
d
ar
d
.
A
d
v
an
ce
d
co
n
tr
o
l
alg
o
r
ith
m
s
ar
e
o
f
ten
em
p
lo
y
ed
to
ef
f
ec
tiv
ely
m
an
a
g
e
th
e
p
o
wer
f
lo
w
b
etwe
en
th
e
PV a
r
r
a
y
an
d
th
e
g
r
i
d
[
1
4
]
-
[
1
5
]
.
2.
G
RID
-
CO
NNE
CT
E
D
DO
U
B
L
E
-
ST
AG
E
P
V
SY
ST
E
M
Fig
u
r
e
1
s
h
o
ws
th
e
b
lo
c
k
d
iag
r
am
o
f
th
e
p
r
o
p
o
s
ed
p
a
p
er
.
T
h
e
PV
p
an
els
ca
p
tu
r
e
s
u
n
lig
h
t
a
n
d
g
en
er
ate
DC
elec
tr
icity
,
r
ep
r
esen
tin
g
th
e
in
itial
en
er
g
y
h
ar
v
esti
n
g
s
tag
e
[
1
6
]
.
A
b
o
o
s
t
co
n
v
e
r
ter
is
u
s
ed
to
o
p
tim
ize
p
o
wer
ex
tr
ac
tio
n
f
r
o
m
th
e
PV
ar
r
ay
.
I
t
in
c
r
ea
s
e
s
th
e
DC
v
o
ltag
e
to
a
lev
el
th
at
m
ax
im
izes
p
o
wer
o
u
tp
u
t
[
1
7
]
-
[
1
8
]
.
Desp
ite
ch
a
n
g
in
g
e
n
v
ir
o
n
m
en
tal
f
ac
to
r
s
,
th
e
s
y
s
tem
will
alwa
y
s
f
u
n
ctio
n
ef
f
ec
tiv
ely
at
o
r
clo
s
e
to
th
e
PV
ar
r
ay
'
s
m
ax
im
u
m
p
o
wer
p
o
in
t
(
MPPT)
.
T
h
e
M
PP
T
s
y
s
tem
co
n
tin
u
o
u
s
ly
m
o
n
ito
r
s
th
e
PV
ar
r
ay
'
s
v
o
ltag
e
an
d
cu
r
r
e
n
t
to
d
eter
m
in
e
th
e
o
p
tim
al
o
p
er
atin
g
p
o
in
t
f
o
r
m
a
x
im
u
m
p
o
wer
p
r
o
d
u
ctio
n
[
1
9
]
.
I
t
a
d
ju
s
ts
th
e
b
o
o
s
t
co
n
v
e
r
ter
'
s
o
p
er
atio
n
to
m
ain
tain
th
e
PV
ar
r
ay
a
t
th
is
m
ax
im
u
m
p
o
wer
p
o
in
t
[
2
0
]
-
[
2
1
]
.
T
h
e
DC
elec
tr
icity
p
r
o
d
u
ce
d
b
y
th
e
PV
ar
r
ay
is
co
n
v
er
ted
in
to
alter
n
atin
g
cu
r
r
e
n
t,
wh
ich
is
ac
ce
p
tab
le
f
o
r
g
r
i
d
co
n
n
ec
tio
n
,
u
s
in
g
a
s
o
p
h
is
ticat
ed
g
r
id
-
tied
in
v
e
r
ter
[
2
2
]
.
T
h
e
g
r
id
-
tied
in
v
er
ter
en
s
u
r
es
t
h
at
th
e
AC
o
u
tp
u
t
clo
s
ely
m
atch
es
th
e
g
r
id
'
s
v
o
lt
ag
e,
f
r
eq
u
en
cy
,
a
n
d
p
h
ase,
en
a
b
lin
g
s
ea
m
less
g
r
id
c
o
n
n
ec
tio
n
with
o
u
t
d
is
r
u
p
tio
n
s
[
2
3
]
.
T
h
e
d
o
u
b
le
-
s
tag
e
p
h
o
to
v
o
ltaic
(
PV)
s
y
s
tem
,
wh
ich
is
c
o
n
n
ec
ted
to
th
e
elec
tr
ical
g
r
id
,
is
lin
k
ed
v
ia
a
p
o
in
t
o
f
co
m
m
o
n
co
u
p
lin
g
.
[
2
4
]
,
[
2
5
]
.
T
h
is
is
th
e
p
o
in
t
w
h
er
e
th
e
AC
o
u
tp
u
t
f
r
o
m
th
e
i
n
v
er
ter
is
s
y
n
ch
r
o
n
ized
with
th
e
g
r
id
'
s
p
ar
am
eter
s
an
d
in
jec
ted
in
to
th
e
g
r
id
with
th
e
h
elp
o
f
a
co
n
tr
o
l sch
em
e.
P
V
P
A
N
E
L
B
O
O
S
T
C
O
N
V
E
R
T
E
R
T
H
R
E
E
-
P
H
A
S
E
I
N
V
E
R
T
E
R
L
C
F
I
L
T
E
R
G
R
I
D
M
P
P
T
C
O
N
T
R
O
L
L
E
R
C
O
N
T
R
O
L
S
C
H
E
M
E
S
U
N
L
I
G
H
T
Fig
u
r
e
1
.
Do
u
b
le
-
s
tag
e
p
h
o
to
v
o
ltaic
s
y
s
tem
b
lo
ck
d
iag
r
a
m
2
.
1
.
P
V
ce
ll
A
p
h
o
to
v
o
ltaic
(
PV)
ce
ll
u
tili
z
es
th
e
p
h
o
to
v
o
ltaic
ef
f
ec
t
to
d
ir
ec
tly
co
n
v
er
t
s
u
n
lig
h
t
in
to
ele
ctr
icity
b
y
d
is
lo
d
g
in
g
elec
tr
o
n
s
f
r
o
m
ato
m
s
in
s
em
ico
n
d
u
cto
r
m
ater
ials
th
r
o
u
g
h
th
e
in
ter
ac
ti
o
n
with
p
h
o
to
n
s
f
r
o
m
s
u
n
lig
h
t.
PV
ce
lls
ar
e
ty
p
ically
m
ad
e
f
r
o
m
s
em
ic
o
n
d
u
cto
r
m
ater
ials
,
s
u
ch
as
s
ilico
n
.
T
h
e
PV
ce
lls
ar
e
co
m
p
o
s
ed
o
f
a
P
-
ty
p
e
lay
er
,
wh
ic
h
is
m
a
d
e
o
f
b
o
r
o
n
-
d
o
p
e
d
s
ilico
n
,
an
d
an
N
-
ty
p
e
la
y
er
,
wh
ich
is
m
ad
e
o
f
p
h
o
s
p
h
o
r
o
u
s
-
d
o
p
ed
s
ilico
n
.
T
h
ese
lay
er
s
ar
e
p
o
s
itio
n
ed
o
n
t
o
p
o
f
a
b
o
r
o
n
-
d
o
p
e
d
s
ilico
n
lay
er
.
W
h
e
n
s
u
n
lig
h
t
in
ter
ac
ts
with
th
e
PV
ce
ll,
it
g
en
er
ates
an
elec
tr
ic
v
o
ltag
e
an
d
cu
r
r
en
t
b
y
in
d
u
cin
g
th
e
m
o
v
em
e
n
t
o
f
elec
tr
o
n
s
f
r
o
m
th
e
P
-
ty
p
e
la
y
er
to
th
e
N
-
ty
p
e
lay
er
.
Ad
d
itio
n
a
lly
,
PV
ce
lls
h
av
e
two
elec
tr
ic
al
co
n
tacts,
with
o
n
e
lo
ca
ted
o
n
th
e
f
r
o
n
t
an
d
th
e
o
th
er
o
n
t
h
e
b
ac
k
.
T
h
ese
co
n
tacts a
llo
w
f
o
r
th
e
c
o
llectio
n
o
f
t
h
e
g
e
n
er
ated
elec
tr
ical
en
er
g
y
.
On
th
eir
o
wn
,
PV
ce
lls
p
r
o
d
u
ce
a
lim
ited
am
o
u
n
t
o
f
elec
tr
ical
p
o
wer
,
ty
p
icall
y
in
th
e
r
an
g
e
o
f
0
.
5
V
t
o
0
.
6
V
as
d
ir
ec
t
c
u
r
r
en
t
wh
en
n
o
t
co
n
n
ec
te
d
to
a
lo
ad
.
A
s
o
lar
m
o
d
u
le,
also
r
ef
er
r
ed
t
o
as
a
PV
m
o
d
u
le
o
r
s
o
lar
p
an
el
m
o
d
u
le,
co
n
s
is
ts
o
f
a
s
er
ies
o
f
in
ter
co
n
n
ec
ted
PV
ce
ll
s
en
clo
s
ed
with
in
a
p
r
o
tectiv
e
m
ater
ial
s
u
ch
as
tem
p
er
ed
g
lass
an
d
en
ca
p
s
u
lan
t.
I
ts
p
r
im
ar
y
p
u
r
p
o
s
e
is
to
in
cr
ea
s
e
p
o
wer
o
u
tp
u
t
co
m
p
ar
e
d
to
in
d
iv
i
d
u
al
PV
c
ells
.
Mo
d
u
les
co
m
e
in
v
ar
io
u
s
s
izes,
with
s
tan
d
ar
d
s
izes
s
u
ch
as
6
0
-
ce
ll
o
r
7
2
-
ce
ll
m
o
d
u
les
b
ein
g
co
m
m
o
n
.
L
ar
g
er
m
o
d
u
les
co
n
tain
m
o
r
e
PV
ce
lls
,
r
esu
ltin
g
in
h
i
g
h
er
p
o
wer
o
u
tp
u
t.
T
h
ey
ar
e
c
o
n
f
ig
u
r
ed
to
p
r
o
d
u
ce
s
p
ec
if
ic
v
o
ltag
e
an
d
cu
r
r
en
t
o
u
tp
u
ts
,
u
s
u
ally
i
n
th
e
r
a
n
g
e
o
f
1
2
to
4
8
v
o
lts
.
2
.
2
.
P
&O
a
lg
o
rit
hm
o
f
M
P
P
T
T
h
e
alg
o
r
ith
m
r
e
f
er
r
e
d
to
as
th
e
"P
an
d
O"
alg
o
r
it
h
m
,
o
r
th
e
"
p
er
tu
r
b
an
d
o
b
s
er
v
e
"
alg
o
r
ith
m
,
is
wid
ely
em
p
lo
y
ed
in
m
ax
im
u
m
p
o
wer
p
o
in
t
tr
ac
k
in
g
(
MPPT)
f
o
r
p
h
o
to
v
o
ltaic
s
y
s
tem
s
.
MPPT
is
an
ess
en
tial
tech
n
iq
u
e
u
tili
ze
d
in
s
o
lar
p
o
wer
s
y
s
tem
s
to
o
p
tim
ize
th
e
p
o
wer
g
e
n
er
a
ted
b
y
s
o
lar
p
an
els
b
y
co
n
s
is
ten
tly
m
o
n
ito
r
in
g
th
e
p
o
in
t a
t w
h
ich
th
e
p
an
els f
u
n
c
tio
n
at
th
eir
h
ig
h
est p
o
wer
o
u
t
p
u
t.
I
n
th
e
P&
O
alg
o
r
ith
m
I
n
it
ially
,
th
e
alg
o
r
ith
m
o
p
er
ates
th
e
PV
s
y
s
tem
at
a
ce
r
tain
o
p
er
atin
g
p
o
in
t.
I
t
s
lig
h
tly
p
er
tu
r
b
s
th
is
o
p
er
atin
g
p
o
in
t
b
y
a
s
m
all
in
cr
em
en
t.
T
h
e
p
o
wer
h
as
in
c
r
ea
s
ed
o
r
d
ec
r
ea
s
ed
.
I
f
th
e
p
o
wer
h
as
in
cr
ea
s
ed
,
it
co
n
tin
u
e
s
p
er
tu
r
b
in
g
in
th
e
s
am
e
d
ir
ec
tio
n
.
I
f
th
e
p
o
wer
h
as
r
ed
u
ce
d
,
th
e
p
er
tu
r
b
atio
n
d
ir
ec
tio
n
is
r
ev
er
s
ed
,
lead
i
n
g
to
a
co
n
tin
u
o
u
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
3
,
No
.
4
,
Dece
m
b
er
20
2
4
:
9
0
0
-
908
902
r
ep
etitio
n
o
f
s
tep
s
wh
er
e
t
h
e
o
p
er
atin
g
p
o
in
t
is
ad
ju
s
te
d
in
ea
ch
iter
atio
n
u
n
til
th
e
alg
o
r
ith
m
r
ea
c
h
es
co
n
v
er
g
en
ce
at
th
e
m
ax
im
u
m
p
o
wer
p
o
in
t.
2
.
3
.
B
o
o
s
t
c
o
nv
er
t
er
A
b
o
o
s
t
co
n
v
er
ter
,
also
r
ef
e
r
r
ed
to
as
a
s
tep
-
u
p
co
n
v
er
ter
,
is
a
DC
-
DC
co
n
v
er
ter
th
at
el
ev
ates
th
e
v
o
ltag
e
lev
el
o
f
a
DC
in
p
u
t
v
o
ltag
e
to
a
h
ig
h
er
DC
o
u
t
p
u
t
v
o
ltag
e.
T
h
e
m
ath
em
atica
l
eq
u
atio
n
s
f
o
r
a
b
o
o
s
t
co
n
v
er
ter
ca
n
b
e
o
b
tain
ed
f
r
o
m
its
o
p
er
atio
n
al
p
r
i
n
cip
les
an
d
cir
cu
it
elem
en
ts
.
Pre
s
en
ted
b
elo
w
ar
e
th
e
ess
en
tial
f
o
r
m
u
las
an
d
eq
u
atio
n
s
f
o
r
a
b
o
o
s
t
co
n
v
e
r
ter
.
T
h
e
d
u
ty
c
y
c
le
r
ep
r
esen
ts
th
e
p
er
ce
n
ta
g
e
o
f
tim
e
d
u
r
in
g
wh
ich
th
e
tr
an
s
is
to
r
s
witch
is
in
th
e
o
n
s
tate,
ty
p
ically
r
eg
u
lated
b
y
a
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
PW
M)
s
ig
n
al.
T
h
e
d
u
t
y
cy
cle
is
g
iv
en
b
y
:
D
=
T
o
n
/
T
,
wh
e
r
e
T
o
n
is
th
e
o
n
-
tim
e
o
f
t
h
e
s
witch
an
d
T
is
th
e
s
witch
in
g
p
er
io
d
.
T
h
e
v
o
ltag
e
g
ain
o
f
a
b
o
o
s
t c
o
n
v
er
ter
is
th
e
r
atio
o
f
t
h
e
o
u
tp
u
t v
o
ltag
e
to
th
e
in
p
u
t
v
o
ltag
e.
Vo
ltag
e
g
ain
: V
o
/Vin
=
1
/ (
1
-
D)
T
h
e
in
p
u
t c
u
r
r
e
n
t c
an
b
e
ca
lcu
lated
u
s
in
g
th
e
o
u
tp
u
t c
u
r
r
en
t
an
d
d
u
t
y
cy
cle.
I
n
p
u
t
c
u
r
r
en
t
:
I
in
=
I
o
/ D
Ou
tp
u
t
p
o
wer
: Po
u
t =
Vo
*
I
o
2
.
4
.
T
hree
-
ph
a
s
e
inv
er
t
er
Fig
u
r
e
2
r
e
p
r
esen
ts
th
e
s
tr
u
ctu
r
e
o
f
a
th
r
ee
-
p
h
ase
b
r
i
d
g
e
in
v
e
r
ter
.
I
t
ty
p
ically
tak
es
a
DC
v
o
l
tag
e
in
p
u
t,
o
f
ten
s
o
u
r
ce
d
f
r
o
m
s
o
lar
p
an
els
o
r
o
th
er
s
o
u
r
ce
s
.
T
h
e
in
v
e
r
ter
is
co
m
p
o
s
ed
o
f
s
ix
s
em
ico
n
d
u
ct
o
r
s
witch
in
g
elem
en
ts
,
co
m
m
o
n
ly
in
s
u
lated
g
ate
b
ip
o
lar
tr
an
s
is
to
r
s
(
I
GB
T
s
)
,
s
et
u
p
in
a
b
r
id
g
e
co
n
f
ig
u
r
a
tio
n
.
T
h
ese
d
ev
ices
ar
e
d
iv
id
ed
in
to
u
p
p
er
an
d
lo
wer
ar
m
s
,
with
ea
ch
ar
m
co
n
tain
in
g
th
r
ee
s
witch
es
co
r
r
esp
o
n
d
in
g
to
th
e
th
r
e
e
p
h
ases
o
f
th
e
AC
o
u
tp
u
t.
T
h
e
p
r
im
ar
y
f
u
n
ctio
n
o
f
th
e
b
r
id
g
e
in
v
er
ter
is
to
g
en
er
at
e
a
th
r
ee
-
p
h
ase
AC
v
o
ltag
e
f
r
o
m
th
e
DC
in
p
u
t.
T
h
is
is
ac
h
iev
ed
th
r
o
u
g
h
s
p
ac
e
v
ec
to
r
p
u
l
s
e
wid
th
m
o
d
u
latio
n
.
V
d
c
Q
1
Q
2
Q
3
Q
4
D
1
D
3
D
2
D
4
T
H
R
E
E
P
H
A
S
E
A
C
L
O
A
D
Q
5
Q
6
D
5
D
6
Fig
u
r
e
2
.
T
h
r
ee
-
p
h
ase
f
u
ll b
r
id
g
e
in
v
e
r
ter
2
.
5
.
S
pa
ce
v
ec
t
o
r
pu
ls
e
width
m
o
du
la
t
io
n
Sp
ac
e
v
ec
to
r
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
SVPW
M)
is
a
p
o
w
er
f
u
l
tech
n
iq
u
e
f
o
r
co
n
tr
o
llin
g
in
v
er
te
r
s
,
esp
ec
ially
in
ap
p
licatio
n
s
wh
er
e
p
r
ec
is
io
n
,
r
ed
u
c
ed
h
a
r
m
o
n
ics,
an
d
g
r
id
s
y
n
ch
r
o
n
izatio
n
ar
e
ess
en
tial.
I
t
o
p
tim
izes
th
e
s
witch
in
g
p
atte
r
n
s
o
f
t
h
e
in
v
e
r
ter
'
s
p
o
wer
d
ev
ices
to
g
en
e
r
ate
h
ig
h
-
q
u
ali
ty
A
C
wav
ef
o
r
m
s
,
en
s
u
r
in
g
a
r
eliab
le
an
d
ef
f
icie
n
t
o
p
e
r
atio
n
,
p
ar
ticu
lar
ly
in
g
r
id
-
co
n
n
ec
te
d
s
y
s
tem
s
.
T
h
e
d
es
ir
ed
o
u
tp
u
t
v
o
ltag
e
m
ag
n
itu
d
e
(
V
ref
)
an
d
p
h
ase
an
g
le
(
θ
ref
)
f
o
r
ea
c
h
p
h
ase
o
f
t
h
e
in
v
er
ter
.
T
h
ese
v
alu
es
a
r
e
o
f
t
en
o
b
tain
e
d
f
r
o
m
a
co
n
tr
o
l
alg
o
r
ith
m
o
r
u
s
er
in
p
u
t.
T
o
s
im
p
lify
co
n
tr
o
l
ca
lcu
latio
n
s
,
th
e
d
esire
d
th
r
ee
-
p
h
as
e
v
o
ltag
es
(
V
ref
)
ar
e
co
n
v
er
ted
in
to
a
two
-
d
im
e
n
s
io
n
al
r
ef
er
e
n
ce
f
r
a
m
e
ca
lled
th
e
α
-
β
r
ef
er
e
n
ce
f
r
a
m
e.
T
h
is
co
n
v
er
s
io
n
is
d
o
n
e
u
s
in
g
th
e
in
v
er
s
e
C
lar
k
e
tr
an
s
f
o
r
m
a
tio
n
.
T
h
e
α
-
β
r
ef
er
e
n
ce
f
r
am
e
r
ep
r
esen
ts
th
e
d
esire
d
v
o
ltag
es
in
a
c
o
o
r
d
in
ate
s
y
s
tem
th
at
s
im
p
lifie
s
th
e
co
n
tr
o
l p
r
o
ce
s
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
Gri
d
-
co
n
n
ec
ted
d
o
u
b
le
-
s
ta
g
e
P
V
s
ystem
w
i
th
s
p
a
ce
ve
cto
r
P
WM
in
ve
r
ter a
n
d
MPP
T
(
A
n
ka
th
i Ma
n
ju
la
)
903
=
2
/
3
[
(
)
+
(
)
+
2
(
)
]
(
1
)
W
h
er
e
α
=
e
j2π
/3
an
d
α
2
=
e
j4π
/3
.
=
=
(
−
120°
)
=
(
−
240°
)
(
2
)
=
√
2
+
2
(
3
)
Fig
u
r
e
3
r
e
p
r
esen
ts
th
e
V
ref
f
o
r
th
e
D
an
d
Q
a
x
es
.
[
0
]
=
(
1
−
1
/
2
−
1
/
2
0
√
3
/
2
−
√
3
/
2
1
/
2
1
/
2
1
/
2
)
[
]
(
4
)
T
h
e
r
elatio
n
s
h
ip
b
etwe
en
th
e
lin
e
-
to
-
lin
e
v
o
ltag
e
v
ec
to
r
[
V
ab
,
V
bc
,
V
ca
]
an
d
t
h
e
s
witch
in
g
v
ar
iab
le
v
ec
to
r
[
a,
b
,
c
]
ca
n
b
e
ex
p
r
ess
ed
as f
o
llo
ws
:
[
]
=
(
1
−
1
0
0
1
−
1
−
1
1
0
)
[
]
t
h
e
p
h
ase
v
o
ltag
e
v
ec
to
r
[
V
a
V
b
V
c
]
an
d
th
e
s
witch
in
g
v
ar
iab
l
e
v
ec
to
r
[
a
,
b
,
c
]
ar
e
r
elate
d
b
y
(
5
)
.
[
]
=
/
3
(
2
−
1
−
1
−
1
2
−
1
−
1
−
1
2
)
[
]
(
5
)
I
n
a
co
m
p
lex
p
lan
e,
two
o
r
t
h
o
g
o
n
al
s
y
s
tem
s
(
V
d
,
V
q
)
f
o
r
m
th
e
b
asis
f
o
r
d
ef
in
in
g
a
v
ec
to
r
.
T
h
e
r
ef
er
en
ce
v
o
ltag
e,
V
ref
,
ca
n
b
e
ex
p
r
ess
ed
as
th
e
s
u
m
o
f
V
d
an
d
jV
q
.
T
o
r
ep
r
esen
t
th
e
eig
h
t
s
witch
in
g
s
tates
o
f
th
e
in
v
e
r
ter
o
u
tp
u
t
in
b
in
a
r
y
co
d
e,
th
r
ee
b
its
(
2
3
=8
)
ar
e
r
eq
u
ir
ed
.
T
h
ese
s
tates
ar
e
d
e
n
o
ted
as
S1
(
0
,
0
,
1
)
,
S2
(
0
,
1
,
1
)
,
S3
(
0
,
1
,
0
)
,
S4
(
1
,
1
,
0
)
,
S5
(
1
,
0
,
0
)
,
S6
(
1
,
0
,
1
)
,
an
d
S7
(
1
,
1
,
1
)
.
Fig
u
r
e
4
s
h
o
ws th
e
7
s
witch
in
g
s
tates.
Fig
u
r
e
3
.
R
ep
r
esen
tatio
n
o
f
V
r
ef
Fig
u
r
e
4
.
Sp
ac
e
v
ec
to
r
p
u
ls
e
wid
th
m
o
d
u
latio
n
r
ep
r
esen
tatio
n
2
.
6
.
L
C
f
ilte
rs
I
t
is
a
k
ey
tech
n
iq
u
e
i
n
m
o
d
er
n
m
o
t
o
r
d
r
iv
es
an
d
p
o
wer
elec
tr
o
n
ics
s
y
s
tem
s
L
C
f
ilter
s
,
wh
i
ch
co
n
s
is
t
o
f
in
d
u
cto
r
s
(
L
)
an
d
ca
p
ac
it
o
r
s
(
C
)
,
ar
e
co
m
m
o
n
l
y
u
s
ed
in
g
r
id
-
co
n
n
ec
ted
p
h
o
to
v
o
ltaic
(
PV
)
s
y
s
tem
s
f
o
r
s
ev
er
al
im
p
o
r
tan
t
p
u
r
p
o
s
es.
L
C
f
ilter
s
ar
e
ess
en
tial
co
m
p
o
n
e
n
ts
th
at
g
r
ea
tly
en
h
a
n
ce
th
e
ef
f
icien
c
y
,
p
o
wer
in
te
g
r
ity
,
an
d
d
e
p
en
d
a
b
ilit
y
o
f
th
ese
s
y
s
tem
s
.
A
k
ey
ap
p
licatio
n
o
f
L
C
f
ilter
s
is
th
eir
ab
ilit
y
to
m
i
n
im
ize
o
r
e
r
ad
icate
h
ar
m
o
n
ic
d
is
to
r
tio
n
in
t
h
e
o
u
t
p
u
t c
u
r
r
en
t o
r
v
o
ltag
e
o
f
g
r
id
-
co
n
n
ec
ted
i
n
v
er
ter
s
.
L
C
f
ilter
s
ca
n
d
o
h
ar
m
o
n
ic
m
itig
atio
n
,
r
ed
u
cin
g
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
to
m
ak
e
th
e
g
r
id
v
o
ltag
e
clea
n
er
an
d
m
o
r
e
s
in
u
s
o
id
al
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
3
,
No
.
4
,
Dece
m
b
er
20
2
4
:
9
0
0
-
908
904
2
.
7
.
G
rid r
equirem
ent
s
t
o
inte
rc
o
nn
ec
t
wit
h
PV
s
y
s
t
em
Gr
id
-
co
n
n
e
cted
PV
s
y
s
tem
s
n
ee
d
to
m
ee
t
s
tr
ict
r
e
q
u
ir
em
e
n
ts
r
eg
ar
d
i
n
g
v
o
ltag
e,
f
r
eq
u
e
n
cy
,
p
h
ase
alig
n
m
en
t,
a
n
d
p
o
wer
q
u
ality
to
en
s
u
r
e
r
eliab
le
an
d
ef
f
icien
t
in
teg
r
atio
n
with
th
e
g
r
id
,
a
n
d
also
PV
s
y
s
tem
s
m
u
s
t
m
in
im
ize
h
ar
m
o
n
ic
d
is
to
r
tio
n
to
m
ain
tain
p
o
wer
q
u
ality
.
Har
m
o
n
ics
ca
n
lead
t
o
o
v
er
h
ea
tin
g
an
d
d
am
a
g
e
to
elec
tr
ical
eq
u
ip
m
e
n
t.
I
n
v
er
t
er
s
ar
e
d
esig
n
ed
to
f
ilter
o
u
t
h
ar
m
o
n
ics
a
n
d
e
n
s
u
r
e
th
at
th
e
o
u
tp
u
t
wav
ef
o
r
m
is
as
clo
s
e
to
a
p
u
r
e
s
in
e
wav
e
as
p
o
s
s
ib
le.
T
h
e
in
teg
r
atio
n
o
f
PV
s
y
s
tem
s
n
ev
er
in
tr
o
d
u
ce
s
f
l
ick
er
o
r
v
o
ltag
e
tr
an
s
ien
ts
.
T
h
e
ad
v
an
ce
d
co
n
t
r
o
l
tech
n
i
q
u
e
SVPW
M,
an
d
th
e
ab
ilit
y
to
m
an
a
g
e
r
ea
ctiv
e
p
o
wer
p
lay
a
c
r
u
cial
r
o
le
in
ac
h
iev
i
n
g
th
ese
o
b
jectiv
es wh
ile
co
n
tr
ib
u
tin
g
to
g
r
id
s
tab
ilit
y
an
d
r
eliab
ilit
y
.
3.
DE
SCR
I
P
T
I
O
N
O
F
T
H
E
C
I
RCUI
T
Fig
u
r
e
5
s
h
o
ws
th
e
g
r
id
-
co
n
n
ec
ted
d
o
u
b
le
-
s
tag
e
PV
s
y
s
tem
with
s
p
ac
e
v
ec
to
r
PW
M
in
v
er
ter
.
T
h
is
s
o
lar
p
o
wer
s
y
s
tem
o
p
tim
izes
t
h
e
ef
f
icien
cy
an
d
in
teg
r
atio
n
o
f
p
h
o
to
v
o
ltaic
(
PV)
ar
r
ay
s
with
th
e
elec
tr
ical
g
r
id
.
T
h
e
PV
ar
r
ay
co
n
s
is
ts
o
f
in
d
iv
id
u
al
s
o
lar
p
an
els
th
at
h
ar
n
e
s
s
s
u
n
lig
h
t
to
p
r
o
d
u
ce
DC
ele
ctr
icity
.
T
o
en
s
u
r
e
o
p
tim
al
p
e
r
f
o
r
m
an
ce
,
a
DC
-
D
C
co
n
v
er
ter
o
r
m
a
x
im
u
m
p
o
w
er
p
o
in
t
tr
ac
k
in
g
co
n
tr
o
ller
is
e
m
p
lo
y
ed
to
m
o
n
ito
r
an
d
m
ax
im
ize
th
e
p
o
wer
o
u
tp
u
t
o
f
th
e
PV
ar
r
ay
b
y
tr
ac
k
in
g
th
e
m
ax
im
u
m
p
o
wer
p
o
i
n
t
(
MPP)
wh
e
r
e
th
e
p
an
els
o
p
er
ate
m
o
s
t
ef
f
ec
tiv
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y
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h
is
s
tag
e
en
s
u
r
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v
o
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e
co
m
p
at
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d
m
ax
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t,
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o
ch
an
g
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g
en
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ir
o
n
m
en
tal
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o
n
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itio
n
s
.
T
h
e
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o
wer
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ef
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icien
tly
o
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d
th
en
r
o
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ted
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to
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e
r
ter
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n
n
ec
ted
to
th
e
g
r
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h
e
p
r
i
m
ar
y
f
u
n
ctio
n
o
f
th
e
in
v
er
ter
i
s
to
ch
an
g
e
th
e
DC
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tr
icity
p
r
o
d
u
ce
d
b
y
th
e
PV
ar
r
ay
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n
to
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atin
g
c
u
r
r
e
n
t,
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ich
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th
e
t
y
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e
o
f
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tr
icity
o
f
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h
o
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d
th
e
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tr
ical
g
r
id
.
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h
e
in
v
e
r
ter
s
y
n
c
h
r
o
n
izes
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e
AC
o
u
tp
u
t
with
th
e
g
r
id
'
s
v
o
ltag
e
an
d
f
r
eq
u
e
n
cy
,
en
s
u
r
in
g
th
at
th
e
p
o
wer
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en
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ated
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atch
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th
e
g
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r
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ir
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en
ts
.
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t
co
n
tin
u
o
u
s
ly
m
o
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ito
r
s
g
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n
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itio
n
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an
d
ef
f
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tly
m
an
ag
es
p
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wer
f
lo
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ee
d
in
g
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s
s
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icity
b
ac
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e
g
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h
en
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an
d
n
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r
d
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wer
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o
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th
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1
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Fig
u
r
e
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h
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tr
o
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atch
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n
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itio
n
s
.
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n
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s
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e
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o
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C
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r
am
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D
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e,
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M,
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d
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n
tr
o
ller
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.
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h
e
f
ir
s
t
s
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o
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ig
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als,
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ich
ty
p
ically
r
ep
r
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t
th
e
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u
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t
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ag
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d
e
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d
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r
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en
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ch
r
o
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iz
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with
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e
g
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a
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r
ce
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th
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e
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ce
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ig
n
als
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e
g
iv
en
i
n
a
s
tatio
n
ar
y
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er
e
n
ce
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a
n
in
v
e
r
s
e
Par
k
tr
an
s
f
o
r
m
atio
n
is
p
er
f
o
r
m
ed
t
o
co
n
v
er
t
t
h
em
in
to
a
r
o
tatin
g
r
e
f
er
en
ce
f
r
am
e,
o
f
te
n
th
e
DQ
f
r
a
m
e.
T
h
is
s
im
p
lifi
es
th
e
co
n
tr
o
l
al
g
o
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ith
m
r
ep
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e
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n
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th
e
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f
r
am
e
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n
th
e
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f
r
a
m
e,
r
ef
e
r
en
ce
s
ig
n
als
ar
e
r
ep
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esen
te
d
a
s
a
r
o
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g
p
h
aso
r
,
m
a
k
in
g
it
ea
s
ier
to
co
n
tr
o
l
th
e
in
v
er
ter
.
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M
d
iv
id
es
th
e
s
p
ac
e
b
etwe
en
th
e
m
in
im
u
m
an
d
m
ax
im
u
m
v
o
lta
g
e
v
ec
to
r
s
in
to
s
ec
to
r
s
an
d
ca
lcu
lates
th
e
s
p
ac
e
v
ec
to
r
r
ep
r
esen
tin
g
th
e
d
esir
ed
o
u
tp
u
t
v
o
ltag
e.
T
h
e
co
n
tr
o
l
s
ch
em
e
id
en
tifie
s
th
e
in
d
u
s
tr
y
in
wh
ich
th
e
s
p
ac
e
v
ec
to
r
f
alls
,
d
eter
m
in
in
g
th
e
co
m
b
in
atio
n
o
f
s
witch
in
g
s
tates r
eq
u
ir
ed
f
o
r
th
e
in
v
er
ter
.
B
ased
o
n
th
e
id
en
tifie
d
s
ec
to
r
an
d
d
esire
d
o
u
tp
u
t
v
o
ltag
e
am
p
litu
d
e,
th
e
c
o
n
tr
o
l
s
ch
e
m
e
ca
l
cu
lates
th
e
d
u
ty
cy
cles n
ec
ess
ar
y
f
o
r
th
e
u
p
p
er
an
d
lo
wer
tr
an
s
is
to
r
s
in
ea
ch
p
h
ase
leg
o
f
th
e
in
v
e
r
ter
.
SVP
W
M
g
en
er
ates
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I
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8
7
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r
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n
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tio
n
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r
e
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n
tr
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Fig
u
r
e
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.
Sp
ac
e
v
ec
to
r
p
u
ls
e
wid
th
m
o
d
u
latio
n
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SI
M
UL
A
T
I
O
N
R
E
S
UL
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S
Fig
u
r
e
8
r
ep
r
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ts
th
e
PV
p
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el
o
u
tp
u
t,
an
d
th
is
v
o
ltag
e
is
in
DC
f
o
r
m
.
Af
ter
0
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5
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n
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at
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m
o
r
e
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ical
o
u
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t
b
y
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n
cr
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g
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e
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o
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n
ec
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Fig
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r
e
9
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ep
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e
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ase
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atch
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o
u
tp
u
t v
o
ltag
e
Fig
u
r
e
9
.
T
h
e
in
v
e
r
ter
'
s
th
r
ee
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p
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ase
o
u
tp
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t v
o
ltag
e
Fig
u
r
e
1
0
r
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e
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r
ier
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s
f
o
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m
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aly
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is
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f
th
e
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r
ee
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h
ase
o
u
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u
t
v
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lt
ag
e
o
f
th
e
in
v
er
ter
.
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t
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n
s
h
o
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o
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h
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an
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ase
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t
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o
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e
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ter
,
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ates
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5
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
Gri
d
-
co
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le
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[
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[
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[
9
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